Implementation of online model updating in hybrid simulation

Hybrid simulation combines numerical and experimental methods for cost‐effective, large‐scale testing of structures under simulated earthquake loading. Structural system level response can be obtained by expressing the equation of motion for the combined experimental and numerical substructures, and solved using time‐stepping integration similar to pure numerical simulations. It is often assumed that a reliable model exists for the numerical substructures while the experimental substructures correspond to parts of the structure that are difficult to model. A wealth of data becomes available during the simulation from the measured experiment response that can be used to improve upon the numerical models, particularly if a component with similar structural configuration and material properties is being tested and subjected to a comparable load pattern. To take advantage of experimental measurements, a new hybrid test framework is proposed with an updating scheme to update the initial modeling parameters of the numerical model based on the instantaneously‐measured response of the experimental substructures as the test progresses. Numerical simulations are first conducted to evaluate key algorithms for the selection and calibration of modeling parameters that can be updated. The framework is then expanded to conduct actual hybrid simulations of a structural frame model including a physical substructure in the laboratory and a numerical substructure that is updated during the tests. The effectiveness of the proposed framework is demonstrated for a simple frame structure but is extendable to more complex structural behavior and models. Copyright © 2013 John Wiley & Sons, Ltd.     

Model updating method for substructure pseudo‐dynamic hybrid simulation

Substructure hybrid simulation has been actively investigated and applied to evaluate the seismic performance of structural systems in recent years. The method allows simulation of structures by representing critical components with physically tested specimens and the rest of the structure with numerical models. However, the number of physical specimens is limited by available experimental equipment. Hence, the benefit of the hybrid simulation diminishes when only a few components in a large system can be realistically represented. The objective of the paper is to overcome the limitation through a novel model updating method. The model updating is carried out by applying calibrated weighting factors at each time step to the alternative numerical models, which encompasses the possible variation in the experimental specimen properties. The concept is proposed and implemented in the hybrid simulation framework, UI‐SimCor. Numerical verification is carried out using two‐DOF systems. The method is also applied to an experimental testing, which proves the concept of the proposed model updating method. Copyright © 2013 John Wiley & Sons, Ltd.     

Hybrid simulation of steel frame structures with sectional model updating

Hybrid simulations that combine numerical computations and physical experiment represent an effective method of evaluating the dynamic response of structures. However, it is sometimes impossible to take all the uncertain or nonlinear parts of the structure as the physical substructure. Thus, the modeling errors of the numerical part can raise concerns. One method of solving this problem is to update the numerical model by estimating its parameters from experimental data online. In this paper, an online model updating method for the hybrid simulation of frame structures is proposed to reduce the errors of nonlinear modeling of numerical substructures. To obtain acceptable accuracy with acceptable extra computation efforts as a result of model parameter estimation, the sectional constitutive model is adopted, therein considering axial‐force and bending‐moment coupling; moreover, the unscented Kalman filter is used for parameter estimation of the sectional model. The effectiveness of the sectional model updating with the unscented Kalman filter is validated via numerical analyses and actual hybrid tests on a full‐scale steel frame structure, with one column as the experimental substructure loaded by three actuators to guarantee the consistency of the boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Parameter identification for on‐line model updating in hybrid simulations using a gradient‐based method

To improve the efficiency of model fitting, parameter identification techniques have been actively investigated. Recently, the applications of parameter identification migrated from off‐line model fitting to on‐line model updating. The objective of this study is to develop a gradient‐based method for model updating to advance hybrid simulation also called hybrid test. A novel modification of the proposed method, which can reduce the number of design variables to improve the identification efficiency, is illustrated in detail. To investigate the model updating, simulated hybrid tests were conducted with a 5‐story steel frame equipped with buckling‐restrained braces (BRBs) utilized in the shaking table tests conducted in E‐Defense in Japan in 2009. The calibrated analytical model that was verified with the test results can serve as the reference model. In the simulated hybrid tests, the physical BRB substructure is numerically simulated by utilizing a truss element with the 2‐surface model identical to the part of the reference model. Such numerical verification allows simulation of measurement errors for investigation on the performance of the proposed method. Moreover, the feasibility of sharing the identified parameter values, which were obtained from the physical substructure responses, with the relevant numerical models is also verified with the artificial component responses derived from the physical experiments.     

A method for estimating specimen tangent stiffness for hybrid simulation

Researchers have long recognized the importance and potential benefits of utilizing the tangent stiffness matrix of a test specimen in hybrid simulations employing implicit and mixed‐integration schemes. However, the computation of the tangent stiffness matrix during testing has proved to be challenging, particularly for test specimens with more than one degree of freedom (dof). This paper presents a new methodology that is more straightforward and simpler than existing techniques for computing the tangent stiffness matrix of a multi‐dof test specimen. The proposed method is combined with the operator‐splitting method (OSM), and the capabilities, advantages and limitations of the new formulation are demonstrated through several examples. The accuracy, stability, and error propagation characteristics of the modified OSM are also studied theoretically as well as numerically. The research results show that the proposed algorithm provides results that are better than those produced via the regular OSM alone, especially for damped structures undergoing highly inelastic behavior during testing. Copyright © 2008 John Wiley & Sons, Ltd.     

往复荷载作用下锈蚀钢筋混凝土柱黏结滑移模型及数值模拟研究

为实现地震作用下锈蚀钢筋混凝土柱精细化数值模拟分析,基于已有研究成果建立往复荷载作用下锈蚀钢筋与混凝土间的黏结滑移本构模型:结合课题组前期试验结果,采用ABAQUS有限元分析软件对建立的黏结滑移本构模型进行有效性验证,通过对数值计算结果与试验结果之间误差分析,进一步对黏结滑移模型中的摩擦黏结应力系数和退化系数进行修正,...     

基于数值模拟和地震活动性统计的混合地震预测: 在中国地震科学实验场的应用

地震数值预测是近年来最为前沿的科学研究问题之一,但是大部分地震数值预测的探索都受困于数值模拟步长的问题.本文引入混合预测方法,探索了较短预测时长的地震数值预测方法,并在中国地震科学实验场区中进行应用.该混合预测方法主要建立在活动块体理论和构造力学分析的基础上,利用数值模拟推测未来长时间的应力变化量,并引入上一次7级地震之后数十年间,中等强度地震同震应力的影响,最后通过重分类和加权,在应力变化量上叠加年尺度小地震活动异常的统计,从而实现区域地震危险程度的混合评估.基于该方法,我们将地震数值预测的预测时间尺度缩短到年尺度,以年为单位滚动预测了中国地震科学实验场自2021—2030年或更长时间段内可能出现中强地震的区域.2022年芦山6.1级地震、2021年漾濞6.4级地震、2021年泸州6.0级地震和2022年泸定6.8级地震均发生在危险性较高的区域,而2022年马尔康6.0级地震则不在预测区域内.本文展示的混合预测尝试为地震数值预测研究提供了一个可供参考的例证,也为解决数值预测步长控制难的问题提供了一个可能的探索途径.

     

Numerical characteristics of the full operator hybrid simulation method

The full operator method (FOM) has been proposed to overcome some of the shortcomings of the commonly used operator splitting method (OSM). In particular, the FOM is improved by increasing the accuracy of both the predictor and corrector using the estimated tangent stiffness of the tested structure. The numerical characteristics of the FOM, including stability and accuracy, are investigated in this study. It is shown that FOM is conditionally stable. The stability and accuracy characteristics are dependent on the accuracy of the estimated tangent stiffness and the parameters associated with the acceleration variation in the time-stepping integration method. Mass-spring systems with different types of nonlinearity, including hardening, stiffening, and softening behavior, are used to evaluate the performance of the FOM. It is found that the FOM can capture these types of nonlinearity with satisfactory accuracy. Using a prototype 12-story composite coupled wall system, the influences of the strong nonlinearity of the system as well as the displacement control errors from hydraulic actuators on the performance of the FOM are explored. The results show that the FOM is capable of generating reasonably accurate results despite the presence of strong structural nonlinearity and displacement control errors.     

基于AUKF的框架结构离线模型更新混合试验方法

模型更新混合试验在传统混合试验方法的基础上更新与试验构件具有相同恢复力特性的构件,扩展了混合试验方法的应用范围。本文旨在提高模型更新混合试验的精度,降低试验的成本并简化模型更新混合试验方法的流程。自适应UKF(AUKF)算法在传统UKF的基础上加入方差自适应模块,能够减轻初始参数设定对参数识别结果的影响,本文基于AUKF提出一种模型更新混合试验方法。对以Bouc-Wen为恢复力模型的防屈曲约束支撑(BRB)进行低周反复加载虚拟试验,通过Matlab编制AUKF算法程序进行参数识别,验证了AUKF算法的高效准确性。对一榀8层4跨带BRB的钢框架进行混合试验数值仿真,结果表明离线模型更新试验结果较在线模型更新更接近真实结果,且简化了试验流程。     

Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method

This paper presents a novel nonlinear finite element (FE) model updating framework, in which advanced nonlinear structural FE modeling and analysis techniques are used jointly with the extended Kalman filter (EKF) to estimate time‐invariant parameters associated to the nonlinear material constitutive models used in the FE model of the structural system of interest. The EKF as a parameter estimation tool requires the computation of structural FE response sensitivities (total partial derivatives) with respect to the material parameters to be estimated. Employing the direct differentiation method, which is a well‐established procedure for FE response sensitivity analysis, facilitates the application of the EKF in the parameter estimation problem. To verify the proposed nonlinear FE model updating framework, two proof‐of‐concept examples are presented. For each example, the FE‐simulated response of a realistic prototype structure to a set of earthquake ground motions of varying intensity is polluted with artificial measurement noise and used as structural response measurement to estimate the assumed unknown material parameters using the proposed nonlinear FE model updating framework. The first example consists of a cantilever steel bridge column with three unknown material parameters, while a three‐story three‐bay moment resisting steel frame with six unknown material parameters is used as second example. Both examples demonstrate the excellent performance of the proposed parameter estimation framework even in the presence of high measurement noise. Copyright © 2015 John Wiley & Sons, Ltd.     

An explicit method for numerical simulation of wave equations

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with M being a positive integer for regular grids are discussed and illustrated by constructing the second order (M = 1) and the fourth order (M = 2) recursion formulas.     

Review of the Kalman-type hydrological data assimilation

ABSTRACT

There is great potential in Data Assimilation (DA) for the purposes of uncertainty identification, reduction and real-time correction of hydrological models. This paper reviews the latest developments in Kalman filters (KFs), particularly the Extended KF (EKF) and the Ensemble KF (EnKF) in hydrological DA. The hydrological DA targets, methodologies and their applicability are examined. The recent applications of the EKF and EnKF in hydrological DA are summarized and assessed critically. Furthermore, this review highlights the existing challenges in the implementation of the EKF and EnKF, especially error determination and joint parameter estimation. A detailed review of these issues would benefit not only the Kalman-type DA but also provide an important reference to other hydrological DA types.

Editor D. Koutsoyiannis; Associate editor F. Pappenberger     

Combined implicit or explicit integration steps for hybrid simulation

Explicit integration procedures have been widely adapted and applied to hybrid simulations of the seismic response of structures due to their simplicity. However, these procedures are only conditionally stable and have limited recent applications of hybrid simulations to simple structural models with few degrees of freedom. A novel integration procedure is proposed herein, in which a fully implicit formulation is applied to solve the equation of motion for the hybrid model, but defaults to an explicit or noniterative formulation in steps that fail to converge. The advantages to this approach are the ensured continuity of the simulation and the reduced accumulation of errors that occur during consecutive explicit steps that may lead to instability. The implicit procedure is applied by loading the experimental substructures beyond the expected displacement for the current step, then using the displacements and forces measured through the load path in the iterative implicit scheme. This approach captures the instantaneous behaviour of experimental substructures without physically imposing iterations. Numerical and experimental simulations demonstrate the effectiveness of the proposed integration scheme for multi‐degree‐of‐freedom models, especially in utilization of longer time steps that exceed stability limits of explicit methods, prevention of excitation of higher modes, and testing of stiff systems. Copyright © 2007 John Wiley & Sons, Ltd.     

越洋海啸的数值模拟

破坏性海啸基本上都是越洋海啸,如1960年智利海啸、2004年苏门答腊海啸。越洋海啸的传播机制与近场海啸不同,进行数值模拟所采用的数学模型也不同。本文分析比较Boussinesq方程和线性浅水方程,选用后者作为进行越洋海啸数值模拟的数学模型,基于有限差分法,运用蛙跃格式求解微分方程。以2004年苏门答腊海啸作为算例,把计算结果与NOAA和NGDC的计算结果进行对比,验证本文的数学模型和计算方法的可靠性,为以后进一步的海啸危险性分析和海啸预警等研究工作提供技术支持。     

Full operator algorithm for hybrid simulation

One of the weaknesses of the operator splitting method (OSM) is that its corrector step employs the approximation that incremental forces are linearly related to the tested structure's initial stiffness matrix. This paper presents a new predictor–corrector technique in which the assumptions about the tested structure's response are shifted to the predictor step, which results in an enhancement in overall simulation accuracy, especially for nonlinear structures. Unlike OSM, which splits the displacement and velocity operators into explicit and implicit terms, the new method uses predicted accelerations to compute fully explicit displacement and velocity values in the predictor step. Another advantage of the proposed technique, termed the full operator method (FOM) is that its formulation makes it suitable for both quasi‐static and real‐time hybrid simulation. The effectiveness of FOM is first evaluated by investigating error propagation in an undamped single degree‐of‐freedom model. It is shown that the corrector step in FOM is able to significantly suppress aberrant simulation results caused by incorrect estimation of the structure's stiffness matrix. The performance of FOM is demonstrated by exercising two additional models, which exhibit significant inelastic behavior under the prescribed excitation. The simulation results show that the proposed FOM algorithm is capable of producing accurate solutions and that the corrector step is influential in effectively reducing simulation errors. It is also shown that FOM suppresses actuator displacement control errors because of its reliance on measured quantities in the corrector step. Copyright © 2009 John Wiley & Sons, Ltd.     

长周期地震动三维有限元数值模拟方法

采用数值方法对长周期地震动进行模拟已成为当前强地面运动预测的研究方向之一。本文提出了一种有限元并行计算的高效地震动数值模拟方法,可以同时考虑震源、传播途径和场地条件对地震动的影响,并根据昆明地区未来可能发生的设定地震对昆明市的影响地震动进行了预测。这一方法可以应用于国内已探测的发震活断层进行地震危害性评价工作。     

小型混凝土空心砌块结构弹塑性数值模拟

由于配筋小型砌块结构在地震作用下的侧向变形曲线形状介于钢筋混凝土框架结构和剪力墙结构之间,因此,将配筋小型砌块结构考虑成“框架-剪力墙”体系。建立分析模型模拟试验模型在地震激励下的弹塑性反应,证明了该模型的有效性。     

An explicit method for numerical simulation of wave equations: 3D wave motion

In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order (M=1) recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.     

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.     

Database application platform for earthquake numerical simulation

Introduction In recent years, all kinds of observation networks of seismology have been established, which have been continuously producing numerous digital information. In addition, there are many study results about 3D velocity structure model and tectonic model of crust （Huang and Zhao, 2006; Huang et al, 2003; Li and Mooney, 1998）, which are valuable for studying the inner structure of the earth and earthquake preparation process. It is badly needed to combine the observed data, experimental study and theoretical analyses results by the way of numerical simulation and develop a database and a corresponding application platform to be used by numerical simulation, and is also a significant way to promote earthquake prediction.