Assessing macroseismic data -

Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Cinzia Zotta,

Assessing macroseismic data Assessing macroseismic data reliability through Rough Set Theory: reliability through Rough Set Theory:

the case of Rapolla the case of Rapolla (Basilicata, southern Italy)(Basilicata, southern Italy)

Laboratory of Urban and Territorial Systems, University of Basilicata, Italy

Lucia Tilio, Maria Danese, Beniamino Murgante

Archaeological and monumental heritage institute, National Research Council, Italy

Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy),F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante

International Conference on Computational Science and Its Applications

March 23 – 26, Fukoka, Japan

IntroductionIntroduction

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.




IntroductionIntroduction

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 SetRough Set

A) (U, IS

4 ,3,2, 1V

2, 1V

3,2, 1V

3

2

1

attribute) of (domain set value V Aa a

Let U be a nonempty finite set of objects called the universe

Let A be a nonempty finite set of attributes

nxxxxxxx ,...,......... , , , ,,U 654321

3 2 1 ,, A AAA




Rough SetRough Set

function ninformatio V U:f aa

U a1 a2 a3

x1 2 1 3

X2 3 2 1

X3 2 1 3

X4 2 2 3

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 SetRough Set

U a1 a2 a3 d1

x1 2 1 3 1

X2 3 2 1 4

X3 2 1 3 5

X4 2 2 3 2

X5 1 1 4 2

X6 1 1 2 4

X7 3 2 1 1

X8 1 1 4 2

X9 2 1 3 3

x10 3 2 1 2

A decision system is an information system in which the values of a special decision attribute classify the cases

Attributes lConditiona

d-A attributes other a

Ad )A (U, DS d




Rough SetRough Set

(B) Ind AB

Bb )b()b( (B) Ind are e jiji xxxx

o The equivalence class of Ind (B) The equivalence class of Ind (B) is called ELEMENTARY SETis called ELEMENTARY SET in Bin B

o For any element xi of U, the EQUIVALENCE CLASSEQUIVALENCE CLASS of R containing xi in relation Ind (B) will be denoted by [Xi] ind B

U/A a1 a2 a3

(X1 , X3 , X9 ) 2 1 3

(X2 , X7 , X10 ) 3 2 1

(X4) 2 2 3

(X5 , X8 ) 1 1 4

(X6) 1 1 2

(X7) 3 2 1




Rough SetRough Set

)( XxUxLX Bindii

LXUXBX

)( XxUxUX Bindii

Equivalence classes

Lower Approximation

Upper Approximation

Boundary Region

)(/)()( UXcardLXcardXB If BX = then the set X is

Crisp If BX ≠ then the set X is

Rough

Accuracy




Rough SetRough Set

In order to have an idea about how much an object x belongs to X we define rough membership.

)(

)()()(

)( and [0,1] : )(Bindi

BindiBindX

BindX

x

XxxUx

The rough membership function quantifies the degree of relative overlap between the set X and the equivalence class to which x belongs.




Rough SetRough Set

A reduct eliminate redundant attributesA 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 SetRough Set

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 SetRough 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 = {(x1, x5), (x6), (x2, x7 , x8), (x3 , x4 )}




Rough SetRough 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}




Rough SetRough SetRough Set Analysis allows to identify patterns and to extract

relations, identifying cause-effect relations. Identified patterns are

represented through a decisional rule set, where rules are

expressed in the “if…then” form. Objects are assigned to a decision

class if it satisfies the conditions of an identified rule; rule strength

is determined by number of objects satisfying that condition; at the

same time, this number of points also gives a measure of

uncertainty into decision class assignment.IF attribute1 ….. AND IF attribute2…. AND IF…

THEN decision attribute is …

Rules can be exact, when they are characterized by an univocal consequence, and supported only by objects from the lower approximation

of the corresponding decision class, or approximate, when they are characterized by not univocal consequence, and supported only by objects

from the boundaries of the corresponding decision class




Study CaseStudy Case

Earthquake 1930

Buildings damage survey 738

Attributes 37

Which relationship between damage

and reconstruction ?

Rapolla




Study CaseStudy CaseEU

RO

PEA

N M

AC

RO

SEIS

MIC

S

CA

LE





Busta Fasc Ditta

Owner

Partita

Synthetic cadastral data

Mappale

IndirizzoAddress

Confini dell'immobileNeighbours

ImpresaContractor

Mappale

Parcel

sub

sub

Sott

U

PT

G

IP

IF

IIP

IIFYES NO

Plans

U GF 1F 2F

Floors

YES NO

SectionsDETAILED CADASTRAL DATA

YES NO

Expiry

YES NO

Works carried out bynational government

Revocation of housing subsidies

MAIN TECHNICAL REPORT

pp DATA

Date

Inizio lavori

Fine lavori

PP imp Proposto: PP DMLP data

PP DMLP N

Date

N.

Cost Decree

Supplementary technical report

PS data

PS importo

Date

Cost:

Supplementary subsidy

PSS data

PSS importo

Date:

Cost :

TEST (acceptance of work) CC data

CC imp1

Work time

From

To

Work costs

Ministry comunication

Total cost

Date

CM approvato

CM data1

CM sussidio

CM data2

Subsidy

Date

Prize for quick execution works

Date

USGCM date

Year income

Concession date

Data richiesta ditta

Data proposta Genio

Reddito annuo

Data concessione Ministero

DAMAGE

Direct

YES NO

NOTESNote

PP NN

PA percent%

Valore immobileProperty value

Imponibile fabbr

Cadastral rent

Imponibile totale fabbr

Particelle confinantiNeighbouring parcels urban rural

Sospensione dal

Sospensione al

From

To

Stoppage

YES NOPublic buildingb

GENERAL DATA AND TECHNICAL REPORT

N. fascicle N. tech. report

Form used in order to record

and to analyse the documentary data

SURVEYS BASED ON FORM





a lot of information about

reconstruction…





Building IDReference (map, envelope, ...)Building demolitionType of Building (religious,public...)Withdrawn subventionCosts of works Effectively FundedCosts of works accountedEstimated costs of works

Start and End Work DateReal estate values of Building Owner Annual Income

Data concerning information about the damage, the post-seismic repairing

procedures with buildings techniques description of the housing units and

technical-economic-administrative data.

What kind of information?

Walls demolition Floors demolitionVault demolitionNew wallNew Floors Toothing projectsShearing stress of masonryCuci-ScuciDamage description Declared DestroyedDamage class EMS

Adoption of tie-beamRoof rebuilding Cracks rebuilding Test date




Study Case – the analysis Study Case – the analysis

Decision

Attribute

Quality of

classification# of Atoms # of Reducts

# of

attribute

s in Core

Analysis 0

DANNO

EMS

0,2665 189 1 17

Analysis 1 0,3887 287 8 9

Analysis 2 0,3874 281 12 4

Analysis 3 0,7084 264 12 8

Analysis 4 0,7411 276 1 9

Analysis 5 0,7057 265 2 8

Rapolla Number of Really analyzed

buildings 728 316

attributes 29 16

RES

ULTS

Six analysis, testing different

datasets, in order to

increase quality of classification

Decision Attribute Quality of classification # of Atoms # of Reducts# of attributes in

Core

Analysis 5 DANNO EMS 0,7057 265 2 8




Study Case – the analysis Study Case – the analysis

Quotient of cardinalities of all lower

approximation of the classes in which the

object set is classified and the cardinality of

the object set

It is determined by application of indiscernibility

relation. Atoms are the elementary

sets.





}CONDITIONAL PART

ASSIGNMENT}IF attribute1 ….. AND IF attribute2…. AND IF…

THEN decision attribute is …




Study Case: rules readingStudy Case: rules readingR

ULE

S M

APPED

ON

GIS

AN

D G

RO

UPED

A

CC

OR

DIN

G T

O D

AM

AG

E

CLA

SSIF

ICA

TIO

N





ULE

S M

APPED

ON

GIS

AN

D G

RO

UPED

A

CC

OR

DIN

G T

O D

AM

AG

E

CLA

SSIF

ICA

TIO

N





ULE

S M

APPED

ON

GIS

AN

D G

RO

UPED

A

CC

OR

DIN

G T

O D

AM

AG

E

CLA

SSIF

ICA

TIO

N





ULE

S M

APPED

ON

GIS

AN

D G

RO

UPED

A

CC

OR

DIN

G T

O D

AM

AG

E

CLA

SSIF

ICA

TIO

N




Study Case: rules interpretationStudy Case: rules interpretation

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.)





Clear discrepancy into damage level

attribution:

Here, the cases of doubt between

d2 and d3EXAMPLE: Rule 13

IF “impcont<3” AND “imprev<3” AND “valimm<4”…THEN “danno_ems=d2”






attribution:



IF “valimm<1” AND “intcopertu in [0, dem/ric]” AND “scucicuci=si” AND “demsolai=0” AND “durlav<28”THEN

“danno_ems=d2”






attribution:



IF “nuovisolai=travi_acc/tav” AND “scucicuci=0” AND “durlav>=102”THEN “danno_ems=d4”






attribution:



IF “impper>=5” AND “impcont=[2,4]” AND “durlav<34”THEN “danno_ems=d4”





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:

Why discrepancy in damage level attribution?





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.

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.

o Occurrence of aftershocks.




A step towards future A step towards future development…development…

TOWN Number of buildings

Buildings really analyzed

Melfi 2256 1190

Rapolla 728 316

Rionero 3373 1213

Ripacandida 754 374

San Fele 1200 175

New study area





Preliminary results:

# of buildings

# of analysed buildings

Quality ofclassificatio

n

Number of

Atoms

Number ofReducts

# Attributes

in Core# of Rules

# of ExactRules

# of Approximate Rules

Melfi 2256 1190 0.4538 557 1 4 270 207 63

Rapolla 728 316 0.7057 235 1 7 111 99 12

Rionero 3373 1213 0.4361 585 1 4 340 252 88

Ripacandida 754 374 0.7406 279 1 7 99 89 10

San Fele 1200 175 0.7371 75 1 5 37 31 6





Preliminary results:Interpretation of rules

producing an overestimation and an underestimation of damage level in

Ripacandida





Preliminary results:Interpretation of rules

producing an overestimation and an underestimation of damage level in

Rionero




Future developmentFuture development

Further extension of 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 developmentFuture development

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)

Documents

Assessing macroseismic data -