Nonlinear dynamic system identification using local model architectures

Abstract

In automotive applications more and more stringent emission regulations lead to an increasing demand for efficient and reliable modelling tools. In this thesis an algorithm for nonlinear static and dynamic identification using Takagi-Sugeno Fuzzy Models is presented.<br />For practical applications the incorporation of prior knowledge and the interpretability of the local models is of great interest. Using a tree structured algorithm in combination with the discrimination between the input arguments of the consequents and of the premises the nonlinear optimisation is performed in an efficient way. The axis oblique decomposition of the partition space is based on an Expectation-Maximisation algorithm. In addition to the above mentioned Neuro-Fuzzy training algorithm novel concepts for the identification of dynamic Neuro-Fuzzy models are developed and tested in the course of this work: First, the problem of biased parameter estimation of the local model parameters in the presence of input and output noise is considered. For that purpose the concept of Total Least Squares for parameter estimation is introduced and statistical criteria for the incorporation in the proposed training algorithm are derived. Later on in this work a proper generalisation of the TLS method, the Generalised Total Least Squares algorithm is discussed and incorporated in the training algorithm. Another important topic in nonlinear dynamic system identification, the accuracy in steady-state phases, is addressed in this thesis. A concept of constrained parameter estimation is reviewed for Least Squares and extended to the TLS parameter estimation method.<br />