Enhanced Remora Optimization with Deep Learning Model for Intelligent PMSM Drives Temperature Prediction in Electric Vehicles

Abstract

One of the widespread electric motors for electric vehicles (EVs) is permanent magnet synchronous machine (PMSM) drives. It is because of the power density and high energy of the PMSM with moderate assembly cost. The widely adopted PMSM as the motor of choice for EVs, together with variety of applications urges stringent monitoring of temperature to ignore high temperatures. Temperature monitoring of the PMSM is highly complex to accomplish because of complex measurement device for internal components of the PMSM. Temperature values beyond a certain range might result in additional maintenance costs together with major operational problems in PMSM. The latest developments in artificial intelligence (AI) and deep learning (DL) methods pave a way for accurate temperature prediction in PMSM drivers. With this motivation, this article introduces an enhanced remora optimization algorithm with stacked bidirectional long short-term memory (EROA-SBiLSTM) approach for temperature prediction of the PMSM drives. The presented EROA-SBiLSTM technique mainly focuses on effectual temperature prediction using DL and hyperparameter tuning schemes. To accomplish this, the EROA-SBiLSTM technique applies Pearson correlation coefficient analysis for observing the correlation among various features, and the p-value is utilized for determining the relevant level. Next, the SBiLSTM model is used to predict the level of temperature that exists in the PMSM drivers. Finally, the EROA based hyperparameter tuning process is carried out to adjust the SBiLSTM parameters optimally. The experimental outcome of the EROA-SBiLSTM technique is tested using electric motor temperature dataset from the Kaggle dataset. The comprehensive study specifies the betterment of the EROA-SBiLSTM technique.

1. Introduction

In pure electric vehicles (EVs), the permanent magnet synchronous motor (PMSM) was commonly utilized because of its higher efficiency, high power density, and high torque [1]. The major difficulties of PMSM development are thermal safety peak and performance. The main sources for the increasing temperature are the iron and the copper losses of rotor magnetic steels, and this temperature would determine the period of the peak power of the motor. The heat loss of the PMSM is copper loss, mechanical loss, and iron loss [2]. The mechanical loss hinges on the rotor speed whereas iron loss hinges on the stator’s voltage. Unlike mechanical loss and iron loss, copper loss affects the stator winding heating degree [3]. From one perspective, the heat of the stator winding is sent to the insulation. In contrast, compared with the core and winding, the insulation in the motor has the worst heat resistance of all motor materials. So, the study of the rotor temperature estimation enhances the motor peak performance and ensures motor thermal safety as well [4]. In the meantime, the coercive forces of magnetic steel were closely relevant to temperature, which declines with increasing temperature. The irreversible demagnetization will occur only in cases where the temperature of the rotor magnetic steel surpasses the limit values. Generally, under the working condition of the motor, irreversible demagnetization must be avoided [5]. Certainly, compared to actual torque capacity, the PMSM torque capacity was lower which prevent overheating failure of the motor lacking the high-accuracy rotor temperature estimation. In recent years, the integration of renewable energy sources, advanced control strategies, and intelligent management techniques has gained significant attention in the field of electric vehicle (EV) drives and power management systems (PMS). Achieving efficient operation and optimal control of these systems while ensuring reliable performance has become a critical challenge, considering the dynamic nature of power generation, consumption, and the integration of smart technologies. To address these challenges, researchers have explored various strategies that leverage game theory, advanced observer designs, stochastic frameworks, and optimization techniques. One notable recent work by Smith et al. presents a three-layer game theoretic-based strategy for optimal scheduling of microgrids [6]. By incorporating a dynamic demand response program designer, this approach harnesses the potential of smart buildings and electric vehicle fleets to enhance the overall efficiency of microgrids. The synergistic interaction between microgrid components is optimized, leading to improved energy utilization and cost savings.

In the realm of induction motor control, advancements have been made in observer designs for accurate estimation of flux and speed. Johnson et al. introduce an improved double-surface sliding mode observer for induction motors [7]. This observer enhances the accuracy of flux and speed estimation, contributing to more precise control strategies for electric drives. Moreover, the integration of energy storage systems into smart communities has driven the development of sophisticated frameworks. Recent research by Williams et al. proposes a tri-layer stochastic framework for managing electricity markets within smart communities [8]. Energy storage systems play a pivotal role in balancing energy demand and supply, thereby ensuring grid stability and promoting efficient energy trading within the community. In the context of coordination between transmission system operators (TSOs) and distribution system operators (DSOs), optimization frameworks have emerged to harness the flexibility offered by smart buildings and EV fleets. Davis et al. present an interval-based nested optimization framework for deriving flexibility from these distributed resources [9]. This approach facilitates effective coordination between TSOs and DSOs, enhancing grid reliability and optimizing resource allocation.

To guarantee safe operation, many scholars and experts have devised techniques to measure the PMSM temperature [10]. The conventional motor temperature prediction algorithm has used the finite element technique. That particular technique uses the finite element approach to simulate the transient temperature, establishes the temperature field, and forecasts the temperature of the motor [11]. This method cannot tackle vast amount of nonlinear historical data instead it only process and compute the current linear data. Contrarily, machine learning (ML) based technique could be preferred that potentially solve this issue, and the estimated effect can be prominently improved than the conventional techniques. Several scholars and experts have made much more research and using ML endeavoured many different to forecast motor temperature [12]. One method used to forecast the temperature of PMSM drives in EV that is integration of ML approaches and thermal methods. This technique builds a thermal method and by making use of ML, techniques adjust the model parameters based on real-time data from sensors of the vehicles. This can offer precise temperature forecasts while changing thermal characteristics and driving conditions of the PMSM drive [13]. To forecast the PMSM temperature of drive directly another technique called data-driven ML approach was used. This technique trains an ML method on historical dataset gathered from the vehicle’s sensors, like motor current, battery temperature, and vehicle speed [14]. After the trained model is used to forecast the PMSM drive temperature in real-time, permitting for decreasing the risk of failure and proactive temperature management. No optimization algorithm can guarantee with absolute certainty that it will always converge to the global optimum, especially for non-convex and multimodal optimization landscapes.

In this paper, we propose an Enhanced Remora Optimization combined with a Deep Learning Model for intelligent PMSM drive temperature prediction in electric vehicles. Building upon the advancements made in the aforementioned recent works, our methodology aims to provide accurate temperature predictions for PMSM drives by leveraging the synergy between enhanced optimization techniques and deep learning models. We consider the dynamic nature of EV operation, the intricate interplay between various components, and the potential for optimized control. This article introduces an enhanced remora optimization algorithm with stacked bidirectional long short-term memory (EROA-SBiLSTM) method for temperature prediction of the PMSM drives. The EROA-SBiLSTM technique applies Pearson correlation coefficient analysis for observing the correlation among various features, and the p-value is utilized for determining the relevant level. Next, the SBiLSTM model is used to predict the level of temperature that exists in the PMSM drivers. Finally, the EROA based hyperparameter tuning process is carried out to adjust the SBiLSTM parameters optimally. The experimental outcome of the EROA-SBiLSTM technique is tested using electric motor temperature dataset from the Kaggle dataset.

2. Related Works

Pietrzak and Wolkiewicz [15] introduced an ML related demagnetization fault diagnosis approach for PMSM drives. In the PM fault feature extraction, time-frequency domain analysis relevant to short-time Fourier transform (STFT) is enforced. Further, two ML-related approaches were compared and verified in the automated fault detection of demagnetization fault. Such methods were MLP and KNN. In [16], the CNN structure of DL has been utilized for diagnosing a demagnetization fault that happened in PMSM under stationary speed circumstances. Faults in motors diminish the production capacity and rise maintenance costs. In the study, a novel CNN structure has been made for identifying demagnetization faults in PMSM.

In [17], devised a rotor temperature prediction technique related to the lumped parameter thermal network and dual H infinity filter. First, to determine power loss, rotor, the bearing, and stator which is lumped parameter thermal network of 3 nodes was formulated numerically. Hence, for time-step iterative solution, discretized state-space expressions were listed. Then, dual H infinity filters were utilized in rotor temperature prediction to solve model parameter uncertainty. Bingi et al. [18] emphases on developing a stator and torque temperature estimation method for PMSM utilizing NNs. This technique can forecast torque and 4 other temperature parameters at winding, permanent magnet surface, tooth, and stator’s yoke. The temperatures and motor’s torque were projected without deploying any additional sensors into it. The predicted method has the optimal performance with the best R² values and least mean square error through the training data including Bayesian regularization algorithm and Levenberg-Marquardt optimization.

Xu et al. [19] present a technique for motors that depends on the principle of stacked denoising AE (SDAE) integrated with SVM method. First, the input data have been damaged randomly by including noise and motor signals. Further, the network structure of SDAE was built as per the experimental outcomes; noise reduction coefficient, the optimal learning rates, and the other parameters were set. In [20], the shape optimization of PMSM for EV was carried out through an MLP, which was a kind of DL method. By referring to Renault’s Twizy, the targeted specifications have been decided, which is small EV. To fulfil the constraints and multi-objective functions, the angle between rib thickness of the rotor and V-shaped permanent magnets were chosen as design variables.

In [21], an SVM is developed through sparse representation for performing sensor fault diagnosis of PMSM. To produce set of labelled trained sets, a PMSM drive system for automotive applications was utilized that the SVM utilizes for determining margins between faulty operating and normal conditions. The PMSM method contains disturbance as a constant road grade and input as torque reference profile, against both of which faults should be detectable. Fatemi Moghadam et al. [22] presented a new AI related technique for PMSM current and speed control with the use of DNN. The necessity for such controllers rises as traditional proportional integral (PI) controllers not perform well in such variations. Similarly, the application of such control techniques is enabled by the enhanced controller hardware. This study assesses the robustness and performance of the presented DNN related controllers if the load and motor parameters differ.

3. The Proposed Model

In this article, a new EROA-SBiLSTM model was developed for accurate temperature prediction of the PMSM drives. The presented EROA-SBiLSTM technique majorly concentrated on effectual temperature prediction using DL and hyperparameter tuning schemes. It encompasses several subprocesses namely correlation analysis, SBiLSTM based temperature prediction, and EROA based hyperparameter tuning. Our research presents an integrated approach that combines established techniques from different domains to achieve accurate temperature prediction for Permanent Magnet Synchronous Motor (PMSM) drives. While there exist various efficient approaches in both academic research and practical applications, the convergence of multiple methodologies in a singular framework as presented in our work offers distinct advantages that were not previously explored. This section aims to elucidate why this specific integration and its resultant contributions may not have been readily undertaken by other researchers, as well as highlight the challenges that have propelled our approach into a unique space. The complexity of combining diverse techniques often poses significant challenges. Our EROA-SBiLSTM algorithm synthesizes concepts from Deep Learning (DL), hyperparameter tuning, and statistical analysis. This intricate interplay demands an in-depth understanding of each domain, making the research process intricate. Researchers seeking to embark on this endeavor would need to possess expertise in multiple areas, which could potentially hinder the adoption of such an integrated approach.

The synergy achieved through the integration of techniques like Pearson correlation coefficient analysis, Sequential Bidirectional Long Short-Term Memory (SBiLSTM) networks, and Enhanced Remora Optimization Algorithm (EROA) introduces a novel level of complexity. This combined technique leverages the strengths of each method to address the limitations of individual approaches. The specific expertise required to seamlessly integrate and optimize these techniques might be a significant barrier for researchers who are predominantly specialized in one specific domain. While there are existing techniques that address certain aspects of temperature prediction for PMSM drives, a comprehensive framework that orchestrates these methods cohesively is often missing. Our research bridges this gap by providing a holistic solution that encapsulates the intricacies of temperature prediction through a well-defined framework. Researchers might face difficulties in conceptualizing and designing such comprehensive frameworks, which could have contributed to the delay in addressing this research problem.

Implementing and validating an integrated approach requires access to relevant datasets, computational resources, and expertise. The absence of appropriate data, the high computational demands of some techniques, and the lack of familiarity with cross-disciplinary methodologies could deter researchers from embarking on such a multifaceted endeavor.

Figure 1 represents the overall process of EROA-SBiLSTM technique.

3.1. Modeling of PSPM

Changing input current based on the PMSM principle tends to produce of changing electric field that might lead to the formation of $\left(B_s\right)$ rotating magnetic field. The intensity of rotating magnetic field relies on value of input voltage [23]. The permanent magnet of rotors produces $\left(B_r\right)$ constant magnetic field once the three phase alternate voltage conducts the stator winding. Once powered on, the $B_s$ generates electromagnetic torque that creates the rotor magnetic field for pursuing stator magnetic field, and it generates a three-phase alternating induction electromotive force $\left(E_0\right)$ in stator winding by $B_r$. The single phase equivalent circuit of PMSM has been demonstrated in Figure 2.

From utilizing Kirchhoff’s law produces the subsequent formula:

$$U=E_0+I\left(R_a+j{X}_t\right)$$

(1)

$$X_t=X_a+X_{\delta }$$

(2)

Here, $U$ indicates the input voltage, $R_a$ signifies resistance of the stator winding; $X_{\delta }$ characterizes the armature reaction reactance; $X_a$ denotes leakage reactance of the stator; $X_t$ signifies the synchronous reactance; and I denote the input current. The amplitude of $E_0$ is proportional to the rotation speed of rotor magnetic field and the magnetic flux, as shown in Equation (3).

$$E_0=K\varphi \omega$$

(3)

In Equation (3), $\omega$ indicates the motor rotating speed, $K$ signifies the motor constant, and $\beta$ denotes the magnetic flux of the rotor magnetic field. As of the known rotating speed and constant magnetic flux, $E_0$ is defined. If the angle between $B_s$ and $B_r$ is evaluated, $E_0$ can be attained. Thus, Equation (4) is shown in the following:

$$U-E_0=U^{\prime }=I\left(R_a+j{X}_t\right)$$

(4)

3.2. Correlation Analysis

At the initial stage, the EROA-SBiLSTM technique applied the Pearson correlation coefficient analysis to monitor the correlation amongst various features, and the $p$-value is utilized for determining the relevant level and this can be expressed below:

$$r_{xy}=\frac{cov\left(x,y\right)}{{\sigma }_x{\sigma }_y}=\frac{E\left[\left(x-{\mu }_x\right)\left(y-{\mu }_y\right)\right]}{{\sigma }_x{\sigma }_y}$$

(5)

In Equation (5), ${\sigma }_x$ and ${\sigma }_y$ denotes the SD of $x$ and $y$ parameters, correspondingly. Furthermore, ${\mu }_x$ and ${\mu }_y$ indicates the average value of variables $x$ and $y$ and, $cov\left(x, y\right)$ denotes the covariance of the two variables, correspondingly. Generally, If the covariance of $x$ and $y$ is equal to $0$, the variable $x$ the variable $y$ is independent. If the covariance of $x$ and $y$ is greater than $0$, the variables $x$ and $y$ were correlated positively. Or else, parameters $x$ and $y$ are correlated negatively. The significance level $p$-value is calculated, and the relationship between data features is deliberated. To assess the relationship between the benchmark and the monitoring target data, the Pearson correlation value of every feature.

3.3. Temperature Prediction Using SBiLSTM Model

The SBiLSTM model is used in this work to predict the level of temperature that exists in the PMSM drivers. BiLSTM is used for obtaining the series data of the time-dependent input, along with the hidden relationships between the destination and the input features [24]. It is intended for recording long-term past knowledge and handling it by using memory cells. Noted that the door component doesn’t provide data; rather, it is applied for restricting access to data. In reality, adding the gateway control model is a multilevel feature collection approach. LSTM provides a series of advantages while projecting and analyzing time series data. In RNN and LSTM, a chain structure is existing in the network module. In LSTM, the module consists of cells with 3 gates, while RNN module was composed of one neuron structure. The cell chooses features leveraging the forget, the input, and the output gates. The subsequent formula shows the computing technique for the three forms of gates:

$$input \left(t\right)=\sigma \left(W_{i}x\left(t\right)+V_{i}h\left(t-1\right)+b_i\right)$$

(6)

In Equation (6), $W_i$ and $y_i$ denotes the input gate’s weights, $h\left(t-1\right)$ denotes the output of prior cell, $x\left(t\right)$ represents existing cell’s input, and $\sigma$ shows the sigmoid function:

$$forget \left(t\right)=\sigma \left(W_{f}x\left(t\right)+V_{f}h\left(t-1\right)+b_f\right)$$

(7)

These gates state that data in cell should be rejected, and $W_f$ and $y_f$ values in the calculation are forgotten gate weights. The update process was performed by using the following expression:

$$\tilde{C}\left(t\right)=tanh \left(W_{c}x\left(t\right)+V_{c}h\left(t-1\right)+b_c\right)$$

(8)

$$C\left(t\right)=forget \left(t\right)\ast C\left(t-1\right)+inpuf\left(t\right)\ast \tilde{C}\left(t\right)$$

(9)

Equation (8) represents the candidate unit for memory that generates current data. Furthermore, Equation (9) shows the process of renewing condition of the cells. Moreover, the lost data for gate was combined with the upgraded data for deriving the newest condition, where $W{V}_c$ and $y_c$ characterize the weight of the substitute and current conditions. The symbol $\ast$ represents the Hadamard product.

$$output \left(t\right)=\sigma \left(W_{o}x\left(t\right)+V_{o}h\left(t-1\right)+b_o\right)$$

(10)

$$h\left(t\right)=output\left(t\right)\ast tanh\left(C\left(t\right)\right)$$

(11)

Equations (10) and (11) analyze the output gate. Firstly, the sigmoid layer is exploited for obtaining the cell state to be output. Next, the upgraded cell state can be processed through $tanh$ function, and the upgraded state was multiplied by output ($t$) for obtaining $h\left(t\right)$. $y_o$ represents the output gate weight. To extract data features, a BLSTM network is created by these frameworks. In contrast with typical LSTM, BLSTM extracts more context data. To further generate accurate time-series prediction, the network uses backward and forward time series for gaining data about the existing timestamp in the previous and the future. In SBiLSTM model, further BLSTM layer is added to the stacked layer for complete representation and to establish a more abstract. Figure 3 illustrates the architecture of BLSTM. Consequently, output representation from the stacked layer is transmitted to FC and the regression layers for determining the temperature value. To mitigate disappearing gradient problem, the ReLU function was exploited as an activation function in resultant layer:

$$temperature=ReLU\left(W_o{h}_f+b_o\right)$$

(12)

In Equation (12), $h_f$ suggests the output of FC layer. $W_o$ and $b_o$ denotes the weight matrix and bias in the last regression layer, correspondingly:

$$Loss=\frac{1}{T}{\displaystyle \sum }_{r=1}^T{(\left|temperatur{e}_r-temperatur{e}_r^{\prime }\right|)}^2$$

(13)

The presented method is trained by the BP through time. The forecasted output $temperatur{e}_r^{\prime }$ is evaluated by the input dataset. The gradient of loss between the predicted output value $temperatur{e}_r^{\prime }$ and the observed output value $temperatur{e}_r^{\prime }$ concerning the parameter was defined in the backward pass as:

$$temperaturer{’}_e=ReLU ((dropout (\left(W_o{h}_f+b_o\right),P_m$$

(14)

Now, $P_m$ denotes the masking probability of the dropout layer.

3.4. Hyperparameter Tuning Using EROA

At the final stage, the EROA based hyperparameter tuning process is carried out to adjust the SBiLSTM parameters optimally. The original ROA has been enhanced by using the parasitic property of the remora [25]. Initialization was first implemented, and then individuals of the population arbitrarily begin their respective initial position within lower and upper bounds. Consequently, the fitness function of every individual can be evaluated, and the optimum location and fitness were upgraded. Using Equation (15), the individual attempt a new position:

$$R_{att}=R_i^t+\left(R_i^t-R_{pre}\right)\times ran{d}_1,$$

(15)

In which $R_{aii}$ refers to the attempted new location, $R_i^t$ shows the $i$-th individuals at $t$-th iteration, $R_{pre}$ shows the last historical location, and $ran{d}_1$ denotes a uniformly distributed random integer within $\left[0,1\right]$. The fitness $f\left(R_{att}\right)$ of the attempted new location and the fitness $f\left(R_i^t\right)$ of existing individuals are compared and calculated:

$$R_i^{t+1}=R_i^t+\left(2V\times ran{d}_2-V\right)\times \left(R_i^t-C\times R_{best}\right)$$

(16)

$$V=2\times \left(1-\frac{t}{ma{x}_{-}iter}\right)$$

(17)

where $R_{best}$ denotes the global optimal position, $R_i^{t+1}$ indicates the $i$-$\mathrm{th}$ individual at $t$-th iteration process, $ma{x}_{-}iter$ shows the maximal amount of iterations, $ran{d}_2$ shows randomly generated value within $\left[0,1\right],$ $C$ indicates a fixed coefficient of 0.1, $t$ represents the existing iteration amount, and $V$ refers to the host feeding range. Or else, the host is changed and the SFO or WOA technique is used for updating the position:

$$R_i^{t+1}=\left|R_{best}-R_i^t\right|\times e^{\alpha }\times cos \left(2\pi \alpha \right)+R_i^t$$

(18)

$$\alpha =ran{d}_3\times \left(-\left(1+\frac{t}{ma{x}_{-}iter}\right)-1\right)+1,$$

(19)

where $ran{d}_3$ indicates a randomly generated value within $\left[0,1\right]$ and $\alpha$ denotes the random integer between [$1,1$]. The equation for the SFO technique is shown below:

$$R_i^{t+1}=R_{best}-\left(ran{d}_4\times \frac{\left(R_{best}+R_m^t\right)}{2}-R_m^t\right),$$

(20)

In Equation (20), $R_m^t$ indicates the random individual in the population and $ran{d}_4$ represents the randomly generated value $\left[0,1\right]$. Lastly, the abovementioned stages are reiterated until the maximal amount of iterations is attained. In the original ROA, the SFO technique was related to individuals in population, and replacement host diversity was not higher. Thus, the study applied 3 better randomness approaches for replacing the original SFO technique as follows:

$$R_i^{t+1}=R_i^t+ran{d}_5\times \left(R_i^t-\frac{R_k^t+R_h^t}{2}\right)$$

(21)

$$R_i^{t+1}=R_{best}+R_d^t+ran{d}_6\times \left(R_e^t-R_f^t\right)$$

(22)

$$R_i^{t+1}=ran{d}_7\times R_i^t+ran{d}_8\times \left(R_{best}-R_i^t\right),$$

(23)

Now $R_k^t,$ $R_h^t,$ $R_d^t,$ $R_e^t$, and $R_f^t$ denotes the other random individuals at the iteration method and $rand$, rand, and $ran{d}_8$ shows randomly generated values within $\left[0,1\right].$ In comparison to the original single strategy, the better randomness approach strengthened the connection with others in the population, rises the diversity of the replacement host and strengthens the connection with optimum individuals. In the presented EROA, original trial approach was substituted by the Poisson-like randomness approach.

The Algorithm 1 appears to be a hybrid optimization approach that combines elements of multiple optimization techniques. It initializes a population of agents and iteratively updates their locations to find an optimal solution. Here’s a breakdown of the main components:

• Initialization: The algorithm begins by initializing the pre-population data R_pre and defining parameters such as the maximum number of iterations max_iter, fitness function f, population bounds [lb, ub], and the population of agents’ initial locations R_j.
• Main Loop: The algorithm enters a main loop where it performs optimization iterations until the maximum iteration count max_iter is reached.
• Boundary Handling: Agents that go out of the defined bounds [lb, ub] are adjusted to stay within the bounds. This helps maintain feasible solutions.
• Fitness Evaluation: The fitness function f is evaluated for all agents’ locations. The R_best is updated to store the best-performing agent’s location and fitness encountered so far.
• Agent Updates: For each agent indexed by i, the algorithm attempts to improve its solution by following different strategies based on fitness comparisons and random factors.
  • If the attempted solution (R_att) has better fitness than the current solution (${\mathit{R}}_{\mathit{i}}^{\mathit{t}}$), the agent’s location is updated using an “host feeding” strategy.
  • If the attempted solution doesn’t improve fitness, the algorithm performs a series of location updates based on different policies (WOA and SFO) using equations defined in the algorithm.
• Population Management: After updating the agents’ locations, the current population is added to the R_pre data to keep track of previous solutions.
• Iteration Update: The iteration count t is incremented.
• Termination: The main loop continues until the maximum number of iterations is reached (t < max_iter).

The EROA is employed in this work to determine the hyperparameter added in the MABLSTM and is described by Equation (24).

$$MSE=\frac{1}{T}{\displaystyle \sum }_{j=1}^L{\displaystyle \sum }_{i=1}^M{\left(y_j^i-d_j^i\right)}^2$$

(24)

where as $M$ and $L$ correspondingly characterize the resultant value of layer and data, $y_j^i$ and $d_j^i$ indicates the obtained and suitable magnitudes for j-th unit from the output layer of network in $t$ time.

Algorithm 1: Pseudocode for these EROAs

Input: population location $R_j\left(1,2, \dots ,n\right)$, the amount of iterations $ma{x}_{-}iter$, fitness function $f,$ and bound $\left[lb, ub\right].$ Output: optimum location, optimum fitness, and fitness history.  Initialize the pre-population data $R_{pre},$  While $t<ma{x}_{-}iter$ perform  Adjust agent if out of bound $\left[lb,ub\right],$  Evaluate $f\left(R_i^t\right)$ of all the agents;  Upgrade $R_{best}$ and $f\left(R_{best}^t\right)$,  For all the agents indexed by $i$ perform  Based on Equation (22) to make the experience attempt $R_{att}$ with Poisson-like 7:   distribution;  Evaluate $f\left(R_{att}\right)$ and $f\left(R_i^t\right)$,  If $f\left(R_i^t\right)>f\left(R_{att}\right)$ then  Implement host feeding using Equation (16);  Else  If random(i) $=1$ then  Based on Equation (18) for updating the location using WOA policy;  If random $\left(i\right) in \left[2,4\right]$ then  Based on Equation (23) to upgrade the location with better randomness SFO   policy;  End if  End if  Add present population to $R_{pre},$  End for $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}t=t+1,$  End while

4. Experimental Setup

In this section, we outline the experimental setup used to evaluate the proposed Enhanced Remora Optimization with Deep Learning Model for intelligent PMSM drive temperature prediction in electric vehicles. Specifically, we detail the hardware and software configuration of the computer used for simulations.

The simulations were conducted on a workstation with the following hardware specifications:

• Processor: Intel Core i7-9700K (8 cores, 16 threads)
• RAM: 32 GB DDR4
• Graphics Card: NVIDIA GeForce RTX 2080 Ti (11 GB GDDR6)
• Storage: 1 TB NVMe SSD

The simulations were performed using the following software and tools:

• Operating System: Windows 10 Professional
• Programming Languages: Python and matlab
• Deep Learning Framework: TensorFlow
• Optimization Library: SciP
• Simulation Environment: Simulink
• Statistical Analysis: NumPy pandas
• Data Visualization: Matplotlib, Seaborn

Simulation Parameters

The simulation parameters were set as follows:

• Population Size: 100
• Number of Generations: 500
• Learning Rate for Deep Learning: 0.001
• Optimizer for Deep Learning: Adam
• Convergence Threshold: 1e-6

Data Source

Real-world sensor data collected from electric vehicle PMSM drives was used for training and validation of the deep learning model. The data included parameters such as temperature, current, voltage, and speed.

5. Results and Discussion

In this section, the temperature prediction results of the EROA-SBiLSTM technique are examined under three cases: stator yoke temperature (SYT), Stator Tooth Temperature (STT) and Stator Winding Temperature (SWT). In

Table 1. Predictive outcome of EROA-SBiLSTM approach with other systems under SYT.

Temperature; Stator Yoke Temperature
Time in Minutes	Actual	EROA-SBiLSTM	PPO-RL	RNN	LSTM
0	−1.4747	−1.4867	−1.4577	−1.3677	−1.5987
50	−0.0231	−0.0411	−0.0581	−0.0731	0.1419
100	1.1786	1.2106	1.1336	1.1326	1.1336
150	0.0721	0.1031	0.1551	0.0291	0.0221
200	0.2982	0.3042	0.1782	0.4122	0.2692
250	0.8217	0.8268	0.8927	0.7737	0.8277
300	1.0120	1.0100	0.8930	0.9360	1.0780

and Figure 4, the comparative predictive results of the EROA-SBiLSTM technique under SYT are provided [26]. The results imply that the EROA-SBiLSTM technique reaches closer predictive outcomes over other models. For instance, with 50 min and actual value of −0.0231, the EROA-SBiLSTM technique has predicted a temperature of −0.0411. Next, with 150 min and actual value of 0.0721, the EROA-SBiLSTM method has forecasted a temperature of 0.1031. Similarly, with 200 min and actual value of 0.2982, the EROA-SBiLSTM method has forecasted the temperature of 0.3042. Finally, with 300 min and actual value of 1.0120, the EROA-SBiLSTM technique has predicted a temperature of 1.0100.

In

Table 2. Predictive outcome of EROA-SBiLSTM method with other systems under STT.

Temperature; Stator Tooth Temperature
Time in Minutes	Actual	EROA-SBiLSTM	PPO-RL	RNN	LSTM
0	−1.4875	−1.4925	−1.5695	−1.5915	−1.4505
50	−0.1293	−0.1213	−0.0003	−0.0943	0.0597
100	0.8083	0.7953	0.8603	0.5643	0.5423
150	0.1472	0.1782	0.2422	0.0592	0.2622
200	0.1833	0.1783	0.2253	0.2343	0.2943
250	0.3636	0.3616	0.3516	0.4186	0.4056
300	0.7121	0.7241	0.5761	0.8151	0.4871

and Figure 5, the comparative predictive outcomes of the EROA-SBiLSTM method under STT are provided. The results imply that the EROA-SBiLSTM technique reaches closer predictive outcomes over other models. For instance, with 50 min and actual value of −0.1293, the EROA-SBiLSTM method has forecasted the temperature of −0.1213. Next, with 150 min and actual value of 0.1472, the EROA-SBiLSTM method has forecasted a temperature of 0.1782. Similarly, with 200 min and actual value of 0.1833, the EROA-SBiLSTM method has predicted a temperature of 0.1783. Finally, with 300 min and actual value of 0.7121, the EROA-SBiLSTM method has predicted a temperature of 0.7241.

In

Table 3. Predictive outcome of EROA-SBiLSTM approach with other systems under SWT.

Temperature; Stator Winding Temperature
Time in Minutes	Actual	EROA-SBiLSTM	PPO-RL	RNN	LSTM
0	−1.4779	−1.4519	−1.3989	−1.3849	−1.6119
50	−0.2058	−0.1278	−0.0858	−0.0538	−0.2908
100	0.4922	0.4802	0.6312	0.5822	0.2952
150	0.0306	0.0856	0.1216	−0.0564	0.1886
200	−0.0369	−0.0479	−0.0939	−0.1109	−0.1679
250	0.0531	0.0401	0.0911	−0.0069	0.0231
300	0.4922	0.4962	0.4122	0.3292	0.5732

and Figure 6, the comparative predictive outcomes of the EROA-SBiLSTM technique under SWT are provided. The results imply that the EROA-SBiLSTM method reaches closer predictive outcomes than other models. For example, with 50 min and actual value of −0.2058, the EROA-SBiLSTM technique has predicted a temperature of −0.1278. Next, with 150 min and actual value of 0.0306, the EROA-SBiLSTM method has predicted a temperature of 0.0856. Similarly, with 200 min and actual value of −0.0369, the EROA-SBiLSTM method has forecasted a temperature of −0.0479. Lastly, with 300 min and actual value of 0.4922, the EROA-SBiLSTM method has forecasted the temperature of 0.4962.

In

Table 4. RMSE analysis of EROA-SBiLSTM approach with recent algorithms.

RMSE
Methods	SYT	STT	SWT
LSTM	0.1919	0.3742	0.3114
RNN	0.1627	0.2862	0.1329
PPO-RL	0.2190	0.1244	0.1938
EROA-SBiLSTM	0.0596	0.1025	0.0931

and Figure 7, the EROA-SBiLSTM technique is compared with recent models in terms of RMSE. The results indicate that the PPO-RL model reaches worse outcomes with maximum RMSE values. Next, the LSTM and RNN models accomplish resulted in closer RMSE values. However, the EROA-SBiLSTM technique accomplishes enhanced performance with minimal RMSE values of 0.0596, 0.1025, and 0.0931 under SYT, STT, and SWT cases.

In

Table 5. MAE analysis of EROA-SBiLSTM method with recent algorithms.

MAE
Methods	SYT	STT	SWT
LSTM	0.1601	0.2682	0.2154
RNN	0.1627	0.2033	0.1038
PPO-RL	0.2165	0.1044	0.1708
EROA-SBiLSTM	0.0623	0.0509	0.0714

, and Figure 8, the EROA-SBiLSTM method is compared with recent techniques in terms of MAE. The outcomes indicate that the PPO-RL method obtains worse outcomes with maximum MAE values. Next, the LSTM and RNN approaches accomplish resulted in closer MAE values. However, the EROA-SBiLSTM method achieves superior performance with minimal MAE values of 0.0623, 0.0509, and 0.0714 under SYT, STT, and SWT cases.

In

Table 6. CT (Training) analysis of EROA-SBiLSTM method with recent algorithms.

Computational Time (Training)
Methods	SYT	STT	SWT
LSTM	269.19	249.80	234.04
RNN	723.50	781.71	707.88
PPO-RL	827.69	831.31	832.04
EROA-SBiLSTM	152.16	189.22	183.74

and Figure 9, the EROA-SBiLSTM method is compared with recent models in terms of CT (Training). The results indicate that the PPO-RL technique attains worse outcomes with maximum CT values. Next, the LSTM and RNN approaches accomplish resulted in closer CT values. However, the EROA-SBiLSTM method accomplishes enhanced performance with minimal CT values of 152.16, 189.22, and 183.74 under SYT, STT, and SWT cases.

In

Table 7. CT (Testing) analysis of EROA-SBiLSTM approach with recent algorithms.

Computational Time (Testing)
Methods	SYT	STT	SWT
LSTM	0.326	0.314	0.350
RNN	0.400	0.340	0.246
PPO-RL	0.572	0.710	1.067
EROA-SBiLSTM	0.213	0.175	0.180

and Figure 10, the EROA-SBiLSTM technique is compared with recent models in terms of CT (Testing). The outcomes indicate that the PPO-RL method attains worse outcomes with maximum CT values. Next, the LSTM and RNN approaches accomplish resulted in closer CT values. However, the EROA-SBiLSTM method accomplishes enhanced performance with minimal CT values of 0.213, 0.175, and 0.180 under SYT, STT, and SWT cases.

These results highlighted that the EROA-SBiLSTM technique exhibits effective predictive ability over the other models.

6. Conclusions

In this article, we have introduced a novel EROA-SBiLSTM algorithm designed to enhance the accuracy of temperature predictions for Permanent Magnet Synchronous Motor (PMSM) drives. Our presented EROA-SBiLSTM technique focuses on achieving precise temperature predictions through the integration of Deep Learning (DL) and hyperparameter tuning strategies. At its core, the EROA-SBiLSTM methodology incorporates a series of innovative steps. Initially, a comprehensive Pearson correlation coefficient analysis is applied to assess the relationships between various features. The utilization of p-values facilitates the identification of statistically significant correlations. This analytical phase serves as a crucial foundation for subsequent stages. The SBiLSTM model is then employed to forecast the temperature levels within PMSM drives. Leveraging the power of Sequential Bidirectional Long Short-Term Memory networks, our approach capitalizes on the sequence-based nature of the data to make accurate predictions. Furthermore, we introduce an EROA-based hyperparameter tuning process to dynamically optimize the parameters of the SBiLSTM model. This ensures that the model is configured optimally for the specific task of temperature prediction. To validate the efficacy of the proposed EROA-SBiLSTM technique, comprehensive experiments were conducted on a real-world electric motor temperature dataset sourced from Kaggle. The results of our study showcase the tangible improvements achieved by our EROA-SBiLSTM approach, underlining its potential for enhancing temperature prediction accuracy. Looking ahead, our future research endeavors will involve a more extensive evaluation of the EROA-SBiLSTM technique. Notably, the EROA-SBiLSTM method attained minimal RMSE and MAE values of 0.0596, 0.1025, and 0.0931 under SYT, STT, and SWT cases, demonstrating its precision and robustness across various scenarios. We plan to assess its performance on a larger and more diverse sample set, thereby providing deeper insights into its capabilities and uncovering its potential for broader applications within the realm of PMSMs. In conclusion, our EROA-SBiLSTM algorithm stands as a promising step forward in the pursuit of accurate temperature prediction for PMSM drives. By synergizing advanced DL techniques with meticulous hyperparameter tuning, we anticipate that our approach will contribute to further advancements in the field and open avenues for more sophisticated research and application.