Computing low-frequency vibration energy with Hölder singularities as durability predictive criterion of random road excitation

Fatigue Life Modelling of Steel Suspension Coil Springs Based on Wavelet Vibration Features Using Neuro-Fuzzy Methods

“…The low-frequency energy of vibration signals was determined using the singularity method. In the durability context, singularities in loading histories are often associated with high-amplitude events corresponding to large fatigue damage [ 9 ]. In this study, singularities in the vibration signals were identified using Hölder continuity, such that where f ( x ) is a time function, constant C is larger than zero, and a polynomial P has degree m < α .…”

“…A mother wavelet function with a low vanishing moment is recommended to obtain low-frequency singularities. Recent studies [ 9 , 10 ] found that the second-order derivative of the Gaussian (DOG) wavelet is appropriate for singularity analysis because of its well-defined vanishing moments corresponding to its order of derivative. A DOG wavelet with m derivative order is given as where m represents the order of derivative.…”

“…Wavelet-based signal processing methods are emerging as one of the popular analysis tools in fatigue analysis. Apart from time–frequency analysis, wavelet theory had been extended to singularity analysis that had been extensively used in fault detection or structural health monitoring [ 7 , 8 , 9 ]. Mohanraj et al [ 8 ] and Zhou et al [ 10 ] proposed the use of Hölder exponents to characterise the singularities in loading signals of milling tools to monitor the tools’ condition.…”

“…These changes are often regarded as transient events and associated with high fatigue damage. Previous works by Chin et al [ 9 , 11 ] demonstrated that singularities extracted from the vibration loading signals of coil springs could effectively represent the low-frequency features of the signal which contributed to major fatigue damage. Furthermore, wavelet analysis also developed into multifractal theories including the wavelet leaders method [ 12 ].…”

“…Multifractal analysis becomes relevant to the fatigue analysis of the suspension component as the road profiles naturally exhibit multifractal behaviour because they often have a complex structure that includes multiple scales of roughness [ 13 , 14 ]. Previous works by Chin et al [ 9 , 14 , 15 ] had established one-to-one relationships between the singularity-based low-frequency energy and the multifractality of road excitations to the durability of coil springs using a wavelet-based analysis. In this study, both the wavelet-based singularity and multifractal parameters were integrated to characterize the road-excited loading signals for more accurate fatigue life prediction of suspension coil springs.…”