Methods for automated model structure selection for the identification of dynamic Takagi-Sugeno fuzzy models

M.Sc. Matthias Kahl

April 2017 - December 2018

State of Hesse

Data driven modelling is based on statistical methods. It enables an extensively automated and application independent generation of models and thereby a substantial decrease of modelling effort and required application specific knowledge. However, it is up to the user to preselect relevant input variables which significantly explain the output variable of interest. In case of identification of dynamical systems this involves the choice of relevant input signals as well as the choice of the dynamical order or model terms of the input signals. Depending on the considered model class the amount of potential influencing variables (so-called regressors) thereby strongly increases and an exclusion of insignificant regressors becomes more challenging. Especially, for nonlinear model classes this problem becomes more severe by the mostly nonlinear parametrization of the models. So e.g. for the class of Takagi-Sugeno fuzzy models, which typically consist of superposed locally affine sub-models weighted by their fuzzy basis functions, the following sub-problems have to be solved: 

1. Choice of relevant premise variables,
2. Finding an optimal fuzzy partitioning of the input space,
3. Finding an optimal structure of the local models or selecting relevant consequent variables, respectively. 

For dynamical systems, the choice of relevant premise and consequent variables coincides with the choice of a suitable dynamical order. If the aim is e.g. to obtain sparse local models or to find a suitable subset of premise variables for prediction, individual model terms can be selected. Especially, for the considered multi-model approach this is of great interest as the curse of dimensionality arises during identification.

In this project, existing model structure selection approaches (especially for the solution of sub-problem 3) are compared, shortcomings for the class of Takagi-Sugeno models are identified, and new methods will be developed. To this end, especially the following approaches and problems are considered: 

• regularization techniques for order selection,
• wrapper methods for order selection,
• influence of the noise assumption on order selection,
• influence of the partitioning strategy on order selection.