Verifying hyperparameter sensitivities of optimal filter design methods for fault signature enhancement

Optimal filters are designed in vibration-based condition monitoring to enhance weak fault signatures for improved diagnosis. While optimisation-based filter design approaches have matured, their validation has typically focused on final objective values and constraint satisfaction. However, ensuring robust and reliable results requires verifying the correctness of design sensitivities, i.e., the gradients of both objective and constraint functions with respect to design variables, as well as hyperparameter sensitivities. This paper emphasises the importance of confirming and quantifying a filter’s response to varying hyperparameters to ensure it meets design specifications. By rigorously verifying sensitivities, engineers can more confidently deploy optimal filter designs that enhance fault-related features, resulting in more effective fault detection and diagnosis in complex engineering systems.