Change Point Detection in the Frequency Domain with Statistical Reliability

TL;DR

This paper introduces a statistically rigorous method for detecting change points in the frequency domain using Selective Inference, improving reliability and accuracy in condition monitoring of complex systems.

Contribution

It extends the Selective Inference framework to the frequency domain, providing valid p-values for change points across multiple frequencies, which was previously challenging.

Findings

Reliable detection of genuine change points with statistical guarantees

Effective identification of structural shifts in frequency domain data

Enhanced root-cause analysis accuracy in complex systems

Abstract

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.