Zonotope-based Set-membership Parameter Identification of Linear Systems with Additive and Multiplicative Uncertainties and Its Application to Engine Condition Monitoring

TL;DR

This paper introduces two zonotope-based algorithms for set-membership parameter estimation in linear systems with uncertainties, enabling accurate and efficient engine health monitoring.

Contribution

It presents two novel recursive algorithms, CAZI and PAZI, for set-membership estimation with explicit handling of additive and multiplicative uncertainties in linear models.

Findings

Both algorithms provide tight overbounds of the feasible solution set.

PAZI allows analysis of estimation results over iterations.

Application to marine engine monitoring demonstrates effectiveness.

Abstract

In this paper, we develop two zonotope-based set-membership estimation algorithms for identification of time-varying parameters in linear models, where both additive and multiplicative uncertainties are treated explicitly. The two recursive algorithms can be differentiated by their ways of processing the data and required computations. The first algorithm, which is referred to as Cone And Zonotope Intersection (CAZI), requires solving linear programming problems at each iteration. The second algorithm, referred to as the Polyhedron And Zonotope Intersection (PAZI), involves linear programming as well as an optimization subject to linear matrix inequalities (LMIs). Both algorithms are capable of providing tight overbounds of the feasible solution set (FSS) in our numerical case studies. Furthermore, PAZI provides an additional opportunity of further analyzing the relation between the estimation results at different iterations. An application to health monitoring of marine engines is considered to demonstrate the utility and effectiveness of the algorithms.