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An explicit design procedure of cross-sections of framed tube high-rise buildings via an inverse problem approach is presented. In the formulation, interstory drift ratios and net deformations of beams are prescribed. The derived expressions clearly express the three-dimensional effect (tube effect) from the orthogonal frame. The expressions are helpful for the preliminary design because cross-sections are rationally and rapidly provided for a set of target deformations without trial-and-error repetition. In the proposed design method, a 2×2-bay basic model under a set of static horizontal loads is designed at first. Then, this 2×2-bay model is transformed into a multi-bay model. The second moments of cross-section of the multi-bay model can be obtained based on the equivalence of the responses of those two models in the case where the elongation of columns is neglected. In addition, assumptions of axial strains of columns are introduced to obtain the equivalent parameters of cross-sections of the 2×2-bay model. It is demonstrated through numerical examples that the proposed method has reasonable accuracy.

This paper aims to obtain an optimal viscous damper placement for a shear building model using H^∞ optimization. The H^∞ norm of the transfer function matrix of interstory drifts is adopted as the objective function. Since it represents the magnitude of vibration transfer, one can attenuate the gain of the frequency response by minimizing this norm. The sequential quadratic programming (SQP) method is employed for optimization. The proposed method is applicable to a multi-story shear building model as well. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

This paper aims to obtain an optimal viscous damper placement for a shear building model using H^∞ optimization. The H^∞ norm of the transfer function matrix of interstory drifts is adopted as the objective function. Since it represents the magnitude of vibration transfer, one can attenuate the gain of the frequency response by minimizing this norm. The sequential quadratic programming (SQP) method is employed for optimization. The proposed method is applicable to a multi-story shear building model as well. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

A simple evaluation method of building resilience is proposed, and the resilience of elastic-plastic high-rise buildings is evaluated under resonant long-duration ground motions. The concept of availability is incorporated into the evaluation model of the building resilience, which was proposed in the previous paper. Not only in-building components but also external factors such as lifelines and redundancy of facility systems are considered in the evaluation model. Based on the evaluation model, the following probabilistic indices are formulated: (1) the expected value of the total recovery time, (2) the expected values of the availability of the structural frame, facilities, and non-structural components just after an earthquake event, and (3) the maximum likelihood recovery curves (MLRCs) of the structural frame, facilities, and non-structural components. Numerical examples are presented for evaluating the resilience of elastic-plastic high-rise building models under a pseudo-multi impulse (PMI), which substitutes for resonant long-duration ground motions. Finally, the influences of the passive viscous dampers, the redundancy of facility systems, and the uncertainty of manpower to repair the components on the building resilience are clarified through the results of numerical examples.

An input velocity adjustment method of the critical double impulse (DI) is presented for efficient design of viscous dampers for elastic-plastic moment frames. The input velocity is adjusted so that the input energy to the lowest eigenmode under the critical DI is equal to those under the selected recorded ground motions. This adjustment makes the critical DI work as the active earthquake. The response bounding property of the critical DI is supported by, (1) the multi-modal property of the critical DI, (2) the usual excitation of the lowest mode response under recorded ground motions, (3) the large proportion of the instantaneous input energy to the total input energy in the critical DI. The proposed method can treat not only pulse-like near-fault ground motions but also ground motions of random nature. To validate the proposed method, the input energies and the maximum interstory drifts under the recorded ground motions and the critical DI with the adjusted input velocity are investigated for elastic single-degree-of-freedom (SDOF) models, elastic proportionally damped MDOF models, and elastic-plastic proportionally damped MDOF models. The optimization method presented in the previous paper is extended so that the critical DI can be treated for the design of viscous dampers for elastic-plastic moment frames.

A new model reduction method is presented for moment-resisting frames with viscous dampers. The proposed method considers (1) the interactive effect of added damping between the horizontal-vertical directions and (2) the direct effect with regard to the vertical direction different from the conventional static condensation method. When brace-type dampers are treated, these effects cannot be neglected originally. The proposed method gives a better correspondence of the fundamental eigenmode with that of the non-reduced moment frame than the static condensation method. In addition, the proposed reduced model can accurately evaluate the maximum interstory drifts of the non-reduced moment frame. The proposed model reduction method is formulated in the frequency domain. The frequency dependency of the stiffness matrix and the damping matrix of the reduced model is investigated. The influences of the added damping matrix by viscous dampers on the natural circular frequencies, the damping ratios and the participation vectors are also investigated. Finally, it is demonstrated through a numerical example that the displacement-based optimization of the damper allocation can be accurately and rapidly conducted by using the reduced models throughout the optimization process.

In this study, a model for the evaluation of a building's resilience and recovery time is proposed, and a new method is developed for the optimal viscous damper placement for a targeted resilience. The features of this model are as follows: 1) building components are categorized into systems in view of their functionality, 2) recovery time is regarded as a function of the damage to building components and human resources for repairing the components, 3) the model is applicable to structural design. This design method uses a type of real-coded genetic algorithm (GA). The effective use of a constraint on the sum of the added damper damping coefficients enables an efficient search for the solution.

Approximate closed-form maximum interstory drifts under the critical pseudo-double impulse (PDI) are derived for undamped multi-story shear building models with bilinear hysteresis by using the proposed updated mode-controlled energy-based approach (UMEA). PDI was proposed in the previous paper to simulate the critical responses of elastic-plastic MDOF models under near-fault fling-step motions. Although a double impulse (DI) is treated as a ground motion, PDI is treated as a set of impulsive lateral forces. PDI excites only the fundamental-mode responses of elastic proportionally-damped MDOF models because the fundamental participation vector is applied to the influence coefficient vector of PDI. UMEA is a kind of displacement control analyses, and the displacement increment, which is proportional to the fundamental mode evaluated by the tangent story stiffnesses, is given to the model. It is demonstrated that UMEA effectively captures the main characteristics of the maximum interstory drifts under the critical PDI and the critical one-cycle sine wave because most of the kinetic energy, which the fundamental mode has just before yielding, is given to the plastic fundamental mode just after yielding except for the case that the post-yielding stiffness is almost zero. The use of UMEA leads to much more efficient estimation of the maximum interstory drifts than the time-history response analysis because UMEA requires only 2N-time evaluations of the elastic and plastic fundamental modes at most for N-story shear mass models with bilinear hysteresis. It is shown through numerical examples that the maximum interstory drifts under the critical PDI and the corresponding one-cycle sine wave correspond well to those evaluated by the proposed method. It is also shown that the correspondence of the responses of elastic-plastic MDOF models under recorded near-fault motions and the estimated responses by the proposed method is fairly good.

A new concept of a “lower-bound transfer function (LBTF)” and a new frequency-domain optimal damper design method are presented. LBTF expresses an ideal performance for response control in the frequency domain under a constant sum of added damping coefficients (or the total cost of dampers). The effectiveness of the damper design for each mode can be captured visually through plotting the transfer function amplitudes of the model and the LBTF. An efficient generation method of LBTFs is also proposed. The proposed design method provides designs with multimodal adaptability (effective for multimodes). It does not require much computational load to implement the method since the optimization is conducted in the frequency domain, and the first-order or second-order sensitivities of the objective function can be derived analytically. The proposed design and the fundamental mode optimal damper placement are compared for shear-mass systems and moment-resisting frames through the transfer functions and the incremental dynamic analysis (IDA). It is demonstrated that the proposed designs effectively reduce the floor acceleration responses and the elastic deformation responses. Moreover, it is shown that the proposed designs can effectively reduce the elastic–plastic responses although the optimization is conducted for linear elastic models.

A new method of optimal damper design is presented for elastic–plastic planar frame structures under large-amplitude earthquake ground motions. The transformation of a moment frame into the 1st-mode equivalent shear mass system leads to an efficient search of the optimal damper placement along the building height for the elastic–plastic moment frame. In the optimization procedure, a linear elastic bare frame is transformed into the 1st-mode equivalent shear mass system first. Then the optimization of the damper placement is conducted for the elastic shear mass system. After that, the damped shear mass system is inversely transformed into the elastic–plastic moment frame with the added dampers. This inversely transformed damper system in the moment frame is employed as an initial design and the local search-based optimization is conducted for the efficient distribution of dampers not only along the building height, but also among the different bay. The proposed method greatly reduces the computational task in the whole optimization procedure because only a limited number of time-history response analyses is required for elastic–plastic moment frames. It is demonstrated through numerical examples that the proposed method efficiently provides the damper designs with high accuracy. Finally, the importance of using the large-amplitude ground motions for damper optimization is demonstrated through the incremental dynamic analysis (IDA) for the optimally designed models.

The viscous-hysteretic hybrid (HVH) damper system recently introduced by one of the authors has a clear property that, when the hysteretic dampers with gap mechanism become active (stiffness element starts working), the acceleration of building frames with this damper system as a stopper attains large values in spite of the advantageous feature to prevent excessive deformation. It is therefore desired that both the maximum interstory drift and the maximum acceleration exhibit an acceptable value with appropriate compromise. The double impulse as a simplified version of one-cycle sine wave as a representative of the main part of near-fault ground motions can simulate the maximum interstory drifts properly. However, it cannot simulate the maximum accelerations due to its impulsive nature. In this case, the sine wave corresponding to the double impulse can play an important role in the reliable simulation of the maximum accelerations. Even in such circumstance, the analysis using the double impulse is important because it enables to obtain the critical timing of the input, i.e. the nonlinear resonant frequency of the sine wave without repetition. The investigations on the criticality of the sine wave corresponding to the critical double impulse show that the critical timing of the double impulse leads to the nonlinear resonant frequency of the sine wave in view of the maximum interstory drift, the maximum top acceleration and the maximum relative acceleration for the constant input acceleration and the constant input velocity except for some cases. It is demonstrated finally that the index in terms of the maximum interstory drift and the maximum acceleration can be introduced as an appropriate parameter for deriving the optimally compromised gap quantity of hysteretic dampers with gap mechanism for various input velocity levels and various hysteretic damper stiffness ratios.

The optimal and smart design of nonlinear building structures with and without passive dampers subjected to earthquake loading is of great concern in the structural design of building structures. The research started around 1980 and many investigations have been conducted. A comprehensive review on this subject is made in this article. After the description of essential features of the optimal design problem of nonlinear building structures under earthquake ground motions, analysis types of optimization problems are explained and the significance of the dynamic pushover analysis is discussed from the viewpoint of analysis of limit states under earthquake ground motions of magnitude larger than the code-specified level. Then, the categorization by the response of frames and dampers was made. In this categorization, several subjects are discussed first: 1) Optimal design of bare nonlinear building frames under seismic loading, 2) Optimal design of nonlinear dampers for elastic building frames under seismic loading, 3) Optimal design of linear dampers for nonlinear building frames under seismic loading, 4) Optimal design of nonlinear building frames with specified nonlinear dampers under seismic loading, 5) Optimal design of nonlinear dampers for specified nonlinear building frames under seismic loading, 6) Simultaneous optimization of elastic-plastic building structures and passive dampers. Finally, the classification of researches in view of solution strategies is conducted for providing another viewpoint.

The critical responses are investigated for a high-rise building with a deformation-concentration seismic control system under double and multi impulses representing pulse-type and long-duration ground motions, respectively. The critical responses were studied for an elastic-plastic multi-degree-of-freedom (MDOF) shear building model under a double impulse and a multi impulse in the previous papers. However, it seems difficult to derive the critical response for a realistic three-dimensional (3-D) nonlinear frame model with a deformation-concentration seismic control system under such double and multi impulses. The criteria on the criticality of the double and multi impulses for the elastic-plastic MDOF shear building model derived in the previous research are extended to this realistic controlled 3-D frame model by regarding the sum of base story shear forces of both main and sub buildings as a key quantity. In the analysis, the concepts of “Double Impulse Pushover (DIP)” and “Multi Impulse Pushover (MIP)” introduced before are used effectively for clarifying the progressive performances for the increasing input level. The analyses of total input energy, frame hysteretic energy and damper dissipation energy are conducted and the criticality of the input derived based on the above-mentioned criteria is investigated in detail.

A new method of robust damper design is presented for elastic-plastic multi-degree-of-freedom (MDOF) building structures under multi-level ground motions (GMs). This method realizes a design that is effective for various levels of GMs. The robustness of a design is measured by an incremental dynamic analysis (IDA) curve and an ideal drift response curve (IDRC). The IDRC is a plot of the optimized maximum deformation under a constraint on the total damper quantity vs. the design level of the GMs. The total damper quantity corresponds to the total cost of the added dampers. First, a problem of generation of IDRCs is stated. Then, its solution algorithm, which consists of the sensitivity-based algorithm (SBA) and a local search method, is proposed. In the application of the SBA, the passive added dampers are removed sequentially under the specified-level GMs. On the other hand, the proposed local search method can search the optimal solutions for a constant total damper quantity under GMs’ increased levels. In this way, combining these two algorithms enables the comprehensive search of the optimal solutions for various conditions of the status of the GMs and the total damper quantity. The influence of selecting the type of added dampers (oil, hysteretic, and so on) and the selection of the input GMs on the IDRCs are investigated. Finally, a robust optimal design problem is formulated, and a simple local search-based algorithm is proposed. A simple index using the IDRC and the IDA curve of the model is used as the objective function. It is demonstrated that the proposed algorithm works well in spite of its simplicity.

A pseudo-double impulse (PDI) is proposed as an extension of the ordinary double impulse (DI) as a substitute of a one-cycle sine wave. PDI is treated as a set of impulsive lateral forces while the ordinary DI was introduced as an impulsive ground acceleration. The deformation and acceleration responses of multi-degree-of-freedom (MDOF) models under DI largely exceed those under the corresponding one-cycle sine wave as a main part of a near-fault ground motion. This is because DI has multiple frequency components and the higher-mode responses are excited. While the influence coefficient vector of the ordinary DI consists of 1 at every component, the influence coefficient vector of PDI is set to be proportional to the undamped fundamental natural mode. Therefore, the fundamental-mode response is mainly excited and the higher-mode responses are hardly excited by PDI. The displacement responses, the velocity responses and the input energy under DI and those under PDI are derived here for both elastic proportionally and non-proportionally damped MDOF models. The critical timing under PDI is also derived. The critical timing can be obtained by the time-history response analysis without repetition. It is demonstrated through the time-history response analysis that the distributions of interstory drifts and floor accelerations under the critical PDI correspond well to those under the critical one-cycle sine wave. Moreover, it is shown that, as far as the input level is large, the critical input period of PDI and that of the one-cycle sine wave correspond well. Since this procedure is not limited to elastic models, the proposed procedure helps to efficiently estimate the critical responses under the one-cycle sine wave for elastic-plastic MDOF models. Finally, the responses under recorded near-fault ground motions are compared with those under PDI. It is shown that the correspondence of the response under PDI and that under the recorded ground motions is fairly good althoug

We revisit a unique building system including a base-isolation, building-connection hybrid control system. The base-isolation system withstands pulse-type earthquake ground motions effectively and the building-connection system resists long-duration earthquake ground motions efficiently. A simple smart critical response evaluation method without nonlinear time-history response analysis is proposed for this hybrid building system under near-fault ground motions. An analytical expression of the maximum elastic-plastic deformation of a damped bilinear hysteretic single-degree-of-freedom (SDOF) model under critical double impulse as a representative of pulse-type ground motions derived in our previous paper plays an important role in the development of the simple critical response evaluation method. A two-step transformation procedure into an SDOF model is proposed. The first step is the transformation of the main base-isolated building into an SDOF system and the second step is the reduction of the connecting dampers supported on a sub building to a damper with a sophisticated compensation factor on an assumed rigid wall. The evaluation of damping coefficients with the consideration of yielding of the base-isolation story is a key step in this paper. Different from the previous work, the equivalent damping coefficient is derived depending on the response range before and after yielding of the base-isolation story. This treatment enhances the accuracy of the proposed method. The accuracy and reliability of the proposed response evaluation method is demonstrated by the time-history response analysis of the multi-degree-of-freedom (MDOF) model.

Knowledge of the camera motion is important in the applications of structural dynamic response measurement using a vision-based approach because in most of the field measurements, such motion can be non-trivial and the accuracy of dynamic response measurements is strongly affected by the camera motion. This paper presents a new framework for camera motion estimation and vision-based displacement measurement, which greatly lowers the barriers to the application of generally positioned cameras from strictly stationary cameras. The contributions in this paper are twofold. First, camera motion as well as reconstructed structural displacement are calculated based on reference planar structures visible in a given scene. In this case, a homography is more effective at describing view changes and planar geometric constraints can be incorporated early in the reconstruction process, thereby improving the quality and effectiveness of the estimates. The second contribution is that the homography of the planar structure is estimated by a newly proposed tracking algorithm that combines RANSAC algorithm and Efficient Second-order Minimization (ESM) technique, which refines the final estimates to sub-pixel accuracy and avoids tracking drift and non-smoothness effectively. Experimental results indicate that the quality of the camera motion estimation and displacement reconstruction can be significantly improved by the judgmatical use of the proposed algorithm for planar structure homography estimation. Furthermore, nonlinear structural system identification is carried out to additionally verify the proposed algorithm using unscented Kalman filter.

We propose a new flexible technique for accurate vision-based seismic displacement measurement of building structures via a single non-stationary camera with any perspective view. No a priori information about the camera’s parameters or only partial knowledge of the internal camera parameters is required, and geometric constraints in the world coordinate system are employed for projective rectification in this research. Whereas most projective rectifications are conducted by specifying the positions of four or more fixed reference points, our method adopts a stratified approach to partially determine the projective transformation from line-based geometric relationships on the world plane. Since line features are natural and plentiful in a man-made architectural building environment, robust estimation techniques for automatic projective/affine distortion removal can be applied in a more practical way. Both simulations and real-recorded data were used to verify the effectiveness and robustness of the proposed method. We hope that the proposed method could advance the consumer-grade camera system for vision-based structural measurement one more step, from laboratory environments to real-world structural health monitoring systems.

The spread of COVID-19 all over the world since the beginning of the year 2020 requires a re-thinking of the meaning of the term “resilience” in the field of architecture and architectural engineering. Resilience from the viewpoint of architecture and architectural engineering has been investigated primarily in terms of conventional natural disaster risks (see, for example, Bruneau et al., 2003; Cimellaro et al., 2010;Architectural Institute of Japan [AIJ], 2020a). However, COVID-19 reminds us of the need to investigate resilience also in terms of infection risks. The places where people become infected are principally within buildings and transportation systems. Especially in buildings, three factors considered to be main risks for infection (closed spaces without ventilation, dense gatherings, close connection) often occur. For this reason, the role of architecture and architectural engineering is essential from the viewpoint of reducing the risk of infection, using versatile knowledge and technologies from the fields of architectural and regional planning. Following the appearance of COVID-19, architectural designers and engineers have an important mandate to think about the role of buildings and their related fields.

The critical response is investigated for a multi-story damped bilinear hysteretic shear building model under a multi impulse as a representative of long-period, long-duration earthquake ground motions. The critical response for an elastic–plastic single-degree-of-freedom (SDOF) model under a multi impulse was derived in previous papers. However, it is difficult to derive the critical response for a multi-degree-of-freedom (MDOF) model under a multi impulse because the phase lag among masses induces a complicated situation. In place of deriving an explicit critical response, a criterion on the criticality of the multi impulse for the elastic–plastic MDOF model is derived and the properties of the critical responses are clarified. In the analysis, a new concept of “Multi Impulse Pushover (MIP)” is introduced and the progressive performance evaluation for the increasing input level is conducted. The analysis of energy response (input energy, dissipated energy, etc.) and the comparison with the response to the corresponding sinusoidal wave are made to enhance the reliability and practicality of the proposed method using the multi impulse as a substitute of sinusoidal waves, which are representatives of long-period, long-duration earthquake ground motions.

A new method for simultaneous optimal design of main building structures and viscous dampers is proposed for elastic-plastic multi-degree-of-freedom (MDOF) building structures subjected to the critical double impulse which is regarded as a representative of the main part of near-fault ground motions. The critical double impulse is characterized by the maximum energy input to the total system by the second impulse and the sum of the restoring force and the damping force in the first story attains zero by this critical input. The objective function is the maximum interstory drift along the building height. The original optimization problem is transformed into a problem of removing the most inactive story stiffness and damper damping coefficient. An efficient sensitivity-based design algorithm is developed for this simultaneous optimal design problem of main building structures and viscous dampers. It is pointed out that the order of changes of structural stiffness and damper damping magnitude is critical to the achievement of reasonable designs and cycle-by-cycle alternating redesign of story stiffness and damper damping coefficient is effective for its achievement. The double impulse pushover (DIP) analysis proposed in the previous paper (Akehashi and Takewaki, 2019) for determining the input velocity level of the critical double impulse is also conducted to disclose the response characteristics of the designed building structures and dampers. It is shown that the proposed design method enables the high yield-strength design with effective seismic energy absorption and the high limit-strength design effective for extremely large disturbances. The distributions of the maximum acceleration responses in an initial design and the final design are also presented for the one-cycle sine wave corresponding to the critical double impulse.

This paper is aimed at proposing a hysteretic-viscous hybrid (HVH) damper system for tall buildings subjected to long-period pulse-type earthquake ground motions of extremely large amplitudes. The HVH system was introduced for a single-degree-of-freedom (SDOF) system in the recent paper (Hashizume and Takewaki, 2020). The HVH system consists of a large-stroke viscous damper and a hysteretic damper with a gap mechanism as a stopper for mitigating catastrophic damage. In the present paper, the effectiveness of the HVH system is shown for tall buildings. Pulse-type earthquake ground motions of an extremely large amplitude have been recorded in the past (for example Northridge 1994 and Kumamoto 2016). These ground motions risk causing catastrophic damage to high-rise and base-isolated buildings with a long natural period. A double impulse is used here as a substitute for pulse-type ground motions of an extremely large amplitude. Time-history response analyses are performed for an amplitude-modulated critical double impulse to reveal the effectiveness of the proposed HVH system. In addition, double impulse pushover (DIP) analysis, which was proposed by Akehashi and Takewaki (2019), is conducted to reveal the critical resonant performance of elastic-plastic tall buildings together with the analysis for recorded ground motion at Kumamoto (2016). A comparison with the dual hysteretic damper (DHD) system composed of parallel-type small- and large-amplitude hysteretic dampers is also conducted to investigate the seismic performance of the proposed HVH system.

This paper aims to develop a hysteretic–viscous hybrid (HVH) damper system for long-period pulse-type earthquake ground motions of large amplitude. Long-period pulse-type earthquake ground motions of large amplitude have been recorded recently (Northridge, 1994; Kumamoto, 2016). It is well-known that these ground motions could cause severe damage to high-rise and base-isolated buildings with long natural period. To mitigate the damage caused by such ground motion, a new viscous–hysteretic hybrid damper system is proposed here, which consists of a viscous damper with large stroke and a hysteretic damper including a gap mechanism. A double impulse is employed as a representative of long-period pulse-type earthquake ground motions of large amplitude and a closed-form maximum response to this double impulse is derived for an elastic–plastic SDOF system including the proposed HVH system. To reveal the effectiveness of the proposed HVH system, time-history response analyses are performed for an amplitude modulated double impulse and a recorded ground motion at Kumamoto (2016). The performance comparison with the previous dual hysteretic damper (DHD) system consisting of small-amplitude and large-amplitude hysteretic dampers in parallel is also conducted to investigate the effectiveness of the proposed HVH system.

A dynamic collapse criterion for elastic–plastic structures under near-fault ground motions is derived analytically by approximately transforming near-fault ground motions into double impulse and using an energy balance law. A negative post-yield stiffness is introduced to treat the P-delta effect in the single-degree-of-freedom (SDOF) model. The principal part of fling-step near-fault ground motions is modeled by a one-cycle sine wave and then a double impulse. The double impulse enables the efficient use of the energy approach in the derivation of compact expressions of complicated elastic–plastic responses of structures with the negative post-yield stiffness. In contrast to the previous work (Kojima and Takewaki, 2016b) for the resonant critical case, a general collapse criterion is provided for the velocity amplitude and the frequency of the double impulse. It is significant that no iteration is needed in the derivation of the dynamic collapse criterion except the solution of transcendental equations. It is shown that discussions on several patterns of dynamic collapse behaviors introduced in the previous critical case are useful for deriving a boundary between the collapse and the non-collapse in the plane of the input velocity and the input frequency. The most important point to be remarked is that the critical state (Kojima and Takewaki, 2016b) corresponding to the non-linear resonance does not necessarily provide the minimum input velocity level with respect to arbitrary impulse timing. The validity of the proposed dynamic collapse criterion is examined by the numerical response analysis for structures under double impulses with collapse or non-collapse parameters.

While linear system identification (SI) has been developed extensively, research advancement in the field of non-linear hysteretic SI is not satisfactory. An innovative method is proposed in this paper for identification of hysteretic restoring-force characteristics of three-dimensional (3D) building structures with in-plane flexible floors. The hysteretic restoring-force characteristics of vertical structural frames in the 3D building structure are identified from the measured floor horizontal accelerations together with the hysteretic restoring-force characteristics of floors without the assumption of hysteresis types or a priori knowledge of restoring force characteristics. Fourier expansion is applied to the time-history responses of story shear forces in vertical frames and in-plane shear forces in horizontal frames (floors). A batch processing least-squares estimation method for measured data is shown to be applicable to the identification of the Fourier coefficients on the story shear forces in vertical structural frames and those on the in-plane shear forces in floors. The proposed method is simple and direct because only Fourier expansion and batch processing least-squares estimation are required. Numerical simulations with and without noise are conducted for investigating the accuracy and reliability of the proposed method. It is demonstrated that the proposed method can identify successfully the hysteretic restoring-force characteristics of plane frames in 3D building structures with in-plane flexible floors.

An innovative structural control system is proposed for high-rise buildings. A damping layer is provided between a stiff upper core frame suspended from the top of the main building and a stiff lower core frame connected to the building foundation. As the ratio of stiffness of both core frames to that of the main building becomes larger, the relative displacement in the damping layer (damper deformation) approaches to the top floor displacement of the main building. The large displacement of the top floor displacement of the main building is taken full advantage in the proposed control system as most of the total displacement of the main building results from the damper deformation instead of interstory drift. Transformation of the multi-degree-of-freedom (MDOF) model into the single-degree-of-freedom (SDOF) model enables a simplified but rather accurate response evaluation for pulse-type and long-duration earthquake ground motions. The results of the time history response analysis of buildings including this control system are presented for various recorded ground motions. Finally, the effectiveness of the proposed structural control system is discussed from the viewpoint of earthquake input energy.

The effectiveness of the optimal viscous damper placement for elastic-plastic multi-degree-of-freedom (MDOF) structures under the critical double impulse is demonstrated through the comparison with the optimal damper placement for elastic MDOF structures designed with respect to transfer function amplitudes at natural frequencies. The method for optimal viscous damper placement was proposed for elastic-plastic MDOF structures subjected to the critical double impulse as a representative of near-fault ground motions in the previous paper [1]. The double impulse is composed of two impulses with opposite directions and the critical interval is determined by using the criterion on the maximum input energy. The critical timing of the second impulse was found to be the timing which requires the vanishing of the sum of the restoring force and the damping force in the first story. Three models with different story stiffness distributions of main structures are treated to demonstrate the effectiveness of the optimal viscous damper placement under the critical double impulse. The double impulse pushover (DIP) procedure proposed in the previous paper for determining the input velocity level of the critical double impulse is examined further in this paper. It is demonstrated that the optimal viscous damper placement for elastic-plastic MDOF structures under the critical double impulse is more effective for pulse-type recorded earthquake ground motions than the optimal damper placement designed with respect to transfer function amplitudes at natural frequencies because several higher modes arising in the elastic-plastic response under pulse-type recorded earthquake ground motions can be well controlled by the design for the double impulse.

This paper proposes a novel model-based damage identification strategy based on minimum constitutive relation error and sparse regularization using the power spectrum density data. Firstly, the stationary random vibration problem is transformed into a series of harmonic vibrations by the pseudo excitation method and the error in constitutive relation is established by the admissible stress field and admissible displacement field. A much more general and simpler strategy so as to build the admissible stress field is addressed by requiring only an extra decomposition of the stiffness matrix. Then, the sparse regularization is added to the original constitutive relation error objective function to circumvent the ill-posedness of the inverse problem. Finally, the solution of this nonlinear optimization problem is solved by the alternating minimization method. The proposed method has the advantage that only measurement power spectrum density data from few limited sensors are needed in the inverse analysis. Numerical and experimental results show the effectiveness and robustness of this approach.

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.

The double-impulse input is introduced as a substitute for the fling-step near-fault ground motion, and a closed-form solution for the approximate elastic-plastic response of a structure with viscous damping under the “critical double impulse” is derived. Since only the free vibration appears under such a double impulse, the energy approach plays an important role in the derivation of the closed-form solution for a complicated elastic-plastic response with viscous damping. The quadratic function approximation for the damping force-deformation relationship is introduced. The validity and accuracy of the proposed theory are investigated through comparison of the results of the response analysis to the corresponding one-cycle sinusoidal input and actual recorded ground motions.

An evaluation method of robustness of base-isolation building-connection hybrid controlled building structures is developed by introducing a measure for robustness (robustness function) and considering shallow and deep ground uncertainties. The earthquake ground-motion amplitude at the earthquake bedrock is evaluated by the Boore’s stochastic method including the fault rupture and the wave propagation into the earthquake bedrock. Then, the phase angle property at the earthquake bedrock is investigated by introducing the concept of phase difference, which is defined for each earthquake type. The ground-motion amplification in the shallow and deep ground is expressed by the one-dimensional wave propagation theory. The robustness of base-isolation building-connection hybrid controlled building structures is measured by use of the robustness function due to Ben-Haim (2006) and is evaluated by taking full advantage of the updated-reference-point method. It is shown that, as the total quantity of damping coefficients of connection dampers increases, the robustness for the deformation of the base-isolation story becomes larger without the drastic reduction of the robustness for the top acceleration.

Multi impulse is used as a representative of a series of many-cycle harmonic waves which substantially simulate the long-duration earthquake event. An analytical formulation is developed for the elastic-plastic response of a single-degree-of-freedom (SDOF) damped structure with bilinear hysteresis under the critical multi impulse condition. Following the procedure for elastic-perfectly plastic models, a novel procedure using an energy balance law is introduced. In this procedure, under the multi impulse condition, only the free-vibration exists, hence the energy balance law can be applied easily. An approximate but effective treatment of the energy dissipated by the viscous damping is a new perspective. It is shown that based on an analytical solution, the critical maximum plastic deformation and the corresponding critical impulse timing can be determined in the steady state condition depending on the input values. To investigate the reliability and accuracy of the proposed approach, a comparison is made with the response analysis outcome to the corresponding sine wave as a representative of the long-duration earthquake ground motion (GM).

Traditional base isolation systems focus on isolating the seismic response of a structure in the horizontal direction. However, in regions where the vertical earthquake excitation is significant (such as near-fault region), a traditional base-isolated building exhibits a significant vertical vibration. To eliminate this shortcoming, a rocking-isolated system named Telescopic Column (TC) is proposed in this paper. Detailed rocking and isolation mechanism of the TC system is presented. The seismic performance of the TC is compared with the traditional elastomeric bearing (EB) and friction pendulum (FP) base-isolated systems. A 4-storey reinforced concrete moment-resisting frame (RC-MRF) is selected as the reference superstructure. The seismic response of the reference superstructure in terms of column axial forces, base shears, floor accelerations, inter-storey drift ratios (IDR) and collapse margin ratios (CMRs) are evaluated using OpenSees. The results of the nonlinear dynamic analysis subjected to multi-directional earthquake excitations show that the superstructure equipped with the newly proposed TC is more resilient and exhibits a superior response with higher margin of safety against collapse when compared with the same superstructure with the traditional base-isolation (BI) system.

The process of theoretical ground motion generation consists of (i) the fault rupture process, (ii) the wave propagation from the fault to the earthquake bedrock, (iii) the site amplification. The uncertainty in the site amplification was taken into account in the previous research (Makita et al., 2018). On the other hand, the uncertainty in the fault rupture slip (slip distribution and rupture front) is dealt with in the present paper. The wave propagation from the fault to the earthquake bedrock is expressed here by the stochastic Green's function method in which the Fourier amplitude of the ground motion at the earthquake bedrock from a fault element is represented by the Boore's model and the phase angle is modeled by the phase difference method. The validity of the proposed method is investigated through the comparison with the existing simulation result by other methods. By using the proposed method for ground motion generation and for optimization under uncertainty in the fault rupture slip, a methodology is presented for deriving the critical ground motion imposing the maximum response of an elastic SDOF model at the earthquake bedrock or at the free ground surface. It is shown that the critical response exhibits the SDOF response several times larger than that due to the average fault rupture slip model. Furthermore, the robustness evaluation with respect to the uncertain fault rupture slip and the uncertain fault rupture front is presented for resilient building design. Since the critical ground motion produces the most detrimental building response among possible scenarios, the proposed method can be a reliable tool for resilient building design.

This paper presents a novel sparse‐regularized minimum constitutive relation error (min‐CRE) approach for structural damage identification with modal 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 that is caused by use of the possibly insufficient modal data and enhance the robustness of the identification process, the sparse regularization is introduced where a sparse (or ℓ₁‐norm) regularization term is added to the original CRE function. In regard to the minimum solution of the sparse‐regularized CRE objective function, a two‐step substitution algorithm is established. The attractive feature of the present damage identification approach is that no sensitivity analysis is involved herein and the additional introduction of the sparse regularization term introduces little computational complexity. The approach is applied to damage identification of one‐ or two‐dimensional beam structures with experimental or simulated modal data. Results show that the sparse regularization indeed improves the effectiveness and robustness of the min‐CRE approach under measurement noises and initial model errors, even in the case of large damages.

A double impulse input is used as a substitute for near-fault earthquake ground motions. An explicit expression is derived on the maximum elastic–plastic response of a single-degree-of-freedom damped structure with bilinear hysteresis under the “critical double impulse input” which causes the maximum response for variable impulse interval with the input level kept constant. Owing to the existence of only the free vibration under the double impulse, the approach of energy balance for the kinetic energy, hysteretic and strain energies, and damping energy plays a crucial role for deriving the explicit expression on a complicated damped bilinear hysteretic response. It is shown that the critical elastic–plastic deformation and the critical impulse timing, the interval of two impulses, can be derived depending on the input level. The accuracy and reliability of the proposed simplified but smart methodology are investigated through the comparison with the results by the response analysis to the critical double impulse and the corresponding one-cycle sine wave as a representative for the near-fault earthquake ground motion.

The critical nonlinear response considering soil-structure interaction is investigated for a base-isolated building under a double impulse as a substitute for near-fault earthquake ground motions. The complicated model of the nonlinear base-isolated building considering soil-structure interaction is first modeled as a two-degree-of-freedom (2DOF) system (SDOF superstructure and base-isolation story) on a swaying-rocking spring-dashpot system. Then the 2DOF system on a swaying-rocking spring-dashpot system is transformed into an SDOF system on a swaying-rocking spring-dashpot system by neglecting the mass on the base-isolation story. Finally the SDOF system on a swaying-rocking spring-dashpot system is further transformed into an SDOF system by neglecting the mass and moment of inertia of the base mat. Since an explicit expression had been derived in the previous paper on the maximum elastic-plastic response of an SDOF damped bilinear hysteretic structure subjected to the “critical double impulse input” causing the maximum response for variable interval of impulses with the input level kept constant, this expression is applied to the finally transformed SDOF system. The transformation of structural viscous damping in different elements is another new aspect in this paper. The reliability and accuracy of the proposed simplification methodology are investigated by comparing with the results by the time-history response analysis under the critical double impulse and the one-cycle sine wave as a representative of the main part of the near-fault earthquake ground motion.

An innovative hybrid control building system of base-isolation and building-connection has been proposed in the previous study. This system has two advantages, (i) to resist an impulsive earthquake input through the base-isolation system and (ii) to withstand a long-duration earthquake input through the building-connection system. A simple response evaluation method without the need of non-linear time–history response analysis is proposed here for this hybrid building system under a long-period and long-duration ground motion. An analytical expression is derived in the plastic deformation of an elastic–perfectly plastic single-degree-of-freedom (SDOF) model with viscous damping under the multi-impulse, which is the representative of long-period and long-duration ground motions. A transformation procedure of a base-isolation building-connection hybrid structural system into an SDOF model is proposed by introducing two steps, one is the reduction of the main base-isolated building to an SDOF system, and the other is the reduction of the connecting oil dampers supported on a free-wall to an oil damper with a newly introduced compensation factor on a rigid wall. Application of the analytical expression of the plastic deformation to the reduced SDOF model including the compensation factor on the connecting oil dampers enables the development of a simplified, but rather accurate response evaluation method. The time–history response analysis of the multi-degree-of-freedom model and the comparison with the proposed simplified formula make clear the accuracy and reliability of the proposed simplified response evaluation method.

A system identification problem is investigated for high-rise buildings to identify the story stiffnesses of a shear-bending model (SB model). In the previously proposed stiffness identification method due to the present authors, the shear and bending stiffnesses of the SB model were identified by means of the subspace and inverse-mode methods. The lowest mode of horizontal displacements and floor rotation angles of the objective building was identified first by using measured data of both horizontal and rotational accelerations via the subspace method. Taking into account the resolution in the measurement of floor rotation angles in lower stories, floor rotation angles in all stories were predicted from the floor rotation angle at the top floor. However, it was difficult to obtain the bending stiffnesses reliably in the previous method. In this paper, to overcome the difficulty in the stiffness identification method using the SB model, a statistical model-updating approach is proposed, where the probability distribution of floor rotation angles in the lowest mode is obtained for the identified SB model, and a conditional probability problem is applied by providing additional measured data on floor rotation angle. The proposed stiffness identification method is useful for the structural health monitoring of high-rise buildings. For investigation of the validity of the proposed stiffness identification method, a 10-story plane-building frame is examined under micro-tremor.