Time domain load extrapolation method for CNC machine tools based on GRA-POT model

Abstract

The load extrapolation is to obtain load data that may occur during the whole life cycle of product based on the limited measured load data, especially extreme load. Aiming at the two problems of traditional time domain extrapolation: without considering the interval time between extreme adjacent values and the high sensitivity of the peak over threshold (POT) model to the extreme threshold, a time domain load extrapolation method for computerized numerical control (CNC) machine tools based on Gray relational analysis-peak over threshold model (GRA-POT) is proposed. Firstly, for the first problem, an improved Markov chain Monte Carlo (MCMC) time domain load reconstruction method is proposed and analysis of reconstructed time domain load; secondly, according to the mean excess function (MEF) method, the extreme threshold range of POT model is determined and divided into multiple sets. The generalized Pareto distribution (GPD) fitting is performed for multiple sets of candidate load extreme samples. Finally, the Gray relational degrees (GRD) between each group of GPD and the median rank distribution are calculated by the Gray relational analysis (GRA), and the extreme threshold corresponding to the maximum GRD is selected as the optimal threshold of the POT model. The dynamic cutting force signal of CNC machine tool under constant speed cutting condition was reconstructed and extrapolated using the proposed method, and the dynamic cutting force spectrum of CNC machine tool was compiled. Case analysis results show that the POT extrapolation model with high fitting precision can be obtained using the proposed method. Furthermore, the precision of load spectrum of CNC machine tool is improved.