Set-membership identification and fault detection using a Bayesian framework

Abstract

This paper deals with the problem of set-membership identification and fault detection using a Bayesian framework. The paper presents how the set-membership model estimation problem can be reformulated from the Bayesian viewpoint in order to, first, determine the feasible parameter set in the identification stage and, second, check the consistency between the measurement data and the model in the fault-detection stage. The paper shows that, assuming uniform distributed measurement noise and uniform model prior probability distributions, the Bayesian approach leads to the same feasible parameter set than the well-known set-membership technique based on approximating the feasible parameter set using sets. Additionally, it can deal with models that are nonlinear in the parameters. The single-output and multiple-output cases are addressed as well. The procedure and results are illustrated by means of the application to a quadruple-tank process.

Keywords:

• set-membership identification
• fault detection
• likelihood function
• Bayes rule

Additional information

Funding

This work has been partially funded by the Spanish Ministry of Education [grant number CICYT SHERECS DPI-2011-26243], [grant number CICYT WATMAN DPI-2009-13744]; EFFINET of the European Commission [grant number FP7-ICT-2012-6-318556]; DGR of Generalitat de Catalunya [SAC group Ref. 2014/SGR/374].

Notes on contributors

Rosa M. Fernández-Cantí

Rosa M. Fernández-Cantí received the telecommunications engineering degree and the PhD degree in control engineering from the Technical University of Catalonia (UPC), Barcelona, Spain, in 1994 and 2013, respectively. She is currently an assistant professor with the Department of Automatic Control (ESAII), UPC, and a member of the Intelligent Control Systems/Advanced Control Systems (SIC/SAC) research group, UPC, Terrassa, Spain. Her main research interests include the application of Bayesian tools to the identification and fault diagnosis of dynamic systems.

Joaquim Blesa

Joaquim Blesa received the telecommunications engineering degree and PhD degree in control, vision and robotics from Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 1997 and 2011, respectively. He is currently a postdoctoral researcher in the Institut de Robòtica i Informàtica Industrial, CSIC-UPC, Barcelona. He is also an assistant professor in the Automatic Control Department, UPC, Terrassa, Spain. He has been involved in several National and European projects and has published several papers in international conference proceedings and scientific journals. His current research interests include robust identification in the automatic control field and the fault diagnosis of dynamic systems.

Vicenç Puig

Vicenç Puig received the telecommunications engineering degree and the PhD degree in control engineering from the Universitat Politècnica de Catalunya, Barcelona, Spain, in 1993 and 1999, respectively. He is currently an associate professor of automatic control and the leader of the Advanced Control Systems research group, Universitat Politècnica de Catalunya, Terrasa, Spain. He is also with the Institut de Robòtica i Informàtica Industrial (CSIC), Universitat Politècnica de Catalunya, Barcelona. He has been involved in several European projects and networks and has published several papers in international conference proceedings and scientific journals. His main research interests are fault detection and isolation and fault-tolerant control of dynamic systems.

Sebastian Tornil-Sin

Sebastian Tornil-Sin received the computer engineering degree and the PhD degree in control, vision, and robotics from the Universitat Politècnica de Catalunya (UPC), Barcelona, Spain, in 1996 and 2006, respectively. He is currently assistant professor at the Automatic Control Department (ESAII) at UPC and member of the Advanced Control Systems research group. His main research interests include the application of interval analysis in the automatic control field and the fault diagnosis and fault tolerant control of dynamic systems.