1. Introduction
Due to increasingly severe energy shortages and environmental degradation, countries around the world have begun to develop more energy-efficient and environmentally friendly electric vehicles, which are gradually replacing traditional fuel vehicles and becoming the main trend of future automotive development [
1,
2]. Lithium-ion batteries are the core power source for electric vehicles and have become widely used in the electric vehicle sector because of their high energy density, low self-discharge rate and long cycle life [
3,
4]. However, the operating temperature of lithium-ion batteries significantly affects their performance and lifespan. The ideal operating temperature range is 25 °C to 40 °C, and the Δ
Tmax should be controlled within 5 °C [
5]. If the temperature exceeds the maximum safety threshold of lithium-ion batteries, it may result in thermal runaway, potentially triggering serious safety accidents such as fires and explosions [
6,
7]. Therefore, establishing an efficient battery thermal management system (BTMS) is extremely important for ensuring the safe and stable operation of the batteries.
Battery thermal management approaches primarily consist of air cooling [
8,
9], liquid cooling [
10,
11], phase change material (PCM) cooling [
12,
13], and heat pipe cooling [
14,
15]. In the past, air cooling was widely applied due to its advantages, such as simple structure and low maintenance cost [
16]. However, as the energy density of batteries rises, air cooling is unable to satisfy the heat dissipation requirements [
17]. Although PCM can effectively absorb the heat generated by batteries, it has not been applied due to its poor thermal conductivity [
18]. Heat pipes possess good thermal conductivity but generally need to be combined with other cooling approaches, which increases system complexity [
19], thus limiting their application in BTMS. In comparison, liquid cooling remains the mainstream form of thermal management for batteries because of its outstanding heat dissipation capability [
20].
Liquid cooling can be categorized into two types: direct contact cooling and indirect contact cooling [
21]. In direct contact cooling, the coolant makes contact with the battery for heat exchange, providing better temperature uniformity for the battery, which, however, requires high-stability dielectric coolant and a well-sealed cooling system [
22]. In comparison to direct contact cooling, indirect contact cooling employs the liquid cooling plates to establish a connection with the batteries, with thermal interface materials in between them to dissipate heat. The key design principle for the liquid cooling plate is to create a reasonable flow channel to ensure that the coolant is evenly distributed in the channels. Li et al. [
23] studied the impact of two layouts of liquid cooling plates with a single channel, multiple small channels, and an S-shaped channel on the thermal management of the battery module. The results indicated that placing liquid cooling plates with multiple small channels on both sides of the battery module achieved optimal cooling performance. Sheng et al. [
24] devised a liquid cooling plate with double serpentine channels, finding that the arrangement of the inlet and outlet significantly affected the temperature difference. Huang et al. [
25] designed a liquid cooling plate with streamlined channels, and the results showed that it can significantly reduce Δ
Tmax and Δ
P.
Besides the conventional liquid cooling plates mentioned above, researchers have shown interest in the design of liquid cooling plates inspired by bionic structures. Wang et al. [
26] designed a liquid cooling plate with a butterfly-shaped flow channel and compared its cooling performance with straight, serpentine, and leaf-shaped liquid cooling plates. The results showed that the butterfly-shaped liquid cooling plate demonstrated superior overall performance. Subsequently, further optimization of its structural parameters resulted in an optimal configuration, reducing the
Tmax to 32.72 °C and Δ
P to 25.7 Pa. Liu et al. [
27] proposed a bionic leaf-vein channel liquid cooling plate and studied the impact of various structural factors. It was found that the channel width and inlet velocity significantly affected the cooling performance. Fan et al. [
28] designed four types of liquid cooling plates with bionic fishbone channels. Compared to the Z-shaped liquid cooling plate, the bionic fishbone channel liquid cooling plate with a single inlet and dual outlets demonstrated better cooling performance.
In most cases, the above methods for optimizing battery thermal management parameters primarily rely on numerical simulations and tedious case experiments. The diverse and complex combinations of different parameters result in the significant consumption of time and computational resources during the analysis and optimization processes. As diverse surrogate models and artificial intelligence algorithms evolve, large amounts of data can be processed quickly, improving work efficiency without human intervention. As such, many researchers have optimized BTMS using surrogate models and optimization algorithms. Due to the nonlinear characteristics of complex BTMS, the BPNN is used as a surrogate model for multi-objective optimization because of its advantages in handling complex nonlinear mapping relationships and strong self-learning ability. Li et al. [
29] used an artificial neural network to establish the relationship between battery spacing, ambient pressure, and both the
Tmax and Δ
Tmax and then improved the temperature uniformity of the battery module through optimized design. Chen et al. [
30] showed that a deep learning neural network model provided more precise output predictions for the cooling performance of carbon/epoxy resin with a microchannel compared to the response surface model. Although progress has been made in performance prediction, the traditional BPNN has certain limitations as a surrogate model. The learning rate and the number of hidden nodes, which are critical hyperparameters affecting model training, are generally set based on personal experience and often require multiple human trials to optimize. Additionally, the initial weights and thresholds of the BPNN are generally initialized randomly, which would lead to the network getting stuck in local optima during training, thereby affecting the prediction performance of the model.
In response to the above issues, this paper introduces the PSO-BPNN surrogate model in combination with multi-objective genetic algorithm for the design optimization of a bionic liquid cooling plate constructed with a spider-web channel structure. The PSO algorithm can automatically optimize the number of hidden nodes, learning rate, initial weights, and thresholds without human intervention. This approach significantly enhances the prediction accuracy of the BPNN. Based on this, a novel spider-web liquid cooling plate is proposed, with the Tmax, ΔTmax, and ΔP selected as optimization objectives. The optimal Latin hypercube sampling (OLHS) method is employed for sampling, and a corresponding dataset of samples is constructed through computational fluid dynamics (CFD) simulations. Based on these data, the PSO-BPNN surrogate model is established. Subsequently, the NSGA-II algorithm is adopted to perform multi-objective optimization on the spider-web cooling plate. The entropy weight method is used to determine the weight of each objective, and the TOPSIS method is applied to rank the optimal solutions, thereby obtaining the optimal structural parameters for the cooling plate.
5. Conclusions
In this paper, a PSO-BPNN surrogate model is proposed to predict the cooling performance of the spider-web liquid cooling plate. The channel width, channel depth, and inlet velocity are selected as optimization variables, while the Tmax, ΔTmax, and ΔP are the optimization objectives. Based on the surrogate model, the NSGA-II algorithm is employed to optimize the variables and obtain the Pareto solution set. The optimal solution is selected by the TOPSIS with entropy weight method. The major conclusions are summarized as follows:
(1) Compared to conventional straight and serpentine flow channels, the spider-web flow channel demonstrates superior cooling performance and has a smaller ΔP than the other two channel types. The channel depth and inlet velocity are the primary factors influencing the cooling performance of the spider-web flow channel, while the channel angle has a relatively minor impact.
(2) Based on the sample point data obtained through OLHS, a PSO-BPNN surrogate model is established to predict the cooling performance of the spider-web liquid cooling plate. The results indicate that the PSO-BPNN model exhibits superior performance in prediction accuracy, as evidenced by lower MAE and RMSE values and a higher R2 value.
(3) By applying the entropy weight method, the weights for the Tmax, ΔTmax, and ΔP are 0.498, 0.225, and 0.277, respectively. Based on these weights and the TOPSIS decision-making method, a good balance between cooling performance and energy consumption is achieved when the channel width, channel depth, and inlet velocity are 6 mm, 3.4 mm, and 0.22 m·s−1, respectively. Compared to the initial structure, the Tmax and ΔTmax are reduced by 1.09 °C and 0.41 °C in the optimized structure, respectively, with an increase in ΔP by 21.24 Pa.