The design of a new sparsogram for fast bearing fault diagnosis: Part 1 of the two related manuscripts that have a joint title as “Two automatic vibration-based fault diagnostic methods using the novel sparsity measurement – Parts 1 and 2”

• A new concept called sparsogram is proposed.
• The sparse representation of bearing fault signal is defined.
• Sparsity is used to quantify the sparse representation of bearing fault signal.
• Sparsogram quickly determines the resonant frequency bands that contain faulty signatures.
• Sparsogram helps to provide initial guessing values for optimizing the parameters of the Morlet wavelet filter.

Rolling element bearings are widely used in rotating machines. An early warning of bearing faults helps to prevent machinery breakdown and economic loss. Vibration-based envelope analysis has been proven to be one of the most effective methods for bearing fault diagnosis. The core of an envelope analysis is to find a resonant frequency band for a band-pass filtering for the enhancement of weak bearing fault signals. A new concept called a sparsogram is proposed in Part 1 paper. The aim of the sparsogram is to quickly determine the resonant frequency bands. The sparsogram is constructed using the sparsity measurements of the power spectra from the envelopes of wavelet packet coefficients at different wavelet packet decomposition depths. The optimal wavelet packet node can be selected by visually inspecting the largest sparsity value of the wavelet packet coefficients obtained from all wavelet packet nodes. Then, the wavelet packet coefficients extracted from the selected wavelet packet node is demodulated for envelope analysis. Several case studies including a simulated bearing fault signal mixed with heavy noise and real bearing fault signals collected from a rotary motor were used to validate the sparsogram. The results show that the sparsogram effectively locates the resonant frequency bands, where the bearing fault signature has been magnified in these bands. Several comparison studies with three popular wavelet packet decomposition based methods were conducted to show the superior capability of sparsogram in bearing fault diagnosis.