CEEMDAN permutation entropy based statistical complexity measure: A new stochastic resonance metric for enhanced detection of feature-unknown weak signals

When studying the adaptive nonlinear stochastic resonance (SR) with noisy periodic signal excitation, the system output resonance effect is typically measured using signal-to-noise ratio (SNR) or SNR gain. However, in practical engineering measurements, the SNR of the noisy input signal is often unknown. To overcome this limitation, this paper proposes a novel metric, “statistical complexity measure based on CEEMDAN permutation entropy (CEEMDAN-PE based SCM)”, to quantify the resonance output effect of the SR system, addressing the challenge of detecting weak signals with unknown features in engineering applications. First, the CEEMDAN is used to preprocess the feature-unknown input signal, and the optimal intrinsic mode function (IMF) is selected. This effectively addresses the modal aliasing problem in EMD that leads to inaccurate experimental results. It also helps filter complex noise components from the signal, aiding effective feature extraction in the subsequent SR processing. Secondly, the improved SCM is selected as the fitness function for the Harris Hawks Optimization (HHO) algorithm, optimizing the best matching parameters of the piecewise linearized bistable SR (PLBSR) system, thus achieving enhanced detection of weak signals with noisy inputs and unknown feature parameters. Simulation experiments show that the proposed CEEMDAN-PE based SCM method can effectively measure the resonance effect of the PLBSR system output and achieve enhanced detection of weak periodic signals. It is also capable of characterizing the system's dynamic complexity and has the potential to detect subtle behaviors induced by noise. Practical experiments demonstrate that the proposed SR measurement method performs well in bearing fault feature extraction.