三相感應馬達在各種工業製造程序和設施中扮演重要角色，作為驅動器，能有效地將電能轉換為機械能。由於其堅固強大的結構，它們可以在各種常壓、高壓和危險環境中安裝和運轉。儘管如此，感應馬達仍然容易因操作條件的重負荷、工業環境的應力和老化而出現故障和失效。這些故障和失效可能導致嚴重的安全問題、昂貴的停機和維修以及能源浪費。因此，保持感應馬達正常運行狀態至關重要，以確保其安全且高效的運作。狀態監診技術在預測性維護中為關鍵之技術，是了解感應馬達運行狀態的主要方法。
基於信號的故障診斷方法，例如馬達電流特徵分析（MCSA），具有成本低、計算要求不高的優勢。它利用簡單快速傅立葉變換（FFT）演算法，可以觀察到不同的異常特徵頻率的能量。這些故障頻率則已在ISO-20958文件中標準化。然而，由於這些故障頻率在電流頻譜中的振幅和能量相對於電流諧波來說較小，因此在電流頻譜中準確找出這些故障頻率並判斷狀態具有一定的挑戰性。
本研究旨在解探討上述之挑戰，應用基於模型的故障診斷方法取代傳統MCSA。基於模型的診斷方法使用正弦波形重疊原理，從頻譜中消除電流諧波和其他與故障無關的頻率。該方法利用測量的電壓訊號和感應馬達的狀態空間模型生成估計的電流訊號。估計的電流訊號與原始電流訊號應具有相同來自電壓信號的頻率成分，但原始電流則在系統有異常時還具有其他頻率成分，即故障特徵頻率。故障特徵頻率是由異常引起的，而非來自電壓訊號。通過將估計的電流訊號減去原始電流訊號，這樣可以消除所有相同頻率成分，同時在頻譜中保留故障特徵頻率。由此減法過程的輸出，即殘差訊號，並且殘差訊號相對於原始電流訊號對異常更敏感。因此殘差訊號是訓練異常診斷機器學習分類器的有效數據。從殘差頻譜中提取故障頻率作為機器學習分類器訓練的特徵。故障頻率具有與異常相關的物理意義，因此在訓練過程中可以為分類器提供有價值的信息。
本研究在一個工業設施中的洗滌機風扇進行了測試驗證。該設備由感應馬達透過皮帶驅動風扇。實驗驗證結果顯示，基於模型殘差的診斷方法在實際應用中展示出比MCSA更好的敏感性和穩健性。基於模型式的診斷方法與機器學習分類器結合使用，可以有效提高故障診斷決策的準確性與性能。

The three-phase induction motor play a crucial role as prime mover in various industrial manufacturing processes and facilities. It converts electrical energy into mechanical energy efficiently. Due to its robust and sturdy structure, it can be installed and operated in a wide range of environments, from general to high-voltage and hazardous ones. However, despite these advantages, induction motors are susceptible to failures and malfunctions caused by heavy operating, environmental stresses and aging. These failures and malfunctions can lead to serious safety issues, costly downtime and maintenance, as well as energy waste. Therefore, ensuring the normal operation of induction motor is paramount for safe and efficient operation. Fault diagnosis techniques play the key role in monitoring the condition of these motors in predictive maintenance.
Signal-based fault diagnosis methods, such as Motor Current Signature Analysis (MCSA), offer cost-effective and low-demand advantages. By utilizing a simple Fast Fourier Transform (FFT) algorithm on the current signal, different fault frequency indicators can be observed, which have been standardized in the ISO-20958 document. However, accurately identifying the positions and severity of these fault frequencies in the current spectrum poses a challenge due to their smaller amplitudes and energies compared to other current harmonics.
This study aims to address these challenges by applying a model-based fault residual signal to replace MCSA. The model-based approach utilizes the principle of sinusoidal waveform overlapping to eliminate current harmonics and other frequency components unrelated to faults in the spectrum. The method employs the measured voltage signal and the state-space model of the induction motor to generate an estimated current signal. The estimated current signal shares the same frequency components from the voltage signal as the original current, but the latter contains additional frequency components if with faults, namely the fault frequencies. By subtracting the estimated current signal from the original current, a destructive sinusoidal waveform overlap occurs, eliminating all identical frequency components while preserving the fault frequency spikes in the spectrum. The output of this subtraction process, known as the residual signal, is observed to be more sensitive to faults compared to the original current signal. The residual signal is valuable data in training machine learning classifiers for fault diagnosis. Extracting fault frequencies from the residual spectrum generates features for training the machine learning classifiers. Fault frequencies carry physical significance related to specific faults, thereby providing valuable information for the classifier's learning during the training process.
The method was applied on a scrubber fan in an industrial facility, where the fan is driven by an induction motor through a belt. The experimental result has demonstrated that the model-based residual signal exhibits higher sensitivity and robustness compared to MCSA. The combination of the model-based residual signal and machine learning classifiers enhances the accuracy of fault diagnosis decision-making.

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