In this study, the model validation is more generally defined that it should be validating statistically accurate models. Some previous studies were carried out on the basis of this definition according to the uncertainty quantification of the numerical model, e.g., [1]. In those works, it was indicated that it was so important to use appropriate response features to compare the numerical output and the measurement data. A response feature is the quantity extracted from the dynamic response that is used to compare the structural system’s experimentally observed response characteristic to those predicted by its numerical model. Fundamentally, the feature extraction process is based on processing the data waveforms or spectra of waveforms, or fitting some model to the data. Many feature extraction techniques have been developed for structural health monitoring. Those include finding indications of nonlinear response and identifying system changes due to damages on structures, e.g., [2] and [3]. Many of these features can potentially be used for the model validation applications. This paper focuses on defining and illustrating some response features that can be used for structural dynamics model validation studies. After a brief general discussion regarding response features, the application of these features for dynamic model validation are studied using experimental and numerical response data from a test-bed structure. Then, a comparison procedure for multivariate feature vectors based on Mahalanobis distance analysis is presented for the statistical model validation. This paper concludes with an additional discussion regarding the importance of appropriate feature selections. 2. Test-bed structure and numerical model description The LANL three-story share building structure shown in Fig.1 (a) was used as a test-bed structure in this study [2]. The structure consists of aluminum plates and columns assembled using bolted joints. The structure slides on rails that allow movement only in the x-direction. The input force was applied in the x-direction by an electromagnetic shaker connected to the base floor. A force transducer was attached at the end of a stinger to measure the input force, and four accelerometers were attached at the centerline of each floor on the opposite side from the excitation to measure the system response at each floor. This structure was modeled as a 4-DOF lumped-mass system as shown in Fig.1 (b). Mass, stiffness and damping of i-th story was defined as mi, ki and ci (i= 1~4), respectively. The values of mi and ki (except k1), were determined from the measured sizes of structural members and nominal values for Young’s Modulus, and the mass density of aluminum. The stiffness ki (i= 2~4) was the summation of the bending stiffness of four columns treated as beams that are constrained against rotation at their ends. For stiffness k1, a relatively low numerical value was assigned because the friction between the rails and the structure was negligible. Notice that the model includes the base mass that slides on the rails. The equation of motion of the structure was described in a matrix notation using mass, stiffness, and damping matrixes; [M], [K], and [C], as follows [ ]{} [ ]{} [ ]{} { ()} M x C x K x F t , (1) where vector {F(t)} is the input force vector, and {x} is the displacement vector of x1~x4 in Fig.1 (b). In the application of time-response analysis, the displacement vector {x(t)} was calculated by a Rungekutta numerical integration scheme. A proportional damping was adopted to assign a damping matrix [C] that could be discribed as > @ > @ > @ C M K D E . (2) Theoretically, coefficients D and E can be related to k-th mode resonant frequency Zk and modal damping ratio ]k as in 1 2 k k k D ] EZ Z § · ¨ ¸ © ¹ . (3) Therefore, D and E can be assigned when two modal parameter sets ( Zk, ]k) are given. 154
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