Multi-Objective Optimization for the Forming Quality of a CeO₂/Al6061 Alloy as an Aluminum–Air Battery Anode Manufactured via Selective Laser Melting

Abstract

To improve the discharge performance of aluminum–air batteries, CeO₂/Al6061 composites were prepared as an anode using selective laser melting (SLM). Response surface methodology (RSM) was employed, and the test results were linearly fitted. A prediction model for the forming quality of the composite anode was established, and the reliability of the model and the interaction between process parameters were explored based on variance analysis and significance testing. On this basis, with corrosion potential, self-corrosion rate, and discharge voltage as optimization objectives, the optimal solution set of the SLM forming CeO₂/Al6061 anode process parameter was solved through a genetic algorithm, and experimental verification was conducted. The results indicate that the optimal process range for the forming quality and various properties of composite materials is laser power of 265~285 W, scanning speed of 985~1025 mm/s, and scanning spacing of 0.116~0.140 mm. The optimized process parameters were selected for reliability testing, and the errors were all within 3.0%, verifying the accuracy and reliability of the model.

1. Introduction

Aluminum–air batteries have the main advantage of high energy density, with a theoretical energy density of up to 8100 Wh/kg, far higher than the current highest energy density lithium-ion battery (about 400 Wh/kg) [1,2,3]. This feature gives aluminum–air batteries a significant advantage in providing longer battery life. In addition, the main raw materials for aluminum–air batteries are aluminum, water, and air, which do not contain harmful substances such as heavy metals [4,5]. The waste generated after use can be recycled and reused, with minimal environmental pollution, making them highly environmentally friendly. At the same time, aluminum–air batteries do not cause safety accidents such as combustion and explosion during use and are highly safe [6,7]. Due to their low manufacturing costs, aluminum–air batteries also perform well in terms of economy. However, there are some challenges in the practical application of aluminum–air batteries, such as hydrogen evolution self-corrosion of the anode, low anode utilization rates, and voltage delay during the discharge process [8,9,10].

At present, most research focuses on using traditional methods, such as casting, forging, powder metallurgy, extrusion, and rolling [11,12,13,14]. On this basis, various new aluminum anode materials have been prepared, such as Al-0.5Mg-0.1Sn-0.05Ga-0.05In, Al-0.5Mg-0.1Sn-0.05Ga, and Al-Mg-Sn [15,16,17,18]. The above methods have drawbacks such as significant time consumption, low efficiency, and immature material preparation processes, and there is not much attention paid to commercial aluminum alloy materials with mature production processes. Based on this situation, Katsoufis et al. studied the use of industrial-grade commercial aluminum as the anode for aluminum–air batteries and found that under the same conditions, the corrosion of the Al6061 anode was much slower, resulting in a slower hydrogen production rate [19]. Wang et al. conducted research on using commercial aluminum alloys as anode materials for alkaline aluminum–air batteries and found that the Al6061 alloy has a low hydrogen evolution rate and excellent electrochemical performance; the anode efficiency is as high as 89.28%, the specific capacity is 2660.69 mA/(h·g), and the energy density is 2119.09 Wh/kg [5]. Katsoufis et al. constructed a thin-film aluminum–air battery using a commercial-grade Al6061 plate as the anode electrode. Tests showed that this type of battery exhibited good battery performance under environmental conditions of 20 °C temperature and approximately 40% humidity [20]. Zhu et al. constructed an aluminum–air battery system with Al6061 as the anode and conducted discharge tests. The results showed that the entire battery exhibited excellent discharge performance, and the Al6061 anode maintained high anode activity and a low corrosion rate [21].

In addition to using commercial aluminum alloy materials, the reinforcing phase is also used to improve the discharge performance of aluminum–air batteries. Bing et al. studied the effect of SiC on the electrochemical performance and discharge behavior of aluminum anodes and found that the composite anode had better corrosion resistance and discharge performance. This is because the addition of SiC significantly changes the dissolution form of the aluminum anode, reduces the corrosion rate of the anode, and improves the efficiency and capacity density of the composite anode [22]. Xie et al. used aluminum-based composite materials containing fluorinated graphene nanosheets as anodes for aluminum–air batteries and studied the discharge behavior of the composite anode. The results showed that under the same conditions, the anode utilization rate of the composite aluminum anode increased by 37.5% and the discharge efficiency increased by 95.3% [23]. Sovizi et al. prepared composite aluminum anodes using ZrO₂ as a reinforcing material and tested their discharge performance. The results showed that ZrO₂ could significantly improve the anode efficiency and discharge capacity of aluminum anodes at higher discharge current densities [24]. Li et al. studied aluminum/graphite composite anodes and found that aluminum–air batteries using this composite anode exhibited superior stable cycling and low voltage delay [25]. In addition, rare earth oxide CeO₂ has active chemical properties and extremely low electronegativity, which can purify impurities, refine grains, and improve microstructure during metallurgical melting processes [26,27]. Therefore, using CeO₂ as a reinforcing phase during preparation is expected to further improve the electrochemical activity and discharge capacity of aluminum anodes, but there are few reports on this aspect.

In addition to traditional anode preparation methods, selective laser melting (SLM) has gradually become a new way of preparing aluminum anodes due to its outstanding advantages such as its high processing flexibility, its ability to prepare multifunctional materials, and its integrated functional components [28]. Xia et al. prepared aluminum anodes using SLM and evaluated their learning and training results using the BP neural network architecture. The results showed that the maximum error rate of the aluminum anode forming quality prediction model was 8.23%. When the laser power is 344.1 W, the scanning speed is 1095.8 mm/s, and the scan spacing is 190.2 μm, the density of the sample reaches 95% and the self-corrosion rate and anode utilization rate reach 4.895 × 10⁻³ A/cm² and 62.2%, respectively [29]. Wang et al. investigated the influence of laser process parameters on the forming quality and discharge performance of aluminum–air battery anodes. They found that when the laser power is 325 W, the scanning speed is 1000 mm/s, the scanning spacing is 0.12 mm, and the powder coating thickness is 0.03 mm, high-quality aluminum anodes can be obtained. At this point, the maximum densification rate of the aluminum anode is 94.97% and the discharge is stable during the testing process [30]. In our previous research, we used SLM to prepare aluminum anodes and conducted performance tests, obtaining aluminum anodes with a low self-corrosion rate and good electrochemical and discharge performance, which laid a theoretical basis for this follow-up study [31].

Based on this, this work investigates the effects of laser process parameters on the self-corrosion rate and electrochemical and discharge performance of a CeO₂/Al6061 anode. On this basis, response surface methodology design was carried out, a forming quality prediction model was established, and variance analysis and significance test were conducted. Taking the above performance as the optimization objective, the optimal combination of laser process parameters was solved through a genetic algorithm.

2. Experiment

2.1. Materials and Equipment

Al6061 powder with an average particle size ranging from 15 to 53 μm was provided by Avimetal Powder Metallurgy Technology Co., Ltd., Beijing, China. CeO₂ raw material powder was provided by Bangrui New Material Technology Co., Ltd., Fuyang, China, with a product purity of ≥99.50%. 1.0 wt.% CeO₂/Al6061 mixed powder was prepared for the anode samples. Ball-milling treatment was used to improve the dispersion uniformity of the aluminum anode composite materials at the speed of 100 rpm for 1 h; the morphology of the treated powder was analyzed using SEM (su1510, Hitachi, Ltd., Tokyo, Japan), as shown in Figure 1. For the aluminum–air battery, a 1.0 wt.% CeO₂/Al6061 anode with a size of 10 mm × 10 mm × 10 mm was formed using SLM; the SLM device (YLM-120) was FS291M, Farsoon, China.

2.2. Experimental Methods

2.2.1. Response Surface Methodology (RSM) Design

This work mainly studies the influence of the process parameters on the corrosion potential, self-corrosion rate, and discharge voltage. Based on the existing process window and conclusions, this section sets the three single parameters of 280 W, 1000 mm/s, and 0.13 mm as the zero-level factor points, with laser power, scanning speed, and scan spacing as optimization independent variables. The specific factor levels of the RSM are shown in

Table 1. RSM factor-level table.

Factor		Level
	−1	0	1
Laser Power [P/W]	260	280	300
Scanning Speed [V/(mm/s)]	900	1000	1100
Scan Spacing [S/mm]	0.11	0.13	0.15

. It should be pointed out that in this work, laser power, scanning speed, and scan spacing are represented by symbols P, S, and V, respectively, and their corresponding units are W, mm/s, and mm, as shown in Table 1.

2.2.2. Self-Corrosion Rate

The weight loss method was applied to describe the self-corrosion rate. All polished samples were first immersed in 4 mol/L NaOH+8 g/L ZnO +2 g/L PAAS solution for 1 h at room temperature and then put in a mixed solution of 2% CrO₃ and 5% H₃PO₄ at 80 °C for 5 min to remove the corrosion product. Recording the weight of the samples before and after soaking as M₀ and M₁, the self-corrosion rate was calculated according to the following formula:

$$V_a={\displaystyle \frac{M_0-M_1}{S_a\cdot T}}$$

(1)

where M₀ and M₁ are the weight of the samples before and after soaking, mg; Sa is the surface area, cm²; T is the soaking time, h; and V_a is the self-corrosion rate, mg/(cm²·h).

2.2.3. Electrochemical Test

The test sample was sealed for insulation with epoxy resin except for one working surface with an area of 10 mm × 10 mm. Before testing, all samples were polished with sandpaper (grades ranging from 200 to 2000) and ultrasonically cleaned in ethanol solution for 5 min. The electrochemical tests were carried out using a CHI750E electrochemical workstation (Chenhua Instrument Co., Ltd., Shanghai, China). In the test, the Pt sheet was used as a counter electrode and Hg/HgO was used as a reference electrode, with the aluminum sample work electrode forming a three-electrode system. The test solution was 4 mol/L NaOH+8 g/L ZnO + 2 g/L PAAS.

2.2.4. Discharge Measurement

A home-made aluminum–air battery test device was used to measure discharge performance. The anode was an aluminum sample, while the cathode was the gas diffusion layer with a MnO₂ catalytic active layer with an effective area of 25 cm². The electrolyte was 4 mol/L NaOH + 8 g/L ZnO + 2 g/L PAAS solution and the discharge performance of the aluminum–air battery was investigated via constant current discharge testing at current densities of 10 mA/cm² using a CT3001AU Land battery (Blue-electric Electronics Co., Ltd., Wuhan, China) testing system for 1 h. After the tests, the sample was also immersed in a mixed solution of 2% CrO₃ and 5% H₃PO₄ at 80 °C for 5 min to remove the corrosion product. The discharge voltage was automatically exported using software. It should be pointed out that in order to prevent errors in the measurement process, all experiments were measured three times, and the average value was taken as the data in this work.

3. Results and Discussion

3.1. Regression Analysis of Forming Quality

Firstly, self-corrosion rate and electrochemical and discharge performance tests were conducted. After the performance tests, the data from each group were analyzed and processed using design expert software to obtain the experimental plan design and response target values, as shown in

Table 2. Experimental plan design and response target values.

Number	Laser Power [P/W]	Scanning Speed [V/(mm/s)]	Scan Spacing [S/mm]	Corrosion Potential [Ecorr/V]	Self-Corrosion Rate [Va/mg/(cm2·h)]	Discharge Voltage [E/V]
1	300	1000	0.15	−1.617	19.1	−1.474
2	280	1000	0.13	−1.635	13	−1.578
3	280	1000	0.13	−1.631	14.4	−1.565
4	280	1000	0.13	−1.64	13.5	−1.573
5	300	900	0.13	−1.616	23.1	−1.458
6	280	1000	0.13	−1.633	14.5	−1.567
7	280	900	0.15	−1.628	21.1	−1.494
8	260	1000	0.15	−1.624	19.5	−1.47
9	260	1100	0.13	−1.623	24.2	−1.447
10	300	1000	0.11	−1.618	18.8	−1.478
11	260	1000	0.11	−1.623	23.3	−1.453
12	260	900	0.13	−1.619	24.2	−1.463
13	280	900	0.11	−1.622	22.5	−1.491
14	300	1100	0.13	−1.614	23.8	−1.497
15	280	1100	0.15	−1.622	21.7	−1.502
16	280	1100	0.11	−1.631	22.4	−1.477
17	280	1000	0.13	−1.637	13.8	−1.57

.

We analyzed and processed the measurement data in Table 2 to determine the accurate relationship between each variable. The mathematical prediction models established for corrosion potential, self-corrosion rate, and discharge voltage are as follows:

$$\begin{array}{l}{E}_{corr}=1.77028-0.016477\cdot P-1.65500\times {10}^{-3}\cdot V-4.46500\cdot S+7.50000\times {10}^{-7}\cdot P\cdot V+1.25000\times {10}^{-3}\\ \cdot P\cdot S+1.87500\times {10}^{-3}\cdot V\cdot S+2.80625\times {10}^{-5}\cdot P^2+5.97500\times {10}^{-7}\cdot V^2+8.68750\cdot S^2\end{array}$$

$$\begin{array}{l}{\nu }_{\mathrm{a}}=1644.70937-6.22512\cdot P-1.20787V-2281.37500\cdot S+8.75000\times {10}^{-5}\cdot P\cdot V+2.56250P\cdot S\\ +0.087500\cdot V\cdot S+0.010294\cdot P^2+5.86750\times {10}^{-4}\cdot V^2+5543.75000\cdot S^2\end{array}$$

$$\begin{array}{l}E=14.94925-0.083914\cdot P-5.94875\times {10}^{-3}\cdot V-26.23875\cdot S-6.87500\times {10}^{-6}\cdot P\cdot V\\ +0.013125\cdot P\cdot S-2.75000\times {10}^{-3}\cdot V\cdot S+1.58250\times {10}^{-4}\cdot P^2+4.10500\times {10}^{-6}\cdot V^2+96.37500\cdot S^2\end{array}$$

$$260\le \mathrm{P}\le 280$$

$$900\le \mathrm{V}\le 1100$$

$$0.11\le \mathrm{S}\le 0.15$$

where E_corr is the corrosion potential, V; V_a is the self-corrosion rate, mg/(cm²·h); E is the discharge voltage, V; P is the laser power, W; V is the scanning speed, mm/s; and S is the scan spacing, mm.

The variance results and estimated regression coefficients of the regression analysis of corrosion potential, self-corrosion rate, and discharge voltage are shown in

Table 3. Regression analysis of variance for corrosion potential.

Source	Square Sum	Free Degree	Mean Square	F-Value	p-Value
Model	9.382 × 10−4	9	1.042	14.58	0.0009 (significant)
Laser Power [P/W]	7.200 × 10−5	1	7.200 × 10−5	10.07	0.0156
Scanning Speed [V/(mm/s)]	3.125 × 10−6	1	3.125 × 10−6	0.44	0.5297
Scan Spacing [S/mm]	1.125 × 10−6	1	1.125 × 10−6	0.16	0.7034
Laser Power and Scanning Speed [PV]	9.000 × 10−6	1	9.000 × 10−6	1.26	0.2989
Laser Power and Scan Spacing [PS]	1.000 × 10−6	1	1.000 × 10−6	0.14	0.7195
Scanning Speed and Scan Spacing [VS]	5.625 × 10−5	1	5.625 × 10−5	7.87	0.0263
Laser Power and Laser Power [P2]	5.305 × 10−4	1	5.305 × 10−4	74.20	<0.0001
Scanning Speed and Scanning Speed [V2]	1.503 × 10−4	1	1.503 × 10−4	21.02	0.0025
Scan Spacing and Scan Spacing [S2]	5.084 × 10−5	1	5.084 × 10−5	7.11	0.0322
Residual	5.005 × 10−5	7	7.150 × 10−6
Lack of Fit	1.250 × 10−6	3	4.167 × 10−7	0.034	0.9903 (not significant)
Pure Error	4.880 × 10−5	4	1.220 × 10−5
Cor Total	9.882 × 10−4	16

,

Table 4. Regression analysis of variance for self-corrosion rate.

Source	Square Sum	Free Degree	Mean Square	F-Value	p-Value
Model	273.90	9	30.43	65.21	<0.0001 (significant)
Laser Power [P/W]	5.12	1	5.12	10.97	0.0129
Scanning Speed [V/(mm/s)]	0.18	1	0.18	0.39	0.5543
Scan Spacing [S/mm]	3.92	1	3.92	8.40	0.0230
Laser Power and Scanning Speed [PV]	0.12	1	0.12	0.26	0.6242
Laser Power and Scan Spacing [PS]	4.20	1	4.20	9.00	0.0199
Scanning Speed and Scan Spacing [VS]	0.12	1	0.12	0.26	0.6242
Laser Power and Laser Power [P2]	71.38	1	71.38	152.95	<0.0001
Scanning Speed and Scanning Speed [V2]	144.96	1	144.96	310.59	<0.0001
Scan Spacing and Scan Spacing [S2]	20.70	1	20.70	44.36	0.0003
Residual	3.27	7	0.47
Lack of Fit	1.70	3	0.57	1.44	0.3566 (not significant)
Pure Error	1.57	4	0.39
Cor Total	277.16	16

and

Table 5. Regression analysis of variance for discharge voltage.

Source	Square Sum	Free Degree	Mean Square	F-Value	p-Value
Model	0.35	9	3.937 × 10−3	101.91	<0.0001 (significant)
Laser Power [P/W]	6.845 × 10−4	1	6.845 × 10−4	17.72	0.0040
Scanning Speed [V/(mm/s)]	3.612 × 10−5	1	3.612 × 10−5	0.94	0.3658
Scan Spacing [S/mm]	2.101 × 10−4	1	2.101 × 10−4	5.44	0.0525
Laser Power and Scanning Speed [PV]	7.562 × 10−4	1	7.562 × 10−4	19.57	0.0031
Laser Power and Scan Spacing [PS]	1.102 × 10−4	1	1.102 × 10−4	2.85	0.1350
Scanning Speed and Scan Spacing [VS]	1.210 × 10−4	1	1.210 × 10−4	3.13	0.1201
Laser Power and Laser Power [P2]	0.017	1	0.017	436.67	<0.0001
Scanning Speed and Scanning Speed [V2]	7.095 × 10−3	1	7.095 × 10−3	183.64	<0.0001
Scan Spacing and Scan Spacing [S2]	6.257 × 10−3	1	6.257 × 10−3	161.96	<0.0001
Residual	2.705 × 10−4	7	3.864 × 10−5
Lack of Fit	1.653 × 10−4	3	5.508 × 10−5	2.09	0.2437 (not significant)
Pure Error	1.052 × 10−4	4	2.630 × 10−5
Cor Total	0.036	16

.

Table 3, Table 4 and Table 5 are the regression analysis of the variance of different performances; the F-value and p-value are the results obtained from the significance test of the model and its coefficients in the analysis of variance. According to the analysis of the regression variance data in Table 3, Table 4 and Table 5, the F-values of the prediction models for corrosion potential, self-corrosion rate, and discharge voltage are 14.85, 65.21, and 101.91, respectively, all of which are relatively large values. At the same time, the p-values of the three models are all less than 0.05, indicating that the mathematical prediction model can significantly predict various performance data.

In the detection and analysis of the lack of fit, it can be seen that the p-values of the model mismatch term are 0.9903, 0.3566, and 0.2437, which are far greater than 0.01. The results of the test are not significant, that is, the predicted values of the regression model are basically consistent with the actual experimental test values, and the deviation is small. At the same time, it can be seen that the p-values of the laser power, the interaction term between laser power and scan spacing, and the quadratic term of the three parameters are all much smaller than 0.05, indicating that these factors have a significant impact on the discharge voltage of aluminum anode materials.

Based on the comparison of significance levels, the process parameters that affect the discharge voltage can be determined as follows: laser power > scan spacing > scanning speed. Similarly, through analysis, it can be concluded that the interaction between laser power, scanning spacing, and scanning speed, as well as the square terms of scanning speed and scanning spacing, have a significant impact on the corrosion potential. The interaction between laser power, scanning spacing, laser power, and scanning spacing, as well as the square terms of the three parameters, have a significant impact on the self-corrosion rate.

Based on the fitting results, combined with the distribution of data points around the regression line and residual analysis, a residual normal probability distribution map was obtained to more intuitively verify the reliability of the prediction models for corrosion potential, self-corrosion rate, and discharge voltage, as shown in Figure 2. It shows the normal probability distribution of residuals, the distribution of residuals and predicted values, and the distribution of predicted values and actual values. If the model has good adaptability, the normal probability distribution of the residuals should be on a straight line. From the figure, it can be seen that the distribution of residuals and predicted values is as close as possible to a straight line, so the response surface method has better adaptability in fitting the model. It can be seen that the vertical distance between each scatter point and the regression line is small and evenly distributed near the line, indicating that the fitting accuracy of the prediction model is high and can be used to characterize the mapping relationship between the process parameters and forming performance.

3.2. Analysis of the Interactive Influence

In the SLM forming process, in addition to a single laser process parameter, the interactive effects between different process parameters can also affect the forming quality of the CeO₂/Al6061 anode. In order to further investigate the interactive effects between three different laser process parameters, the data were processed and analyzed, as shown in Figure 3, Figure 4 and Figure 5.

The influence of the interaction of the three process parameters on the corrosion potential of the sample is shown in Figure 3. It can be seen that the response surface generally shows a trend of high around and low in the middle, indicating that excessive or insufficient laser power and scanning speed can have adverse effects on the corrosion potential of the sample, and there is an appropriate value for laser power and scanning speed that can maximize the corrosion potential of the sample. In addition, according to Table 3, the interaction term p-value between laser power and scanning speed is less than 0.01, indicating that the interaction between the two has a highly significant impact on the corrosion potential of the sample. From Figure 3b, it can be seen that the contour lines are relatively sparse, and the overall response surface is relatively flat, indicating that the interaction between laser power and scanning spacing does not have a significant effect on the corrosion potential of the sample. Figure 3c shows the same trend of change. Compared to Figure 3b,c, it can be observed that the contour lines in Figure 3a have a steeper slope and the 3D response surface is steeper, indicating that changes in laser power and scanning speed have a more significant impact on the experimental results. This is consistent with the F-value results in Table 3, indicating that changes in laser power and scanning speed have a greater effect on the corrosion potential prediction model of the sample.

The influence of the interaction of the three process parameters on the corrosion potential of the sample is shown in Figure 4. It can be seen that the overall response surface also shows a trend of being high around the circumference and low in the middle, indicating that there is an optimal value for laser power and scanning speed that can minimize the self-corrosion rate of the sample. It can be seen that the response surface shows a trend of first decreasing and then increasing from the upper left region to the lower right region from Figure 4a. However, from Figure 4b,c, it can be observed that the change in response surface is not significant, indicating that the interaction between laser power and scanning speed has a significant impact on the self-corrosion rate of the sample.

The influence of the interaction of the three process parameters on the corrosion potential of the sample is shown in Figure 5. It can be observed that the response surfaces in Figure 5a–c all show a trend of high around the circumference and low in the middle. Figure 5a,b are particularly evident, indicating that any process parameter that is too high or too low will affect the discharge voltage of the sample. From the analysis of the dense contour lines and the steeper response surface, it can be seen that the interaction between laser power and scanning speed has a greater impact on the discharge voltage of the sample, while the interaction between scanning speed and scan spacing has a smaller impact on the discharge voltage. This is consistent with the analysis results of corrosion potential and self-corrosion rate.

3.3. Optimization of Multi-Objective Forming Process Parameters

In this section, the objective functions are corrosion potential, self-corrosion rate, and discharge voltage. Laser power, scanning speed, and scanning spacing were selected as optimization variables. Based on the NSGA-II genetic algorithm, the gamultiobj function was called to explore its optimal solution and seek the process parameter combination that maximizes the performance of the CeO₂/Al6061 anode. The multi-objective programming is as follows:

$$X={\left(x_1,x_2,x_3\right)}^T$$

(2)

where $x_1$ is the laser power; $x_2$ is the scanning speed; and $x_3$ is the scan spacing.

The constraint range for the optimization interval of the set process parameters is: laser power: 260 W ≤ $x_1$ ≤ 280 W; scanning speed: 900 mm/s ≤ $x_2$ ≤ 1100 mm/s; and scan spacing: 0.11 mm ≤ $x_3$ ≤ 0.15 mm.

We converted the mathematical prediction models for corrosion potential, self-corrosion rate, and discharge voltage established through response surface methodology into multi-objective optimization functions, as shown below:

$$\begin{array}{ll}F(1)=& 1.77028-0.016477\cdot x(1)-1.65500\times {10}^{-3}\cdot x(2)-4.46500\cdot x(3)+7.50000\times {10}^{-7}\cdot x(1)\cdot x(2)+\\ & 1.25000\times {10}^{-3}\cdot x(1)\cdot x(3)+1.87500\times {10}^{-3}\cdot x(2)\cdot x(3)+2.80625\times {10}^{-5}\cdot {x(1)}^2\\ & +5.97500\times {10}^{-7}\cdot {x(2)}^2+8.68750\cdot {x(3)}^2\end{array}$$

$$\begin{array}{ll}F(2)=& 1644.70937-6.22512\cdot x(1)-1.20787\cdot x(2)-2281.37500\cdot x(3)+8.75000\times {10}^{-5}\cdot x(1)\cdot x(2)+\\ & 2.56250\cdot x(1)\cdot x(3)+0.087500\cdot x(2)\cdot x(3)+0.010294\cdot {x(1)}^2+5.86750\times {10}^{-4}\cdot {x(2)}^2\\ & +5543.75000\cdot {x(3)}^2\end{array}$$

$$\begin{array}{ll}F(3)=& 14.94925-0.083914\cdot x(1)-5.94875\times {10}^{-3}\cdot x(2)-26.23875\cdot x(3)-6.87500\times {10}^{-6}\cdot x(1)\cdot x(2)+\\ & 0.013125\cdot x(1)\cdot x(3)-2.75000\times {10}^{-3}\cdot x(2)\cdot x(3)+1.58250\times {10}^{-4}\cdot {x(1)}^2+4.10500\times {10}^{-6}\cdot \\ & {x(2)}^2+96.37500\cdot {x(3)}^2\end{array}$$

where F(1) is the corrosion potential, F(2) is the self-corrosion rate, and F(3) is the discharge voltage.

The calculation and solution of the multi-objective optimization of the CeO₂/Al6061 forming process parameters are completed by calling the gamultiobj function built-in in Matlab software. Prior to this, the M file of the objective function needs to be written and then the fitness function fitnessfcn needs to be called using the command line. The specific main program code is shown in Supplementary Figure S1. We set the optimal front-end individual coefficient to 0.3, the population size to 200, the number of iterations to 400, the termination iteration count to 400, and the fitness deviation to 1 × 10⁻¹⁰, as shown in Supplementary Table S1. Some of the codes and their meanings are shown in Supplementary Table S2; the details of the calculation codes, the principles, and an overview of the calculations can be found in Xia’s research [29].

Multiple sets of optimized solutions for CeO₂/Al6061 anode performance were obtained through Matlab software (Matlab 2020) calculations, and 30 sets of data were selected, as shown in

Table 6. Optimal process parameter solution set and response values for the SLM forming of the CeO₂/Al6061 anode.

Number	Laser Power [P/W]	Scanning Speed [V/(mm/s)]	Scan Spacing [S/mm]	Corrosion Potential [Ecorr/V]	Self-corrosion Rate [Va/(mg/(cm2·h)]	Discharge Voltage [E/V]
1	291.5023	989.2788	0.139287	−1.632673	13.81666	−1.57123
2	281.5944	998.3899	0.132807	−1.63362	13.784	−1.57083
3	277.2189	1009.925	0.128042	−1.63362	14.22881	−1.56678
4	288.2283	1010.055	0.141985	−1.63532	14.22954	−1.56678
5	277.5921	1005.743	0.129369	−1.6343	14.07631	−1.5683
6	289.9363	1006.301	0.129417	−1.63529	14.04879	−1.56871
7	277.441	1009.011	0.118084	−1.63532	14.19302	−1.56719
8	267.5184	1012.895	0.128606	−1.63351	14.13265	−1.56776
9	281.0063	995.212	0.131208	−1.63485	13.83003	−1.57118
10	281.9377	1004.124	0.116115	−1.63458	13.80748	−1.57115
11	278.3544	1023.219	0.119869	−1.63526	13.99577	−1.56934
12	277.5667	1009.466	0.128332	−1.63532	14.17154	−1.56749
13	267.2362	1010.146	0.125042	−1.63532	14.22993	−1.56679
14	278.1991	1008.395	0.130091	−1.63526	14.02032	−1.56914
15	269.3623	1003.072	0.136672	−1.63514	13.88364	−1.57046
16	278.2344	1005.55	0.129128	−1.63528	14.03226	−1.56895
17	277.2475	988.725	0.126705	−1.63532	14.17215	−1.56733
18	277.6509	1008.859	0.138496	−1.63531	14.14704	−1.56775
19	279.437	1013.918	0.131586	−1.63409	13.8631	−1.57056
20	280.1428	1005.363	0.129733	−1.63506	13.89503	−1.57066
21	278.1138	1015.675	0.131093	−1.63523	13.96792	−1.56936
22	277.5955	989.272	0.128699	−1.63431	14.14565	−1.56776
23	278.0763	1005.09	0.130619	−1.63525	13.98045	−1.56927
24	277.4882	1008.988	0.128115	−1.63362	14.18632	−1.56728
25	267.5423	1025.522	0.129356	−1.6353	14.08802	−1.56819
26	281.1806	1017.831	0.139083	−1.63477	13.79264	−1.57111
27	274.2685	1009.783	0.128044	−1.63532	14.2219	−1.56686
28	278.7324	1005.845	0.130231	−1.63422	13.95284	−1.56982
29	288.1044	1016.219	0.129869	−1.63527	14.01479	−1.56908
30	291.2523	1014.278	0.143287	−1.63419	13.81863	−1.57122

.

Observing the Pareto solution set, it can be observed that the originally set laser process parameter range has been greatly reduced. After optimization, the laser power P is between 265 and approximately 285 W, the scanning speed is between 985 and approximately 1025 mm/s, and the scan spacing is between 0.116 and approximately 0.140 mm. In addition, the performance prediction values provided in the solution set are also similar to the experimental data. The corrosion potential distribution is around −1.634 V, the self-corrosion rate is around 14.0 mg/(cm²·h), and the discharge voltage is around −1.568 V. All values indicate that the optimized process parameters provided by this algorithm theoretically have good electrochemical and discharge performance, but the rationality of the solution set needs to be verified through experiments.

To verify the rationality of the optimized variables and the accuracy of the response values, reliability verification was conducted on experimental schemes 5, 15, and 25, as shown in

Table 7. Error analysis of optimization value reliability testing.

No.	Response Target	Pareto Theory Predicted Values	Experimental Value	Error
5	Corrosion potential Ecorr/V	−1.634	−1.632	1.23%
15		−1.635	−1.632	1.84%
25		−1.635	−1.633	1.23%
5	Self-corrosion rate va/mg/(cm2·h)	14.1	14.5	2.76%
15		13.9	13.5	2.96%
25		14.1	14.3	1.40%
5	Discharge voltage E/V	−1.568	−1.565	1.92%
15		−1.570	−1.567	1.91%
25		−1.568	−1.569	0.64%

. The predicted response values were compared with the actual experimental results, and the error percentages are shown in Table 7. It can be seen that there is a certain degree of error between the actual value and the theoretical predicted value. The error of corrosion potential is 1.23~1.84%, the error of self-corrosion rate is 1.40~2.96%, and the error of discharge voltage is 0.64~1.92%. The analysis shows that the target value is within the allowable error range; therefore, the obtained prediction model and optimization model are reliable.

4. Conclusions

This work mainly focuses on multi-objective process optimization research on the forming quality of a CeO₂/Al6061 composite as an aluminum–air battery anode manufactured via SLM. The main conclusions are as follows.

(1)

In the construction of the regression prediction model for anode forming quality, the p-values of all three are less than 0.0001, far less than 0.05, indicating that the established model is reliable. The interaction between laser power and scanning speed has a significant impact on the forming quality, while the interaction between laser scanning speed and scan spacing has a small impact on the forming quality.

(2)

The originally set laser process parameter range was significantly reduced, resulting in the optimal process parameter range for composite forming quality and performance being laser power of 265–285 W, scanning speed of 985–1025 mm/s, and scanning spacing of 0.116–0.140 mm.

(3)

According to the optimization results, three sets of process parameter combinations were randomly selected for experimental verification, with errors all within 3.0%. The second-order mathematical prediction model and multi-objective optimization process parameter solution set regarding the multiple factors and responses of corrosion potential, self-corrosion rate, and discharge voltage are reliable.