A Model-Free Approach to Fault Detection, Localization, and Virtual Sensing in Deformable Mirrors

Deformable mirrors (DMs) are the critical components in adaptive optics (AO) systems, particularly for high-precision applications in industry and academia. However, due to their complex and highly dynamic behavior, developing accurate mathematical models of DMs remains challenging. Additionally, DMs are prone to faults, such as material fatigue and sensor failures, making it essential to implement a robust health-monitoring system capable of detecting faults in real time. In this article, we propose a model-free health monitoring algorithm for DMs. The algorithm leverages transmissibility operators—mathematical models that describe the relationship between a system’s outputs. Using measurements from sensors that capture the deflection of the DM at different locations, we construct transmissibility relationships under healthy operating conditions, achieving model-fit accuracies exceeding 99.8% on validation data. These relationships are then used, along with real-time sensor data, to generate virtual sensor measurements. The discrepancy between actual and virtual measurements serves as an indicator of potential faults, which can be used for fault detection and localization. To demonstrate the effectiveness of the proposed algorithm, we apply it to a DM model simulated using COMSOL Multiphysics, incorporating scenarios involving actuator failures, sensor failures, and structural failures, such as fatigue.