Refined composite multivariate multiscale weighted permutation entropy and multicluster feature selection-based fault detection of gearbox

As a valuable method for quantifying irregularity and randomness, multivariate multiscale permutation entropy (MMPE) has found widespread application in feature extraction and complexity analysis of synchronized multi-channel data. Nonetheless, MMPE fails to consider the amplitude information of the data, and its coarse-graining process possesses inherent flaws, resulting in inaccuracies in evaluating entropy values. To address these issues, a novel nonlinear dynamic characteristic evaluation index, named refined composite multivariate multiscale weighted permutation entropy (RCMMWPE), has been developed. This index aims to comprehensively rectify the shortcomings of disregarding amplitude characteristics and incomplete coarse-graining analysis in MMPE, thereby preserving crucial information present in the original time series data. Through the analysis and comparison of multi-channel synthetic signals, the efficacy and superiority of RCMMWPE in assessing the complexity of synchronized multi-channel data have been confirmed. Subsequently, an intelligent fault detection framework is introduced, leveraging RCMMWPE, multicluster feature selection (MCFS), and kernel extreme learning machine optimized by the particle swarm optimization algorithm (PSO-KELM). The proposed fault detection scheme is then applied to test gearbox fault data and extensively benchmarked against other fault detection schemes. The results demonstrate that the proposed gearbox fault detection scheme excels in accurately and consistently identifying fault categories, outperforming the comparison schemes.