Function Based Fault Detection for Uncertain Multivariate Nonlinear Non-Gaussian Stochastic Systems Using Entropy Optimization Principle

Abstract

In this paper, the fault detection in uncertain multivariate nonlinear non-Gaussian stochastic systems is further investigated. Entropy is introduced to characterize the stochastic behavior of the detection errors, and the entropy optimization principle is established for the fault detection problem. The principle is to maximize the entropies of the stochastic detection errors in the presence of faults and to minimize the entropies of the detection errors in the presence of disturbances. In order to calculate the entropies, the formulations of the joint probability density functions (JPDFs) of the stochastic errors are presented in terms of the known JPDFs of both the disturbances and the faults. By using the novel performance indexes and the formulations for the entropies of the detection errors, new fault detection design methods are provided for the considered multivariate nonlinear non-Gaussian plants. Finally, a simulation example is given to illustrate the efficiency of the proposed fault detection algorithm.

Learning Entropy: Multiscale Measure for Incremental Learning

“…Also similarly to E in (20), E A introduced in Equation (21) is also a normalized measure and it's possible maximum value E A = max = 1 can be obtained if all AP markers for a sample y(k) appear for all detection sensitivities in . The possible minimum value of E A of a sample y(k) is zero if no markers appear [similarly as to E in Equation (20)].…”

“…For every individual sample, the measure E A in Equation (21) approximates E in (20), because larger values of E A , corresponds to a steeper slope H ( Figure 5). Thus E A can be called the…”

“…then, we have arrived in Equation (20) to the normalized entropy measure E that quantifies learning activity of a sample-by-sample adaptive models (1-4). Thus, the variable E in Equation (20) is a novel non-Shannon and non-probabilistic measure for evaluation of novelty of each single sample of data in respect to it's consistency to the temporary governing law learned by a predictor.…”

“…Therefore, this particular technique by Equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) …”

Another Adaptive Approach to Novelty Detection in Time Series

“…The Sample Entropy (SampEn) and the Approximate Entropy (ApEn) are very typical and very relevant examples to be mentioned [3]- [4]. These approaches are closely related to the multi-scale evaluation of fractal measures, where further case studies utilizing SampEn, ApEn, and Multiscale Entropy (MSE) can be found in [5]- [7]. Further to this, probabilistic entropy approach to the concept shift (sometimes the concept drift) detection in sensory data is reported in [8].…”