Neural Network Approach to Railway Stand Lateral SKEW Control

NEURAL NETWORK APPROACH TO RAILWAY
STAND LATERAL SKEW CONTROL
Peter Mark Beneš1, Matouš Cejnek1, Jan Kalivoda2 and Ivo Bukovsky1
1

Department of Instrumentation and Control Engineering, Czech Technical
University, Prague, Czech Republic
{PeterMark.Benes;Matous.Cejnek;Ivo.Bukovsky}@fs.cvut.cz
2

Department of Automobiles, Internal Combustion Engines and Railway
Vehicles, Czech Technical University, Prague, Czech Republic
Jan.Kalivoda@fs.cvut.cz

ABSTRACT
The paper presents a study of an adaptive approach to lateral skew control for an experimental
railway stand. The preliminary experiments with the real experimental railway stand and
simulations with its
3-D mechanical model, indicates difficulties of model-based control of
the device. Thus, use of neural networks for identification and control of lateral skew shall be
investigated. This paper focuses on real-data based modelling of the railway stand by various
neural network models, i.e; linear neural unit and quadratic neural unit architectures.
Furthermore, training methods of these neural architectures as such, real-time-recurrentlearning and a variation of back-propagation-through-time are examined, accompanied by a
discussion of the produced experimental results.

KEYWORDS
Roller Rig, Linear Neural Unit, Quadratic Neural Unit, Real-Time-Recurrent-Learning
(RTRL), Back-Propagation-Through-Time (BPTT)

1. INTRODUCTION
An ongoing problem, which is currently under research in the railway industry, is that of lateral
skew control of railway carriage wheel sets with Independently Rotating Wheels (IRW). In
particular, the control of position of the leading wheel set of a railway carriage bogie, such to
achieve central positioning of the wheel set, with respect to the span of the rail track. Or
furthermore, to control the lateral deviation of the wheel set to follow a given desired set point.
The primary necessity for such control arises from the need to improve behaviour of IRW wheel
sets, as currently under study at CTU, on an experimental railway stand (roller rig). Particularly,
for minimisation of wheel flange and rail head wearing as well as lateral forces and, furthermore,
optimal stability at higher speeds of the wheel set. To date, various methods for control of the
wheel set lateral position of IRW wheel sets have been under investigation, with both mechanical
and electrical means of control [2], each featuring their own, individual drawbacks.
At CTU, the latest study features active control of the roller rig through manipulation of the yaw
torque of the rig wheel set [1], via a state feedback and cascade PID control for a linearization of
the model of the CTU roller rig. However, the results from this initial experimentation shows, that
David C. Wyld et al. (Eds) : CCSIT, SIPP, AISC, PDCTA, NLP - 2014
pp. 327–339, 2014. © CS & IT-CSCP 2014

DOI : 10.5121/csit.2014.4228

328

Computer Science & Information Technology (CS & IT)

such method is not suitable for real time control. Thus, this paper aims to investigate the possible
use of a neural network approach for lateral control of such railway wheel sets. The suitability of
application to this problem is motivated by promising theoretical studies of higher-order neural
units (HONUs), especially the quadratic neural unit for engineering problems for [3]-[7]. These
studies are focused on the use of supervised learning based approaches for polynomial structured
neural units, also known as a class of HONUs, for adaptive identification and control of real
engineering systems. Further motivation arises from the successful implementation of a quadratic
neural unit controller (Neuro-controller), for control of a bathyscaphe system located in the
automatic control laboratories of CTU [12]. Where, here, such controller adhered more closely to
the desired behaviour of the system than the conventionally used PID controller. An extension on
this result can be recalled in the work [11]. Where, further study was made via introduction of a
new software for adaptive identification and control, along with further testing on both a
theoretical system and the previously mentioned bathyscaphe system. Given this, in this paper we
aim to investigate use of neural network (NN) approaches in the following manner. We will begin
by explaining in more depth the problem behind the recently employed state feedback and
cascade PID control of the linearization of the CTU roller rig. The proceeding section will then
describe the principles and control schemes behind the various experimented methods, for
adaptive identification and control. Following this, an experimental analysis of the various
approaches of NN, focusing firstly on adaptive identification of the CTU roller rig system and
then to test the various NN methods for control. The final component of this paper will then be, to
analyse and compare the produced experimental results, with a conclusion to be drawn at the end.

2. PROBLEM DESCRIPTION
This section aims to describe in more depth, the functionality behind the previously introduced
experimental railway stand (CTU roller rig). More importantly, for the scope of this paper, we
will elaborate on the necessity for control of such roller rig and the issues of conventional linear
PID control or state feedback control, for controlling the lateral skew.

1.1

Experimental Setup of the Roller Rig at CTU

The below figure (Figure 1) depicts the experimental setup of the CTU roller rig, along with the
3-D model for design and simulation purposes. This rig features 5 motor drives, two pairs of 0.5m
diameter rollers are independently driven, via the largest of the set of drives (FM1 & 2). To
simulate both straight and curved tracks, similar to those present on real railway networks. A
central servo motor (FM4) was introduced, to yaw the lower roller pair for replicating curved
track motion. This setup however, assumes simulation of a rail pair without effects of rail
buckling. For manipulation of the wheel set yaw, a separate servo motor, central to the wheel set
(FM3) is installed. For the scope of this paper, this is the most crucial component, as it is the
action of this servo motor that is used for control actuation for the lateral skew of the wheel sets.
Where, the discussed control setups in this paper will analyse control via manipulation of this
servo motor torque. Finally, a fifth drive FM5 is located between the front roller set, as a control
differential.


329

Figure 1: CTU Roller Rig (real left, PTC Pro/Engineer 3-D model on the right)

1.2

Problem of the State Feedback and Cascade PID Control

In the work [1], the method of lateral skew control via state feedback with cascade PID setup is
introduced. In this presented setup, a linearization of the roller rig is used, via translation to a state
space representation, achieved via a 12x12 matrix of dynamics. However, according to theory,
this linearization of the roller rig system appeared to be uncontrollable and unobservable via
analysis by common linear algebra and control approaches.

Figure 2: Control loop on linearization of the roller rig with State feedback + Cascade PID control

The above figure (Figure 2), depicts the control scheme for this setup. After numerous testing, it
was found that a simulation step of approximately < 1E-6 was necessary, in order to achieve
stability of the continuous control loop, which cannot be used for practical application. Hence, it
is for this reason that an alternative approach is necessary for the lateral skew control of such
railway wheel set. Thus, this paper aims on investigating the possibility of adaptive identification
and control of the stand, based on measured data. For the purposes of this paper the data will be
generated via a 3-D simulation model via software SIMPACK, linked via SIMAT toolbox with
MATLAB Simulink, to provide real time simulation of the roller rig as a plant system for the
investigated control approaches. Then, this data will be used as the training data for neural
network models, to simplify otherwise complex simulation models and to allow a constant
sampling for real time usability, furthermore, investigation into the potentials for real-time neuralnetwork based control.

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3. APPLIED METHODS
In this section, the various NN approaches, aimed for adaptive identification and control of the
previously introduced lateral skew problem, will be described. These approaches are based on the
well know Gradient Descent (GD) method used as a tool for defining the learning rule of the
applied neural units. These applied neural units (adaptive models) are trained via two methods,
which will be focused on in this paper. These methods are namely, the method of incremental
training or Real Time Recurrent Learning (RTRL) [8] applicable for dynamic adaptive models or
a batch form of training, which is a variation of the back propagation through time or (BPTT)
training [10], as an extension of RTRL training in combination with the famous LevenbergMarquardt equation.

1.1

Preliminaries

This subsection aims to review the important theories from works [11]-[13], behind the GD
method and structures of the neural units used within this paper. Firstly, we will begin by
introducing the famous GD algorithm for the linear and quadratic neural units. To understand
this, we must begin with the polynomial models of the linear and quadratic (LNU and QNU)
neural units respectively, as follows
n

y = ∑ xi wi = w0 .x0 +w1.x1 + ... + wn .xn = w.x

(1)

i =0

n

n

y = ∑∑ xi x j wi , j = w0,0 x0 x0 +w0,1 x0 x1 + ... + wn, n xn 2 = rowx.colW

(2)

i =0 j =0

Where, y represents the output of the LNU (1) and QNU (2) respectively. In regards to the LNU,
w stands for an updatable vector of neural weights and x, represents the input values of the
engineering system in the case of a purely static model and in the sense of a dynamic model, a
combination of inputs of the real system and neural model outputs. Looking at equation (2), rowx
is a long-vector representation of the utilised input vector. Where, colW represents a weight
matrix of the quadratic neural unit in general. From this, we may then understand the GD
algorithm as applied to such neural units.

∂y (k )
∂wi
∂y (k + 1)
colW (k +1) = colW (k ) + µ .e(k ).
∂colW
wi +1 = wi + µ.e(k ).

(3)
(4)

Here, equation (3) & (4) depicts the GD algorithm for both the LNU and QNU respectively. Here
the output of the GD algorithm is to incrementally over sample-by-sample, update the neural
weights such to adaptively teach the LNU or QNU model, to learn the engineering system. Here,
µ represents the learning rate of the GD algorithm. This is analogical to humans where, setting µ
relatively high, corresponds to faster learning of the human and consequently, means the less
detail the human can remember and digest from their learning. Furthermore, setting this
parameter to a smaller value, corresponds to a slowing rate of learning i.e. the human may
remember the information learned, quite well, but less information overall about the subject. The
next parameter is e(k) (k representing the number of the sample), this represents the current error
∂y (k )
between the real and calculated output of the model. The final term
, corresponds to the
∂wi
partial derivatives of the neural unit output, with respect to the individual neural weights.


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Regarding the QNU in equation (4), we see that the GD algorithm is analogical, with exception of
updating the matrix of neural weights as opposed to a vector in the sense of the LNU.
Till now, the structures of GD for LNU and QNU were reviewed in the format of RTRL or
sample-by-sample method of learning. Where, the neural weights are updated over each new
sample of the engineering system data. However for certain engineering processes, it is more
advantageous to use the BPTT batch method of training these neural weights, over runs of the
algorithm rather than over each sample. This is because the RTRL method focuses on the
contemporary governing law of the system as opposed the BPTT which focuses more so on the
main governing law of the input and outputs of the engineering system. The BPTT method is
achieved via an extension of the RTRL method with combination of the famous LevenbergMarquardt equation. It is also important to note that this method is more preferable in cases where
the data may be affected by noise. The following equation denotes the weight update rule for the
BPTT method;

∆w = (J T .J +

1

µ

.I ) −1 .J T .e

(5)

Here, the neural weights are updated over each run of the algorithm (or batch trained) in the
following way w=w+∆w. Here equation (5) describes the change, necessary for the update of the
batch trained weights. Where, J represents the Jacobian matrix of derivatives for the neural unit.
This may be the complete partial derivatives of the neural model with respect to each neural
weights, or in practical applications it seems useful to simply introduce this Jacobian matrix as
the input vector or matrix itself, being x and colx for LNU and QNU respectively. Furthermore, it
is important to note that colx = rowx T .
Often in such adaptive neural units, it is apparent that a modification of the normalised learning
rate may be used to solve issues associated with instability of learning. In practise, it is possible to
employ the simplified normalised learning rate as presented in the work [11], as follows;

η=

µ
x(k)x(k)T + 1

(6)

Where, equation (6) represents the normalised learning rate in the sense of LNU. This is
analogically represented in the QNU, by replacement of x(k) (i.e. each k th sample of the input
vector x) with colx(k). It should be noted that the above representation holds for RTRL training
for dynamic adaptive models, where the algorithms used in this paper for BPTT method of
training, take the learning rate µ itself.

1.2

Adaptive Identification and control

The previous section focused on usage of neural units in the sense of adaptive identification of a
real engineering system. In this subsection, we extend on these neural units as a method of
control, with brief review from works [11]-[13], and extension as applied to the lateral skew
problem, which is indeed our focus within this paper.

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Figure 3: Adaptive Identification with supervised learning of neural networks (where, w.x=LNU,
rowX.colW=QNU)

The above figure (Figure 3), depicts the identification scheme for the previously reviewed neural
network architectures. Where, for the scope of this paper a simulation of the real roller rig will be
used for data generation of the investigated neural network approaches for control. u, represents
the input data of the roller rig, in our case this is the yaw torque of the servo motor system for
manipulating the lateral skew of the wheel set. The output yreal, is the simulated output from the
real time 3-D SIMPACK model and y, being the output of the neural unit, and the difference
being the error, e.

Figure 4: Adaptive control loop for experimental study of a neural network controller (where, w.x=LNU,
rowX.colW=QNU)

The above (Figure 4), shows an extension of the discussed neural architectures for application to
lateral skew control of the roller rig system. Here, once the neural unit as a model is identified, it
may be utilised as the foundation for a neural network based control setup. For the scope of this
paper, we will propose an offline tuned control scheme, as the goal here, is to investigate the
potentials of applying a neural network based control, for this application. However, the
extension to online control is indeed the ultimate aim of our research to this problem, beyond this
paper. Figure 4, depicts use of a second neural unit as a controller. Similarly to the previously
mentioned architectures, as a controller here too the neural unit may take shape to that of the
LNU or QNU adaptive models. However, in this case the adaptive neural weights are tuned
differently to that of those used for the neural unit as a model and hence, depicted as v.
Analogically, should a QNU structure be applied, these neural weights would be represented in a
matrix form. Further to this, the above figure (Figure 4) introduced a new vector ξ. This vector
comprises of a combination of outputs from the neural unit as a model and the difference between
the desired behaviour (in our case desired yaw torque or lateral skew of the roller rig) and the


333

output of the neural model. v. ξ or collectively, the variable q, thus serves as a manipulator for the
newly feed samples of the neural unit as an identified model. Here the GD algorithms are
employed in the following manner to achieve sample-by-sample adaptation of the neural weights
for the controller, as follows;

vi +1 = vi + µ.ereg (k ).

∂y (k )
∂vi

(7)

Where vi , are adaptable neural weights of the neural unit as a controller and ereg(k) is the error
between the desired value of the real system (in our case the roller rig, where the desired value
will be denoted as d) and the real system output value at sample k.

∂y (k )
, is the partial
∂vi

derivative of the output of the neural unit as a model, with respect to the individual adaptive
neural weights of the neural unit as a controller. An extension of this weight update scheme for
BPTT training would result in the following form v=v+∆v, where the change of neural weights
for each batch would be analogical to equation (5).

4. EXPERIMENTAL ANALYSIS
This section aims to analyse the previously reviewed methods of adaptive identification and
control, via the introduced neural network architectures. Particularly, we aim to investigate the
applicability of the discussed neural architectures for this problem of the lateral skew control of
railway wheel sets. In this section, we will simulate our results using simulation data of the
previously described 3-D SIMPACK model (at mid-range speed) linked with MATLAB Simulink
in real time simulation. The data was produced with 0.001 sampling over a 10 second interval.
First, we will analyse the results for identification of the roller rig as a system, via the different
methods of the neural network models, followed by an extension of control, where the various
combinations of neural network architectures will be tested.

DLNU with RTRL
Almost exact identification of
Roller Rig data (lines are superimposed)

Deviation of the model with the Roller Rig
data, over each sample

Figure 5: Testing of the adaptive identification, where the plant (roller rig) is represented by blue colour
and green being the neural model. Trained by DLNU with RTRL Training; µ=1,
epochs =10, For ny=3 (previous samples of model output) and nu=5 (previous samples of real system input)

334


The above figure (Figure 5) and following figure (Figure 6), illustrates the adaptive identification
process of the roller rig system data. We can note, that both methods of the dynamic LNU or
(DLNU) and dynamic QNU or (DQNU), for RTRL learning methods, achieved almost exact
identification. Where, the DQNU performed slightly faster in terms of convergence to minima of
sum of square errors, as opposed to the DLNU.

DQNU with RTRL. Excellent identification with slightly
faster learning than the DLNU of same parameters

Error of model is still within an
excellent range

Sum of square errors decreases more quickly
with the DQNU for same parameters.

Figure 6 : Testing of the adaptive identification, where the plant (roller rig) is represented by blue colour
and green being the neural model. Trained by DQNU with RTRL Training; µ=1, epochs =10, For ny=3
(previous samples of model output) and nu=5 (previous samples of real system input)


Desired (black dashed)

335

Roller Rig system data (blue)
Neural controller (magenta) applied to
identified Roller Rig data

Error plot illustrates deviation of the Neural
Controller and desired behaviour.

Sum of Square Errors reaches
close to 10-4 after 50 epochs

Figure 7: Testing of the adaptively tuned control loop, where the roller rig is represented by trained DLNU with constant and
previously trained parameters (Figure 5) and the adaptive feedback controller is trained via LNU, after 10 epochs Adaptive
Identification (of DLNU with RTRL) + Neural Unit Controller for lateral skew control of roller rig system - Using LNU with
Incremental training µ=0.1, Data re-sampling = each 5th sample, epochs =200, for nqy=0 (previous samples of neural model output)
and nqe=2 (previous samples of difference of the neural model output and desired behaviour of the system.

Closer to desired behaviour of the
system with QNU + BPTT

The difference of the Neural Controller
and desired behaviour is within +0.2 to
-0.2 mm.

Sum of Square Errors reaches close to 10after only few epochs, with QNU and
BPTT training.

4

Figure 8: Testing of the adaptively tuned control loop, where the roller rig is represented by trained DQNU with constant and
previously trained parameters (Figure 6) and the adaptive feedback controller is trained via QNU,
after 10 epochs Adaptive Identification (of DQNU with RTRL) + Neural Unit Controller for lateral skew control of roller rig system Using QNU with BPTT Training µ=0.00818,
epochs=5, for nqy=0 and nqe=3

e

336


Here, Figure 7 & Figure 8 show the application of the various neural units for control of the
lateral skew. The black dotted line, illustrates the chosen desired behaviour of the roller rig lateral
skew. It was found that the BPTT training method used in combination with the QNU had the
best performance. Providing closer control to the desired behaviour, as compared with the
incremental training methods of both LNU and QNU architectures.

Desired lateral skew (black dashed line)
set to ideal position of zero

Model provides almost exact response to the
desired after the first few samples.

Figure 9: Testing of the adaptively tuned control loop, where the roller rig is represented by trained DQNU
with constant and previously trained parameters (Figure 6) and the adaptive feedback controller is trained
via QNU,
after 10 epochs Adaptive Identification (of DQNU with RTRL) + Neural Unit Controller for lateral skew
control of roller rig system - Using QNU with BPTT Training µ=0.001, epochs=5, for nqy=3, nqe=3

Figure 9 depicts a theoretical test of the roller rig system under an idealised case of zero lateral
skew. This is included in our results to investigate the capability of the used neural controller.
From this figure, we see that after several small samples at the beginning of the controller’s
application the controller provides almost exactly zero lateral skew. This result however, must be
reasoned with what is really possible in terms of actuation of the real system and real conditions
of the rig, such to achieve this ideal of a result.

5. DISCUSSION OF EXPERIMENTAL RESULTS
In the previous section, the experimental results of the various neural network architectures for
adaptive identification and control were presented. From the first set of figures, regarding the
adaptive identification for the roller rig system, it was found that the most suitable learning
method for both the DLNU and DQNU was the RTRL training method. Here, relatively few
epochs were adequate for both architectures to identify the system data, with almost exact


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identification. The DQNU model was slightly faster in learning the behaviour of the system, thus,
was used as the identified neural unit as a model, in the control section. The extension of these
various architectures for control showed more distinguishable results. The application of both
LNU and QNU with incremental learning for the neural controller was only possible when a
higher number of epochs were run, or higher learning of the model with a small learning rate.
Few runs of the algorithm were unable to match the desired behaviour even moderately.
However, after the first few samples of application as in Figure 7, reasonable behaviour of the
controller was achieved. The combination of identification via the DQNU followed by extension
of a QNU trained by BPTT on the neural controller, showed to follow more closely to the desired
behaviour of the roller rig system than the other tested combinations. Where, the setup of the
QNU with BPTT neural controller featured input vector ξ, being comprised only of several errors
or differences of the desired behaviour, with the output of the neural unit as a model. Further to
this, the training was substantially quicker than the incremental training method, showing that
only several epochs were sufficient for the model to achieve its optimal behaviour with respect to
the desired of the system.
In the above results, two forms of the desired behaviour were used. The first was under proposal
that the lateral derivation of the wheel set would be within a small tolerance range, which is most
realistic in real application of such control. The presented desired data is relative to the small
range of lateral skew in the simulation data. Where, within this exampled range, we could be sure
the wheel flanges would not contact the rails of the real roller rig. The desired behaviour is
however relative to the setup of the wheel sets and rails, thus the desired deviation and lateral
skew outputs may indeed vary for real railway applications. The second was an idealised situation
where no lateral skew at all would occur. This is principally unrealistic for the neural controller to
achieve zero lateral skew, due to a combination of natural factors on real railway wheel sets,
however for demonstrational purposes, we may note the capability of the neural controller,
providing almost exact behaviour of the idealised lateral skew, as applied on the identified roller
rig system.

6. CONCLUSION
Referring back to the original control loop depicted in Figure 1 (as presented in work [1]), of the
Simulink model of the linearization of the roller rig system and state feedback with cascade PID
controller. We can recall that a minimum sampling of <1E-6 seconds for numerical stability was
necessary, which is not possible for practical application. After investigation of the presented
neural network approaches, we may conclude that it has promising potential for real application
on controlling the lateral skew of IRW railway wheel sets. Now, we note that the achieved
sampling can be within order of 0.005 (5E-3) seconds, for adequate functionality of the neural
network based, adaptive identification and control system as applied to the roller rig. The tested
models in this paper were DLNU and DQNU for adaptive identification models and LNU or
QNU architectures as a controller. The experimental results of these architectures showed that
both DLNU and DQNU, precisely approximated the complex SIMPACK model of the roller rig
system. This result however could vary when using more or, real training data measured from the
rig itself. In terms of control of the lateral skew, the QNU architecture showed better results to
keep the lateral skew within close limits to the desired behaviour of the system, which is also in
general consensus with our previous findings on using QNU for control. We also can note the
significantly faster tuning of the control loop via QNU as compared to the LNU, more
particularly, the BPTT training method as applied to the controller compared to the incremental
method. Where, more desirable control was shown, in much fewer epochs or runs of the
controller algorithm. Thus, this case study shows that with proper tuning of the investigated
neural units, application to the real system is theoretically possible, to achieve adequate control

338


for this investigated problem. Thus, real application of such adaptive control loop of neural
network based architecture, is indeed the very next step of our research.

ACKNOWLEDGEMENTS
The authors would like to acknowledge the following grant for support during this work:
SGS12/177/OHK2/3T/12SGS12/177/OHK2/3T/12, Non-conventional and Cognitive Signal
Processing Methods of Dynamic Systems.
And also the Technology Agency of Czech Republic. Project No: TE01020038 “Competence
Center of Railway Vehicles”.

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Short Biography of the Authors
Peter Mark Beneš received his Bachelor’s degree with honours at Czech Technical University (CTU) in
Prague in 2012. Currently he is a Master’s student, with expected PhD studies to follow in 2014. His
research focuses on non-conventional neural networks for adaptive identification and control of industrial
systems including hoist mechanisms and skew control of rail-based mechanisms as such cranes and
railway vehicles. Peter’s work has been awarded in local and international student competitions also with
an industrial BOSCH award in 2013.
Matouš Cejnek received his Bachelor’s degree at Czech Technical University (CTU) in Prague in 2012.
Currently he is a Master’s student at Czech Technical University in Prague. His research focuses on nonconventional neural networks for adaptive systems and novelty detection in time series and biomedical
applications. Matous’s work has been awarded in local and international student competitions 2013.
Jan Kalivoda graduated from Czech Technical University (CTU) in Prague where he received his
Master’s degree with honours in 1996 and Ph.D. in the field of Machines and Equipment for
Transportation in 2006. Currently he is a teacher and active researcher in the Department of Automotive,
Combustion Engine and Railway Engineering at CTU. His research interests include MBS models of
railway vehicles, Mechatronics for railway vehicles, Active control of railway vehicle suspensions and
wheel sets.
Ivo Bukovsky graduated from Czech Technical University in Prague (CTU) where he received his Ph.D.
in the field of Control and System Engineering in 2007 and became associate professor since 2013. His
research interests include higher-order neural networks, adaptive evaluation of time series and systems,
multi-scale-analysis approaches, control and biomedical applications. He was a visiting researcher at the
University of Saskatchewan (2003), at the University of Manitoba in Canada (2010), and he was a
visiting professor at Tohoku University (2011)

Neural Network Approach to Railway Stand Lateral SKEW Control

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