Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

Simulation of large-scale numerical substructure in real-time dynamic hybrid testing

A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element （FE） numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom （DOFs）. Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.

Velocity plus displacement equivalent force control for real-time substructure testing

This paper employs a velocity plus displacement（V＋D）-based equivalent force control（EFC） method to solve the velocity/displacement difference equation in a real-time substructure test. This method uses type 2 feedback control loops to replace mathematical iteration to solve the nonlinear dynamic equation. A spectral radius analysis of the amplification matrix shows that the type 2 EFC-explicit, Newmark-β method has beneficial numerical characteristics for this method. Its stability limit of Ω = 2 remains unchanged regardless of the system damping because the velocity is achieved with very high accuracy during simulation. In contrast, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation are shown to decrease with an increase in system damping. In fact, the EFC-average acceleration method is shown to change from unconditionally stable to conditionally stable. We also show that if an over-damped system with a damping ratio of 1.05 is considered, the stability limit is reduced to Ω =1.45. Finally, the results from an experiment with a single-degree-of-freedom structure installed with a magneto-rheological（MR） damper are presented. The results demonstrate that the proposed method is able to follow both displacement and velocity commands with moderate accuracy, resulting in improved test performance and accuracy for structures that are sensitive to both velocity and displacement inputs. Although the findings of the study are promising, additional test data and several further improvements will be required to draw general conclusions.

Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing （RTDHT）. This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Pad6 approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.

Flexible substructure online hybrid test system using conventional testing devices

This paper presents a substructure online hybrid test system that is extensible for geographically distributed tests. This system consists of a set of devices conventionally used for cyclic tests to load the tested substructures onto the target displacement or the target force. Due to their robustness and portability, individual sets of conventional loading devices can be transported and reconfigured to realize physical loading in geographically remote laboratories. Another appealing feature is the flexible displacement-force mixed control that is particularly suitable for specimens having large disparities in stiffness during various performance stages. To conduct a substructure online hybrid test, an extensible framework is developed, which is equipped with a generalized interface to encapsulate each substructure. Multiple tested substructures and analyzed substructures using various structural program codes can be accommodated within the single framework, simply interfaced with the boundary displacements and forces. A coordinator program is developed to keep the boundaries among all substructures compatible and equilibrated. An Interuet-based data exchange scheme is also devised to transfer data among computers equipped with different software environments. A series of online hybrid tests are introduced, and the portability, flexibility, and extensibility of the online hybrid test system are demonstrated.

Substructure hybrid testing of reinforced concrete shear wall structure using a domain overlapping technique

An online hybrid test was carried out on a 40-story 120-m high concrete shear wall structure. The structure was divided into two substructures whereby a physical model of the bottom three stories was tested in the laboratory and the upper 37 stories were simulated numerically using ABAQUS. An overlapping domain method was employed for the bottom three stories to ensure the validity of the boundary conditions of the superstructure. Mixed control was adopted in the test. Displacement control was used to apply the horizontal displacement, while two controlled force actuators were applied to simulate the overturning moment, which is very large and cannot be ignored in the substructure hybrid test of high-rise buildings. A series of tests with earthquake sources of sequentially increasing intensities were carried out. The test results indicate that the proposed hybrid test method is a solution to reproduce the seismic response of high-rise concrete shear wall buildings. The seismic performance of the tested precast high-rise building satisfies the requirements of the Chinese seismic design code.

Real-Time Hybrid Simulation of Seismically Isolated Structures with Full-Scale Bearings and Large Computational Models

Hybrid simulation can be a cost effective approach for dynamic testing of structural components at full scale while capturing the system level response through interactions with a numerical model.The dynamic response of a seismically isolated structure depends on the combined characteristics of the ground motion,bearings,and superstructure.Therefore,dynamic full-scale system level tests of isolated structures under realistic dynamic loading conditions are desirable towards a holistic validation of this earthquake protection strategy.Moreover,bearing properties and their ultimate behavior have been shown to be highly dependent on rate-of-loading and scale size effects,especially under extreme loading conditions.Few laboratory facilities can test full-scale seismic isolation bearings under prescribed displacement and/or loading protocols.The adaptation of a full-scale bearing test machine for the implementation of real-time hybrid simulation is presented here with a focus on the challenges encountered in attaining reliable simulation results for large scale dynamic tests.These advanced real-time hybrid simulations of large and complex hybrid models with several thousands of degrees of freedom are some of the first to use high performance parallel computing to rapidly execute the numerical analyses.Challenges in the experimental setup included measured forces contaminated by delay and other systematic control errors in applying desired displacements.Friction and inertial forces generated by the large-scale loading apparatus can affect the accuracy of measured force feedbacks.Reliable results from real-time hybrid simulation requires implementation of compensation algorithms and correction of these various sources of errors.Overall,this research program confirms that real-time hybrid simulation is a viable testing method to experimentally assess the behavior of full-scale isolators while capturing interactions with the numerical models of the superstructure to evaluate system level and in-structure response.

Seismic performance evaluation of VCFPB isolated storage tank using real-time hybrid simulation

Variable curvature friction pendulum bearings(VCFPB)effectively reduce the dynamic response of storage tanks induced by earthquakes.Shaking table testing is used to assess the seismic performance of VCFPB isolated storage tanks.However,the vertical pressure and friction coefficient of the scaled VCFPB in the shaking table tests cannot match the equivalent values of these parameters in the prototype.To avoid this drawback,a real-time hybrid simulation(RTHS)test was developed.Using RTHS testing,a 1/8 scaled tank isolated by VCFPB was tested.The experimental results showed that the displacement dynamic magnification factor of VCFPB,peak reduction factors of the acceleration,shear force,and overturning moment at bottom of the tank,were negative exponential functions of the ratio of peak ground acceleration(PGA)and friction coefficient.The peak reduction factors of displacement,acceleration,force and overturning moment,which were obtained from the experimental results,are compared with those calculated by the Housner model.It can be concluded that the Housner model is applicable in estimation of the acceleration,shear force,and overturning moment of liquid storage tank,but not for the sliding displacement of VCFPBs.

Geographically distributed hybrid testing & collaboration between geotechnical centrifuge and structures laboratories

Distributed Hybrid Testing（DHT） is an experimental technique designed to capitalise on advances in modern networking infrastructure to overcome traditional laboratory capacity limitations. By coupling the heterogeneous test apparatus and computational resources of geographically distributed laboratories, DHT provides the means to take on complex, multi-disciplinary challenges with new forms of communication and collaboration. To introduce the opportunity and practicability afforded by DHT, here an exemplar multi-site test is addressed in which a dedicated fibre network and suite of custom software is used to connect the geotechnical centrifuge at the University of Cambridge with a variety of structural dynamics loading apparatus at the University of Oxford and the University of Bristol. While centrifuge time-scaling prevents real-time rates of loading in this test, such experiments may be used to gain valuable insights into physical phenomena, test procedure and accuracy. These and other related experiments have led to the development of the real-time DHT technique and the creation of a flexible framework that aims to facilitate future distributed tests within the UK and beyond. As a further example, a real-time DHT experiment between structural labs using this framework for testing across the Internet is also presented.

基于BP神经网络的离线迭代混合试验方法研究

利用反向传播(误差逆传播算法back propagation algorithm,BP简称反向传播算法)神经网络对非线性结构位移-力系统进行拟合,将训练好神经网络作为试验子结构与数值子结构联合求解,省去了混合试验中试验子结构与数值子结构之间的实时数据交互,并通过迭代训练样本的方法不断逼近真实响应,克服了神经网络需要大量训练样本的问题。通过对两个自由度的非线性结构进行混合试验数值仿真,验证了该方法的可行性。以实际工程的一榀框架为混合试验对象,取一个隔震垫作为试验子结构进行数值仿真,进一步验证了该方法的有效性。

ENERGY MANAGEMENT STRATEGY FOR PARALLEL HYBRID ELECTRIC VEHICLES

Energy management strategy (EMS) is the core of the real-time controlalgorithm of the hybrid electric vehicle (HEV). A novel EMS using the logic threshold approach withincorporation of a stand-by optimization algorithm is proposed. The aim of it is to minimize theengine fuel consumption and maintain the battery state of charge (SOC) in its operation range, whilesatisfying the vehicle performance and drivability requirements. The hybrid powertrain bench testis carried out to collect data of the engine, motor and battery pack, which are used in the EMS tocontrol the powertrain. Computer simulation model of the HEV is established in the MATLAB/Simulinkenvironment according to the bench test results. Simulation results are presented for behaviors ofthe engine, motor and battery. The proposed EMS is implemented for a real parallel hybrid carcontrol system and validated by vehicle field tests.

基于卡尔曼滤波的振动台子结构试验方法研究

振动台子结构试验是一种有效的实时结构混合试验方法,持续受到国内外学者的关注。利用振动台和其它加载装置进行联合加载,从而提升和扩展振动台的加载能力,实现大比例甚至足尺结构试验的目的。基于主动质量驱动器(AMD)加载方法的振动台子结构试验中,在试验子结构和数值子结构完全拆分的情况下,无论采用位移PID还是三参量控制,在界面加速度输入情况下AMD系统在3~5 min后会产生失稳现象,通过调整控制增益、对加速度反馈信号进行滤波无法消除这种现象。在加速度传感器噪声的影响下,子结构试验系统无法保持长期稳定,通过数值仿真表明现有的时滞补偿算法也无法消除这种失稳现象。考虑这种情况,将卡尔曼滤波引入界面加速度的量测环节,通过整体结构模型求得的界面加速度对实测界面加速度进行修正,从而提升了振动台子结构试验的系统稳定性和试验精度。数值仿真结果表明,通过设置合理的卡尔曼滤波参数,可以抑制加速度传感器随机噪声对子结构试验精度的影响,系统时滞稳定性也得到显著改善。文中的研究结果为振动台子结构试验的成功实施提供了一种可行的解决方案。

固定式海上风力机实时混合试验加载方式研究

在传统的海上风力机模型试验中,湍流风载荷在实验室中复现困难,实验室场地的空间限制无法进行大型海上风力机模型试验,上部风力机与下部平台存在的缩尺矛盾也无法深入研究海上风力机全耦合作用机理.随着计算能力的提升、数值积分算法以及控制等关键问题研究取得突破,上述矛盾可由实时混合试验方法解决.本文以美国国家可再生能源实验室(NREL)5 MW固定式海上风力机为研究对象,按照1∶90进行缩尺,制作物理子结构模型,开发AeroDyn程序作为数值子结构,添加UDP/IP通信机制作为数据采集与传输方式,以推杆式作动器为加载装置,搭建了完整的实时混合试验系统,进行无海浪工况下的固定式海上风力机实时混合模型试验.将试验结果与FAST软件结果进行对比分析,结果吻合良好,说明了实时混合模型试验方法的可行性.研究结果为海上风力机实时混合模型试验技术的进一步发展提供了参考,为海上风力机结构设计与安全运行提供技术支撑.

基于OpenSees Navigator的子结构混合仿真试验系统及其验证

将有限元软件OpenSees Navigator应用于子结构混合仿真试验,介绍了基于OpenSees Navigator的子结构混合仿真试验方法的试验原理、试验系统组成和误差控制方法,并通过八层实腹式SRC异形柱框架子结构混合仿真试验结果和有限元软件OpenSees Navigator的数值模拟结果来验证该试验系统及方法的有效性和准确性。研究结果表明,试验预加载得到的命令位移和反馈位移时程曲线吻合程度较好,验证了该试验系统的有效性;模型结构的加速度反应、位移反应和层间剪力试验结果和模拟结果较为接近,表明该子结构混合仿真试验系统和试验方法能够较好地反映SRC异形柱框架结构在地震作用下的动力反应,将该试验系统应用于工程结构的抗震性能研究能够取得良好的效果。

水平及竖向地震作用下多高层RC框架混合试验

以往混合试验方法大多只考虑水平地震作用,为进一步拓展混合试验方法的应用,本文提出一种水平及竖向地震共同作用下多高层钢筋混凝土(RC)框架混合试验方法。该方法对框架结构计算模型和子结构边界条件进行合理简化,框架结构水平振动和竖向振动分别采用串联质点系模型和串并联多质点系模型进行模拟。在此方法基础上开发出一套完整的混合试验程序,该程序利用Matlab编写运动方程求解模块,采用OpenSees模拟数值子结构,并结合加载设备HNU-MUST开发出混合试验控制程序。为验证本方法和程序,设计并制作一根足尺RC框架柱作为试验子结构,并以一榀七层三跨RC框架作为整体结构进行混合试验,试验的顺利进行和良好稳定的试验控制效果验证了本方法的可行性与有效性。试验结果表明:在水平和竖向地震共同作用下RC框架柱轴力会发生剧烈变化,该轴力变化会使试件的受力状态和破坏形态变得较为复杂,同时可能会降低试件的强度和延性,并最终导致滞回曲线呈现不对称性和一定的“捏缩”现象。

基于串联长短时记忆网络的振动台子结构试验模拟

振动台子结构试验具有试验测试与数值模拟的双重优势,可实现大尺度甚至足尺模型结构的地震作用复现;振动台子结构试验中数值子结构的实时求解是影响试验精度和系统稳定性、决定试验能否顺利实现的关键因素之一。为提升数值子结构的求解性能,将长短时记忆(long short-term memoryk, LSTM)网络引入到振动台子结构试验中,分别构建了用于模拟试验子结构和数值子结构的神经网络模型,并且在训练数据中引入时滞以模拟系统延迟带来的影响。选择5层钢框架模型结构对神经网络模型进行验证,结果显示,所构建的神经网络模型具有良好的精度、稳定性和时滞补偿能力,计算效率可满足实时控制要求;所提出的神经网络模型可用于振动台子结构试验的数值子结构实时求解。

位移控制的子结构地震模拟振动台混合试验方法

为了解决地震模拟振动台承载能力及台面尺寸对大型结构试验的限制,扩展振动台的功能,提出了位移控制子结构地震模拟振动台混合试验方法,包括试验原理、试验过程及数值积分方法,并给出了2种子结构边界条件的模拟形式。通过1个简单框架结构的地震模拟振动台试验和子结构混合加载试验验证了该方法的可行性,并指出了该试验方法的主要技术问题。混合试验方法通过子结构技术和振动台试验相结合,解决了目前的地震模拟振动台试验和拟动力试验在设备规模和加载速度上的局限性。

加载速率对速度控制型实时子结构拟动力实验结果的影响

运用DSP高速数字信号处理器的实时信号处理与控制技术,研究基于速度控制法、Operator Splitting(OS)数值积分法和相应的实验误差控制法的实时子结构拟动力实验系统.该试验控制系统对试验动力加载装置采用速度控制,通过速度控制程序实现了减少加载速率对实验结果的影响,使橡胶隔震支座的速度相关性能在试验过程中得到充分体现,同时也有效地减少了实验的时滞误差;并进一步通过实时子结构拟动力试验研究加载速度对桥梁实时子结构实验结果的影响.实验结果证明,橡胶隔震支座是速度相关性很强的实验构件,不同时间因子的地震波拟动力子结构试验结果有很大的不同.实时地震波拟动力子结构试验的实验结果比时间因子为0.2和0.5的实验结果小.

子结构地震模拟振动台混合试验原理与实现

为了解决地震模拟振动台承载能力及台面尺寸对大型结构试验的限制,扩展振动台的功能,本文提出了子结构地震模拟振动台混合试验方法、试验过程及实时数值积分方法,并给出了试验子结构边界条件的两种模拟形式。通过一个简单框架结构的地震模拟振动台试验和子结构混合加载试验验证了该方法的可行性,并指出了该试验方法的主要技术问题。混合试验方法通过子结构技术和振动台试验相结合,解决了目前的地震模拟振动台试验和拟动力试验在设备规模和加载速度上的局限性。

OpenSees混合模拟试验技术发展与应用

将现代结构地震性能模拟与试验分为整体结构模拟试验和子结构模拟试验两类.在此基础之上详细讨论了混合模拟试验的基本概念背景及其应用与发展现状.结合面相对象有限元程序OpenSees的高层程序架构和并行计算程序架构,详细论述了基于OpenSees的4种混合模拟试验系统,并简要介绍了多尺度一体化混合建模的概念与应用.证明基于商业或非商业有限元软件平台开展混合模拟试验是可行的;混合模拟试验所要处理的核心问题是如何将不同的有限元软件平台以及各个试验站点的设备联系起来,并实现相互之间的协同工作.混合模拟试验在强震作用下结构连续倒塌问题的研究中具有一定的优势.指出混合模拟试验这一新技术的实质性发展离不开目前所强调的多学科之间的无缝融合.