On optimal experiment design for identifying premise and conclusion parameters of Takagi-Sugeno models: Nonlinear regression case

• Published in: Applied soft computing Vol. 60; pp. 407 - 422
• Main Authors: Kroll, A., Dürrbaum, A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2017
• Subjects: Design of experiments; Nonlinear regression; Nonlinear system identification; Optimal experiment design; Takagi-Sugeno fuzzy models; Nonlinear regression; Design of experiments; Optimal experiment design; Nonlinear system identification; Takagi-Sugeno fuzzy models
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2017.07.015

[Display omitted] •Optimal experiment design for Takagi-Sugeno models.•Design considers both local model and membership parameters.•2-stage design process: space filling design followed by Fisher Information Matrix-based design.•Sequential optimal design used for robustness of model-based design.•Demonstration in 3 case studies: an industrial axial compressor characteristic map and two test functions. Optimal Experiment Design (OED) is a well-developed concept for regression problems that are linear-in-the-parameters. In case of experiment design to identify nonlinear Takagi-Sugeno (TS) models, non-model-based approaches or OED restricted to the local model parameters (assuming the partitioning to be given) have been proposed. In this article, a Fisher Information Matrix (FIM) based OED method is proposed that considers local model and partition parameters. Due to the nonlinear model, the FIM depends on the model parameters that are subject of the subsequent identification. To resolve this paradoxical situation, at first a model-free space filling design (such as Latin Hypercube Sampling) is carried out. The collected data permits making design decisions such as determining the number of local models and identifying the parameters of an initial TS model. This initial TS model permits a FIM-based OED, such that data is collected which is optimal for a TS model. The estimates of this first stage will in general not be ideal. To become robust against parameter mismatch, a sequential optimal design is applied. In this work the focus is on D-optimal designs. The proposed method is demonstrated for three nonlinear regression problems: an industrial axial compressor and two test functions.