Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Cinzia Zotta, Assessing macroseismic data Assessing macroseismic data iability through Rough Set Theor iability through Rough Set Theor case of Rapolla case of Rapolla (Basilicata, southe (Basilicata, southe Italy) 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) - Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Cinzia Zotta, Lucia Tilio, Maria Danese, Beniamino Murgante
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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.
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
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.
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
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
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
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
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
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
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
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
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
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
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
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.
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
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.
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
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
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
Rough SetRough Set
U = {x1, x2, x3, x4, x5, x6, x7, x8}
A = {color, size, shape} color(green, blue, red, yellow)
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
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
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
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
Study CaseStudy Case
Earthquake 1930
Buildings damage survey 738
Attributes 37
Which relationship between damage
and reconstruction ?
Rapolla
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
Study CaseStudy CaseEU
RO
PEA
N M
AC
RO
SEIS
MIC
S
CA
LE
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
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
Study CaseStudy Case
a lot of information about
reconstruction…
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
Study CaseStudy Case
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
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
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
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
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.
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
Study CaseStudy Case
}CONDITIONAL PART
ASSIGNMENT}IF attribute1 ….. AND IF attribute2…. AND IF…
THEN decision attribute is …
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
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
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
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
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
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
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
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
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
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.)
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
Study Case: rules interpretationStudy Case: rules interpretation
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”
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
Study Case: rules interpretationStudy Case: rules interpretation
Clear discrepancy into damage level
attribution:
Here, the cases of doubt between
d3 and d2EXAMPLE: Rule 40
IF “valimm<1” AND “intcopertu in [0, dem/ric]” AND “scucicuci=si” AND “demsolai=0” AND “durlav<28”THEN
“danno_ems=d2”
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
Study Case: rules interpretationStudy Case: rules interpretation
Clear discrepancy into damage level
attribution:
Here, the cases of doubt between
d4 and d2EXAMPLE: Rule 79
IF “nuovisolai=travi_acc/tav” AND “scucicuci=0” AND “durlav>=102”THEN “danno_ems=d4”
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
Study Case: rules interpretationStudy Case: rules interpretation
Clear discrepancy into damage level
attribution:
Here, the cases of doubt between
d4 and d3EXAMPLE: Rule 67
IF “impper>=5” AND “impcont=[2,4]” AND “durlav<34”THEN “danno_ems=d4”
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
Study Case: rules interpretationStudy Case: rules interpretation
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?
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
Study Case: rules interpretationStudy Case: rules interpretation
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.
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
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
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
A step towards future A step towards future development…development…
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
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
A step towards future A step towards future development…development…
Preliminary results:Interpretation of rules
producing an overestimation and an underestimation of damage level in
Ripacandida
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
A step towards future A step towards future development…development…
Preliminary results:Interpretation of rules
producing an overestimation and an underestimation of damage level in
Rionero
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
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.
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
Future developmentFuture development
Compare Rough Set results with other intelligent methods using Visual Analytics: