Radial basis function interpolation-multiscale optimized dual-threshold permutation entropy and its application to mechanical fault diagnosis

Permutation entropy (PE) and multiscale PE (MPE) are effective methods for measuring the complexity of nonlinear signals and have been widely utilized in mechanical fault diagnosis. However, PE neglects the specific differences of amplitude and MPE suffers from information loss at larger scales. To address the limitation of PE, dual-threshold permutation entropy (DPE) is proposed, which exactly characterizes the complexity of nonlinear signals by precise division of permutation patterns to fully take into account the specific differences of amplitude through introducing the double thresholds. Furthermore, optimized DPE (ODPE) is developed to solve the threshold selection issues of DPE and thus improve applicability. To address the issue of MPE, radial basis function interpolation-multiscale ODPE (RIMODPE) is introduced as a multiscale extension of ODPE, which compensate for the loss of information on large scales by employing interpolation-multiscale techniques to supplement more information points. The four sets of synthetic signal experiments verify that compared to permutation entropy, dispersion entropy, sample entropy and fuzzy entropy, ODPE has excellent sensitiveness and robustness, and RIMODPE has superior separability and stability. Two sets of real-signal experiments reveal that mechanical fault diagnosis accuracy of RIMODPE both exceeds 97%, and it maintains reliable performance in diagnosing mechanical faults even with limited sample, which indicates that RIMODPE is well-suited for practical industrial machinery fault diagnosis.