A unified threshold-constrained optimization framework for consistent and interpretable cross-machine condition monitoring
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".