随机非线性动态系统数值模拟与性态分析

针对具有随机参数非线性系统和随机非线性系统的数值模拟与性态分析问题,提出将蒙特卡罗模拟方法与数值积分法相结合,建立了迭代积分算法求取随机非线性系统在不同随机序列作用下的数值解集,分析了计算误差.其次,利用数值解集的样本值进行解过程性态分析,建立了系统状态的概率分布、均方和矩函数的数值计算公式,实现了该类系统数值模拟分析的完整算法和程序流程设计.最后,通过两类典型示例系统的数值仿真结果验证本文算法与流程的正确性和有效性.

随机大系统的Lyapunov函数构造与符号计算

讨论了如何利用随机第一积分为构造非线性随机动态系统的Lyapunov函数的基本原理与方法 ,并在这个基础上建立孤立子系统的第一积分与随机大系统 Lyapunov函数的关系 ,然后利用这个基本原理来构造随机大系统的备选 Lyapunov函数 .这一方法即可以得到一般随机系统的Lyapunov函数的结构 。

基于SCKF方法的非线性随机动态系统故障诊断方法

基于平方根容积卡尔曼滤波方法(Square root cubature Kalman filter,SCKF),研究一类非线性随机动态系统的故障检测与估计问题。SCKF对解决复杂非线性系统的状态估计问题,具有精度高、稳定性优和计算复杂度低等优点。针对发生执行器故障的非线性随机动态系统,采用SCKF估计系统状态,并根据状态估计结果,利用滑动时间窗口技术设计残差信号,检测故障发生。在检测到故障之后,构造增广系统,实现对执行器故障幅值的估计。通过仿真试验验证了所提出方法的有效性。

Analysis of some large-scale nonlinear stochastic dynamic systems with subspace-EPC method

The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.