Function Based Fault Detection for Uncertain Multivariate Nonlinear Non-Gaussian Stochastic Systems Using Entropy Optimization Principle
<p>Function based fault detection.</p> "> Figure 2
<p>Flow chart of function based fault detection.</p> "> Figure 3
<p>The response of the fault <span class="html-italic">δ</span>.</p> "> Figure 4
<p>The response of the input disturbance <math display="inline"> <msub> <mi>ω</mi> <mi>k</mi> </msub> </math>.</p> "> Figure 5
<p>The response of the output disturbance <math display="inline"> <msub> <mi>v</mi> <mi>k</mi> </msub> </math>.</p> "> Figure 6
<p>The PDF of the fault signal <span class="html-italic">δ</span>.</p> "> Figure 7
<p>The PDF of the input disturbance <math display="inline"> <msub> <mi>ω</mi> <mi>k</mi> </msub> </math>.</p> "> Figure 8
<p>The PDF of the output disturbance <math display="inline"> <msub> <mi>v</mi> <mi>k</mi> </msub> </math>.</p> "> Figure 9
<p>The residual value when fault occurs.</p> "> Figure 10
<p>The residual value when no fault occurs.</p> "> Figure 11
<p>3-D mesh of the system output <span class="html-italic">y</span>.</p> "> Figure 12
<p>The optimization performance index <span class="html-italic">J</span>.</p> ">
Abstract
:1. Introduction
2. Preliminary
2.1. Plant Models
2.2. Filter and Error Dynamics
2.3. Entropy and Its Formulation
3. Main Results
3.1. Performance Indexes
3.2. Formulations for the Error JPDFs
3.3. Simplified Calculation of the Error JPDFs
3.4. Optimal FD Filter Design Strategy
- Initialize and
- At the sample time compute , based on Theorem 3;
- At the sample time compute , and then obtain via (18);
- Increase k by 1 to the next step.
4. Simulation Results
5. Conclusions
- The detected fault and system noises do not have to be Gaussian.
- The entropy optimization principle for FD problems is in parallel to the main results to [2], where linear Gaussian systems were studied and the minimax technology was applied to the variance of errors. It has therefore generalized variance optimization for Gaussian signal.
- This fault detection approach is applicable to multivariate and uncertain systems. It is a generalization of the method in [8] where only single-input-signal-output system is concerned.
Acknowledgment
References
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Yin, L.; Zhou, L. Function Based Fault Detection for Uncertain Multivariate Nonlinear Non-Gaussian Stochastic Systems Using Entropy Optimization Principle. Entropy 2013, 15, 32-52. https://doi.org/10.3390/e15010032
Yin L, Zhou L. Function Based Fault Detection for Uncertain Multivariate Nonlinear Non-Gaussian Stochastic Systems Using Entropy Optimization Principle. Entropy. 2013; 15(1):32-52. https://doi.org/10.3390/e15010032
Chicago/Turabian StyleYin, Liping, and Li Zhou. 2013. "Function Based Fault Detection for Uncertain Multivariate Nonlinear Non-Gaussian Stochastic Systems Using Entropy Optimization Principle" Entropy 15, no. 1: 32-52. https://doi.org/10.3390/e15010032