Bayesian Inference Based Parameter Calibration of the LuGre-Friction Model

Load redistribution in smart load bearing mechanical structures can be used to reduce negative effects of damage or to prevent further damage if predefined load paths become unsuitable. Using controlled friction brakes in joints of kinematic links can be a suitable way to add dynamic functionality for desired load path redistribution. Therefore, adequate friction models are needed to predict the friction behavior. Possible models that can be used to model friction vary from simple static to complex dynamic models with increasing sophistication in the representation of friction phenomena. The LuGre-model is a widely used dynamic friction model for friction compensation in high precision control systems. It needs six parameters for describing the friction behavior. These parameters are coupled to an unmeasurable internal state variable, therefore, parameter identification is challenging. Conventionally, optimization algorithms are used to identify the LuGre-parameters deterministically. In this paper, the parameter identification and calibration is formulated to achieve model prediction that is statistically consistent with the experimental data. By use of the R2 sensitivity analysis, the most influential parameters are selected for calibration. Subsequently, the Bayesian inference based calibration procedure using experimental data is performed. Uncertainty represented in former wide parameter ranges can be reduced and, thus, model prediction accuracy can be increased.