IET control theory and applications

Vol. 9, num. 9, p. 1392-1398

DOI: 10.1049/iet-cta.2013.1124

Date of publication: 2015-06-06

Abstract:

This study deals with the problem of set-membership identification of non-linear-in-the-parameters models. To solve this problem, this study illustrates how the Bayesian approach can be used to determine the feasible parameter set (FPS) by assuming uniform distributed estimation error and flat model prior probability distributions. The key point of the methodology is the interval evaluation of the likelihood function and the result is a set of boxes with associated credibility indices. For each box, the credibility index is in the interval (0, 1] and gives information about the amount of consistent models inside the box. The union of the boxes with credibility value equal to one provides an inner approximation of the FPS, whereas the union of all boxes provides an outer estimation. The boxes with credibility value smaller than one are located around the boundary of the FPS and their credibility index can be used to iteratively refine the inner and outer approximations up to a desired precision. The main issues and performance of the developed algorithms are discussed and illustrated by means of examples.]]>

IEEE International Conference on Control Applications

p. 116-121

DOI: 10.1109/CCA.2014.6981338

Presentation's date: 2014-10-08

Abstract:

This paper deals with the problem of setmembership identification of nonlinear-in-the-parameters models. To solve this problem a Bayesian approach is presented. The paper illustrates how the Bayesian approach can be used to approximate the feasible parameter set (FPS) by assuming uniform distributed estimation error and flat model prior probability distributions. The methodology leads to an approximation of the FPS consisting of a set of boxes, where two regions can be identified. The inner region constitutes an inner approximation of the FPS whereas the external region can be viewed as an outer approximation of the FPS. Also, the boxes in the border give information about the percentage of consistent models inside each box and it can be used to iteratively refine the inner and outer approximations.]]>

IEEE Conference on Decision and Control

p. 496-501

DOI: 10.1109/CDC.2013.6759930

Presentation's date: 2013-12-10

Abstract:

This paper deals with the problem of nonlinear set-membership identification and fault detection using a Bayesian framework. The paper presents how the set-membership model estimation can be reformulated from a Bayesian viewpoint in order to determine the feasible parameter set and, in a posterior fault detection stage, to check the consistency between the model and the data. The paper shows that the Bayesian approach, assuming uniform distributed measurement noise and flat model prior probability distribution, leads to the same feasible parameter set as the set-membership technique. To illustrate this point a comparison with the subpavings approach is included. Finally, by means of the application to the wind turbine benchmark problem, it is shown how the Bayesian fault detection test works successfully.]]>

Mediterranean Conference on Control and Automation

Presentation's date: 2013-06-27

Abstract:

This paper deals with the problem of nonlinear set-membership identification. To solve this problem, the Bayesian approach and the subpavings approach are presented. The paper illustrates how the Bayesian approach can be used to determine the feasible parameter set and to check the consistency between measurement data and model. In particular, it is shown that the Bayesian approach, assuming uniform distributed estimation error and flat model prior probability distributions, leads to the same feasible parameter set than the subpavings technique. Main issues and performance of both approaches are compared and discussed by means of an application example.]]>