Fault detection for non-linear non-Gaussian stochastic systems using entropy optimization principle
Fault detection for non-linear non-Gaussian stochastic systems using entropy optimization principle
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DOI：
10.1191/0142331206tm169oa
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发表时间：
2006-06
影响因子：
1.8
通讯作者：
Lei Guo;Hong Wang;T. Chai
中科院分区：
文献类型：
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作者：
Lei Guo;Hong Wang;T. Chai
本文研究了具有非高斯扰动和故障（或系统参数突变）的非线性动态随机系统的故障检测（FD）问题。在构建滤波器来生成检测到的误差之后，FD问题被简化为误差系统的优化问题，该系统由非线性非高斯随机系统表示。由于通常（扩展）卡门滤波方法不足以表征非高斯变量，因此我们提出了随机误差系统的熵优化原理。设计目标是在故障发生时最大化随机检测误差的熵，并最小化由其他随机噪声引起的随机估计误差的熵。根据干扰和故障的概率密度函数公式化了随机误差的概率密度函数，建立了新的递归方法来计算检测误差的熵。通过使用新颖的性能指标和熵公式，提供了实时最优FD滤波器设计方法。最后，通过仿真验证了所提出的 FD 滤波算法的有效性。
In this paper, a fault detection (FD) problem is studied for non-linear dynamic stochastic systems with non-Gaussian disturbances and faults (or abrupt changes of system parameters). After a filter is constructed to generate the detected error, the FD problem is reduced to an optimization problem for the error system, which is represented by a non-linear non-Gaussian stochastic system. Since generally (extended) Kalmen filtering approaches are insufficient to characterize the non-Gaussian variables, we propose the entropy optimization principle for the stochastic error system. The design objective is to maximize the entropies of the stochastic detection errors when the faults occur, and to minimize the entropies of the stochastic estimator errors resulting from the other stochastic noises. Following the formulation of the probability density functions of the stochastic error in terms of those of both the disturbances and the faults, new recursive approaches are established to calculate the entropies of the detection errors. By using the novel performance index and the formulations for the entropies, the real-time optimal FD filter design method is provided. Finally, simulations are given to demonstrate the effectiveness of the proposed FD filtering algorithms.