非高斯随机激励下滞迟系统响应与首次穿越失效

针对由有界噪声、泊松白噪声和高斯白噪声共同构成的非高斯随机激励,通过Monte Carlo数值模拟方法研究了此激励作用下双线性滞迟系统和Bouc-Wen滞迟系统这两类经典滞迟系统的稳态响应与首次穿越失效时间。一方面,分析了有界噪声和泊松白噪声这两种分别具有连续样本函数和非连续样本函数的非高斯随机激励,在不同激励参数条件下对双线性滞迟系统和Bouc-Wen滞迟系统的稳态响应概率密度、首次穿越失效时间概率密度及其均值的不同影响;另一方面,揭示了在这类非高斯随机激励荷载作用下,双线性滞迟系统的首次穿越失效时间概率密度将出现与Bouc-Wen滞迟系统的单峰首次穿越失效时间概率密度截然不同的双峰形式。     

On-line identification of non-linear hysteretic structures using an adaptive tracking technique

System identification and damage detection based on vibration data have received considerable attention recently because of their importance to structural health monitoring. Various technical approaches have been proposed in the literature; however, the on-line identification of the changes of parameters for non-linear structures due to damages is still a challenging problem. In this paper, we propose an on-line adaptive tracking technique, based on the least-square estimation, to identify the system parameters and their changes of non-linear hysteretic structures. The method proposed is capable of tracking abrupt or slow changes of the system parameters from which the damage event and the severity of the structural damage can be detected and evaluated. Simulation results for tracking the parametric changes of non-linear hysteretic structures are presented to demonstrate the application and effectiveness of the proposed technique in detecting the structural damages.     

随机激励下滞迟系统的稳态响应闭合解

滞迟系统属于一类典型的强非线性系统,滞迟力不仅取决于系统的瞬时变形,还与变形历程有关.虽然滞迟系统的随机振动问题已被广泛研究,但至今尚未得到滞迟系统随机响应概率密度函数的精确闭合解.本文运用迭代加权残值法获得了高斯白噪声激励下Bouc-Wen滞迟系统稳态响应概率密度函数的近似闭合解.首先,运用等效线性化法求出系统的稳态高斯概率密度函数;然后以此构造权函数,应用加权残值法求得了系统指数多项式形式的非高斯概率密度函数;最后引入迭代的过程,逐步优化权函数,提高计算所得结果的精度.以随机地震激励下钢纤维陶粒混凝土结构的稳态响应作为算例,其中Bouc-Wen模型的参数是基于拟静力学试验数据,并应用最小二乘法辨识获得.与Monte Carlo模拟结果相比,等效线性化法得到的结果精度较差;由加权残值法得到的结果能够表现出非线性特征,但其精度依然无法令人满意;采用迭代加权残值法得到的近似闭合解与Monte Carlo模拟的结果吻合非常好;对于较强随机激励情形,采用渐进迭代加权残值法具有较高的求解效率,所获得的理论解析解具有较高的精度.结果表明,所获得的近似闭合解不仅对于土木工程领域具有重要的实际应用价值,而且还可作为检验其他非线性系统随机响应预测方法的精度的标准.     

STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES＊

The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.     

Development of adaptive modeling techniques for non-linear hysteretic systems

Adaptive estimation procedures have gained significant attention by the research community to perform real-time identification of non-linear hysteretic structural systems under arbitrary dynamic excitations. Such techniques promise to provide real-time, robust tracking of system response as well as the ability to track time variation within the system being modeled. An overview of some of the authors’ previous work in this area is presented, along with a discussion of some of the emerging issues being tackled with regard to this class of problems. The trade-offs between parametric-based modeling and non-parametric modeling of non-linear hysteretic dynamic system behavior are discussed. Particular attention is given to (1) the effects of over- and under-parameterization on parameter convergence and system output tracking performance, (2) identifiability in multi-degree-of-freedom structural systems, (3) trade-offs in setting user-defined parameters for adaptive laws, and (4) the effects of noise on measurement integration. Both simulation and experimental results indicating the performance of the parametric and non-parametric methods are presented and their implications are discussed in the context of adaptive structures and structural health monitoring.     

Random vibration of hysteretic systems under Poisson white noise excitations

Hysteresis widely exists in civil structures, and dissipates the mechanical energy of systems. Research on the random vibration of hysteretic systems, however,is still insufficient, particularly when the excitation is non-Gaussian. In this paper, the radial basis function(RBF) neural network(RBF-NN) method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations. The solution to the reduced generalized Fokker...     

Real-time parameter estimation for degrading and pinching hysteretic models

Many civil and mechanical structures exhibit hysteresis with degradation and/or pinching when subject to severe cyclic loadings such as earthquakes, wind, or sea waves. The modeling and identification of non-linear hysteretic systems with degradation and pinching is therefore a practical problem encountered in the engineering mechanics field. On-line identification of degrading and pinching hysteretic systems is quite a challenging problem because of its complexity. A recently developed technique, the unscented Kalman filter (UKF) which is capable of handling any functional non-linearity, is applied to the on-line parametric system identification of hysteretic differential models with degradation and pinching. Simulation results show that the UKF is efficient and effective for the real-time state estimation and parameter identification of highly non-linear hysteretic systems with degradation and pinching.     

时变结构的参数识别方法

较详细地叙述了时变结构参数识别方法在国内外的研究进展,指出了这一工作深入研究的理论与实际意义．对其中的典型研究成果,包括自动控制理论领域的研究成果,给出了简要介绍,叙述了将广义系统的识别方法用于结构系统的思路和问题,特别是在线识别技术和神经网络技术．介绍了使用小波理论来识别时变结构参数的新思想．最后简要地展望了这一领域的发展前景．     

基于时间响应函数的结构阻尼识别方法比较

研究了3种基于时间响应函数的结构阻尼识别方法, 包括对数衰减法、希尔 伯特方法和小波方法. 给出了3种方法的实现算法, 分析了对密集模态的识别能力. 构造仿真算例, 采用3种方法识别了5{\%}, 10{\%}和30{\%}噪声条件下的模态阻尼. 结果表明, 小波方法比对数衰减法和希尔伯特方法具有更好的噪声鲁棒性. 采用小波方法分析了润扬大桥结构健康监测系统获得的实测数据, 识别出了润扬大桥悬索桥前6阶模态参数, 第2阶和第3阶模态频率相差仅为0.015\,Hz. 研究表明, 小波方法具备噪声条件下密集模态的识别能力, 是工程中阻尼识别的优选方法.     

A robust online parametric identification method for non-deteriorating and deteriorating distributed element models with viscous damping

The online parametric identification of deteriorating and non-deteriorating distributed element models (DEMs) with viscous damping is studied using a generalization of Masing model to provide the proper framework for identification. The approach renders the hysteretic response of the DEM into a time-independent single-valued mapping from equivalent displacement values into equivalent force values, while considering the effect of damping as a parallel element. This approach allows for parametric identification of this non-linear rate-dependent hysteretic behavior to be performed using non-linear optimization techniques. A changing objective function, defined as a norm of force estimation error over a shifting window of recent data, is employed so that classic non-linear optimization techniques can be used for the online identification problem. A variation of the steepest descent method is used with significant modifications. Special measures are taken to guarantee robustness of the results in presence of noise. The results show that the proposed identification method exhibits a very good performance in identifying the correct values of the parameters in real time, and is robust in dealing with noise. The proposed method can be applied to many other types of hysteretic behavior as well.     

Sequential non-linear least-square estimation for damage identification of structures

An early detection of structural damage is an important goal of any structural health monitoring system. In particular, the ability to detect damages on-line, based on vibration data measured from sensors, will ensure the reliability and safety of the structures. In this connection, innovative data analysis techniques for the on-line damage detection of structures have received considerable attentions recently, although the problem is quite challenging. In this paper, we proposed a new data analysis method, referred to as the sequential non-linear least-square (SNLSE) approach, for the on-line identification of structural parameters. This new approach has significant advantages over the extended Kalman filter (EKF) approach in terms of the stability and convergence of the solution as well as the computational efforts involved. Further, an adaptive tracking technique recently proposed has been implemented in the proposed SNLSE to identify the time-varying system parameters of the structure. The accuracy and effectiveness of the proposed approach have been demonstrated using the Phase I ASCE structural health monitoring benchmark building, a non-linear elastic structure and non-linear hysteretic structures. Simulation results indicate that the proposed approach is capable of tracking on-line the changes of structural parameters leading to the identification of structural damages.     

Improvement of parameter estimation for non-linear hysteretic systems with slip by a fast Bayesian bootstrap filter

Modeling and identification of non-linear hysteretic systems are widely encountered in the structural dynamics field, especially for the hysteresis with slip. A model, called SL model, which can describe the pinching of most practical hysteresis loops perfectly was proposed by Baber and Noori (J. Eng. Mech. 111 (1985) 1010). A method of estimating the parameters of SL model on the basis of input-output data based on bootstrap filter was proposed by the writers. Bootstrap filter is a filtering method based on Bayesian state estimation and Monte Carlo method, which has the great advantage of being able to handle any functional non-linearity and system and/or measurement noise of any distribution. The standard bootstrap filter, however, is not time efficient, i.e., it is very time consuming and is not suitable for real-time applications. In this paper, previous work by the writers is extended to do the parameter estimation of SL model by a fast Bayesian bootstrap filtering technique. Simulation results are presented to demonstrate the performance of the algorithm.     

A Re-Configurable Test Apparatus for Complex Nonlinear Dynamic Systems

This paper reports the results of an analytical and experimental study to design, analyze, construct, test, and evaluate a re-configurable test-bed to allow the convenient performance of sophisticated experiments in a laboratory setting for investigating a broad category of important nonlinear, time-varying phenomena that are widely encountered in the applied mechanics field. The essential elements of the test apparatus include an electro-dynamic exciter that drives an oscillating mass whose restoring force is easily adjustable from one resembling a linear SDOF mass-spring-damper system with constant coefficients, to one that can represent systems with nonlinear elastic forces, to one that models systems possessing hysteretic properties with precisely-controlled time-varying characteristics. The apparatus design is economical to fabricate, convenient to manipulate, and it provides results that can be accurately replicated under repeated test combinations of system parameters and dynamic loads. The utility of the apparatus to provide an investigational tool for studying the dynamic response of systems with time-varying dry-friction forces that give rise to hysteretic phenomena is demonstrated. Sophisticated on-line system-identification techniques are used to estimate the parameters of reduced-order models that capture the dominant features of the physical model. It is shown that the apparatus under discussion is a useful research tool for investigators conducting studies in physics-based models of generic nonlinear dynamic systems.     

未知集中荷载和风荷载共同作用下的结构识别问题研究

对同时作用有未知集中荷载和未知风荷载的剪切型结构的参数识别问题进行了研究。首先提出了直接消去法以解决顶部作用有集中未知荷载时程的剪切型结构的识别问题。对于仅作用未知风荷载的情况，使用简洁的直接代入方法识别结构参数。继而对同时作用有以上两种未知荷载的情况进行了研究。当相邻层的风载时程在时域上完全相关的假定成立时，结合直接消去法和直接代入法在识别出所有结构参数蹬同时反演出未知的集中荷载时程和风荷载时程。文后以文章的最后用仿真算例验证了所提算法的正确性，并对测量噪声对识别结果的影响进行了讨论。     

线性时不变系统集员辨识的区间算法

在不确定但有界(UBB)噪声假设下，提出一种针对线性时不变系统参数集员辨识的区间算法. 借助区间数学，寻求与观测数据和噪声相容的参数的最小超长方体(或区间向量)，推导了递 推列式，并分析了算法的收敛性. 此算法不仅可以给出参数估计值，还可以给出参数的不确 定性界限. 通过数值算例，将此算法与Fogel椭球算法和最小二乘算法进行了比较，显示 了其计算量小和精度高的优点。     

Structural health monitoring and damage detection using an intelligent parameter varying (IPV) technique

Most structural health monitoring and damage detection strategies utilize dynamic response information to identify the existence, location, and magnitude of damage. Traditional model-based techniques seek to identify parametric changes in a linear dynamic model, while non-model-based techniques focus on changes in the temporal and frequency characteristics of the system response. Because restoring forces in base-excited structures can exhibit highly non-linear characteristics, non-linear model-based approaches may be better suited for reliable health monitoring and damage detection. This paper presents the application of a novel intelligent parameter varying (IPV) modeling and system identification technique, developed by the authors, to detect damage in base-excited structures. This IPV technique overcomes specific limitations of traditional model-based and non-model-based approaches, as demonstrated through comparative simulations with wavelet analysis methods. These simulations confirm the effectiveness of the IPV technique, and show that performance is not compromised by the introduction of realistic structural non-linearities and ground excitation characteristics.     

滞变智能隔震结构的序列最优控制算法

将地震波简化为一系列脉冲,在每个时间步长上重新构造控制目标函数,建立了一种新的时域内的结构振动最优控制算法,并在滞变模型的智能隔震结构中用状态转移法加以实现.文中采用Bouc-Wen模型描述结构恢复力,并利用等效线性化方法处理非线性运动方程,分别导出了状态反馈和输出加权的两种表达式.文末选用作者承担设计过的实际隔震建筑中的一个单体工程作为算例,比较了输入三种不同地震波时各种算法的控制效果.结果表明,在相同控制能量下,本文算法对滞变结构能有效地削减响应峰值,综合性能优于现有的两种时域内的结构最优控制算法.     

基于state-space-split法的滞回非线性系统随机动力响应分析

采用SSS(state-space-split)法,建立了引入Bouc-Wen滞回模型的杜芬非线性系统在高斯白噪声激励下的概率密度函数(PDF)的近似求解方法,分析了其随机动力响应变化规律.首先,将Bouc-Wen滞回模型引入杜芬非线性系统,分别考虑非线性系统中的几何非线性和材料非线性对动力响应的影响.随后,对该模型进行了等效线性化(EQL)处理,基于等效线性化法结果,介绍了SSS法的简化方法和计算原理,并通过该方法求解了三维FPK方程的近似联合概率密度函数.最后,将该方法应用于三个案例和一个工程实例,通过求解其概率密度函数分布及动力可靠度验证了提出方法的适用性、可行性和优越性.     

Identification of non-linear structural parameters under limited input and output measurements

In this paper, an algorithm is proposed for the identification of non-linear structural parameters under limited input and output measurements. The algorithm is based on the sequential application of extended Kalman estimator for the non-linear structural parameters and the least-squares estimation for the unmeasured excitation. First, the identification of small size non-linear structural parameters is studied. Then, based on the substructure approach, the algorithm is extended to identify large size non-linear structural parameters. Interconnection effect between adjacent substructures is accounted by considering the interconnection forces at substructural interfaces as ‘additional unknown inputs’ to the substructures. The general case that measurements at the substructure interfaces are not available is considered. Two numerical examples which identify non-linear hysteretic parameters of a four-story and an eight-story hysteretic shear-beam building subject to unmeasured excitation respectively, demonstrate the efficiency of the proposed algorithm.     

基于梁连续抗弯刚度与小波变换的结构损伤识别方法研究

为了解决基于小波变换系数难以识别结构边缘损伤的问题,以及试验中损伤对周边的影响导致小波系数难以精确定位损伤位置的问题,提出了基于梁连续抗弯刚度与小波变换的结构损伤位置识别方法。该方法结合梁结构连续抗弯刚度与小波系数边缘的特点,在未知无损梁结构振动参数的情况下,能有效识别出梁结构边缘损伤且能准确定位试验中梁结构的损伤,通过损伤梁的数值模拟与试验证明了该方法的正确性。