發展具特徵向量校準與可解釋性之視窗式主成份分析框架以有效分類多變量時間序列

Abstract

在大數據時代，先進技術與數據分析的整合正在重塑各行各業對複雜系統的監控與分析方式。多變量時間序列（Multivariate Time Series, MTS）數據由多個相互關聯的感測器訊號隨時間所記錄而成，已成為檢測模式、識別異常及進行預測決策的關鍵資訊來源。然而，MTS數據因其高維度、特徵間的相依性，以及需保留時間結構而帶來極大分析挑戰。傳統的特徵工程方法往往透過簡化處理而忽略時間相關模式，導致可解釋性降低，並限制了將模型預測結果追溯至具體時間點的能力。因此，若欲有效且具可解釋性地建模MTS數據，方法需能同時捕捉時間結構與特徵間的關係。 本研究提出一套專為製造診斷設計的多變量時間序列分類框架，協助理解MTS感測器數據的複雜特性。我們提出CPCA演算法，融合了基於視窗的主成分分析（PCA），並透過特徵向量校正來確保特徵的一致性與穩定性。結合1D-CNN與LSTM等深度學習模型進行故障檢測與分類（Fault Detection and Classification, FDC），分類準確率超過99.50%。其中，分段平均近似（Piecewise Aggregate Approximation, PAA）作為前處理方法，較動態時間扭曲（Dynamic Time Warping, DTW）能更有效提升模型效能。為提升模型可解釋性，我們採用GradSHAP方法分析，發現第七視窗是區分正常與異常製程狀態的最具預測力區段。研究結果顯示，CPCA在提升模型準確率與特徵穩定性方面表現卓越，並能提供關鍵診斷特徵的重要洞察。同時，研究亦透過Hotelling’s T²分解技術，在最具影響力之視窗中執行根因分析，以進一步了解異常來源。 本研究展示了所提出之CPCA框架在實現高分類性能的同時，也確保時間與特徵層面的可解釋性。透過結合深度學習、校正後的降維技術與可解釋性分析方法，本框架提供一套穩健且具高度通用性的MTS分類解決方案，適用於各種仰賴時間資訊之多變量數據分析應用場景。

In the era of big data, the integration of advanced technologies and data analytics is reshaping how complex systems are monitored and analyzed across various domains. Multivariate time series (MTS) data comprising multiple correlated sensor signals recorded over time has emerged as a critical source of information for detecting patterns, identifying anomalies, and enabling predictive decision-making. However, MTS data presents significant analytical challenges due to its high dimensionality, interdependencies and the need to preserve temporal relations. Traditional feature engineering approaches often simplify the data by removing time-based patterns which limits interpretability and constrains the ability to trace back predictions to specific time point. Therefore, effective and interpretable modeling of MTS data requires methods that capture both temporal structure and spatial relationships. In this study, we propose an multivariate time series (MTS) classification framework specifically for manufacturing diagnostics that help to comprehend the complexities of multivariate time series sensor data. We present Calibrated PCA algorithm, which integrates window-based PCA to extract and ensure stability and consistency based on eigenvector calibration. Using deep learning models, such as 1D-CNN, and LSTM also for the fault detection and classification (FDC), the classification accuracy is over 99.50%. One of preprocessing techniques PAA, improves model performance more than DTW. GradSHAP is also used to provide interpretability of the model, finding that Window 7 is the most predictive segment to differentiate between normal and abnormal states of the manufacturing process. The results demonstrate the effectiveness of CPCA in improving both model performance and feature stability, while also providing critical insights into key diagnostic features. Hotelling’s T² decomposition is applied to perform root cause analysis for significant features within the most influential windows. This research demonstrates the effectiveness of the proposed CPCA framework in achieving high classification performance while ensuring temporal and feature-level interpretability. By integrating deep learning, calibrated principal component analysis and explainability methods, the framework offers a robust and generalizable approach to MTS classification, applicable across various domains where temporal relation is important for multivariate data.