Fast robust enhanced trend filter: A promising tool for automatically extracting high precision friction coefficient under unknown noise

Friction coefficient is the core parameter of material friction performance test. However, it often suffers from complex unknown noise, which frequently follows non-Gaussian distribution, such as outliers during the test phase. Moreover, the amount of test data is often very large that lead to the heavy computational burden. Thus, how to efficiently and accurately extract the friction coefficient is becoming a challenging task. To address this challenge, this paper proposes a fast trend filtering method based on Robust Enhanced Trend Filtering (RobustETF) which combines mix of Gaussian (MoG) and non-convex sparsity-inducing functions to extend l1 trend filtering, called Fast RobustETF. First, the sliding window strategy is used to segment the original data, and the wear stage is distinguished via judging the data margin factor inside the window. Then the window data with the largest and smallest margins is selected as the characteristic data segment of the stable and severe wear stage, and we consider the trend kurtosis and variance into the selection of optimal regularization parameters for different wear stages. Then, RobustETF is used in each window for extracting high precision friction coefficient under unknown noise. Finally, the trend signals in all windows are integrated and reconstructed to complete the precise extraction of the friction coefficient. Finally, simulation signals and real friction coefficient signals are used to verify the performance of Fast RobustETF by the comparison with other filtering methods.