Optimization of the Battery Pack Heat Dissipation Structure of a Battery-Type Loader

Abstract

The development of a battery-type loader is an important research direction in the field of industrial mining equipment. In the energy system, the battery will inevitably encounter the problem of heat dissipation when using high-power electricity. In this study, we took the power battery pack of a 3 m³ battery-type underground loader as the research object. The influence of single factors, such as the position of the air outlet of the battery pack, the size of the air outlet, the width of the separator, and the reverse plate, on the heat dissipation characteristics of the battery pack were studied. Then, a prediction model between the structural parameters and temperature was established using a radial basis function (RBF) neural network. This prediction model was then used as an adaptation evaluation model for global optimization through the multiobjective particle swarm optimization (PSO) algorithm, using which the optimal combination of structural parameters was obtained. The maximum temperature of the battery pack after optimization was reduced by 22%, compared to that before optimization, and the average temperature was reduced by 12.5%. Overall, the heat dissipation effect significantly improved. The optimization results indicate that the method proposed in this paper is feasible for use in optimizing battery heat dissipation systems in electric vehicles, thus providing a reference for research related to battery pack heat dissipation.

1. Introduction

In recent years, the development of battery-type loaders has become an important development direction in the mining equipment field. Due to the long working hours, the battery pack is often charged and discharged over a long period, generating a large amount of heat. If this heat is not dissipated appropriately, it can lead to a rapid increase in battery temperature, which can result in a serious misfire or explosion [1,2]; therefore, it is especially important to have a good thermal design for battery packs [3,4,5,6].

During the operation of the battery, reducing the battery’s maximum temperature to ensure the battery works in an appropriate temperature range and increasing the uniformity of temperature between battery modules are always a difficult challenge faced in battery thermal management. In the current power battery cooling situation, forced air cooling is still faced with the challenges of low heat transfer coefficient and poor internal temperature uniformity, which will affect battery life. To date, various scholars have carried out relevant research on battery pack heat dissipation: Arun K. Jaura [7] studied the effect of the air outlet shape on the cooling effect of a battery pack compared the cooling effect of radial and axial fans and finally proposed a better cooling solution for the battery. Park et al. [8] conducted a theoretical and numerical analysis of a specific design for an air-cooled battery system and showed that the required cooling performance could be achieved by using a conical manifold and pressure relief ventilation without changing the layout of the existing battery pack. Xu and He [9] have studied the cooling performance of different air-cooling methods using forced air cooling and proposed a new, double “U”-shaped air duct to improve thermal performance. Sabbah et al. [10] compared the effectiveness of phase-change materials in forced air cooling; Seham Shahid et al. [11] studied a passive technique for enhancing the heat dissipation of a simple battery pack by adding an air intake chamber, reducing the maximum temperature, and improving the temperature uniformity of a simple battery pack. Mohsen Mousavi [12] studied a battery pack containing 150 cylindrical Li-ion cells in a PVC housing, where the analysis showed that the heat dissipation capability could be improved by increasing the diameter of the tubes on the cells and keeping the air velocity within a certain range. Xinke Li et al. [13] analyzed and improved the cooling effect of battery cells by optimizing the airflow configuration and layout used in the U-shaped air-cooled battery thermal management system, and their analysis showed that cooling performance could be significantly improved when the number of both inlet and outlet manifolds was increased to three. Xie et al. [14] investigated the effects of three factors—namely, inlet air angle, outlet air angle, and inter-cell airflow passage width—on the cooling of lithium-ion battery packs. Lu et al. [15] developed a three-dimensional model of a staggered battery pack in order to study the thermal behavior of the pack, and their numerical results showed that packing more cells along the flow direction could better meet the battery power density and cooling requirements. Ravindra D. Jilte et al. [16] modified the conventional battery layout system to provide active and passive cooling for each cell of the battery module. Seham Shahid et al. [17] investigated a passive method for improving the temperature uniformity in a simple battery pack, where an air inlet chamber was added as a secondary air inlet to a battery pack with axial airflow, leading to an average maximum temperature reduction of about 4% and an improvement of about 39% in the temperature uniformity of the battery pack. Tao Wang et al. [18] quantitatively described the temperature distribution of the cells based on different module modes, fan positions, and cell spacing, and recommended the optimal cell spacing in the cell module structure based on the cooling effect of the cells. Naixing Yang et al. [19] discussed the effects of longitudinal and transverse spacing on the cooling performance of cylindrical battery packs and, based on the analysis results, showed that the average temperature rise in individual cells decreased with increasing longitudinal spacing, while increased transverse spacing led to an increase in cell temperature rise. Research by Manickam Minakshi et al. [20] shows that the hierarchical porous carbon extracted from MS husk can be used in symmetric/asymmetric capacitors, which has positive implications for the development of new carbon materials. Arun Mambazhasseri Divakaran et al. [21,22] have summarized the cathode and anode materials and provided a reasonable cell and material design. They present a novel design, preliminary development, and results for an inexpensive reusable, liquid-cooled, modular, hexagonal battery module that may be suitable for some mobile and stationary applications that have high charge and/or discharge rate requirements. Finally, Han et al.’s research in “Next Generation Battery Management System” shows that not only the cooling structure, but also the battery connection structure influences the charge and thermal imbalances of the battery pack [23].

Although researchers have analyzed heat dissipation in battery packs, there are still many factors to be further studied in the heat dissipation structure, and few studies have focused on the optimization of heat dissipation structure parameter combinations. In this study, we took a 3 m³ battery-type loader power battery pack as the research object and investigated the influence of various structural parameters, including the battery pack outlet location, outlet size, bulkhead width, and inverted flow plate angle, on the heat dissipation performance of the battery pack. However, there existed differences in the battery’s temperature performance under different structural parameters; therefore, the optimal combination of structural parameters was determined using an RBF neural network and the PSO algorithm. Based on the thermal performance of the battery pack under each structural parameter, the optimal combination of structural parameters was obtained, and the thermal effect of the optimized battery pack was improved significantly, demonstrating that the optimization method proposed in this paper is feasible and can be used as a reference for research related to the heat dissipation structure of battery packs.

2. Heat Dissipation Structure Design

Due to the limited installation space reserved for the battery pack in a downhole loader (located at position 1 in Figure 1 below), the volume of the battery pack is constrained in that it cannot be too large or too small without affecting heat dissipation. Considering the volume of this battery pack, a conventional serpentine airflow channel was used inside to ensure that it would have good ventilation conditions, and the battery pack structure was designed in advance. The battery pack heat dissipation structure and parameters are shown in Figure 1 and

Table 1. Battery parameters.

Parameters	Value
Battery Type	LiFePO4
Nominal voltage	3.2 V
Operating voltage range	2.5–3.65 V
Rated capacity	277 Ah
Single cell size	72 × 174 × 200 mm
Maximum sustained charge/discharge rate	1 C

below.

To simplify the simulation model, the effect of the thickness of the bulkhead inside the pack on the heat dissipation effect of the battery pack was ignored. Inside the battery pack, air enters from the first layer at the bottom and exits from the third layer at the top, which creates a serpentine flow of air inside the battery pack. To facilitate modeling and simulation analysis, the influences of the controller, wiring, and mounting structure inside the battery pack on battery heat dissipation were omitted.

3. Numerical Simulations and Experiments

3.1. Simulation Model and Boundary Conditions

3.1.1. Simulation Model

To carry out the simulation and analysis, division of the battery pack model into a grid was necessary. In hydrodynamics, the types of grids used can be divided into structured and unstructured grids. A structured grid is not suitable for complex structures, while an unstructured grid can automatically select the topology according to the structural characteristics of the model, which is more efficient. Therefore, we adopted an unstructured grid to partition the battery pack model.

The ICEM software was used to grid the battery pack structure. As the battery pack and the air inlet and outlet are rectangular structures, an unstructured grid dominated by a hexagonal grid was used for partitioning. At the end of the delineation, the number of grid sections reached 1,538,146; the results of the grid delineation are shown in Figure 2.

After griding, a quality check was performed on the divided grid. As shown in Figure 3 the determinant and aspect ratio of the grid were checked. The grid determinant check is shown in Figure 3a below.

Generally speaking, most solvers can accept a value of 0.3 or more for the grid determinant. As seen in the Figure 3a, the determinant was 0.36594 at minimum and 1 at maximum, such that the grid satisfied the determinant requirements.

The aspect ratio check for the grid is shown in Figure 3b, although different grid cells require different calculation methods; for solvers in general, the aspect ratio should be greater than 0.2, and an aspect ratio equal to 1 is best. As shown above Figure 3, the minimum aspect ratio was 0.371313 and the maximum was 0.99978, so the grid quality was generally better.

From the above analysis, the quality of the grid divided in this way was relatively good and was considered to meet the simulation requirements.

3.1.2. Simulation Boundary Condition Setting

After dividing the grid, the next step was to set the specific conditions for the simulation. For this purpose, the following assumptions were made.

(1) Heat exchange between the air outside the battery case and the battery shell was not considered (i.e., the battery shell is an adiabatic boundary);

(2) During the heating process of the battery, thermal parameter changes of the battery due to heating are not considered, and the battery will not be deformed by the heat;

(3) The cooling air is an incompressible fluid.

After the assumptions of the simulation model were made, the boundary conditions, solver, and turbulence model of the simulation were set.

• Boundary conditions

The boundary conditions mainly include the cell pack material parameters, air parameters, inlet boundary conditions, outlet boundary conditions, cell pack shell boundary conditions, air and cell wall boundary conditions, and the initial temperature.

The battery pack shell and separator are made of steel, and the thermal physical parameters of air were required. The air parameters and the thermal physical parameters of the battery are given in

Table 2. (a) Air parameters. (b) The thermal physical parameters of the battery.

(a) Air parameters.
Density	Specific Heat Capacity	Thermal Conductivity
1.225 $\mathrm{kg}/{\mathrm{m}}^3$	1006.43 J/(kg·K)	0.0242 W/(m·K)
(b) The thermal physical parameters of the battery.
Density	Specific Heat Capacity	Thermal Conductivity
		${\lambda }_x$	${\lambda }_y$	${\lambda }_z$
1760 $\mathrm{kg}/{\mathrm{m}}^3$	956J/(kg·K)	0.67 W/(m·K)	3.69 W/(m·K)	3.69 W/(m·K)

.

The entrance boundary condition was set as a velocity entrance boundary condition, and the exit boundary condition was set as a free exit boundary condition; the air and battery wall surface were set as a coupled wall surface; the initial temperature was set as 35 °C, as the battery-type downhole loader operates in a well where the ambient temperature range is 25–45 °C. The boundary conditions for the battery pack shell wall were set as follows:

(1) The wall of the housing was set as a slip-free wall (i.e., u = v = w = 0);

(2) To reduce the interference of structural changes of the wall of the housing on the subsequent heat dissipation optimization, the heat dissipation effect at the wall of the housing on the interior of the battery pack was not considered, and the wall was set as an adiabatic environment (i.e., the heat flow on the wall was zero);

(3) The normal gradient of the wall surface is zero.

2.

Solvers

The considered solver is considered a semi-implicit solver based on a system of coupled pressure equations (i.e., the SIMPLE algorithm).

3.2. Numerical Simulations and Experiments

3.2.1. Experimental Conditions

To verify the accuracy of the simulation and exclude the possible influence of data variability due to different experimental objects, five different combinations of structural parameters were arbitrarily selected for the experiments, and the experimental results were compared with the simulation results. The experimental conditions are shown in Figure 4 below.

To ensure sufficient air for cooling, the cooling fans were evenly arranged at the air inlet of the battery pack. Two wind speed meters were used to measure the wind speed at various times, and the average value was taken to ensure that the airflow speed through the entire air inlet was virtually the same. The cooling fans could change speed to meet the experimental requirements of different inlet wind speeds. To accurately and reliably obtain the changes in battery temperature, a temperature sensor was positioned at the upper and lower ends of the same side of each battery, are shown in Figure 4b, and the temperature value of the battery pack surface was collected using a thermometer.

3.2.2. Simulation Model Validation

As shown in Figure 5 below, the temperature trends of the simulation and experimental results were basically the same. The reason why the simulation value was slightly lower than the experimental value is that the heat generation rate of the battery increased during the actual test, while the heat generation rate in the simulation was constant throughout the charging and discharging process.

The simulated values for the developed model and the real values obtained experimentally can be quantified using the mean and maximum values of the relative errors [24,25,26]:

$$AARE(\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.)=\frac{1}{N}{\displaystyle \sum _{\mathrm{i}=1}^N\left|\frac{E_i-S_i}{E_i}\right|}\times 100\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.,$$

(1)

$${\epsilon }_{\max }=\max \left\{{\epsilon }_1,{\epsilon }_2,{\epsilon }_3\cdots {\epsilon }_i\right\},$$

(2)

where ${\epsilon }_i=\left|\frac{E_i-S_i}{E_i}\right|\times 100\raisebox{1ex}{$0$}\!\left/ \!\raisebox{-1ex}{$0$}\right.$, E denotes the experimental measurements, and S denotes the model simulation values.

As can be seen from Figure 5, the average relative error between the highest temperature simulation and experimental results was 4.6%, while the maximum relative error was 5.1%; the average relative error between the average temperature simulation and experimental results was 5.4%, while the maximum relative error was 5.9%; finally, the average value of the relative error between the simulation and experimental results was 7.3%, while the maximum value of the relative error was 9.2%.From the above error analysis, it can be seen that although there were some individual cases with large errors, the overall temperature simulation results for the battery pack with five sets of structural parameters were in good agreement with the experimental results and were within the acceptable range. Therefore, the simulation results obtained with the numerical model described in this paper can describe the temperature variation of the modeled battery pack well.

4. Results and Discussion of Single-Factor Analysis

4.1. Analysis of the Influence of the Outlet Position on the Heat Dissipation Characteristics of the Battery Pack

To ensure that the battery pack still has a serpentine air duct, the air outlet position was kept within the range of the third layer of the battery pack and moved. Keeping the other structures of the battery pack unchanged, four different air outlet location schemes were proposed as shown in Figure 6, where 1 denotes the air inlet and 2 denotes the air outlet.

We developed models and conducted simulations according to these air outlet schemes for the battery pack. The inlet wind speed was set to 1 m/s, 2 m/s, or 3 m/s, and other conditions were kept constant. In this way, we obtained battery pack temperature cloud diagrams for the four packs, as shown in Figure 7, Figure 8, Figure 9 and Figure 10:

As the air outlets of the four battery packs were all located at the third layer and other structural parameters remained unchanged, the temperature of the batteries in the first and second layers did not change considerably compared with that in the third layer. Therefore, we only compare the temperatures of the battery packs in the third layer.

As can be seen from Figure 7, Figure 8, Figure 9 and Figure 10, different air outlet locations led to different heat dissipation effects in the battery packs. Among the four outlet positions, regardless of whether the inlet wind speed was 1 m/s, 2 m/s, or 3 m/s, the heat dissipation effect of type I and II packs was the worst, and the highest temperatures were observed in the third layer of the battery pack in these models. The heat dissipation effect of the type III pack was better, but the highest temperature of the third layer at the outlet position of the type IV pack was the lowest; therefore, the heat dissipation effect of this type of battery pack was the best. To explore the specific reasons for the heat dissipation effect of the type Ⅳ battery pack, the airflow line inside the type Ⅳ battery pack was analyzed, as shown in Figure 11.

In the type IV battery pack, when the air flows to the third layer, it is forced to flow to the left and right sides of the third layer due to blockage of the wall behind, which greatly increases the turbulence effect of the air and leads to the best heat dissipation effect. As a result, the temperature of the batteries in the rear rows of the third layer was the lowest when compared to that in the other schemes. Therefore, the air outlet location in the following mainly adopts the type IV battery pack scheme.

However, for the battery pack as a whole, no matter which of the above-mentioned battery pack solutions was selected, only the temperature of the battery pack in the third layer changed significantly, and very high temperatures were still maintained in the first and second layers; even when the air velocity at the air inlet reached a maximum of 3 m/s, the maximum temperature in the battery pack still reached 64.7 °C. Obviously, the temperature does not meet the operating temperature requirements of the battery pack; therefore, further study of the influence of other structural parts of the battery pack on its thermal characteristics is needed.

4.2. Comprehensive Analysis of the Effect of Air Outlet Size and Bulkhead Width on the Heat Dissipation Characteristics of Battery Packs

Based on the best air outlet location being that of the Type IV battery pack, the comprehensive effects of the variation of air outlet size and bulkhead length on the heat dissipation characteristics of the battery pack were studied. Schematic diagrams of the partition gap and air outlet are shown in Figure 12.

As shown in the figure, with other conditions kept unchanged, the comprehensive effects of different air outlet sizes and bulkhead lengths on the thermal characteristics of the battery pack were further analyzed by varying the partition gap width x and air outlet length y to optimize the heat dissipation effect of the battery pack. The value of x was set as a series of equal differences with the first term being 10 mm and the difference being 10 mm, while the value of y is set as a series of equal differences with the first term being 100 mm and the difference being 100 mm. The wind speed of the air inlet was taken as the maximum value of 3 m/s, while other parameters and conditions (e.g., the location of the air inlet) were kept unchanged. The simulation results are shown in Figure 13 below. As the battery pack usually has the best heat dissipation effect at the air inlet, the lowest temperature of the battery pack was distributed near the air inlet. The lowest temperature was 35.4 °C and was not affected by the length of the air outlet or the width of the gap of the partition. Therefore, the lowest temperature of the battery pack is not discussed below: only the maximum temperature, average temperature, and temperature difference of the battery pack affected by the length of the air outlet and the width of the partition gap are discussed.

As shown in Figure 13a, for the maximum temperature of the battery pack, the fluctuation of the maximum temperature of the battery pack is more drastic with a change in the width of the partition gap and the length of the air outlet. From the overall curve, the width of the partition gap had a greater effect on the maximum temperature of the battery, compared to the length of the air outlet. When the width of the partition gap was 10 mm and the length of the air outlet was 800 mm, the maximum temperature of the battery pack was 58.1 °C, which was the lowest temperature at that time. At the same time, when the width of the partition gap was 100 mm and the length of the air outlet was 800 mm, the maximum temperature of the battery pack was 62.8 °C, which was close to the overall maximum temperature of the battery pack.

Considering the average temperature with the change in the width of the partition gap and the length of the air outlet, the fluctuation of the average temperature was not as drastic as that with the highest temperature and appeared to be gentler. Roughly speaking, compared with the length of the air outlet, the width of the partition gap had a greater effect on the average temperature of the battery. Aside from a few exceptions, the basic trend was that when the vent size was kept constant, the average temperature of the battery pack tended to increase gradually as the width of the partition gap increased.

As the minimum temperature was basically the same, the variation of the temperature difference of the battery pack and the variation of the maximum temperature of the battery pack was basically the same with the changes in the width of the partition gap and the length of the air outlet.

In summary, changes in the size of the outlet and the length of the partition have certain effects on the heat dissipation characteristics of the battery pack; however, from the overall curve, the width of the partition gap has a greater effect on the temperature compared to the length of the air outlet. The overall heat dissipation effect of the battery pack was best when the gap width of the partition was 10 mm but the maximum temperature and temperature difference of the battery pack was still high, and the ideal operating temperature and temperature difference range of the battery pack was not reached. Therefore, other methods must be considered to improve the heat dissipation performance of the battery pack. From the aforementioned analysis, it can be seen that the high temperature in each layer of the battery pack is mainly distributed in the rear rows, so we considered the use of cooling air deflectors to force the cooling air closer to the surface of the battery packs to strengthen the air turbulence situation in the rear rows of the battery packs. Therefore, the effect of the deflector on the heat dissipation characteristics of the battery packs was further studied.

4.3. Analysis of the Effect of Deflector on the Heat Dissipation Characteristics of Battery Packs

4.3.1. Analysis of the Effect of the Deflector Covering a Row of Battery Packs on the Heat Dissipation Characteristics of Battery Packs

In Figure 14a, the red part is the deflector, which is denoted by 1 in Figure 14b. According to the above analysis of the heat dissipation characteristics of the battery packs, other structural parameters were kept unchanged, the width of the baffle gap was taken as 10 mm, the length of the air outlet was taken as 800 mm, and the air was guided to flow downward through the angle of the deflector to strengthen the turbulent airflow effect.

First, we kept the width of the spacer at a value that covers the top of a row of cells; this was used as a basis to discuss the effect of the position and angle of the deflector on the heat dissipation characteristics of the battery pack. The deflectors were positioned on top of the first, second, third, fourth, fifth, sixth, or seventh rows of the battery pack, respectively, and the angle α of the deflectors was set to 4°, 5°, or 6°, to study the comprehensive effect of the position and angle of the deflectors on the heat dissipation effect of the battery pack. Through simulation analysis, we obtained the changes in the maximum temperature, average temperature, and temperature difference of the battery packs with respect to the change in position and angle of the deflectors, as shown in Figure 15 below.

As can be seen from Figure 15, the heat dissipation effect was better when the deflector was positioned above the fifth row of the battery pack and the angle of the baffle was 6° and when the baffle was above the fourth row of the battery pack and the angle of the baffle was 6°; however, the temperature of the battery pack was still higher than desired, so further research and optimization of the heat dissipation effect of the deflector is still necessary.

4.3.2. Analysis of the Effect of Deflectors Covering Two Rows of Battery Packs on the Heat Dissipation Characteristics of the Battery Packs

According to the results of the previous analysis, under the condition that other structures of the battery pack are kept constant, the width of the deflectors was lengthened such that they could cover two rows of battery packs, as shown in Figure 16 below.

The deflectors were placed above the first and second, second and third, third and fourth, fourth and fifth, and fifth and sixth rows in each layer of the battery pack, and the angles α were still set at 4°, 5°, or 6°, to study the comprehensive effect of the position and angle of the deflector on the heat dissipation effect of the battery pack. Other conditions were kept constant, and the obtained analysis results for the maximum temperature, average temperature, and temperature difference of the battery pack with respect to the position and angle of the deflector are shown in Figure 17.

Compared with the previous results, with an increase in the width of the deflector, the maximum temperature of the battery pack decreased by 2.2 °C, the average temperature of the battery pack decreased by 1.6 °C, and the temperature difference of the battery pack decreased by 2.3 °C. It can be seen that increasing the width of the deflector in this way can improve the heat dissipation effect of the battery pack. Therefore, the width of the deflector was further increased, and the change in the heat dissipation characteristics of the battery pack under the effect of further increases in the width of the deflector was studied.

4.3.3. Analysis of the Effect of the Deflector Covering Three Rows of Battery Packs on the Heat Dissipation Characteristics of Battery Packs

Based on the above analysis, the width of the deflector was further increased such that the deflector covered three rows of battery packs, as shown in Figure 18.

As shown in Figure 18, with the other structural parameters of the battery pack kept unchanged, the deflectors were placed above the 2-3-4, 3-4-5, 4-5-6, and 5-6-7 rows of the battery pack in each layer of the battery pack. Due to the width after this further increase, when the angle α was 5°, the deflectors had access to the upper surface of the battery pack, and the angle can be slightly increased due to the lengthening of the deflectors. Thus, this time, the value of the angle was set to 3.5° or 4° in the modeling and analysis, and we assessed how the positions of the deflectors of this width and their angles changed the heat dissipation effect of the battery pack. The analysis results are shown in Figure 19.

Compared with the analysis results in the previous section, it can be seen that with the further increase in the width of the deflector, the maximum temperature of the battery pack only decreased by 0.2 °C, while the average temperature of the battery pack remained largely unchanged and the temperature difference of the battery pack only decreased by 0.1 °C. Overall, the heat dissipation effect of the battery pack was only slightly enhanced, which indicates that even if the deflector is further widened, the heat dissipation effect of the battery pack will not be significantly optimized.

5. Combined Parameter Optimization

The above analysis was a single-factor analysis with other structural parameters fixed; however, we wished to obtain a set of optimal structural parameters which give the best heat dissipation effect. Therefore, based on the above analysis results, a prediction model between structural parameters and temperature was established through training an RBF neural network, which was used as an adaptive evaluation model for global optimization of the multi-objective PSO algorithm. This algorithm solves the optimal values in the sample space and seeks out the structural parameters that lead to extreme values of heat dissipation temperature along with a numerical simulation of the obtained optimal solution. The optimized thermal performance was compared with the thermal performance before the initial optimization.

5.1. Model Establishment

As RBF neural networks can approximate arbitrary nonlinear functions and can deal with the intrinsic unresolved regularities of systems, we used an RBF neural network to establish a prediction model between the structural parameters and battery pack temperature. An RBF neural network is a three-layer neural network which includes an input layer, an implicit layer, and an output layer; where the transformation from the input space to the implicit layer space is non-linear; and where the transformation from the implicit layer space to the output layer spatial transformation is linear [27], as detailed in Figure 20.

The output of an RBF neural network [23] can be given as:

$$y_j={\displaystyle \sum _{i=1}^h{w}_{ij}\exp \left(-\frac{1}{2{\sigma }^2}{‖x_p-c_i‖}^2\right)}\hspace{1em}j=1,2,\cdots ,n\hspace{1em}i=1,2,\cdots ,h,$$

(3)

where n is the number of samples or classifications of the output and w_ij is the weight between the ith implied layer node to the jth output layer node.

The neural network training sample was established according to the n × 10 principle and should be uniformly distributed within the range of the independent variables. Considering that the number of levels in this experiment was relatively large, a uniform experimental design table was adopted to establish the RBF neural network training sample. According to the previous single-factor study, when the heat dissipation performance of the battery pack is relatively good, the air outlet location of the battery pack is on both sides and the gap width of the partition is 10 mm. Therefore, the optimization variables to be studied in this paper were the remaining three factors; that is, air outlet width, deflector location, and deflector angle. According to previous research and the actual situation of this case, the optimization variables and their levels were determined, as shown in

Table 3. Design factors and their levels.

Variables	Parameters	Low Level (−)	High Level (+)
X1	air outlet width (mm)	100	900
X2	deflector location	2-3-4	5-6-7
X3	angle of deflector (°)	1.5°	4.5°

.

According to the n × 10 principle, at least 30 samples were required to train the neural network. Therefore, a uniform experimental design with three factors and 31 levels was selected; that is, the U₃₁ (31¹²) table was taken as the sample training schedule. The use table and uniform design table are shown in

Table 4. Use table of U₃₁ (31¹²).

S	Column No.
2	1	5
3	1	4	8
4	1	6	7	9
5	1	4	8	10	12
6	1	4	8	10	11	12
7	1	2	3	6	7	8	9

and

Table 5. Uniform design table of U₃₁ (31¹²).

No.	1	2	3	4	5	6	7	8	9	10	11	12
1	1	6	8	12	14	15	19	20	22	23	26	28
2	2	12	16	24	28	30	7	9	13	15	21	25
3	3	18	24	5	11	14	26	29	4	7	16	22
4	4	24	1	17	25	29	14	18	26	30	11	19
5	5	30	9	29	8	13	2	7	17	22	6	16
6	6	5	17	10	22	28	21	27	8	14	1	13
7	7	11	25	22	5	12	9	16	30	6	27	10
8	8	17	2	3	19	27	28	5	21	29	22	7
9	9	23	10	15	2	11	16	25	12	21	17	4
10	10	29	18	27	16	26	4	14	3	13	12	1
11	11	4	26	8	30	10	23	3	25	5	7	29
12	12	10	3	20	13	25	11	23	16	28	2	26
13	13	16	11	1	27	9	30	12	7	20	28	23
14	14	22	19	13	10	24	18	1	29	12	23	20
15	15	28	27	25	24	8	6	21	20	4	18	17
16	16	3	4	6	7	23	25	10	11	27	13	14
17	17	9	12	18	21	7	13	30	2	19	8	11
18	18	15	20	30	4	22	1	19	24	11	3	8
18	18	15	20	30	4	22	1	19	24	11	3	8
19	19	21	28	11	18	6	20	8	15	3	29	5
20	20	27	5	23	1	21	8	28	6	26	24	2
21	21	2	13	4	15	5	27	17	28	18	19	30
22	22	8	21	16	29	20	15	6	19	10	14	27
23	23	14	29	28	12	4	3	26	10	2	9	24
24	24	20	6	9	26	19	22	15	1	25	4	21
25	25	26	14	21	9	3	10	4	23	17	30	18
26	26	1	22	2	23	18	29	24	14	9	25	15
27	27	7	30	14	6	2	7	13	5	1	20	12
28	28	13	7	26	20	17	5	2	27	24	15	9
29	29	19	15	7	3	1	24	22	18	16	10	6
30	30	25	23	19	17	16	12	11	9	8	5	3
31	31	31	31	31	31	31	31	31	31	31	31	31

, respectively [28].

As we included three optimization variables in the study, it can be seen from the experimental table that columns 1, 4, and 8 were selected for the experimental arrangement, which was converted into the corresponding structural parameters while the other parameters were kept unchanged. Then, ANSYS numerical simulation was used for calculation. For this paper, the MATLAB software was used for the writing and running of the RBF neural network, where the newrb function was used to construct the RBF neural network topology, as shown in Equation (4):

net = newrb(P,T,GOAL,SPREAD,MN,DF),

(4)

where P is the input vector, T is the output vector, GOAL is the mean square error (which takes the value of 0.001), SPREAD is the RBF function distribution density (which takes the value of 2), MN is the maximum number of neurons, and DF is the display frequency of the training process. The data from the experimental arrangement were input into the main RBF neural network program in MATLAB for training. To verify the reliability of the neural network training, the rand function of MATLAB was used to randomly generate five sets of structural parameters, and the predicted values generated by the neural network were compared with the simulation calculation values, as shown in

Table 6. Comparison and error analysis between predicted and calculated values.

No.	Max. Temperature			Average Temperature			Temperature Difference
	Simulation Calculated Value (°C)	RBF Predicted Value (°C)	Error (%)	Simulation Calculated Value (°)	RBF Predicted Value (°C)	Error (%)	Simulation Calculated Value (°C)	RBF Predicted Value (°C)	Error (%)
1	59.0	60.93	3.2	48.2	46.7	3.1	24.0	25.3	5.4
2	59.6	58.10	2.5	48.0	47.1	1.8	25.5	25.8	1.2
3	59.7	60.49	1.3	47.8	46.5	2.7	24.3	25.4	4.5
4	59.4	60.31	1.5	47.7	48.8	2.3	24.8	23.9	3.6
5	59.3	60.61	2.2	48.1	49.0	1.9	23.9	24.6	2.9

.

The error analysis showed that the maximum error in the maximum temperature was 3.2%, the maximum error in the average temperature was 3.1%, and the maximum error in the temperature difference was 5.4%, all of which are within the scope of engineering permission.

5.2. Particle Swarm Algorithm Global Optimization Search

The particle swarm algorithm is an optimization algorithm that simulates the migration process of a group of birds when foraging, which has the advantages of simplicity, fast convergence, and few setup parameters compared to optimization algorithms such as genetic algorithms and simulated annealing algorithms. As such, it was found to be very suitable for solving the structural parameter optimization problem considered in this study. In the particle swarm algorithm, each solution to the problem of finding the best parameter combination is imagined as a bird, called a “particle”, and all particles search within a D-dimensional space [29], as shown in Figure 21.

This group of random particles (random solutions) finds the optimal solution through iteration. In each iteration, the position and velocity of the particles are updated, where the velocity update formula is [29]:

$$v_{id}^k=w{v}_{id}^{k-1}+c_1{r}_1\left(pbes{t}_{id}-x_{id}^{k-1}\right)+c_2{r}_2\left(gbes{t}_{id}-x_{id}^{k-1}\right).$$

(5)

The position update formula is:

$$x_{id}^k=x_{id}^{k-1}+v_{id}^{k-1}\mathrm{m},$$

(6)

where $v_{id}^k$ is the dth component of the flight velocity vector of particle i in the kth iteration, $x_{id}^k$ is the dth component of the position vector of particle i in the kth iteration, $c_1,c_2$ are acceleration constants to adjust the maximum learning step, $r_1,r_2$ are two random functions taking values in the range [0, 1] to increase the randomness of the search, and w is the inertia weight (non-negative), which regulates the search range within the solution space.

The basic workflow of the particle swarm algorithm is as follows: first, to initialize the particle swarm and the external reserve set, particle positions are randomly generated in the given variable space, the particle velocity is initialized, the particle adaptation value is evaluated, and non-inferior solutions are saved to the external reserve set. Then, we enter the loop phase, in which the adaptation values of the particles in the reserve set are evaluated and the global guide is selected. After that, the velocity and position of particles are updated according to the guide, and the adaptation value of the particles is evaluated. Then, according to the evaluation result, the individual particle guide and the external reserve set are updated. Finally, we determine whether the target or the maximum number of cycles has been reached; if not, the above loop steps are repeated until the loop requirement is satisfied. The algorithm flowchart is briefly shown in Figure 22 below.

5.3. Optimization Results and Comparative Analysis

The prediction model between the structural parameters and the temperature was used as an adaptive evaluation model. The basic parameters of the particle swarm algorithm used in this paper were set as follows: particle size N = 100, particle reserve set size nRep = 100, inertia weight w = 0.7298, learning factors c₁, c₂ = 1.49445, and the number of optimization-seeking iterations T = 500. The optimal structural parameters, obtained through the use of the optimization algorithm, are given in

Table 7. Optimal parameters.

Parameters	Value
Size of air outlet	800 mm
Width and position of deflector	Cover the top of 4-5-6 rows of battery packs
Angle of deflector	4°

.

The optimized nephogram of battery temperature was compared and analyzed with the nephogram of battery pack temperature of the initial preset battery pack, and the following results were obtained:

As shown in Figure 23, the maximum temperature of the preset battery pack reached 63 °C and the average temperature reached 50.1 °C. After heat dissipation structure optimization, the maximum temperature of the battery pack dropped to 49 °C, a reduction of 22%; meanwhile, the average temperature dropped to 43.8 °C, a reduction of 12.5%. Overall, the heat dissipation effect was greatly improved.

6. Conclusions

In this paper, the battery pack of a battery-type underground loader was taken as the research object, and the influences of single factors—such as the position and the size of the air outlet, the width of the baffle, and the angle of the deflector—on the heat dissipation characteristics of the battery pack were analyzed. To obtain more favorable structural parameters for heat dissipation, an RBF neural network and the PSO algorithm were used to optimize all of the analyzed structural parameters, and an optimal combination of structural parameters was obtained. When the air outlets are located on both sides of the battery pack, the width of the air outlet is 800 mm, the angle of the guide plate is 4°, and the width and position of the deflector cover the 4-5-6 rows of the battery pack, the maximum temperature of the battery pack was reduced by 22% and the average temperature was reduced by 12.5%, compared to the values before optimization, and the heat dissipation effect was significantly improved. Therefore, the heat dissipation optimization method mentioned in this work is feasible and can improve the heat dissipation performance of battery packs. As such, it has a greater engineering reference value for the study of battery heat dissipation systems as well as other complex thermal systems.