Shear Building Research Articles

Nontarget-Based Measurement of 6-DOF Structural Displacement Using Combined RGB Color and Depth Information

Structural displacement is an important physical quantity that provides essential information regarding the structural conditions and the safety of a structure. To date, a wide variety of displacement measurement methods have been developed. As a noncontact type of measurement, the computer-vision-based approach receives significant attention for its cost effectiveness, measurement convenience, and great performance. However, most existing methods are limited to one- or two-degrees-of-freedom (DOF) displacement measurement and require known dimensions of structural members or predefined target markers attached to the target structure, which limits real-world application. This article proposes a nontarget-based 6-DOF displacement measurement method using the combined RGB and depth information. The proposed method utilizes three-dimensional information of measurement points on the target structure obtained using the RGB-D camera, and suggests a coordinate transform scheme to determine the 6-DOF displacement in the physical domain. The proposed method is validated in two laboratory experiments using a shear building model and a pan-tilt with a measurement plate, in which both translational and rotational displacements are measured.

Exploiting convexification for Bayesian optimal sensor placement by maximization of mutual information

Bayesian optimal sensor placement, in its full generality, seeks to maximize the mutual information between uncertain model parameters and the predicted data to be collected from the sensors for the purpose of performing Bayesian inference. Equivalently, the expected information entropy of the posterior of the model parameters is minimized over all possible sensor configurations for a given sensor budget. In the context of structural dynamical systems, this minimization is computationally expensive because of the large number of possible sensor configurations. Here, a very efficient convex relaxation scheme is presented to determine informative and possibly optimal solutions to the problem, thereby bypassing the necessity for an exhaustive, and often infeasible, combinatorial search. The key idea is to relax the binary sensor location vector so that its components corresponding to all possible sensor locations lie in the unit interval. Then, the optimization over this vector is a convex problem that can be efficiently solved. This method always yields a unique solution for the relaxed problem, which is often binary and therefore the optimal solution to the original problem. When not binary, the relaxed solution is often suggestive of what the optimal solution for the original problem is. An illustrative example using a 50‐story shear building model subject to sinusoidal ground motion is presented, including a case where there are over 47 trillion possible sensor configurations. The solutions and computational effort are compared with greedy and heuristic methods.

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. A semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

A Novel Approach for Evaluating Nonstationary Response of Dynamic Systems to Stochastic Excitation

The transient state of a dynamic system, such as offshore structures, to random excitation is always nonstationary. Many studies have contributed to evaluating response covariances at the transient state of a linear multi-degree-of-freedom (MDOF) system to random excitations, but a closed-form solution was not available unless the excitation was assumed to be a physically unrealizable white noise process. This study derives explicit, closed-form solutions for the response covariances at the transient state by using a pole-residue (PR) approach operated in the Laplace domain when the excitations are assumed to be stationary random processes described by physically realizable spectral density functions. By using the PR method, we can analytically solve the triple integral in evaluating the nonstationary response covariance. As this approach uses the poles and residues of system transfer functions, rather than the conventional mode superposition technique, the method is applicable to MDOF systems with non-classical damping models. Particular application of the proposed method is demonstrated for multi-story shear buildings to stochastic ground acceleration characterized by the Kanai-Tajimi spectral density function model, and a numerical example is provided to illustrate the detailed steps. No numerical integrations are required for computing the response covariances as the exact closed-form solution has been derived. The correctness of the proposed method is numerically verified by Monte Carlo simulations.

Statistical seismic performance assessment of tuned mass damper inerter

In this study, the robust optimum design of a recently developed passive control device, i.e., tuned mass damper inerter (TMDI) is investigated to control a 10-story base-excited shear building benchmark. The H2 and H∞ of three different objective functions (i.e., minimizing roof displacement, minimizing 7th-story displacement, and maximizing the TMD stroke) are selected as objective functions for two different single and double inerter configurations. Optimum free vibration parameters of the TMDI (i.e., natural frequency and damping ratios) are calculated using a metaheuristic technique for two different structural damping values. Additionally, the performance of the optimum designed damper and its robustness under 25 far-fault (FF) ground motions are assessed in the time domain with 12 different performance criteria (i.e., the mean and standard deviation of the maximum and norm of response histories for roof displacement, roof acceleration, and the total kinetic energy of the building). Based on current work, the best performance index for single TMDI for all three objective functions is the roof absolute acceleration, showing a maximum of 45% reduction in the mean maximum roof acceleration for 25 earthquake records. Therefore, the TMDI is most effective when the goal is to reduce the floor accelerations. The double inerter configuration shows approximately the same values for the performance indices for all three objective functions and demonstrates similar reduction for a single TMDI. However, it increases the robustness of the control method by adding redundancy and enhancing the performance for different combinations of inertance and mass ratios.

Robust optimum design of a tuned mass damper inerter

The current work describes the optimum design of a tuned mass damper inerter (TMDI) to control a benchmark 10-story base-excited linear shear building under seismic excitations. Mass and inertance ratios are preselected, and optimum free vibration parameters of the TMDI (i.e., natural frequency and damping ratios) are calculated for single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF) models with different configurations of single and double inerter TMDIs at different locations using the colliding bodies optimization technique. Four different inherent damping values are considered for each analysis. Minimizing the $$H_{\mathrm{\infty }}$$ norm of the roof displacement transfer function is considered as the objective function for robust control of the building. Additionally, the optimum designed damper performance and its robustness is assessed in both the frequency and time domains. Results show that while being robust, the SDOF-based optimized TMDI approach should be used with caution and it is recommended to optimize and employ the TMDI using the MDOF model. Results indicate the superior performance of the proposed well-tuned damper with proper configuration in comparison to a same weight/mass classical TMD.

Development of semi-active mass damper with impulsive reaction

A new semi-active mass damper, included active joint to control Lock/Unlock between the mass of damper and structure, is proposed to avoid “de-tuning effect” in this study. A ten-floor shear building with Tuned Mass Damper (TMD) and Semi-Active Mass Damper (SAMD) under excitation of 26 earthquake records is simulated by numerical analysis to compare the shock absorption effects. Analysis results show that: (1) Shock absorption of roof displacement and root mean square (RMS) roof displacement is 9.9%, 15.8% and 67.9%, 70.9% for structure with TMD and SAMD under excitation of Kobe 1995 earthquake respectively. Shock absorption of roof displacement and RMS roof displacement 52.7%, 62.1% and 55.7%, 66.3% for structure with TMD and SAMD under excitation of Sumatra 2007 earthquake respectively. (2) Structural response of building with SAMD controlled is very low sensitivity to frequency ratio. SAMD control effect is better than that of TMD on near fault earthquakes and suitable for far-field earthquakes. Otherwise, SAMD is almost without “de-tuning effect”. (3) Shock absorption ratio of the roof displacement responses and RMS displacement responses for structure with SAMD under excitation of far-field earthquake is above 38% and 62%, respectively. The frequency ratio of SAMD controlled should be limited to less than 4.0 to avoid enlarging the maximum acceleration responses. The practicability of this proposed SAMD has been verified by numerical analysis.

The Effect of Nonlinear Soil–Structure Interaction on the Ductility and Strength Demands of Vertically Irregular Structures

Soil–structure interaction (SSI) is key to the elastic and inelastic seismic responses of buildings. In this research, the ductility and strength demands of vertically irregular MDOF buildings, considering nonlinear SSI effects, are parametrically investigated. The superstructure is modeled as a nonlinear multi-story shear building, and the beam on nonlinear Winkler foundation (BNWF) concept is employed to simulate the response of shallow foundations. Specifically, combined stiffness–strength irregularities are introduced by reducing lateral properties at a specific story of the regular (reference) models. Soil–structure systems with 5, 10, and 15 stories are analyzed under three sets of earthquake records corresponding to different soil classes. A wide range of key parameters including number of stories, fundamental period, level of inelasticity, aspect ratio, and site class are scrutinized through nonlinear time history analyses. The results reveal that SSI can reduce the strength and ductility demands of the vertically irregular structures, especially those with short periods. This beneficial effect becomes even more significant for systems with low ductility ratios. It is also concluded that the median ductility demand increases in the modified story owing to the softness/weakness of the first story. Furthermore, this increase due to the code strength regularity limit reached up to 78% and 36% in fixed-base and flexible-base conditions, respectively. Finally, simplified equations are proposed to estimate the maximum ductility demands of regular and irregular structures with flexible-base conditions.

Multi‐resolution broad learning for model updating using incomplete modal data

A novel multi-resolution broad learning (MRBL) approach is proposed for model updating using identified modal data. Due to measurement noise and limited monitoring locations, the identified modal data are incomplete and noise corrupted. Besides, it is inevitable to have modeling errors in finite element models. Therefore, it is nontrivial to establish simple explicit relationship to represent the nonlinear mapping from modal data to structural model parameters. The proposed approach aims to model this implicit mapping using a nonparametric approach. For this purpose, the nonlinear relationship is learnt based on a multi-resolution recursive procedure with expandable broad learning networks. In contrast to conventional deep learning, the proposed approach is computationally very economical. Instead of requiring large volumes of training data, the multi-resolution approach adaptively zooms into the important region for sampling. Hence, satisfactory accuracy in model updating can be achieved by using a feasible amount of training data. Moreover, the broad learning network is expandable to adopt architectural modification, so it can be reconfigured incrementally based on the inherit information from the trained network. To demonstrate the efficacy of the proposed approach, illustrative examples of a shear building and a three-dimensional braced frame with unobserved torsional mode are presented. Finally, an application using real data of Canton Tower is also presented.

Effective live load mass for storage buildings on friction-pendulum isolators

This paper presents the results from finite element models of based-isolated storage buildings subjected to ground motion excitation and supporting rigid blocks with the possibility to slide. Main components of the models were first compared and calibrated with the results from numerical solutions, finite element software, and shake table tests. The successfully verified finite element models were then used to assess ASCE 7–16 design provisions for the treatment of storage loads as seismic weight in base-isolated structures. The analyses included multi-story shear buildings of different heights and three-dimensional buildings of three-stories with both regular and irregular plans under combined horizontal and vertical ground excitation. Alternative low and high friction between the rigid blocks (representing the storage live load) and the floor deck were evaluated in the analyses as well as the effect of light versus heavy storage live loads. Ground excitation consisted of 100 records, covering scenarios that range from low to high seismic risk. The combination of cases included in the parametric study led to thousands of nonlinear time history analyses. Selected engineering design parameters (EDP) to conduct the evaluation consisted of isolator deformation and maximum force demands in the lateral load resting system. Calculated EDPs from the detailed models (accounting for inelastic response of the lateral load resisting system coupled with potential sliding of rigid blocks) were compared with calculated EDPs from simplified models with no blocks but having additional floor mass equal to 25% of the design live load. The latter models represented analysis conditions that ASCE 7–16 minimum provisions would allow in consulting practice. This study demonstrates that using the Standard’s minimum provision can lead to: i) significant underestimations of the deformation demand and thus unconservative designs of base isolators; ii) significant underestimations of design forces, and consequently, improper design of the lateral load resisting elements. In order to address these issues, a simple expression recently developed by the authors to estimate the portion of the design live load as seismic weight was also evaluated. It is shown that using the portion of the live load given by this equation in the simplified models with no blocks but having additional floor mass produce very similar EDPs as those obtained from the detailed models with sliding blocks and thus representing a significant improvement over the existing ASCE 7–16 minimum provisions when applied to base-isolated storage structures.

Online identification of torsionally coupled shear buildings using virtual synchronization method

In this study, the virtual synchronization method is developed for online identification of parameters in torsionally coupled shear buildings. In this method, first, a virtual model of the building is made and excited simultaneously with the actual building. Then, a proper virtual controller is designed, which forces the virtual model to follow the dynamic response of the actual building by converging the unknown parameters to the actual values. A major difficulty of the virtual synchronization method originates from the determination of its design parameters, which greatly affects the final performance. The main contribution of this study is an optimum scenario for defining the design parameters of the virtual synchronization method to maintain desirable accuracy and convergence speed. Provided numerical studies show that the proposed design scenario makes the virtual synchronization method a competitor to the other well-known methods. Also, the effect of building height and excitation on the performance of the virtual synchronization method is studied. Besides, robustness against measurement noise and modeling uncertainties are investigated.

Online jointly estimation of hysteretic structures using the combination of central difference Kalman filter and Robbins–Monro technique

Rapid assessment of structural safety and performance right after the occurrence of significant earthquake shaking is crucial for building owners and decision-makers to make informed risk management decisions. Hence, it is vital to develop online and pseudo-online health monitoring methods to quantify the health of the building right after significant earthquake shaking. Many Bayesian inference–based methods have been developed in the past which allow the users to estimate the unknown states and parameters. However, one of the most challenging part of the Bayesian inference–based methods is the determination of the parameter noise covariance matrix. It is especially difficult when the number of unknown states and parameters is large. In this study, an effective online joint estimation method for nonlinear hysteretic structures, with consideration of degradation and pinching phenomena, is proposed. Simultaneous estimation of states and parameters is conducted using the combination of a central difference Kalman filter as an effective estimator and the Robbins–Monro stochastic approximation technique as the parameters noise covariance matrix regulator. The proposed algorithm is implemented on three shear buildings with 36, 54, and 90 unknown states and parameters. To verify the performance of the system identification method, robust simulations with synthetic measurement noises and modeling errors were generated using the Monte Carlo random simulation method. The result shows the proposed method can be used to estimate the unknown parameters and states of highly nonlinear systems efficiently and effectively.

Generalized algorithms for the identification of seismic ground excitations to building structures based on generalized Kalman filtering under unknown input

The exact information of seismic excitation and structural state is a prerequisite for structural seismic safety assessment and vibration control. When the seismic excitation to a structure is not measured, the seismic excitation can be identified as an inversed problem from measured structural responses. Although some relevant approaches have been developed, there are certain limitations or drawbacks in the existing approaches. To circumvent these problems, two generalized algorithms are proposed for the identification of seismic ground excitation to multi-story and tall buildings, respectively. When the seismic ground excitation to a structure is not measured, the data measured by a structural health monitoring system are structural absolute responses. So the structural motion equation in the absolute coordinate system is derived, in which the unknown seismic ground excitation is treated as unknown external force acting on the structure. First, the identification of unknown seismic excitations to multi-story building structures is studied. A generalized Kalman filtering under unknown input is proposed for the identification of structural state and unknown seismic excitation without the observation of structural absolute acceleration responses at the location of unknown external force. The derivation of the proposed generalized Kalman filtering under unknown input is based on the classical Kalman filter, but is more general than the existing identification approaches based on Kalman filter with unknown input in the deployments of accelerometers in the building structure. Then, it is extended to explore the identification of unknown seismic excitations to tall building structures. To avoid substructural identification from the top to bottom in a sequential manner, the motion equation in absolute coordinate system is reduced by modal expansion. Moreover, instead of the identification of unknown modal forces in previous approaches, the seismic excitation is directly identified without increasing the number of unknown forces. To demonstrate the proposed algorithms, numerical examples of identifying seismic excitations to a 6-story shear building and an 18-story tall building are investigated.

Multi-objective optimal design of semi-active fluid viscous dampers for nonlinear structures using NSGA-II

This paper presents an effective method to design semi-active fluid viscous damper (SAFVD) system for mitigating the seismic responses of the nonlinear frames considering multiple safety and convenience criteria. This method is based on defining a multi-objective optimization problem with discrete objective functions of minimization of inter-story drift as safety criterion as well as absolute acceleration as convenience criterion where an improved version of the non-dominated sorting genetic algorithm (NSGA-II) has been used to solve it and find out the Pareto-optimal solutions. For this purpose, the maximum damping coefficient of the semi-active damper and parameters of the control algorithm have been selected as design variables. The effect of the uncertainty of the input seismic excitation has been considered using the mean responses under multiple real earthquakes recommended for the site that the structure is located in. To assess the effectiveness of the proposed methodology, a numerical example has been conducted on an eight-story nonlinear shear building frame with hysteretic bilinear elasto-plastic behavior. The results show that the designed optimal SAFVD system has the capability of a significant reduction in seismic responses and improving both the safety and convenience of the entire building. Also comparing the seismic performance of SAFVD system with that of active control system shows that SAFVD could perform as effective as active control system in structural response mitigation.

Investigating the Effect of Seismic Loads on Multi-Story Buildings with Different Shear Wall Configurations and Building’s Ratios

One of the main and major drawbacks of conventional and rather high rise buildings is developing lateral displacements arising from lateral loads which finally make the whole structure uneconomical. In this research, a considerable effort has been made in order to investigate the effect of shear walls configurations on the lateral displacement in addition to maximum storey drift of the structure. Shear walls can be considered as one of the basic important structural elements. When a structure is subjected to external lateral loads, such as wind loads, earthquake loads etc. these walls play the main role in increasing both the strength and the safety of the structures. Therefore, this study presents the effect of configurations of shear walls, which significantly affect the behavior of the structure under loading. In order to investigate this hypothesis, four different shapes and locations of shear walls have been considered. Additionally, three different building heights (10, 20 and 30 stories), and three various ratios of the building’s length to its width (1:1, 1:1.5 and 1:2) have been taken in order to finish this research. Finite Element based software ETABS 2015 has been used for modeling and analyzing purposes. All the models have been analyzed, and the comparison of the results has been done for lateral displacement and storey drift ratio.

Retrieval of True Lateral Load–Deformation Behavior of Axially Loaded Columns from Experimental Data

AbstractThe lateral load-deformation capacity of any structure is the most important aspect of seismic design. The lateral capacity of a shear building is highly dependent on the lateral load-defor...

Identification of Structural Matrices of Shear Buildings Using Ambient Vibration Tests with Incomplete Measurements

System identification methods (SIMs) are powerful tools for structural health monitoring. SIMs are used either for identification of modal parameters or for extraction of structural characteristic matrices. The current study aims to identify the real matrices of a structure using structural dynamics theory and stochastic subspace identification based on realization theory. The study focuses on extraction of the condensed mass and stiffness matrices of shear buildings by means of ambient excitation responses for limited structural degrees of freedom. Realization theory states that there are minimal realizations for appropriate identification of the main real-system matrices. The present study shows that, by using values smaller than the minimal realization, condensed structural matrices can be correctly identified. This is accomplished by accurate estimation of the full real-system order. It is shown that successive repetitions of this approach can lead to complete structural matrices. The practical application of this procedure is examined using an experimental model and an analytical six-story shear model. Analysis revealed that, even in the presence of noise, this method can accurately identify structural matrices in all cases with high precision.

Numerical simulation of base-isolated buildings in collisions with surrounding moat walls during earthquakes: a nonsmooth mechanics approach

In this paper, we present a formulation and a numerical simulation method for earthquake-induced collisions between a seismically base-isolated building structure and its surrounding moat walls. The base isolator is assumed to undergo plastic deformation. We use the conventional shear building model for a superstructure. Based on nonsmooth mechanics, we formulate a measure differential inclusion that describes the time evolution of the entire structure. For numerical computation, we apply Moreau’s time-stepping scheme to the presented formulation. As a consequence, we solve a quadratic programming problem for each time-step. Our preliminary numerical experiments demonstrate that the presented method is more robust and numerically stable compared with the conventional Newmark method. We also present two numerical examples of mid-rise base-isolated building structures.

Feasibility study on model-based damage detection in shear frames using pseudo modal strain energy

This paper proposes a model-based approach for structural damage identification and quantification. Using pseudo modal strain energy and mode shape vectors, a damage-sensitive objective function is introduced which is suitable for damage estimation and quantification in shear frames. Whale optimization algorithm (WOA) is used to solve the problem and report the optimal solution as damage detection results. To illustrate the capability of the proposed method, a numerical example of a shear frame under different damage patterns is studied in both ideal and noisy cases. Furthermore, the performance of the WOA is compared with particle swarm optimization algorithm, as one the widely-used optimization techniques. The applicability of the method is also experimentally investigated by studying a six-story shear frame tested on a shake table. Based on the obtained results, the proposed method is able to assess the health of the shear building structures with high level of accuracy.

Damping estimates from reconstructed displacement for low-frequency dominant structures

This paper proposes a new concept for the estimation of modal damping ratios. This new concept is based on an operational modal analysis (OMA) technique that uses dynamic displacement reconstructed from measured acceleration. The reconstructed displacement physically suppresses the high-mode components in measured acceleration data and leads to modal participant factors that are sequentially arranged from low- to high-frequency modes. Thus, compared with the conventional approach that utilizes acceleration data, the proposed procedure provides a more reliable and robust damping estimate regardless of the model order selection. Furthermore, the use of reconstructed displacement guarantees the equilibrium of the system all the time. The OMA adopts a natural excitation technique (NExT) combined with an eigensystem realization algorithm (ERA). A finite element method (FEM)-based finite impulse response filter is adopted to reconstruct the dynamic displacement. The effectiveness and accuracy of the proposed approach is demonstrated for low-frequency dominant structures by using the numerical simulation study of a 9-story shear building and an actual field test of a cable-stayed bridge under operation in Korea. These examples allow a comparison of modal damping ratio estimates using reconstructed displacement and accelerations.