Network‐based robust fault detection with incomplete measurements

Abstract

In this paper, we deal with the robust fault detection problem for a class of discrete-time networked systems with unknown inputs. Three types of incomplete measurements frequently occurred in a network environment are simultaneously considered, which include (1) measurements with communication delays, (2) measurements with packet dropouts, and (3) measurements with signal quantization. A unified measurement model utilizing a set of Kronecker delta functions is proposed to describe the delay and missing phenomenon, and the quantization is assumed to be of the logarithmic type. Attention is focused on the analysis and design of a robust full-order fault detection filter such that, for all admissible unknown inputs and incomplete measurements, the error between residual and fault is kept as small as possible. By augmenting the states of the original system and the fault detection filter, the addressed robust fault detection problem is converted into an auxiliary robust H ∞ filtering problem. Parameter-dependent and delay-probability-dependent approaches are developed in the design process in order to have a less conservative result. Sufficient conditions for the existence of the desired robust fault detection filters are established in terms of certain linear matrix inequalities (LMIs), and explicit parameters of the desired filter are then characterized if these LMIs are feasible. A numerical example is provided to illustrate the applicability of the proposed technique.

Fault detection for multi‐rate sensor fusion under multiple uncertainties

“…Some important progresses on dealing with such network‐induced uncertainties have been made, including distributed filtering for Markovian jump systems with both quantisation errors and packet dropouts along with deficient statistics of mode transitions [22], robust filtering for non‐linear systems under multiple stochastic communication delays and packet dropouts [23], distributed filtering for time‐varying systems with quantisation errors and successive packet dropouts [24], consensus filtering under multiple missing measurements [25] and robust filtering in the presence of sensor saturations and missing measurements [26]. Moreover some work on the FD of such sensor networks have been made, such as robust FD for networked systems with communication delay and data missing [27], network‐based robust FD with incomplete measurement [28], leakage fault diagnosis for an Internet‐based three‐tank system [29], and least‐squares FD and diagnosis for networked sensing systems with incomplete measurements [30]. One interesting but still open question is how to develop multi‐rate FD schemes under network‐induced uncertainties.…”

Fault Detection for Linear Discrete Time‐varying Systems with Intermittent Observations and Quantization Errors

“…The benefits accrued by using the proposed FD method are threefold: first, the stochastic ajoint operator based FD scheme provides a unified framework for achieving two-objective optimization performance index (9), which covers the results of deterministic linear systems in [1,13,14,34]. Second, comparing to the LMI-based FD approaches in [24,[26][27][28], the derived results are analytical and can be utilized to (4) with time-varying i (i = 1, … , q), by which lower computational cost is loaded. Third, if we apply the H ∞ filtering based method in [9,22] to (4), r(k) is always '0' no matter whether the fault occurs, since the fault distribution matrices in y(k) are zero.…”

“…In view of , the quantization errors are transformed into sector‐bounded uncertainties. A reasonable way to tackle the sector‐bounded uncertainties is the ‘S‐procedure’ which is widely used for infinite‐horizon case with the aid of LMI techniques . Another way is to treat the uncertain term as a disturbance, which may be adopted for time‐varying systems for deriving analytical solutions to related problems .…”

Fault detection and diagnosis for networked Three-tank Systems

“…In this subsection, we use polytopic uncertainty to describe unmodeled dynamics. System matrices A, B u B d , B f and C are assumed to belong to a known convex compact set within polytopic type [12], [11] Γ := (A, B u , B d , B …”

“…. , q} and is used to represent how large the communication delay is and whether the data is dropped [11], [12]. For −1 ≤ i ≤ q, denote P r{τ k = i} = p i , which are known scalars.…”