Intelligent analysis for historical macroseismic damage scenarios Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Maria Danese, Cinzia Zotta - Archaeological and monumental heritage institute, National Research Council, Potenza (Italy), Lucia Tilio,

Intelligent Analysis of Environmental Data (S4 ENVISA
Workshop 2009) 18-20 June 2009, University of Palermo, Italy

Intelligent analysis for historical
macroseismic damage scenarios

Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Cinzia Zotta,
Archaeological and monumental heritage institute, National Research
Council, Italy

Lucia Tilio, Maria Danese, Beniamino Murgante
Laboratory of Urban and Territorial Systems, University of
Basilicata, Italy

Introduction

Analysis concerning earthquake events, are normally strictly
related to damage survey.
It is evident that documentary sources concerning urban
historical damage can provide useful information for seismic
microzonation.
This research concerns historical earthquake (1930) damage
related to towns of a seismic area of southern Italy (Vulture
district, Basilicata).
4,000 dossiers compiled by the Special Office of Civil
Engineers have been analyzed.

Intelligent analysis for historical macroseismic damage scenarios
Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Maria Danese, Workshop 2009) 18-20 June 2009, Palermo, Italy
Cinzia Zotta, Lucia Tilio, Beniamino Murgante

Introduction

Why Rough Set Analysis for the analysis of
earthquake events?

o The aim is to verify the dependence of the damage
level attribution to each building from some socio-
economical local dynamics

o All available variables have been take into account
and searching some patterns, able to create a
cross-data control.

Rough set
Information System
IS = (U, A)
Let U be a nonempty finite set of objects called the universe
U = { x1 , x 2 , x 3 , x 4 , x 5 , x 6 ,............, xn }

Let A be a nonempty finite set of attributes
A = {A 1 , A 2 , A 3 }
∀ a ∈ A → Va = value set (domain of attribute)
V1 = {1 ,2, 3 }
V2 = {1 , 2}
V3 = {1 ,2, 3, 4}


Rough set

U a1 a2 a3
x1 2 1 3
Information System X2 3 2 1
X3 2 1 3
X4 2 2 3
f : U → Va
a informatio n function X5 1 1 4
X6 1 1 2
X7 3 2 1
X8 1 1 4
X9 2 1 3
x10 3 2 1


Rough set

Decision System U a1 a2 a3 d1
x1 2 1 3 1
A decision system is an
information system in which X2 3 2 1 4
the values of a special X3 2 1 3 5
decision attribute classify X4 2 2 3 2
the cases X5 1 1 4 2
X6 1 1 2 4
DS = (U, A ∪ d ) d≠A
X7 3 2 1 1
other attributes a ∈ A - { d} X8 1 1 4 2
X9 2 1 3 3
Conditiona l Attributes
x10 3 2 1 2


Rough set
Indiscernibility Relation
∀ B ⊂ A → Ind (B)

xi e x j are Ind (B) → b(xi ) = b(x j ) ∀ b∈B

o The equivalence class of Ind (B) is U/A a1 a2 a3
called ELEMENTARY SET in B (X1 , X3 , X9 ) 2 1 3
(X2 , X7 , X10 ) 3 2 1
o For any element xi of U, the (X4) 2 2 3
EQUIVALENCE CLASS of R (X5 , X8 ) 1 1 4
containing xi in relation Ind (B) will (X6) 1 1 2
be denoted by [Xi] ind B (X7) 3 2 1


Rough set

Lower Approximation
LX = { xi ∈ U [ xi ] ind ( B ) ⊂ X }
Equivalence classes

Upper Approximation
{
UX = xi ∈ U [ xi ] ind ( B ) ∩ X ≠ ∅ }
Boundary Region
BX = UX − LX
Accuracy If BX = ∅ then the set X is Crisp
µ B ( X ) = card ( LX ) / card (UX ) If BX ≠ ∅ then the set X is
Intelligent analysis for historical macroseismic damage scenarios Rough

Rough set
Rough membership
In order to have an idea about how much an object x belongs
to X we define rough membership.
[ xi ] ind ( B ) ∩ X
µ ind ( B )
→ [0,1] and µ
( x) : U  ind ( B )
( x) =
X X
[ xi ] ind ( B )
The rough membership function quantifies the
degree of relative overlap between the set X and
the equivalence class to which x belongs.


Rough set
Reducts
A reduct eliminate redundant attributes
A reduct is a minimal set of attributes (from the
whole attributes set) that preserves the
partitioning of the of U and therefore the original
classes.


Rough set
Reducts
Color Size Shape Accept
x1 G Small Square Yes
x2 B Medium Triangular No
x3 R Small Rectangular No
x4 G Medium Rectangular Yes
x5 G Small Square Yes
x6 Y Large Round No
x7 Y Medium Triangular Yes
x8 B Medium Triangular No

Rough set
U = {x1, x2, x3, x4, x5, x6, x7, x8}

A = {color, size, shape}
color(green, blue, red, yellow)
size(small, large, medium)
shape(square, round, triangular, rectangular)

U/color = {(x1, x4, x5), (x2, x8), (x3), (x6, x7)}

U/size = {(x1, x3, x5), (x6), (x2, x4, x7 , x8)}

U/shape = {(x , x ), (x ), (x , x , x8), Workshop x4 )} June 2009, Palermo, Italy
(x3 , 2009) 18-20
Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Maria Danese,
Cinzia Zotta, Lucia Tilio, Beniamino Murgante 6
1 5 2 7

Rough set
U/IND(A) = {(x1, x5), (x2, x8), (x3), (x4), (x6), (x7)}

U/ IND(A –{color}) = {(x1, x5), (x2, x7 , x8), (x3), (x4) (x6)} ≠
U/IND(A)

U/ IND(A –{size}) = {(x1, x5), (x2, x8), (x3), (x4), (x6), (x7)}
= U/IND(A)

U/ IND(A –{shape}) = {(x1, x5), (x2, x8), (x3), (x4), (x6), (x7)}
= U/IND(A)

RED(A) = {(color, size), (color, shape)}

CORE(A) = {color}

Case Study

Rapolla

Earthquake 1930

Buildings damage
survey 738

Attributes 37

Which relationship
between damage and
reconstruction

Case Study


Case Study
GENERAL DATA AND TECHNICAL REPORT

N. fascicle N. tech. report Owner Synthetic cadastral data

Busta Fasc Ditta Partita Mappale

Address Indirizzo

Neighbours Confini dell'immobile

Neighbouring parcels Particelle confinanti urban rural
b
Contractor Impresa Public building YES NO

DETAILED CADASTRAL DATA Plans Sections
YES NO YES NO
Parcel sub U G IF IIF Cadastral rent Floors

Form used in order to record
Mappale sub Sott PT IP IIP Imponibile fabbr
U GF 1F 2F 3F

Revocation of housing subsidies
Expiry
YES NO
Works carried out by
national government
and to analyse the
documentary data
Imponibile totale fabbr YES NO

MAIN TECHNICAL REPORT Supplementary technical report

Date Cost Decree PP N
N
pp DATA PP imp Proposto: Date PP DMLP data Date PS data
N. PP DMLP N Cost: PS importo

TEST (acceptance of work) CC data Property value Valore immobile Supplementary subsidy
Work time Stoppage Work costs
Date: PSS data
From Inizio lavori From Sospensione dal CC imp1
Cost : PSS importo
To Fine lavori To Sospensione al

Ministry comunication Prize for quick execution works % PA percent DAMAGE

Total cost CM approvato Date Data richiesta ditta Direct

Date CM data1 USGCM date Data proposta Genio YES NO
Subsidy CM sussidio Year income Reddito annuo

Date CM data2 Concession date Data concessione Ministero

NOTES
Note


Case Study
a lot of information
about reconstruction

budget amount,
effective expense,
presence of some interventions,
building value,
annual income
and so on…

Case Study
Data concerning information about the damage, the post-seismic
repairing procedures with buildings techniques description of the
housing units and technical-economic-administrative data.
Building ID Start Work Date
Reference – Map End Work Date
Reference – Envelope Real estate values of Building
Reference – Folder Owner Annual Income
Reference – Street Adoption of tie-beam
Building demolition Roof rebuilding
Public Building Cracks rebuilding
Religious Building Test date
Withdrawn subvention Estimated costs of works
Assessment of damage Date Costs of works accounted
Costs of works Effectively Funded

Case Study

Walls demolition
Floors demolition
Vault demolition
New wall
New Floors
Toothing projects
Shearing stress of masonry (technical procedure for walls
rebuilding)
Cuci-Scuci (technical procedure for walls rebuilding)
Damage description
Declared Destroyed (if the building was damaged and
declared not reconstructable)
Damage class EMS
Presence of caves under the building

Case Study

} CONDITIONAL
PART

} ASSIGNMENT


Case Study
There is a certain number of rules (25/88) that present a
clear discrepancy into damage level attribution:

The analysis permits the identification of such discrepancy
and a possible interpretation: differences in damage
distribution are not spatially clusterized, but they concerns
areas having different social and building features (rich and
poor owners, big and small housing, building well preserved and
lacking of maintenance ect.)


Case Study
Changes in damage classification seem not to be due to
voluntary human influences (e.g. acquaintance with
technicians to get increase of damage attribution by
favoritism) rather differences may be imputable to other
factors, among which:

o Rough initial inspection of buildings (e.g. only some rooms
were surveyed, damage assessment was carried out from
outside of buildings).

o Different vocational training of engineers entrusted to
survey affected housing units.


Case Study

o Feature of damage description: during initial post-seismic
phases, report of damage included improvements and/or
extension works unrelated to the seismic event.

o Incompleteness of descriptive data:
administrative/technical parametric information on which
the rules are based on, sometimes supply more constraints
of some very concise description of effects given by the
engineer surveys.


Future developments
New study area

It is known that during
an earthquake the
damage to buildings
with comparable
features can differ
enormously between
points.
In a wider area it could
be interesting to
analyze also effects
of geological surface.

Future developments

Compare Rough Set results with other intelligent methods
using Visual Analytics:

o Multiform Bivariate Matrix

o Self-Organising Map (SOM)

o Parallel Coordinates Plot (PCP)


Intelligent analysis for historical macroseismic damage scenarios Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Maria Danese, Cinzia Zotta - Archaeological and monumental heritage institute, National Research Council, Potenza (Italy), Lucia Tilio,

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Intelligent analysis for historical macroseismic damage scenarios Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Maria Danese, Cinzia Zotta - Archaeological and monumental heritage institute, National Research Council, Potenza (Italy), Lucia Tilio,