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In most building structures, floors with sufficient in-plane stiffness exist and an assumption of rigid in-plane stiffness is valid. However, in some building structures, an assumption of rigid in-plane stiffness does not hold. A method of system identification (SI) for physical parameters (stiffness, damping) is proposed for three-dimensional (3D) building structures with in-plane flexible floors. The stiffness and damping parameters of each vertical structural frame in the 3D building structure are identified from the measured floor horizontal accelerations together with the stiffness and damping parameters of each floor. It is shown that a batch processing least-squares estimation method for many discrete time-domain measured data enables the direct identification of both the stiffness and damping parameters of each vertical structural frame and the stiffness and damping parameters of each floor. The proposed method possesses an advantage that all stiffness and damping parameters of vertical frames and horizontal frames (floors) can be identified simultaneously without search iteration. The accuracy and reliability of the proposed method are made clear by numerical simulations for measured data without noise and measured data with noise. A method of noise elimination is proposed to enhance the identification accuracy. Finally, experiments using a shaking table are conducted for the accuracy investigation of the proposed identification method. It is confirmed that the proposed identification method possesses a reliable ability to identify the stiffness and damping parameters for 3D building structures with in-plane flexible floors.

The collapse-limit input velocity level of the critical double impulse simulating the principal part of near-fault ground motions is derived for an elastic-plastic structure with viscous damping and P-delta effect. The structural system is modeled by a bilinear hysteretic SDOF system with negative post-yield stiffness reflecting the P-delta effect which plays a key role in the collapse behavior. Since the critical timing of the second impulse in the double impulse has been proven as the zero-restoring force timing after the first impulse for the elastic-plastic SDOF system with viscous damping, that property is used again in this paper. It is shown that the collapse-limit input level of the critical double impulse can be obtained as a function of the post-yield stiffness and the damping ratio by using the energy balance law and the quadratic-function approximation of the damping force-deformation relation. The applicability of the collapse-limit level to actual recorded ground motions is investigated through the time-history response analysis for the stable models and the collapse models under two actual earthquake ground motions.

An equi-spaced consecutive impulse input is treated as a simplified representative for a long-duration earthquake ground motion. The key property of such input can be captured approximately by using harmonic waves. An approximate closed-form solution is derived for the elastic-plastic response of a two-degree-of-freedom (2DOF) system under the “critical multiple impulse input” based on some assumptions. The 2DOF system is assumed to consist of an elastic-perfectly plastic restoring-force characteristic in the first story and a linear elastic restoring-force characteristic in the second story. The fact that only the free vibration emerges under such multiple impulse input enables the utilization of the energy approach in the derivation of the explicit expression for a complicated elastic-plastic response. The critical timing of the impulses is found to correspond to the zero restoring-force timing in the first story. The validation and accuracy check of the proposed theory are conducted by implementing the response analysis to the corresponding sinusoidal input as a representative of the long-duration earthquake ground motion. It is also demonstrated that the proposed theory can be applied to a base-isolated building with hysteretic property in the base-isolation story regardless of the number of stories of superstructures.

The uncertainties in ground motions may result from several factors, e.g., (i) the fault rupture process, (ii) the wave propagation, (iii) the site amplification from the earthquake bedrock to the ground surface. The uncertainty in the fault rupture slip is taken as a main factor of uncertainties in the present paper and the critical fault rupture slip distribution causing the maximum structural response is found by using the stochastic Green's function method as a generator of ground motions. Then, a multi-degree-of-freedom (MDOF) building structure is introduced as a model structure and an optimal damper placement problem is discussed for the critical ground motion. The main topic in this paper is the simultaneous determination of the critical fault rupture slip distribution and the optimal damper placement. The sequential quadratic programming method is used in the problem of critical fault rupture slip distribution and a sensitivity-based method is introduced in the optimal damper placement problem. Furthermore, the robustness for the maximum interstory drift in MDOF building structures under the uncertainty in fault rupture slip distributions is presented for resilient building design by using the robustness function. Since the critical case leads to the most unfavorable structural response, the proposed method can provide structural designers with a promising tool for resilient building design.

The objective of this paper is to provide a new damage identification method using frequency response data. In this approach, the inverse identification problem is treated as a nonlinear optimization problem whose objective function is just the constitutive relation error (CRE). To circumvent the ill-posedness of the inverse problem which is caused by use of the possibly insufficient data and enhance the robustness of the identification process, the sparse regularization is introduced where the ℓ1-norm regularization term is added to the original CRE function. In regard to the minimum solution of the sparse-regularized CRE objective function, the alternating minimization (AM) method is established. The attractive features of the present damage identification approach are: (a) while coping with the sparse regularization, a closed-form solution is obtained due to the decoupling of the CRE function with respect to the damage parameters and hence the sparse regularization term would introduce little computational complexity; (b) the sparse regularization parameters are directly determined by a simple threshold setting method; (c) no sensitivity analysis is involved herein. Numerical examples are conducted to verify the proposed approach and the results show that the sparse regularization obviously improves the accuracy and robustness for the identified damages.

Extracting physical parameters for damage identification problems from full-field measurements is a promising research because of the recent spread of vision-based measurement techniques in the experimental mechanics. This paper presents a vision-based measurement framework using the camera system for damage identification. The framework is composed of four procedures: camera calibration, image processing, system identification and sensitivity analysis. In contrast to traditional finite-point measurements, the camera system allows considerably greater non-contact measurement flexibility. Such flexibility has two important benefits: first, less number of modes is required for modal-based damage identification problems; and second, more physical parameters could be extracted, taking advantage of the plentiful experimental data. A laboratory test comparing the camera system to traditional accelerometer measurement is conducted to confirm the above advantages. Further statistic analysis shows that the major drawback of this technique is that the camera system presents high levels of noise in small vibration responses at higher frequencies. Suitable strategies to circumvent this disadvantage are developed. Moreover, a technique for practical camera calibration without the requirement that the objective plane should be strictly perpendicular to the camera axis is also demonstrated and verified by the proposed laboratory test.

A novel static identification approach to beam damage is presented. It is based on the minimum constitutive relation error (CRE) principle where the exact stiffness, the exact displacement and the exact bending moment are shown to make the CRE functional minimal. For practical implementation, two cases regarding full-field displacement measurements and finite-point displacement data, respectively, are considered. For full-field displacement measurements, the CRE functional is directly treated as the objective functional while in case of finite-point measurement data, the CRE functional along with additional penalty terms for treatment of the finite-point displacement measurements is defined as the objective functional. Multiple loads and associated sets of measurements are also considered to improve the identifiability and robustness of the procedure. Convergence is finally verified through numerical examples.

Multi impulse with constant time interval is used as a representative of a long-duration earthquake ground motion. An analytical expression is derived for the elastic-plastic response of a single-degree-of-freedom (SDOF) model with nonlinear viscous damping subjected to the “critical multi impulse” which maximizes the response. The fact that only free vibration appears under such multi impulse enables the smart application of an energy approach in deriving the analytical expression for a complicated elastic-plastic response with nonlinear viscous damping. The nonlinear viscous damping characteristic for deformation is approximated in terms of a quadratic or elliptical function. The critical timing of the impulses is found to correspond to the zero restoring-force timing or the maximum velocity timing depending on the input level. It is shown that the nonlinearity in viscous damping causes a remarkable influence on the earthquake response in some cases. The reliability and accuracy of the proposed theory are investigated through the comparison with the results by the time-history response analysis to the tuned sine wave as a representative of the long-duration earthquake ground motion.

It is known that, while the stochastic Green's function method is suitable for generating ground motions with short periods, the three-dimensional finite difference method (FDM) is appropriate for ground motions with rather long periods. In the previous research, the stochastic Green's function method was used for finding the critical earthquake ground motion for variable fault rupture slip (slip distribution and rupture front). However, it cannot be used for ground with irregularities and for wave component with rather long periods. In responding to this request, the FDM is used in this paper for finding the critical ground motion for structures with rather long natural period. Since the FDM is time-consuming, it seems unfavorable to use it in a simple sensitivity algorithm where an independent response sensitivity is calculated for many design parameters. To overcome this difficulty, the bi-cubic spline interpolation of uncertain parameter distributions (seismic moment distribution in this paper) and the response surface method for predicting the response surface from some sampling points are used effectively in this paper. The uncertainty parameter is the fault rupture slip distribution described in terms of seismic moments. It is found that the critical ground motion for structures with rather long natural period can be found effectively by the proposed method.

A new method for optimal viscous damper placement is proposed for elastic-plastic multi-degree-of-freedom (MDOF) structures subjected to the critical double impulse as a representative of near-fault ground motions. The double impulse consists of two impulses with different directions and the critical interval between those two impulses is characterized by the criterion on the maximum input energy that is expected to lead to the maximum deformation. The critical timing of the second impulse is the timing at which the sum of the restoring force and the damping force in the first story attains zero. The objective function and constraint in terms of the maximum interstory drift along the building height or the sum of the maximum interstory drifts in all stories are selected and the corresponding optimization algorithm based on time-history response analysis and sensitivity analysis is investigated. Since the objective function in terms of the sum of the maximum interstory drifts in all stories is superior to the objective function in terms of the maximum interstory drift along the building height, it is employed in this paper. A new concept of double impulse pushover (DIP) is proposed for determining the input velocity level of the critical double impulse. It is demonstrated that the combination of two algorithms, one for effective reduction of the overflowed maximum interstory drift via the concentrated allocation of dampers and the other for effective allocation of dampers via the use of stable objective function, is effective for finding a stable optimal damper placement.