A unified threshold-constrained optimization framework for consistent and interpretable cross-machine condition monitoring

Accurate detection of incipient faults during lifecycle degradation is crucial for continuous condition monitoring of industrial equipment. Condition indices (CIs) with pre-set thresholds are widely used in engineering practice due to their intuitiveness, simplicity, and convenience. However, uncertainties and variations in degradation patterns and fault initiation times across different industrial systems or even within the same system lead to inconsistent CI scales and thresholds, creating challenges for reliable and practical monitoring. To address this challenge, we propose a unified threshold-constrained optimization framework for consistent and interpretable cross-machine condition monitoring based on frequency-domain data fusion. Rather than directly using CIs, we introduce degradation rates of CIs, computed via first-order differences, which enable a consistent definition of normal operating levels across heterogeneous degradation patterns and multiple machines. Afterwards, a degradation rate and threshold constrained convex optimization model is formulated to automatically optimize weights in the frequency domain, ensuring sensitivity to incipient faults while preserving consistent thresholds across machines. Extensive experiments on multiple endurance datasets of rotating equipment demonstrate the consistency and superiority of the proposed approach over some famous and advanced CIs. Results show that a unified threshold can be established for the proposed CIs across diverse degradation patterns and multiple machines. Furthermore, the optimized frequency-domain weights highlight diagnostic frequency bands closely associated with system faults, thereby enhancing incipient fault sensitivity and offering interpretability compared with existing data-driven approaches.