A new robust fault diagnosis approach based on bond graph method

Abstract

In this paper, a new robust fault diagnosis approach based on the combination of Bond Graph (BG) method and a robust observer is proposed. Different criteria including disturbance attenuation level, enhanced fault sensitivity and robustness against parametric uncertainties are considered in the proposed fault diagnosis system. A new form of analytical redundancy relations (ARRs), which is called error-based analytical redundancy relations (EARRs), is introduced and is used as the residuals for fault diagnosis purposes in considered uncertain linear systems. This form of the residuals is obtained using the output estimation error of the observer and satisfies considered criteria of the fault diagnosis system. The ARRs and state space representation of the system can be derived based on the BG model. The robust observer design is defined as an LMI problem in which the region of robustness against parametric uncertainty is achieved by the feasibility constraint of the obtained LMI. Finally, in order to show the performance of the proposed method, a quarter-car model is considered and different criteria are compared with the conventional ARRs method.

Bond graph observer for mode identification and discernibility study

“…Another method based on the Lyapunov’s Second Method is elaborated in Kazemi et Montazeri (2017), but it is a pure analytical procedure reposing on states’ matrices extraction from the BG model and the calculation of the Lyapunov function and its derivative function. In contrast to our method, this approach does not use the graphical aspect of the BG, it starts from the BG then extract the states ‘matrices to achieve an ordinary problem of LMI.…”

Trajectory Tracking Control Design of a Mass-Damping-Spring System with Uncertainty using the Bond Graph Approach

“…The introduction of uncertainty addition [2, 3] was followed by [4]. This technique can be applied to the design of robust diagnosis algorithms of bond graph models [5][6][7]. In the literature, two types of consideration can be found on the study of uncertainties: structured and unstructured uncertainties [29].…”

“…These uncertainties are included by adding some bond graph elements which describe their effect in the system, as described in Section IV. This work consists of the design of a trajectory-tracking control law using uncertain bond graph models, in the same way as they are used in the development of diagnostic algorithms for industrial systems [5][6][7]. Therefore, this work can represent a foundation stone for the design of robust control laws using bond graphs to ensure the control of complex systems.…”

A New Hybrid Robust Fault Detection of Switching Systems by Combination of Observer and Bond Graph Method

“…Lemma 3 [33]: For a given m × m symmetric matrix Z ∈ S m and two matrices U and V of column dimension m, there exists matrix X that is unstructured and will satisfy Eq. (15).…”

“…Bond Graph (BG) method may be considered as a convenient tool for modeling and fault diagnosis of dynamic systems. Different applications of the BG method can be found in the literature for modeling [7], [8], [9], [10], [11], [12] and fault diagnosis [12], [13], [14], [15], [16] applications. Because of its efficiency in modeling and fault diagnosis of continuous dynamic systems, the BG method is developed to represent switching phenomenon in hybrid dynamic systems, which leads to numerous applications of the method for modeling and fault diagnosis of hybrid systems in the literature.…”