An Improved Empirical Mode Decomposition Based on Adaptive Weighted Rational Quartic Spline for Rolling Bearing Fault Diagnosis

As a powerful time-frequency signal analysis technique, empirical mode decomposition (EMD) has been commonly applied in fault diagnosis. However, the cubic spline-curve often causes outstanding over and undershoot problem, which significantly limits the performance of conventional EMD. To address this problem, an improved EMD (I-EMD) based on adaptive weighted rational quartic spline is proposed. Firstly, the original cubic spline interpolation in conventional EMD is replaced with the weighted rational quartic spline interpolation (WRQSI) which has two adjustable shape control parameters. Secondly, a novel parameter selection criterion termed envelope characteristic frequency ratio (ECFR) is designed to guide the construction of the optimal local envelope. And simulation analysis proved that ECFR is not only sensitive to the characteristic information but also robust to the weak noise and sudden impulses. Subsequently, the optimal shape control parameter can be searched by grasshopper optimization algorithm (GOA) using the maximum ECFR as the objective function. Then the sensitive modes selected via weighted Kurtosis index are employed for further Hilbert envelope spectrum analysis. Finally, two case studies on rolling bearing fault diagnosis are constructed to verify the rationality and effectiveness of the I-EMD method. The results show that I-EMD method can evidently solve the over and undershoot problem and restrain the mode mixing phenomenon. Moreover, I-EMD also performs better fault feature extraction ability under the same conditions compared with EMD, VMD and CEEMDAN. So it is expected that I-EMD will serve as a potential improvement for signal processing, fault feature extraction and fault diagnosis.