The use of Artificial Neural Networks to estimate seismic damage and derive vulnerability functions for traditional masonry

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Frontiers of Structural and Civil Engineering CN 10-1023/X https://doi.org/10.1007/s11709-020-0623-6 ISSN 2095-2430 RESEARCH ARTICLE

The use of artificial neural networks to estimate seismic damage

and derive vulnerability functions for traditional masonry

Tiago Miguel FERREIRAa*, João ESTÊVÃOb, Rui MAIOc, Romeu VICENTEc a

ISISE, Institute of Science and Innovation for Bio-Sustainability (IB-S), Department of Civil Engineering, University of Minho, Guimarães 4800-058, Portugal

b

Department of Civil Engineering, University of Algarve, Faro 8005-139, Portugal c

RISCO, Department of Civil Engineering, University of Aveiro, Aveiro 3810-193, Portugal *Corresponding author. E-mail: [email protected]

Front. Struct. Civ. Eng., Just Accepted Manuscript • https://doi.org/10.1007/s11709-020-0623-6

http://journal.hep.com.cn on Apr 19, 2020

Just Accepted This is a “Just Accepted” manuscript, which has been examined by the peer‐review process and has been accepted for publication. A “Just Accepted” manuscript is published online shortly after its acceptance, which is prior to technical editing and formatting and author proofing. Higher Education Press (HEP) provides “Just Accepted” as an optional and free service which allows authors to make their results available to the research community as soon as possible after acceptance. After a manuscript has been technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an Online First article. Please note that technical editing may introduce minor changes to the manuscript text and/or graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event shall HEP be held responsible for errors or consequences arising from the use of any information contained in these “Just Accepted” manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI(r)), which is identical for all formats of publication.”

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Verso: Front. Struct. Civ. Eng. 2020

Recto:Tiago Miguel FERREIRA et al. Damage and vulnerability analysis based on ANNs Front. Struct. Civ. Eng. 2020

RESEARCH ARTICLE

https://doi.org/10.1007/s11709-020-0623-6

The use of artificial neural networks to estimate seismic damage

and derive vulnerability functions for traditional masonry

Tiago Miguel FERREIRAa*_{, João ESTÊVÃO}b_{, Rui MAIO}c_{, Romeu VICENTE}c

a_{ISISE, Institute of Science and Innovation for Bio-Sustainability (IB-S), Department of Civil Engineering,} University of Minho, Guimarães4800-058, Portugal

b_{Department of Civil Engineering, University of Algarve, Faro8005-139, Portugal}

c_{RISCO, Department of Civil Engineering, University of Aveiro, Aveiro3810-193, Portugal} *Corresponding author. E-mail: [email protected]

ABSTRACTThis paper discusses the adoption of Artificial Intelligence-based techniques to estimate seismic damage, not with the goal of replacing existing approaches, but as a mean to improve the precision of

empirical methods. For such, damage data collected in the aftermath of the 1998 Azores earthquake (Portugal) is used to develop a comparative analysis between damage grades obtained resorting to a classic damage formulation and an innovative approach based on Artificial Neural Networks (ANNs). The analysis is carried out on the basis of a vulnerability index computed with a hybrid seismic vulnerability assessment methodology, which is subsequently used as input to both approaches. The results obtained are then compared with real post-earthquake damage observation and critically discussed taking into account the level of adjustment achieved by each approach. Finally, a computer routine that uses the ANN as an approximation function is develop and applied to derive a new vulnerability curve expression. In general terms, the ANN developed in this study allowed to obtain much better approximations than those achieved with the original vulnerability approach, which has revealed to be quite non-conservative. Similarly, the proposed vulnerability curve expression was found to provide a more accurate damage prediction than the traditional analytical expressions.

KEYWORDSArtificial Neural Networks, seismic vulnerability, masonry buildings, damage estimation, vulnerability curves

1 Introduction

Large-scale seismic vulnerability assessment methods are often based on a few empirical-based parameters defined through the statistical analysis of large sets of post-earthquake damage data [1], and normally uses simplified expressions, which are very easy to implement in Geographical Information Systems (GIS software), being a worldwide adopted approach. Some of these methods have been reviewed and discussed in depth in recent review articles [2,3]. However, the inability of traditional statistical methods to handle missing or noisy data, as well as to manage nonlinearities and to identify certain behavior patterns, opens up space to the use of innovative computer-based solutions. In the last couple of years, the use of Artificial Neural Networks (ANNs) is becoming increasingly popular in many civil engineering applications [4–6], namely in the field of

earthquake engineering [4–17]. Traditionally, ANNs are used as “black boxes” to obtain a problem solution without a clear understanding about the mathematical relations between the inputs and the outputs, which are often considered as being a handicap for engineering purposes. Moreover, as discussed by Estêvão [18], the precision of the results obtained from ANNs-based approaches is very dependent on the dimension of training data set required, which often makes it impossible to use this kind of techniques when only small data sets are available. Trying to overcome this issue and taking the best of these two important group of approaches, a simplified large-scale seismic vulnerability assessment approach and an ANN are used together. It is worth noting that the ANN is used herein, not only to obtain a problem solution, as usual, but also as a guiding line function to develop a new simplified vulnerability curve expression with a good approximation to the observed damage data. Despite not solving the above mentioned “black box” problem, using the proposed approach opens the possibility of deducing new simplified expressions using the well-known mapping capabilities of ANNs to better correlate input and output variables. For such, a set of computer routines were developed to find an expression that best fits the results of a Multi-layer Feed-Forward Neural Network (MFFNN), which

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https://doi.org/10.1007/s11709-020-0623-6

was previously trained with data obtained from a post-earthquake damage data set collected in the aftermath of the 9th of July 1998 Azores earthquake. A comparative analysis between the vulnerability functions derived from the application of a widely used seismic vulnerability assessment approach and an approach based on the use of ANNs was carried out to understand how capable an ANN is to find a problem solution, even when using a low number of training sets. This comparative analysis was carried out by evaluating the relative deviations between observed damage and the damage estimated by both approaches. Results shows that the ANN solutions are more accurate than the ones obtained with traditional approaches. Moreover, it was also possible to develop a computer routine that uses the ANN as an approximation function, which led to another simplified expression, yet with almost the same precision obtained with the ANN. More than simply deducing a new simplified expression, which domain of validation is obviously limited to Azores and just for the effect of a single earthquake, in this paper is presented a new approach for developing worldwide simplified expressions to describe vulnerability, namely if more data are used to train an ANN.

2 The earthquake of July 9, 1998

With a macroseismic intensity VII on the Modified Mercalli Intensity (MMI) scale [19], the July 9th 1998 Azores earthquake is considered one of the most destructive events in the recent seismic history of Portugal, having affected a total of more than 5,000 people, within which 8 fatalities, 150 injured and about 1500

homeless were reported [20]. Final estimates reported that about 70% of the building stock of Faial, Pico and S. Jorge islands was buffeted by this earthquake. From the technical and academic point of view, the 1998 event allowed to gather an unprecedented amount of good quality post-earthquake data concerning different variables related with the building stock, namely concerned to their main architectural and constructive features, damage report, and the costs associated with repair and/or retrofitting interventions. The database (hereinafter mentioned as “Faial database”) resulting from the 10-year reconstruction process of Faial Island, which was carried out under the supervision of the Society of Promotion for Housing and Infrastructures Rehabilitation (SPRHI), was gathered in 2007 by the Regional Secretariat for Housing and Equipment (SRHE) of Faial Island and subsequently assembled in the book edited by Oliveira et al. [21].

The quality and uniqueness of this database in both national and international context have encouraged the development of several advanced studies throughout the following years. Even though the authors were allowed to access the full database, a complementary field work was conducted to understand the evolution and the diachronic process resulting from rehabilitation interventions implemented since 1998 [21]. Zonno et al. [22] presented a proposal of a macroseismic intensity distribution map for the Faial island, which was constructed on the basis of the post-earthquake field survey and observation campaigns that followed the earthquake of July 9, 1998.

As referred in the introductory section, this extensive database was used in this work to compare the feasibility of the vulnerability function proposed by Bernardini et al. [23] with that resulting from an innovative approach based on the use of ANNs. Using as input data the same vulnerability parameters that compose the vulnerability index method, ANNs were trained to predict the damage grade for a given

macroseismic intensity, IEMS-98. The data set of 90 stone masonry buildings is distributed in Table 1 by the four observed macroseismic intensities mapped for the island of Faial (from IEMS-98 = V to VIII).

Table 1 Location and distribution of the assessed buildings considering the Macroseismic Intensity registered in situ

geographical location observed macroseismic intensity, IEMS-98

V VI VII VIII Angústias (7/90) _– 7 _– _– Castelo Branco (5/90) _– 4 1 _– Cedros (6/90) _– _– 4 2 Conceição (12/90) 7 5 _– _– Feteira (5/90) _– 5 _– _– Flamengos (5/90) _– _– 5 _–

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RESEARCH ARTICLE https://doi.org/10.1007/s11709-020-0623-6 Pedro Miguel (5/90) _– _– 5 _– Praia de Almoxarife (16/90) 5 1 10 _– Ribeirinha (8/90) _– _– _– 8 Salão (5/90) _– _– _– 5

number and percentage of

buildings per intensity 25 (27.8%) 25 (27.8%) 25 (27.8%) 15 (16.6%)

The traditional stone masonry buildings comprised in this sample are considered representative of the Azorean vernacular heritage, not only in terms of material and constructive technology, but also in terms of typology, which differs significantly depending on whether the building is located within a rural or an urban environment. The following Table 2 presents the distribution of these buildings by parish and the respective frequency in terms of observed discrete damage grades, Di, which are classified according to the European Macroseismic Scale, EMS-98 [24].

Table 2 Location and distribution of the assessed buildings considering their observed damage grades

geographical location observed damage grades, Di

no damage (D0) D1 D2 D3 D4 D5 Angústias (7/90) _– 7 _– _– _– _– Castelo Branco (5/90) _– 1 3 _– _– 1 Cedros (6/90) _– _– 3 3 _– _– Conceição (12/90) 1 4 5 2 _– _– Feteira (5/90) _– 2 1 1 1 _– Flamengos (5/90) _– _– 3 0 2 _– Matriz (16/90) 1 13 2 _– _– _– Pedro Miguel (5/90) _– _– _– _– 2 3 Praia de Almoxarife (16/90) 2 3 4 7 _– _– Ribeirinha (8/90) _– 1 _– 2 1 4 Salão (5/90) _– 1 1 1 _– 2

number and percentage of

buildings 4 (4.4%) 32 (35.6%) 22 (24.4%) 16 (17.8%) 6 (6.7%) 10 (11.1%)

As one can observe, about 60% of the considered buildings present a damage grade ranging between D1 and D2, which corresponds to “negligible” and “moderate damage,” 25% show a damage grade between D3 and D4, which corresponds to “substantial” to “very heavy damage,” and finally, about 11% present a damage grade D5, corresponding to a “total or near total collapse.” The remaining 4% don’t present any damage (D0).

3 The seismic vulnerability assessment approach

3.1 General formulation

The seismic vulnerability assessment approach used in this work was originally developed in Italy and has been successfully applied during the past 25 years in several research works all over the globe, particularly in Europe. Most recently, it was adapted and calibrated to the Portuguese masonry building stock reality by Vicente et al. [25] and Ferreira et al. [20], respectively. In conceptual terms, the methodology is based on the calculation of a vulnerability index that results from the weighted sum of the 14 evaluation parameters given in Table 3, each of which focused on a specific aspect related to the seismic response of the building.

Table 3 Vulnerability index parameters, classes and weights, adapted from [13].

parameters vulnerability class cvi weight,

wi

relative weight

A B C D

Group 1. structural building system P1 Type of resisting system 0 5 20 50 2.50 50/100 P2 Quality of resisting system 0 5 20 50 2.50

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P3 Conventional strength 0 5 20 50 1.00

P4 Maximum distance between

ll 0 5 20 50 0.50

P5 Number of floors 0 5 20 50 0.50

P6 Location and soil conditions 0 5 20 50 0.50 Group 2. irregularities and interactions P7 Aggregate position and

i t ti

0 5 20 50 1.50 20/100

P8 Plan configuration 0 5 20 50 0.50

P9 Height regularity 0 5 20 50 0.50

P10 Wall facade openings and

li t

0 5 20 50 0.50

Group 3. floor slabs and roofs P11 Horizontal diaphragms 0 5 20 50 0.75 18/100

P12 Roofing system 0 5 20 50 2.00

Group 4. conservation status and other

elements P13 Fragilities and conservation status 0 5 20 50 1.00 12/100

P14 Non-structural elements 0 5 20 50 0.75

As presented in Table 3, the 14 parameters that compose the method are distributed over 4 vulnerability classes, Cvi of growing vulnerability: A, B, C and D. Each class is associated to a weight, wi, that reflects the importance of that parameter in particular; ranging from 0.5 for the less important to a 1.5 for the most important. A complete discussion on the relative importance of each parameter can be found in Ref. [25].

Equation (1) gives the seismic vulnerability index associated to each building, ∗. The higher the

vulnerability index, the more vulnerable is the building. For ease of use, it is usually normalized to fall within the range of 0 to 100, assuming from that moment on the notation, .

∗ _∑ _. (1)

3.2 Damage estimation

Based on the above-presented vulnerability index formulation, mean damage grades, , can be estimated for different seismic hazard scenarios. To this end, an analytical expression that correlates macroseismic intensities with the mean damage grade, , of the damage distribution in terms of the vulnerability value, Iv, was proposed by Bernardini et al. [23]. Such formulation is expressed by Eqs. (2) and (3):

2.5 3 tanh _.. . , (2)

, , if 7

1 , if 7 (3)

where, IEMS-98 is the seismic hazard described in terms of Macroseismic Intensity [24], V is the vulnerability index used in the Macroseismic Method [26], given in Eq. (4), and f (V, IEMS-98) is a function depending on the vulnerability index and intensity, which was introduced in the expression to adjust the trend of the

vulnerability curves for the lower extremes of the macroseismic intensity grades, namely for IEMS-98 V. This expression was proposed within the framework of an innovative macroseismic approach allowing the

vulnerability analysis of building typologies defined according to the European Macroseismic Scale, EMS-98 [24], and relate it to its vulnerability classes. Moreover, this expression has been widely used and validated in literature, see for example [22].

0.592 0.0057 (4)

To simplify the interpretation of the mean damage grade value, , and to compare it with the discrete damage grades, Di, used in Section 2, these two descriptors can be indirectly correlated through a set of damage factors, DF, which represent the cost of returning a building to its original condition. To this purpose, a probabilistic distribution of damage, derived from the discretisation of the beta distribution defined within

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that no overfi al point (or g s also clear in d for each buil re, the averag arative terms N when comp e maximum r In statistical te n of 14.14. . Eng. 2020 RREIRA et al. D 2020 11709-020-062 distribution w nce found bet ce is lower tha has been done rability functi n Fig. 8.

damage grades of Fig. 9, one ugh the use o MS-98 = VIII), d fitting has occ group of point n the bar char lding assesse ge relative dev

, these values ared with tha relative devia erms, it was o Damage and vu 23-6 with quite a g tween observ an 5%. e in the previo ions derived b versus ANN-d e can observe of the ANN w depicted in F curred, since t ts) of the data rt presented in ed and for eac

viations rang s reflect the s at obtained wi ation obtained obtained a me ulnerability anal good precisio ed and estima ous Section 3 by the ANN f (a)(b) (c)(d) derived vulnerab that a very sa was achieved, ig. 8(c) and 8 the curves do a set. n Fig. 9(a), w ch macroseism ge from 1.4% ignificant im ith the traditi d with the AN ean relative d lysis based on A on. In fact, wi ated damage 3, the compar for macroseis bility functions atisfactory ag particularly 8(d), respectiv o not reveal a

where the rela mic intensity to 3.2%, re mprovement of onal vulnerab NN is also low deviation valu ANNs

ith the except was about 1

rison between smic intensiti

:(a) IEMS-98 = V

greement betw for the higher vely. Furtherm

particular ad

tive and the a are illustrated spectively, fo f the approxim bility index ap wer, falling fr ue of about 0. tion of discret 11%, for all o n observed me ies in the rang

; (b) IEMS-98 =V

ween the mea r macroseism more, it is als djustment to a average devia d. As one can or intensities mation achiev pproach, show rom about 55. .8%, with a s te damage D3 other damage ean damage ge of IEMS-98= VI; (c) IEMS-98 an damage mic intensities so possible to any ations n observe in

VIII and VI. ved through wn in Fig. .5% to tandard 3 = s o

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Verso: Fro Recto:Tia Front. Stru RESEARC https://doi The hi Fig. 9(b) found be (highligh values ob presented Fig. 9 R histogram

5 Prop

The fact somehow obtain th each mac o EMS the slope

ont. Struct. Civ go Miguel FER uct. Civ. Eng. 2 CH ARTICLE i.org/10.1007/s istogram and ), from where etween analyt hted in pink a btained with d in Fig. 9(b) Relative deviatio m with best-fit G

posal of

that the origi w resembles a he parameters croseismic in 98 , in Eq. (9 e of the sigmo . Eng. 2020 RREIRA et al. D 2020 11709-020-062 the best-fit n e it is possible tical and obse and light red)

the traditiona ) is characteri on between obs Gaussian curve.

a new an

inal formulati a sigmoid fun s that best fits ntensity. Then 9), which will oid function: Damage and vu 23-6 normal curve e to observe t erved damage , representing al vulnerabilit ized by a mea

erved and estim

nalytical

ion for estima nction (Eq. (7 s the ANN res n, the Least S l center the cu ulnerability anal resulting from that in about 8 e falls within g an improvem ty index appr an value of 0. (a) (b) mated damage, r

expressio

ating damage 7)), has led to sults. First, th quares Metho urve, and the

lysis based on A m the statistic 81% and 56% the range of ment of abou roach, present .80 and a stan resorting to the

on for da

e in traditiona the idea of p he inflection p od (LSM) wa function ANNs cal treatment % of the cases 20% and ut 22.2% and ted in Fig. 3( ndard deviatio

ANN: (a) for e

amage es

al masonry bu programming point of the c as applied to o , in E of this data a s, the relative 10%, respect 20% in relati (b). The distri on of 14.84. each building as

stimation

uildings, give a series of ro curve was ide

obtain the fun Eq. (10), whic are given in e deviation tively ion to the ibution ssessed; and (b)

n

en by Eq. (2), outines to ntified for nction ch will adjust ) t

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Verso: Fro Recto:Tia Front. Stru RESEARC https://doi As the expressio intensity where, given by The an macrosei character Fig. 10 A This c (11), not importan seismic d increase increase The fi Section 2 for macr between pink and As it i work, giv tradition 90 buildi

ont. Struct. Civ go Miguel FER uct. Civ. Eng. 2 CH ARTICLE i.org/10.1007/s e original exp on proposed h y, IEMS-98, and i y Eq. (12) whi nalytical vuln ismic intensit ristic “S-shap Analytical vuln configuration t only because nt, because th damage in ma of the level o for higher in inal comparis 2, and the new roseismic inte

observed and d light red, res is possible to ven by Eq. (1 al mean dam ings) the devi

. Eng. 2020 RREIRA et al. D 2020 11709-020-062 pression propo herein (Eq. (1 the vulnerab s a third-degr ich was also

nerability fun ties, IEMS-98. A ped” or sigmo nerability functi can be interp e it follows th he configurati asonry buildi of damage for ntensities (IEM son between t w analytical v ensities from d analytical d spectively. observe, the 11), presents a

age grade for iation found b Damage and vu 23-6 0 EMS 98 osed by Bern 11)) estimate bility index, Iv 1 ree polynomi obtained usin 0.109 nction obtaine As can be see oid curve.

ion for different preted as a go he same spati ion of the sigm ings: low leve

r the central i MS-98> X). the observed m vulnerability V to VIII. To damage is low analytical vu a better adjus rmulation exp between the a ulnerability anal 86.8 7 0.037 0.0 nardini et al. [ s the mean da v. tanh ial that define ng the LSM: 0.82 ed through Eq en in Fig. 10, t macroseismic ood indicator ial shape of th moid curve a els of damage intensities (V mean damage functions giv o simplify the wer than 20% ulnerability fu stment to the pressed by Eq analytical val lysis based on A .7 EMS 98 004 [23], in Eqs. ( amage grade, es the upper li 0.032 q. (11) is pres the resulting intensities. of the suitabi he original ex djusts very w e for lower in V <IEMS-98 ≤ X e grades, , ven by Eqs. (2 e analysis, the and 10% are unction derive observed dam q. (2). Actual lue, obtained ANNs (9) (10) (2) and (3), th , ì , as a func (11 imit of the vu 2 sented in Fig. vulnerability ility of the pa xpression, but well to the the

ntensities (IEM X), and final s

for the build 2) and (11), a e cases for wh e given in foll

ed through th mage than tha ly, only in 17 through Eq. he vulnerabili ction of the m 1) ulnerability fu (12) 10 for differ y function fol arameters defi t also, and mo eoretical prog MS-98 ≤ V), a su tabilization o

ding stock des are presented hich the devia lowing Fig. 1 he ANN devel at resorting to 7% of the cas (11), is highe ity curve macroseismic unction, ent llows a

fined for Eq. ore gression of udden of this scribed in in Fig. 11, ation found 11, colored in loped in this o the es (15 out of er than 20%, n

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whereas, in the case of the traditional mean damage grade formulation, in Eq. (2), that percentage increases to 41% (37 out of 90 buildings). Moreover, it is important to note that this better approximation is observed for all the macroseismic intensity spectrum, not only for certain subsets of its domain.

(a)

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https://doi.org/10.1007/s11709-020-0623-6

(c)

(d)

Fig. 11 Comparison between observed and estimated damage resorting to Eqs. (11) and (2) for macroseismic intensities: (a)

IEMS-98= V; (b) IEMS-98= VI; (c) IEMS-98 = VII; and (d) IEMS-98 = VIII.

Finally, Fig. 12 shows the vulnerability curves obtained with the new proposed analytical expression for different vulnerability index values, Iv.

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Verso: Fro Recto:Tia Front. Stru RESEARC https://doi Fig. 12 V

6 Fina

The pres tradition vulnerab data coll tradition through t from the In gen in the inp approxim vulnerab underest (D0 and D slight ten observed 5%. The an 3 for the ANN, w the ANN Finally expressio analyzed to the Az the resea might be possessio

ont. Struct. Civ go Miguel FER uct. Civ. Eng. 2 CH ARTICLE i.org/10.1007/s

Vulnerability cu

al remark

sent paper dis al masonry b bility index m lected after th al stone maso the referred a e ANN results neral terms, th put layer, 16 mations than t bility index-ba timate damag D5), the appro ndency to ove d and estimate nalysis of the vulnerability ith a mean re N was slightly y, when comp on, presented d. However, th zorean traditi arch process h e used to obta on of sufficie . Eng. 2020 RREIRA et al. D 2020 11709-020-062

urves for differ

ks

scusses the po buildings thro method and an he 1998 Azore onry building approaches. F s. he ANN adop AN in one hi those obtaine ased approach ge, particularly oximation ob erestimate the ed damage w e deviations fo y index metho elative deviati y lower than t pared to the o d in Eq. (11), his expressio onal masonry herein idealiz ain optimized ently large po Damage and vu 23-6 rent vulnerabilit otential of usi ugh the comp n innovative a es earthquake gs, which was Furthermore, pted in this st idden layer, a ed with the or h has reveale y for the extr btained with A e damage for was about 11 found between od and in Fig ion value of a that obtained original expre provides a m on cannot be s y building typ zed can be see d vulnerability ost-earthquake ulnerability anal ty index values ing alternativ parative analy approach base e was used to s then critical a new analyti tudy, a genera and one AN in riginal seismi ed to be quite reme upper an ANN was qui

damage grad %, for all oth

n analytical a g. 11 for the A

about 0.8% ag with the vuln ession of Bern much more acc

seen as a univ pology, but al en as a repres y functions fo e damage dat lysis based on A , Iv. e strategies to ysis of two di ed on the use o generate a d ly compared ical expressio al MFFNN co n the output l ic vulnerabilit non-conserv nd lower boun ite accurate. A de D3, for wh her damage g and observed ANN has conf gainst 16%. T nerability ind

nardini et al. curate predict versal alterna

lso to the eart sentative and or a specific b ta sets. ANNs o estimate sei ifferent appro of ANNs. Po data set of rea

with analytic on for damag omposed by t layer, allowed ty index appr ative, present nds of the me As discussed ich the differ rades such di damage, pres firmed the be The standard dex approach, [23], it is cle tion of damag ative, being na thquake of Ju compelling e building typol ismic damage oaches, a wid ost-earthquak al damage eva cal results obt e estimation w two artificial d to obtain m roach. In fact ting a tenden ean damage d in Section 4. rence found b ifferences are sented respec etter performa deviation obt 14.14 over 1 ear that the ne ge for the dat aturally limite uly 9, 1998. In example on h logy, whenev e in dely used ke damage aluation for tained was derived neurons (AN much better , whereas the cy to distributions 2, despite a between e lower than ctively in Fig. ance of the tained with 15.84. ew analytical ta set herein ed not only n any case, how ANN ver in the N) e .

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AcknowledgementsThis work was funded by the Portuguese Foundation for Science and Technology (FCT) through the postdoctoral Grant SFRH/BPD/122598/2016. The authors acknowledge to the Society of

Promotion for Housing and Infrastructures Rehabilitation (SPRHI) and to the Regional Secretariat for Housing and Equipment (SRHE) of Faial for their support and contribution to the development of this work. They would also like to express their gratitude to the anonymous reviewer for their insightful and constructive comments.

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