## 5 Conclusions  
In this paper, a sensor fault detection and classification approach based on the multi-step-ahead prediction technique is explored. An LSTM autoencoder model is used to predict multiple time steps to capture the trend of a sensor signal. In the autoencoder training stage, normal sensor signals are used. As the autoencoder model predicts a window of 20% time steps, estimated time steps are utilized to compute features. In the initial phase of data preparation, feature importance is determined using SHAP analysis to select the most significant features from a set of statistical features that effectively discern bias, drift, and stuck fault patterns in the sensor signals. Based on SHAP analysis, only three features are selected and calculated using an estimated prediction window that has a length of 20% time steps. Considering only three features will ensure less computation complexity and faster classification of faults in the next stage. Once a feature is obtained from the predicted windows, two classifiers are used in the subsequent stages. The first classifier takes the feature point and tries to determine whether the estimated future time steps are faulty or normal. Since the feature point represents characteristics of future data points, the classifier output based on the feature point provides early fault detection. If the next prediction window is classified as faulty by the first classifier, a second classifier in the next stage is used to classify the type of fault. For the two classifiers (fault detection and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Model** & **Faults Considered** & **Task** &
\begin{tabular}{c} **Performance** \\ **Metric (Accuracy)** \\ \end{tabular} \\ \hline
[16] & SVM &
\begin{tabular}{c} Drift, bias, stuck, \\ spike, erratic \\ \end{tabular} & Fault classification & 100\% \\ \hline
[21] & ET &
\begin{tabular}{c} Drift, bias, stuck, \\ spike, erratic, \\ dataloss, random \\ \end{tabular} & Fault classification & 81\% \\ \hline
[48] & ET &
\begin{tabular}{c} Drift, bias, stuck, \\ spike, erratic, \\ dataloss, random \\ \end{tabular} & Fault classification & 90\% \\ \hline
[45] & Multi-layer perceptron & Drift, bias &
\begin{tabular}{c} Fault detection \\ and classification \\ \end{tabular} & 89.8\% and 86\% \\ \hline
[22] & DNN & Drift, bias & Fault classification & 99.6\% \\ \hline
[49] & BLCCA & Drift & Fault classification & 92.40\% \\ \hline
[55] & FDNN & \begin{tabular}{c} Drift, bias, stuck, \\ spike, degradation \\ \end{tabular} & Fault classification & 92.89\% \\ \hline This paper & \
\begin{tabular}{c} LSTM-based \\ multi-step prediction \\ \end{tabular} & Drift, bias, stuck &
\begin{tabular}{c} Fault detection \\ and classification \\ \end{tabular} & 93\(\sim\)97\% and 100\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of the proposed method with other works. classification), two datasets were created for training. In the dataset for fault detection, all the time steps corresponding to the fault were labeled as faulty, irrespective of the type of fault, and the rest were labeled as normal. But the dataset for fault classification consisted of only faulty time step information and had three classes: bias, drift, and stuck faults. The labels are determined from the location of faults in the time steps extracted from synthetic fault injection in the data preparation stage. The proposed methodology was conducted on two different datasets, and five common classification algorithms were used in fault detection and classification. For the first dataset, most of the classifiers achieved about 93% accuracy in fault detection, whereas with the second dataset, around 97% accuracy was attained. In the fault classification step, the identification of bias and drift faults was uncertain, unlike for stuck faults. However, fault classification performance improved if an extended number of time steps were considered for calculating features after fault detection.