由於物聯網的快速發展，人們在生活周遭部署的感測器產生大量的時間序列，造成對時間序列分析的需求大量增加，而異常檢測則是時間序列的重要分析需求。由於近年來有許多做異常檢測的研究，本論文聚焦於非平穩和非週期性時間序列的異常檢測研究，因為開發此類時間序列的異常檢測方法較具挑戰性。
本論文針對非平穩和非週期性的單變數時間序列提出一個名為WAAD(wavelet autoencoder anomaly detection)的異常檢測方法。此方法首先針對經由移動時窗切割的時間序列執行離散小波轉換來得到小波轉換係數，之後再藉由一個自動編碼器來對這些係數進行編碼和解碼(重建)。WAAD會對每個移動時窗計算重建誤差，並檢查是否存在連續k個上升而且同時都超過λ的重建誤差，其中k和λ為事先訂好的閥值。如果前述條件成立，就判斷為有異常發生。
目前有個已知的方法可以將時間序列分類為三類，分別是平穩時間序列、週期性時間序列和非平穩且非週期性時間序列。然後WAAD可以用來進行非平穩和非週期時間序列的異常偵測。本論文使用五個來自NAB資料庫的非平穩和非週期時間序列來評測WAAD的效能並和其他相關的方法進行比較。比較的結果顯示WAAD相較於其他方法具有較佳的精確度、召回率和F1-分數。

Due to the rapid development of the Internet of Things, sensors attached to people around their living environments generate a large number of time series data. This causes a huge demand for time series analysis. Anomaly detection is important for time series analysis; there has been much anomaly detection research in recent years. This thesis focuses on anomaly detection for non-stationary and non-periodic time series, as it is more challenging to perform anomaly detection for such a type of time series.
This thesis proposes an anomaly detection method called wavelet autoencoder anomaly detection (WAAD) for non-stationary and non-periodic univariate time series. The proposed method first applies discrete wavelet transform on time series of a sliding time window to obtain wavelet transform coefficients, and then uses an autoencoder to encode and decode (reconstruct) these coefficients. WAAD calculates the reconstruction error for every time window and checks if there exist k increasing and continuous errors larger than λ, where k and λ are pre-specified thresholds. If so, an anomaly is assumed to be detected.
An existing method can be applied to classify time series as one of the following classes: stationary, periodic, and non-stationary and non-periodic time series. The proposed WAAD is then applied for non-stationary and non-periodic time series anomaly detection. Five non-stationary and non-periodic time series from NAB datasets are used for evaluating WAAD performance. The evaluated results are also compared with those of related methods. The comparison results show that WAAD outperforms others in terms of the precision, recall, and F1-score.

中文摘要 V
Abstract VI
誌謝 VIII
圖目錄 XI
表目錄 XII
一、 緒論 1
1.1 研究背景與動機 1
1.2 研究方法與貢獻 1
1.3 論文架構 2
二、 背景知識 3
2.1 異常檢測 3
2.2 時間序列 3
2.3 小波轉換 4
2.4 深度學習 6
2.4.1 類神經網路 6
2.4.2 深度學習介紹 10
2.4.2.1 監督式學習 11
2.4.2.2 非監督式學習 11
2.4.2.3 半監督式學習 11
2.4.3 激勵函數 12
2.4.4 多層感知器 13
2.4.5 自動編碼器 13
2.5 相關文獻研究 15
2.6使用自動編碼器之相關文獻探討 16
2.7基於統計與深度學習之單變數時間序列異常檢測 18
三、 研究方法 23
3.1 資料集 23
3.2 資料前處理 25
3.3 Wavelet Autoencoder Anomaly Detection 25
3.4 評估標準 29
四、 實驗和分析 31
4.1 實驗環境 31
4.2 實驗結果與分析 31
五、 結論和未來展望 41
參考文獻 42

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