| 引用本文: | 彭云建,程培,邓飞其.随机非线性动态系统数值模拟与性态分析[J].控制理论与应用,2011,28(8):1126~1132.[点击复制] |
| PENG Yun-jian,CHEN Pei,DENG Fei-qi.Numerical simulation and behavior analysis of stochastic nonlinear dynamic systems[J].Control Theory and Technology,2011,28(8):1126~1132.[点击复制] |
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| 随机非线性动态系统数值模拟与性态分析 |
| Numerical simulation and behavior analysis of stochastic nonlinear dynamic systems |
| 摘要点击 2445 全文点击 1759 投稿时间：2010-05-10 修订日期：2010-12-07 |
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| DOI编号 10.7641/j.issn.1000-8152.2011.8.CCTA100539 |
| 2011,28(8):1126-1132 |
| 中文关键词 随机非线性动态系统 数值模拟 性态分析 |
| 英文关键词 stochastic nonlinear dynamic systems numerical simulation behavior analysis |
| 基金项目 国家青年科学基金资助项目(60904032); 中央高校基本科研业务费专项资金资助项目(2009ZM0140). |
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| 中文摘要 |
| 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. |
| 英文摘要 |
| This paper investigates the numerical simulation and behavior of nonlinear dynamic systems with random parameters or state-dependent noise, and proposes an iterative integral formula to calculate the numerical solutions set of stochastic nonlinear dynamic systems(SNDSs) based on Monte-Carlo simulation scheme and numerical integration method. The evaluation of the algorithm errors is also presented. For analyzing the behavior of SNDSs with sample solutions from the solutions set, we put forward several formulas to calculate the probability distribution of system states, mean-square values and moment function values of SNDSs, by which an integrated simulation algorithm and programming flow are designed for SNDSs. Simulation results of two typical systems are discussed to validate the presented scheme and the programming flow. |