用统计检验+预测集实现故障检测的风险可控,确保结果可信。
Calibrated Prediction Set in Fault Detection with Risk Guarantees via Significance Tests
- 将故障检测转为假设检验,基于残差定义不一致度量。
- 实测覆盖率稳定在设定水平(1-α),即使模型表现差也有效。
- 可调节风险容忍度,高容忍度对应更小的预测集,适合安全场景。
故障检测对现代工业系统的安全与可靠性至关重要。现有诊断模型普遍缺乏严格的風險控制和可靠的不确定性量化,尤其在分布偏移等复杂场景下更为突出。本文提出一种新方法,将显著性检验与同构预测框架结合,提供形式化的风险保障。该方法基于模型残差定义非一致性度量,将故障检测转化为假设检验任务;利用校准数据集计算新样本的p值,构建数学上保证以用户指定概率 $1-α$ 包含真实标签的预测集。通过分析预测集与预设正常/故障标签集的交集完成故障分类。跨域故障诊断实验验证了该方法的理论性质:在多种条件下,经验覆盖率始终不低于名义水平 $1-α$,且即使点预测模型性能不佳仍具鲁棒性。此外,用户定义的风险水平 $α$ 与效率间存在可控权衡——风险容忍度越高,平均预测集越小。本研究为故障检测提供了理论扎实的框架,支持显式风险控制,提升安全关键系统中诊断结果的可信度,推动从简单点预测迈向具不确定性感知的智能输出。
原文摘要 · Abstract (English)
Fault detection is crucial for ensuring the safety and reliability of modern industrial systems. However, a significant scientific challenge is the lack of rigorous risk control and reliable uncertainty quantification in existing diagnostic models, particularly when facing complex scenarios such as distributional shifts. To address this issue, this paper proposes a novel fault detection method that integrates significance testing with the conformal prediction framework to provide formal risk guarantees. The method transforms fault detection into a hypothesis testing task by defining a nonconformity measure based on model residuals. It then leverages a calibration dataset to compute p-values for new samples, which are used to construct prediction sets mathematically guaranteed to contain the true label with a user-specified probability, $1-α$. Fault classification is subsequently performed by analyzing the intersection of the constructed prediction set with predefined normal and fault label sets. Experimental results on cross-domain fault diagnosis tasks validate the theoretical properties of our approach. The proposed method consistently achieves an empirical coverage rate at or above the nominal level ($1-α$), demonstrating robustness even when the underlying point-prediction models perform poorly. Furthermore, the results reveal a controllable trade-off between the user-defined risk level ($α$) and efficiency, where higher risk tolerance leads to smaller average prediction set sizes. This research contributes a theoretically grounded framework for fault detection that enables explicit risk control, enhancing the trustworthiness of diagnostic systems in safety-critical applications and advancing the field from simple point predictions to informative, uncertainty-aware outputs.
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