CN113946995A - Multi-objective fuel cell cooling flow channel optimization design method - Google Patents

Multi-objective fuel cell cooling flow channel optimization design method Download PDF

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CN113946995A
CN113946995A CN202111209562.3A CN202111209562A CN113946995A CN 113946995 A CN113946995 A CN 113946995A CN 202111209562 A CN202111209562 A CN 202111209562A CN 113946995 A CN113946995 A CN 113946995A
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甘全全
娄轩宇
李印实
张翼翀
王禹
戴威
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Shanghai Shenli Technology Co Ltd
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Abstract

The invention relates to a multi-objective fuel cell cooling flow channel optimization design method, which comprises the following steps: a two-dimensional two-phase non-isothermal fuel cell mathematical model is constructed by utilizing a control equation in a coupling mode, and the model is used as a data driving source after model verification is completed; extracting cooling flow channel structure optimization parameters, optimization targets, optimization parameter variation ranges and constraint conditions; substituting the changed optimization parameters into the mathematical model according to the variation range of the optimization parameters and the constraint conditions so as to output and obtain an original data set; based on the original data set, a machine learning algorithm is applied to construct and obtain a data-driven multi-target agent model; and (4) optimizing and solving the multi-target agent model by adopting a genetic algorithm to obtain the optimal cooling flow channel structure parameters. Compared with the prior art, the method can comprehensively optimize the structural parameters of the cooling flow channel in a multi-angle, rapid and accurate manner, and provides guidance for the structural design of the actual fuel cell.

Description

Multi-objective fuel cell cooling flow channel optimization design method
Technical Field
The invention relates to the technical field of fuel cells, in particular to a multi-objective fuel cell cooling flow channel optimization design method.
Background
The hydrogen-oxygen proton exchange membrane fuel cell has the characteristics of high energy density, no pollution, no catalyst poisoning and the like, and is therefore always taken as the first direction for the industrialization of the fuel cell. However, the high thermal load due to the high energy density becomes an important factor for preventing the development of the battery, mainly because the large amount of reaction heat affects the temperature distribution of the battery, causing the temperature of the whole or part of the battery to be too high. As a low-temperature fuel cell, the typical working temperature of a proton exchange membrane fuel cell needs to be controlled to be 60-85 ℃, the temperature difference between the typical working temperature and the environment is small, and the working temperature is difficult to maintain only through the self heat dissipation of the cell.
In order to solve the above-mentioned heat generation problem of the battery, a current mainstream method is to use a bipolar plate having a cooling water flow channel to cool the fuel cell by using cooling water. The good cooling water flow channel structure design and arrangement mode greatly help the heat management of the fuel cell, and the performance of the cell can be further improved while the temperature of the cell is controlled and the uniformity of the internal temperature is improved.
In the related optimization work of the proton exchange membrane fuel cell, the traditional method is to directly carry out multiple experimental comparisons to design an optimized cooling flow channel structure, but a large amount of manpower and material resources are necessarily consumed, so that the simulation modeling is used as an important means of the current design optimization, the simulation modeling means can be used for calculating the internal temperature distribution, the material transportation condition and the like of the cell which are difficult to reach in the experiment, the valuable information is provided for solving the practical problems, and the optimization design cost of the cell is greatly reduced. However, the traditional fuel cell model optimization usually uses a control variable method, the optimization target is single, the application scene is severely limited due to the limitation of the control variable method, and the advantages of modeling simulation cannot be fully exerted; the problem can be solved to a certain extent by simply using a method of combining an optimization algorithm with a mathematical model, but the optimization process needs thousands of times of calculation on the mathematical model, so that the time and the labor cost are greatly increased.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a multi-objective fuel cell cooling flow channel optimization design method, which can quickly and accurately optimize the cooling flow channel structure of a fuel cell by comprehensively optimizing flow channel parameters at multiple angles.
The purpose of the invention can be realized by the following technical scheme: a multi-objective fuel cell cooling flow channel optimization design method comprises the following steps:
s1, constructing a mathematical model: a two-dimensional two-phase non-isothermal fuel cell model is constructed by utilizing a control equation in a coupling mode, and a mathematical model is constructed by grid division and discrete calculation by using a finite element analysis method;
s2, constructing a multi-target agent model: determining the structure optimization parameters, optimization targets, optimization parameter variation ranges and constraint conditions of the cooling flow channel;
substituting the changed optimization parameters into the mathematical model according to the variation range of the optimization parameters and the constraint conditions so as to output and obtain an original data set;
constructing and obtaining a multi-target agent model based on an original data set in a machine learning training mode;
s3, genetic algorithm optimization: and (4) optimizing and solving the multi-target agent model by adopting a genetic algorithm to obtain the optimal cooling flow channel structure parameters.
Further, the governing equations in step S1 include a mass conservation equation, a momentum conservation equation, an energy conservation equation, a material conservation equation, a charge conservation equation, a concentration-dependent Butler-Volmer equation, and an oxygen transport process equation, wherein the mass conservation equation includes a gas-phase and liquid-phase mass conservation equation, and the momentum conservation equation includes a gas-phase and liquid-phase momentum conservation equation.
Further, the step S2 specifically includes the following steps:
s21, selecting the following structural parameters as optimization parameters according to the structure of the cooling flow channel:
X＝(Bias,WCH,w,HCH,w,HBP,a,HBP,c)T
wherein X is a cooling flow channel structure parameter set, Bias is a central axis deviation of a fuel flow channel and a cooling water flow channel, and W isCH,wFor the width of the cooling water flow passage HCH,wIs a height of a semi-cooling water flow passage HBP,aIs the anode fuel-cooling water plate thickness, HBP,cThe cathode fuel-cooling water electrode plate thickness;
determining optimization targets as the rated point power density and the section temperature difference of the battery;
the specific determination of the variation range of the optimization parameters is as follows:
{Bias|(0,0.6)}
{WCH,w|(0.4,1)}
{HCH,w|(0.1,0.5)}
{HBP,a|(0.2,1)}
{HBP,c|(0.2,1)}
{Htotal|(1.2,1.6)}
meanwhile, the thickness of the bipolar plate needs to meet the following constraint conditions:
Htotal＝HBP,a+HBP,c+2HCH,w
{Htotal|(1.2,1.6)}
wherein HtotalIs the bipolar plate thickness;
s22, randomly generating a plurality of groups of optimization parameters as input data sets according to the variation range of each optimization parameter, substituting the input data sets into a mathematical model to obtain output data sets, and correspondingly combining the input data sets and the output data sets to obtain original data sets;
and S23, constructing and obtaining the multi-target agent model based on the original data set in a machine learning training mode.
Further, the step S23 specifically includes the following steps:
s231, carrying out normalization preprocessing on input and output of the original data set, recording the rule of each parameter normalization mapping method, and dividing the preprocessed original data set into a training set and a test set according to a set proportion;
s232, taking a support vector machine as a machine learning training algorithm, carrying out agent model training on a training set by using the support vector machine, and carrying out agent model accuracy verification by using a test set to obtain a multi-target agent model related to different optimization targets, wherein the multi-target agent model comprises a battery rated point power density agent model and a cross section temperature difference agent model.
Further, the configuration of the support vector machine specifically includes: and selecting a radial basis function as a kernel function, and obtaining a regularization parameter c with the highest coefficient and a Gaussian kernel width g of the model determination coefficient by a grid search method.
Further, the multi-target agent model specifically includes:
Figure BDA0003308381870000031
Figure BDA0003308381870000032
Figure BDA0003308381870000033
wherein the content of the first and second substances,
Figure BDA0003308381870000034
for the battery rated power density proxy model,
Figure BDA0003308381870000035
is a cross-section temperature difference proxy model.
Further, the step S3 specifically includes the following steps:
s31, configuring a genetic algorithm, and initializing a population: configuring the population number, the elite number, the maximum population algebra and the stagnation algebra, and generating an initialized population by using the same optimized parameter variation range and constraint conditions as those in the original data set;
s32, carrying out normalization pretreatment on the initialized population, and then coding the normalized population;
s33, substituting the population individuals into the multi-target agent model, and calculating to obtain individual fitness;
s34, performing genetic operation according to the individual fitness, calculating to obtain a new population, and performing convergence judgment by adopting a set cut-off condition to obtain an optimal parameter set;
and S35, decoding and performing anti-normalization processing on the optimal parameter set to obtain the optimal cooling flow channel structure parameters.
Further, the step S33 specifically includes the following steps:
s331, substituting the population individuals into the multi-target agent model to obtain a corresponding output result;
s332, carrying out weighted summation calculation on the output result obtained in the step S331 to obtain individual fitness:
Fit＝WTY
WT＝(w1,w2)
wherein Fit is individual fitness WTAs a set of parameter weights, Y is the output summary data set of the multi-objective proxy model, w1For the weight value, w, corresponding to the rated point power density proxy model of the battery in the multi-target proxy model2And the weight value is corresponding to the cross section temperature difference agent model in the multi-target agent model.
Further, the genetic operation in step S34 includes a selection function, a cross function, and a variance function, where the selection function adopts a random uniform distribution selection method, the cross function adopts a discrete recombination method, and the variance function adopts a gaussian variance method.
Further, the step S34The cutoff condition set in (1) is specifically a multiple cutoff condition, the multiple cutoff condition includes a first cutoff condition and a second cutoff condition, the first cutoff condition is that the population generation number reaches a maximum generation number, and the second cutoff condition is that: within the stagnant algebra, the variation of the population fitness weighted mean is less than 10-6；
When the first cutoff condition or the second cutoff condition is satisfied, it is determined that convergence is reached.
Compared with the prior art, the optimization design method aims at the optimization design of the cooling water flow channel structure of the fuel cell, a mathematical model is built as a data set source, parameters required to be optimized are extracted to generate an original data set, a multi-objective agent model optimization mode is adopted, the data set is substituted into a machine learning to generate an agent model, and the optimal parameters are calculated by using a genetic algorithm based on the agent model to realize the optimization of the cooling water flow channel structure.
The invention uses the mathematical model as the original data source, greatly reduces the cost of the optimization design of the battery, provides the information of the temperature distribution condition and the like in the battery which is difficult to touch in the experiment, and provides the possibility for generating the multi-objective agent model; the optimization time can be greatly reduced by adopting a multi-objective agent model optimization mode, and compared with the traditional modes such as a control variable method and the like, the optimization time can be effectively shortened by adopting the multi-objective agent model optimization mode; the fuel cell can be comprehensively optimized from multiple angles, and a more scientific and reasonable result can be obtained compared with single-target optimization; the invention also uses the genetic algorithm to carry out optimization calculation, compared with the qualitative optimization of the traditional method, the method is quicker and more accurate, the parameter coverage is wider, and the specific optimal solution which is difficult to be solved by the traditional method can be obtained.
Therefore, the method can comprehensively optimize the flow channel parameters in a multi-angle, rapid and accurate manner, and provides guidance for the structural design of the actual fuel cell.
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FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic diagram of a process for applying the method of the present invention in an example;
FIG. 3 is a schematic diagram of a two-dimensional two-phase non-isothermal fuel cell model calculation domain in an embodiment;
FIG. 4 is a schematic diagram of the optimization parameters selected in the example;
FIG. 5 is a comparison graph of the mathematical model versus the actual polarization curve of the cell stack in the example;
FIG. 6a is a comparison graph of the training set surrogate model versus the mathematical model nominal power density in an example;
FIG. 6b is a comparison of the test set surrogate model versus the mathematical model power density rating for the example embodiment;
FIG. 6c is a graph showing the maximum temperature difference between the training set surrogate model and the mathematical model in the example;
FIG. 6d is a graph showing the maximum temperature difference between the test set surrogate model and the mathematical model in the example;
the notation in the figure is: 1. the anode gas diffusion layer 2, the anode microporous layer 3, the anode catalyst layer 4, the proton exchange membrane 5, the cathode catalyst layer 6, the cathode microporous layer 7, the cathode gas diffusion layer 8, the anode cooling water flow channel 9, the anode plate 10, the anode fuel flow channel 11, the cathode fuel flow channel 12, the cathode plate 13 and the cathode cooling water flow channel.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
As shown in fig. 1, a method for optimally designing a multi-objective fuel cell cooling flow channel includes the following steps:
s1, constructing a mathematical model: the method comprises the following steps of establishing a two-dimensional two-phase non-isothermal fuel cell model by utilizing a control equation in a coupling mode, and completing mathematical model establishment by grid division and discrete calculation by using a finite element analysis method, wherein the control equation comprises a mass conservation equation (comprising a gas phase mass conservation equation and a liquid phase mass conservation equation), a momentum conservation equation (comprising a gas phase momentum conservation equation and a liquid phase momentum conservation equation), an energy conservation equation, a material conservation equation, a charge conservation equation, a concentration-dependent Butler-Volmer equation and an oxygen transmission process equation;
s2, constructing a multi-target agent model: determining the structure optimization parameters, optimization targets, optimization parameter variation ranges and constraint conditions of the cooling flow channel;
substituting the changed optimization parameters into the mathematical model according to the variation range of the optimization parameters and the constraint conditions so as to output and obtain an original data set;
constructing and obtaining a multi-target agent model based on an original data set in a machine learning training mode;
specifically, the method comprises the following steps:
firstly, according to the structure of a cooling flow channel, the following structural parameters are selected as optimization parameters:
X＝(Bias,WCH,w,HCH,w,HBP,a,HBP,c)T
wherein X is a cooling flow channel structure parameter set, Bias is a central axis deviation of a fuel flow channel and a cooling water flow channel, and W isCH,wFor the width of the cooling water flow passage HCH,wIs a height of a semi-cooling water flow passage HBP,aIs the anode fuel-cooling water plate thickness, HBP,cThe cathode fuel-cooling water electrode plate thickness;
determining optimization targets as the rated point power density and the section temperature difference of the battery;
the specific determination of the variation range of the optimization parameters is as follows:
{Bias|(0,0.6)}
{WCH,w|(0.4,1)}
{HCH,w|(0.1,0.5)}
{HBP,a|(0.2,1)}
{HBP,c|(0.2,1)}
{Htotal|(1.2,1.6)}
meanwhile, the thickness of the bipolar plate needs to meet the following constraint conditions:
Htotal＝HBP,a+HBP,c+2HCH,w
{Htotal|(1.2,1.6)}
wherein HtotalIs the bipolar plate thickness;
then, randomly generating a plurality of groups of optimization parameters according to the variation range of each optimization parameter to be used as an input data set, substituting the input data set into a mathematical model to obtain an output data set, and correspondingly combining the input data set and the output data set to obtain an original data set;
based on the original data set, carrying out normalization pretreatment on the input and output of the original data set, recording the rule of each parameter normalization mapping method, and dividing the pretreated original data set into a training set and a test set according to a set proportion;
taking a support vector machine (selecting a radial basis function as a kernel function, and obtaining a regularization parameter c and a Gaussian kernel width g with the highest model determination coefficient by a grid search method) as a machine learning training algorithm, carrying out agent model training on a training set by using the support vector machine, and carrying out agent model accuracy verification by using a test set to obtain a multi-target agent model related to different optimization targets, wherein the multi-target agent model comprises a battery rated point power density agent model and a section temperature difference agent model:
Figure BDA0003308381870000071
Figure BDA0003308381870000072
Figure BDA0003308381870000073
wherein the content of the first and second substances,
Figure BDA0003308381870000074
for the battery rated power density proxy model,
Figure BDA0003308381870000075
a cross-section temperature difference proxy model;
s3, genetic algorithm optimization: optimizing and solving the multi-target agent model by adopting a genetic algorithm to obtain the optimal cooling flow channel structure parameters, specifically:
s31, configuring a genetic algorithm, and initializing a population: configuring the population number, the elite number, the maximum population algebra and the stagnation algebra, and generating an initialized population by using the same optimized parameter variation range and constraint conditions as those in the original data set;
s32, carrying out normalization pretreatment on the initialized population, and then coding the normalized population;
s33, substituting the population individuals into the multi-target agent model to obtain a corresponding output result;
and then carrying out weighted summation calculation on the output result of the multi-target agent model to obtain individual fitness:
Fit＝WTY
WT＝(w1,w2)
wherein Fit is individual fitness WTAs a set of parameter weights, Y is the output summary data set of the multi-objective proxy model, w1For the weight value, w, corresponding to the rated point power density proxy model of the battery in the multi-target proxy model2Calculating a weight value corresponding to a cross-section temperature difference agent model in the multi-target agent model to obtain individual fitness;
s34, carrying out genetic operation (including a selection function, a cross function and a variation function, wherein the selection function adopts a random uniform distribution selection method, the cross function adopts a discrete recombination method, the variation function adopts a Gaussian variation method), calculating to obtain a new population, and carrying out convergence judgment by adopting a set cut-off condition (the multiple cut-off condition comprises a first cut-off condition and a second cut-off condition, the first cut-off condition is that the population algebra reaches the maximum algebra, and the second cut-off condition is that the variation of the population fitness weighted average value is less than 10 in the stagnation algebra-6(ii) a When the first cutoff condition or the second cutoff condition is met, namely convergence is judged to be achieved), and an optimal parameter set is obtained;
and S35, decoding and performing anti-normalization processing on the optimal parameter set to obtain the optimal cooling flow channel structure parameters.
In conclusion, aiming at the optimization design of the cooling water flow channel of the fuel cell, the invention builds a mathematical model as a data set source, extracts the needed optimization parameters to generate an original data set, adopts a multi-objective agent model optimization mode, substitutes the data set into a machine learning to generate an agent model, and uses a genetic algorithm to calculate based on the agent model to obtain the optimal parameters, thereby realizing the optimization of the cooling water flow channel structure.
The main process of the method applied in the embodiment is as shown in fig. 2, and includes the steps of establishing a mathematical model, generating a proxy model, optimizing a genetic algorithm, and verifying reliability of an optimization result:
1) constructing a mathematical model: according to the model optimization requirements, under the condition of considering both the model accuracy and the calculation economy, a two-dimensional two-phase non-isothermal fuel cell model is built, the specific calculation domain of the model is shown in fig. 3, and the model comprises an anode gas diffusion layer 1, an anode microporous layer 2, an anode catalyst layer 3, a proton exchange membrane 4, a cathode catalyst layer 5, a cathode microporous layer 6, a cathode gas diffusion layer 7, an anode cooling water flow channel 8, an anode plate 9, an anode fuel flow channel 10, a cathode fuel flow channel 11, a cathode plate 12 and a cathode cooling water flow channel 13, and the basic control equation of the model is as follows:
gas phase and liquid phase mass conservation equation:
▽·(ρgug)＝mg
▽·(ρlul)＝ml
where ρ isg、ρlRespectively gas phase and liquid phase density, ug、ulRespectively gas phase and liquid phase velocity, mg、mlRespectively gas phase and liquid phase mass source items;
gas phase and liquid phase momentum conservation equation:
Figure BDA0003308381870000081
Figure BDA0003308381870000082
wherein K is the absolute permeability in the porous medium,kr,g、kr,lrelative permeability of gas phase and liquid phase, pg、plGas phase and liquid phase pressure respectively;
using capillary pressure pcCoupling gas-liquid two-phase motion:
Figure BDA0003308381870000083
wherein σ is the surface tension of liquid water, θcThe contact angle of liquid water, epsilon, the porosity, K, the absolute permeability and s, the volume fraction of the liquid water;
energy conservation equation:
Figure BDA0003308381870000091
wherein ε is the porosity, CpIs the specific heat capacity of the component, T is the component temperature, lambdaiIs the component thermal conductivity, STIs a temperature source term;
material conservation equation:
Figure BDA0003308381870000092
wherein, CiAs a result of the concentration of the components,
Figure BDA0003308381870000093
in order to have an effective diffusion coefficient of the component,
Figure BDA0003308381870000094
is the component thermal diffusivity, SiIs the component molar generation rate;
conservation of charge equation:
Figure BDA0003308381870000095
Figure BDA0003308381870000096
wherein the content of the first and second substances,
Figure BDA0003308381870000097
respectively effective proton conductivity, effective electron conductivity, phil、φsElectrolyte potential and electrode potential respectively; ql、QsRespectively, proton generation rate and electron generation rate;
the hydrogen oxidation reaction and the oxygen reduction reaction which respectively occur at the anode and the cathode are described by using a concentration-dependent Butler-Volmer equation:
Figure BDA0003308381870000098
Figure BDA0003308381870000099
wherein j is0,a、j0,cThe exchange current density of the anode and the cathode respectively,
Figure BDA00033083818700000910
reference concentrations of hydrogen and oxygen, respectively, alphaa、αcRespectively anode and cathode reaction charge transmission coefficients, F is a Faraday constant, and R is a gas constant;
Aa、Acthe active specific surface areas, eta, of the anode catalyst layer 3 and the cathode catalyst layer 5 respectivelya、ηcThe overpotential for the anode and cathode is calculated by the following formula:
Figure BDA00033083818700000911
Figure BDA00033083818700000912
η＝φs-φl-Eeq
wherein E isa、EcElectrochemical surface areas m of the anode catalyst layer 3 and the cathode catalyst layer 5, respectivelypt,a、mpt,cPlatinum loading amounts, H, of the anode catalyst layer 3 and the cathode catalyst layer 5, respectivelyACL、HCCLThe thicknesses of the anode catalyst layer 3 and the cathode catalyst layer 5 are respectively;
Figure BDA0003308381870000101
is the concentration of the hydrogen and oxygen activation sites,
Figure BDA0003308381870000102
calculating by adopting a one-dimensional oxygen transmission process equation:
Figure BDA0003308381870000103
Figure BDA0003308381870000104
wherein, deltaw、δnRespectively the thickness of the water film on the surface of the catalyst agglomerate and the thickness of the ionomer film,
Figure BDA0003308381870000105
diffusion coefficient of oxygen in liquid water and ionomer respectively, C1Is the equilibrium concentration of the oxygen water film surface,
Figure BDA0003308381870000106
is the oxygen concentration, H, in the cathode catalyst layer 5nIs the ionomer surface Henry coefficient, kn、kptRespectively the adsorption coefficients of oxygen on the surfaces of ionomer and platinum;
the net flux of liquid water transmission between the cathode and the anode on both sides of the proton exchange membrane 4 is:
Figure BDA0003308381870000107
wherein n isdIs the electroosmotic coefficient, I is the reaction current density, pl,c-aThe liquid water pressure difference between the cathode and the anode at the two sides of the proton exchange membrane 4,
Figure BDA0003308381870000108
is liquid water molar mass, mulIs liquid hydrodynamic viscosity, HMEMIs the thickness of the proton exchange membrane 4;
and based on the mathematical equation coupling, carrying out grid division, and carrying out discrete calculation by using a finite element analysis method to complete the establishment of a mathematical model. As shown in FIG. 5, the mathematical model was validated using actual fuel cell stack test polarization curves, which determined the coefficient R20.9893, namely proving that the model is valid, and taking the verified mathematical model as a data set source;
2) generating a proxy model:
2.1) determining optimization parameters and optimization targets, determining the variation range and constraint conditions of the optimization parameters: referring to fig. 4, 5 cooling water flow channel structure parameters as shown in the figure are selected as optimization parameters, which are respectively: center axis deviation Bias of fuel flow passage-cooling water flow passage, width W of cooling water flow passageCH,wHeight H of semi-cooling water flow passageCH,wAnode fuel-cooling water plate thickness HBP,aCathode fuel-cooling water plate thickness HBP,cIt is summarized as follows: x ═ W (Bias, W)CH,w,HCH,w,HBP,a,HBP,c)TIn this embodiment, the optimized parameter values of the original version are: x ═ 0,0.8,0.6,0.4,0.45)T；
Selecting rated point power density P of batteryratedTemperature difference Delta T from cross sectionratedAs an optimization target, comprehensive optimization is carried out from two aspects of battery performance and temperature uniformity, and in order to ensure that the battery structure reasonability and the battery volume power density do not change too much, optimization parameters and the thickness H of the bipolar plate need to be controlledtotal＝HBP,a+HBP,c+2HCH,wThe variation range is specifiedIn the interval, the value ranges of the optimized parameters are respectively as follows: { Bias | (0,0.6) } mm, { WCH,w|(0.4,1)}mm，{HCH,w|(0.1,0.5)}mm，{HBP,a|(0.2,1)}mm，{HBP,c|(0.2,1)}mm，{Htotal|(1.2,1.6)}；
2.2) substituting the variation optimization parameters into a mathematical model to generate an original data set: based on the mathematical model which is built and verified, compiling scripts to randomly generate 150 groups of optimized parameters within a specified range as input data sets, substituting the optimized parameters into the mathematical model to guide calculation and solution, and recording a required output data set Prated、ΔTratedObtaining an original data set;
2.3) carrying out normalization preprocessing on the original data set and dividing the data set: in order to improve the model training precision and eliminate the influence caused by different data magnitude, the input and the output of an original data set are subjected to normalization preprocessing, various parameter normalization mapping rules are recorded, and the preprocessed data set is subjected to normalization mapping according to the following rule of 0.75: dividing the training set and the test set by a proportion of 0.25;
2.4) substituting machine learning training to generate a multi-target agent model: generating a proxy model by using a Machine learning algorithm Support Vector Machine (SVM) training data set, and compiling a script to perform algorithm configuration and model training, wherein the configuration of the SVM specifically comprises the following steps: selecting a Radial Basis Function (RBF) as a kernel Function, and obtaining a regularization parameter c with the highest coefficient of a model determination and a Gaussian kernel width g by a simple grid search method;
model training is carried out by using a training set, model accuracy verification is carried out by using a test set, and battery performance P is obtainedratedTemperature difference of cross section delta TratedThe proxy model of (2):
Figure BDA0003308381870000111
Figure BDA0003308381870000112
wherein the content of the first and second substances,
Figure BDA0003308381870000113
all the results are normalized results, and can be summarized into
Figure BDA0003308381870000114
As shown in fig. 6a to 6d, the training precision of the proxy model obtained by training is:
determining coefficients
Figure BDA0003308381870000115
Figure BDA0003308381870000116
The training precision meets the training requirement, and the agent model is used for subsequent optimization;
3) genetic algorithm optimization:
3.1) initializing the population and configuring a genetic algorithm: after the establishment of the multi-target agent model is completed, further performing model optimization by using a genetic algorithm, firstly configuring the genetic algorithm, wherein in the embodiment, the population number is 60, the elite number is 2, the maximum population Generation number is 300, the Stall Generation number (Stall Generation) is 50, and generating an initialization population by using the same parameter range and limiting conditions as those of the generated original data set;
3.2) normalization and encoding of population data: carrying out normalization pretreatment on the initial population by adopting each parameter normalization mapping rule of the original data, and coding the normalized population for subsequent genetic operation;
3.3) calculating the fitness by applying the multi-target agent model: substituting the population individuals into the multi-target agent model to obtain corresponding output results, wherein the output results of the multi-target agent model are normalized results, so that the problem of magnitude deviation does not exist, and the output results of each agent model can be directly weighted and summed according to actual requirements to determine the individual fitness Fit as WTY, where Y is the output summary data set, WTAs a parameter weightCollection, WT＝(w1,w2) In the embodiment, the main purpose is to obtain lower temperature difference of the battery, and it is desired to obtain better battery performance at the same time, and the specific calculation method is
Figure BDA0003308381870000121
3.4) determining new population by genetic operation. After the individual fitness is obtained through calculation, genetic operation is carried out according to the fitness condition of the individual fitness, wherein the genetic operation comprises a selection function, a cross function and a variation function, in the embodiment, the selection function adopts a random uniform distribution selection method (Stochastic uniform), the cross function adopts a discrete recombination method (Scattered), the cross probability is 0.8, the variation function adopts Gaussian variation (Gaussian), the variation probability is 0.2, and a new population is obtained through the genetic operation and statistical result;
3.5) applying a cutoff condition to judge whether convergence occurs: in order to ensure the stability of the algorithm, a multi-cutoff condition setting is adopted for cutoff judgment, and a cycle is skipped when any one of the following conditions is met: the population algebra reaches the maximum algebra or the weighted average value of population fitness in the stagnation algebra
Figure BDA0003308381870000122
Variation less than 10-6If the above cutoff condition is met, jumping out of the loop, namely completing parameter set optimization;
3.6) decoding and inverse normalizing parameter sets to obtain an optimal solution: decoding the optimized result, performing inverse normalization according to the normalization mapping rule of each parameter, and converting the normalized result into the parameters required by the actual product, wherein the optimized parameter values in the embodiment are as follows: xopti＝(0.6,0.65,0.8,0.2,0.2)；
4) Verifying the reliability of the optimization result: substituting the optimized parameter result into a mathematical model for calculation to obtain the rated point power density P under the optimized versionratedTemperature difference Delta T from cross sectionratedAnd comparing the result with the original version result, verifying the reliability of the optimization result and finishing the optimization design.
By applying the method provided by the invention, the structural parameters of the cooling flow channel can be comprehensively optimized in a multi-angle, rapid and accurate manner, and guidance is provided for the structural design of the actual fuel cell; compared with the traditional modes such as a control variable method and the like, the optimization time can be greatly shortened by adopting the multi-objective agent model optimization mode.

Claims (10)

1. A multi-objective fuel cell cooling flow channel optimization design method is characterized by comprising the following steps:
s1, constructing a mathematical model: a two-dimensional two-phase non-isothermal fuel cell model is constructed by utilizing a control equation in a coupling mode, and a mathematical model is constructed by grid division and discrete calculation by using a finite element analysis method;
s2, constructing a multi-target agent model: determining the structure optimization parameters, optimization targets, optimization parameter variation ranges and constraint conditions of the cooling flow channel;
substituting the changed optimization parameters into the mathematical model according to the variation range of the optimization parameters and the constraint conditions so as to output and obtain an original data set;
constructing and obtaining a multi-target agent model based on an original data set in a machine learning training mode;
s3, genetic algorithm optimization: and (4) optimizing and solving the multi-target agent model by adopting a genetic algorithm to obtain the optimal cooling flow channel structure parameters.
2. The method of claim 1, wherein the governing equations in the step S1 include mass conservation equations including gas phase and liquid phase mass conservation equations, momentum conservation equations including gas phase and liquid phase momentum conservation equations, energy conservation equations, material conservation equations, charge conservation equations, concentration dependent Butler-Volmer equations, and oxygen transport process equations.
3. The method as claimed in claim 1, wherein the step S2 specifically comprises the following steps:
s21, selecting the following structural parameters as optimization parameters according to the structure of the cooling flow channel:
X＝(Bias,WCH,w,HCH,w,HBP,a,HBP,c)T
wherein X is a cooling flow channel structure parameter set, Bias is a central axis deviation of a fuel flow channel and a cooling water flow channel, and W isCH,wFor the width of the cooling water flow passage HCH,wIs a height of a semi-cooling water flow passage HBP,aIs the anode fuel-cooling water plate thickness, HBP,cThe cathode fuel-cooling water electrode plate thickness;
determining optimization targets as the rated point power density and the section temperature difference of the battery;
the specific determination of the variation range of the optimization parameters is as follows:
{Bias|(0,0.6)}
{WCH,w|(0.4,1)}
{HCH,w|(0.1,0.5)}
{HBP,a|(0.2,1)}
{HBP,c|(0.2,1)}
{Htotal|(1.2,1.6)}
meanwhile, the thickness of the bipolar plate needs to meet the following constraint conditions:
Htotal＝HBP,a+HBP,c+2HCH,w
{Htotal|(1.2,1.6)}
wherein HtotalIs the bipolar plate thickness;
s22, randomly generating a plurality of groups of optimization parameters as input data sets according to the variation range of each optimization parameter, substituting the input data sets into a mathematical model to obtain output data sets, and correspondingly combining the input data sets and the output data sets to obtain original data sets;
and S23, constructing and obtaining the multi-target agent model based on the original data set in a machine learning training mode.
4. The method as claimed in claim 3, wherein the step S23 specifically comprises the following steps:
s231, carrying out normalization preprocessing on input and output of the original data set, recording the rule of each parameter normalization mapping method, and dividing the preprocessed original data set into a training set and a test set according to a set proportion;
s232, taking a support vector machine as a machine learning training algorithm, carrying out agent model training on a training set by using the support vector machine, and carrying out agent model accuracy verification by using a test set to obtain a multi-target agent model related to different optimization targets, wherein the multi-target agent model comprises a battery rated point power density agent model and a cross section temperature difference agent model.
5. The method as claimed in claim 4, wherein the configuration of the support vector machine is specifically as follows: and selecting a radial basis function as a kernel function, and obtaining a regularization parameter c with the highest coefficient and a Gaussian kernel width g of the model determination coefficient by a grid search method.
6. The multi-objective fuel cell cooling flow channel optimization design method as claimed in claim 4, wherein the multi-objective proxy model is specifically:
Figure FDA0003308381860000021
Figure FDA0003308381860000022
Figure FDA0003308381860000023
wherein the content of the first and second substances,
Figure FDA0003308381860000024
proxy model for battery rated power densityThe shape of the mould is as follows,
Figure FDA0003308381860000025
is a cross-section temperature difference proxy model.
7. The method as claimed in claim 6, wherein the step S3 specifically comprises the following steps:
s31, configuring a genetic algorithm, and initializing a population: configuring the population number, the elite number, the maximum population algebra and the stagnation algebra, and generating an initialized population by using the same optimized parameter variation range and constraint conditions as those in the original data set;
s32, carrying out normalization pretreatment on the initialized population, and then coding the normalized population;
s33, substituting the population individuals into the multi-target agent model, and calculating to obtain individual fitness;
s34, performing genetic operation according to the individual fitness, calculating to obtain a new population, and performing convergence judgment by adopting a set cut-off condition to obtain an optimal parameter set;
and S35, decoding and performing anti-normalization processing on the optimal parameter set to obtain the optimal cooling flow channel structure parameters.
8. The method as claimed in claim 7, wherein the step S33 specifically comprises the following steps:
s331, substituting the population individuals into the multi-target agent model to obtain a corresponding output result;
s332, carrying out weighted summation calculation on the output result obtained in the step S331 to obtain individual fitness:
Fit＝WTY
WT＝(w1,w2)
wherein Fit is individual fitness WTAs a set of parameter weights, Y is the output summary data set of the multi-objective proxy model, w1Acting on model for multiple targetsWeight value, w, corresponding to battery rated point power density proxy model2And the weight value is corresponding to the cross section temperature difference agent model in the multi-target agent model.
9. The method as claimed in claim 7, wherein the genetic algorithm in step S34 includes a selection function, a cross function and a variance function, wherein the selection function is a random uniform distribution selection method, the cross function is a discrete recombination method, and the variance function is a gaussian variance method.
10. The method as claimed in claim 7, wherein the cutoff conditions set in step S34 are multiple cutoff conditions, and the multiple cutoff conditions include a first cutoff condition and a second cutoff condition, the first cutoff condition is that the number of generation groups reaches a maximum number of generation, and the second cutoff condition is that: within the stagnant algebra, the variation of the population fitness weighted mean is less than 10-6；
When the first cutoff condition or the second cutoff condition is satisfied, it is determined that convergence is reached.
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CN114707365A (en) * 2022-06-02 2022-07-05 中汽研新能源汽车检验中心(天津)有限公司 Water-heat-mass transfer simulation method for gas diffusion layer of fuel cell
CN115000471A (en) * 2022-05-18 2022-09-02 西安交通大学 Fuel cell catalyst layer prediction-analysis-optimization method based on machine learning
CN115470581A (en) * 2022-08-29 2022-12-13 华北电力大学 Fuel cell gas flow channel optimization design method, system, electronic device and medium
CN117592224A (en) * 2024-01-19 2024-02-23 中国石油大学(华东) Solid oxide fuel cell flexible bipolar plate structure optimization design method

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115000471A (en) * 2022-05-18 2022-09-02 西安交通大学 Fuel cell catalyst layer prediction-analysis-optimization method based on machine learning
CN114707365A (en) * 2022-06-02 2022-07-05 中汽研新能源汽车检验中心(天津)有限公司 Water-heat-mass transfer simulation method for gas diffusion layer of fuel cell
CN115470581A (en) * 2022-08-29 2022-12-13 华北电力大学 Fuel cell gas flow channel optimization design method, system, electronic device and medium
CN115470581B (en) * 2022-08-29 2024-02-20 华北电力大学 Fuel cell gas flow channel optimization design method, system, electronic equipment and medium
CN117592224A (en) * 2024-01-19 2024-02-23 中国石油大学(华东) Solid oxide fuel cell flexible bipolar plate structure optimization design method
CN117592224B (en) * 2024-01-19 2024-04-30 中国石油大学(华东) Solid oxide fuel cell flexible bipolar plate structure optimization design method

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