Robust Fuzzy Modeling and Symbolic Regression for Establishing Accurate and Interpretable Prediction Models in Supervising Tribological Systems

Abstract

In this contribution, we discuss data-based methods for building regression models for predicting important characteristics of tribological systems (such as the friction coefficient), with the overall goal of improving and partially automatizing the design and dimensioning of tribological systems. In particular, we focus on two methods for synthesis of interpretable and potentially non-linear regression models: (i) robust fuzzy modeling and (ii) enhanced symbolic regression using genetic programming, both embedding new methodological extensions. The robust fuzzy modeling technique employs generalized Takagi-Sugeno fuzzy systems. Its learning engine is based on the Gen-Smart-EFS approach, which in this paper is (i) adopted to the batch learning case and (ii) equipped with a new enhanced regularized learning scheme for the rule consequent parameters. Our enhanced symbolic regression method addresses (i) direct gradient-based optimization of numeric constants (in a kind of memetic approach) and (ii) multi-objectivity by adding complexity as a second optimization criterion to avoid over-fitting and to increase transparency of the resulting models. The comparison of the new extensions with state-of-the-art non-linear modeling techniques based on nine different learning problems (including targets wear, friction coefficients, temperatures and NVH) shows indeed similar errors on separate validation data, but while (i) achieving much less complex models and (ii) allowing some insights into model structures and components, such that they could be confirmed as very reliable by the experts working with the concrete tribological system.