On approximate maximum likelihood estimation of dynamic Takagi-Sugeno multi-models: method and application to a servo-pneumatic drive

This contribution addresses the identification of Takagi-Sugeno models for nonlinear stochastic dynamical systems. In case knowledge about the stochastic properties of a dynamic process is available, it can be exploited to improve the estimation of the model parameters. In this regard, it has to be acknowledged that the common assumption of independent and identically distributed random variables seldom holds for technical systems. Therefore, in this contribution the corresponding probability density functions will be estimated as Gaussian mixture models using a multi-start expectation maximization algorithm. As the residual density functions required for maximum likelihood estimation of Takagi-Sugeno models are not available at the beginning of the identification procedure, they are approximately estimated from the variation observed in repeated experiments with identical excitation signals. Particle swarm optimization is used for parameter estimation due to the non-convexity of the likelihood function. The proposed method is demonstrated for an industrial servo-pneumatic drive, which features uncertainties due to friction. It is shown that the mean validation error can be reduced by 9 % with the proposed method as compared with standard least squares estimation.