Adaptive Cost Function Ridge Estimation for Rolling Bearing Fault Diagnosis Under Variable Speed Conditions

Rolling bearing health condition evaluation under time-varying operating speed requires information about shaft rotational speed. However, it is not always feasible to install a sensor such as a tachometer or an encoder to collect rotational speed signals due to space limitations or safety considerations. Time-frequency ridge estimation is an alternative approach that directly extracts the fault-related characteristic curves in a time–frequency representation (TFR) without phase reference. The cost function ridge estimation (CFRE) is the most widely used contemporary ridge estimation method. However, there is no explicit principle for the selection of search bandwidth. Moreover, the definitions of weight factor and cost function lack rationality, which causes the CFRE to degrade partially into coarse direct maximum ridge estimation (DMRE) or possibly extract the least frequency-varying curve. A time–frequency ridge estimation method, which is called adaptive CFRE (ACFRE), is developed in this study to address these deficiencies. We improve the original cost function and redefine its mathematical model to better balance searching for peak amplitude and guaranteeing a continuous curve. Numerical simulations and experimental investigations show that the proposed ACFRE is more robust to interferences derived from adjacent curves and noise than CFRE and another well-known ridge estimation approach, fast path optimization (FPO). The proposed method has a smaller root mean square error (RMSE) in estimating bearing characteristics under variable speed conditions.