Guaranteed fault detection and isolation for switched affine models

Abstract

This paper considers the problem of fault detection and isolation (FDI) for switched affine models. We first study the model invalidation problem and its application to guaranteed fault detection. Novel and intuitive optimizationbased formulations are proposed for model invalidation and T -distinguishability problems, which we demonstrate to be computationally more efficient than an earlier formulation that required a complicated change of variables. Moreover, we introduce a distinguishability index as a measure of separation between the system and fault models, which offers a practical method for finding the smallest receding time horizon that is required for fault detection, and for finding potential design recommendations for ensuring T -distinguishability. Then, we extend our fault detection guarantees to the problem of fault isolation with multiple fault models, i.e., the identification of the type and location of faults, by introducing the concept of I-isolability. An efficient way to implement the FDI scheme is also proposed, whose run-time does not grow with the number of fault models that are considered. Moreover, we derive bounds on detection and isolation delays and present an adaptive scheme for reducing isolation delays. Finally, the effectiveness of the proposed method is illustrated using several examples, including an HVAC system model with multiple faults.

Optimal Input Design for Affine Model Discrimination with Applications in Intention-Aware Vehicles

“…If Assumption 1 does not hold, the problem (P DID ) results in a mixedinteger nonlinear program (MINLP). A particular solution to this problem is provided in [10], where a sequence of restriction approach reduces this MINLP into a sequence of computationally tractable optimization problems.…”

“…Given N well-posed affine models G i , and state, input and noise constraints, (3), ( 6), ( 8)-( 10), find an optimal input sequence u * T to minimize a given cost function J(u T ) such that for all possible initial states x 0 , uncontrolled inputs d T , process noise w T and measurement noise v T , only one model is valid, i.e., the output trajectories of any pair of models have to differ by a threshold in at least one time instance. The optimization problem can be formally stated as follows: 3),( 6),( 8)- (10) hold…”

“…Given N well-posed affine models G i , and state, input and noise constraints (3),( 6),( 8)- (10), find an optimal input sequence u * T to minimize a given cost function J(u T ) such that there exists at least one time instance at which the output trajectories of each pair of models are different by a threshold for all possible initial states x 0 , uncontrolled inputs d T , process noise w T and measurement noise v T . The optimization problem can be formally stated as follows: 3),( 5),( 6),( 8)-( 10) hold.…”

“…Lemma 1 (Bilevel Optimization Formulation). Given a separability index , the active model discrimination problem in Problem 1 is equivalent to a bilevel optimization problem with the following outer problem: 3),( 6),( 8)- (10) hold…”

“…Approaches in the literature can be categorized into passive and active methods. While passive techniques seek the separation of the models regardless of the input [7], [8], [9], [10], active methods search for an input such that the behaviors of different models are distinct. The focus of this paper is on active model discrimination techniques.…”