LU505849B1 - A multi-objective optimization method for the cathode multilayer catalyst in proton exchange membrane fuel cells (PEMFC) - Google Patents

Abstract

This invention relates to a multi-objective optimization method for the cathode multilayer catalyst in PEMFC (Proton Exchange Membrane Fuel Cell). It includes the following steps: Establishing a PEMFC model that utilizes a layered design for the cathode catalyst layer, determining evaluation metrics, which include performance-related indicators and oxygen distribution uniformity-related indicators, running the PEMFC model at different cathode catalyst layer structural parameters and operational voltages to gather a dataset, train a proxy model, utilizing the NSGA III algorithm based on optimization goals, the trained proxy model for multi-objective optimization, obtaining a set of Pareto optimal solutions, employing the TOPSIS method based on the Pareto optimal solutions to select corresponding strategies and acquire the optimal combination of structural parameters and operating voltage for the PEMFC cathode multilayer catalyst. This invention efficiently enhances the efficiency of multi-objective optimization and designs fuel cells that are high-performance, highly durable, cost-effective or a combination thereof.

Description

DESCRIPTION LU505849

A MULTI-OBJECTIVE OPTIMIZATION METHOD FOR THE CATHODE

MULTILAYER CATALYST IN PROTON EXCHANGE MEMBRANE FUEL CELLS

(PEMFC)

TECHNICAL FIELD

This invention pertains to the field of electrochemical fuel cells, specifically involving a multi-objective optimization method for the cathode multilayer catalyst in Proton

Exchange Membrane Fuel Cells (PEMFC).

BACKGROUND

Proton Exchange Membrane Fuel Cells (PEMFC) directly convert chemical energy into electrical energy and are widely used in transportation, stationary power generation, and portable devices due to their high energy conversion efficiency, low operational noise, and zero-pollution emissions. The Membrane Electrode Assembly (MEA) is a crucial component of PEMFC, comprising the gas diffusion layer (GDL), microporous layer (MPL), catalyst layer (CL), and proton exchange membrane (PEM). The catalyst layer provides the site for electrochemical reactions in PEMFC, and its structure and parameters directly impact the performance, durability, and cost of fuel cells. A stratified design in the cathode catalyst layer (CCL) can enhance fuel cell performance while reducing costs. However, this design may sacrifice the uniformity of oxygen concentration, consequently shortening the PEMFC's lifespan. Thus, optimization of the structural parameters of the cathode multilayer catalyst is necessary to design Proton

Exchange Membrane Fuel Cells with high performance, durability, and low cost.

Existing techniques focus primarily on optimizing the parameters of the catalyst layer for PEMFC performance without considering cost-related optimization and lifespan-related uniformity of oxygen distribution.

Particularly, there's a lack of consideration for optimizing the uniformity of oxygear505849 distribution directly involved in the electrochemical reactions at the platinum surface.

Furthermore, current optimization techniques for PEMFC parameters typically target 1 to 3 objectives without considering multi-objective optimization involving four or more objectives.

SUMMARY

The present invention aims to provide a multi-objective optimization method for

PEMFC cathode multilayer catalysts based on a data-driven proxy model. The technical solution of the invention includes the following steps:

Establishment of a PEMFC model, employing a stratified design for the cathode catalyst layer within the PEMFC model.

Determination of evaluation criteria, including performance-related indicators and oxygen distribution uniformity-related indicators.

Collection of datasets from the PEMFC model under different cathode catalyst layer structural parameters and operating voltages. The collected data is then utilized for training the proxy model, establishing a data-driven proxy model.

Multi-objective optimization is performed using the NSGA III algorithm based on optimization goals and the data-driven proxy model, resulting in a set of Pareto optimal solutions. The optimization goals are constructed according to the evaluation criteria.

Utilization of the TOPSIS method based on the Pareto optimal solutions to determine corresponding strategies for target goals, achieving the optimal combination of structural parameters and operating voltage for the PEMFC cathode multilayer catalyst.

Furthermore, the PEMFC cathode multilayer catalyst comprises an outer and inner layer, with the outer layer adjacent to MPL and the inner layer close to PEM, both layers having equal thickness.

Additionally, the input parameters of the proxy model include platinum loading for the inner and outer layers of the cathode catalyst, content of aggregates in the inner and outer layers of the cathode catalyst, platinum-to-carbon ratio, and operating voltage.

The output parameters of the proxy model are performance-related indicators and)505849 oxygen distribution uniformity-related indicators.

Performance-related indicators encompass power density (Pw) and local oxygen transport resistance (Rlocal), while oxygen distribution uniformity-related indicators include Variation Coefficient of Oxygen Concentration (VCO) and Variation Coefficient of

Oxygen Concentration at the Pt Surface (VCOP).

The optimization targets involved correspond to the set values of the evaluation criteria.

Further, the target strategies consist of Strategy 1 and Strategy 2. Strategy 1 aims to optimize PEMFC performance and extend its lifespan without considering costs, compared to the baseline scenario. Strategy 2, on the other hand, aims to reduce the usage of platinum-based catalysts and aggregates in the cathode catalyst layer while maintaining PEMFC performance and durability similar to the baseline scenario, ultimately reducing PEMFC costs.

The baseline scenario involves a cathode catalyst layer without a layered design, with a platinum loading of 0.2 mg/cm?, an aggregate content of 0.3, a platinum-to-carbon ratio of 0.45, operating at a voltage for maximum power density at 0.55V.

Regarding the training of the proxy model, the dataset is divided into training and testing sets, accounting for 70% and 30%, respectively. Each output parameter is trained and tested using both the BP and SVR algorithms. After optimizing the proxy model based on three predictive performance indicators—coefficient of determination (R?), mean absolute percentage error (MAPE), and root mean square error (RMSE)—the best-performing proxy model after optimization training is designated as the data-driven proxy model.

The technical benefits of this invention are significant, this multi-objective optimization method for the PEMFC cathode multilayer catalysts effectively enhances the efficiency of multi-objective optimization and facilitates the design of high-performance, durable, and cost-effective fuel cells. The introduction of four optimization indicators better captures the overall performance and oxygen distribution uniformity of the PEMFC.

In dealing with problems involving four or more target functions, compared td/505849

NSGA-II, the NSGA-IIl optimization algorithm offers improved diversity in providing solutions. The adopted TOPSIS multi-criteria decision-making method along with six decision indicators enables the ranking and selection of the optimal solutions and parameter combinations corresponding to various strategies based on cost, performance, and oxygen distribution uniformity.

BRIEF DESCRIPTION OF THE FIGURES

The figures illustrate various embodiments generally by way of example and not limitation, and together with the description and claims serve to explain embodiments of the invention. Where appropriate, the same reference numbers will be used throughout the figures to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the apparatus or method.

Figure 1 is a two-dimensional structural diagram of the PEMFC of the present invention;

Figure 2 is a schematic diagram of the optimization process of the present invention;

Figure 3 is a regression diagram of the data-driven agent model test set of the present invention;

Figure 4 is a Pareto solution diagram of the present invention;

Figure 5 is a comparison chart between the optimized parameters of the best solutions 1 and 2 of the present invention and the parameters of the benchmark case;

Figure 6 is a comparison chart between the optimization results of the best solutions 1 and 2 of the present invention and the benchmark case; wherein, 1. Anode gas diffusion layer; 2. Anode microporous layer, 3. Anode catalytic layer; 4. Proton exchange membrane; 5. Cathode catalytic layer; 6. Cathode microporous layer; 7. Cathode gas diffusion layer; 51. Cathode catalysis Inner layer; 52.

Outer layer of cathode catalytic layer.

DETAILED DESCRIPTION OF THE INVENTION LU505849

It should be noted that, as long as there is no conflict, the embodiments and features in the embodiments of this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and embodiments.

The present invention proposes a multi-objective optimization method for the

PEMFC cathode layered catalytic layer based on a data-driven agent model. The specific steps of the optimization method embodiment are as follows:

Step 1: Establish a PEMFC model with a two-phase, non-isothermal, coupled agglomerate sub-model as shown in Figure 1, and the model adopts a layered design of the cathode catalytic layer. As shown in Figure 1, the two-dimensional structure of

PEMFC consists of anode gas diffusion layer 1, anode microporous layer 2, anode catalytic layer 3, proton exchange membrane 4, cathode catalytic layer 5, cathode microporous layer 6, and cathode gas diffusion layer 7. The cathode catalytic layer is designed in layers along the thickness direction, and is composed of an inner cathode catalytic layer 51 and an outer cathode catalytic layer 52 of equal thickness. Parameter variables use Outer superscripts in the outer layer 52 of the cathode catalytic layer, and use Inner superscripts in the inner layer 51 of the cathode catalytic layer.

Step 2: Propose 4 evaluation indicators. Among them, two performance-related indicators are: power density Pw and local oxygen transmission resistance Rica. The other two indicators are indicators related to oxygen distribution uniformity, namely: oxygen concentration variation coefficient (VCO) and platinum surface oxygen concentration variation coefficient (VCOP). The specific indicators in the embodiment are defined as follows:

Power density Pw calculation formula:

P, = Ul wherein, U is the operating voltage; | is the current density;

Calculation formula of oxygen local transmission resistance Rica:

Riocal = Togo TOUT Ow = Ow (50 + po)

wherein, 1,44 is the radius of the agglomerate; 6, is the thickness of the ionomé#S05849 film; ôw is the thickness of the liquid water film; Do, ; and Do, i, are the diffusivities of oxygen in the ionomer film and the liquid water film respectively.

Oxygen concentration variation coefficient (VCO) calculation formula: 8 _ T5) 2 (CE. a cg) voo-Ÿ 2-1

Co, wherein, n is the number of grid nodes defined in the cathode catalytic layer; Com is the concentration of oxygen in the pores of node n in the cathode catalytic layer 5;

Con is the average oxygen concentration in the pores in the cathode catalytic layer 5.

Calculation formula of platinum surface oxygen concentration variation coefficient (VCOP):

Pt _ opt)’ > Css a C8) vcop=X #1 cht wherein, ch, is the oxygen concentration on the platinum surface at node n in the cathode catalytic layer 5; CE is the average oxygen concentration on the platinum surface in the cathode catalytic layer 5. The formula for calculating the oxygen concentration on the platinum surface is: cht = cg a No, Riocal

CE RT

CH =—2—

Ho,

Co, is the concentration of oxygen at the gas-ionomer interface; No, is the molar flux of oxygen entering the platinum surface from the pores of the cathode catalytic layer 5; Ris the gas constant; T is the temperature; Hy, is the oxygen Henry constant.

Step 3: Under different cathode catalytic layer 5 structural parameters and operating voltages, run the PEMFC model to obtain the data set, and use BP and SVR algorithms to train the agent model.

Specific implementation examples are as follows:

The input parameters of the agent model are 6, which are: the platinum loading of the inner layer 51 and the outer layer 52 of the cathode catalytic layer, the ionomer content of the inner layer 51 and the outer layer 52 of the cathode catalytic layer, the platinum-to-carbon ratio and the operating voltage. The output parameters of the proxy model are the 4 evaluation indicators proposed in step 2. The variation range of the input parameters is shown in Table 1.

Table 1 Agent model input parameter range

CC outer layer platinum

CCL inner layer platinum

Therefore, by combining the input parameters listed in Table 1 and their ranges, the amount of data used to train the surrogate model is 3 x 3 x 3 x 3 x 3 x 11 = 2673. As shown in Figure 2, the data set used to train the agent model comes from the PEMFC physical model established in step 1. The data set is divided into training set and test set, accounting for 70% and 30% respectively. In the agent model training process, BP and

SVR algorithms are used to train and test each output parameter respectively. Then the training and test results are compared through three prediction performance indicators: coefficient of determination R2, mean absolute percentage error (MAPE) and root mean square error (RMSE).

At the same time, compared with the training results of other common machiré/505849 learning algorithms, for each Select the most accurate algorithm for each output parameter.

The results of surrogate model training and testing are shown in Table 2.

Table 2 Comparison of prediction performance based on machine learning)505849 algorithms

Coefficient of determination of training set(R?)

Evaluation

SVR RBF LSTM index

Power 0.9909 | 0.9991 0.9723 0.9787 0.9953 density 0.9998 | 0.9988 0.9953 0.9962 0.9920

VCO 0.9873 0.9975 0.9179 0.9572 0.9919

VCOP 0.9495 | 0.9998 0.8584 0.9043 0.9714

Coefficient of determination of testing set(R?)

Power 0.9914 | 0.9988 0.9755 0.9746 0.9945 density 0.9998 | 0.9987 0.9957 0.9963 0.9902 veo |o.9857 0.9961 0.9213 0.9473 0.9890

VCOP 0.9437 | 0.9949 0.8652 0.8942 0.9630

Mean absolute percentage error (MAPE) on the testing set

Power 5.17 1.75 9.56 9.21 4.20 density

VCOP 18.63 746 |32.03 26.96 14.33

Root mean square error on the testing set(RMSE)

Power 0.0492 | 0.0071 0.0840 0.0807 0.0389 density

Roi | 1.9863 5.3352 9.7789 8.8913 13.7397

VCO |0.0081 0.0042 0.0197 0.0157 0.0066

VCOP 0.0199 | 0.0062 0.0334 0.0291 0.0173

The SVR algorithm is most accurate in predicting power density (Pw), VCO, and)505849

VCOP according to Table 2, while the BP algorithm performs better than other algorithms in predicting Ricai. Figure 3 illustrates the regression graphs of physical model simulation data versus predicted data for each evaluation indicator in the test dataset. The coefficient of determination, R?, represents the correlation between actual and predicted values. For the test set, the R? values for SVR algorithm predictions of Pw, VCO, and

VCOP are 0.9988, 0.9961, and 0.9949, respectively. The BP algorithm predicts Rlocal with an R? value of 0.9988. These results indicate that the established proxy model can accurately and rapidly predict the four evaluation indicators.

Step 4: Based on the optimization goals and the proxy model, utilize the NSGA-III algorithm for parameter optimization, obtaining a set of Pareto solutions and their corresponding parameter combinations. An Embodimentis provided below:

The parameter optimization method in the embodiment involves optimizing the six input parameters from the data-driven proxy model in step 3. The optimization objectives involve the four evaluation indicators mentioned in step 2. The objective functions for the

NSGA-III multi-objective optimization are as follows: min{ — Py, Roca, VCO,VCOP} 0.1 < möer < 0,3 01< loner < 03 st ; < Outer < 0.37 0.23 < Mer < 0.37 03 <U<08 0.35 < Rpyc < 0.55

Wherein, mare and mils are the platinum loadings of the outer layer 52 and the inner layer 51 of the cathode catalytic layer; eo" and e/12°" are the ionomer contents of the outer layer 52 and the inner layer 51 of the cathode catalytic layer; U is the operating voltage; Rpyc Is the platinum-to-carbon ratio.

The optimization of multiple objectives aims for minimizing the objective functions.

Therefore, selecting the negative value of power output serves as the objectiké/505849 function. A smaller value of local oxygen transport resistance (Rlocal) implies less resistance for oxygen to diffuse from the pores of the cathode catalyst layer (CCL) 5 through the ionomer film to the platinum surface, resulting in higher oxygen concentration on the platinum catalyst surface, faster electrochemical reaction rates, and higher current density. A smaller VCO value indicates more uniform oxygen distribution within the pores of the CCL 5. Uniform oxygen distribution in the pores of the CCL 5 is a prerequisite for uniform oxygen distribution on the platinum catalyst surface. A smaller VCOP value signifies a more uniform oxygen distribution on the platinum catalyst surface. Uniform oxygen concentration participating in electrochemical reactions leads to more uniform current density distribution and longer life for the PEMFC.

Additionally, as part of the objective function's input variables (6 optimization parameters), incorporating the optimization ranges as constraints for the upper and lower limits of the input variables serves as constraint conditions. The optimization ranges for the parameters align with the input parameter ranges defined in step 3, as outlined in

Table 1.

The optimization process, as depicted in Figure 2, uses the NSGA-III algorithm, initiating from population and reference point initialization. The settings include 10 reference points, a population of 200 individuals, a maximum iteration count of 100, crossover rate of 0.6, and mutation rate of 0.2. Employing the trained proxy model as the

NSGA-III algorithm's fitness evaluation function for initializing populations and generating offspring via crossover and mutation. The algorithm halts upon reaching the maximum iteration count, yielding a set of Pareto solutions, as illustrated in Figure 4.

Step 5: Propose a benchmark case and two optimization strategies, Strategy 1 and

Strategy 2, for comparing the optimization results. Strategy 1 aims to improve PEMFC performance and lifespan compared to the benchmark case, disregarding costs. Strategy 2 aims to reduce PEMFC costs while maintaining performance and durability, specifically decreasing the usage of platinum-based catalyst and ionomer in the cathode catalyst layer 5. The specific implementation is as follows:

The benchmark case presented does not involve the stratified design in the cathodé/505849 catalyst layer 5. The structural parameter values for the cathode catalyst layer 5 align with the mid-values within the ranges specified in Table 1. Specifically, the platinum loading in the cathode catalyst layer 5 is 0.2 mg/cm?, ionomer content is 0.3, and platinum-to-carbon ratio is 0.45. The operation is at a voltage corresponding to the maximum power density, which is 0.55V.

For Strategy 1, the specific objectives are to achieve higher power density (Pw), lower Rlocal, VCO, and VCOP compared to the benchmark case, without considering the usage of platinum-based catalyst and ionomer in the cathode catalyst layer 5. Strategy 2 aims to reduce the usage of platinum-based catalyst and ionomer in the cathode catalyst layer 5 compared to the benchmark case while maintaining Pw, Rlocal, VCO, and VCOP nearly constant.

Step 6: To address both optimization strategies, TOPSIS method is employed to select the corresponding optimal solutions, Optimal Solution 1 and Optimal Solution 2, for

Strategy 1 and Strategy 2, respectively. This leads to two sets of optimal combinations for the structural parameters and operational voltage in the PEMFC cathode stratified catalyst layer. The specific implementation is outlined below:

The TOPSIS method uses six decision criteria for sorting and selecting Pareto optimal solutions, which include two cost-related indicators (average usage of platinum loading and ionomer content in the cathode catalyst layer 5), two performance-related indicators (Pw and Rlocal), and two oxygen distribution quality indicators (VCO and

VCOP). During the TOPSIS sorting and selection process, different weights are assigned to these six decision criteria for Strategy 1 and Strategy 2. Strategy 1 allocates higher weights to performance and oxygen distribution quality indicators and lower weights to cost-related indicators, while Strategy 2 employs the opposite weight allocation. The weight assignments are detailed in Table 3. Table 3 also lists the top three solutions produced by TOPSIS for each strategy and their respective scores.

Table 3 Sorts and selects the optimal solutions of the two strategies through tHé/505849

TOPSIS method

Platin

Platinu Platin um lono | lono m um to loade | mer | mer Volta VCO

Score | loaded carbo Pw Riocal VCO d outer | inner ge P outer n inner | layer | layer layer ratio layer

Strategy 1 TOPSIS Ranking 0.6404 0.258 | 0.230 | 0.234 | 0.361 | 0.656 | 0.655 | 41.394 | 0.086 | 0.089 1 0.2384 4 4 0 2 3 3 8 8 6 6 0.6403 0.259 | 0.233 | 0.250 | 0.357 | 0.655 | 0.670 | 47.174 | 0.090 | 0.091 2 0.2257 0 2 9 9 8 6 2 6 6 2 0.6402 0.261 | 0.252 | 0.243 | 0.365 | 0.616 | 0.747 | 82.512 | 0.114 | 0.135 3 0.1550 2 7 8 4 3 2 7 7 5 6

Weight 0.040 0.080 / / 0.240 | 0.090 0.275 | 0.275 s

Strategy 2 TOPSIS Ranking 0.5662 0.225 | 0.259 | 0.324 | 0.364 | 0.653 | 0.601 | 143.49 | 0.076 | 0.114 1 0.1197 6 5 7 3 9 8 2 58 3 4 0.5662 0.233 | 0.240 | 0.335 | 0.358 | 0.686 | 0.531 | 142.88 | 0.060 | 0.085 2 0.1075 6 0 7 4 5 9 1 44 5 5 0.5635 0.124 | 0.257 | 0.339 | 0.367 | 0.731 | 0.319 | 239.01 | 0.025 | 0.037 3 0.1075 8 1 4 1 3 9 4 54 7 8

Weight 0.20 0.060 / / 0.220 | 0.150 0.185 | 0.185 s

In Figures 5 and 6, the optimization results for proposed Strategy 1 demonstrate that, compared to the benchmark case, Optimal Solution 1 leads to a 7.92% increase in power density (Pw), a 76.38% decrease in Rica, a 5.65% reduction in VCO, and a

16.18% decrease in VCOP. Simultaneously, the average usage of ionomer in thHéJ505849 cathode catalyst layer 5 decreased by 22.64% (with ionomer content in the outer layer 52 and inner layer 51 reduced by 23.33% and 21.94%, respectively). However, the average platinum loading in the cathode catalyst layer 5 increased by 24.19% (with platinum loading in the outer layer 52 and inner layer 51 increased by 19.21% and 29.18%, respectively). Thus, Optimal Solution 1 meets the requirements of Strategy 1, designing a PEMFC with better performance and stronger durability.

Similarly, in Figures 5 and 6, for proposed Strategy 2, the optimization results show that compared to the benchmark case, Optimal Solution 2 led to a 40.17% decrease in platinum loading in the outer layer 52, a 12.76% increase in platinum loading in the inner layer 51, resulting in a 13.71% reduction in average platinum loading. Additionally, the ionomer content decreased by 13.44% in the outer layer 52 while increasing by 8.09% in the inner layer 51, leading to a 2.67% reduction in average ionomer content. Moreover,

Optimal Solution 2 exhibited only a 1.87% decrease in power density (Pw), and reduced

Riocal by 18.50%, VCO by 18.61%, and VCOP by 8.54%. Therefore, Optimal Solution 2 not only meets the requirements of Strategy 2 but also further improves the uniform distribution of oxygen in the pores of the cathode catalyst layer 5 and on the platinum surface, enhancing the durability of the PEMFC.

It should be noted that the embodiments described above represent preferred implementations of the invention. The scope of the invention is not limited to these embodiments. Those skilled in the art may make equivalent substitutions or changes based on the technical solutions and inventive concepts disclosed in the invention within the scope of the claims of the invention.

Claims (8)

CLAIMS LU505849

1.A multi-objective optimization method for the cathode multilayer catalyst in PEMFC comprises the following steps: establishing a PEMFC model utilizing a layered design for the cathode catalyst layer; determining evaluation metrics including performance-related indicators and oxygen distribution uniformity-related indicators; running the PEMFC model at different cathode catalyst layer structural parameters and operational voltages, obtaining datasets, and training a data-driven proxy model; utilizing the NSGA Ill algorithm based on optimization goals and the data-driven proxy model to achieve multi-objective optimization, resulting in a set of Pareto optimal solutions constructed according to the evaluation metrics; employing the TOPSIS method based on the Pareto optimal solutions to determine corresponding strategies for target objectives, obtaining the optimal combination of structural parameters and operating voltage for the PEMFC cathode multilayer catalyst.

2. The multi-objective optimization method for the cathode multilayer catalyst in PEMFC as described in claim 1 further includes an outer layer and an inner layer within the cathode multilayer catalyst; the outer layer is close to the MPL (Membrane Electrode Assembly), while the inner layer is close to the PEM (Proton Exchange Membrane), and both layers have equal thicknesses.

3. The multi-objective optimization method for the cathode multilayer catalyst in PEMFC according to claim 1 involves a data-driven proxy model with input parameters including platinum loading in the inner and outer layers of the cathode catalyst, content of ionomers in the inner and outer layers of the cathode catalyst, platinum-to-carbon ratio, and operational voltage; the output parameters of the proxy model are performance-related indicators and oxygen distribution uniformity-related indicators.

4. The multi-objective optimization method for the cathode multilayer catalyst iJ505849 PEMFC according to claim 1 includes performance-related indicators such as power density (Pw) and local oxygen transport resistance (Rlocal), and oxygen distribution uniformity-related indicators such as oxygen concentration variation coefficient and platinum surface oxygen concentration variation coefficient.

5. The multi-objective optimization method for the cathode multilayer catalyst in PEMFC according to claim 1 involves optimization targets based on the predetermined values corresponding to the evaluation metrics.

6. According to claim 1, the multi-objective optimization method for the cathode multilayer catalyst in PEMFC involves two target strategies: strategy 1 and strategy 2; strategy 1 aims to optimize PEMFC performance and prolong lifespan compared to the baseline case without considering costs; strategy 2 aims to reduce the usage of platinum-based catalyst and ionomers in the cathode catalyst layer while maintaining PEMFC performance and durability almost unchanged compared to the baseline case, effectively reducing PEMFC costs.

7. According to claim 1, in the multi-objective optimization method for the cathode multilayer catalyst in PEMFC, the baseline case refers to a cathode catalyst layer without a layered design; the platinum loading in the cathode catalyst layer is 0.2 mg/cm2, ionomer content is 0.3, platinum-to-carbon ratio is 0.45, and it operates at the voltage of maximum power density, which is 0.55V.

8. According to claim 1, in the multi-objective optimization method for the cathode multilayer catalyst in PEMFC, the training of the proxy model specifically involves: dividing the dataset into training and testing sets, with 70% and 30% respectively, employing the BP algorithm and SVR algorithm for training and testing each output parameter, optimizing the proxy model based on three predictive performance indicators: coefficient of determination (R2), mean absolute percentage error (MAPE), and root mean square error (RMSE), selecting the best-performing data-driven proxy model aftét/[505849 optimizing training based on these predictive performance metrics.