Jtam-A4.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 51, 4, pp. 1013-1026, Warsaw 2013 EXPERIMENTAL STUDY ON DAMAGE DETECTION OF BASE-ISOLATED STRUCTURE USING AN ADAPTIVE EXTENDED KALMAN FILTER Qiang Yin School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China e-mail: yinqiang@njust.edu.cn Li Zhou, Tengfei Mu State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China Jann N. Yang University of California, Department of Civil and Environmental Engineering, Irvine, USA In this paper, experimental studies are performed and presented to verify the capability of the adaptive extended Kalman filter (AEKF) approach for identifying and tracking dama- ges in nonlinear structures. A base-isolated building model consisting of a scaled building model mounted on a rubber-bearing isolation system has been tested experimentally in the laboratory. The non-linear behavior of the base isolators is represented by the Bouc-Wen model. To simulate the structural damages during the test, an innovative device, referred to as the stiffness element device (SED), is proposed to reduce the stiffness of the upper storey of the structure. Various damage scenarios have been simulated and tested. The measured acceleration response data and the AEKF approach are used to track the variation of the stiffness during the test. The tracking results for the stiffness variations correlate well with that of the referenced values. It is concluded that the AEKF approach is capable of trac- king the variation of structural parameters leading to the detection of damages in nonlinear structures. Key words: damage detection, adaptive extended Kalman filter, base-isolated structure 1. Introduction High damping rubber-bearing isolation systems have been used in buildings and bridges. These base isolation systems will become more popular in the future due to their ability to reduce significantly the structural responses subject to earthquakes and other dynamic loads (Naeim and Kelly, 1999; Komodromos, 2000; Narasimhan et al., 2006; Nagarajaiah et al., 2008). To ensure the integrity and safety of these base isolation systems, a structural health monitoring system should be developed. In this regard, analysis techniques for damage identification of structures, based on vibration datameasured from sensors, have received considerable attention. Various approaches to system identification and damage detection have been proposed in the literature, such as the least-square estimation (LSE) (Loh et al., 2000; Lin et al., 2001; Yang et al., 2007), the extended Kalman filter (EKF) (Hoshiya and Saito, 1984; Sato et al., 2001; Yang et al., 2006; Zhou et al., 2008; Yin et al., 2012), unscented Kalman filter (UKF) (Wu and Smyth, 2008), sequential non-linear least-square estimation (SNLSE) (Huang and Yang, 2008), quadratic sum-squares error (QSSE) (Yang et al., 2009), Monte Carlo filter (Sato and Chung, 2005), wavelet multiresolution technique (Chang and Shi, 2010), and others (e.g., Ching et al., 2006; Yin and Zhou, 2006). In these techniques mentioned above, an adaptive tracking technique has been proposed for tracking the time-varying parameters on-line (e.g., Zhou et al., 2008; Huang and Yang, 2008; Yang et al., 2009). Simulation results demonstrate that this 1014 Q. Yin et al. adaptive EKF approach (AEKF) is capable of tracking the variations of structural parameters, such as the degradation of stiffness due to structural damages. In this paper, experimental studies are performed and presented to verify the capability of theAEKFapproach for identifying and tracking damages in nonlinear structures. Experimental tests using a base-isolated buildingmodel consisting of a scaled shear-beam type buildingmodel mounted on a rubber-bearing isolation system have been conducted in the laboratory. The Bouc-Wen model is selected to describe the non-linear behavior of rubber-bearings, which has the advantages of being smooth-varying. To simulate structural damages during the test, an innovative device, referred to as the stiffness element device (SED), is used herein to reduce the stiffness of the model. Different earthquake excitations have been used to drive the shake table, including the El Centro earthquake andKobe earthquake. Various damage scenarios have been simulated and tested.Measured acceleration data and theAEKFapproach are used to track the stiffness variation of the upper structure during the test. The experimental results demonstrate that the AEKF approach is capable of tracking the variation of structural parameters leading to the detection of damages in nonlinear structures. 2. Analytical model for Rubber-bearings One challenging problem associated with the rubber-bearing isolator is the modeling of its nonlinear hysteretic behavior. Different hysteretic models for describing the dynamic behavior of rubber-bearings have been proposed in the literature, including the bi-linear model (Tan and Huang, 2000), tri-linear model (Furukawa et al., 2005), Bouc-Wen model (Wen, 1989; Ma et al., 2004; Yin et al., 2010), etc. However, little test data are available aiming at the rigorous characterization of nonlinear hysteretic models (Abe et al., 2004). Among these models, the Bouc-Wen model seems to be more flexible, involving more model parameters to be adjusted. Thus, the Bouc-Wen model is investigated to describe the hysteretic character of the rubber- -bearings in this paper. When subject to an earthquake acceleration ẍ0(t), the equation ofmotion of rubber-bearing isolation system described by the uniaxial hysteretic Bouc-Wen model can be expressed as mẍ(t)+RT(x,z)=−mẍ0(t) (2.1) where x is the relative displacement, z is a hysteretic variable, and m is the mass coefficient. The total restoring force RT(x,z) consists of elastic and hysteretic components as follows RT(x,z) = cẋ+αkx+(1−α)kz (2.2) where cand k are, respectively, thedampingand stiffness coefficients, and 0¬ α ¬ 1 is the ratio of post-yielding stiffness to pre-yielding stiffness.The restoring force is purely hysteretic if α =0 and is purely elastic if α = 1. The hysteretic variable is related to the relative displacement, and a general Bouc-Wen hysteresis model with degradation and pinching given by ż = 1 η h(z)[Aẋ−ν(β|ẋ||z|n−1z+γẋ|z|n)] (2.3) In the above expression ν and η are degradation shape functions, and h(z) is a pinching shape function. ν and η are defined as ν(ε)= 1+ δ1ε η(ε) = 1+ δ2ε (2.4) inwhich, δ1 and δ2 are two constant degradation parameters, ε is a quantity used as ameasure of response duration and severity, introduced as follows ε(t) = t∫ 0 zẋ dt (2.5) Experimental study on damage detection of base-isolated structure ... 1015 And the pinching function h(z) takes the following form h(z) = 1−ζ1e −[z sgn(ẋ)−qzx] 2/ζ2 2 (2.6) where sgn(ẋ) is the signum function of ẋ, and zx is the ultimate value of z given by zx = ( A v(β +γ) )1 n (2.7) The two functions ζ1(ε) and ζ2(ε) in Eq. (2.6) control the progress of pinching given by ζ1(ε)= ζs(1− e −pε) ζ2(ε)= (ψ+ δ3ε)(λ+ ζ1) (2.8) From Eqs. (2.2)-(2.8), there are 13 loop parameters (A, α, β, γ, n, δ1, δ2, ζs, q, p, ψ, δ3 and λ) in the general Bouc-Wenmodel describing the hysteretic behavior. However, it has been shown that A =1 is quite reasonable (Ma et al., 2004), and hence it will be used in this study. Consequently, there remain 12 parameters (α, β, γ, n, δ1, δ2, ζs, q, p, ψ, δ3 and λ) in the Bouc-Wen model. To ravel the contributions of these parameters to the system responses, the one-factor-at-a-time method (Ma et al., 2004; Yin et al., 2010) is adopted to address sensitivity of the 12 parameters relative to the chosen base values to understand the influence of each parameter on the system response. As a typical example of local sensitivity analysis, a SDOF hysteretic structure subject to an earthquake acceleration ẍ0(t) as shown in Eq. (2.1) is used. Selected base values are: m = 125.53kg, c = 0.07kNs/m, k = 24.5kN/m, α = 0.2, β = 2, γ = 1, n = 2, δ1 = 0.02, δ2 = 0.02, ζs = 0.8, q = 0.02, p = 1, ψ = 0.2, δ3 = 0.005, and λ = 0.1. The scaled E-W component of the El Centro earthquake over a duration of 20 seconds is used as the excitation. Then, each of these 12 loop parameters is varied, one at a time, by up to ±50% from its ba- se value while holding all other parameters at the base position. Denote the system response by [x1,x2,x3] T = [x,ẋ,RT(x,z)] T at the base values and by [y1,y2,y3] T when one parame- ter, say w, is varied, where x, ẋ and RT(x,z) denote the relative displacement, velocity and restoring force, respectively. A root-mean-square error is defined as follows ew = √√√√ 1 M M∑ i=1 [(x1i−y1i)2+(x2i−y2i)2+(x3i−y3i)2] (2.9) where M = 1000 is the number of sampling points with the sampling time of ∆t = 0.02s. As each w is varied over its range (from−50% to 50% of the base value), the maximum error ‖ew‖=max(ew) (2.10) is recorded.Thesemaximumvaluesmaybeusedas ameasure of sensitivity.Basedupon ‖ew‖, all the 12 loop parameters of the hysteretic model are ranked in Table 1 in the order of decreasing sensitivity for different earthquake intensities PGA (Peak ground acceleration). In order to consider the influence of the energy of the excitation, the results for three different PGAs of the excitations are also listed inTable 1. As can be observed fromTable 1, although the order of the sensitivities of each parameter has slightly changed under different excitations, the parameters n,α,β and γ have remarkable influenceon the responseof the structure comparedwith theother eight parameters, i.e., δ1, δ2, ζs, q, p, ψ, δ3 and λ.With several different sets of the base values, it is found that the sensitivity conclusion is the same as that obtained from sensitivity analysis above. Further, the above conclusion does not change when subject to another excitations, i.e., Kobe earthquake. It is emphasized that these conclusions are elicited based on the sets of base values and excitations used in this study. 1016 Q. Yin et al. Table 1.Parameter sensitivity ranking Parameter ‖ew‖ w PGA=0.3g Rank PGA=0.5g Rank PGA=1.0g Rank α 0.028 4 0.1281 4 0.7452 4 β 0.098 2 0.4716 2 2.8892 2 γ 0.04 3 0.1914 3 1.2095 3 n 5.137 1 11.6161 1 28.7566 1 δ1 0 11 0 11 0.0005 11 δ2 0.001 10 0.0027 10 0.0317 9 ζs 0.008 7 0.0234 7 0.2156 5 q 0.005 9 0.0103 9 0.029 10 p 0.008 7 0.0234 7 0.2149 6 ψ 0.0083 5 0.0293 5 0.2099 7 δ3 0 11 0 11 0 12 λ 0.0083 5 0.0291 6 0.202 8 From the results of the parameter sensitivity analysis above, it seems that the contributions of these degradation and pinching parameters could gnored. In order to determine the final hystereticmodel for the rubber-bearings, i.e., the parameters contained in theBouc-Wenmodel, aperformance testingon theGZN110 rubber-bearing is conductedas shown inFig. 1a. Sinusoidal excitations with different frequencies are used to drive the actuator, and the displacement-force curves of the rubber bearing under different excitation frequencies are given in Fig. 1b. It is observed from Fig. 1b that there are no significant effects of degradation and pinching. For this reason, we consider the hysteretic model for the rubber-bearings without degradation and pinching, i.e., δ1 = 0, δ2 = 0 and ζs = 0 for simplicity. Then, the unknown hysteresis loop parameters in the Bouc-Wen model are reduced to α, β, γ and n. Equation (2.3) could be rewritten as ż = ẋ−β|ẋ| |z|n−1z−γẋ|z|n (2.11) Fig. 1. (a) Performance testing onGZN 110 rubber bearing; (b) force-displacement curves of GZN 110 rubber bearing Kasalanati and Constantinou (1999) have proposed that A/(β +γ)= 1. Chen et al. (2006) used A = 1, β = 0.1, γ = 0.9, n = 2 for the laminated and stirruped rubber bearings. Huang and Zhao (2000) used A =1, β =0.5, γ =0.5, n =3 for the laminated rubber bearings. Yin et al. (2010, 2012) also suggested that A =1, β =0.5, γ =0.5, n =2 for rubber bearings. In this Experimental study on damage detection of base-isolated structure ... 1017 paper, these parameter values suggested by Yin et al. (2010, 2012) are adopted for a reference, and the following experimental results are compared with these suggested values. 3. Adaptive extended Kalman filter In this section, a brief summary of the adaptive extended Kalman filter (AEKF) approach to be used is given, and the details are referred toYang et al. (2006). Consider am-DOF structure with the displacement vector x, and velocity vector ẋ. Let us introduce an extended state vector, Z(t) = {xT, ẋT,θT}T, where θT = [θ1,θ2, . . . ,θn] T is an n-unknown parametric vector with θi (i =1,2, . . . ,n) being the i-th unknownparameter of the structure, including damping, stiffness, nonlinear and hysteretic parameters. In what follows, the boldface letter represents either a vector or a matrix. The vector equation of motion of the structure can be expressed as dZ(t) dt =g(Z,f, t)+w(t) (3.1) in which w(t) is the model noise (uncertainty) vector with zero mean and a covariance matrix Q(t), and f is the excitation vector. A nonlinear discrete vector equation for an observation vector (measured responses) can be expressed as follows Yk+1 =h(Zk+1,fk+1,k+1)+vk+1 (3.2) inwhich Yk+1 is a l-dimensional observation (measured) vector at t =(k+1)∆t (sampling time step ∆t), i.e., Yk+1 =Y(t =(k+1)∆t),Zk+1 =Z(t =(k+1)∆t), and fk+1 = f(t =(k+1)∆t). In Eq. (3.2), vk+1 is a measurement noise vector assumed to be a Gaussian white noise vector with zero mean and a covariance matrix E[vkv T j ] =Rkδkj, where δkj is the Kronecker delta. Let Ẑk+1|k+1 be the estimate of Zk+1 at t =(k+1)∆t, and Ẑk+1|k be the estimate of Zk+1 at t = k∆t. The recursive solution for the estimate Ẑk+1|k+1 of the extended state vector is given by Ẑk+1|k+1 = Ẑk+1|k+Kk+1[Yk+1−h(Ẑk+1|k,fk+1,k+1)] Ẑk+1|k = E{Zk+1|Y1,Y2, . . . ,Yk}= Ẑk|k+ (k+1)∆t∫ k∆t g(Ẑt|k,f, t) dt (3.3) in which Kk+1 is the Kalman gain matrix Kk+1 = Pk+1|kH T k+1|k[Hk+1|kPk+1|kH T k+1|k+Rk+1] −1 (3.4) In Eq. (3.4), Pk+1|k and Hk+1|k are given by Pk+1|k =Λk+1[Φk+1,kPk|kΦ T k+1,k]Λ T k+1+Qk+1 Hk+1|k = [ ∂h(Zk+1,fk+1,k+1) ∂Zk+1 ] Zk+1=Ẑk+1|k (3.5) where Φk+1,k is the transition matrix of the extended state vector from Zk to Zk+1, and Pk|k is given by Pk|k = [I2m+n−KkHk|k−1]Pk|k−1[I2m+n−KkHk|k−1] T+KkRkK T k (3.6) In Eq. (3.5)1, Λk+1 is a diagonal matrix referred to as the adaptive factor matrix. The de- termination of Λk+1 has been described in Yang et al. (2006). In the recursive solution above, 1018 Q. Yin et al. Pk|k is the error covariance matrix of the estimated extended state vector. To initiate the re- cursive solution, the initial values for the unknown extended state vector Z(t)= {xT, ẋT,θT}T, including theunknownparameters and theunknown state vector, shouldbe estimated. Likewise, the initial error covariance matrix P0|0 of the estimated extended state vector, the covariance matrix R of themeasurement noise vector v(t), and the covariancematrix Q of the systemno- ise vector w(t) should be assigned as will be described later. Finally, in computing the adaptive factor matrix Λk+1 for the on-line damage identification, a constrained optimization procedure was used, in which a small number (constraint) δ =0.01 was suggested. Further, in computing the covariance matrix of the predicted output error, it was suggested by Yang et al. (2006) that G1,0 = 0, G2,0 = 0. These values, i.e., δ = 0.01, G1,0 = 0 and G2,0 = 0, will be used in the following analysis of all experimental data. 4. Experimental studies 4.1. Experimental set-up Rubber-bearings GZN110 supplied by Hengshui Zhentai Seismic Isolation Instrument CO., LTD were used as the base isolator. The base-isolation system consists of 8 circular rubber- -bearings each with a diameter of 11cm and an upper floor mate. A 400mm by 300mm small- -scale shear-beamtypebuildingmodelmountedona600mmby500mmfloormateof the rubber- -bearing isolation system, as shown in Figs. 2a is used for the experiments. The base-isolated building can be simplified to be a 2-DOF shear-beam model consisting of an upper storey and an isolation storey, as shown inFig. 2b.The total height of this buildingmodel is 660mm,where the height of upper storey is 345mmand the height of the isolation storey is 315mm.The total weight of the model is 350kg, in which themass of the upper floor is 50kg and themass of the base mate is 300kg. The first two natural frequencies of the test specimen are: 1.955Hz and 5.376Hz, respectively. Based on the discretized 2-DOF shear-beam model, the stiffness of each storywas estimated to be52kN/mand46kN/m, respectively, using thefinite-element approach. The base-isolated building model was placed on the shake table that simulates different kinds of earthquakes. Two earthquake excitations were used, including the El Centro and the Kobe earthquakes. During the tests, each floor was installed with one acceleration sensor and one displacement sensor to measure the floor responses. Fig. 2. (a) The based-isolated building model on the shake table; (b) schematic figure for the rubber-bearing isolated building (shear-beammodel) The damage in a storey unit is assumed to be reflected by the reduction of its stiffness. To simulate the reduction of stiffness in the upper storey, a stiffness element device (SED), Experimental study on damage detection of base-isolated structure ... 1019 consisting of a hydraulic cylinder-piston (HCP) and a bracing system, with an effective stiffness of Khi is installed in the upper storey, so that stiffness of the upper storey is increased by Khi. During the experimental test, the effective stiffness of the SED is reduced to zero to simulate the reduction of the stiffness in the upper storey. During the tests, the shake table and the masses were each installed with one accelera- tion sensor and one displacement sensor to measure the responses. The absolute acceleration responses of the isolation storey a1, and the upper storey a2, as well as the earthquake gro- und acceleration ad were measured. Also, the displacements of each storey and the base were measured for the correlation study. 4.2. Experimental results To demonstrate the capability and accuracy of the adaptive extendedKalman filter (AEKF) approach for tracking the damage of base-isolated structures, experimental tests were conducted herein for different damage scenarios. For shake table tests, two earthquakes will be used, inclu- ding theElCentro earthquake scaled to a peak groundacceleration (PGA) of 0.6g and theKobe earthquake scaled to a PGA of 0.5g. For each earthquake, the acceleration responses (a1,a2) of both floors and the shake table acceleration ad were measured. The sampling frequency of all measurements was 500Hz. To identify the parameters of the rubber-bearing isolated structure, and to track the damage in the upper storey when it occurs, different unknown parameters in theBouc-Wenmodel will be considered. From the hysteresis loop shown inFig. 1b, the effects of degradation and pinching are negligible. Further, from the sensitivity analysis conducted in the previous section, only four loop parameters, i.e., α, β, γ, n in Bouc-Wenmodel for the isolation system will be considered in this study. 4.2.1. Bouc-Wen model I (3 unknown parameters for isolation system) First, we consider the loop parameters β, γ and n of the Bouc-Wen model for the isolation storey to be constants, i.e., β = 0.5, γ = 0.5 and n = 2. Hence, the unknown parameters for the isolation system consist of c, k and α. Hence, the hysteretic non-linear equation can be rewritten as ż = ẋ− 1 2 |ẋ| |z|z − 1 2 ẋ|z|2 (4.1) Case 1: El Cento earthquake (PGA=0.6g) In this test, a stiffness element device (SED) is installed in the upper storey unit as shown in Fig. 2. The cylinder of the SED is filled by air with an air pressure of 0.7MPa. From the expe- rimental test, the air pressure at P0 = 0.7MPa results in an effective stiffness of 7.0kN/m for the SED, i.e., Khi = 7.0kN/m. Thus, the stiffness of the upper storey was estimated to be k2 = 53kN/m, whereas the stiffness of the base-isolated storey was estimated to be k1 = 52kN/m. During the test with the El Centro earthquake excitation, both valves of the SED unit were open simultaneously at t =14 seconds, so that the stiffness of the upper storey reduces abruptly from 53kN/m to 46kN/m at t = 14 seconds. The acceleration responses of both floors and the shake table acceleration, a1, a2 and ad in m/s 2, weremeasured and presen- ted inFig. 3. Further, the displacement responses of both floors and the basewere alsomeasured for correlation studies later. For the AEKF approach, the test specimen is considered as a 2-DOF shear-beam building model, and the equations of motion can be written, in which the stiffness and damping of each storey as well as the nonlinear hysteretic parameters of the base-isolator, are unknown parameters.Consequently, the vector equation ofmotion,Eq. (3.1), for the extended state vector 1020 Q. Yin et al. Fig. 3. Measured acceleration responses and shake table acceleration due to El Centro earthquake can be established analytically.With themeasured shake table acceleration ad and acceleration responses (a1,a2) shown inFig. 3, the unknown structural parameters, i.e., ki, ci (i =1,2), and α can be identified on-line using the recursive solution, Eqs. (3.3)-(3.6), of the AEKF approach. For the AEKF recursive solution described previously, the following initial values are assu- med: (i) the initial values for ki and ci are: ki0 = 40kN/m and ci0 = 0.1kNs/m (i = 1,2), (ii) the initial values for the displacements and velocities are zero, i.e., x= [0,0]T, ẋ= [0,0]T, (iii) the initial error covariance matrix P0|0 of the extended state vector is a (10×10) diagonal matrix with the first 5 diagonal elements being 1 and the last 5 diagonal elements being 1000, and (iv) the covariance matrices of the measurement noise vector v(t) and the system noise vector w(t) are chosen to be R= 0.1I2 and Q= 10 −9I10, respectively, where Ij is a (j × j) unit matrix. In the following experimental studies in Case 1 and Case 2 to be presented later, these same initial values will be used. Fig. 4. The identified system parameters, Case 1: El Centro earthquake Based on the AEKF recursive solution and the measured data, the identified unknown pa- rameters for both storeys are presented in Fig. 4 as solid curves (black color). Also shown in Fig. 4 as dashed curves (grey color) for comparison are the estimated results based on the finite- element method. Further, the identified inter-storey drifts (x1,x2) and displacements (d1,d2) of each floor using the AEKF approach are presented in Fig. 5 as solid curves (black color), whereas the dashed curves (grey color) are the measured experimental results for comparison. The identified numerical results based on the AEKF approach are as follows: (i) prior to da- mage, k1 = 51.7kN/m and k2 = 55.2kN/m, and (ii) after damage, k1 = 51.7kN/m and Experimental study on damage detection of base-isolated structure ... 1021 k2 =48.5kN/m. It is observed from both Fig. 4 (solid curves) and the numerical results above that the identified structural parameters based on the AEKF approach are very reasonable in comparison with that estimated by the finite element method (dashed curves). The difference between the solid and dashed curves has been expected due to the structural uncertainty of the test model, including the shear-beam assumption. Figures 4 and 5 clearly demonstrate that the AEKF approach is capable of tracking the variation of stiffness parameters, leading to the detection of structural damages. Fig. 5. The identified relative and absolute displacements, Case 1: El Centro earthquake Case 2: Kobe earthquake (PGA=0.5g) Instead of the El Centro earthquake, the Kobe earthquake was used to drive the shake table. The test configuration is identical to that of Case 1 presented previously, except that the air pressure of the SED installed in the first storey is P0 = 0.75MPa. This results in a stiffness of 7.5kN/m for the SED. Hence, the stiffness of the upper storey prior to damage is k2 = 46kN/m+7.5kN/m = 53.5kN/m, whereas the stiffness of the base isolator remains the same, i.e., k1 = 52kN/m. During the test, valves of the SED were open at t = 8.0 seconds following the most intensive portion of the earthquake. After t = 8.0 seconds, k2 is reduced to 46kN/m. Acceleration responses (a1,a2) of both floors and the shake table acceleration ad were measured and presented in Fig. 6. Based on the measured data in Fig. 6 and the AEKF approach, the identified unknown parameters for both storeys are presented in Fig. 7 as solid curves (black color), whereas the dashed curves (grey color) are the finite-element results. The predicted inter-storey drifts (x1,x2) and displacements (d1,d2) of each floor are presented in Fig. 8 as solid curves (black color), whereas the dashed curves (grey color) are themeasureddata for comparison.The identifiednumerical resultsusingtheAEKFapproachareas follows: (i)prior to damage, k1 = 52.2kN/m and k2 = 55.6kN/m, and (ii) after damage, k1 = 52.2kN/m and k2 = 47.6kN/m. As observed from Figs. 7 and 8, the AEKF predictions are quite reasonable, and that the trend of predictions is consistent with that of the previous case. 4.2.2. Bouc-Wen Model II (5 unknown parameters for isolation system) In this situation,we consider the parameter n of theBouc-Wenmodel for the isolation storey to be 2.0, i.e., n =2, and the other loop parameters, α, β, and γ to be unknown in Eqs. (2.2) and (2.11). Then, the hysteretic non-linear equation can be rewritten as ż = ẋ−β|ẋ| |z|z −γẋ|z|2 (4.2) For theAEKFrecursive solution, the initial values assumed forCase 3 andCase 4 are similar to that of Case 1 and 2, except that P0|0 is a (12×12) diagonalmatrixwith the first 5 diagonal 1022 Q. Yin et al. Fig. 6. Measured acceleration responses and shake table acceleration due to Kobe earthquake Fig. 7. The identified model parameters, Case 2: Kobe earthquake Fig. 8. The identified relative and absolute displacements, Case 2: Kobe earthquake elements being 1 and the last 7 diagonal elements being 1000, R=0.1I2 and Q=10 −9I10. In the following experimental studies in Case 3 andCase 4 to be presented, these initial values will be used. Note that these initial values are basically identical to that of Case 1 and Case 2. Case 3: El Centro earthquake (PGA=0.6g) Similar to Case 1, a scaled El Centro earthquake was applied to the base. Based on the acceleration measurements shown in Fig. 3 and the AEKF solution, the identified parameters Experimental study on damage detection of base-isolated structure ... 1023 are presented in Fig. 9. Further, the identified displacements are shown in Fig. 10 as black solid curves, whereas themeasured displacements are shown as grey dashed curves for comparison. It is observed from Fig. 10 that the identified displacements match the experimental ones well. Fig. 9. The identified model parameters, Case 3: El Centro earthquake Fig. 10. The identified relative and absolute displacements, Case 3: El Centro earthquake Case 4: Kobe earthquake (PGA=0.5g) Similar to Case 2, a scaled Kobe earthquake was applied to the base. Based on the acce- leration measurements shown in Fig. 6 and the AEKF solution, the identified parameters are presented in Fig. 11. As observed fromFig. 11, all parameters converge nicely after 2.5 seconds. The identified displacements are shown in Fig. 12 as black solid curves, whereas the measured displacements are shown as grey dashed curves for comparison. Again, the AEKF approach is capable of identifying structural damages. 5. Conclusions Recently, a new adaptive extended Kalman filter (AEKF) has been proposed for the on-line damage identification of structures based on simulation results. In this paper, we have perfor- med experimental studies to verify the capability of this AEKF in identifying the damage of 1024 Q. Yin et al. Fig. 11. The identified model parameters, Case4: Kobe earthquake Fig. 12. The identified relative and absolute displacements, Case 4: Kobe earthquake base-isolated structures by conducting a series of experimental tests on a scaled rubber-bearing isolated buildingmodel. TheBouc-Wenmodels with 3 and 5 unknown parameters, respectively, have been investigated to represent the hysteretic behavior of rubber-bearing isolators. To si- mulate the structural damage during the test, an innovative stiffness element device (SED) has been used to reduce the stiffness of the upper storey. Different damage scenarios under different earthquakes have been simulated and tested. Themeasured acceleration response data and the AEKF approach have been used to identify the unknown structural parameters, and to track the stiffness variation of the structure during the test. The identified stiffness parameters based on the AEKF approach correlate reasonably well with those estimated by the finite-element method despite the stiffness of the upper storey is uniformly bigger than that estimated by the finite-elementmethod.This trend is consistent for all the test results, including different loading conditions and different damage scenarios. Such discrepancies have been expected due to the structural uncertainties of the test model. Experimental studies conducted herein demonstra- te that the AEKF approach is capable of: (i) identifying nonlinear structural parameters, and (ii) tracking the variation of stiffness parameters leading to the detection of structural damages. In addition to the AEKF approach, the initial values, such as the initial parametric values and the covariance matrices of the measurement noise vector v(t), have an important influence on the stability and convergence of the AEKF and, consequently, on the estimations of the struc- tural parameter and the measured noise level, e.g., stiffness coefficients ki and R, conducted previously and experientally. Experimental study on damage detection of base-isolated structure ... 1025 Acknowledgements This research is partially supported by the National Natural Science Foundation of China under Grant No. 10572058 and US National Science Foundation Grant No. CMMI-0853395. 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