Title: Damage Identification of Structures Based on Pattern Classification Using Limited Number of Sensors

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1 Cover page Title: Damage Idetificatio of Structures Based o Patter Classificatio Usig Limited Number of Sesors Authors: Yuyi QIAN Akira MITA PAPER DEADLINE: **JULY, ** PAPER LENGTH: **8 PAGES MAXIMUM ** SEND PAPER TO: Professor Fu-Kuo Chag Orgaizig Chairma Aeroautics ad Astroautics Departmet Staford Uiversity Durad Buildig Room Staford, Califoria 9, U.S.A. Tel: 6/7-66 Fax: 6/ fkchag@staford.edu NOTE: Sample guidelies are show with the correct margis. Follow the style from these guidelies for your page format. Pages ca be output o a high-grade white bod paper with adherece to the specified -- margis (8/ x ich paper. Adjust outside margis if usig A paper). Please umber your pages i light pecil or o-photo blue pecil at the bottom.

2 ABSTRACT This paper proposes a odestructive testig techique based o modal aalysis i order to develop a ew, efficiet ad simple damage detectio method for civil structures. Structural idetificatio for health moitorig ivolves compariso of chages i structural properties or respose, ad it ca be viewed as patter classificatio problems. However, a very large database is required to store traiig data for complicated damage cases if o techique to reduce the size is used. This paper presets a approach with the purpose of usig the least possible sesors. The structural damage locatio ad damage extet are idetified respectively by two differet methods of patter classificatio, that are, the Parze-widow method for the structural damage locatio firstly ad the feed-forward back-propagatio eural etwork used to idetify damage extet secodly. The results of umerical simulatios show that our proposed approach ca ideed idetify the structural damage usig small umber of sesors. Fially, a series of vibratio experimets for a -story shear frame structure were performed to verify the performace of our proposed approach.. INTRODUCTION Structural health moitorig (SHM) has received great attetio ad iterest to predict the oset of damage ad deterioratio of buildig structures because of icreased umber of aged buildigs ad upredictable atural hazard. I geeral, structural idetificatio for health moitorig ivolves the compariso of the chages i structural properties or respose, ad it ca be viewed as a patter classificatio problem. The amout of literature usig statistical discrimiatio of features for damage detectio is quite large. Cawley & Adams (979) proposed the very first damage detectio method usig the patter matchig approach []. A study by Masi et al. (99) has demostrated that eural etworks (NNs) are a powerful tool for the Departmet of System Desig Egieerig, Keio Uiversity, -- Hiyoshi, Kohoku-ku, Yokohama -8, Japa

3 idetificatio of system typically ecoutered i the structural dyamics fields []. Faravelli ad Pisao (997) made use of a feed-forward eural etwork to detect ad locate damage i a umerical simulatio of a two-dimesioal ie-bay truss structure []. Vaik et al. () preseted a Bayesia probabilistic methodology for structural health moitorig which uses a sequece of idetified modal parameter data sets to compute the probability that cotiually updated model stiffess parameters are less tha a specified fractio of the correspodig iitial model stiffess parameters []. Krawczuk et al. () applied a geetic algorithm (GA) to idetify ad locate damage i a lamiated composite beam []. A method usig the support vector machie (SVM) to detect local damages i a buildig structure was proposed by Mita ad Hagiwara () [6]. The fudametal idea of the patter classificatio approach is to use traiig data to determie the classifier referred to as traiig the classifier ad accordig to the classifier to evaluate the category of the test data. However, a very large database is required to store traiig data for as may damage cases as oe may wish to cosider. I geeral, damage cases of sigle-damage ad multiple-damage with differet ad/or the same damage extets should be cosidered. This study presets a possible solutio for this problem by dividig the damage idetificatio process ito two steps. I the first step, oly damage locatio is idetificated while is igored so that umerous traiig data with respect to are ot required. The is idetified i the secod step durig which by virtue of havig kow damage locatio the traiig data associated with the other udamaged locatio eed ot be take ito cosideratio. The damage locatio is idetified i the first step usig Parze-widow approach, while the correspodig is estimated i the secod step usig feed-forward back-propagatio eural etworks.. DAMAGE LOCATION IDENTIFICATION USING PARZEN-WINDOW APPROACH Amog previous studies o patter classificatio methods applied to structural damage idetificatio, may studies treated the supervised learig uder the assumptio that the forms of the uderlyig desity fuctios were kow. For istace, Vaik et al. () assumed the probability desity fuctio to have the form of Gaussia distributio []. However, i practical patter classificatio problems for structural damage idetificatio this assumptio is doubtful. Especially for damage locatio idetificatio, it is difficult to estimate the desity fuctio of damage locatio to have ay form covictively. This study try to get out of this dilemma by applicatio of oparametric techiques that ca be used with arbitrary distributios ad without the assumptio that the forms of the uderlyig desities are kow.. Basis of Noparametric Techiques The basic ideas of oparametric techiques are very simple. It relies o the fact that the probability desity p (x) for a vector x i a regio R is give by

4 k p = V ( x) () where three coditios are required: limv lim k lim k = = = () Here, V is the volume of R, k the umber of samples fallig i R, ad the total umber of samples. There are two commo ways of obtaiig sequeces of regios that satisfy these coditios listed i Eq. (). Oe way is to shrik a iitial regio by specifyig the volume V as some fuctio of, such as V =. This is basically the Parze-widow method. The secod method is to specify k as some fuctio of, such as k =. Parze-Widow Apprach. This is the k -earest-eighbor estimate method. The Parze-widow approach to estimate probability desities ca be itroduced by temporarily assumig that the regio R is a d -dimesioal hypercube whose volume is give by d V = h () where h is the legth of a edge of that hypercube. We ca obtai a aalytic expressio for k, the umber of samples fallig i the hypercube, by defiig the followig widow fuctio: ( ) u ϕ u = j j =, K, d () otherwise Thus, ϕ ( u) defies a uit hypercube cetered at the origi. It follows that (( ) ) V cetered ϕ x x i h is equal to uity if x i falls withi the hypercube of volume at x, ad is zero otherwise. The umber of samples i this hypercube is therefore give by

5 k = i= x xi ϕ () h ad whe we substitute this ito Eq. () we obtai the estimate p x xi x ϕ (6) i= V h ( ) = I essece, the widow fuctio is beig used for iterpolatio---each sample cotributig to the estimate i accordace with its distace from x. The Parze-widow approach ca be implemeted as a eural etwork kow as a Probabilistic Neural Network (PNN) [7]. Suppose we wish to form a Parze estimate based o patters, each of which is d -dimesioal, radomly sampled from c classes. The PNN for this case cosists of d iput uits comprisig the iput layer, where each uit is coected to each of the patter uits; each patter uit is, i tur, coected to oe ad oly oe of the c category uits. The coectios from the iput to patter uits represet modifiable weights, which will be traied. Each category uit computes the sum of the patter uits coected to it.. Idetificatio of Damage Locatio Usig Parze-Widow Approach Based o Numerical Simulatio I this study, a -story shear frame structure show i Figure is cosidered as the object structure. The structural parameters of the structure are show i Table I. A PNN is created to implemet the Parze-widow approach. I this study, we use frequecy chage rates as damage features. The traiig data s damage states are sigle damage of %, % ad % i stiffess reductio for each story ad the healthy state whose total umber is 6. Ad the category is the umber of floor where the damage exists. We form a Parze-widow estimate based o 6 patters, each of which is -dimesioal, from classes. The PNN for this case show i Figure cosists of iput uits comprisig the iput layer, where each uit is coected to each of the 6 patter uits; each patter uit is, i tur, coected to oe ad oly oe of the m m m m m k k k k k TABLE I. STRUCTURAL PARAMETERS DOF Mass (kg) Stiffess (kn/m) Figure. Five-story structure

6 category ω ω ω ω ω patter iput x x x x x Figure. Probability Neural Network category uits. The coectios from the iput to patter uits represet modifiable weights, which will be traied by the traiig data. Each category uit computes the sum of the patter uits coected to it. We cosider a series of damage cases as the test patters. The first group cosists of sigle damage of % i stiffess reductio for each story. The umber of the patters is. The secod cotais double damage of % i stiffess reductio for each two stories. The total umber is. Each output uit sums the cotributios from all patter uits coected to it. The oliear fuctio is ( et ) σ e k, where σ is chose as. which determies the width of the effective Gaussia widow. The results of umerical simulatios are show i Figure ad Figure. Figure is the simulatio result of sigle damage of % i stiffess reductio for each story. Simulatio results show that usig Parze-Widow method damage locatio ca be accurately idetified. Figure is the simulatio result of double damage of % i stiffess reductio for each two stories. From the maximal two discrimiat fuctios, we ca determie the locatio of the damage floors. Usig Parze-Widow method damage locatio ca be idetified based o a relatively small quatity of traiig data from the maximal discrimiat fuctio. % sigle-damage. discrimiat fuctio floor umber Figure. Simulatio of sigle damage discrimiat fuctio % double-damage floor umber Figure. Simulatio of double damage

I this study the possibility of usig a Multilayer perceptro (MLP) etwork traied with the Back-propagatio Algorithm as a odestructive damage assessmet techique to quatify damage i buildig structures

7 . DAMAGE DEGREE IDENTIFICATION USING ARTIFICIAL NEURAL NETWORKS. Artificial Neural Networks (ANNs) NNs (Bishop, 99) have bee viewed as potetial saviour for solutio of difficult problems i damage locatio [8]. I this study the possibility of usig a Multilayer perceptro (MLP) etwork traied with the Back-propagatio Algorithm as a odestructive damage assessmet techique to quatify damage i buildig structures is ivestigated. Sice ANNs are provig to be a effective tool for patter recogitio, the basic idea is to trai a eural etwork with simulated values of modal parameters i order to recogize the behaviour of the damaged as well as the udamaged structure. Usig this traied etwork to measure modal parameters should iclude iformatio about damage states.. Numerical Simulatio of Damage Quatificatio Usig ANNs The same -story shear frame structure show i Figure, is used as the object structure. Based o the damage locatio kow before had, a three-layer eural etwork is costructed ad traied to idetify the of the structure. Frequecy chage rates are also used as damage features. The traiig data s damage states are sigle damage of %, %, %, % ad % i stiffess reductio at each damage story. The iput is -dimesioal frequecy chage rates ad the output is -dimasioal stiffess reductio at each floor. Because the damage locatio has already bee idetified by Parze-Widow methods, remaiig our target is to idetify the of the correspodig floor. The iput, hidde ad output layer icludes, ad euros for sigle damage, ad,, ad euros for double damage. We use Leveberg-Marquardt back-propagatio etwork traiig fuctio that updates weights ad bias values to improve the etwork. We cosider a series of damage cases as the test patters, the first of which is sigle damage of %, %, %, %, %, % i stiffess reductio for st floor ad o damage whose total umber is seve. Firstly the etwork was traied by the traiig data whose damage states are sigle damage at st floor. The the traied etwork ca be used to quatify the damage by iputtig frequecy chage rates. Similarly, we cosider the damage cases for the other four floors floor umber Figure. Simulatio of sigle damage Figure 7. Replace colums

8 % double-damage floor umber Figure 6. Simulatio of double damage The umerical simulatio results are show i Figure ad double damage simulatio results i Figure 6. All of these simulatio results show that usig ANNs ca be idetified ot oly for sigle-damage cases but also for multi-damage cases based o the ANNs usig relatively small umber of traiig data.. EXPERIMENTAL VERIFICATION A series of experimets were performed to verify the performace of our proposed approach. The model structure is depicted i Figure 7. The damage was itroduced by replacig colums by weak colums. By replacig two colums story, the story stiffess was reduced by %. The impulse loadig was geerated by a impulse hammer. The colums for the first floor were firstly replaced, the the secod floor, followed by third, fourth ad fifth story. The frequecies of healthy ad damaged structures were measured ad frequecy chage rates were calculated as feature vectors. discrimiat fuctio Figure 8. Damage Locatio Idetificatio floor umber damage at st floor damage at d floor damage at rd floor damage at th floor damage at th floor floor umber floor umber floor umber floor umber floor umber Figure 9. Damage degree idetificatio by ANNs

9 Usig the Parze-Widow approach the damage locatio ca be decided as i Figure 8. Ad the the stiffess reductio rates ca be idetified eve whe variety rate is iputted to the ANNs traied by simulated values i which some oise is icluded. The level of the oise is %. The results of idetificatio is show i Figure 9. Figure 8 shows that the damage locatios ca be decided accurately. I additio it ca be see from Figure 9 that the was also idetified correctly..concluding REMARKS The algorithm that ca be applied to idetify the structural damage icludig damage locatio ad damage extet was proposed. The algorithm uses oly small umber of traiig data. The structural damage locatio ad damage extet were idetified respectively by two differet methods of patter classificatio, that were, the Parze-widow method for the structural damage locatio ad the feed-forward back-propagatio eural etwork used to idetify. The results of umerical simulatios show that by our proposed approach the structural damage ca be quatitatively idetified. A series of vibratio experimets for a -story shear frame structure were coducted to verify the performace of our proposed approach. The results show that for shear buildigs, the ad extet ca be determied through usig the frequecy chage rates as feature vectors. REFERENCES. Cawley, P. & Adams, R. D The Locatio of Defects i Structures from Measuremets of Natural Frequecies, Joural of Vibratio ad Acoustics (): 9-7. Masi, S. F. et al. 99. Idetificatio of Noliear Dyamic System Usig Neural Networks., Joural of Applied Mechaics., Tras., ASME, 6:-. Faravelli, L. & Pisao, A.A Damage Assessmet Toward Performace Cotrol. Structural Damage Assessmet Usig Advaced Sigal Processig Procedures, Proceedigs of DAMAS 97, Uiversity of Sheffield, UK: Vaik, M. W. et al.. Bayesia Probabilistic Approach to Structural Health Moitorig, Joural of Egieerig Mechaics 6(7): Krawczuk, M. et al.. Detectio of Delamiatios i Catilevered Beams Usig Soft Computig Methods, Europea COST F Coferece o System Idetificatio ad Structural Health Moitorig, Madrid, Spai: - 6. Mita, A. & Hagiwara, H.. Damage Diagosis of a Buildig Structure Usig Support Vector Machie ad Modal Frequecy Patters, Smart Structures ad Materials : Smart Systems ad NDE for Civil Ifrastructures, Vol.7:8-7. Duda R. O. et al.. Patter Classificatio, d Editio. New York: Joh Wiley & Sos, USA 8. Bishop, C. M. 99. Neural Networks ad their Applicatios, Review of Scietific Istrumetatio 6(6): 8-8

Pattern Classification, Ch4 (Part 1)

Pattern Classification, Ch4 (Part 1) Patter Classificatio All materials i these slides were take from Patter Classificatio (2d ed) by R O Duda, P E Hart ad D G Stork, Joh Wiley & Sos, 2000 with the permissio of the authors ad the publisher