A novel distributed fault detection strategy for a class of nonlinear stochastic systems is presented. Different from the existing design procedures for fault detection, a novel fault detection observer, which consists of a nonlinear fault detection filter and a consensus filter, is proposed to detect the nonlinear stochastic systems faults. Firstly, the outputs of the nonlinear stochastic systems act as inputs of a consensus filter. Secondly, a nonlinear fault detection filter is constructed to provide estimation of unmeasurable system states and residual signals using outputs of the consensus filter. Stability analysis of the consensus filter is rigorously investigated. Meanwhile, the design procedures of the nonlinear fault detection filter are given in terms of linear matrix inequalities (LMIs). Taking the influence of the system stochastic noises into consideration, an outstanding feature of the proposed scheme is that false alarms can be reduced dramatically. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed fault detection approach.

In recent years, with the increasing complexity of modern dynamic systems, more and more researchers are now investigating new fault detection and identification (FDI) schemes to ensure safety and reliability of these modern complex dynamic systems. Effective FDI schemes can help find the early indication of system faults and avoid breakdowns of these complicated plants. The model-based analytical redundancy approaches have been proved to be an effective way to detect and diagnose faults for linear systems in the last two decades [

However, in many practical applications, a large number of dynamic systems are inherently nonlinear systems with some uncertainty, which include the transformer, some chemical processes, and robotic manipulators with homonymic constraints. There are fruitful research results on fault diagnosis schemes for nonlinear systems in recent years. In [

Due to the existence of some Gaussian or non-Gaussian noises, fault detection and identification for nonlinear stochastic systems are always challenging tasks [

The main difficulty of designing an effective fault detection observer is the influence of stochastic noises on residual signals, which can give rise to false alarm and reduce the accuracy of fault detection. In this paper, we present a novel distributed fault detection scheme for a class of nonlinear stochastic systems. The objective of the fault detection scheme is to minimize the influence of system stochastic noises on residual signals using parameter optimization techniques. Firstly, by constructing a consensus filter to filter system outputs, a novel fault detection filter is proposed to estimate system states and generate residual signals. Secondly, the properties of the consensus filter are analyzed in detail, and the existence of the proposed fault detection filter is rigorously investigated in terms of linear matrix inequalities. An outstanding feature of the proposed scheme is that the influence of system stochastic noises on residual signals is reduced greatly, and, as a result, fault detection accuracy can be improved dramatically.

An outline of this paper is as follows. In Section

Consider a class of nonlinear stochastic systems described by

System faults

The nonlinear function

In order to estimate system states, one gives the following full order Luenberger-like observer [

We can clearly see from (

In this section, we will give detailed design procedures for fault detection observer. The stability analysis of consensus filter and the existence of the fault detection filter are rigorously investigated.

Generally speaking, it is often difficult to get an exact description of a real plant system. Some unavoidable stochastic noises will have an influence on the practical engineering systems. As a result, some false alarms will be generated using the existing fault detection techniques. Also, with the increasing complexity of a real plant system, it is inevitable to use distributed sensors to measure system outputs at the same time. Take the high voltage direct current transmission system, for instance, we have to use distributed sensors to measure voltages, currents, and resistors along the transmission lines. Therefore, distributed fault diagnosis schemes are now attracting a lot of attentions from researchers.

In this work, we propose a novel distributed fault detection observer for a class of nonlinear stochastic systems. From (

Architecture of fault detection observer.

For the convenience of designing the fault detection observer, we rewrite (

In recent years, the study of information flow and coordination among different dynamic agents had aroused a larger amount of interests for researchers from all over the world. Among them, how to control each agent in a group to reach consensus is the key point in the condition that information exchange is limited and unreliable. The conceptions and ideas of consensus filter can be found in [

Suppose that system (

From (

We choose small world networks

Let

This completes the proof.

According to Theorem

In this section, design procedures of fault detection filter are given in details. The matrix parameters are designed in terms of linear matrix inequality using robust control theory and nonlinear matrix inequality methods.

Let

Suppose that the systems (

Considering the system (

So the system described by (

When the system uncertainty

This completes the proof.

Theorem

We consider a class of nonlinear stochastic systems:

In the simulation study, we take the step-function fault into consideration. Figure

Stochastic noises.

System outputs.

Outputs of fault detection filter.

(a) System outputs, (b) measurements by distributed sensors, and (c) outputs of fault detection filter.

This paper has proposed a novel distributed fault detection scheme for a class of nonlinear stochastic systems. A novel fault detection observer is developed using a consensus filter and a nonlinear fault detection filter. By combining these two kinds of filters, a distributed fault detection observer is designed to minimize the influence of stochastic noises on residual signals. The stability of consensus filter is rigorously analyzed in detail. Meanwhile, the parameter optimization of the fault detection filter is given in terms of LMIs. In the simulation study, numerical examples are given to demonstrate the validity and applicability of the proposed approach.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported by the Special Fund of East China University of Science and Technology for Basic Scientific Research (WH14027 and WJ1313004-1) and National Natural Science Foundation of China (nos. 21327807, H200-4-13192, and 51207007). The authors would like to thank the reviewers for the detailed comments that have helped us significantly improve the quality of our presentation.