摘要
离线变点检测(Change Point Detection, CPD)算法被用于以最优方式实现信号分割。通常,这些算法基于信号统计特性发生变化这一先验假设,并采用适当的模型(如度量标准、代价函数)进行变点识别。然而,若信号的统计特性未知,合适的模型选择过程将变得繁琐且耗时,结果也具有不确定性。尽管集成方法在提升个体算法鲁棒性、应对上述挑战方面具有显著优势,但其在变点检测问题中的应用仍缺乏充分的形式化表达,远不及在异常检测或分类任务中受到重视。本文提出了一种无监督的变点检测集成方法(CPD Ensemble, CPDE),并提供了所提集成算法的伪代码及Python实现链接。该方法的核心创新在于:在离线分析过程中,于变点搜索之前对多个代价函数进行聚合处理。数值实验表明,所提出的CPDE方法在性能上优于传统的非集成CPD方法。此外,本文系统分析了常见CPD算法、数据缩放方法以及聚合函数,并在实验中进行了对比评估。实验结果基于两个包含工业故障与失效场景的异常检测基准数据集——田纳西-伊斯曼过程(Tennessee Eastman Process, TEP)与斯科尔科沃科技学院异常检测基准(Skoltech Anomaly Benchmark, SKAB)。本研究的潜在应用之一是为技术诊断中的故障识别与隔离问题提供故障发生时间的估计,从而提升工业系统运行的安全性与可靠性。
基准测试
| 基准 | 方法 | 指标 |
|---|---|---|
| change-point-detection-on-skab | BinSeg CPD algorithm (Mahalanobis metric) | NAB (LowFN): 25.04 NAB (lowFP): 21.69 NAB (standard): 24.1 |
| change-point-detection-on-skab | Opt CPD algorithm (Mahalanobis metric) | NAB (LowFN): 23.37 NAB (lowFP): 19.9 NAB (standard): 22.37 |
| change-point-detection-on-skab | Win CPD algorithm (l1 metric) | NAB (LowFN): 19.19 NAB (lowFP): 16.22 NAB (standard): 18.4 |
| change-point-detection-on-skab | WinEnsemble CPDE algorithm (Sum+MinAbs) | NAB (LowFN): 20.35 NAB (lowFP): 17.03 NAB (standard): 19.38 |
| change-point-detection-on-skab | BinSegEnsemble CPDE algorithm (WeightedSum+Rank) | NAB (LowFN): 19.51 NAB (lowFP): 15.36 NAB (standard): 18.1 |
| change-point-detection-on-skab | OptEnsemble CPDE algorithm (WeightedSum+Rank) | NAB (LowFN): 24.35 NAB (lowFP): 20.52 NAB (standard): 23.07 |
| change-point-detection-on-tep | Win CPD algorithm (Mahalanobis metric) | NAB (LowFN): 28.05 NAB (lowFP): 27 NAB (standard): 27.79 |
| change-point-detection-on-tep | BinSeg CPD algorithm (Mahalanobis metric) | NAB (LowFN): 37.29 NAB (lowFP): 35.82 NAB (standard): 36.88 |
| change-point-detection-on-tep | BinSegEnsemble CPDE algorithm (Min+MinMax/Rank) | NAB (LowFN): 42.16 NAB (lowFP): 41 NAB (standard): 41.81 |
| change-point-detection-on-tep | Opt CPD algorithm (Mahalanobis metric) | NAB (LowFN): 37.29 NAB (lowFP): 35.82 NAB (standard): 36.88 |
| change-point-detection-on-tep | WinEnsemble CPDE algorithm (WeightedSum+MinAbs) | NAB (LowFN): 26.29 NAB (lowFP): 24.33 NAB (standard): 25.14 |
| change-point-detection-on-tep | OptEnsemble CPDE algorithm (Min+MinMax/Rank) | NAB (LowFN): 42.16 NAB (lowFP): 41 NAB (standard): 41.81 |