在频域中用统计显著性检测系统结构变化点，确保发现的异常真实可靠。
Change Point Detection in the Frequency Domain with Statistical Reliability
- 基于选择性推断框架，结合离散傅里叶变换扩展到频域
- 对多频率同时变化的拐点给出有效p值，保证统计可靠性
- 适合需要精准故障定位的复杂系统监测场景
复杂系统中的有效状态监测需要识别频域中的变化点（CPs），因为结构变化常出现在多个频率上。本文将基于选择性推断（SI）的统计显著性检测方法拓展至频域。所提SI方法通过p值量化频域中检测到的CPs的统计显著性，确保所发现的变化反映目标系统的真正结构转变。为实现此目标，解决了两个关键技术挑战：首先，通过合理利用离散傅里叶变换（DFT）的性质，将现有SI框架推广至频域；其次，提出一种可在多频率同时发生改变时提供有效p值的SI方法。实验结果表明，该方法能可靠识别真实的CPs，具有强统计保障，有助于复杂系统频域中的更精确根因分析。
原文摘要 · Abstract (English)
Effective condition monitoring in complex systems requires identifying change points (CPs) in the frequency domain, as the structural changes often arise across multiple frequencies. This paper extends recent advancements in statistically significant CP detection, based on Selective Inference (SI), to the frequency domain. The proposed SI method quantifies the statistical significance of detected CPs in the frequency domain using $p$-values, ensuring that the detected changes reflect genuine structural shifts in the target system. We address two major technical challenges to achieve this. First, we extend the existing SI framework to the frequency domain by appropriately utilizing the properties of discrete Fourier transform (DFT). Second, we develop an SI method that provides valid $p$-values for CPs where changes occur across multiple frequencies. Experimental results demonstrate that the proposed method reliably identifies genuine CPs with strong statistical guarantees, enabling more accurate root-cause analysis in the frequency domain of complex systems.
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