Approximation of the Feasible Parameter Set in Bounded-Error Parameter Estimation of Takagi-Sugeno Fuzzy Models for Large Problems by Using a Ray Shooting Method

Because reliable data-driven modeling methods require quantifying model uncertainty, an estimation of the parameter uncertainty is important. Usually maximum-likelihood methods with a known probability distribution of the noise are used. In practice, for many problems the stochastic properties of the errors are unknown and cannot be determined. In such cases, bounded error parameter estimation methods can be beneficial. These assume that the error lies within prior specified bounds. However, parameter estimation in the bounded error setting can be difficult and computationally expensive for data-driven modeling as a high number of parameters results. In this paper a new method for an approximate estimation with reduced effort of the set of feasible parameters for nonlinear data-driven modeling with Takagi-Sugeno fuzzy models is introduced. This permits to tackle large real-world problems. For this, a sampling based ray shooting method is proposed that guarantees an inner approximation of the feasible parameter set. The capability of the proposed method is demonstrated in two case studies, including one with data from an industrial hard turning process.