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.     

Interval stochastic matrices: A combinatorial lemma and the computation of invariant measures of dynamical systems

The concept of an interval stochastic matrix is introduced. We prove a combinatorial theorem which describes the network flow associated with an interval matrix. The semi-invariant vectors of are characterized in terms of eigenvectors with unit eigenvalue of stochastic matrices . These results are then applied to the approximation and machine computation of invariant measures of dynamical systems.Funded under Australian Research Council Grant A 8913 2609.     

Three-dimensional unsaturated flow in heterogeneous systems and implications on groundwater contamination: A stochastic approach

A stochastic approach for modeling transient unsaturated flow in large-scale spatially variable soils is developed in order to overcome the problem of limited information about the local details of spatial soil variability. It is assumed that local soil properties are realizations of three-dimensional stationary random fields, and a large-scale model representation is derived by averaging the local governing flow equation over the ensemble of realizations of the underlying soil property random fields. The three-dimensionality of the local flow equations and the nonlinear dependence of the local flow output on the local soil properties are considered. The resulting mean representation (structure) is in the form of a partial differential equation in which averaged or effective model parameters occur. These effective model parameters are evalutated using a quasi-linearized fluctuation equation and a spectral representation of stationary processes. The large-scale model structure considers the large-scale effects of soil variability and have relatively few parameters which should be identifiable from a realistic data set. The general stochastic theory is then applied to the case of flow in stratified soil formations, which is of practical importance in applications such as waste disposal control. An important finding of this study is that spatial variability of the hydraulic soil properties produces significant large-scale effects, such as large-scale hysteresis and anisotropy of the effective parameters. These large-scale effects should be considered in field applications such as for predicting the movement of liquid wastes in the unsaturated zone.     

钢筋混凝土梁临界斜裂缝倾角计算的概率模型

综合考虑剪跨比、混凝土强度、配筋率和配箍率等重要因素的影响,研究建立了RC梁临界斜裂缝倾角计算的概率模型。首先,基于修正压力场理论,建立了RC梁临界斜裂缝倾角的确定性计算模型;然后,引入剪跨比修正系数,并综合考虑主观不确定性和客观不确定性因素的影响,结合贝叶斯理论和马尔科夫链蒙特卡洛法（MCMC）,建立了RC梁临界斜裂缝倾角计算的概率模型;最后,通过与试验数据和传统确定性计算模型的对比分析,验证了该模型的有效性和适用性。分析结果表明,随着剪跨比的增大,RC梁的临界斜裂缝倾角逐渐减小;临界斜裂缝倾角的试验测试值的范围为23°～41°,具有显著的离散性;本文概率模型不仅可以合理描述临界斜裂缝倾角的概率分布特性,而且可以校准传统确定性计算模型的计算精度和置信水平,以及根据预定的置信水平确定临界斜裂缝倾角的概率特征值,具有良好的计算精度和适用性。     

基于Kriging模型和改进MCMC算法的随机有限元模型修正

针对待修正参数维数较高时,标准马尔可夫链蒙特卡罗MCMC (Markov Chain Monte Carlo)算法不易收敛、拒绝率高的问题,提出了基于Kriging模型和在MCMC中融合花朵授粉算法的修正方法.首先,以待修正参数作为输入,以应变模态作为输出,建立Kriging模型,通过蝙蝠算法确定Kriging模型的相关系数;然后,采用最大熵的贝叶斯方法估计参数的后验概率密度函数,将花朵授粉算法融入MH (M etropolis-Hasting)抽样算法,提高局部寻优和全局寻优能力;最后,通过三自由度弹簧-质量系统和三维桁架结构的数值算例验证所提模型修正方法,修正后参数相对误差均低于0.86％.结果 表明,所提方法修正后较高维参数的马尔可夫链能够快速收敛且样本接受率也有所提高,该方法也对随机噪声具有一定的鲁棒性.     

基于有限材料参数试验数据的横观各向同性板结构随机有限元分析与验证

当材性试验数据有限时,为了研究各力学参数的离散性和不确定性对结构性能计算的影响,需要对材料参数采用随机变量建模并基于概率理论构建刚度矩阵的随机模型。为此,首先将随机弹性张量分解为一组基张量和由材料参数构成的随机系数的线性组合,以考虑刚度矩阵各分量间的统计相关性;并利用最大熵原理确定由上述随机系数组成的随机向量的概率密度函数。采用基于Metropolis-Hasting算法的马尔科夫链蒙特卡罗方法用于计算与之相关的概率模型的拉格朗日乘子,并通过Matlab生成材料参数的随机样本。最后采用蒙特卡罗随机有限元法对横观各向同性材料构成的板式结构在不同荷载下的力学行为进行了数值分析。以刨花板材料为典型案例,与试验结果对比,验证了本文方法的效果和实用性。     

Qualitative Theory and Identification of Dynamic System with One Degree of Freedom

Dynamic systems described by nonlinear differential equations of the second order are studied. It is assumed that certain preliminary information on the dissipative or elastic characteristics of systems is known. A new approach is demonstrated to obtaining full information on unknown or partially known characteristics of a system from measurements of not only displacements but also velocities and accelerations __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 139–143, June 2005.