## 3 Methods, Application, and Result Discussion
### Proposed Approach
\[\forall\left\{w^{i}_{s},w^{r}_{s},\ b_{s}\right\}_{s=1}^{n}\in\left\{w^{i}_{(c, f,k)},\ w^{r}_{(c,f,k)},\ b_{(c,f,k)}\right\}_{k=1}^{m}\Bigm{|}Accuracy\geq\ 90\%,\]  
\[\left\{w^{i}_{0},w^{r}_{0},\ b_{0}\right\}=\frac{1}{n}\sum_{s=1}^{n}\left\{w^ {i}_{s},w^{r}_{s},\ b_{s}\right\} \tag{3}\]  
\[n=n_{k}+n_{k-1}\mid n_{0}=0 \tag{4}\]  
If we consider this approach as an algorithm running on a single microprocessor in a sort of repetitive loop under different working conditions, the pseudo-code of such CSIDTL can be presented as in Algorithm 1. ``` Inputs: Inputs \(x\) and labels \(y\); Number of conditions \(c\); Number of cross-validation folds \(f\); Maximum number of rounds \(m\); Outputs: Best initialization parameters \(\left\{w^{i}_{0},w^{r}_{0},\ b_{0}\right\}\) % Initialize the learning model randomly \(\left\{w^{i}_{0},\ w^{r}_{0},\ b_{0}\right\}=P(\mu,\delta)\); For \(k=1:m\) For \(c=1:13\) For \(f=1:3\) % Train the model and extract its parameters; s.t. \(l_{G(k)}=\|l_{(k-1)+}l_{(k)}\|\) % Involvement of transfer learning % Selectmental aggregate best learners' parameters according to a specified criterion; % Initialize learning parameters for upcoming rounds \(\forall\left\{w^{i}_{s},w^{r}_{s},\ b_{s}\right\}_{s=1}^{n}\in\left\{w^{i}_{(c, f,k)},\ w^{r}_{(c,f,k)},\ b_{(c,f,k)}\right\}_{k=1}^{m}\Bigm{|}Accuracy\geq\ 90\%\), \(\left\{w^{i}_{0},w^{r}_{0},\ b_{0}\right\}=\frac{1}{n}\sum_{s=1}^{n}\left\{w^ {i}_{s},w^{r}_{s},\ b_{s}\right\}\); \(n=n_{k}+n_{k-1}\mid n_{0}=0\); Endparticular rounds in an amount of time of 5.9170 h. Since the process is very slow, there is a small chance of involving random search algorithms and the grid search mechanism for hyperparameter tuning. Therefore, the LSTM network parameters were manually tuned based on an error-and-trial basis instead. Three-fold cross-validation was involved in studying the performance of the proposed approach, while well-known metrics, such as _Accuracy_, _Recall_, _Precision_, and _F1 score_, were used to evaluate the performance of the training process. For the mathematical background and significance of these metrics, please refer to the paper [27]. During the evaluation, we focused on collecting testing performance, as it is very important to assess both the approximation and generalization capabilities of learning models. The selection of the best learners was constrained by _Accuracy_\(\geq\) 90%. All trained models of three-folds were involved in the transfer learning-based selection and aggregation process, while the resulting illustration of each model per condition is the average value of the values obtained from the results. Accordingly, a single-layer LSTM network with 40 neurons, \(l_{2}\) regularization parameter = 1 \(\times\) 10\({}^{-4}\), initial learning rate = 1 \(\times\) 10\({}^{-2}\), minibatch size of 200 samples, and the maximum number of epochs of 600 was adopted for the used hyperparameters. After the training process, the best results were collected and labeled as best-round training. It should be mentioned that the results, in this case, were numerous, as a matrix of 4 \(\times\) 13 elements was obtained per round. Additionally, about 13 \(\times\) 3 \(\times\) 5 confusion matrices were analyzed in this case. Therefore, an average of the entire matrix was used to better illustrate and compare global results, because it is difficult to showcase such numerous results. #### 3.2.1 Variable-Speed and -Load Experiment

Accordingly, Figure 9 is introduced to showcase the obtained global results of the CSIDTL approach compared with the LSTM network, while Table 3 is used to indicate in which rounds the best learners were obtained under each condition. In this case, the classification performance metrics were improved by about 12.15% compared with traditional LSTM. This means that the accuracy was about 93.63% for the entire variable-speed and -load dataset. This is considered an excellent improvement in the field.