Parameter Identifiability for Nonlinear LPV Models

• Published in: International journal of applied mathematics and computer science 2022-06, Vol.32 (2), p.255-269
• Main Authors: Srinivasarengan, Krishnan, Ragot, José, Aubrun, Christophe, Maquin, Didier
• Format: Article
• Language: English
• Subjects: Automatic; Engineering Sciences; Fault diagnosis; identifiability; linear parameter varying models; Model-based systems; null space; Parameter estimation; Parameter identification; parity space approach; State space models
• ISSN: 1641-876X; 2083-8492
• DOI: 10.34768/amcs-2022-0019

Linear parameter varying (LPV) models are being increasingly used as a bridge between linear and nonlinear models. From a mathematical point of view, a large class of nonlinear models can be rewritten in LPV or quasi-LPV forms easing their analysis. From a practical point of view, that kind of model can be used for introducing varying model parameters representing, for example, nonconstant characteristics of a component or an equipment degradation. This approach is frequently employed in several model-based system maintenance methods. The identifiability of these parameters is then a key issue for estimating their values based on which a decision can be made. However, the problem of identifiability of these models is still at a nascent stage. In this paper, we propose an approach to verify the identifiability of unknown parameters for LPV or quasi-LPV state-space models. It makes use of a parity-space like formulation to eliminate the states of the model. The resulting input-output-parameter equation is analyzed to verify the identifiability of the original model or a subset of unknown parameters. This approach provides a framework for both continuous-time and discrete-time models and is illustrated through various examples.