Lagrangian-weighted squared envelope entropy-based early fault detection of railway bearing

Entropy is an effective nonlinear measure to characterize the health of a rolling element bearing. However, under extreme noise, fault impulses are submerged into the unwanted noise component. As a result, traditional entropy algorithms not only fail to identify the fault in its earliest stages of emergence but also fail to track the progress of the fault. Due to the inability of traditional methods to accurately identify fault components in high-noise environments, extracting key fault components can be employed to enhance subsequent outcomes. Hence, the proposed method has extract transient impulses associated with rolling element bearing faults by applying weights to the squared envelope of the vibration signal. Therefore, to enhance noise resistance and early fault detection ability, method named Lagrangian-weighted squared envelope entropy (LWSEE) is proposed in this paper, which involves applying weights to the frequency spectrum to extract key fault components and then calculating entropy values. First, the weighting model is built by using Lagrangian multiplier-based optimization technique for calculating the Lagrangian-weighted squared envelope (LWSE). Then, extracted LWSE has been incorporated into the calculation of entropy for dynamic monitoring of rolling element bearing health as LWSEE. To validate the performance of the proposed LWSEE, two distinct experimental case studies on run-to-failure rolling element bearings have been utilized. The results indicate that the proposed LWSEE not only detects faults at their earliest stages but also outperforms direct entropy calculation, squared envelope-based entropy, and weighted squared entropy methods in tracking fault progression.