From Structural Analysis to Observer–Based Residual Generation for Fault Detection

Abstract

This paper combines methods for the structural analysis of bipartite graphs with observer-based residual generation. The analysis of bipartite structure graphs leads to over-determined subsets of equations within a system model, which make it possible to compute residuals for fault detection. In observer-based diagnosis, by contrast, an observability analysis finds observable subsystems, for which residuals can be generated by state observers. This paper reveals a fundamental relationship between these two graph-theoretic approaches to diagnosability analysis and shows that for linear systems the structurally over-determined set of model equations equals the output connected part of the system. Moreover, a condition is proved which allows us to verify structural observability of a system by means of the corresponding bipartite graph. An important consequence of this result is a comprehensive approach to fault detection systems, which starts with finding the over-determined part of a given system by means of a bipartite structure graph and continues with designing an observerbased residual generator for the fault-detectable subsystem found in the first step.

Simultaneous state and process fault estimation in linear parameter varying systems using robust quadratic parameter varying observers

“…Then, the observer structure (7) with L(𝜃(t)) = P −1 Γ(𝜃(t)) causes the estimation error e(t) to converge toward zero with a guaranteed decay rate 𝛼 for any x(0) ∈  x and e(0) ∈  e while ensuring the constraint (12) on the  2 gain from w to z.…”

“…causes that the estimation error e(t) converges to zero with guaranteed decay rate 𝛼 for any x(0) ∈  x and e(0) ∈  e , while ensuring the constraint (12).…”

“…Classical model-based fault diagnosis methods aim at generating a signal, called residual, which is different from zero when a fault occurs. [10][11][12] By exploiting well-known geometric properties, it is possible to associate various residual behaviors with a given set of faults, thus enabling fault isolation. [13][14][15] Although obtaining information about the presence (detection) and location (isolation) of the occurring faults is sufficient for performing some kind of fault-tolerant control reconfiguration, on-line fault estimation is a crucial component in active FTC schemes.…”

Robust detection of intermittent multiplicative sensor fault

“…They can be roughly classified into two general categories: model-based methods and data-driven methods. The model-based methods primarily contain: state estimation-based methods [7][8][9][10][11][12][13], parameter estimation-based methods [14][15][16], and parity space-based methods [17][18][19][20]. And the data-driven methods mainly include: multivariate statistics-based methods [21][22][23][24], signal processing-based methods [25][26][27], and machine learning-based methods [28][29][30].…”

A Combined H 2 / H ∞ Approach for Robust Joint Actuator and Sensor Fault Estimation: Application to a DC Servo-Motor System

“…Thus, FD can be perceived as a multi-level task aimed at deciding if a fault has occurred (fault detection), finding its location (fault isolation), and estimating its size (fault identification and estimation) [10]. In the literature, the FDI problem has been tackled from various angles and with a large spectrum of tools, e.g., [1,3,5,6,7,8,9,11,12,13,14,15,16,17,18]. On the other hand, fault estimation has received significantly less research attention.…”