![2 n Digital Twin Technology and Applications
work along with entities in the digital world. Buildings, factories, and even cities
can now have digital twins thanks to technology. Some people have even suggested
that processes handled by people might have digital twins, further broadening the
idea. A digital twin is an accurate and constantly updated logical real product or
procedure that is used to test different scenarios, forecast problems, and identify
optimization opportunities. A DT handles distinctive, real-
world implementation
of a counterpart, receives real-
time data from it, and adjusts as necessary to repli-
cate the origin throughout its existence, in contrast to conventional computer-
aided
design and engineering (CAD/
CAE) models [33]. However, the twinning is not a
random occurrence. There are many parts to this process, but they all function as one
cohesive one. A digital twin is essentially computer software that makes simulations
using actual data regarding a physical entity or system as inputs or predictions of
how those inputs will impact the actual data or system as outputs.
1.2 History of Digital Twin Technology
The concept of digital twin technology was originally introduced with the publica-
tion of David Gelernter’s book [37] “Mirror Worlds” in 1991. However, Dr. Michael
Grieves, a professor at the University of Michigan, is credited with introducing the
concept of digital twin software and using it in production for the first time in
2002. Finally, in 2010, NASA’s John Vickers created the phrase “digital twin.” The
fundamental procedure to use a digital doppelganger to analyze a physical object
was incorporated earlier. In fact, NASA was the first to utilize digital twin tech-
nology for space exploration missions during the period of the 1960s. Because of
this, NASA’s traveling spacecraft was exactly invoked with replicas of its object in
an earthbound version. The effect was hugely inherited by flight crews with NASA
personnel observing for research and simulation purposes. The idea of a digital twin
first came about at NASA, when full-
scale replicas of early spacecraft were used to
diagnose and mirror issues in orbit. Eventually, fully digital simulations took their
place. After Gartner suggested “digital twins” as one of the major technologies on the
highest utilized lists for 2017, the predictions were geared up with the specific nature
of dynamic software models for physical models. Within 3 to 5 years, the predictions
came true and billions of things happened through the use of digital twins. With an
anticipated 21 billion sensor connections and important devices, “digital twins” were
identified by Gartner as a top trend for 2020.
1.3 Digital Twin System Architecture
A digital twin majorly consists of hardware and software components connected with
network devices [15]. This system contains data handling concepts with middleware](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-17-320.jpg)
![Digital Twin Past, Present, and Future n 3
for data management in between. Figure 1.1 shows the system architecture for a
digital twin system.
Hardware components: the major components include exchange of information
between assets and software integration through Internet of Things (IoT)
sensors [11]. The basic technology behind DTs that use actuators to con
vert digital impulses into hardware-
based powered motions. The hardware
component also includes network devices, such as edge servers, routers, and
IoT gateways, among others.
Data management middleware: its core component is a centralized repository
that aggregates data from many sources. In an ideal scenario, the middle-
ware platform would also manage connectivity, data integration, processing,
quality assurance, data visualization, data modeling, and governance, as
well as other related responsibilities. Such systems include common IoT
platforms and industrial (IIoT) platforms, which usually feature pre-
built
tools for digital twinning.
Software components: because it translates simple observations into rele-
vant business information, the analytics engine is a critical component of
digital twinning. It frequently draws power from machine learning models.
Dashboards for real-
time monitoring, modeling design tools, and simula-
tion software are all important pieces of the DT puzzle.
1.4
Digital Thread: A Bridge Between Physical and
Virtual Worlds
In a closed loop known as a “digital thread,” physical systems and their virtual
counterparts can be linked as soon as you have all the required components [16].
Within it, the following iterative procedures are performed (see Figure 1.2).
Figure 1.1 System architecture for a digital twin system.](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-18-320.jpg)
![4 n Digital Twin Technology and Applications
1. A physical object’s environment and environment at large are both sources of
data that are transferred to the central warehouse.
2. The information within data is produced for updating the DT after evaluation.
3. The digital twin uses new data to assess and decide what would occur if the
environment changed, bottlenecks were found, and the object’s operation was
replicated in real-
time. At this point, algorithms can be used to alter product
designs, spot dangerous trends, and prevent costly downtimes.
4. The control panel displays and visualizes analytic perceptions.
5. Participants make decisions based on actionable data.
6. Accordingly, the specifications, practices, or upkeep programs of a physical
thing are altered.
The procedure is then iterated using the updated information. The complexity
of the physical world is distilled down to its core components via digital twins. The
technology is embraced by many industries as a result.
Digital twin examples
The exponential rise of digital twin technologies in the near future is projected
to be significantly impacted by the development of the IoT, AI, extended
reality (ER), and cloud computing [26]. Nevertheless, it has already gained
popularity across a wide range of industries, where it is used for anything
from production to maintenance and product creation. Here are a few
instances of how the digital twins are put to use on a daily basis in the
real world.
Manufacturing:
The complex manufacturing sector includes a significant amount of the
physical production of commodities using both manual and automated
labor, raw material procurement and transportation across global supply
Figure 1.2 Steps within a digital thread.](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-19-320.jpg)
![Digital Twin Past, Present, and Future n 5
networks, and product research and development (RD). Manufacturing
is a suitable industry for the introduction of digital twins because to its
complexity, which can assist companies in boosting efficiency and reducing
costs at practically every stage of the production process [14]. In the early
stages of designing new automobile parts, engineers at an automotive com-
pany might, for instance, model and test prototypes using digital twins.
They may then simulate prototypes in different simulations, iterating the
design until they reach the final result. Analysts may utilize, before actual
production starts, digital twins to simulate and subsequently enhance the
supply chain and manufacturing process required to generate the finished
product [29].
Healthcare:
In just a few decades, data-
driven technology has fundamentally changed
the healthcare sector. Digital twinning can model treatment plans, enable
the creation of cutting-
edge medical equipment, and give individualized
care for specific patients whether it is utilized in biomedical engineering,
healthcare analytics, or healthcare management [34]. However, monitoring,
managing, and improving physical healthcare facilities, such as hospitals,
may be the most widespread application of digital twins in healthcare [38].
Healthcare providers can utilize digital twins to simulate the daily activities
of their staff members and the availability of vital resources, such as hospital
beds or ventilators, to improve patient care and their overall organizational
effectiveness.
1.5
Types of Digital Twin
■ Stand-
alone digital twins: these are digital twins of specific goods or pieces of
equipment.
■ They can aid in keeping track of and improving the effectiveness of particular
assets, people, and other physical resources.
■ Duplicated digital twins: this aids in monitoring and optimizing the use of
several related discrete digital twins, such as virtual representations of complex
multipart systems like vehicles, machinery, or structures.
■ Enhanced digital twins: these are virtual representations of large-
scale,
complicated entities (e.g., an entire organization or a city). They are constructed
from digital twins of the parts that make them up. They aid in analyzing and
improving higher-
order performance.
1.5.1 Standalone Digital Twins
A standalone digital twin will have enough information to build a model of a system
component.](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-20-320.jpg)
![6 n Digital Twin Technology and Applications
A view of the asset’s health, for instance, can be obtained by tracking sensors
connected to a heating, ventilation, and air conditioning (HVAC) system’s digital
twin. The standalone digital twin typically contains a small number of data sources.
Now, a toolkit that may be built can be used to enhance the twin utilizing accurate
data that is now available from a variety of sources [27]. To match sensor output
with data from CAD systems, three-
dimensional (3D) models, or point clouds are
produced by laser scanning, for instance. To monitor important measurements or
states from a single asset, such as HVAC or environmental systems, limited digital
twins can be helpful. They can also be used to confirm that important building site
components comply with regulations and adhere to the original design.
1.5.2 Duplicated Twin
A digital twin’s duplicate version includes all the significant and quantifiable data
sources needed to replicate the entire asset. The limited digital twins’ components
could be combined to create the duplicate model. This is when the model’s level of
detail may prove to be too fine for your purposes.
To prevent collecting excessive amounts of data, your aims must be clear. By
switching from gauges and dashboards to enhanced, virtual representations of
actual assets, it is possible to increase complexity while maximizing the poten-
tial of duplicated digital twins. The value and utility of this type of digital twin
can be multiplied while the dangers are reduced by modeling and executing the
proper digital twin [28]. Duplicate models have an interesting foundation thanks
to building information modeling (BIM) database-
first models. BIM was created
to promote better teamwork in the building sector. Additionally, it offers a plat-
form with a single source of truth that enables flexible data viewing. These features
would also aid digital twin models in providing the appropriate information to the
appropriate individuals at the appropriate time. As changes are made to the phys-
ical twin, Artificial intelligence (AI) and software analytics would update the digital
twin. Duplicated digital twin computer simulations can aid in averting actual issues.
Sensor data can be collected by smart components that are connected to a cloud-
based system, allowing for real-
time analysis and performance comparisons.
1.5.3 Enhanced Twin
Digital twins are capable of going much beyond just one building or one piece
of machinery. Scale will determine the digital twin’s destiny. The connected asset’s
additional data sources are added to the enhanced digital twin. Correlated envir-
onmental data from outside sources as well as information from outside analytics
and algorithms would fall under this category. The difficulty of managing and
controlling every component of a system increases with its complexity. Because of
this, digital twins represent a huge possibility for future, networked cities [35]. The](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-21-320.jpg)
![Digital Twin Past, Present, and Future n 7
information and analysis required maximizing personnel, planning, and resources
will be provided by them.
Digital twins can be used to model anything, from lone components to com-
plete systems. While every kind of digital twin accomplishes the same basic task—
virtually imitating a physical system or object—
their goals and application domains
are significantly different. The following are the four main categories of digital twins.
1.5.4 Component Twins
Digital representations of a particular system or product component, like a gear
or screw, are known as component twins. Component twins are typically used to
represent integral parts, such as those under specific stress or heat, rather to simply
modeling all the various components of a product [39]. Designers and engineers
can discover how the parts might be modified to maintain their integrity in fore-
seen conditions by digitally modeling the parts and running dynamic simulations
on them.
1.5.5 Asset Twins
Digital reproductions of an entire product rather than simply its parts are called asset
twins, also referred to as product twins [41]. Though theoretically made up of many
component twins, asset twins’ main goal is to show how the many components of
a real-
world product interact with one another. For example, a wind turbine’s asset
twin may be used to track performance and spot component breakdown due to
normal wear and tear.
1.5.6 System Twins
System twins, commonly referred to as unit twins, are computer simulations of
actual product systems. System twins represent these several items as components
of a bigger system, whereas asset twins simulate real-
world products made up of
numerous parts [40]. It is possible to enhance the relationships between assets by
having a better understanding of how they interact, which will boost productivity
and efficiency.
1.5.7 Process Twins
Digital representations of interconnected systems are called process twins [42]. For
instance, a process twin could simulate the complete factory down to the workers
working the machinery on the factory floor, whereas a system twin might simulate
a production line.](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-22-320.jpg)
![8 n Digital Twin Technology and Applications
1.6 Working Principles—Digital Twin
A digital twin is first invented by specialists, frequently data scientists or applied
mathematicians.
These programmers investigate the physics underlying the physical system or
object being imitated, and then use the information they learn to create a mathem-
atical model that replicates the original in digital space. The twin is designed to be
able to take information from sensors collecting data from a physical counterpart.
Because of this, the twin can duplicate the physical object in real-
time and offer
information into its functionality for inculcating potential issues [13]. The physical
counterpart’s prototype may have served as the basis for the twin’s design, in which
case the twin can offer input as the product is developed or even act as a prototype
before the physical counterpart is constructed. Eniram, a company that develops
digital twins of the enormous container ships that transport a large portion of global
trade, describes the procedure in some depth in this post. This kind of application
for digital twins is quite complex. The amount of data you utilize to create and
update a digital twin, though, will decide how well you are imitating a physical
object [25]. A digital twin can be as complex or as straightforward as you wish. For
instance, this lesson shows how to create a straightforward digital replica of an auto-
mobile that computes mileage using only a few input variables.
1.6.1
Digital Twin vs. Simulation
Although they are two distinct concepts, the words “simulation” and “digital twin”
are frequently used interchangeably. A simulation can be created using a CAD system
or other comparable platform and put through its paces, but it might not be a per-
fect duplicate of an actual object in the real world. However, data usage by utilizing
digital twin through IoT sensors on actual equipment, which allows it to duplicate
real-
world systems and adapt to those systems’ changing needs [36]. A digital twin
gives all elements of the organization insight into how a product or system they are
presently using is performing right now, unlike simulations, which are typically used
during the planning phase of a product’s lifecycle to predict how a future product
would work.
1.6.2 Digital-Twin Use Cases
The car and the cargo ship, the digital twin examples we highlighted earlier, give an
idea of possible use cases. Before being built physically, items like turbines, railways,
offshore oil platforms, and aeroplane engines can be developed and tested digitally
[43]. The utilization of these digital twins for maintenance tasks is another poten
tial application. For instance, technicians could test a suggested patch for a piece of
equipment using a digital twin before actually performing the fix.](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-23-320.jpg)
![Digital Twin Past, Present, and Future n 9
1.6.3
Technology Involved in Digital Twin
Digital twins incorporate a range of technologies, including artificial intelligence
and machine learning. Future advancements in 3D laser scanning and IoT sensors
will significantly influence the development of digital twins. Processing of a cloud
framework is the main focus of the construction of the digital twin model frame-
work, scanning technologies, and LiDAR when there is a visual component, such as
in the built environment [44].
1.6.4 IoT Sensors
IoT sensors are primarily responsible for making digital twins conceivable [3].
Directly integrating IoT functionality into modules or hardware is expected to sig-
nificantly disrupt the market [9]. This will cut the cost of deploying IoT devices and
simplify setup and deployment considerably [19].
1.6.5
3D Laser Scanning Software
One of the digital twin technology’s unsung heroes is reality capture. Using
vector-
based, multi-
stage point cloud processing, the visual data for digital twins
is created (or stitched). Additional details are available in our point cloud pro-
cessing guide.
1.6.6
AI and Machine Learning
The only techniques available are artificial intelligence and machine learning [23]
to analyze the model of operations represented by the digital twin because of the
massive amount of data generated [5–
8]. If digital twins are to fulfil their potential,
they must be able to perform analysis in real-
time or more quickly, provide a high
level of prediction accuracy, and incorporate data from numerous distinct and usu-
ally incompatible sources [10].
1.6.7 5G Connectivity
Every use case for a digital twin is supported by connection. 5G is increasingly
important. Low latency, high bandwidth, large capacity, excellent reliability,
enhanced mobility, and extended battery life are just a few of the features that 5G
claims will revolutionize digital twin capabilities. For instance, a single cell on a 4G
network may accommodate 5500–
6000 IoT devices [19, 20]. Up to one million
devices can be supported by a 5G network [21].](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-24-320.jpg)
![10 n Digital Twin Technology and Applications
1.6.8 Cloud Computing
Digital twins can be processed and executed using cloud technologies. Microsoft
already offers an expanding selection of Azure Digital Twin application to assist
in line with cloud deployment [18]. The concept of “device shadow” offered by
Amazon Web Services (AWS) is implemented as a division of AWS IoT [22].
1.6.9
Benefits of Digital Twin
Digital twins have as many uses as there are advantages to using them. But some of
their more well-
known advantages are as follows:
■ By developing, testing, and fine-
tuning systems or products in virtual environ-
ments before putting them into mass production or launching them, you can
cut expenses overall [30].
■ Improve operational efficiency by modeling systems with the most recent data
and testing changes in dynamic simulations before implementing them in the
real world [31].
■ Continually monitor the performance of physical assets and functioning
systems, such as structures or aircraft, and identify issues as soon as
they arise.
■ By simulating the customer’s journey, you may enhance the experience they
have while making a purchase or entering a store.
1.6.10
Advantages of Digital Twin Technology
■ Improved RD
Utilizing digital twins generates a lot of information about anticipated per-
formance outcomes, supporting more effective product research and develop-
ment. Businesses can utilize this data to get insights that will help them make
the necessary product adjustments before they start production [17].
■ Enhanced effectiveness
Even after a new version of the product has gone into production, digital twins
can help in monitoring and mirroring application deployment with the aim
of achieving and targeting peak efficiency for the entire manufacturing pro-
cess [32].
■ Product implementation lifecycle
Digital twins can also assist producers in determining how to handle products
that have reached the end of their useful lives and require final processing, such
as recycling or important further actions [46]. By using digital twins, they can
choose which product materials can be gathered.](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-25-320.jpg)
![Digital Twin Past, Present, and Future n 11
1.6.11
Digital Twin Market and Industries
Despite the advantages that digital twins offer, not every business or every product
manufactured must use them. Not all items are complex enough to require the con-
stant and intense influx of highly processed sensor data that digital twins precisely
demand [45]. Additionally, investing a significant amount of money in the creation
of a digital twin is not always profitable (remember that a digital twin is an exact
replica of a physical thing that has been pre-
defined; as such, creating one might
be costly). However, there are certain clear benefits to employing digital models for
various applications:
Physically substantial projects: buildings, bridges, and other complex structures
are governed by strict technical standards.
Mechanically difficult projects: vehicles, jet turbines, and aircraft. Digital twins
can contribute to increased productivity in massive engines and intricate
machinery.
Power devices: this includes both the transmission and generation of power.
Manufacturing initiatives: digital twins are effective at increasing process effi-
ciency [24], much like industrial settings with cooperating machine systems.
As a result, industries that handle large-scale products or projects benefit the most
from using digital twins, such as the following: system engineering; manufacturing;
Power utilities; railcar design; automobile manufacturing; aircraft production.
1.6.12
Digital Twin Market: Poised for Growth
Although digital twins are already utilized in a variety of industries, the market for
them is expanding swiftly, which indicates that demand will continue for a while
[47]. In 2020, the digital twin market was expected to be valued USD 3.1 billion.
Some industry analysts predict it will develop quickly through at least 2026, reaching
an estimated USD 48.2 billion.
1.6.13 Applications
Digital twins are utilized frequently and invoked in the following applications:
1.6.14 Power-Generation Equipment
Large engines, including jet engines, locomotive engines, and power-
generation
turbines, benefit greatly from the use of digital twins, particularly when assessing
whether routine maintenance is necessary [4, 12].](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-26-320.jpg)
![12 n Digital Twin Technology and Applications
1.6.15
Systematic and Structures
Digital twins can improve massive physical structures, notably when designing large
structures like offshore drilling rigs or tall towers [2]. Furthermore, they are useful
for designing the HVAC systems that function inside those structures.
1.6.16 Manufacturing Operations
Given that they are designed to simulate a product’s whole lifecycle, digital twins
have spread throughout all stages of manufacturing, from product concept to
finished product and every step in between [1].
1.6.17 Medical Services
Similar to how items can be profiled, patients seeking medical treatment can be
as well.
The same type of sensor data that the system generates can be used to track various
health markers and generate crucial insights [49].
1.6.18 Automobile Sector
In the automotive business, digital twins are frequently used to increase vehicle per-
formance and production efficiency. Automobiles stand in for a number of complex,
interrelated systems [48].
1.6.19 Urban Design
Civil engineers that work in the field of urban planning greatly benefit from the
use of digital twins, which may show real-
time applications that use 3D and four-
dimensional (4D) spatial data and also incorporate augmented reality systems into
constructed surroundings.
1.7
The Future of Digital Twin
There is no denying that the present operational paradigms are drastically changing.
A disruptive digital revolution is currently taking place in asset-
intensive indus-
tries, and this revolution asks for an integrated physical and digital perspective of
assets, machinery, facilities, and processes. Digital twins are a key element of that
readjustment. The potential of digital twins is essentially limitless because more and
more cognitive resources are continuously being allocated to their use. Given that
they are always learning new skills, digital twins can keep producing the insights](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-27-320.jpg)
![Digital Twin Past, Present, and Future n 13
needed to improve products and streamline processes [50–
51]. In this context, on
using digital twins to transform asset operations, learn how change will affect your
industry. Similar to royal food tasters or stunt doubles for movie stars, digital twins
serve the same purpose for complex technologies and processes: they guard priceless
assets from harm that may otherwise befall them. Duplicates have entered the virtual
world, saving many enterprises time, money, and effort while preserving the health
and security of valuable resources.
1.8 Conclusion
With the establishment of IoT devices, there is a huge number of distributed levels in
local and remote storage processes. There are powerful tools in generating data using
data analytics and AI algorithms to process batch and real-
time approaches. Digital
twin technology and the latest recent machine learning and artificial intelligence
tools, are assisting businesses across numerous industries in lowering operational
costs, boosting productivity, and changing the way that predictive maintenance is
carried out. For product producers, in particular, to attain more productive processes,
digital twin technology is vital and has a shorter time to be established in the market.
On the other hand, there are digital twins being developed for IoT devices
to fully comprehend and describe their structural characteristics and behavior in
various settings. Therefore, the range of applications and advantages of digital twins
include continually increasing IoT devices. However, digital twin applications can be
remotely penetrated. And also, smart hackers cause irreversible damage to the device
networks, and damage to IoT applications and systems. With blockchain’s increased
stability and maturity, IT professionals are looking into the prospect of connecting
it to digital twins to fend off security concerns. These two technologies working
together to offer a promising future for both the commercial and IT sectors. By com-
bining cutting-
edge technologies including machine and deep learning (ML/
DL)
algorithms, computer vision (CV), and natural language processing (NLP), digital
twins are also regularly updated and improved. Thus, the cool synchronization with
blockchain will enable the digital twin industry to grow over the upcoming years.
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![facerent iniquitatem. e N O V A. rapinam : 47. Et lapidentur lapidibus
populorum , confodiantur gladiis eorum : lios filias earum
interficient , domos earum igne fuccendent. VERSIO ANTIQ 48. Et
auferam impietatem de terra, difcent Q U A. omnes mulieres ne
faciant fecundüm i impietatem earum. 49. Et dabuntimpietatem
veftram fuper vos... NoT£E AD VERSIONEM ANTIQUA M. Y. 36. Gr. à,
ayacyTeneis (9 annuntialis Ὁ c. ut fupra. Y. 37. Gr. τὰ ὠθυμήμαγα
ἀυτῶν ἐμοιχώγ]ο κα τὰ τέχνα εἐυτῶν, οἷ ἐγέννησάν μοι 5 δειήγαγον
αὐτοῖς M ἐμ ύρων, Y.40. Grac. Z ἅμα τῷ ἐρχ eau ἀυτὸς., c. ut fup.
Y. 42. Grec. Καὶ φωνὴν ἁρμονίας εχρξονῖο E, πρὸς ἀνδρας ἐκ πλήθες
av pal ov ἥχοντας ἐκ τῆς ἐρήμε' MÍ. Alex. cum edd. Ald. Compl.
οὐωμένες ἐχ τῆς , δες. Y. 44. Sic eft in Grzco, prater hoc, πρὸς
Οὐλαν., E, πρὸς ᾽Οολιζαν. Y.48. Grac. Kai ὠποσρέψω, Et avertam,
loco Et auJeram ; paulóque poft, ὁ ἐ μὴ ποιήσεσι» [Ὁ non facien,
loco ne faciant 5 ultimóque num, plur. χαταὰ τας ἀσεξείας ἀυτὼν.
Y.49. Grac. Καὶ διοβήσεται καὶ acc Geim υἱμῶν ἐφ᾽ ἱμὰς, Et dabitur
impietas veflra [uper vos. Nonnulla autem fup:a addita funt verba ex
Hebr, aut Vulg. que nonnifi leviter differunt ἃ Graco, ur fcilicet nexu
aliquo colligarentur variantes lectiones LXX. paffim adhibite ab
Hieronymo. E NSPIUDT. XX I'V. VULGATA NOVA. I. T faum eft
verbum Domini ad me , in anno nono, in meníe decimo , decima die
menfis, dicens : 2. Fili hominis fcribe tibi nomen diei hujus, in qua
confirmatus eft rex Babylonis adversum Jerutalem hodie. 3. Et dices
per proverbium ad domum irriVERSIO ANTIQU A. T fadus eft fermo
Domini ad me , in anno nono, in menfe decimo, decimá men3 ,
diens. . Fili hominis fcribe tibi diem ab hac die, qua abito: eft rex
Babylonis fuper Jerufalem ab hodierna die. ;. Et dic ad domum
exafperantem parabolam, / Nor£ AD VERSIONEM ANTIQUA M. Υ.1τ.
Ita Grecé, ad verbum, X.2, Eadem exítant Grecé, pofito uno ei, 7z ,
ante diem. Y. 3. Itidem Gracé, prater vocem Dess , que abeft ;
Hieron. ubi fup. col, 059. d. e. Ibid, ER in Exech. 24. «οἱ, 961. ex
Lxx.](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-36-320.jpg)
![fuper quibus; poniturque X ,ante vocem filz; ; cet. ut in textu. In Mf.
Alex. pro Adonai Dominus , eft Κύριος Κύριος ὁ Θεός, Y.22. Itidem
Grzcé , pofito uno ἀπὸ. ante ore, 799 VERSIO ANTIQUA. derabilia
oculorum tuorum in przparatione : non planges, neque flebis, nec
venient lacrymae tibi. 17. Gemitus fanguinis, renum luctus eft : erunt
crines tui colligati fuper te, calceamenta tua in pedibus tuis, nec
confolaberis in labiis eorum, panem hominum non comedes. 18.
Locutus füm ad populum mane ficut przceperat mihi, mortua eft
uxor mea vefperi : fecique mané ficut preceptum eít mibi. 19. kt dixit
ad me populus : Non annuntias nobis, quid funt hzc, qua tu facis?
20. Et dixi ad eos : Sermo Domini fadus cft ad me, dicens : 21. Dic
ad domum Iírael : Hzc dicit Adonai Dominus : Ecce ego contaminabo
fanca mea, fuperbiam fortitudinis veítrz , defiderabilia oculorum
veftrorum , quibus parcunt animz veftrz : filii veftri, filie veftrz,
quos reliquiftis , in gladio cadent. 22. Et facietis ficut feci : Ore
eorum non confolabimini, panem virorum non comedetis. 23. Et
come veftra fuper capita veftra , calceamenta veftra in pedibus
veftris : non plangeüs nec flebitis, contumemini in iniquitatibus
veftris, confolabitur unufquifque fratrem fuum. 24. Et erit Jezekiel
vobis in portentum : fecundum omnia, quz fecit, facietis : cumque
venerint hec, cognoícetis quoniam ego Adonai Dominus. 25. Et tu fili
hominis , nonne in die , quando abítulero fortitudinem ab eis ,
elationem gioriationis eorum , defiderabilia oculorum eorum , ὅς
elationem anima eorum, filios filias eorum; 26. In die illa veniet
qui falvus factus fuerit ad te, ut annuntiet in auribus tuis? 27. ἴῃ
dieilla aperietur os tuum ad eum qui fugerit : loquéris ,
nequaquam ultra reticebis : eriseis in portentum , cognofcent
quoniam ego Dominus. Y.23. Vix melius de Graco, nifi exciplatur
verbum fingul. comfolabittr , pro quo. plur. zapaxeoéac]t , confola«
bimisi. Y. 24. Grece, pro fecit , habetur ἐποίησα, feci ; preponiturque
z , verbo cogzofcetis , deleto fup. que , antc venerint, cum voce
Adozaz; ct. ut in textu. In ed, veró Compl. eft ἐποίησε , ut fup.
abfque z , ante cogaofcetis 5; ὃς in Ald. Af'ova? Κύριος. Y.25.
Similiter in Greco , nifi quód additur ἀυτῶν » poft fizos ; loco
defiderabilia , hab. ἐπιθυμύήμαγα,, defideria. Υ. 26. Ita rurfum
Graecé, addito uno annuntiet ; deleto veró tuis , 1n fine. Y. 27. lta](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-41-320.jpg)
![conftanter Gracé, nifi excipiatur verbum ἀνασωζόμδιον., quà. evaferit
, loco qui fugerit ; deeft etiam feq. t9 ; at in Mf. Alex. eft . καὶ
λαλήσεις 5 ficut in edd. Ald, Compl. (οἱ, tibi, verbo οὐ n. Χ Ἀν:
VULGATA NOVA. 1. T faus eft fermo Domini ad me , dicens: 2. Fili
hominis pone faciem tuam contra filios Ammon, prophetabis de
eis. ;. Et dices filis Ammon : Audite verbum Domini Dei : Hzc dicit
Dominus Deus :. Pro eo quód dixifti : Euge , euge fuper fanuarium
meum, quia pollutum eft ; fuper terram Ifrael , quoniam detolata
eft; fuper domum Juda , quoniam duci funt in captivitatem :
VERSIÓ ANTIQUA. M T factus e(t fermo Domini ad me, dicens: Hz»,
i5 Fo 4 2. Fili hominis obfirma faciem tuam fü- 13. c2. 775. per filios
Ammon..... j« Quiagavifi e(tis fuper fanduarium meum... 75- cof.
ΝΟΤΕ AD VERSIONEM ANTIQUA M. YY.1. 2. Similiter in Greco, Y. 3.
Sic apud Hieron, pro his de Vulg. Pre eo qud dixifli : Emge , euge
[uper fantluarium meum. Grac, hod, ( I , 3 ᾿ N ru , AW! ὧν
ἐπεχάρη]ε ἐπὶ τα ἁγιᾶ us. Hieron, ubi fup. Ilzd, δός. 8, ldem zm o o
Ezech, 67. ex](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-42-320.jpg)
![LXX. interpretatz fit , domum Beth Iafimuth , citz boc vocabitlum
villam defertam /ignifiet ;. Beelmeon quoque ufque bodie in Moab
vicus fit maximus , quem illi vevterunt fuper fontem ; t$ Cariathaim ,
civitatem maritimam, Vide euam inf, col, 871. a. Y. 10. Ita in Greco ,
excepto uno Kedzu , loco Or£entis ; extremó etiam deeft τὸ zz
gentibus ; fed in Mf, Alex, ac ed. Compl. additur ἐν τοῖς ἔθνεσι. Y. 11.
Siceft in Greco, preter vocem exd ίχησιν, ultzozem , loco ultzones. Y.
12. Eadem leguntur Grzcé , excepta voce /4dozai , quz deeft;
habetur tamen in Mí. Alex. necnon in edd, Ald. Compl. de more. Y.
13. [τὰ Grecé, deleta femper voce 42ozai ; pofitaque conjunct.
z,ante extendam. . Y. 14. lta rurfum in Graco , repetita voce xad ,
juxta » ante furorem meum. Y. 15. Sic habetur Grecé , hoc excepto ,
ὧν ἐχδιχήσει , in ultione , loco ultionem ; ab ed. veró Ald.abeft 5
fubinde in Vatic. loco zz aternum , eft ἕως évóc , ad «num ; in Ald.
veró Compl. in Mf. Alex. ἕως αἰῶνος , ut fup. Y. 16. Grac. hab.
ἐχτείνω . extesdo , non extendam 5 loco veró reliquias littoris
maritima , lic, τὸς Xa]aAciTES τὸς x«]omÉv|az τὴν παραλίαν ,
reliquos babitantes. maritiqam; ct. ut in textu, Y. 17. Eadem funt in
Greco , prater hoc , i» vindida furoris , quod deeft ; ed. fola Compl.
addit, ἐν ἐλεγμοῖς ϑυμῦ. ἔ](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-45-320.jpg)
![fufpenderunt in te : ipfi dederunt gloriam tuam. 11. Filii Aradiorum,
fortitudo tua fuper muros tuosin circuitu : cuftodesin turribus tuis
erant , pharetras fias fufpenderunt fuper propugnacula tua per
gyrum : ipfi perfecerunt decorem tuum. 15. Grzcia univerfa ,
adjacentia ejus , 1pfi negotiatores tui in animabus hominum : vafa
enea dederunt mercatum tuum. 14. De domo Thorgama, equos,
equites, mulos dederunt nundinas tuas. r5. Filii Rhodiorum
negotiatores tui ex infulis multiplicaverunt negotiationem tuam
denteselephantinos: his, qui introducebantur , reddebas mercedes
tuas : 16. homines, negotiationem tuam à multitudine mercatüs tui
in Aphec , ftaem , polymita de Tharfis, ramoth, chodchod
dederunt in nundinas tuas. 17. Judas filii Ifrael ifti negotiatores tui
in frumenti commercio , unguentis , primum mel, oleum,
refinam dederunt in nundinis tuis. 18. Damafcus negotiator tuus in
multitudine operum tuorum, ex multitudine omnis fortitudinis tuz,
vinum ex Chelbon, lanas de Mileto. 19. Ferrum faum opere,
rota in commiftione tua eft. 20. Dedan negotiatores tui cum jumentis
electis Nor£ AD VERSIONEM ANTIQUA M. Y. 7. Concinit Grac. nifi
quód tollit zz , ante flratzm ; pra ponitque 5, , verbo fada funt ;
Compl. veró hab. cy σρωM, abfque conjunct. ὁ» ante ἐγένεο. X.8. Àd
verbum é Greco , pofitá uná conjun. c, ante principes, Y.9. Gr. Οἱ
πρεσδύγερφι Βιβλίων, X, οἱ (Copo av]ow , o? ἦσαν cy (Col, c.
Senzores Bibliorum , Q5 fapientes eorum , qui erant in ie, c. ut
fupra ; fed à Mf. Alex. abeft οἷ. ante ἤσαν. Hieron. inf. 890. f. ait
juxta edit. LXX. legi confsiliarios Bybli; que Hebraice appellatur
Gebal. Y. το. Itidem Grace, X. 1I. Totldem verba in Greco, detracto
uno zz cireniti ; fed in Mf. Alex. ac ed. Ald. eft ἐπὶ τῶν τειχέων
χύχλῳ, |tem in Vatic, loco propugnacttla , legitur opue 5 in mulis ,
tefte Nobilio , puav (09 . compages , armos titos. Y. 13. Gr. Ἧ
Ἑλλὰς, Z, καὶ (umen , αὶ τὰ παραΊείνον7a. $To ἐγεπορεύοντο Co ;
c. Gracia , £5 univerfa » 9 adjacentia , bi uegotiabantitr tibi , c.
utin textu : in Compl. 4» Exc; πᾶσα; in Mf. Alex. 'Exd;, X τὰ
(ὑμαανΊα. Y. 14. In Greco Varic. eft Θογαρμα ; deinde , ἵπισοι E]
ἑαωπεῖς 5. ulimóque , ἀγοράν (€, forum tuum , abfque hoc ant. C9
mulos. In ed. veró Compl. ὃς Mf. Alex, Oegyzgz 5 in Ald. Θοργαξ οἱ ;
tum in quibufque , lez , X ἱππεῖς y X ἡἡἱμιόνες ἐδωχαν. ut in. Lat.](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-53-320.jpg)
![habetur , fed de Theedotionis editioue additum efl. Eadem etiam ad
hoc ufque, g affument , non leguntur in Gr. Vat. nec apud
Tichonium fupra. : Y.32. Gracé : Καὶ λήψονγαι οἱ υἱοὶ ἀυτῶν ἐπὶ (ὲ
.rgnvoy, ϑιρννήμα Xóp* nec plura : Et affiment filii eorum fuper te
lamentum , lamentationem Sor ; al. Cet tibi, non Ser. Hieron. etiam
in comment. col. 891. f. ait fequentia ( de Vulg. ) Qua eft ut Tyrus ,
qua obmutuit , five conticuit , in medio maris? in LXX. non haberi :
nunc etiam abfunt à Gr. Vatic. nec admittuntur à Tichonio. Y. 33.
Similiter in Graco , pofito uno ἀπὸ, ante vocem oinltitudine; pro
commi[lione autem , conftanter habetur ('uuulu] , commiflo.
Hieron. in comment. 892. a. hgc habet : Qua ip exitu negotiationum
tuarum » f£ve, Quam invenifti mercedem de mari ὃ ὁ Gr. Πύσον τιγὰ
εὗρες μιὼ ὃν ἀπὸ- c. Y.34. Edit. hab. Nauac autem contriflata ες;
ΜΙ, veró B. M. Rem. n. 35. contrita , quod fubftituimus ; Grace
pariter , Nor ('we]pleus » Nune contrita es ; Compl. wv —€—— ](https://image.slidesharecdn.com/7693-250725135722-d7b4539e/85/Digital-Twin-Technology-and-Applications-1st-Edition-A-Daniel-57-320.jpg)
![I. EZECHIEL. Cap. XXVIII VULGATA NOYA. 3 $. Univerli
habitatores infularum obftupuerunt fuper te : reges earum omnes
tempeftate perculfi mutaverunt vultus. 36. Negotiatores populorum
fibilaverunt fuper te : ad nihilum dedua es, non eris ufque in
perpetuum. 905 VERSIO ANTIQUA. 35. Omnes qui inhabitant infulas
contriftati funt füper te: remiges eorum mentis alienatione
ftupuerunt, lacrymatus eít vultus eorum füper te. 36. Mercatores
eorum de gentibus exfibilabunt te : perditio facta es, ultra non eris in
«ternum , dicit Dominus, Tzcbon. ubi fup. Nor AD VERSIONEM
ANTIQUA M. reliqua utin Lar. Apud Hieron. in comment. col. 892. a.
non commz[Ho , ed negotiatio tta ; Grecé conftanter , CvaΜικτός (Ce
, commiflus 12u5. Y. 35. Hzc tora Graeco fimillima , dempto ult.
fitper te , quod tamen eft in ed. Ald. Mf. Alex. loco veró reiSes ,
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- 6. Digital Twin Technology and Applications The Fourth Industrial Revolution is being accelerated by the digital twin techno- logical revolution, which converges intelligent technologies and defines the con- nectivity between physical and digital items. The Internet of Things (IoT) connects the real and digital worlds, allowing connected items to deliver a vast array of ser- vices to internet users. IoT devices create large amounts of data that may be fed into AI systems for decision- making. In a decentralized architecture, digital twin technology may be utilized to protect platforms and create smart contracts. Digital twins decentralized ledger, immutability, self- sovereign identification, and con- sensus procedures hold a lot of promise for improving AI algorithms. Furthermore, leveraging smart contracts in a digital twin system to facilitate user interaction via IoT might have a big influence, and this integrated platform is expected to revolu- tionize many fields. Digital Twin Technology and Applications examines the problems, issues, and solutions for using big data to enable streaming services using IoT and AI with digital twin technology. The IoT network concept is the key to success, and to estab- lish a solid IoT platform on which large data transmission may take place, it must handle protocol, standards, and architecture. The book provides insight into the principles and techniques of IoT and AI. It explores the idea of using blockchain to provide security in a variety of sectors. The book also covers the application of integrated technologies to strengthen data models, improve insights and discov- eries, innovate audit systems, as well as digital twin technology application to intel- ligent forecasting, smart finance, smart retail, global verification, and transparent governance.
- 8. Digital Twin Technology and Applications Edited by A. Daniel, Srinivasan Sriramulu, N. Partheeban, and Santhosh Jayagopalan
- 9. MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. First edition published 2025 by CRC Press 2385 Executive Center Drive, Suite 320, Boca Raton, FL 33431 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN CRC Press is an imprint of Taylor & Francis Group, LLC © 2025 selection and editorial matter, A. Daniel, Srinivasan Sriramulu, N. Partheeban, and Santhosh Jayagopalan; individual chapters, the contributors Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978- 750- 8400. For works that are not available on CCC please contact mpkbookspermissions@tandf.co.uk Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. ISBN: 9781032430591 (hbk) ISBN: 9781032745176 (pbk) ISBN: 9781003469612 (ebk) DOI: 10.1201/9781003469612 Typeset in Garamond by Newgen Publishing UK
- 10. v Contents About the Editors...........................................................................................vii Contributors..................................................................................................viii 1 Digital Twin Past, Present, and Future.....................................................1 A.M. SERMAKANI, R. RADHIKA, AND V. SUJATHA 2 Digital Twin Types and Design..............................................................17 PALLAVI JAIN, SUNIL KUMAR BORAN, BHAIRVEE SINGH, AND PANKAJ SINGH 3 Real Issues, Opportunities, and Open Investigations in Digital Twins..........................................................................................33 V. SHEEJA KUMARI, T. MANIKANDAN, M.J. CARMEL MARY BELINDA, A. SELVA KUMAR, AND K. PRABU 4 Twin Technology: Exploring Types and Applications of Digital Twins......................................................................................81 S. DINESH KRISHNAN, K.V. MAHALAKSHMI, DYAGALA NAGA SUDHA, V. SATHYA PRIYA, AND A. DANIEL 5 The Convergence of Data Analytics, Digital Twins, and the IoT/ IIoT: A New Era of Data- Driven Decision Making.......................109 S. GEERTHIK, N. VEL MURUGESH KUMAR, P.V. GOPIRAJAN, AND B. JAISON 6 Simulation Strategies for Analyzing Data.............................................130 S.S. DARLY AND D. KADHIRAVAN 7 Navigating the Complexities of Digital Twin Implementation: Challenges and Strategies for Success...................................................171 M. ARVINDHAN, S. NIVETHA, RAGHVENDRA AJAY MISHRA, AND A. DANIEL
- 11. vi n Contents 8 Using Improved Finite Element Modeling to Combat Cardiovascular Disease: A Review of a Developing Area at the Intersection of Several Disciplines.......................................................187 V. SHEEJA KUMARI, T. MANIKANDAN, A. SELVA KUMAR, S. PONMANIRAJ, AND K. PRABU 9 Comprehensive Study of Digital Twin in Smart and Customized Healthcare............................................................................................211 SALNA JOY, R. BABY CHITHRA, AND AJAY SUDHIR BALE 10 Sustainable Organic Farming in Indian Rural Areas with the Aid of the Internet of Things..........................................................239 R. RAJESH, S. SIVAKUMAR, AND S. PREMKUMAR 11 Predictive Analysis of Toxic Ions and Water Quality Based on Sensor Data Using LSTM and ARIMA Models...............................265 VALLIDEVI KRISHNAMURTHY, P.R. JOE DHANITH, R. SUJITHRA KANMANI, SURENDIRAN BALASUBRAMANIAN, AND N. REKHA 12 Digital Representation of Agriculture Forms.......................................296 K. RAJASATHIYA 13 Accelerators for Clustering Applications in Machine Learning............328 MRINALIKA DURAIRAJU, MRINALINI DURAIRAJU, VALLIDEVI KRISHNAMURTHY, V. SAKTHIVEL, AND SURENDIRAN BALASUBRAMANIAN 14 Design of a Smart Healthcare Environment with Digital Twinning and Machine Learning.........................................................355 S. GEETHA, J. MADHUSUDANAN, AND V. PRASANNA VENKATESAN 15 FloodWatch: Suggesting an IoT- Driven Flood Monitoring and Early Warning System for the Flood- Prone Cuddalore District in the Indian State of Tamilnadu.............................................374 R. INDRAKUMARI, SRINIVASAN SRIRAMULU, N. PARTHEEBAN, AND RAJKUMAR RAJAVEL Index.............................................................................................................389
- 12. vii About the Editors A. Daniel is an associate professor in ASET-CSE, Amity University, Madhya Pradesh, India. He has 13 years of experience in academics. He has expertise in AIML, deep learning, and quantum computing. Srinivasan Sriramulu is a professor in the School of Computing Science and Engineering, Galgotias University, India. He has more than 22 years of experience of teaching. He has expertise in image processing, big data, cloud, IoT, and artificial intelligence. N. Partheeban is an associate dean and professor at the School of Computer Science and Engineering, Galgotias University. He has more than 23 years of experience in academics. He has expertise in artificial intelligence and machine learning. Santhosh Jayagopalan is with the Faculty in Computer Science, British Applied College, Umm Al Qwain, United Arab Emirates. He has 14 years of academic experience. He has expertise in IoT, networks, and machine learning.
- 13. viii Contributors M. Arvindhan Galgotias University Greater Noida, Uttar Pradesh, India Ajay Sudhir Bale New Horizon College of Engineering Bengaluru, India Surendiran Balasubramanian National Institute of Technology Puducherry, India M.J. Carmel Mary Belinda Institute of AI & ML, Saveetha School of Engineering SIMATS University Chennai, India Sunil Kumar Boran Galgotias University Greater Noida, India R. Baby Chithra New Horizon College of Engineering Bengaluru, India A. Daniel Amity School of Engineering and Technology Amity University Madhya Pradesh, India S.S. Darly Anna University Chennai, India P.R. Joe Dhanith Vellore Institute of Technology Chennai, India Mrinalika Durairaju Shiv Nadar University Chennai, India Mrinalini Durairaju Shiv Nadar University Chennai, India S. Geetha Pondichery University, Kalapet Puducherry, India S. Geerthik Agni College of Technology Chennai, India P.V. Gopirajan SRM Institute of Science and Technology Chennai, India R. Indrakumari Galgotias University Greater Noida, India
- 14. Contributors n ix Pallavi Jain SCSE, Galgotias University Greater Noida, India B. Jaison RMK Engineering College Kavaraipettai, Tamil Nadu, India Salna Joy New Horizon College of Engineering Bengaluru, India D. Kadhiravan University College of Engineering Tindivanam Anna University Chennai, India R. Sujithra Kanmani Vellore Institute of Technology Chennai Campus Chennai, India S. Dinesh Krishnan B V Raju Institute of Technology Narsapur, Telangana, India Vallidevi Krishnamurthy Vellore Institute of Technology Chennai, India A. Selva Kumar SIMATS University Chennai, India N. Vel Murugesh Kumar RMK Engineering College Kavaraipettai, Tamil Nadu, India V. Sheeja Kumari SIMATS University Chennai, India J. Madhusudanan Pondichery University, Kalapet Puducherry, India K.V. Mahalakshmi B V Raju Institute of Technology Narsapur, Telangana, India T. Manikandan SIMATS University Chennai, India Raghvendra Ajay Mishra Galgotias University Greater Noida, Uttar Pradesh, India S. Nivetha RVS College of Engineering & Technology Coimbatore, India K. Prabu Galgotias University Greater Noida, Uttar Pradesh, India S. Premkumar Galgotias University, Greater Noida Uttar Pradesh, India V. Sathya Priya B V Raju Institute of Technology Narsapur, Telangana, India S. Ponmaniraj SIMATS University Chennai, India R. Radhika S.A.Engineering College, Chennai Tamil Nadu, India
- 15. x n Contributors K. Rajasathiya P.S.R.R College of Engineering Sivakasi, India Rajkumar Rajavel Department of CSE Christ University Bangalore, Karnataka, India R. Rajesh Vellore Institute of Technology Tamil Nadu, India N. Rekha National Institute of Technology Puducherry, Karaikal, India V. Sakthivel Vellore Institute of Technology Chennai Campus Chennai, India A.M. Sermakani S.A. Engineering College, Chennai Tamil Nadu, India S. Sivakumar SRM Institute of Science and Technology Tiruchirappalli, India Bhairvee Singh GLBITM Greater Noida, India Pankaj Singh SCSE, Galgotias University Greater Noida, India Dyagala Naga Sudha B V Raju Institute of Technology Narsapur, Telangana, India V. Sujatha S.A. Engineering College Chennai, Tamil Nadu, India V. Prasanna Venkatesan Pondichery University Kalapet, India newgenprepdf
- 16. 1 DOI: 10.1201/9781003469612-1 Chapter 1 Digital Twin Past, Present, and Future A.M. Sermakani, R. Radhika, and V. Sujatha 1.1 Introduction A digital twin (DT) is a modern technology for representing actual assets and cor- porate operations. Real- time monitoring of data and systems is made possible by this fusion of the virtual and physical worlds. Sensors and various wireless technologies are utilized to gather structure of the data for digital twin models of physical items. They lower maintenance costs while also enhancing project design and quality. An exact clone of a physical functionality is known as a “digital twin,” which simulates the performance, identifies inefficiencies, and creates improvements for the counter- part in the real world. In addition to a simulated environment, digital twins function in virtual worlds and are unavailable in the outside world, they are exact replicas of certain physical objects integrated with sensors that constantly update their virtual counterparts in real- time with accurate, and highly valuable information. Organizations utilize digital twins to plan, design, develop, operate, and explore products across the course of their lives. Since digital twins have access to the most recent information on actual objects, they can be utilized in conjunction with intel- ligent technology like machine learning to generate exact prediction models and anticipate outcomes that are more accurate than most simulations. Data scientists and IT specialists can run simulations on digital twins before actual devices are built and deployed, which are virtual reproductions of pre- built devices. Furthermore, digital twins can employ AI and data analytics to improve performance by utilizing real- time IoT data. A digital twin is an indication of pre- built actual devices that
- 17. 2 n Digital Twin Technology and Applications work along with entities in the digital world. Buildings, factories, and even cities can now have digital twins thanks to technology. Some people have even suggested that processes handled by people might have digital twins, further broadening the idea. A digital twin is an accurate and constantly updated logical real product or procedure that is used to test different scenarios, forecast problems, and identify optimization opportunities. A DT handles distinctive, real- world implementation of a counterpart, receives real- time data from it, and adjusts as necessary to repli- cate the origin throughout its existence, in contrast to conventional computer- aided design and engineering (CAD/ CAE) models [33]. However, the twinning is not a random occurrence. There are many parts to this process, but they all function as one cohesive one. A digital twin is essentially computer software that makes simulations using actual data regarding a physical entity or system as inputs or predictions of how those inputs will impact the actual data or system as outputs. 1.2 History of Digital Twin Technology The concept of digital twin technology was originally introduced with the publica- tion of David Gelernter’s book [37] “Mirror Worlds” in 1991. However, Dr. Michael Grieves, a professor at the University of Michigan, is credited with introducing the concept of digital twin software and using it in production for the first time in 2002. Finally, in 2010, NASA’s John Vickers created the phrase “digital twin.” The fundamental procedure to use a digital doppelganger to analyze a physical object was incorporated earlier. In fact, NASA was the first to utilize digital twin tech- nology for space exploration missions during the period of the 1960s. Because of this, NASA’s traveling spacecraft was exactly invoked with replicas of its object in an earthbound version. The effect was hugely inherited by flight crews with NASA personnel observing for research and simulation purposes. The idea of a digital twin first came about at NASA, when full- scale replicas of early spacecraft were used to diagnose and mirror issues in orbit. Eventually, fully digital simulations took their place. After Gartner suggested “digital twins” as one of the major technologies on the highest utilized lists for 2017, the predictions were geared up with the specific nature of dynamic software models for physical models. Within 3 to 5 years, the predictions came true and billions of things happened through the use of digital twins. With an anticipated 21 billion sensor connections and important devices, “digital twins” were identified by Gartner as a top trend for 2020. 1.3 Digital Twin System Architecture A digital twin majorly consists of hardware and software components connected with network devices [15]. This system contains data handling concepts with middleware
- 18. Digital Twin Past, Present, and Future n 3 for data management in between. Figure 1.1 shows the system architecture for a digital twin system. Hardware components: the major components include exchange of information between assets and software integration through Internet of Things (IoT) sensors [11]. The basic technology behind DTs that use actuators to con vert digital impulses into hardware- based powered motions. The hardware component also includes network devices, such as edge servers, routers, and IoT gateways, among others. Data management middleware: its core component is a centralized repository that aggregates data from many sources. In an ideal scenario, the middle- ware platform would also manage connectivity, data integration, processing, quality assurance, data visualization, data modeling, and governance, as well as other related responsibilities. Such systems include common IoT platforms and industrial (IIoT) platforms, which usually feature pre- built tools for digital twinning. Software components: because it translates simple observations into rele- vant business information, the analytics engine is a critical component of digital twinning. It frequently draws power from machine learning models. Dashboards for real- time monitoring, modeling design tools, and simula- tion software are all important pieces of the DT puzzle. 1.4 Digital Thread: A Bridge Between Physical and Virtual Worlds In a closed loop known as a “digital thread,” physical systems and their virtual counterparts can be linked as soon as you have all the required components [16]. Within it, the following iterative procedures are performed (see Figure 1.2). Figure 1.1 System architecture for a digital twin system.
- 19. 4 n Digital Twin Technology and Applications 1. A physical object’s environment and environment at large are both sources of data that are transferred to the central warehouse. 2. The information within data is produced for updating the DT after evaluation. 3. The digital twin uses new data to assess and decide what would occur if the environment changed, bottlenecks were found, and the object’s operation was replicated in real- time. At this point, algorithms can be used to alter product designs, spot dangerous trends, and prevent costly downtimes. 4. The control panel displays and visualizes analytic perceptions. 5. Participants make decisions based on actionable data. 6. Accordingly, the specifications, practices, or upkeep programs of a physical thing are altered. The procedure is then iterated using the updated information. The complexity of the physical world is distilled down to its core components via digital twins. The technology is embraced by many industries as a result. Digital twin examples The exponential rise of digital twin technologies in the near future is projected to be significantly impacted by the development of the IoT, AI, extended reality (ER), and cloud computing [26]. Nevertheless, it has already gained popularity across a wide range of industries, where it is used for anything from production to maintenance and product creation. Here are a few instances of how the digital twins are put to use on a daily basis in the real world. Manufacturing: The complex manufacturing sector includes a significant amount of the physical production of commodities using both manual and automated labor, raw material procurement and transportation across global supply Figure 1.2 Steps within a digital thread.
- 20. Digital Twin Past, Present, and Future n 5 networks, and product research and development (RD). Manufacturing is a suitable industry for the introduction of digital twins because to its complexity, which can assist companies in boosting efficiency and reducing costs at practically every stage of the production process [14]. In the early stages of designing new automobile parts, engineers at an automotive com- pany might, for instance, model and test prototypes using digital twins. They may then simulate prototypes in different simulations, iterating the design until they reach the final result. Analysts may utilize, before actual production starts, digital twins to simulate and subsequently enhance the supply chain and manufacturing process required to generate the finished product [29]. Healthcare: In just a few decades, data- driven technology has fundamentally changed the healthcare sector. Digital twinning can model treatment plans, enable the creation of cutting- edge medical equipment, and give individualized care for specific patients whether it is utilized in biomedical engineering, healthcare analytics, or healthcare management [34]. However, monitoring, managing, and improving physical healthcare facilities, such as hospitals, may be the most widespread application of digital twins in healthcare [38]. Healthcare providers can utilize digital twins to simulate the daily activities of their staff members and the availability of vital resources, such as hospital beds or ventilators, to improve patient care and their overall organizational effectiveness. 1.5 Types of Digital Twin ■ Stand- alone digital twins: these are digital twins of specific goods or pieces of equipment. ■ They can aid in keeping track of and improving the effectiveness of particular assets, people, and other physical resources. ■ Duplicated digital twins: this aids in monitoring and optimizing the use of several related discrete digital twins, such as virtual representations of complex multipart systems like vehicles, machinery, or structures. ■ Enhanced digital twins: these are virtual representations of large- scale, complicated entities (e.g., an entire organization or a city). They are constructed from digital twins of the parts that make them up. They aid in analyzing and improving higher- order performance. 1.5.1 Standalone Digital Twins A standalone digital twin will have enough information to build a model of a system component.
- 21. 6 n Digital Twin Technology and Applications A view of the asset’s health, for instance, can be obtained by tracking sensors connected to a heating, ventilation, and air conditioning (HVAC) system’s digital twin. The standalone digital twin typically contains a small number of data sources. Now, a toolkit that may be built can be used to enhance the twin utilizing accurate data that is now available from a variety of sources [27]. To match sensor output with data from CAD systems, three- dimensional (3D) models, or point clouds are produced by laser scanning, for instance. To monitor important measurements or states from a single asset, such as HVAC or environmental systems, limited digital twins can be helpful. They can also be used to confirm that important building site components comply with regulations and adhere to the original design. 1.5.2 Duplicated Twin A digital twin’s duplicate version includes all the significant and quantifiable data sources needed to replicate the entire asset. The limited digital twins’ components could be combined to create the duplicate model. This is when the model’s level of detail may prove to be too fine for your purposes. To prevent collecting excessive amounts of data, your aims must be clear. By switching from gauges and dashboards to enhanced, virtual representations of actual assets, it is possible to increase complexity while maximizing the poten- tial of duplicated digital twins. The value and utility of this type of digital twin can be multiplied while the dangers are reduced by modeling and executing the proper digital twin [28]. Duplicate models have an interesting foundation thanks to building information modeling (BIM) database- first models. BIM was created to promote better teamwork in the building sector. Additionally, it offers a plat- form with a single source of truth that enables flexible data viewing. These features would also aid digital twin models in providing the appropriate information to the appropriate individuals at the appropriate time. As changes are made to the phys- ical twin, Artificial intelligence (AI) and software analytics would update the digital twin. Duplicated digital twin computer simulations can aid in averting actual issues. Sensor data can be collected by smart components that are connected to a cloud- based system, allowing for real- time analysis and performance comparisons. 1.5.3 Enhanced Twin Digital twins are capable of going much beyond just one building or one piece of machinery. Scale will determine the digital twin’s destiny. The connected asset’s additional data sources are added to the enhanced digital twin. Correlated envir- onmental data from outside sources as well as information from outside analytics and algorithms would fall under this category. The difficulty of managing and controlling every component of a system increases with its complexity. Because of this, digital twins represent a huge possibility for future, networked cities [35]. The
- 22. Digital Twin Past, Present, and Future n 7 information and analysis required maximizing personnel, planning, and resources will be provided by them. Digital twins can be used to model anything, from lone components to com- plete systems. While every kind of digital twin accomplishes the same basic task— virtually imitating a physical system or object— their goals and application domains are significantly different. The following are the four main categories of digital twins. 1.5.4 Component Twins Digital representations of a particular system or product component, like a gear or screw, are known as component twins. Component twins are typically used to represent integral parts, such as those under specific stress or heat, rather to simply modeling all the various components of a product [39]. Designers and engineers can discover how the parts might be modified to maintain their integrity in fore- seen conditions by digitally modeling the parts and running dynamic simulations on them. 1.5.5 Asset Twins Digital reproductions of an entire product rather than simply its parts are called asset twins, also referred to as product twins [41]. Though theoretically made up of many component twins, asset twins’ main goal is to show how the many components of a real- world product interact with one another. For example, a wind turbine’s asset twin may be used to track performance and spot component breakdown due to normal wear and tear. 1.5.6 System Twins System twins, commonly referred to as unit twins, are computer simulations of actual product systems. System twins represent these several items as components of a bigger system, whereas asset twins simulate real- world products made up of numerous parts [40]. It is possible to enhance the relationships between assets by having a better understanding of how they interact, which will boost productivity and efficiency. 1.5.7 Process Twins Digital representations of interconnected systems are called process twins [42]. For instance, a process twin could simulate the complete factory down to the workers working the machinery on the factory floor, whereas a system twin might simulate a production line.
- 23. 8 n Digital Twin Technology and Applications 1.6 Working Principles—Digital Twin A digital twin is first invented by specialists, frequently data scientists or applied mathematicians. These programmers investigate the physics underlying the physical system or object being imitated, and then use the information they learn to create a mathem- atical model that replicates the original in digital space. The twin is designed to be able to take information from sensors collecting data from a physical counterpart. Because of this, the twin can duplicate the physical object in real- time and offer information into its functionality for inculcating potential issues [13]. The physical counterpart’s prototype may have served as the basis for the twin’s design, in which case the twin can offer input as the product is developed or even act as a prototype before the physical counterpart is constructed. Eniram, a company that develops digital twins of the enormous container ships that transport a large portion of global trade, describes the procedure in some depth in this post. This kind of application for digital twins is quite complex. The amount of data you utilize to create and update a digital twin, though, will decide how well you are imitating a physical object [25]. A digital twin can be as complex or as straightforward as you wish. For instance, this lesson shows how to create a straightforward digital replica of an auto- mobile that computes mileage using only a few input variables. 1.6.1 Digital Twin vs. Simulation Although they are two distinct concepts, the words “simulation” and “digital twin” are frequently used interchangeably. A simulation can be created using a CAD system or other comparable platform and put through its paces, but it might not be a per- fect duplicate of an actual object in the real world. However, data usage by utilizing digital twin through IoT sensors on actual equipment, which allows it to duplicate real- world systems and adapt to those systems’ changing needs [36]. A digital twin gives all elements of the organization insight into how a product or system they are presently using is performing right now, unlike simulations, which are typically used during the planning phase of a product’s lifecycle to predict how a future product would work. 1.6.2 Digital-Twin Use Cases The car and the cargo ship, the digital twin examples we highlighted earlier, give an idea of possible use cases. Before being built physically, items like turbines, railways, offshore oil platforms, and aeroplane engines can be developed and tested digitally [43]. The utilization of these digital twins for maintenance tasks is another poten tial application. For instance, technicians could test a suggested patch for a piece of equipment using a digital twin before actually performing the fix.
- 24. Digital Twin Past, Present, and Future n 9 1.6.3 Technology Involved in Digital Twin Digital twins incorporate a range of technologies, including artificial intelligence and machine learning. Future advancements in 3D laser scanning and IoT sensors will significantly influence the development of digital twins. Processing of a cloud framework is the main focus of the construction of the digital twin model frame- work, scanning technologies, and LiDAR when there is a visual component, such as in the built environment [44]. 1.6.4 IoT Sensors IoT sensors are primarily responsible for making digital twins conceivable [3]. Directly integrating IoT functionality into modules or hardware is expected to sig- nificantly disrupt the market [9]. This will cut the cost of deploying IoT devices and simplify setup and deployment considerably [19]. 1.6.5 3D Laser Scanning Software One of the digital twin technology’s unsung heroes is reality capture. Using vector- based, multi- stage point cloud processing, the visual data for digital twins is created (or stitched). Additional details are available in our point cloud pro- cessing guide. 1.6.6 AI and Machine Learning The only techniques available are artificial intelligence and machine learning [23] to analyze the model of operations represented by the digital twin because of the massive amount of data generated [5– 8]. If digital twins are to fulfil their potential, they must be able to perform analysis in real- time or more quickly, provide a high level of prediction accuracy, and incorporate data from numerous distinct and usu- ally incompatible sources [10]. 1.6.7 5G Connectivity Every use case for a digital twin is supported by connection. 5G is increasingly important. Low latency, high bandwidth, large capacity, excellent reliability, enhanced mobility, and extended battery life are just a few of the features that 5G claims will revolutionize digital twin capabilities. For instance, a single cell on a 4G network may accommodate 5500– 6000 IoT devices [19, 20]. Up to one million devices can be supported by a 5G network [21].
- 25. 10 n Digital Twin Technology and Applications 1.6.8 Cloud Computing Digital twins can be processed and executed using cloud technologies. Microsoft already offers an expanding selection of Azure Digital Twin application to assist in line with cloud deployment [18]. The concept of “device shadow” offered by Amazon Web Services (AWS) is implemented as a division of AWS IoT [22]. 1.6.9 Benefits of Digital Twin Digital twins have as many uses as there are advantages to using them. But some of their more well- known advantages are as follows: ■ By developing, testing, and fine- tuning systems or products in virtual environ- ments before putting them into mass production or launching them, you can cut expenses overall [30]. ■ Improve operational efficiency by modeling systems with the most recent data and testing changes in dynamic simulations before implementing them in the real world [31]. ■ Continually monitor the performance of physical assets and functioning systems, such as structures or aircraft, and identify issues as soon as they arise. ■ By simulating the customer’s journey, you may enhance the experience they have while making a purchase or entering a store. 1.6.10 Advantages of Digital Twin Technology ■ Improved RD Utilizing digital twins generates a lot of information about anticipated per- formance outcomes, supporting more effective product research and develop- ment. Businesses can utilize this data to get insights that will help them make the necessary product adjustments before they start production [17]. ■ Enhanced effectiveness Even after a new version of the product has gone into production, digital twins can help in monitoring and mirroring application deployment with the aim of achieving and targeting peak efficiency for the entire manufacturing pro- cess [32]. ■ Product implementation lifecycle Digital twins can also assist producers in determining how to handle products that have reached the end of their useful lives and require final processing, such as recycling or important further actions [46]. By using digital twins, they can choose which product materials can be gathered.
- 26. Digital Twin Past, Present, and Future n 11 1.6.11 Digital Twin Market and Industries Despite the advantages that digital twins offer, not every business or every product manufactured must use them. Not all items are complex enough to require the con- stant and intense influx of highly processed sensor data that digital twins precisely demand [45]. Additionally, investing a significant amount of money in the creation of a digital twin is not always profitable (remember that a digital twin is an exact replica of a physical thing that has been pre- defined; as such, creating one might be costly). However, there are certain clear benefits to employing digital models for various applications: Physically substantial projects: buildings, bridges, and other complex structures are governed by strict technical standards. Mechanically difficult projects: vehicles, jet turbines, and aircraft. Digital twins can contribute to increased productivity in massive engines and intricate machinery. Power devices: this includes both the transmission and generation of power. Manufacturing initiatives: digital twins are effective at increasing process effi- ciency [24], much like industrial settings with cooperating machine systems. As a result, industries that handle large-scale products or projects benefit the most from using digital twins, such as the following: system engineering; manufacturing; Power utilities; railcar design; automobile manufacturing; aircraft production. 1.6.12 Digital Twin Market: Poised for Growth Although digital twins are already utilized in a variety of industries, the market for them is expanding swiftly, which indicates that demand will continue for a while [47]. In 2020, the digital twin market was expected to be valued USD 3.1 billion. Some industry analysts predict it will develop quickly through at least 2026, reaching an estimated USD 48.2 billion. 1.6.13 Applications Digital twins are utilized frequently and invoked in the following applications: 1.6.14 Power-Generation Equipment Large engines, including jet engines, locomotive engines, and power- generation turbines, benefit greatly from the use of digital twins, particularly when assessing whether routine maintenance is necessary [4, 12].
- 27. 12 n Digital Twin Technology and Applications 1.6.15 Systematic and Structures Digital twins can improve massive physical structures, notably when designing large structures like offshore drilling rigs or tall towers [2]. Furthermore, they are useful for designing the HVAC systems that function inside those structures. 1.6.16 Manufacturing Operations Given that they are designed to simulate a product’s whole lifecycle, digital twins have spread throughout all stages of manufacturing, from product concept to finished product and every step in between [1]. 1.6.17 Medical Services Similar to how items can be profiled, patients seeking medical treatment can be as well. The same type of sensor data that the system generates can be used to track various health markers and generate crucial insights [49]. 1.6.18 Automobile Sector In the automotive business, digital twins are frequently used to increase vehicle per- formance and production efficiency. Automobiles stand in for a number of complex, interrelated systems [48]. 1.6.19 Urban Design Civil engineers that work in the field of urban planning greatly benefit from the use of digital twins, which may show real- time applications that use 3D and four- dimensional (4D) spatial data and also incorporate augmented reality systems into constructed surroundings. 1.7 The Future of Digital Twin There is no denying that the present operational paradigms are drastically changing. A disruptive digital revolution is currently taking place in asset- intensive indus- tries, and this revolution asks for an integrated physical and digital perspective of assets, machinery, facilities, and processes. Digital twins are a key element of that readjustment. The potential of digital twins is essentially limitless because more and more cognitive resources are continuously being allocated to their use. Given that they are always learning new skills, digital twins can keep producing the insights
- 28. Digital Twin Past, Present, and Future n 13 needed to improve products and streamline processes [50– 51]. In this context, on using digital twins to transform asset operations, learn how change will affect your industry. Similar to royal food tasters or stunt doubles for movie stars, digital twins serve the same purpose for complex technologies and processes: they guard priceless assets from harm that may otherwise befall them. Duplicates have entered the virtual world, saving many enterprises time, money, and effort while preserving the health and security of valuable resources. 1.8 Conclusion With the establishment of IoT devices, there is a huge number of distributed levels in local and remote storage processes. There are powerful tools in generating data using data analytics and AI algorithms to process batch and real- time approaches. Digital twin technology and the latest recent machine learning and artificial intelligence tools, are assisting businesses across numerous industries in lowering operational costs, boosting productivity, and changing the way that predictive maintenance is carried out. For product producers, in particular, to attain more productive processes, digital twin technology is vital and has a shorter time to be established in the market. On the other hand, there are digital twins being developed for IoT devices to fully comprehend and describe their structural characteristics and behavior in various settings. Therefore, the range of applications and advantages of digital twins include continually increasing IoT devices. However, digital twin applications can be remotely penetrated. And also, smart hackers cause irreversible damage to the device networks, and damage to IoT applications and systems. With blockchain’s increased stability and maturity, IT professionals are looking into the prospect of connecting it to digital twins to fend off security concerns. These two technologies working together to offer a promising future for both the commercial and IT sectors. By com- bining cutting- edge technologies including machine and deep learning (ML/ DL) algorithms, computer vision (CV), and natural language processing (NLP), digital twins are also regularly updated and improved. Thus, the cool synchronization with blockchain will enable the digital twin industry to grow over the upcoming years. References [1] A. A. Malik, T. Masood and A. Bilberg, “Virtual reality in manufacturing: Immersive and collaborative artificial- reality in design of human- robot workspace”, Int. J. Comput. Integr. Manuf., vol. 33, no. 1, pp. 22– 37, Jan. 2020. [2] A. Bilberg and A. A. Malik, “Digital twin driven human– robot collaborative assembly”, CIRP Ann., vol. 68, pp. 499– 502, 2019. [3] A. Čolaković and M. Hadžiali, “Internet of Things (IoT): A review of enabling tech- nologies challenges and open research issues”, Comput. Netw., vol. 144, pp. 17– 39, Oct. 2018.
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- 32. 17 DOI: 10.1201/9781003469612-2 Chapter 2 Digital Twin Types and Design Pallavi Jain, Sunil Kumar Boran, Bhairvee Singh, and Pankaj Singh 2.1 Introduction Many scholars are now interested in the function of Industry 4.0 and intelligent developing. The Industry 4.0 enabler is the digital twin (DT), which combines the real physical system with a virtual counterpart utilizing prototypical, sensor devices, facts, and software to track and examine data. To predict the upcoming corresponding abstract twin, DT is a model of the arrangement or physical strength that can continuously adjust to operative changes grounded on the information and facts gathered online. It is nondestructive testing, which was introduced by Industry 4.0. NASA’s Apollo program is where the “twin/ twins” manufacturing idea first appeared. NASA was tasked with creating two identical spacecraft for the project. The term “twin” is used to describe the reputation or state of the spacecraft while it is still in service and refers to the spacecraft that is left behind. Before a journey, the twin spacecraft are frequently used for training. To assist the astronauts in space in making the best choice in an emergency, the twins were hired to recreate the mod- eling approach on the surface during the voyage. This model can as closely as possible reflect and take into account the operating environment of the space automobile. It is clear from this vantage point that the twins are obviously a sample or version that faithfully replicates the operational environment in reality. It has two main benefits: (1) the twins of the objects to be taken into account are almost the same in
- 33. 18 n Digital Twin Technology and Applications terms of presentation (the Bezier curves and size of the object), subject matter (the entity’s framework and its macro-and components of the system characteristics), and residence (the object’s character trait and ultimately results), and (2) it enables you to make realistic operations and nations and reflect them, among other things. It is important to stress that the twin is still in good physical condition at this time. This creative prototype significantly improves the “twins” in the Apollo software in three ways: (1) it turns the twin model into a digital one and uses virtual expres- sion to create a simulated item with the same subject matter and essence as the item object in style; (2) it presents the immersive area and establishes a connection in com- parison to the actual area so that information and records can be shared between the two; and (3) it demonstrates the idea of fusing the corporal and simulated creations. The idea and extension might be strengthened to incorporate a wider range of goods, manufacturing facilities, workstations, production lines, and production resources (painting positions, systems, the bodies of workers, substances, etc.). A comparable digital twin model can then be developed in the online world. 2.2 Problem and Motivation Industry 4.0 has become one of the most popular topics in creation engineering in recent years. Industry 4.0 techniques are now underutilized in industrial processes nonetheless. On the one hand, this is predicated due to the inconsistent meaning of Industry 4.0, a problem which recent announcements combat. Nevertheless, recur- ring issues like the lack of standards and uncertainties surrounding the economic benefits while addressing the requirement for frequently significant expenditures point to a clear need for alternative approaches to the implementation of a cyber- physical production system (CPPS). Its primary goals are to provide real- time pro- duction control and to improve transparency in the production system. Production engineering is dominated by the theme of “Industry 4.0,” par- ticularly the applied sciences that are linked to each other in recent automation. The value chain’s digitalization demonstrates its necessity for the industrial future, supporting, for instance, the power of adapting something from various systems that are automated. Vertical integration, or integration inside firms, in businesses, and hence in the manufacturing system as it is created by its center value, must be secured in order to achieve Industry 4.0’s horizontal integration, or integration between companies. Though most future business initiatives will center on issues like Industry 4.0, online real systems, systems that automatically make, etc., the lack of specialized expertise is severely impeding the adoption of digitalization technolo- gies at all levels of experience (Figure 2.1). Thus, professional and academic education is crucial for the adoption and success of Industry 4.0. In order to inform industry users about the advantages and disadvantages of using inter innovations and, consequently, Industry 4.0,
- 34. Digital Twin Types and Design n 19 demonstrators are crucial. The chapter puts forth the idea of a “studying place” to contrast the benefits of a digital twin of the contribute series to the traditional method of mapping the value streams for enhancing transparency and discovering opportunities for improvement actions in workflows. 2.3 Definition and Characteristics Digital twin technology is fast emerging and has gained fame in the current scen- ario. It digitally signifies an actual resource, procedure, or setup that may be used for simulation, analysis, optimization, and monitoring, among other things. It is possible to construct a digital twin for anything, from a single machine to a whole city, and use it to simulate a variety of physical systems, from power grids to indus- trial processes. 2.4 Definition of Digital Twin Technology A digital twin is a signifier of an actual item, process, or setup in technology. It is a computer- generated presentation of the factual thing, which may be applied to model, evaluate, improve, and track its work. Although the idea of digital twins has been around for a while, new developments in sensors, analytics, and machine learning have made it possible to create more advanced and precise digital twins. 2.4.1 Features of Digital Twin Technology Features of a digital twin are demonstrated in Figure 2.2. Figure 2.1 Industry 4.0’s challenges and opportunities.
- 35. Exploring the Variety of Random Documents with Different Content
- 36. facerent iniquitatem. e N O V A. rapinam : 47. Et lapidentur lapidibus populorum , confodiantur gladiis eorum : lios filias earum interficient , domos earum igne fuccendent. VERSIO ANTIQ 48. Et auferam impietatem de terra, difcent Q U A. omnes mulieres ne faciant fecundüm i impietatem earum. 49. Et dabuntimpietatem veftram fuper vos... NoT£E AD VERSIONEM ANTIQUA M. Y. 36. Gr. à, ayacyTeneis (9 annuntialis Ὁ c. ut fupra. Y. 37. Gr. τὰ ὠθυμήμαγα ἀυτῶν ἐμοιχώγ]ο κα τὰ τέχνα εἐυτῶν, οἷ ἐγέννησάν μοι 5 δειήγαγον αὐτοῖς M ἐμ ύρων, Y.40. Grac. Z ἅμα τῷ ἐρχ eau ἀυτὸς., c. ut fup. Y. 42. Grec. Καὶ φωνὴν ἁρμονίας εχρξονῖο E, πρὸς ἀνδρας ἐκ πλήθες av pal ov ἥχοντας ἐκ τῆς ἐρήμε' MÍ. Alex. cum edd. Ald. Compl. οὐωμένες ἐχ τῆς , δες. Y. 44. Sic eft in Grzco, prater hoc, πρὸς Οὐλαν., E, πρὸς ᾽Οολιζαν. Y.48. Grac. Kai ὠποσρέψω, Et avertam, loco Et auJeram ; paulóque poft, ὁ ἐ μὴ ποιήσεσι» [Ὁ non facien, loco ne faciant 5 ultimóque num, plur. χαταὰ τας ἀσεξείας ἀυτὼν. Y.49. Grac. Καὶ διοβήσεται καὶ acc Geim υἱμῶν ἐφ᾽ ἱμὰς, Et dabitur impietas veflra [uper vos. Nonnulla autem fup:a addita funt verba ex Hebr, aut Vulg. que nonnifi leviter differunt ἃ Graco, ur fcilicet nexu aliquo colligarentur variantes lectiones LXX. paffim adhibite ab Hieronymo. E NSPIUDT. XX I'V. VULGATA NOVA. I. T faum eft verbum Domini ad me , in anno nono, in meníe decimo , decima die menfis, dicens : 2. Fili hominis fcribe tibi nomen diei hujus, in qua confirmatus eft rex Babylonis adversum Jerutalem hodie. 3. Et dices per proverbium ad domum irriVERSIO ANTIQU A. T fadus eft fermo Domini ad me , in anno nono, in menfe decimo, decimá men3 , diens. . Fili hominis fcribe tibi diem ab hac die, qua abito: eft rex Babylonis fuper Jerufalem ab hodierna die. ;. Et dic ad domum exafperantem parabolam, / Nor£ AD VERSIONEM ANTIQUA M. Υ.1τ. Ita Grecé, ad verbum, X.2, Eadem exítant Grecé, pofito uno ei, 7z , ante diem. Y. 3. Itidem Gracé, prater vocem Dess , que abeft ; Hieron. ubi fup. col, 059. d. e. Ibid, ER in Exech. 24. «οἱ, 961. ex Lxx.
- 37. Hieron, nbi fup. Jb;. 882. * £, e, fervor. Ijia. 864. f. 799 VERSIO ANTIQUA. dices ad eos : Hzc dicit Dominus Deus: Pone lebetem, infunde fuper eum aquam. 4. Et mitte in eum divifiones , omnem incifuram bonam, crus humerum 9 carnibus feparatis ab ofüibus, ἢ «. de eleis pecoribus affumpta; incende offa fub eis : ferbuit, funt cota offa ejus in medio illius. 6. Propterea hzc dicit Adonai Dominus : O civitas fanguinum , lebes , in quo eft rubigo in eo, rubigo non eft egrefla ex eo : per partes fuas protulit, non cecidit füper eam fors. 7. Quia fanguis ejus in medio illius e(t , fuper levillimam petram pofui illum : non effudi illum fuper terram ut operiretur terra. : 9. Ut afcenderet furor in ultionem vindidlz : dedi fanguinem ejus fuper limpiditlimam petram ut non operiretur. — . g. Propterea hzc dicit Adonai Dominus : Vz civitas fanguinum , ego magnificabo torrem. το. Et multiplicabo ligna , ὅς füccendam ignem, ut tabefcant carnes, imminuatur jus, offa concrementur, 11. fet fuper carbones fuos : incenfa eft ut exuratur, frigatur 2s ejus: concremetur in medio illius immunditia ejus, deficiat rubigo ejus : 12. humiliabitur rubigo, non exiet de ca multa rubigo ejus : confandetur rubigo illius. 15. Immunditia tua. * zemma : pro eo quód Contaminata es tu , non esemundata ab immunditia tua : quid erit fi non fueris emundata ultra , donec impleam furorem meum in te? 14. Ego Dominus locutus fum : Et veniet, faciam : non differam , nec miferebor , nec deprecabilis ero : fecundüm vias tuas, fecundum adinventiones tuas judicabo te, dicit Adonai Dominus. Propterea ego judicabo te juxta fanguinem tuum, juxta cogitationes tuas judicabo te, immunda atque famofa, nimia ad irritandum. 15. Et fadus eft íermo Domini ad me, dicens : 16. Fili hominis, ecce ego auferam à te defiNorxsE AD VERSIONEKM EZECHIEL. Cap. XXIV. VULGATA NOVA. tatricem parabolam , loquéris ad eos : Hxc dicic Dominus Deus : Pone ollam ; pone, inquam , mitte in eam aquam. 4. Congere frufta ejus in eam, omnem partem bonam , femur armum, elea offibus plena. ;. Pinguiffimum pecus affume , compone quoque ftrues offium fub ea : efferbuit coio ejus, difcoa funt offa illius in medio ejus. 6. Propterea hzc dicit Dominus Deus: Vae civitati fanguinum , olla ,
- 38. cujus rubigo inea eft, ὃς rubigo ejus non exivit de ea: per partes per partes fuas ejice eam, non cecidit fuper eam fors. 7. Sanguis enim ejus in medio ejus eft, fuper limpidiffimam petram effudit illum : non effudit illum fuper terram ut poffit operiri pulvere. 8. Ut faperinducerem indignationem meam , vindictà ulcifcerer : dedi fanguinem ejus fuper petram limpidiffimam ne operiretur, 9. Propterea hec dicit Dominus Deus : Vc civitati fanguinum , cujus ego grandem faciam pyram. το, Congere offa, quz igne fuccendam : confumentur carnes, coquetur univerfa compofitio, offa tabefcent. 11, Pone quoque eam fuper prunas vacuam , ut incalefcat , liquefiat zes ejus : confletur in medio ejus inquinamentum ejus, confumatur rubigo ejus : i2, multo labore fudatum eft, non exivit de ea nimia rubigo ejus, neque per ignem, 13. Immunditia tua. exfecrabilis : quia mundare te volui, non es mundata à fordibus tuis : fed nec mundaberis prius , donec quiefcere faciam indignationem meam in te. 14. Ego Dominus locutus fum : Veniet , faciam : non tranfeam, nec parcam , nec placabor : juxta vias tuas, juxta adinventiones tuas judicabo te , dicit Dominus, τς. Et faum eft verbum Domini ad me, dicens : τό. Fili hominis, ecce ego tollo à te defideANTIQUA M. at in Mf. Alex. ac ed. Compl. eft 'Adwrar Kéei 5 in Ald. Κύριος Κύριος. YY.4. ς. Concinit Grec. ad verbum. Y.6. Vox Ádonai abeft à Grzco ; cet. ipfi confonant ; quin in Mf, Alex. ac edd. Ald. Compl. eft Ad'evet Κύριος. Y.7. Fadem leguntur Grzcé , nifi hoc ult. excipias , τῷ καλύψαι ἐπ᾽ ἀυτὸ γῆν. loco wt operiretur terra ; Mf. Alex. aret przp. ei 5 ficut ed. Ald. Y. ὃ. Grac. hab. λεωπετρίαν., levem petram , loco limpidifíimam ; cxt. fatis quadrant. Y.9. A Graxco Vatic. abeft vox Adona:, ficut τὸ Κα civitas fanguinum ; cxt. fimilia. Sed in Mf. Alex. ac edd. Ald. Compl. eft 'Ad'eyz! Kreis 5 deinde , Οὐαὶ πόλις ( Αἰεχ. πόλεις) τῶν αἱμάτων, κάγω , c. loco veró torrem , edit. nov. Hieron. fert terrorem , fed. manifefto mendo; Grecé enim conftanter , διαλόν ; fola Compl. hab. χαόν. Ambrof. in Pf. 38. col. 856. c. fed ego magnum faciam zétsonem., y. 10. Sic hab. Grac. preter ult. c9 offa concrementur , uibus caret : ed. tamen Compl. addit , £, τὰ ὀσὰ ( υν7θιἐὐσοναι. Ald. ((υμφρυγύήσον)αι , al. Cuugpuys. Ambrof. in Pí. 38. col. 856. c. Et multzplicabo ligna, «9 [uccendam ignem , wt liquefiat. caro , 9 imminuatur jus abfque feqq.
- 39. Y.1r. Grac. Vatic. X, σὴ ἐπὶ τὸς ἀγθραχας. ὅπως πρφύκαυθῆ , X Θερμανθῇ δ χαλκὸς ἀυτῆς X, τακῇ ἐν μέσῳ ἀκαθαροίας ἀυτῆς » X, ἐκλίπη ὁ ἰὸς ἀυτῆς 9 flet fuper carbones , t exuratur , 9 concalefiat es ejus : €9 tabefcat :m medio immunditia fe , τὸ deficiat rubigo ejus. Edd. veró Ald. ὅς ompl. hab. καὶ 53 ἐπὶ τὸς ἄνθρακας ἀυτῆς' ἐξηψήθη» ὅπως. δες, ut fup. Mf. Alex. ὠυτῆς ἐξήφθη . ὅπως ἐχκαυθῇ . ὅπως ur φρυγῇ ὁ χαλκὸς ἀυτὴς καὶ vex ἐν μέσω ἀυτῆς καὶ ἀκαθαρσία CUTMG 5 x εχλι 0 ἰὸς αὑτῆς. y. 12. Prima pars abeft ἃ Gr. In edit. tamen Compl. eft, X, ταπεινωθήσεαι ὁ ἰὸς ἀυτῆς reliqua ut in Lar. fup. Y. 13. Eadem leguntur Graecé, prater feqq. que defunt , videlicet, Lpsmtunditia tta zemma 5 paulóque pott E €9 noz es emundata ab. immunditia tua ; ulámóque τὸ 25 10. Qux autem. hic defiderantur in Gr. Vatic. exftant in Mf. Alex. ac editt. Ald. Compl, ubi fic : Ἔν τῇ exaθαρσίᾳ (Cw ζέμα ( Alex. ζέμμα ) fubinde, καὶ ἐχ ἐκαθαρίδϑης ἀπὸ ἀκαθαρσίας (^ extremóque , ἐν (οἱ. Vide Not. feq. Y. 14. Α Gr. Vatic. abeft τὸ zec deprecabilis ero 5 fed in edit. Compl. eft, καὶ g μὴ παρακληθῶ fubinde in Vatic. al. ὠθυμύήμαγα. cogitationes , loco adimventiones ; inf, αἵμαγά (ὁ. fanguimes tuos , loco fanguinem tuum , abíque fup. voce 4denai ; que tamen habetur in edd. Ald. δὲ Compl. necnon in Mf. Alex. cet. congruunt ad verbum, Horum autem pleraque ( YY. 12. 13. c. ) inquit Hieron, ibid. de Thbeodotione addita funt ; (9 verbum Hebraicum zemma , pro quo nos , inquit , exfecrabilem immunditiam interprezati fumus : illudque ab eis ( LXX.) additum eft , quod in Hebraico nom babettr , 5 obelo prenotandum eft , Propterea ego judicabo te juxta fang. δες, quz fup. Y. 15. Sic eft in Greco. Y.16. ha Grecé , exceptis his, (48 ἐγὼ λαμβάνω ἐκ (ΟΣ τὰ ἐαιδυμύμαα y ecce ego artfero à te defideria : hzc etiam defunt in fine , zec venient lacryma tibi ; que tamen fequuntur in Compl. Hieron. fcribit fup. zz acze, /fve, à praparatione; Íed inf. hab. zz plaga, free ut LXX. verterunt , in Nah. 3. 1. Hab. 2. 12.
- 40. DEZEGILPBEL. Cep. XXV. VULGATA NOVA. rabile oculorum tuorum in plaga : non planges , neque plorabis, neque fluent lacryma tuz. 17. Ingemifce tacens, mortuorum luctum non facies : corona tua circumligata fit tibi, calceamenta tua erunt in pedibus tuis, nec amictu ora velabis, nec cibos lugentium comedes. 18. Locutus fum ergo ad populum mané , mnortua e(t uxor mea vefperé : fecique mané ficut praeceperat mihi. 5 *19. Et dixit ad me populus : Quare non indicas nobis , quid ifta fignificent , quz tu facis? 20. Etdixi ad eos: Sermo Domini fatus eft ad me, dicens : χα. Loquere domui Ifrael : Hzec. dicit Dominus Deus : Ecce ego polluam fanctuarium meum, fuperbiam imperii veftri, defiderabile oculorum veftrorum , fuper quo pavet anima veftra : fli vetri, filiz veftra, quas reliquiftis , gladio cadent. 22. Et facietis ficut feci : Ora amictu non velabitis, cibos lugentium non comedetis. 23. Coronas habebitis in capitibus veftris , ὃς calceamenta in pedibus : non plangetis neque flebitis, fed tabefcetis in iniquitatibus veftris , unufquifque gemet ad fratrem fuum. z4. Eritque Ezechiel vobis in portentum : juxta omnia, qua fecit , facietis cüm venerit iftud : fcietis quia ego Dominus Deus. 25. Et tu fili hominis, ecce in die, qua tollam ab eis fortitudinem eorum , gaudium dignitatis , defiderium oculorum eorum, fuper quo requiefcunt animz eorum, filios filias eorum : 26. In die illa cüm venerit fugiens ad te, ut annuntiet tibi : 27. In die , inquam , illa aperietur os tuum cum eo qui fugit : loquéris, non filebis ultra : erifque eis in portentum , fcietis quia ego Dominus. Nor£ ἀν VERSIONEM ANTIQUA M. praeparatione ; Gr. conftanter , ἐν παρατάξᾳ. Y. 17. In Gr. Vatic. eft , πένθος £6» luilus eris, loco ludus eft 5 at in ed. Ald. πένθος, ἐσίν , ut fup. tum in Vatic. al. οὐκ ἔσαι τὸ τρίχωμά (Ce, ad litt. gon erit capilliium tuum 5. cxt. ut fupra. Hieron, quoque inf. ait : juxta LXX. coronam capillorzim intelligamus. ca[ariem. Y. 12. Itidem Grace, preter hoc, Q9 sorta eft uxor mea , quod deeft ; at in Mf. Alex. ac edd. Ald. Compl. d;iüzyer w γυνή uv , deinde , ἑσπέρας xj, c. ín Vatic. etiam al. ipfo initio habetur Καὶ» fequitur : Z ut fupra : ante Jocutus. fam. YY.19.20. Totidem verba leguntur Grace. Y.21. A Greco conftanter abeft vox. Adozai ; inf. autem pro quib , eft ὑπὲρ ὧν.
- 41. fuper quibus; poniturque X ,ante vocem filz; ; cet. ut in textu. In Mf. Alex. pro Adonai Dominus , eft Κύριος Κύριος ὁ Θεός, Y.22. Itidem Grzcé , pofito uno ἀπὸ. ante ore, 799 VERSIO ANTIQUA. derabilia oculorum tuorum in przparatione : non planges, neque flebis, nec venient lacrymae tibi. 17. Gemitus fanguinis, renum luctus eft : erunt crines tui colligati fuper te, calceamenta tua in pedibus tuis, nec confolaberis in labiis eorum, panem hominum non comedes. 18. Locutus füm ad populum mane ficut przceperat mihi, mortua eft uxor mea vefperi : fecique mané ficut preceptum eít mibi. 19. kt dixit ad me populus : Non annuntias nobis, quid funt hzc, qua tu facis? 20. Et dixi ad eos : Sermo Domini fadus cft ad me, dicens : 21. Dic ad domum Iírael : Hzc dicit Adonai Dominus : Ecce ego contaminabo fanca mea, fuperbiam fortitudinis veítrz , defiderabilia oculorum veftrorum , quibus parcunt animz veftrz : filii veftri, filie veftrz, quos reliquiftis , in gladio cadent. 22. Et facietis ficut feci : Ore eorum non confolabimini, panem virorum non comedetis. 23. Et come veftra fuper capita veftra , calceamenta veftra in pedibus veftris : non plangeüs nec flebitis, contumemini in iniquitatibus veftris, confolabitur unufquifque fratrem fuum. 24. Et erit Jezekiel vobis in portentum : fecundum omnia, quz fecit, facietis : cumque venerint hec, cognoícetis quoniam ego Adonai Dominus. 25. Et tu fili hominis , nonne in die , quando abítulero fortitudinem ab eis , elationem gioriationis eorum , defiderabilia oculorum eorum , ὅς elationem anima eorum, filios filias eorum; 26. In die illa veniet qui falvus factus fuerit ad te, ut annuntiet in auribus tuis? 27. ἴῃ dieilla aperietur os tuum ad eum qui fugerit : loquéris , nequaquam ultra reticebis : eriseis in portentum , cognofcent quoniam ego Dominus. Y.23. Vix melius de Graco, nifi exciplatur verbum fingul. comfolabittr , pro quo. plur. zapaxeoéac]t , confola« bimisi. Y. 24. Grece, pro fecit , habetur ἐποίησα, feci ; preponiturque z , verbo cogzofcetis , deleto fup. que , antc venerint, cum voce Adozaz; ct. ut in textu. In ed, veró Compl. eft ἐποίησε , ut fup. abfque z , ante cogaofcetis 5; ὃς in Ald. Af'ova? Κύριος. Y.25. Similiter in Greco , nifi quód additur ἀυτῶν » poft fizos ; loco defiderabilia , hab. ἐπιθυμύήμαγα,, defideria. Υ. 26. Ita rurfum Graecé, addito uno annuntiet ; deleto veró tuis , 1n fine. Y. 27. lta
- 42. conftanter Gracé, nifi excipiatur verbum ἀνασωζόμδιον., quà. evaferit , loco qui fugerit ; deeft etiam feq. t9 ; at in Mf. Alex. eft . καὶ λαλήσεις 5 ficut in edd. Ald, Compl. (οἱ, tibi, verbo οὐ n. Χ Ἀν: VULGATA NOVA. 1. T faus eft fermo Domini ad me , dicens: 2. Fili hominis pone faciem tuam contra filios Ammon, prophetabis de eis. ;. Et dices filis Ammon : Audite verbum Domini Dei : Hzc dicit Dominus Deus :. Pro eo quód dixifti : Euge , euge fuper fanuarium meum, quia pollutum eft ; fuper terram Ifrael , quoniam detolata eft; fuper domum Juda , quoniam duci funt in captivitatem : VERSIÓ ANTIQUA. M T factus e(t fermo Domini ad me, dicens: Hz», i5 Fo 4 2. Fili hominis obfirma faciem tuam fü- 13. c2. 775. per filios Ammon..... j« Quiagavifi e(tis fuper fanduarium meum... 75- cof. ΝΟΤΕ AD VERSIONEM ANTIQUA M. YY.1. 2. Similiter in Greco, Y. 3. Sic apud Hieron, pro his de Vulg. Pre eo qud dixifli : Emge , euge [uper fantluarium meum. Grac, hod, ( I , 3 ᾿ N ru , AW! ὧν ἐπεχάρη]ε ἐπὶ τα ἁγιᾶ us. Hieron, ubi fup. Ilzd, δός. 8, ldem zm o o Ezech, 67. ex
- 43. Hieron, ubi fup. Ibid. 970. Ilid. 871. f. Iid, 872. Ibid, 873. b. 900 VERSIO ANTIQU A. 4. Idcirco ego tradam te filiis Cedem..... ipfi bibent ubertatem tuam. s. Daboque civitatem Ammon in paícua camelorum..... 6..... infonuifti pede , ὅς infultafti ex animo tuo... €. Hzc dicit Adonai Dominus : Pro eo quód dixit Moab : Ecce ficut omnes gentes , domus Juda : 9. Idcirco ecce ego diffolvam humerum Moab de civitatibus promontoriorum ejus , electam terram, domum Beth lafimuth fuper fontem urbis maritimz, 1o. filios Orientis fuper filios Ammon , dedi eiin hereditatem : ut non fit memoria filiorum Ammon in gentibus. ir. Et in. Moab faciam ultiones : cognofcent quoniam ego Dominus. r2. Haec dicit Adonai Dominus : Pro eo quód fecit Idumza ut ulcifcerentur ultionem de domo Juda, memoriam retinuerunt mali, ulti funt ultione; 15. Propterea hzc dicit Adonai Dominus : Extendam manum meam fuper Idumzam , interficiam de ea hominem pecus, € ponam eam defertam : de Theman fugientes, gladio cadent. 14. Et dabo ultionem meam fuper Idumzam in manu populi mei líraél: facient in Idumza juxta iram meam , furorem meum : cognofcent ultionem meam, dicit Adonai Dominus. 15. Propterea hac dicit Adonai Dominus : Pro eo quód fecerunt. Alienizenz ultionem , fufcitaverunt vindictam , infultantes ex animo, ut delerent uíque in eternum : τό. propterea hzc dicit Adonai Dominus : Ecce ego extendam manum meam fuper Alienigenas, difperdam Cretenfes, perdam reliquias littoris maritimz Σ΄ ! 17. faciam in eis ultiones magnas in vindicta furoris : cognofcent quia ego Adonai Dominus, ciim dedero ultionem meam fuper eos. Nor£ Ap VERSIONEM EZECHIEL..'Cap. XXV. VULGATA NOVA. 4. Idcirco ego tradam te filiis orientalibus τὰ hereditatem , ὃς collocabunt caulas fuas in te , ponent in te tentoria fua : ipfi comedent fruges tuas : ipfi bibent lac tuum. 5. Daboque Rabbath in habitaculum camelorum , filios Ammon in cubile pecorum : fcietis quia ego Dominus. 6. Quia hec dicit Dominus Deus : Pro eo quód plaufifti manu , percuffifli pede, gavifa es ex toto affeu fuper terram Ifrael : 7. Idcirco ecce ego extendam manum meam fuper te, tradam te in direptionem gentium, interfciam te de populis, perdam de terris, conteram
- 44. : fcies quia ego Dominus. 8. Hzc dicit Dominus Deus : Pro eo quód dixerunt Moab Seir : Ecce ficut omnes gentes, domus Juda : 9. Idcirco ecce ego aperiam humerum Moab de civitatibus, de civitatibus, inquam, ejus , ὃς de finibus ejus inclytas terre Bethiefimoth , Beelmeon, Cariathaim , ro. filiis Orientis cum filiis Ammon , dabo eam in hereditatem : ut non fit ultra memoria filiorum Ammon in gentibus. 11. Etin Moab faciam judicia : ὃς fcient quia ego Dominus. 12. Hzc dicit Dominus Deus: Pro eo quód fecit Idumza ultionem ut fe vindicaret de filiis Juda, peccavitque delinquens, vindictam expetivit de eis ; 13. Idcirco hec dicit Dominus Deus : Extendam manum meam fuper Idumaam , auferam de ea hominem jumentum , faciam eam defertam ab Auftro : qui funt in Dedan , gladio cadent. 14. Et dabo ultionem meam fuper Idumzeam per manum populi mei Ifrael : facient in Edom juxta iram meam, furorem meum : fcient vindidam meam, dicit Dominus Deus. 15. Hac dicit Dominus Deus : Pro eo quód fecerunt Palzftini vindictam, ulti fe funt toto animo , interficientes , implentes inimicitias veteres : 16. propterea hzc dicit Dominus Deus : Ecce ego extendam manum meam fuper Palaítinos , interficiam interfetores , perdam reliquias maritimz regionis : 17. faciamque in eis ultiones magnas arguens in furore : ἃς fcient quia ego Dominus , cüm dedero vindictam meam fuper eos. ANTIQUA M. Y.4. Grxc. initio hab. Διατῷτο (dà ἐγὼ παραδίδωμι ὑμᾶς. Idcirco ecce ego trado vos ; reliqua ut in textu. Y. 5. Itidem Grace. Υ. ὅ. Gr. ἐψόφησας τῷ ποδί (e, ἃ ἐπέχαρας ἐκ ψυχὺς Ce. Υ. ὃ. A Gr. Vatic. abeft vox Adozai ; fed in Mf. Alex. ponitur de more, ficut in edd. Ald. Compl. fubinde in Vatic. poft ecce , ita fubjicitur , gx, ὃν τρόπον 5 fed ab editt, Ald. Compl. abeft ἐχ , ut à Mf. Alex. denique in Vatic. eft οἶκος Ἰσραὴλ καὶ 'Ifd'a 5; fed in Compl. deeft Ἰσραὺλ x5 cxt. conveniunt. Apud Hieron. fup. nomini Moab , hoc additur , (5 Ser , premií(fo tamen afteriíco ; nec malé, nam Hieron. infra ait : Hec quod os interpretatz famis , Seir , zn LXX. non babetur , fed de Theodotzonis editione additum eft. Y. 9. Gr. initio hab. παραλύω, diffolvo ; al. veró παραλύ“ὦ ; reliqua quadrant, nifi excipias vocabulum Βεθασιμιδθ , al. Beliacipdü. Pro Beth. lefimotb. autem , 9 Beelmeon , «9 Cariatbaim , inquit Hieron. infra , uefczo quid volentes
- 45. LXX. interpretatz fit , domum Beth Iafimuth , citz boc vocabitlum villam defertam /ignifiet ;. Beelmeon quoque ufque bodie in Moab vicus fit maximus , quem illi vevterunt fuper fontem ; t$ Cariathaim , civitatem maritimam, Vide euam inf, col, 871. a. Y. 10. Ita in Greco , excepto uno Kedzu , loco Or£entis ; extremó etiam deeft τὸ zz gentibus ; fed in Mf, Alex, ac ed. Compl. additur ἐν τοῖς ἔθνεσι. Y. 11. Siceft in Greco, preter vocem exd ίχησιν, ultzozem , loco ultzones. Y. 12. Eadem leguntur Grzcé , excepta voce /4dozai , quz deeft; habetur tamen in Mí. Alex. necnon in edd, Ald. Compl. de more. Y. 13. [τὰ Grecé, deleta femper voce 42ozai ; pofitaque conjunct. z,ante extendam. . Y. 14. lta rurfum in Graco , repetita voce xad , juxta » ante furorem meum. Y. 15. Sic habetur Grecé , hoc excepto , ὧν ἐχδιχήσει , in ultione , loco ultionem ; ab ed. veró Ald.abeft 5 fubinde in Vatic. loco zz aternum , eft ἕως évóc , ad «num ; in Ald. veró Compl. in Mf. Alex. ἕως αἰῶνος , ut fup. Y. 16. Grac. hab. ἐχτείνω . extesdo , non extendam 5 loco veró reliquias littoris maritima , lic, τὸς Xa]aAciTES τὸς x«]omÉv|az τὴν παραλίαν , reliquos babitantes. maritiqam; ct. ut in textu, Y. 17. Eadem funt in Greco , prater hoc , i» vindida furoris , quod deeft ; ed. fola Compl. addit, ἐν ἐλεγμοῖς ϑυμῦ. ἔ
- 46. Je. 7. EZECHIEL. Cap. XXVI. 9o1 CAUTE UM VvLGATA NOYA. x. EAT faum eft in undecimo anno, prima menfis, faus eft fermo Domini ad me, dicens : ;. Fili hominis, pro eo quód dixit Tyrus de Jerufalem : Euge confrae funt porte populorum, convería eft ad me : implebor , deferta eft. 3. Propterea hec dicit Dominus Deus: Ecce ego fuper te Tyre, aícendere faciam ad te gentes multas, ficut afcendit mare fluctuans. 4. Et diffipabunt muros Tyri, deftruent turres ejus: radam pulverem ejus de ea , dabo eam in limpidiffimam petram. $- Siccatio fagenarum erit in medio maris , quia ego locutus fum, ait Dominus Deus : erit in direptionem gentibus. 6. Filis quoque ejus, qua funt in agro, gladio interficientur : fcient quia ego Dominus. 7. Quia hzc dicit Dominus Deus: Ecce ego adducam ad Tyrum Nabuchodonofor regem Babylonis ab Aquilone , regem regum, cum equis , curribus , equitibus , ccetu , populoque magno. TUN VITE VERSs10 ANTIQUA. I E T faum eft in undecimo anno , una menHieron.in Exech, fis, faus eft fermo Domini ad me, dicens ; 26. «dl. 874. a. ex 2. Fili hominis, pro eo quód dixit Sor de Jerufalem : Euge confratz funt gentes , converfa eft ad me : quz fuit plena, deferta eft. 3. Propterea hzc dicit Dominus Deus : Ecce ego fuper te Sor..... 4.....ὄ δ ventilabo pulverem ejus de ea, dabo eam 1n nitidiffimam petram. , 6. Filiz quoque ejus , quz funt in campo, gladio interficientur : fcient quia ego Dominus, 7. Quia hzc dicit Dominus : Ecce ego adducam ad te Sor, Nabuchodonofor regem Babylonis ab Aquilone... VurGATA NOVA. 8. Filias tuas, qua funt in agro, gladio interficiet: circumdabit te munitionibus, comportabit ag elevabit contra te clypeum. gerem in gyro : VULGATA NOVA. ro. Inundatione equorum ejus operiet te pulvis eorum : à fonitu equitum, rotarum , curruum , movebuntur muri tui, càm ingreffus fuerit portas tuas quafi per introitum urbis diffipata. rr. Ungulisequorum fuorum conculcabit omnes plateas tuas : populum tuum gladio cedet , δὲ Íílatue tuz nobiles in terram corruent. 12. Vaftabunt opes tuas, diripient negotiationes tuas: ὅς deílruent muros tuos, domos tuas przclaras fubvertent : lapides tuos, ὃς ligna tua, pulverem tuum in medio aquarum 9. Et vineas , arietes temperabit in muros tuos, turres
- 47. tuas deflruet in armatura fua, 9.«. Pide Not, VERSIO ANTIQU A. 10... quafi ingrediens urbem de campo. 11... fübftantiam fortitudinis tux in tetra deducet. 12. Vaftabit opes tuas, fpoliabit fübftantiam tuam : deftruet muros tuos, domos tuas defiderabiles vertet : lapides tuos, ligna tua, pulverem tuum in medio maris injiciet. ponent. 13. Et quiefcere faciam multitudinem canticorum tuorum , fonitus cithararum tuarum non audietur ampliüs. 14. Et dabo te inlimpidiffimam petram, ficcatio fagenarum eris, nec zdilcaberis ultra : quia ego locutus fum, ait Dominus Deus. 15. Hzc dicit Dominus Deus Tyro : Nunquid non à fonitu ruine tuz, gemitu interfeorum tuorum , cüm occiíi fuerint in medio tui, commovebuntur infule ? 16, Et deícendent de fedibus fuis omnes prin15, Et deftruam multitudinem muficorum tuorum, vox organorum tuorum non audietur amplius. 14. Et dabo te in nitidiffimam petram..... 15. Quia hzc dicit Dominus Deus Sor : Nonne à voce ruinz tuz, cüm ingemuerint vulnerati tui, cum evaginatus fuerit gladius in medio tui , commovebuntur infulz? 16. Et defcendent de fedibus fuis omnes prinNor£ AD VERsIONEM ANTIQUA M. X. I. Sic euam in Graco. y. 2. Grgc. hab. ἐπὶ Ἱερεσαλιὴμ » fuper Jerttalem ; deinde, Εὖγε (υνερίθη, ἀπόλωλε τὰ ἔθνη, ἐπεσράφη πρός με. c. ut fupra. Y. 3. Sic iterum Grece, deleta voce Deus; at in Mf. Alex. necnon in edd. Ald, Compl. pro more , ᾿Αϑωναΐ Kvexus. Y. 4. Confonat Grac. nifi quód hab. »ewze7play , levem petram , loco. nitidiffimam. Y.6. Gr, Καὶ ai ϑυγαγέρες ἀντῆς ἐν πεδίω (Mf. Alex. αἱ ἐν τῷ παιδίῳ) μαχαίρᾳ ἀναιρεθήσονται , c. ut fupra. Y.7. Grec. Ἰδὸ ἐγὼ ἐπάγω. adduco j cet. ut fup. Y.9. Hieron. in hunc loc. 875. a. ad hec Vulg. (9 uineas , 9 arietes , addit , ffve lanceas , € Gr. τὰς λόγχας. Y. το. Sic eft in Graco pro ult, his de Vulg. quaft per introitum urbis diffpata. Y. 11. lta Graece, horum loco de Vulg. c9 flatzua tue , c. Y.12. Grzc. in principio hab. Kal προνομεύσει τὴν dvdom. 11. γαμίν e y ἃ σκυλεύτσει , ὅς, Ft depradabitur potentiam tuam , 5 [poliabit ; reliqua ut. in Lat. fup. addito uno (ἕξ. ad vocem maris. Y.13. Gr. initio habet, Καὶ xaaxvc4, Et ceff'are faciet , pro Er deffruam ; paulóque poft , ψαλγηρίων., p/alteriorum ; loco ergamorum 5 cat. ut fupra. Υ. 14. Grec. conftanter , λεωπετρίαν, abíque prep. 27. Hieron. addit : Utramque Editionem ex more conjunxi ; Q9 in quibus difirepant , ex
- 48. latere copulavi , brevitati voluminum providens, Y. 15. Indem Grzcé, nifi quód geminatur Ki/e;;; Ki» Θίος , loco Dominus Deus; deeftque uz, poft vulnerati atin Compl. Mf. Alex. eft τεαυμαῆας (7v. Tichon. reg. 4. lta legit ex Mf. B. M. Rem. n. 35. Hac dicit Dominus ad Ser : Nonne à voce ( edit. p. 58. h. à die) ruine tua , in gemitu vulneraterum , dum interficiuntur gladio im medio ti , commovebuntur. infula ? Y. 16. Grece variant nonnulla : nempe poft vocem przzpe; , hoc additur , ex τῶν eror s ex. gentibus 5 fubinde loco liiii XX, lbid. 975. 0. Ili4, 877. b,
- 49. Hieron, ubi fup. ILid. 878. c. Ibid. «9 879. a. Hieron, in Ezech, 27. col, 879. c. Iti. 980. ex Lxx. Ibid.881. 802 VERSIO ANTIQUSA. cipes maris : auferent coronas fuas, veftimentis fuis variis nudabuntur , furore infanient : in terra fedebunt , formidabunt perditionem fuam , gement fuper te. i 17. Et affument fuper te lamentum , dicent tibi : Quomodo perifti, diffipata es in mari, urbs laudata, quz fuifti fortisin mari, ipfa , habitatores ejus, quz dedit timorem fuum omnibus habitatoribus [15 18. Et formidabunt infüle in die ruinz tuz : turbabuntur infülz in mari in exitu tuo. 20. Etdetraxero te ad eos qui defcendunt in foveam ad populum fempiternum , collocavero te in profundo terrarum ficut folitudines veteres , cum his qui defcendunt in foveam , ut non habiteris , non refurgas in terra viventium : 21. perditionem dabo te , ultra non erisin EZECHIEL. Cap. XXVII. VurLGATA NOVA. cipes maris : auferent exuvias fuas , veftimenta fua varia abjicient, induentur ftupore: in terra fedebunt , attoniti fuper repentino cafu tuo admirabuntur. 17. Et affumentes fuper te lamentum , dicent tibi : Quomodo perifti , quz habitas in mari , urbs inclyta, quz fuifti fortis in mari cum habitatoribus tuis, quos formidabant univerfi ? 18. Nunc ftupebunt naves in die pavoris tui : turbabuntur infule in mari, eó quód nullus egrediatur ex te. 19. Quia hzc dicit Dominus Deus : Cüm dedero te urbem defolatam , ficut civitates que non habitantur : adduxero fuper te abyflum , operuerint te aquz multe : 20. Et detraxero te cum his qui defcendunt inlacum ad populum fempiternum, collocavero te in terra noviífima ficut folitudines veteres , cum his qui deducuntur in lacum , ut non habiteris : porro cüm dedero gloriam in terra viventium , 21. in nihilum redigam te, non cris, fempiternum , dicit Dominus Deus. requifita non invenieris ultra in fempiternum ; dicit Dominus Deus, Nor£ AD VERSIONEM ANTIQUA M. coronas fuas , hab. μίτρας οἶπὸ τῶν κεφαλῶν ἀυτῶν , mitras de capitibus fuis 5 mox ita : καὶ τὸν ἱμαγιομὸν τὸν ποιχίλον ἀυτῶν ἐχ-διύσονγαι., ἐχςάσει ἐχοήσογ)αι., Q5 veftimento [ito varie [pelíabuntur, flupore [iupebunt : ied. ab edit. Compl. abeft 2x τῶν ἐθνῶν, ut inf. zzo τῶν χεφαλῶν. Apud Tichon.reg. 4. ita ex Mf. Rem. E: defcendent καὶ edibus fuis ovzues
- 50. priudipes maris : ξδ auferent mitras , (9 veflem variam [uam difpolinbunt fe : in flupore mentis [ltpebunt , cg timebunt in interittt fuo , 69 ingemi[cent (uper te. Edit, Compl. pro zn interit fo , hab. ἀπώλειάν (e, perditionem tuam. Y. 17. À Graco Vatic, abeft verbum perfi ; abfunt pariter ifta , qma fuifli fortis in mari , ipfa, 9 babitatores ejus; pro iu mari vero , fic, £x ϑαλάοσης , de mari ; cxt. concordant ad verbum : quin in Mf, Alex. acin edd, Ald. ὅς Compl. eft, Πῶς ἀπώλῳ , X, κατελύθης 5 tum in Compl. ὧν ϑαλάοση ; fubinde ram in Compl. quàm in Ald. Mf. Alex. ἡτις ἐγενήθη up ἐν Sean toyn, dull, ἃ οἵ καTexzy/es ἐυτὴν» ἡ διξσα, c. ut fupra. Tichon. veró reg. 4. p. $8. h. fic legit: Er accipient fuper te lamentationem , €9 dicent tibi : Quomodo deftrutta eft de mari civitas illa laudabilis , qua dedit timorem [uum omnibus inbabitantibus in ea ὃ Y. 18. Tichon. reg. 4. p. 58. h. hec tantüm refert : Ez timebunt in(ulz ex die (Mf. Rem. zn die ) ruina tua. Ya quoque in Graco Vatic. pretermiffis aliis , quz leguntur fupra : addunt tamen edd. Ald. Compl. cum Mf. Alex. xai ταδαχθήσον)αι νῆσοι cy τῇ Θαλάοση ἀπὸ τὴς ἐξοδίας Cs, Ald. ἐξόδο. Hieronymus inf. dicit LXX. tranftuliffe, in die egreffionis tue. Y.20. Grac. initio habet , Καὶ καγαξιξασω (c, Es defcendere faciam te , pro Er derraxero te 5; infra : z, xa7οικιῶ (Qe εἰς βάθη τὴς γῆς ὡς ἔρημον αἰώνιον..... μηδὲ ἀνα-sno ἐπὶ γὴς ζωῆς. X.21. Sic eftin Greco, excepto ult. Κύριος Κύριος. ($4 Po. T XX W LI. VurLGATA NOVA. T faum eft verbum Domini ad me, dicens : 2. Tuergo filí hominis affume fuper TyVERSIO ANTIQU A. ;3.. negotiationi populorum ab. iníulis multis..... dixifti : Circumdedi mihi ego decorem..... 4... Beelim , filii tui circumdederunt tibi decorem : s. cedrus de Sanir xdificata eft tibi: tenues tabulas cypreílinas de Libano tulerunt ut facerent tibi malos abiegnos. 6. De Dafan fecerunt remos tuos, templa tua : fecerunt tibi ex ebore domos filveílres de infulis Chettiim. Nor£ AD VERSIONEN y. 3. Similiter in Greco , addito uno ug in fine ; pro negotiationi autem , legitur £uaopío , quod forum nundinarium Íonat , feu mercatum. Y.4. Grace ita : ἐν καρδίᾳ Srandoyus τῷ Βεελεὶμ., c. ut in Lat. Ad hocautem Vulg. Figirimi tui, c. Hieron. ait: pro quo nefcio quid volentes , ita LXX. tranflulerunt : Beelim filii tui , c. tum addit : Sermo euim Beelim zn boc loco aptid Hebraos penitus non babetur ,
- 51. fed pro Beelim , fcriptum. eff gebulaich , qtd /rgnificat verminos tuos. Iz eo quoque quod. dixerunt , filii vul, verbi ambiguitate decepti funt , 9. feriptura fimilitudine ; dum pronunciatione diver(a eedem rum lamentum : VuLGATA NOYA. 3. Et dices Tyro, qux habitat in introitu maris, negotiationi populorum ad infulas mukas : Haec dicit Dominus Deus : O Tyre, tu dixifli: Peifei decoris ego fum , 4. in corde maiis fita. Finitimi tui , qui te ediücaverunt, impleverunt decorem tuum : $. abietibusde Sanir exftrnxerurt te cum omnibus tabulatis maris: cedrum de Libano tulerunt ut facerent tibi malum. 6. Quercus de Baían dolaverunt in remos tuos : tranílra tua fecerunt tibi ex ebore Indico, prattoriola de infulis Italiz, ANTIQUA M. littera , co mentariorum , [5 filiorum , bonaich , £5 benaich , leguntuy. Vide fis Nobil. Not. X. 5. Gr. Varic. pro Sanir , fcribit Xeveip, Alex. veró Σανείρ 9 fübindein Vatic. ταινίαι σανίδων κυπαρίοσυ ( Mf. Alex. κυποριοσίνων. Ald. κυπάριοσοι) €x 4€ AiGavg ἐλήφθησαν» c. tenia tabularum cyprefft de Libano [umpte funt cer. ut in Lar. fup. Y. 6. Grzcé fic habetur initio ; ex τῆς ΒασανίτιΠος , de Bafauitide 5 vollitur autem conjunét, (9 , tum ante templa , tum ante fecerant , cum feq. tib? j ct, verba. funt fimi lia.
- 52. EZECHIEL. Cap. XXVII. VULGATA NOVA. 7. Byffüs varia de /Egypto texta elt tibi in velum ut poneretur in malo : hyacinthus purpura de infulis Elifa faa funt operimentum tuum. 8. Habitatores Sidonis Aradii fuerunt remiges tui : fapientes tui , Tyre, faci funt gubernatores tui. 9. Senes Giblii, prudentes ejus , habuerunt nautas ad minillerium varie fupellectilis tuz : omnes naves maris , naute earum, fuerunt in populo negotiationis tuz. το. Perfe , Lydii, Libyes erant in exercitu tuo viri bellatores tui : clypeum , galeam fufpenderunt in te pro ornatu tuo. ri. Filii Aradii cum exercitu tuo erant fuper muros tuos in circuitu : fed Pigmzi , qui erant in turribus tuis , pharetras fuas fufpenderunt in muris tuis per gyrum : ipfi compleverunt pulchritudinem. tuam. 12. Carthaginenfes negotiatores tui, à multitudine cunctarum divitiarum, argento, ferro, ftanno , plumboque, repleverunt nundinas tuas. 13. Gracia, Thubal, Mofoch , ipfi inttitores tui : mancipia, vafa erea advexerunt populo tuo. 14. De domo Thogorma, equos, equites, mulos adduxerunt ad forum tuum. τς. Filii Dedan negotiatores tui : infulze multze negotiatio manus tuz : dentes eburneos , hebeninos commutaverunt in pretio tuo. τό. Syrus negotiator tuus propter mul:itudinem operum tuorum, gemmam , purpuram , Ícutulata, byflum, fericum , chodchod propofuerunt in mercatu tuo. 17. Juda terra Ifrael ipii inftitores tui in frumento primo , balfamum , mel, oleum, refinam propofuerunt in nundinis tuis. 18. Damafcenus negotiator tuus in multitudine operum tuorum , in multitudine diverfarum opum , in vino pingui , in lanis coloris optimi. rg. Dan, Grzcia, Mofel, in nundinis tuis propofuerunt ferrum fabrefaum : ftacte , ὅς calamus in negotiatione tua. 20. Dedan inftitores tui in tapetibus ad fe$03 VreRsS10 ANTIQUA. 7. Byffus cum varietate de Egypto facta eft tibi in ftratum , ut circumdaret tibi gloriam , operiret te hyacintho purpura : de infulis Eliffa fada funt opertoria tua. 8. Principes tui, qui habitabant in Sidone, Aradii fuerunt remiges tui : fapientes tui, Sor, qui erant in te , ifti gubernatores tui. 9. Senes Piblii, fapientes ejus erant in te; ifti confortabant confilium tuum : omnes naves maris, remiges earum, fadi funt tibi in Occidentem Occidentis. peltas galeas
- 53. fufpenderunt in te : ipfi dederunt gloriam tuam. 11. Filii Aradiorum, fortitudo tua fuper muros tuosin circuitu : cuftodesin turribus tuis erant , pharetras fias fufpenderunt fuper propugnacula tua per gyrum : ipfi perfecerunt decorem tuum. 15. Grzcia univerfa , adjacentia ejus , 1pfi negotiatores tui in animabus hominum : vafa enea dederunt mercatum tuum. 14. De domo Thorgama, equos, equites, mulos dederunt nundinas tuas. r5. Filii Rhodiorum negotiatores tui ex infulis multiplicaverunt negotiationem tuam denteselephantinos: his, qui introducebantur , reddebas mercedes tuas : 16. homines, negotiationem tuam à multitudine mercatüs tui in Aphec , ftaem , polymita de Tharfis, ramoth, chodchod dederunt in nundinas tuas. 17. Judas filii Ifrael ifti negotiatores tui in frumenti commercio , unguentis , primum mel, oleum, refinam dederunt in nundinis tuis. 18. Damafcus negotiator tuus in multitudine operum tuorum, ex multitudine omnis fortitudinis tuz, vinum ex Chelbon, lanas de Mileto. 19. Ferrum faum opere, rota in commiftione tua eft. 20. Dedan negotiatores tui cum jumentis electis Nor£ AD VERSIONEM ANTIQUA M. Y. 7. Concinit Grac. nifi quód tollit zz , ante flratzm ; pra ponitque 5, , verbo fada funt ; Compl. veró hab. cy σρωM, abfque conjunct. ὁ» ante ἐγένεο. X.8. Àd verbum é Greco , pofitá uná conjun. c, ante principes, Y.9. Gr. Οἱ πρεσδύγερφι Βιβλίων, X, οἱ (Copo av]ow , o? ἦσαν cy (Col, c. Senzores Bibliorum , Q5 fapientes eorum , qui erant in ie, c. ut fupra ; fed à Mf. Alex. abeft οἷ. ante ἤσαν. Hieron. inf. 890. f. ait juxta edit. LXX. legi confsiliarios Bybli; que Hebraice appellatur Gebal. Y. το. Itidem Grace, X. 1I. Totldem verba in Greco, detracto uno zz cireniti ; fed in Mf. Alex. ac ed. Ald. eft ἐπὶ τῶν τειχέων χύχλῳ, |tem in Vatic, loco propugnacttla , legitur opue 5 in mulis , tefte Nobilio , puav (09 . compages , armos titos. Y. 13. Gr. Ἧ Ἑλλὰς, Z, καὶ (umen , αὶ τὰ παραΊείνον7a. $To ἐγεπορεύοντο Co ; c. Gracia , £5 univerfa » 9 adjacentia , bi uegotiabantitr tibi , c. utin textu : in Compl. 4» Exc; πᾶσα; in Mf. Alex. 'Exd;, X τὰ (ὑμαανΊα. Y. 14. In Greco Varic. eft Θογαρμα ; deinde , ἵπισοι E] ἑαωπεῖς 5. ulimóque , ἀγοράν (€, forum tuum , abfque hoc ant. C9 mulos. In ed. veró Compl. ὃς Mf. Alex, Oegyzgz 5 in Ald. Θοργαξ οἱ ; tum in quibufque , lez , X ἱππεῖς y X ἡἡἱμιόνες ἐδωχαν. ut in. Lat.
- 54. fupra. Ἵ Y.15. Niltam fimile Graco eft. Ad hoc autem εχ Hebr. ἘΠῚ: Dadan negotiatores tii , addit Hieron. ubi fup. Nefczo quid volentes LXX. filios. Rhodiorum zmterpretati fent : nifi forié prima littere falft. fimilitudine , ut pro Dadan , dom. 41. legerent Radan , qua Q9 zpfa Cycladum maxima eft , Q5 in lonio mari quendam urbs. potentiffima..... Jed. melius eft Dadan alterius loci nomen accipere 5 [9 ut n. Hebraico , 5 apud ceteros. Interpretes babetur, Y. τό. Grec. Vatic. loco mercatzs ttti , hab. τῷ Cvuuíaτὺ (* , commifli twi, abfque feq. im Apbhec, quod etiam de Theodotionis editione in LXX. addztum cfl , vefte Hieron. ubi fupra : in edit, tamen Compl. eft, τῆς égecpiac (^s ἐν Agéx exuremó in Vatic. x; χορχὸρ ἐδωχαν τὴν ἀγοράν (C » €g chorchor. dederunt forum tuum 5. cet. congruunt ad verbum. Y. 17. Gracé legitur πράσει» venditione , pro. commerεἶσ; deinde , x, μύρων , X, κασίας., X, €9 wnguentorum s 9 cafe ,9 , pro Q9 unguentis ; ultimóque , τὸν (ὑμμικ7όν (Ce » commzflum tuum , pro nundinis tuis 5 ciet. ut in Lac. fupra. Y. 18. In Gr. ἐμσοροί (€ . megotiatores tui, abfque feq. in multitudine operum ttorum ; caet, ut fupra. Edit. Compl. addit, £v πλήθει ἔργων (ε΄ exinde in Mf. Alex. οἶνον ἐκ Χεῦρων» non οἶνος ex Χελξωὼν , ut in Vatic. Y.19. Apud Hieron. premittuntur ifta, fed fub aíterifco : Daa , (9 Javan , 69 Moezel in nundinis tuis : abfunt etiam hodie à Gréco : obfervat Hieron. ibid. ipía in edit. LXX. de Theodorionis editione addita effe. Gracé nunc id priüs ponitur , 'F£ ᾿Ασὴλ , deinde ut fup. (7deos εἰργασμένος, X, τρφχιαὰς (al. τροχὸς) ἐγ τὼ Cage τῷ Üwésgi ab edit. vero Compl. abeft τὸ primum , 'E£ Aofa. X. 20. Confonat Grac. nifi quód fcribit. Δαθαν. Dadaa. ΠΥ ον Iiiii ij Hieron. ubi fup. Ii;4. 222. Ili4. 23. 1,14, 884. Ibid. c5 885. Ili2. 886, Ibid. 887. Τρ, 888.
- 55. Hieron. ubi fup. Il;4. 989. Tichon. veg. 7. p. 65. f. ldem veg. 4. p. $9. 5. 904 VERSIO ANTIQUA. ad currus. 21. Arabia , univerfi principes Cedar , ipfi negotiatores manus tux , camelos, arietes , agnos..... 25. Charran, Chana, Edne, ifti negotiatores tui : Sabba, Affur, Chalman , inftitores tui, 24. deferentes negotiationem , hyacinthum, ὅς thefauros eletos funibus colligatos, cyparitfos. 25... fatiata honorata es nimis in corde maris. 26. In aqua multa deduxerunt te remiges tui : fpiritus auftri contrivit te in corde maris. 28. Ad clamorem vocis tux gubernatores tui timore timebunt : 29. Et difcedent de navibus omnes remiges tui : veores, prorete maris fuper terram ftabunt : 3o. ululabunt fuper te voce fua, clamabunt fuper te amarum : imponent fuper caput fuum terram, cinerem fternent. 31... Fide Not. 52. Et accipient fuper te lamentationem filiorum, lamentum Sor : 533. Quantum inveniíti mercedis de mari? fatiaíti gentes multitudine tua, à commiftione tua locupletafti omnes reges terra. 34. Nunc autem contrita es in mari , in profundo aque commiítio tua , omnis congregatio tua in medio tui; ceciderunt omnes remiges tul. BEECHDB Cap. xXOGVLY VULGATA NOVA. dendum. i1. Arabia, δὲ univerfi principes Cedar , ipfi negotiatores manus tus: cum agnis, arietibus, hcedis venerunt ad te negotiatores tui, 221. Venditores Saba, ὅς Reema, ipfi negotiatores tui : cum univerfis primis aromatibus , lapide pretiofo , auro , quod propofuerunt in mercatu tuo, 23. Haran, Chene, Eden , negotiatores tui : Saba, Affur, Chelmad , venditores tui: 24. ipfinegotiatores tui multifariam involucris hyacinthi , polymitorum , gazarumque pretiofarum , quz obvolutze aftrictz erant funibus : cedros quoque habebant in. negotiationibus tuis. 25. Naves maris, principes tui in negotiatione tua : repleta es, glorificata nimis in corde maris. 26. In aquis multis adduxerunt te remiges tui: ventus aufter contrivit te in corde maris. 17. Divitie tuz, thefauri tui, multiplex inftrumentum tuum , nautz tui gubernatores tui, qui tenebant fupelleilem tuam , populo tuo praeerant: viri quoque bellatores tui, qui erant in te, cum univerfa multitudine tua, quz eft in medio tui : cadent in corde maris in die ruinz tux. 28. A fonitu clamoris gubernatorum tuorum
- 56. conturbabuntur clafles : 29. Et defcendent de navibus fuis omnes qui tenebant remum : nautze univerfi gubernatores maris in terra ftabunt : 30. ejulabunt fuper te voce magna, ὅς clamabunt amaré : fuperjacient pulverem capitibus fuis, cinere confpergentur. 31. Ft radent fuper te calvitium, accine gentur ciliciis : plorabunt te in. amaritudine anima ploratu amariffimo. 3i. Et aflument fuper te carmen lugubre, plangent te : Que eft ut Tyrus, quz obmutuit in medio maris ? 33. Qua in exitu negotiationum tuarum de mari implefti populos multos: in multitudine divitiarum tuarum , populorum tuorum , ditafti reges terra. 34. Nunc contrita es à mari, in profundis aquarum opes tuz , omnis multitudo tua , qux erat in medio tui , ceciderunt. Nors£ AD VERSIONEM ANTIQUA M. y.21. Ita rurfum in Greco, prater hoc med. ὅποι ἐμποροί (Cu dud χειρός (Qs 2Π1 negotiatores tui per manm inam. ἄν Y.23. Grec. Vat. Χαῤῥὰ» ὃ Χαναὰ , ὅτοι ἐμποροί (Cs Aoyüp , X, Χαρμὰν .» ἐμποροί Cs. Mf. Alex. hab. Χαρρὰν» ὼ Χαναὰν. ἃ Δαιάν. Ed, Ald. Kappa , x; Καννὰν » ὁ Δεd'dr, ὁ Σαξξὰ, X Aosép, ὁ Χαλμάν. Compl. XaG , ἡ 'Aoyip, E XexuaG, c. Υ. 24. Similiter in Gr. prater ult. κυσαρίοσινα ,. cyparifji za , loco cypariffos : Hieron. tamen ibid. ait pro cedrzs, LXX. cranftuliffe cyparzffos. Ixem fup. apud ipfum, poft zegotiatzotiem , hecfequuntur fubafterifco : 27 Machbalzm , «5 zn Galima; poft byaciatbim , itud , (9 polymita ; fed monet τὸ in Machalim , (9 in. Galzma , de Theodotionein LXX. additum effe ; feq. veró polymita , de Aquila Symmacho. Y. 25. Gr. X, ἐνεσλήϑης» καὶ ἐξαρύνθης σφόδρα - c. ut fup. Hieron. etiam in comment. col. 89o. ad hanc Vulg. vocem, glorificata , addit de LXX. ive aggravata ; legendum forταῦτα fup. emerata , non bonorata, Y. 26. Ita in Graco eft. y.28. Confonat Grec. ad verbum, Y. 29. Gr. in principio hab. Καὶ καγαξήσονγαι., Ft defsendent , abfque voce tuz , poft remiges , que tamen exftat in ΜΙ, Alex. ac edd, Ald. Compl. reliqua ut in textu, Y. 30. Eadem funt in Greco, preter unum firper. te , quod deeft. Hieron. in comment. col. 89r. a. ultimó leg. cinerem. flernent fibi , € Gr. σποδὸν ςρώσον)αι. Y.31. Hieron. in comment. col. 891r. a. ait : Quod auiem fequititr : (in Vulg.) Et radent fuper te calvitium, accingentur ciliciis : plorabunt te in amaritudine anima ploratu amariffimo. Et affument fuper te carmen lugubre , plangent te : 2) LXX. zn
- 57. habetur , fed de Theedotionis editioue additum efl. Eadem etiam ad hoc ufque, g affument , non leguntur in Gr. Vat. nec apud Tichonium fupra. : Y.32. Gracé : Καὶ λήψονγαι οἱ υἱοὶ ἀυτῶν ἐπὶ (ὲ .rgnvoy, ϑιρννήμα Xóp* nec plura : Et affiment filii eorum fuper te lamentum , lamentationem Sor ; al. Cet tibi, non Ser. Hieron. etiam in comment. col. 891. f. ait fequentia ( de Vulg. ) Qua eft ut Tyrus , qua obmutuit , five conticuit , in medio maris? in LXX. non haberi : nunc etiam abfunt à Gr. Vatic. nec admittuntur à Tichonio. Y. 33. Similiter in Graco , pofito uno ἀπὸ, ante vocem oinltitudine; pro commi[lione autem , conftanter habetur ('uuulu] , commiflo. Hieron. in comment. 892. a. hgc habet : Qua ip exitu negotiationum tuarum » f£ve, Quam invenifti mercedem de mari ὃ ὁ Gr. Πύσον τιγὰ εὗρες μιὼ ὃν ἀπὸ- c. Y.34. Edit. hab. Nauac autem contriflata ες; ΜΙ, veró B. M. Rem. n. 35. contrita , quod fubftituimus ; Grace pariter , Nor ('we]pleus » Nune contrita es ; Compl. wv —€——
- 58. I. EZECHIEL. Cap. XXVIII VULGATA NOYA. 3 $. Univerli habitatores infularum obftupuerunt fuper te : reges earum omnes tempeftate perculfi mutaverunt vultus. 36. Negotiatores populorum fibilaverunt fuper te : ad nihilum dedua es, non eris ufque in perpetuum. 905 VERSIO ANTIQUA. 35. Omnes qui inhabitant infulas contriftati funt füper te: remiges eorum mentis alienatione ftupuerunt, lacrymatus eít vultus eorum füper te. 36. Mercatores eorum de gentibus exfibilabunt te : perditio facta es, ultra non eris in «ternum , dicit Dominus, Tzcbon. ubi fup. Nor AD VERSIONEM ANTIQUA M. reliqua utin Lar. Apud Hieron. in comment. col. 892. a. non commz[Ho , ed negotiatio tta ; Grecé conftanter , CvaΜικτός (Ce , commiflus 12u5. Y. 35. Hzc tora Graeco fimillima , dempto ult. fitper te , quod tamen eft in ed. Ald. Mf. Alex. loco veró reiSes , quod editio PP. Lugd. fert cum Mf. Rem. Grace legitur conftanter , οἱ βασιλεῖς , reges. Hieron. in comment. €ol. 892. a. utramque Verfionem fic jungit de more : Uz;verf babitatores infalarum obfiupuerunt , ffve contriti funt fuper te : Q9 reges eartm omnes tempe[late perculfi , froe verfi in amentiam outaveruat uttltus , vel fleverunt.. Mf. amena ama asta. CAPUT B. M. Rem. legit //]vas , non znfulas ; at in Gr. γῴους. Y. 36. Grec. delet eorum , poft mercatores 5 loco veró exfibilabunt ( edit. vitiose exbilabunt ,) hab. ἐσύρισαν. Μbilauerunt, extremóque ,. Z, ἐχέτι ἔσῃ εἰς τὸν αἰῶνα, αὐίque feq. dicit Dominus ; in Mf. tamen Alex. ac ed. Ald. eft, εἰς τὸν αἰῶνα» γέγει Ἱζύξιος ὁ Θεό cet. congruunt. Hieron, in comment. col. $92. a. fic habet : Negotiatores gentium , fre populorum..... ad nibilum. deduüla es, five facta perditio es, qg son eris altra ufque ia. feculum , frve in perpetuum. Mf. Rem, Tichon. habet , £9 perditio fada es, 9 ttltra non eris , δίς, quse fupra. A X MIL VurGATA NOVA. x. ἘΠΛ T. faus eft fermo Domini ad me, diLU cens: 2. Fili hominis, dic principi Tyri; Hzc dicit Dominus Deus : Eó quód elevatum eft cor tugm, ὃς dixiti: Deus ego fum , in cathedra Dei fedi in corde maris : cüm fis homo , non Deus, ὃς dediíti cor tuum quafi cor Dei, 3. Ecce fapientior es tu Daniele : omne fecretum non eft abfconditum à te. 4. In fapientia prudentia tua feciíli tibi fortitudinem : acquififti aurum argentum in thefauris tuis, $. In multitudine fapientim tuz ,
- 59. in negotiatione tua multiplicafli tibi fortitudinem ; elevatum eft cor tuum in robore tuo. T 6. Propterea hec dicit Dominus Deus : Eó quód elevatum eft cor tuum quaá cor Dei : 7. idcirco ecce ego adducam fuper te alienos , robufliffimos gentium : nudabunt gladios fuos fuper pulchritudinem fapientiz tuz, polluent decorem tuum. 8. Interficient , detrahent te : morieris VEgRS10 ANTIQUA. τ᾿ H T faus eft fermo Domini ad me , dicens : Hieron. in Exch, 28. col. 693. «x 2. Et tu fili hominis, dic principi Tyri : Hzc L«s. dicit Dominus Deus : l'ro eo quód exaltatum eft cor tuum, dixifti : Deus ego fum, habitationem Dei habitavi in corde maris : tu autem es homo, non Deus, dedifti cor tuum quafi cor Dei. ; Nunquid fipientior es Daniele ὃ fapientes nonerudierunt te difcipliná fuá. 4. Nunquid in eruditione tua, aut prudentia tua fecifti tibi fortitudinem : fecifti aurum ὃς argentum in thefauris tuis? 5. Aut in multa eruditione tua, negotiatione tua multiplicafti fortitudinem tuam? elatum eft cor tuum in fortitudine tua. 6. Propterea hac dicit Dominus Deus : Quia dedifti cor tuum quafi cor Dei : 7. propter hoc ecce ego adducam fuper te alier1os peftilentes de gentibus : evaginabunt gladios fuos in te füper pulchritudine dorinz tuz, humiliabunt pulchritudinem tuam in perditione. 8. Et deducent te, difponent te : morieNorTr£Z£ AD VERSIONEM ANTIQUA M. Y. 1. Sic eft in Graco. Y.2. Totddem verba exftant Grzcé , detracto uno Der; at in Mf. Alex. eft Κύριος ὁ Θείς. Eadem rurfus habet idem Hieron. in lfai, 14. col. 160. b, excepto uno ablat, babitatzone , loco accuf. babitationem. ]tem Tichon. reg.7. p. 65. d. Si Dens, inquit, zgcrepat. rezem Tyri : Quoniam exaltatum eft cor tuum , (9 dixiflfi : Deus ego fum, habitatione Dei babitavi im ordine (l. corde ) maris : tu auzem bomo ἐς. 5 non. Deus , 69. dedzfli cor tuum tanquam cor De. Optat. l. 3. conr, Donat. p. 52. c. ἘΣ bominis , dic adqersüs priacipem Tyri : Hac dicit Dominus Deus ; Quia exaltatiia efl cor tuum , C9. dixifi ; Ego fum Deus. Au, 1. de promilT. p. 4. ap. Profp. col. 197. b. Elevatum eft cor tum, Qj dixifla : Deus ego fum, «9 in catbedra Des. [edeo in corde maris : citm fis bomo , $ non Deus , τ ded;fl; cor tunm Quafi cor Dei. T Y. 3. Sic etiam in Gr. eft, addità voculà (y , ad verbum es, Ambrof. veró in Pf. 118. col. 987. f. legit : Quis prudentior , quàm Daniel : ὃς l. 2. off. to. 2. 83. f. Quis Daniele
- 60. fapientior ? Ax Hieron. in Ifai, 4. conftanter : Nzzquid [apientior es Daniele ? Auguft. ep. 111. to. 2. 320. g. Nuaquid tm fapientior , quam Daniel ? 'Tichon, reg, 7. p. 65. d. Nunquid Japientzor es ttt Daniele? Japieutes argiterunt te fapientia {πᾶς Optat. l. 3. conr. Donar. p. 5s. b. Nunquid fapientior tw , quàm Daniel ? Jfüpientes τὸ non. daeuerunt. (apientiam fuam : 1n. mulüs eft , ἢ (οφοὶ, aut fapientes, Y. 4. Idem Grace, detracto verbo fecifi, ante an*m ; at in Mf, Alex. eft , ἐποίησας χρυσίον, Apud Tichon. reg. 7. p. 65. d. Nunquid fapientià tu4 , aut. dollrina t4 Jfeciftá tibi virtutem ; (9 aurum , 9 argentum the[auris tuis? infra : Nunquid in fcientia tua , aut fapientia tua feat Hbi, c. ut fup. Y. 5. Eadem fert Grec. Vat. fed abfque 1. conjunt, att; in edd. tamen Ald. Compl. eft 5 ἐν τὴ “πολλὴ » ficut in Mf. Alex. Apud Tichon. reg. 7. P. ὅς: d. πὰ: Nanquid in multa doilrina tua , Q9 in mercati tuo muliiplica virtutem. tuam ?. deinde , Propterea. bac dicit , c. de Y. 6. pratermiífis intermediis : infra : Nunquid in multa fiientia , aut im merca tuo multiplicafa tibi wirtutem tuam? Υ΄. 6. Sic iterum in Greco, preter vocem Der, qux deeft : at in Mf. Alex. eft. Κύριος Κύριος ὁ Θεός ; in Ald. Κύριος Κύριος ; in Compl. 'Ad'era? Κύριος. Ap. Tichon. reg. 7. p. ὅς. d. h. Propterea bec dicit Dominus : Quoniam dedifli cor tuum ftcut. cor Dei. Y.7. Grac. initio hab. ἀντὶ zíés ἰδ ἐγὼ ἐπάγω , pro boc ecce ego addutco 5 paulóque poft, ncc, loco peflilentes 5 item infra addit Z , poft hoc, zz τὸ; qua conjunct, abeft ab ed. Compl. extremó hab. ςρώσεσι..... εἰς ἀπώλειαν, flernent..... in perditionem , loco bumiliabunt..... im perditione ; al. ταιεινώονοι , al. βεξηλώσεσι 5 catera ut in. Lar, fup. Apud Tichon. reg. 7. p. 65. d. Propter boc ecce ego induco fisper te alienas pelles ex gentibus : (6 exinansent. gladzos ρος fuper te , 5 fuper. decorem doclrine tus , qg vulnerabuns decorem tuum in. perditionem : eadem quoque refert. infra , preter vocem fcentie, loco doürime 5 Gr. ἐπισήμως. Y.8. Grzcé , Kai καγαδιξάσυσί (e y ἐδ defcendere facient
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