A method for predicting ionomer volume fraction and gradient distribution in cathode catalyst layer

Abstract

The present invention discloses a method for predicting the volume fraction and gradient distribution of ionomers in a cathode catalyst layer, and relates to the technical field of proton exchange membrane fuel cells, and comprises the following steps: obtaining the maximum power density under different parameters based on an aggregate model; and training a neural network model to obtain the optimal volume fraction of ionomers in a first non-gradient catalyst layer; obtaining the optimal volume fraction of ionomers in a second non-gradient catalyst layer by dichotomy iteration; setting a gradient according to the optimal volume fraction of ionomers in the first non-gradient catalyst layer, and training the neural network model by ionomer gradient to obtain the first optimal ionomer gradient distribution; combining the correlation between the ionomer gradient and the average ionomer volume fraction with the optimal volume fraction of ionomers in the second non-gradient catalyst layer to obtain the second optimal ionomer gradient distribution. The present invention greatly improves the accuracy of predicting the optimal volume fraction of ionomers in a non-gradient catalyst layer and the optimal gradient distribution of a gradient catalyst layer.

Description

Technical Field

[0001] The invention relates to the technical field of proton exchange membrane fuel cells, and in particular to a method for predicting the volume fraction and gradient distribution of ionomers in a cathode catalyst layer. Background Art

[0002] Proton exchange membrane fuel cells (PEMFCs) have attracted much attention due to their excellent energy conversion efficiency and environmental protection characteristics. Despite their promising prospects, the high cost has hindered the widespread application of PEMFCs. The cathode catalyst layer (CL), a porous structure composed of platinum (Pt) nanoparticles and ionomers supported by a carbon carrier, is a key component in PEMFCs. Platinum and ionomers account for nearly half of the total cost of fuel cells and are expensive materials. A direct and effective way to reduce costs is to improve the output performance of PEMFCs. In the cathode CL, ionomers play the role of proton and oxygen conduction. The higher the ionomer content, the easier the proton conduction, but it also hinders the transmission of oxygen. At the same time, the reaction rates of different parts in the CL are uneven, and the demand for ionomers is also different. Therefore, in order to reasonably distribute the ionomers, it is necessary to design them in a gradient.

[0003] The agglomerate model is a relatively mature physical model of cathode CL. It assumes that CL is composed of agglomerates composed of multiple carbon carriers, Pt particles and ionomers. Compared with the traditional homogeneous model, it is more consistent with the actual microstructure of CL. In the agglomerate model, the volume fraction of ionomers mainly affects the thickness of the ionomer film wrapped outside the agglomerates. This key parameter determines the way in which ionomers affect the performance of cathode CL and even the entire PEMFC. The interaction between the complex structures of CL greatly affects the performance calculation of PEMFC, thus hindering the structural optimization of CL.

[0004] Data-driven models are usually used to predict the ionomer volume fraction and its gradient in PEMFC. Machine learning, as an efficient tool for building data-driven models, has been widely used in the PEMFC field, greatly reducing the computational cost of determining the optimal parameters. The establishment of a data-driven model dominated by machine learning requires a large amount of basic data as support. However, in practice, the data obtained through the aggregate model is limited. Therefore, after inputting it into the data-driven model, the model may over-fit the training data, resulting in overfitting, which will lead to a decrease in model performance and reduce the accuracy of the prediction of the ionomer volume fraction and its gradient. In addition, the data-driven model is a black box model with ambiguous physical meaning. Summary of the invention

[0005] The present invention provides a method for predicting the volume fraction and gradient distribution of ionomers in a cathode catalyst layer, which solves the problem of low accuracy of existing data-driven models when predicting the volume fraction and gradient of ionomers.

[0006] In a first aspect, the present invention provides a method for predicting the volume fraction and gradient distribution of ionomers in a cathode catalyst layer, comprising the following steps:

[0007] Different parameters of the PEMFC cathode catalyst layer are input into the aggregate model of the PEMFC cathode catalyst layer to obtain polarization curves of output voltage and current density under different parameters, and the corresponding maximum power density is obtained according to the polarization curves; wherein the different parameters include multiple structural parameters and relative humidity of intake air;

[0008] The neural network model is trained with different parameters as input and the corresponding maximum power density as output to obtain a first data-driven model, and the optimal ionomer volume fraction of the first gradient-free catalyst layer is obtained based on the first data-driven model;

[0009] Based on the agglomerate model, a rapid prediction formula for limiting current density is obtained, and the rapid prediction formula for limiting current density is combined with the performance index corresponding to the optimal ionomer volume fraction of the first gradient-free catalyst layer to obtain a dimensionless output voltage correlation formula. Based on the rapid prediction formula for limiting current density and the dimensionless output voltage correlation formula, the optimal ionomer volume fraction of the second gradient-free catalyst layer is obtained through binary division iteration;

[0010] Setting a gradient according to the optimal ionomer volume fraction of the first non-gradient catalyst layer to obtain an ionomer gradient; training a neural network model through the ionomer gradient to obtain a second data-driven model, and obtaining a first optimal ionomer gradient distribution based on the second data-driven model;

[0011] Based on the agglomerate model, a correlation between the ionomer gradient and the average ionomer volume fraction is established, and the correlation is combined with the optimal ionomer volume fraction of the second non-gradient catalyst layer to obtain the second optimal ionomer gradient distribution.

[0012] Preferably, the structural parameters include platinum loading, carbon loading, ionomer volume fraction, catalytic layer thickness and agglomerate radius.

[0013] Preferably, obtaining the optimal ionomer volume fraction of the first gradient-free catalyst layer based on the first data-driven model comprises the following steps:

[0014] A genetic algorithm was used to obtain multiple maximum power densities under different conditions of platinum loading, carbon loading, catalyst layer thickness and intake air relative humidity;

[0015] Based on the first data-driven model, multiple maximum power densities are sorted from high to low, and the ionomer volume fraction corresponding to the highest ranked maximum power density is used as the optimal ionomer volume fraction of the first gradient-free catalytic layer.

[0016] Preferably, the neural network model is trained by the ionomer gradient to obtain a second data-driven model, and the first optimal ionomer gradient distribution is obtained based on the second data-driven model, comprising the following steps:

[0017] The neural network model is trained by taking different platinum loading, carbon loading, catalyst layer thickness, intake relative humidity conditions and ionomer gradient as input and the maximum power density as output to obtain a second data-driven model;

[0018] Based on the second data-driven model, multiple maximum power densities under different platinum loading, carbon loading, catalyst layer thickness and intake air relative humidity conditions are obtained through genetic algorithm;

[0019] The multiple maximum power densities are sorted from high to low, and the ionomer gradient distribution corresponding to the highest-ranked maximum power density is taken as the first optimal ionomer gradient distribution.

[0020] Preferably, obtaining a rapid prediction formula for limiting current density based on an aggregate model comprises the following steps:

[0021] Based on the aggregate model, it is assumed that all the oxygen entering the aggregate participates in the electrochemical reaction, that is, the oxygen flux is equal to the oxygen consumption, as shown in the following formula:

[0022] .

[0023] In the formula, is the oxygen flux of a single agglomerate, O2 is oxygen, r is the radial distribution along a single agglomerate, is the specific surface area of ​​a single aggregate, agg is the aggregate, is the diffusion coefficient of oxygen in the ionomer m, and are the radius of the aggregate and the thickness of the ionomer film covering the aggregate, and are the oxygen concentration in the pores of the catalyst layer and the oxygen concentration reaching the Pt reaction site, is the oxygen partition coefficient based on Henry's law;

[0024] Assuming that the oxygen concentration at the reaction site is 0 when the limiting current density is reached, the limiting current density is shown as follows:

[0025] .

[0026] In the formula, I lim is the limiting current density, lim is the limit symbol, F is Faraday's constant, 4 means that 4 moles of electrons are required to consume 1 mole of oxygen. lCL is the thickness of the cathode catalyst layer;

[0027] Considering the adsorption and consumption of oxygen by the channel and gas diffusion layer GDL before entering the CL, the relationship between the oxygen concentration in the CL pores and the oxygen concentration at the gas inlet is obtained, as shown in the following formula:

[0028] .

[0029] In the formula, is the oxygen concentration at the inlet, is the resistance of the channel and GDL to oxygen, is the partial pressure of oxygen at the inlet, and T are the gas constant and temperature respectively;

[0030] The quick prediction formula of the limiting current density corresponding to the gradient-free CL is as follows:

[0031] .

[0032] In the formula, I lim,NG is the limiting current density of the non-gradient cathode catalyst layer;

[0033] The limiting current density corresponding to the gradient-free CL is integrated to obtain the rapid prediction formula of the limiting current density of the gradient CL:

[0034] .

[0035] In the formula, X is the dimensionless coordinate in the thickness direction of the catalyst layer, I lim,G is the limiting current density of the gradient cathode catalyst layer.

[0036] Preferably, the dimensionless output voltage correlation formula is as follows:

[0037] .

[0038] In the formula, η act is the activation loss, η ohm,total is the ohmic loss, η conc is the concentration loss, E ner is the Nernst voltage, a 1. b 1. c 1 and d 1 is a constant, δ agg is the thickness of the ionomer film coated on the aggregate,n agg is the number density of aggregates per unit volume CL.

[0039] Preferably, obtaining the optimal ionomer volume fraction of the second non-gradient catalyst layer by bisection iteration comprises the following steps:

[0040] Given the upper and lower limits of Pt loading, carbon loading, CL thickness, and inlet relative humidity, the initial ionomer volume fraction;

[0041] Obtain the average value of the upper and lower limits of the initial ionomer volume fraction, substitute the average value as the initial value into the limiting current density rapid prediction formula corresponding to the gradient-free CL, and obtain the limiting current density;

[0042] Three loss values ​​are obtained according to activation loss, ohmic loss and concentration difference loss, and the output voltage is obtained;

[0043] The output voltage is compared with the output voltage obtained by the dimensionless output voltage correlation formula. If it is greater than, the initial value is set as the lower limit and the average value is re-obtained. Otherwise, it is used as the upper limit and the average value is re-obtained. The new ionomer volume fraction is substituted into the cycle for calculation;

[0044] When the deviation of the ionomer volume fraction obtained from two iterations is less than the tolerance of 10 -5 The cycle ends when , and the corresponding ionomer volume fraction, i.e., the optimal ionomer volume fraction of the second gradient-free catalyst layer, is output.

[0045] Preferably, the correlation between the ionomer gradient and the average ionomer volume fraction is as follows:

[0046] .

[0047] In the formula, k ion is the ionomer gradient, ω 0 is the average ionomer volume fraction in CL, i.e., the optimal ionomer volume fraction in the second gradient-free catalyst layer, a 2. b 2 and c 2 is a constant;

[0048] Combining this correlation with the optimal ionomer volume fraction of the second non-gradient catalyst layer, the second optimal ionomer gradient distribution is obtained, as shown below:

[0049] .

[0050] In the formula, ω is the volume fraction of ionomer.

[0051] In a second aspect, the present invention further provides a system for predicting the volume fraction and gradient distribution of ionomers in a cathode catalyst layer, comprising:

[0052] An input module is used to input different parameters of the PEMFC cathode catalyst layer into the aggregate model of the PEMFC cathode catalyst layer, obtain polarization curves of output voltage and current density under different parameters, and obtain the corresponding maximum power density according to the polarization curves; wherein the different parameters include multiple structural parameters and relative humidity of intake air;

[0053] A first training module is used to train the neural network model with different parameters as input and the corresponding maximum power density as output to obtain a first data-driven model, and obtain the optimal ionomer volume fraction of the first gradient-free catalytic layer based on the first data-driven model;

[0054] An iterative module is used to obtain a fast prediction formula for limiting current density based on an aggregate model, combine the fast prediction formula for limiting current density with a performance index corresponding to an optimal ionomer volume fraction of the first gradient-free catalyst layer, obtain a dimensionless output voltage correlation formula, and obtain an optimal ionomer volume fraction of the second gradient-free catalyst layer through a binary search iteration based on the fast prediction formula for limiting current density and the dimensionless output voltage correlation formula;

[0055] The second training module is used to set the gradient according to the optimal ionomer volume fraction of the first gradient-free catalyst layer to obtain the ionomer gradient; train the neural network model through the ionomer gradient to obtain the second data-driven model, and obtain the first optimal ionomer gradient distribution based on the second data-driven model;

[0056] The output module is used to establish a correlation between the ionomer gradient and the average ionomer volume fraction based on the agglomerate model, and combine the correlation with the optimal ionomer volume fraction of the second gradient-free catalyst layer to obtain a second optimal ionomer gradient distribution.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] The present invention first obtains different parameters and corresponding maximum power density through the agglomerate model of the cathode catalyst layer of PEMFC, and then inputs them into the neural network model for training to obtain a first data-driven model, and obtains the optimal ionomer volume fraction of the first non-gradient catalyst layer based on the first data-driven model, that is, the optimal ionomer volume fraction under the data-driven model. The present invention combines the optimal ionomer volume fraction under the data-driven model with the limiting current density rapid prediction formula derived based on the agglomerate model, combines the physical model and the data-driven model, and then obtains the optimal ionomer volume fraction of the second non-gradient catalyst layer through dichotomy iteration, that is, the optimal ionomer volume fraction under the physical model. The deviation of the optimal ionomer volume fractions of different model structures obtained by the present invention is very small, which greatly improves the accuracy of the prediction of the optimal ionomer volume fraction of the non-gradient catalyst layer.

[0059] According to the optimal ionomer volume fraction of the first non-gradient catalyst layer, the gradient is set, and the neural network model is trained by the ionomer gradient to obtain the second data-driven model. Based on the second data-driven model, the first optimal ionomer gradient distribution is obtained, that is, the optimal ionomer gradient distribution under the data-driven model. The present invention combines the correlation between the ionomer gradient and the average ionomer volume fraction established based on the agglomerate model with the optimal ionomer volume fraction of the second non-gradient catalyst layer to obtain the second optimal ionomer gradient distribution. The deviation of the optimal gradient distribution of the gradient catalyst layer under different structures obtained by the present invention is very small. The accuracy of the prediction of the optimal gradient distribution of the gradient catalyst layer is greatly improved. The present invention also derives a specific limiting current density rapid prediction formula, a dimensionless output voltage correlation formula, and a correlation formula between the ionomer gradient and the average ionomer volume fraction, and clarifies multiple physical meanings of the PEMFC structure. The present invention can quickly predict the ionomer content and gradient distribution with the best performance in the PEMFC cathode non-gradient catalyst layer and the gradient catalyst layer under different structural parameters and inlet relative humidity, and has good versatility and accuracy compared with the traditional data-driven model. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0061] Figure 1 It is a flow chart of a method for predicting the volume fraction and gradient distribution of ionomer in a cathode catalyst layer of the present invention;

[0062] Figure 2The flow chart of the binary method of the present invention for predicting the optimal ionomer volume fraction in CL;

[0063] Figure 3 : are polarization curves under different CL after current density normalization of an embodiment of the present invention;

[0064] in, Figure 3 (a): Polarization curve under non-gradient CL, Figure 3 (b): Polarization curve under gradient CL;

[0065] Figure 4 This is a diagram showing the limit current prediction deviation results under different CLs according to an embodiment of the present invention;

[0066] in, Figure 4 (a): Limiting current prediction deviation result diagram under non-gradient CL, Figure 4 (b): Limiting current prediction deviation result diagram under gradient CL;

[0067] Figure 5 is a dimensionless output voltage and dimensionless current density deviation diagram corresponding to the maximum power density of an embodiment of the present invention;

[0068] in, Figure 5 (a): Dimensionless output voltage deviation graph, Figure 5 (b): dimensionless current density deviation diagram;

[0069] Figure 6 is a predicted deviation diagram of the optimal ionomer volume fraction and the optimal gradient distribution in the cathode CL of an embodiment of the present invention;

[0070] in, Figure 6 (a): Optimal ionomer volume fraction prediction deviation diagram, Figure 6 (b): Best gradient distribution prediction prediction deviation map;

[0071] Figure 7 This is a diagram of the optimal ionomer distribution gradient deviation in the gradient CL of an embodiment of the present invention. DETAILED DESCRIPTION

[0072] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0073] The present invention provides a method for predicting the volume fraction and gradient distribution of ionomers in the cathode catalyst layer. By combining the physical model with the data-driven model, the method can save costs while ensuring high accuracy, and is more conducive to the design of the ionomer content and distribution in the cathode catalyst layer of PEMFC in engineering applications. Figure 1 , specifically including the following steps:

[0074] The first step is to input different parameters of the PEMFC cathode catalyst layer into the aggregate model of the PEMFC cathode catalyst layer, obtain the polarization curves of the output voltage and current density under different parameters, and obtain the corresponding maximum power density according to the polarization curves.

[0075] Firstly, the aggregate model of the cathode catalyst layer of PEMFC is derived and solved to obtain the polarization curves of output voltage and corresponding current density.

[0076] Different structural parameters and relative humidity of inlet air were input into the agglomerate model of the cathode catalyst layer of PEMFC, and the overpotential control equation of the agglomerate model was solved to obtain the polarization curves under different parameters. Among them, the structural parameters include platinum loading, carbon loading, ionomer volume fraction, catalyst layer thickness and agglomerate radius.

[0077] The power density is obtained by multiplying the voltage and current density of the polarization curve. The power density varies with the current density, and the maximum point is the maximum power density. The original data set of different parameters of the non-gradient cathode catalyst layer and the corresponding maximum power density is established.

[0078] In this embodiment, the radius of the agglomerate is compared with the existing experiments, and it is well consistent with the experimental data when its size is 300 nm, so its value is fixed to 300 nm in subsequent calculations, and the remaining parameters are selected within a reasonable range.

[0079] Step 2: Input the original data set obtained in the previous step into the neural network model, iteratively train the neural network model, and obtain a stable and reliable neural network model, namely the first data-driven model. The input parameters of the neural network model are various structural parameters and intake relative humidity, and the output parameter is the maximum power density, that is, the neural network model establishes a simple correspondence between various structural parameters and intake relative humidity and maximum power density. The output parameters can be obtained through the input parameters without solving the complex agglomerate model control equation, which simplifies the calculation.

[0080] The optimal ionomer volume fraction that can achieve the maximum power density under different platinum loadings, carbon loadings, catalyst layer thicknesses and intake relative humidity conditions was obtained through genetic algorithm optimization. Within a reasonable parameter range, other parameters are monotonically related to the maximum power density, and only the effect of the ionomer volume fraction on the performance is not monotonically related. The previously established neural network model was optimized through a genetic algorithm to obtain the ionomer volume fraction that can achieve the maximum power density under different platinum loadings, carbon loadings, catalyst layer thicknesses and intake relative humidity conditions, and the optimal ionomer volume fraction of the first non-gradient catalyst layer was obtained, that is, the optimal ionomer volume fraction of the non-gradient catalyst layer under the data-driven model.

[0081] Step 3: The fast prediction formula for limiting current density is derived through the agglomerate model, and combined with the structural parameters corresponding to the optimal ionomer volume fraction obtained in the previous step, the dimensionless output voltage correlation formula is obtained at this time, and the optimal ionomer volume fraction of the gradient-free catalyst layer is obtained through bisection iterative approximation.

[0082] The limiting current prediction method is derived as follows:

[0083] Based on the aggregate model, assuming that all the oxygen entering the aggregate participates in the electrochemical reaction, that is, the oxygen flux is equal to the oxygen consumption, we can get:

[0084] (1).

[0085] in, is the oxygen flux of a single aggregate, is the specific surface area of ​​a single aggregate, is the diffusion coefficient of oxygen in the ionomer and is related to the water content of the membrane, that is, the relative humidity of the inlet air. and are the radius of the aggregate and the thickness of the ionomer film covering the outer surface of the aggregate, and are the oxygen concentration in the pores of the catalyst layer and the oxygen concentration reaching the Pt reaction site, Divide by is the oxygen concentration on the outer surface of the ionomer membrane obtained based on Henry's law.

[0086] Assuming that the oxygen concentration at the reaction site is 0 when the limiting current density is reached, the limiting current density can be expressed as:

[0087] (2).

[0088] In the formula, F is Faraday's constant, 4 means that 4 moles of electrons are required to consume 1 mole of oxygen. l CL is the thickness of the cathode catalyst layer.

[0089] In addition, considering that oxygen is adsorbed and consumed by the channel and gas diffusion layer GDL before entering the CL, the relationship between the oxygen concentration in the CL pores and the oxygen concentration at the gas inlet can be obtained:

[0090] (3).

[0091] In the formula, is the oxygen concentration at the inlet, is the resistance of the channel and GDL to oxygen, is the partial pressure of oxygen at the inlet, and T are the gas constant and temperature respectively. So far, the limiting current density calculation formula corresponding to the gradient-free CL can be obtained:

[0092] (4).

[0093] For gradient CL, the ionomer content changes in the CL thickness direction, and this change dominates the change in the limiting current density. Therefore, the limiting current density of the gradient CL can be obtained by integrating equation (4):

[0094] (5).

[0095] In the formula, X is the dimensionless coordinate in the thickness direction of the catalyst layer.

[0096] Evolution of the optimal ionomer volume fraction prediction method:

[0097] By observing the polarization curve after normalizing the current density, it is found that the polarization curves of the output voltage and dimensionless current density at different inlet relative humidity are almost coincident, and the difference between the power density curves is only reflected by the difference in current density. Based on the aggregate model, the Pt loading ( m Pt )、Carbon loading( m C )、CL thickness( l CL ) and ionomer volume fraction ( ω ) is mainly reflected in two hypothetical structural parameters after evolution: the thickness of the ionomer film coated on the aggregate body ( δ agg ) and the number density of aggregates per unit volume CL ( n agg ), which affects the limiting current density. Therefore, the dimensionless output voltage correlation (6) and dimensionless current density correlation (7) for the optimal ionomer volume fraction corresponding to the maximum power density can be established based on these two structural parameters. The optimal ionomer volume fraction is obtained by data-driven model optimization. The two dimensionless correlations can be given as follows:

[0098] (6).

[0099] (7).

[0100] In the formula, E ner is the Nernst voltage, a constant other than 1 a 1. b 1. c 1 and d 1 can be obtained by fitting the actual data. I p,m is the current corresponding to the maximum power density. The recommended values ​​of the constants in formula (6) are 0.8237, 0.2395, 0.2693 and 0.1841 respectively. The constants in formula (7) are a , b and c ) are recommended values ​​of 0.0831, 0.5606 and 0.2042, respectively, for thicknesses of 7-20 μm and Pt loadings of 0.05-0.3 mg∙cm -2 , carbon loading is 0.2-0.6mg∙cm -2 , catalyst layer and operating conditions with intake air relative humidity of 0.4-0.9.

[0101] δ agg and n agg The expression is:

[0102] (8).

[0103] (9).

[0104] In the formula, ε CL and ε agg are the CL porosity and the porosity of a single aggregate, respectively. The pores in a single aggregate are filled with ionomers, and their values ​​are generally taken as 0.1. ε Pt / C is the solid volume fraction.

[0105] In formula (6) and formula (7), r is the radius of the aggregate, which is 300 nm after comparison with the experimental value in the existing experiment. There are three types of losses in formula (6), namely activation loss ( η act )、Ohmic loss( η ohm,total ) and concentration loss ( η conc ) are:

[0106] (10).

[0107] (11).

[0108] (12).

[0109] In formula (10), α is the proton conduction efficiency, which can be set to 0.5; n is 4, which means that 4 moles of electrons are required to consume 1 mole of oxygen; i ref is the reference current density, which can be taken as 1.5×10 -5 A∙m -2 In formula (11), l PEM is the thickness of the proton exchange membrane; κ is the proton conductivity in the ionomer; I lim It can be determined by formula (4): I is the current density.

[0110] First, given the Pt loading ( m Pt )、Carbon loading( m C )、CL thickness( l CL ) and the relative humidity of the intake air ( RH ). Reference Figure 2 Then, according to the dichotomy method, the upper limit of the initial ionomer volume fraction can be given first: ω top and lower limit ω bottom , take the average value ω 0. Substituting this average value as the initial value into equation (4) yields the limiting current density. Three loss values ​​are obtained through equations (10) to (12): η loss , get the output voltage E cell,2 . And the output voltage is compared with the output voltage obtained by formula (6) E cell,1 If the voltage is greater than the voltage calculated by equation (6), the initial value in the previous step is set as the lower limit and the average value is recalculated. Otherwise, it is used as the upper limit to obtain the new ionomer volume fraction and bring it into the loop for calculation. -5 The cycle ends when , and the ionomer volume fraction at this time is output to obtain the optimal ionomer volume fraction of the second gradient-free catalyst layer, which is the optimal ionomer volume fraction of the gradient-free catalyst layer under the physical model.

[0111] Step 4: According to the optimal ionomer volume fraction of the first non-gradient catalyst layer, a gradient is set, that is, a linear gradient distribution is made along the thickness direction (X direction) of the catalyst layer, and the average value in the thickness direction is the optimal ionomer volume fraction obtained previously. Repeat the first and second steps to establish the input parameters as m Pt , m C , l CL and the ionomer gradient ( k ion ), the output parameter is the maximum power density ( P max ) to obtain the second data-driven model that can output the maximum P max The first optimal ionomer gradient distribution is obtained, that is, the optimal ionomer gradient distribution under the data-driven model. Then, based on the agglomerate model, a correlation between the gradient and the average ionomer volume fraction is established. Combined with the optimal ionomer volume fraction obtained in the third step, the ideal ionomer gradient distribution can be obtained, and the second optimal ionomer gradient distribution is obtained, that is, the optimal ionomer gradient distribution under the physical model.

[0112] The first optimal ionomer gradient is obtained after optimization by the second data-driven model established in the fourth step. When other structural parameters are the same, the ratio of the ionomer gradient to the total volume fraction of the ionomer is approximately a constant when the relative humidity of the intake air is changed. Therefore, we can continue to establish δ agg and n agg The relationship with the dimensionless gradient is:

[0113] (13).

[0114] In the formula, the constants except 2 are a 2. b 2 and c 2 can be fitted from the actual data, and the recommended values ​​are 0.1307, 0.3516 and -0.1253 respectively. k ion is the ionomer gradient, and its relationship with the ionomer volume fraction is:

[0115] (14).

[0116] In the formula, X is the dimensionless coordinate in the thickness direction, ω is the ionomer volume fraction, ω0 is the average ionomer volume fraction in CL, which is the volume fraction predicted in the gradient-free CL. So far, the second best ionomer distribution gradient can be obtained.

[0117] Based on the same concept, the present invention also provides a system for predicting the volume fraction and gradient distribution of ionomers in a cathode catalyst layer, comprising an input module, a first training module, an iteration module, a second training module and an output module.

[0118] The input module is used to input different parameters of the PEMFC cathode catalyst layer into the agglomerate model of the PEMFC cathode catalyst layer, obtain the polarization curves of the output voltage and current density under different parameters, and obtain the corresponding maximum power density according to the polarization curves; wherein the different parameters include multiple structural parameters and intake relative humidity.

[0119] The first training module is used to train the neural network model with different parameters as input and the corresponding maximum power density as output to obtain a first data-driven model, and obtain the optimal ionomer volume fraction of the first gradient-free catalytic layer based on the first data-driven model.

[0120] The iteration module is used to obtain a rapid prediction formula for limiting current density based on the agglomerate model, and combine the rapid prediction formula for limiting current density with the performance index corresponding to the optimal ionomer volume fraction of the first gradient-free catalytic layer to obtain a dimensionless output voltage correlation formula. Based on the rapid prediction formula for limiting current density and the dimensionless output voltage correlation formula, the optimal ionomer volume fraction of the second gradient-free catalytic layer is obtained through binary iteration.

[0121] The second training module is used to set the gradient according to the optimal ionomer volume fraction of the first gradient-free catalyst layer to obtain the ionomer gradient; the neural network model is trained through the ionomer gradient to obtain the second data-driven model, and the first optimal ionomer gradient distribution is obtained based on the second data-driven model.

[0122] The output module is used to establish a correlation between the ionomer gradient and the average ionomer volume fraction based on the agglomerate model, and combine the correlation with the optimal ionomer volume fraction of the second gradient-free catalyst layer to obtain the second optimal ionomer gradient distribution.

[0123] Example

[0124] The catalyst layer thickness of this embodiment is 7-20 μm, and the Pt loading is 0.05-0.3 mg∙cm -2 , carbon loading is 0.2-0.6 mg∙cm -2 , the volume fraction of the ionomer is 0.08-0.5, the relative humidity of the intake air is 0.4-0.9, and an original data set with a total of 2730 sets of data is established for subsequent analysis and testing.

[0125] (1) Based on the above non-gradient original data set, a non-gradient catalyst layer artificial neural network model was established. The input parameters of the model are platinum loading, carbon loading, ionomer volume fraction, catalyst layer thickness and intake relative humidity, and the output parameter is the maximum power density. By comparison, the average deviation Dev between the physical model and the data-driven model is 1.32%.

[0126] (2) Reference Figure 3 and Figure 4 , with a catalyst layer thickness of 7 μm and a Pt loading of 0.1 mg∙cm -2 and carbon loading of 0.4 mg∙cm -2 Take the structure of as an example, the current density is normalized, and the relative humidity of different intake air RH The corresponding output voltage polarization curves coincide with each other. P max Appears near the dimensionless current density of 0.8023, such as Figure 3 As shown in (a). After calculation, the prediction deviation of the limiting current density of formula (4) is 0.48%, as shown in Figure 4 As shown in (a), refer to Figure 5 The deviations of dimensionless output voltage and dimensionless current density in equations (6) and (7) are 0.93% and 0.21%, respectively. The average deviation of the predicted optimal ionomer volume fraction in the gradient-free catalyst layer is 1.13%, and the maximum deviation is 2.64%. Figure 6 As shown in (a).

[0127] (3) Based on the previous step, a gradient design is introduced, and the gradients of carbon loading, catalyst layer thickness, intake relative humidity, Pt loading, and ionomer volume fraction are set as input parameters. P max Set as output parameter, establish original data set, and train artificial neural network proxy model. The average deviation between physical model and data-driven model is 2.19%. Figure 4 as shown in (b).

[0128] (4) According to calculations, the setting of the Pt loading gradient has little effect on the limiting current density and the current density corresponding to the maximum power density, and the current density is mainly affected by the ionomer gradient. -2 and a carbon loading of 0.4 mg∙cm -2 Take the structure of as an example. Normalize the current density, different RH The corresponding output voltage polarization curves coincide with each other. P max Appears near the dimensionless current density of 0.5885, such as Figure 3 As shown in (b). After calculation, the prediction deviation of the limiting current density of formula (5) is 2.19%, as shown in Figure 4The increase in deviation here is due to the uneven distribution of oxygen at the reaction sites in the gradient catalytic layer. Figure 7 , and then the dimensionless ionomer volume fraction correlation was fitted, with an average deviation of 0.45%. Based on this result, the average deviation of the optimal ionomer volume fraction of the non-gradient catalyst layer was predicted to be 1.08%, and the maximum deviation was 2.84%, as shown in Figure 6 So far, the prediction and verification of the optimal ionomer volume fraction of the cathode non-gradient CL and the optimal gradient distribution of the gradient CL in PEMFC have been completed.

[0129] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0130] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for predicting the volume fraction and gradient distribution of ionomers in a PEMFC cathode catalyst layer, characterized in that: The following steps are involved: Different parameters of the PEMFC cathode catalyst layer are input into the aggregate model of the PEMFC cathode catalyst layer to obtain polarization curves of output voltage and current density under different parameters, and the corresponding maximum power density is obtained according to the polarization curves; wherein the different parameters include multiple structural parameters and relative humidity of intake air; The neural network model is trained with different parameters as input and the corresponding maximum power density as output to obtain a first data-driven model, and the optimal ionomer volume fraction of the first gradient-free catalyst layer is obtained based on the first data-driven model; Based on the agglomerate model, a rapid prediction formula for limiting current density is obtained, and the rapid prediction formula for limiting current density is combined with the performance index corresponding to the optimal ionomer volume fraction of the first gradient-free catalyst layer to obtain a dimensionless output voltage correlation formula; based on the rapid prediction formula for limiting current density and the dimensionless output voltage correlation formula, the optimal ionomer volume fraction of the second gradient-free catalyst layer is obtained through binary division iteration; Setting a gradient according to the optimal ionomer volume fraction of the first non-gradient catalyst layer to obtain an ionomer gradient; training a neural network model through the ionomer gradient to obtain a second data-driven model, and obtaining a first optimal ionomer gradient distribution based on the second data-driven model; A correlation between ionomer gradient and average ionomer volume fraction is established based on the agglomerate model, and the correlation between ionomer gradient and average ionomer volume fraction is combined with the optimal ionomer volume fraction of the second non-gradient catalyst layer to obtain the second optimal ionomer gradient distribution; The structural parameters include platinum loading, carbon loading, ionomer volume fraction, catalyst layer thickness and agglomerate radius; Obtaining an optimal ionomer volume fraction of a first non-gradient catalyst layer based on a first data-driven model includes the following steps: Based on the first data-driven model, multiple maximum power densities under different platinum loading, carbon loading, catalyst layer thickness and intake air relative humidity conditions are obtained through genetic algorithm; Arrange the multiple maximum power densities from high to low, and use the ionomer volume fraction corresponding to the highest ranked maximum power density as the optimal ionomer volume fraction of the first non-gradient catalytic layer; The neural network model is trained by the ionomer gradient to obtain a second data-driven model, and a first optimal ionomer gradient distribution is obtained based on the second data-driven model, comprising the following steps: The neural network model is trained by taking different platinum loading, carbon loading, catalyst layer thickness, intake relative humidity conditions and ionomer gradient as input and the maximum power density as output to obtain a second data-driven model; Based on the second data-driven model, multiple maximum power densities under different platinum loading, carbon loading, catalyst layer thickness and intake air relative humidity conditions are obtained through genetic algorithm; sorting the multiple maximum power densities from high to low, and taking the ionomer gradient distribution corresponding to the highest ranked maximum power density as the first optimal ionomer gradient distribution; The method for quickly predicting the limiting current density based on the aggregate model includes the following steps: Based on the aggregate model, it is assumed that all the oxygen entering the aggregate participates in the electrochemical reaction, that is, the oxygen flux is equal to the oxygen consumption, as shown in the following formula: In the formula, is the oxygen flux of a single agglomerate, O2 is oxygen, r is the radial distribution along a single agglomerate, a agg is the specific surface area of ​​a single aggregate, agg is the aggregate, is the diffusion coefficient of oxygen in the ionomer m, r agg and δ agg are the radius of the aggregate and the thickness of the ionomer film covering the aggregate, and are the oxygen concentration in the pores of the catalyst layer and the oxygen concentration reaching the Pt reaction site, is the oxygen partition coefficient based on Henry's law; Assuming that when the limiting current density is reached, the oxygen concentration at the reaction site is 0, the limiting current density is shown as follows: In the formula, I lim is the limiting current density, lim is the limit symbol, F is the Faraday constant, 4 means that 4 moles of electrons are required to consume 1 mole of oxygen, l CL is the thickness of the cathode catalyst layer; Considering that oxygen is adsorbed and consumed by the channel and gas diffusion layer GDL before entering the CL, the relationship between the oxygen concentration in the CL pores and the oxygen concentration at the gas inlet is obtained, as shown in the following formula: In the formula, is the oxygen concentration at the inlet, R CH_GDL is the resistance of the channel and GDL to oxygen, P in is the oxygen partial pressure at the inlet, R and T are the gas constant and temperature, respectively; The quick prediction formula of the limiting current density corresponding to the gradient-free CL is as follows: In the formula, I lim,NG is the limiting current density of the non-gradient cathode catalyst layer; The limiting current density corresponding to the gradient-free CL is integrated to obtain the rapid prediction formula of the limiting current density of the gradient CL: Where X is the dimensionless coordinate in the thickness direction of the catalyst layer, I lim,G is the limiting current density of the gradient cathode catalyst layer; The dimensionless output voltage correlation is as follows: Where η act is the activation loss, η ohm,total is the ohmic loss, η conc is the concentration loss, E ner is the Nernst voltage, a1, b1, c1 and d1 are constants, δ agg is the thickness of the ionomer film coated on the aggregate, n agg is the number density of aggregates per unit volume of CL; The optimal ionomer volume fraction of the second non-gradient catalyst layer is obtained by bisection iteration, including the following steps: Given the upper and lower limits of Pt loading, carbon loading, CL thickness, and inlet relative humidity, the initial ionomer volume fraction; Obtain the average value of the upper and lower limits of the initial ionomer volume fraction, substitute the average value as the initial value into the limiting current density rapid prediction formula corresponding to the gradient-free CL, and obtain the limiting current density; Three loss values ​​are obtained according to activation loss, ohmic loss and concentration difference loss, and the output voltage is obtained; The output voltage is compared with the output voltage obtained by the dimensionless output voltage correlation formula. If it is greater than, the initial value is set as the lower limit and the average value is re-obtained. Otherwise, it is used as the upper limit and the average value is re-obtained. The new ionomer volume fraction is substituted into the cycle for calculation; When the deviation of the ionomer volume fraction obtained from two iterations is less than the tolerance of 10 -5 The cycle ends when , and the corresponding ionomer volume fraction is output, i.e., the optimal ionomer volume fraction of the second non-gradient catalytic layer; The relationship between the ionomer gradient and the average ionomer volume fraction is as follows: In the formula, k ion is the ionomer gradient, ω0 is the average ionomer volume fraction in CL, i.e., the optimal ionomer volume fraction in the second non-gradient catalytic layer, a2, b2, and c2 are constants; Combining this correlation with the optimal ionomer volume fraction of the second non-gradient catalyst layer, the second optimal ionomer gradient distribution is obtained, as shown below: ω=ω0+k ion (X-1 / 2); Where ω is the volume fraction of ionomer.

2. A system for predicting the volume fraction and gradient distribution of ionomers in a PEMFC cathode catalyst layer, characterized in that: include: An input module is used to input different parameters of the PEMFC cathode catalyst layer into the aggregate model of the PEMFC cathode catalyst layer, obtain polarization curves of output voltage and current density under different parameters, and obtain the corresponding maximum power density according to the polarization curves; wherein the different parameters include multiple structural parameters and relative humidity of intake air; A first training module is used to train the neural network model with different parameters as input and the corresponding maximum power density as output to obtain a first data-driven model, and obtain the optimal ionomer volume fraction of the first gradient-free catalytic layer based on the first data-driven model; An iterative module is used to obtain a fast prediction formula for limiting current density based on an aggregate model, combine the fast prediction formula for limiting current density with a performance index corresponding to an optimal ionomer volume fraction of the first gradient-free catalyst layer, obtain a dimensionless output voltage correlation formula, and obtain an optimal ionomer volume fraction of the second gradient-free catalyst layer through a binary search iteration based on the fast prediction formula for limiting current density and the dimensionless output voltage correlation formula; The second training module is used to set the gradient according to the optimal ionomer volume fraction of the first gradient-free catalyst layer to obtain the ionomer gradient; train the neural network model through the ionomer gradient to obtain the second data-driven model, and obtain the first optimal ionomer gradient distribution based on the second data-driven model; An output module is used to establish a correlation between the ionomer gradient and the average ionomer volume fraction based on the agglomerate model, and combine the correlation between the ionomer gradient and the average ionomer volume fraction with the optimal ionomer volume fraction of the second non-gradient catalyst layer to obtain a second optimal ionomer gradient distribution; The structural parameters include platinum loading, carbon loading, ionomer volume fraction, catalyst layer thickness and agglomerate radius; Obtaining an optimal ionomer volume fraction of a first non-gradient catalyst layer based on a first data-driven model includes the following steps: Based on the first data-driven model, multiple maximum power densities under different platinum loading, carbon loading, catalyst layer thickness and intake air relative humidity conditions are obtained through genetic algorithm; rank the multiple maximum power densities from high to low, and use the ionomer volume fraction corresponding to the highest ranked maximum power density as the optimal ionomer volume fraction of the first non-gradient catalytic layer; The neural network model is trained by the ionomer gradient to obtain a second data-driven model, and a first optimal ionomer gradient distribution is obtained based on the second data-driven model, comprising the following steps: The neural network model is trained by taking different platinum loading, carbon loading, catalyst layer thickness, intake relative humidity conditions and ionomer gradient as input and the maximum power density as output to obtain a second data-driven model; Based on the second data-driven model, multiple maximum power densities under different platinum loading, carbon loading, catalyst layer thickness and intake air relative humidity conditions are obtained through genetic algorithm; sorting the multiple maximum power densities from high to low, and taking the ionomer gradient distribution corresponding to the highest ranked maximum power density as the first optimal ionomer gradient distribution; The method for quickly predicting the limiting current density based on the aggregate model includes the following steps: Based on the aggregate model, it is assumed that all the oxygen entering the aggregate participates in the electrochemical reaction, that is, the oxygen flux is equal to the oxygen consumption, as shown in the following formula: In the formula, is the oxygen flux of a single agglomerate, O2 is oxygen, r is the radial distribution along a single agglomerate, a agg is the specific surface area of ​​a single aggregate, agg is the aggregate, is the diffusion coefficient of oxygen in the ionomer m, r agg and δ agg are the radius of the aggregate and the thickness of the ionomer film covering the aggregate, and are the oxygen concentration in the pores of the catalyst layer and the oxygen concentration reaching the Pt reaction site, is the oxygen partition coefficient based on Henry's law; Assuming that when the limiting current density is reached, the oxygen concentration at the reaction site is 0, the limiting current density is shown as follows: In the formula, I lim is the limiting current density, lim is the limit symbol, F is the Faraday constant, 4 means that 4 moles of electrons are required to consume 1 mole of oxygen, l CL is the thickness of the cathode catalyst layer; Considering that oxygen is adsorbed and consumed by the channel and gas diffusion layer GDL before entering the CL, the relationship between the oxygen concentration in the CL pores and the oxygen concentration at the gas inlet is obtained, as shown in the following formula: In the formula, is the oxygen concentration at the inlet, R CH_GDL is the resistance of the channel and GDL to oxygen, P in is the oxygen partial pressure at the inlet, R and T are the gas constant and temperature, respectively; The quick prediction formula of the limiting current density corresponding to the gradient-free CL is as follows: In the formula, I lim,NG is the limiting current density of the non-gradient cathode catalyst layer; The limiting current density corresponding to the gradient-free CL is integrated to obtain the rapid prediction formula of the limiting current density of the gradient CL: Where X is the dimensionless coordinate in the thickness direction of the catalyst layer, I lim,G is the limiting current density of the gradient cathode catalyst layer; The dimensionless output voltage correlation is as follows: Where η act is the activation loss, η ohm,total is the ohmic loss, η conc is the concentration loss, E ner is the Nernst voltage, a1, b1, c1 and d1 are constants, δ agg is the thickness of the ionomer film coated on the aggregate, n agg is the number density of aggregates per unit volume of CL; The optimal ionomer volume fraction of the second non-gradient catalyst layer is obtained by bisection iteration, including the following steps: Given the upper and lower limits of Pt loading, carbon loading, CL thickness, and inlet relative humidity, the initial ionomer volume fraction; Obtain the average value of the upper and lower limits of the initial ionomer volume fraction, substitute the average value as the initial value into the limiting current density rapid prediction formula corresponding to the gradient-free CL, and obtain the limiting current density; Three loss values ​​are obtained according to activation loss, ohmic loss and concentration difference loss, and the output voltage is obtained; The output voltage is compared with the output voltage obtained by the dimensionless output voltage correlation formula. If it is greater than, the initial value is set as the lower limit and the average value is re-obtained. Otherwise, it is used as the upper limit and the average value is re-obtained. The new ionomer volume fraction is substituted into the cycle for calculation; When the deviation of the ionomer volume fraction obtained from two iterations is less than the tolerance of 10 -5 The cycle ends when , and the corresponding ionomer volume fraction is output, i.e., the optimal ionomer volume fraction of the second non-gradient catalytic layer; The relationship between the ionomer gradient and the average ionomer volume fraction is as follows: In the formula, k ion is the ionomer gradient, ω0 is the average ionomer volume fraction in CL, i.e., the optimal ionomer volume fraction in the second non-gradient catalytic layer, a2, b2, and c2 are constants; Combining this correlation with the optimal ionomer volume fraction of the second non-gradient catalyst layer, the second optimal ionomer gradient distribution is obtained, as shown below: ω=ω0+k ion (X-1 / 2); Where ω is the volume fraction of ionomer.

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