Model‐based multi‐metric control of uniaxial shake tables

Shake tables provide a direct means by which to evaluate structural performance under earthquake excitation. Because the entire structure is mounted on the base plate and subjected to the ground motion in real time, dynamic effects and rate‐dependent behavior can be accurately represented. Shake table control is not straightforward as the desired signal is an acceleration record, while most actuators operate in displacement feedback for stability. At the same time, the payload is typically large relative to the capacity of the actuator, leading to pronounced control‐structure interaction. Through this interaction, the dynamics of the specimen influence the dynamics of the shake table, which can be problematic when specimens change behavior because of damage or other nonlinearities. Moreover, shake tables are themselves inherently nonlinear, making it difficult to accurately recreate a desired acceleration record over a broad range of amplitudes and frequencies. A model‐based multi‐metric shake table control strategy is proposed to improve tracking of the desired acceleration of a uniaxial shake table, remaining robust to nonlinearities including changes in specimen condition. The proposed strategy is verified for the shake table testing of both linear and nonlinear structures. Copyright © 2013 John Wiley & Sons, Ltd.     

加速度谐波失真度对速度型地震计振动台标定的影响

本文对加速度和速度谐波失真度进行了理论计算, 并基于美国国家仪器公司研发的实验室虚拟仪器工程平台(Labview), 设计出低频振动信号数字化测量系统, 实现了振动台面对加速度波形、 速度波形及其失真度的测量. 基于该系统的实验数据与中国计量科学研究院设定的参考值偏差较小. 对地震计的测试结果表明, 加速度波形及其失真度对振动波形的精度描述更为严格, 能有效提高地震计振动测试的准确程度.      

An approach for shake table performance evaluation during repair and retrofit actions

Large‐scale, servo‐hydraulic shake tables are a central fixture of many earthquake engineering and structural dynamics laboratories. Wear and component failure from frequent use may lead to control problems resulting in reduced motion fidelity, necessitating repairs and replacement of major components. This paper presents a methodology to evaluate shake table performance pre‐ and post‐repair, including the definition of important performance metrics. The strategy suggested is presented in the context of the rebuilding of a 4.9 × 3.1 m, 350‐kN‐capacity uniaxial shake table. In this case, the rebuild consisted of characterization of wear to table components, replacement of worn bearing surfaces, and replacement of hydraulic accumulators. To assess the effectiveness of the repair actions, sinusoidal and triangular waves, white noise, and earthquake histories were run on the table before and after the rebuild. The repair actions were successful in reducing the position and velocity dependence of friction, improving the ability of control algorithms to accurately reproduce earthquake motions. The maximum and average response spectral misfits in the period range of 0.1–2 seconds were reduced from approximately 50% to 15%, and from 5% to less than 2.5%, respectively.     

Experimental characterization,modeling and identification of the NEES‐UCSD shake table mechanical system

This paper proposes a simple conceptual mathematical model for the mechanical components of the NEES‐UCSD large high‐performance outdoor shaking table and focuses on the identification of the parameters of the model by using an extensive set of experimental data. An identification approach based on the measured hysteresis response is used to determine the fundamental model parameters including the effective horizontal mass, effective horizontal stiffness of the table, and the coefficients of the classical Coulomb friction and viscous damping elements representing the various dissipative forces in the system. The effectiveness of the proposed conceptual model is verified through a comparison of analytical predictions with experimental results for various tests conducted on the system. The resulting mathematical model will be used in future studies to model the mechanical components of the shake table in a comprehensive physics‐based model of the entire mechanical, hydraulic, and electronic system. Copyright © 2007 John Wiley & Sons, Ltd.     

Development of high‐performance shake tables using the hierarchical control strategy and nonlinear control techniques

Conventional shake tables employ linear controllers such as proportional‐integral‐derivative or loop shaping to regulate the movement. However, it is difficult to tune a linear controller to achieve accurate and robust tracking of different reference signals under payloads. The challenges are mainly due to the nonlinearity in hydraulic actuator dynamics and specimen behavior. Moreover, tracking a high‐frequency reference signal using a linear controller tends to cause actuator saturation and instability. In this paper, a hierarchical control strategy is proposed to develop a high‐performance shake table. A unidirectional shake table is constructed at the University of British Columbia to implement and evaluate the proposed control framework, which consists of a high‐level controller and one or multiple low‐level controller(s). The high‐level controller utilizes the sliding mode control (SMC) technique to provide robustness to compensate for model nonlinearity and uncertainties experienced in experimental tests. The performance of the proposed controller is compared with a state‐of‐the‐art loop‐shaping displacement‐based controller. The experimental results show that the proposed hierarchical shake table control system with SMC can provide superior displacement, velocity and acceleration tracking performance and improved robustness against modeling uncertainty and nonlinearities. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison between real‐time dynamic substructuring and shake table testing techniques for nonlinear seismic applications

Results from real‐time dynamic substructuring (RTDS) tests are compared with results from shake table tests performed on a two‐storey steel building structure model. At each storey, the structural system consists of a cantilevered steel column resisting lateral loads in bending. In two tests, a slender diagonal tension‐only steel bracing member was added at the first floor to obtain an unsymmetrical system with highly variable stiffness. Only the first‐storey structural components were included in the RTDS test program and a Rosenbrock‐W linearly implicit integration scheme was adopted for the numerical solution. The tests were performed under seismic ground motions exhibiting various amplitude levels and frequency contents to develop first and second mode‐dominated responses as well as elastic and inelastic responses. A chirp signal was also used. Coherent results were obtained between the shake table and the RTDS testing techniques, indicating that RTDS testing methods can be used to successfully reproduce both the linear and nonlinear seismic responses of ductile structural steel seismic force resisting systems. The time delay introduced by actuator‐control systems was also studied and a novel adaptive compensation scheme is proposed. Copyright © 2010 John Wiley & Sons, Ltd.     

High-fidelity control of a seismic shake table

A high-fidelity PC-based control system has been developed to improve the tracking characteristics of a small-scale seismic motion simulator used for testing structural control designs. This work outlines the development and testing of the control system. First, the simulator hardware is described in detail. The process of constructing a mechanistic model of the system and identifying model parameters is then described. Next, a closed-loop feedback/feed-forward control algorithm, based on an optimal receding horizon formulation, is developed. The control design was tested and the results indicate that the seismic shake table precisely tracked reference seismic motions. Copyright © 1999 John Wiley & Sons, Ltd.     

Experimental assessment of the seismic performance of hospital cabinets using shake table testing

An experimental investigation of hospital building equipment is presented. Dynamic properties and seismic performance of typical ambulatory freestanding cabinets are assessed by unidirectional and bidirectional shake table tests, also considering the presence of internal partitions and cabinet contents. Vulnerability analysis is performed according to the most recent and reliable assessment methods, evaluating the influence of different parameters of the sample cabinets. The performance criteria referred within this research are the limit states reached by the specimens (ie, rocking and overturning) and by their contents (ie, overturning and breaking). Fragility curves are evaluated for the components and the contents, considering both acceleration and velocity intensity measures, and also using dimensionless intensity measures developed in recent studies. The outcomes of the present study confirm the findings of previous laboratory tests and numerical simulations carried out by the same authors and provide a further insight for the reliable seismic performance assessment of hospital cabinets and their contents.     

Simulation of floor response spectra in shake table experiments

Among several different experimental techniques, used to test the response of structures and to verify their seismic performance, the shake table testing allows to reproduce the conditions of true effects of earthquake ground motions in order to challenge complex model structures and systems. However, the reproduction of dynamic signals, due to the dynamics of the shake table and of the specimen, is usually imperfect even though closed‐loop control in a shake table system is used to reduce these errors and obtain the best fidelity reproduction. Furthermore, because of the dynamic amplifications in the specimen, the signal recorded at desired locations could be completely different from the expected effect of shake table motion. This paper focuses on the development of practical shake table simulations using additional ‘open loop’ feedforward compensation in form of inverse transfer functions (i.e. the ratio of the output structural response to an input base motion in the frequency domain) in order to obtain an acceptable reproduction of desired acceleration histories at specific locations in the specimen. As the first step, a well‐known global feedforward procedure is reformulated for the compensation of the table motion distortions due to the servo‐hydraulic system. Subsequently, the same concept is extended to the table‐structure system to adjust the shake table input in order to achieve a desired response spectrum at any floor of the specimen. Implementations show how such a method can be used in any experimental facility. Copyright © 2010 John Wiley & Sons, Ltd.     

On the acceleration‐based adaptive inverse control of shaking tables

Accurate reproduction of time series with diverse frequency characteristics is a central issue in structural testing. This is true not only for simple experimental tests performed by reaction walls or shaking tables but also for more sophisticated ones, such as hybrid testing. Especially in the latter case, where actual feedback from an ongoing test is used in the calculation of the next excitation value, any possible mismatch may be fatal for both the validity of the test and the safety. The objective of this study is to propose a framework for the adaptive inverse control of shaking tables, which succeeds in this matching to a certain degree. By formulating a critical set of design specifications that correspond to safety, implementation, robustness and ease of use, the conducted research results in a design that is based on a modified version of the filtered‐X algorithm with very competitive features. These are the following: (i) default operation in hard real‐time and acceleration mode; (ii) very low hardware requirements; (iii) effective cancelation of the shaking table's dynamics; and (iv) robustness against specimen dynamics. For its practical evaluation, the method is applied to shaking table waveform replication tests under the installation of an approximately linear specimen of sufficiently high mass and complex geometry. The results are promising and suggest further research toward this field, especially in conjunction with hybrid testing, as the method retains certain global applicability attributes and it can be easily extended to other transfer systems, apart from shaking tables. Copyright © 2014 John Wiley & Sons, Ltd.     

Predominant period and equivalent viscous damping ratio identification for a full‐scale building shake table test

The predominant period and corresponding equivalent viscous damping ratio, also known in various loading codes as effective period and effective damping coefficient, are two important parameters employed in the seismic design of base‐isolated and conventional building structures. Accurate determination of these two parameters can reduce the uncertainty in the computation of lateral displacement demands and interstory drifts for a given seismic design spectrum. This paper estimates these two parameters from data sets recorded from a full‐scale five‐story reinforced concrete building subjected to seismic base excitations of various intensities in base‐isolated and fixed‐base configurations on the outdoor shake table at the University of California, San Diego. The scope of this paper includes all test motions in which the yielding of the reinforcement has not occurred and the response can still be considered ‘elastic’. The data sets are used with three system identification methods to determine the predominant period of response for each of the test configurations. One of the methods also determines the equivalent viscous damping ratio corresponding to the predominant period. It was found that the predominant period of the fixed‐base building lengthened from 0.52 to 1.30 s. This corresponded to a significant reduction in effective system stiffness to about 16% of the original stiffness. The paper then establishes a correlation between predominant period and peak ground velocity. Finally, the predominant periods and equivalent viscous damping ratios recommended by the ASCE 7‐10 loading standard are compared with those determined from the test building. Copyright © 2017 John Wiley & Sons, Ltd.     

Validation of nonlinear time history analysis models for single‐storey concentrically braced frames using full‐scale shake table tests

The concentrically braced frame (CBF) structure is one of the most efficient steel structural systems to resist earthquakes. This system can dissipate energy during earthquakes through braces, which are expected to yield in tension and buckle in compression, while all other elements such as columns, beams and connections are expected to behave elastically. In this paper, the performance of single‐storey CBFs is assessed with nonlinear time‐history analysis, where a robust numerical model that simulates the behaviour of shake table tests is developed. The numerical model of the brace element used in the analysis was calibrated using data measured in physical tests on brace members subjected to cyclic loading. The model is then validated by comparing predictions from nonlinear time‐history analysis to measured performance of brace members in full scale shake table tests. Furthermore, the sensitivity of the performance of the CBF to different earthquake ground motions is investigated by subjecting the CBF to eight ground motions that have been scaled to have similar displacement response spectra. The comparative assessments presented in this work indicate that these developed numerical models can accurately capture the salient features related to the seismic behaviour of CBFs. A good agreement is found between the performance of the numerical and physical models in terms of maximum displacement, base shear force, energy dissipated and the equivalent viscous damping. The energy dissipated and, more particular, the equivalent viscous damping, are important parameters required when developing an accurate displacement‐based design methodology for CBFs subjected to earthquake loading. In this study, a relatively good prediction of the equivalent viscous damping is obtained from the numerical model when compared with data measured during the shake table tests. However, it was found that already established equations to determine the equivalent viscous damping of CBFs may give closer values to those obtained from the physical tests. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of a passive gap damper to control displacements in a shaking test of a seismically isolated three‐story frame

Recent studies have indicated uncertainty about the performance limit states of seismically isolated buildings in very large earthquakes, especially if the isolator displacement demands exceed the seismic gap and induce pounding. Previous research has shown the benefit of providing phased supplemental damping that does not affect the isolation system response in a design event. A phased passive control device, or gap damper, was designed, fabricated, and experimentally evaluated during shake table testing of a quarter scale base‐isolated three‐story steel frame building. Identical input motions were applied to system configurations without a gap damper and with a gap damper, to directly assess the influence of the gap damper on displacement and acceleration demands. The gap damper was observed to reduce displacement demands by up to 15% relative to the isolated system without the gap damper. Superstructure floor accelerations increased substantially because of damper activation, but were limited to a peak of about 1.18 g. The gap damper reduces displacement most effectively if the ground motion contains one or more of the following characteristics: the spectral displacement increases with increasing period near the effective period of the isolation system, the motion is dominated by a single large pulse rather than multiple cycles at a consistent intensity, and the motion has a dominant component aligned with a major axis of the structure. Copyright © 2016 John Wiley & Sons, Ltd.     

Compensation of actuator delay and dynamics for real‐time hybrid structural simulation

Compensation of delay and dynamic response of servo‐hydraulic actuators is critical for stability and accuracy of hybrid experimental and numerical simulations of seismic response of structures. In this study, current procedures for compensation of actuator delay are examined and improved procedures are proposed to minimize experimental errors. The new procedures require little or no a priori information about the behavior of the test specimen or the input excitation. First, a simple approach is introduced for rapid online estimation of system delay and actuator command gain, thus capturing the variability of system response through a simulation. Second, an extrapolation procedure for delay compensation, based on the same kinematics equations used in numerical integration procedures is examined. Simulations using the proposed procedures indicate a reduction in high‐frequency noise in force measurements that can minimize the excitation of high‐frequency modes. To further verify the effectiveness of the compensation procedures, the artificial energy added to a hybrid simulation as a result of actuator tracking errors is measured and used for demonstrating the improved accuracy in the simulations. Copyright © 2007 John Wiley & Sons, Ltd.     

Shake table testing of a miniature steel building with ductile-anchor,uplifting-column base connections for improved seismic performance

Previous research has demonstrated that uplifting-column or rocking building systems may exhibit improved seismic performance, including reductions in total base shear and decreased residual drift, when compared with systems rigidly connected to the foundation. These beneficial effects may be due to lengthened periods, activation of rocking modes, and energy dissipation of base fuse elements. In the current work, several configurations of a miniature steel building with different combinations of base connection and traditional superstructure fuse strength and stiffness were subjected to identical earthquake motions to evaluate differences in demands and performance. The uplifting base connections incorporate highly ductile concrete anchors with long stretch lengths, allowing robust connection performance and easy replacement of damaged connection elements following the seismic event, an advantage over previously tested systems. Testing and dynamic numerical analysis indicates that ductile anchor uplifting systems may reduce total base shear by over 20%, as well as reducing residual structural drift by more than 80%.     

基于加速度反馈的结构地震反应半主动MR阻尼控制试验

本文针对安装有半主动磁流变阻尼器（MR damper)的一座二层模型结构进行了抗震振动台试验研究，通过采用基于加速度反馈控制策略的两种半主动控制算法进行了在各种地震动作用下模型结构的半主动控制的抗震试验研究，并进行了Passive-on和Passive-off两种被动控制的试验研究。试验结果表明，MR阻尼器作为一种半主动控制装置可以有效地控制结构的峰值位移和均方差反应，且半主动控制对结构顶层的峰值位移和均方差的控制效果均优于两种被动控制方法。因此，本文提出的两种半主动控制算法都是有效的，并宜于实现。     

Control strategies and experimental verifications of the electromagnetic mass damper system for structural vibration control

The electromagnetic mass damper （EMD） control system, as an innovative active control system to reduce structural vibration, offers many advantages over traditional active mass driver/damper （AMD） control systems. In this paper, studies of several EMD control strategies and bench-scale shaking table tests of a two-story model structure are described. First, two structural models corresponding to uncontrolled and Zeroed cases are developed, and parameters of these models are validated through sinusoidal sweep tests to provide a basis for establishing an accurate mathematical model for further studies. Then, a simplified control strategy for the EMD system based on the pole assignment control algorithm is proposed. Moreover, ideal pole locations are derived and validated through a series of shaking table tests. Finally, three benchmark earthquake ground motions and sinusoidal sweep waves are imposed onto the structure to investigate the effectiveness and feasibility of using this type of innovative active control system for structural vibration control. In addition, the robustness of the EMD system is examined. The test results show that the EMD system is an effective and robust system for the control of structural vibrations.     

Predictive optimal control for seismic analysis of non-linear and hysteretic structures

In this paper, an effective active predictive control algorithm is developed for the vibration control of non-linear hysteretic structural systems subjected to earthquake excitation. The non-linear characteristics of the structural behaviour and the effects of time delay in both the measurements and control action are included throughout the entire analysis (design and validation). This is very important since, in current design practice, structures are assumed to behave non-linearly, and time delays induced by sensors and actuator devices are not avoidable. The proposed algorithm focuses on the instantaneous optimal control approach for the development of a control methodology where the non-linearities are brought into the analysis through a non-linear state vector and a non-linear open-loop term. An autoregressive (AR) model is used to predict the earthquake excitation to be considered in the prediction of the structural response. A performance index that is quadratic in the control force and in the predicted non-linear states, with two additional energy related terms, and that is subjected to a non-linear constraint equation, is minimized at every time step. The effectiveness of the proposed closed-open loop non-linear instantaneous optimal prediction control (CONIOPC) strategy is presented by the results of numerical simulations. Since non-linearity and time-delay effects are incorporated in the mathematical model throughout the derivation of the control methodology, good performance and stability of the controlled structural system are guaranteed. Copyright © 1999 John Wiley & Sons, Ltd.