# Optimization of Design Parameters in LSTM Model for Predictive Maintenance
## 4 A Numerical Experiment
### Experimental Results
#### 4.2.2 Exploring Optimal Hyperparameters of LSTM  
Using the feature vector obtained in Section 4.2.1, we performed numerical experiments to find the optimal hyperparameter configuration of LSTM by using the GA. A pre-experiment was conducted to set the parameters of the GA, which determined a population size \(P=20\) and a probability of mutation \(p_{m}=0.01\). Furthermore, the ranges for time steps, number of LSTM layers, and number of neurons we considered for generating initial population of chromosomes in the GA were [2; 10], [1; 5], [10; 50], respectively. Similar to the experiment executed for feature selection, we considered 20 repetitions and recorded the mean and standard deviation. Table 5 displays the experimental results. We included the results of previous research using the same IMS bearing dataset to compare with our work [3; 40; 41]. Furthermore, we addressed the information of hyperparameters used for each method in order to compare the performance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Vector** & \
\begin{tabular}{c} **Training Accuracy** \\ **Mean (std. dev.)** \\ \end{tabular} &
\begin{tabular}{c} **Validation Accuracy** \\ **Mean (std. dev.)** \\ \end{tabular} \\ \hline (Kurtosis) & 0.8043 (0.0079) & 0.7946 (0.0084) \\ (Skewness) & 0.8188 (0.0078) & 0.7950 (0.0098) \\ (CF) & 0.7432 (0.0194) & 0.7113 (0.0188) \\ (WFE) & 0.8341 (0.0125) & 0.8296 (0.0137) \\ (Kurtosis, Skewness) & 0.8703 (0.0114) & 0.8678 (0.0107) \\ (Kurtosis, CF) & 0.8654 (0.0123) & 0.8642 (0.0147) \\ (Kurtosis, WFE) & 0.9897 (0.0149) & 0.8413 (0.0188) \\ (Skewness, CF) & 0.8422 (0.0144) & 0.8063 (0.0164) \\ (Skewness, WFE) & 0.9011 (0.0129) & 0.8710 (0.0135) \\ (CF, WFE) & 0.9237 (0.0138) & 0.8823 (0.0156) \\ (Kurtosis, Skewness, CF) & 0.9568 (0.0124) & 0.9234 (0.0121) \\ (Kurtosis, Skewness, WFE) & 0.9612 (0.0110) & 0.9175 (0.0099) \\ (Kurtosis, CF, WFE) & 0.9301 (0.0105) & 0.8958 (0.0129) \\ (Skewness, CF, WFE) & 0.8939 (0.0149) & 0.8813 (0.0156) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Accuracy of trained LSTM by using feature vectors. Firstly, validation accuracy obtained from this paper had the third highest value among all approaches. The accuracy of LSTM-based approaches dominated other deep learning-based ones such as BP, SAE, and CNN in most cases. This showed the superiority of LSTM for processing vibration data of bearings, which stems from the advantage of LSTM in dealing with time series data. Exceptionally, the CNN considered in [41] slightly outperformed the result of this paper by devising an extremely deep network with a complex trained structure with many features, four times more than those used in this paper. Additionally, they used different proportions of training and test sets, namely 0.8 and 0.2, respectively. Contrary to their work, we defined the compact feature vector used as the HI, maintaining the competitive performance level. Other techniques used for predictive maintenance were also examined to demonstrate the efficiency of our work. For instance, k-nearest neighbor (k-NN) is easy to implement and has a computational advantage. [PERSON] [42] designed elaborate feature selection techniques to improve validation accuracy about 6% from original features. Still, however, our work offers slightly better classification performance represented by validation accuracy. Random forest, a representative machine learning approach, was also considered for predictive maintenance. [PERSON] et al. [43] applied their random forest-based method using two different feature sets, which showed validation accuracy of 0.9790 and 0.9824, respectively. Although the latter shows a slightly more accurate result than our work, it has limitations such that complicated