Proton exchange membrane fuel cell power density and operation parameter optimization method

Abstract

The invention provides a proton exchange membrane fuel cell power density and operation parameter optimization method, which comprises the following steps of: constructing a proton exchange membrane fuel cell proxy model based on a random forest algorithm by taking the working temperature, the anode pressure, the cathode / anode relative humidity and the current density of a galvanic pile as input and the power density as output; and the input and output of the proxy model are optimized in combination with an improved spectrum algorithm, so that the maximum power density and corresponding operation parameters can be predicted. When the load demand changes, the fitness function of the improved spectrum algorithm can be changed, the corresponding power density meeting the load demand is calculated, and the corresponding operation parameters of the power density are predicted. According to the method, the optimization time is shortened, the calculation burden in the optimization process is reduced, and the optimization efficiency is improved.

Description

Technical field:

[0001] The present invention relates to the field of proton exchange membrane fuel cells, and in particular to a method for optimizing the power density and operating parameters of a proton exchange membrane fuel cell. Background technology:

[0002] Proton exchange membrane fuel cell (PEMFC) is a new type of clean and efficient energy device with the advantages of low operating temperature, high power density and environmental protection. It has been widely used in transportation, residential, fixed and portable power systems. Power density is a key parameter for evaluating the efficiency of fuel cells and is closely related to various operating parameters, including operating temperature, pressure, humidity, current density, etc. Higher power density helps to improve the output power and overall performance of PEMFC, so the optimization of power density is crucial. The data used in the power density optimization process is usually obtained from models or experiments, and the iteration of the algorithm requires a large amount of data to ensure the accuracy and precision of the optimization. These data are difficult to obtain from experiments, and the PEMFC model involves complex electrochemical reactions and requires a long running time.

[0003] In actual applications, the output power will change according to the load demand. The current PEMFC power density optimization method mainly focuses on the maximum power density, which cannot meet the changes in load demand. At the same time, the agent model based on machine learning can reduce the optimization time, but the agent model must maintain high accuracy and reliability. Summary of the invention:

[0004] Based on this, it is necessary to propose a method for optimizing the power density and operating parameters of proton exchange membrane fuel cells in response to the above problems. First, with the operating temperature, anode pressure, cathode / anode relative humidity and current density of the stack as inputs and the power density as output, a proton exchange membrane fuel cell proxy model based on the random forest algorithm (RF) is constructed. Then, the input and output of the proxy model are optimized in combination with the improved spectral algorithm (ILSO), which can predict the maximum power density and corresponding operating parameters. When the load demand changes, the fitness function of the improved spectral algorithm can be changed to calculate the power density corresponding to the load demand and predict its corresponding operating parameters. At the same time, it can also shorten the optimization time and improve the optimization efficiency.

[0005] The present invention discloses a method for optimizing the power density and operating parameters of a proton exchange membrane fuel cell, comprising the following steps:

[0006] Step 1: Establish a mathematical model of electrochemical reactions in the proton exchange membrane fuel cell stack.

[0007] Step 2: Taking the power density of the fuel cell stack as the target quantity, the operating temperature, anode pressure, cathode / anode relative humidity and current density as decision variables, the data set is obtained using matlab / simulink software.

[0008] Step 3: Use the random forest algorithm to train and predict the data set to obtain the proxy model. At the same time, the random forest algorithm is combined with the support vector machine (SVM) and radial basis neural network (RBF) three machine learning proxy models to obtain the mean absolute error (MAE), mean square error (MSE) and determination coefficient (R 2 ) and training time for comparison.

[0009] Step 4: Optimize the prediction results by combining the improved spectral algorithm, and compare the optimization performance of the improved spectral algorithm with the traditional spectral algorithm, particle swarm algorithm and differential evolution algorithm. Predict the maximum power density and the corresponding operating parameter set, and compare the optimization time of the original model and the proxy model.

[0010] The beneficial effects of the present invention are as follows:

[0011] The present invention discloses a method for optimizing the power density and operating parameters of a proton exchange membrane fuel cell based on a random forest and an improved spectral algorithm. In the training and optimization of a proton exchange membrane fuel cell proxy model, the random forest algorithm of the present invention has a faster training speed, smaller mean absolute error, mean square error and determination coefficient than a support vector machine and a radial basis neural network, and can further improve the accuracy and prediction ability of the proxy model; the improved spectral algorithm has a stronger global search capability and a faster convergence speed than a traditional spectral algorithm, a differential evolution algorithm and a particle swarm optimization algorithm; at the same time, the optimization method based on the present invention can effectively predict the maximum power density of a proton exchange membrane fuel cell, and can also predict its corresponding operating parameters according to different power requirements; compared with the optimization method based on the original mathematical model, it has a shorter optimization time, reduces the calculation burden of the optimization process, and improves the optimization efficiency. Description of the drawings:

[0012] Figure 1 It is a technical flow chart of the present invention;

[0013] Figure 2 This is a working principle diagram of the random forest algorithm;

[0014] Figure 3 To analyze the predictive performance of surrogate models based on three methods: random forest, support vector machine, and radial basis neural network;

[0015] Figure 4 The basic principle diagram for improving the spectral algorithm;

[0016] Figure 5 To improve the optimization performance analysis of spectral algorithms and traditional spectral algorithms, differential evolution algorithms, and particle swarm algorithms;

[0017] Figure 6 Comparison of optimization time between the random forest-based proxy model and the original model;

[0018] Figure 7 Power density curves of the random forest-based proxy model and the original model. Specific implementation method:

[0019] In order to facilitate the understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thoroughly understood.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0021] The method for optimizing the power density and operating parameters of a proton exchange membrane fuel cell based on random forest and improved spectral algorithm described in the present invention has the following overall technical process: Figure 1 As shown, the specific steps include:

[0022] Step 1: Establish a mathematical model of electrochemical reactions in the proton exchange membrane fuel cell stack.

[0023] The following unavoidable losses occur during the electrochemical reaction of a proton exchange membrane fuel cell: activation loss, ohmic loss, and concentration loss. The actual voltage output voltage V cell It can be expressed as:

[0024] V cell =E Nernst -V act -V ohm -V con (1)

[0025] Where E Nernst is the open circuit voltage; V act 、V ohm and V con represent activation loss, ohmic loss and concentration loss respectively;

[0026] E Nernst Calculated by the Nernst equation:

[0027]

[0028] Where T st is the operating temperature of the battery stack; is the effective partial pressure of anode hydrogen; is the effective partial pressure of oxygen at the cathode.

[0029]

[0030] RH an and RH ca are the relative humidity of the anode and cathode respectively; P an and P ca are the inlet pressures of the anode and cathode, respectively; is the saturated vapor pressure of water, which can be described by the following formula:

[0031]

[0032] The expression of activation loss is:

[0033]

[0034] Among them, ξ1, ξ2, ξ3, ξ4 are empirical parameters; Ix t is the operating current of the battery stack; is the dissolved oxygen concentration, which can be calculated by Henry's theorem, namely:

[0035]

[0036] Ohmic loss can be expressed as:

[0037] V ohm =I st ·R m (8)

[0038]

[0039] Where R m is the membrane impedance of a single cell; A is the active area of ​​a single cell in the stack; l is the thickness of the membrane (cm); ρ m is the resistivity of the proton exchange membrane; m Represents the water content of the proton exchange membrane; its specific function expression is as follows:

[0040]

[0041] where a an and aca are the anode and cathode water activities respectively; a m is the average water activity.

[0042] The concentration loss expression is:

[0043]

[0044] Where b is a parameter determined by the system; i and i max are the actual current density and the maximum current density respectively; the output voltage and power of the battery stack can be described as:

[0045] V st =V cell ·N cell (14)

[0046] P st =V st I st (15)

[0047] Where V cell is the voltage of a single cell; N cell It is the number of single cells in the battery stack.

[0048] Step 2: Taking the power density of the fuel cell stack as the target quantity, the operating temperature, anode pressure, cathode / anode relative humidity and current density as decision variables, the data set is obtained using matlab / simulink software.

[0049] Furthermore, a code was written in the Matlab editor to adjust the temperature (50-80°C), anode pressure (1-3 bar), cathode / anode relative humidity (50%-100%) and current density (0-1.9 A / cm 2 ) Generate several uniform random arrays within the specified range, substitute these decision variables into the Simulink model to get the corresponding power density values, and save these decision variables and target quantities as data sets in the Matlab workspace.

[0050] Step 3: Use the random forest algorithm to train and predict the data set to obtain the proxy model. At the same time, compare the mean absolute error, mean square error and determination coefficient of the three machine learning proxy models of the random forest algorithm, support vector machine and radial basis neural network.

[0051] Furthermore, the random forest algorithm performs prediction and regression analysis by building multiple decision trees and integrating them, which has good robustness because it reduces the overfitting risk of a single decision tree by merging multiple decision trees. It also has high interpretability, can handle large-scale data sets, and can be trained and predicted efficiently.

[0052] Figure 2 The figure shows the working principle of the PEMFC proxy model based on random forest. First, the TreeBagger function in matlab is used to randomly divide the data set obtained in Step 2 into a training set and a test set at a ratio of 8:2. The regression method is used, the number of decision trees is set to 100, the minimum number of leaf node samples is 1, and 5 features are randomly selected for each tree for training. Then the test set is brought into the training set to calculate the mean absolute error, mean square error, and determination coefficient of the proxy model.

[0053] The basic steps of the random forest algorithm can be expressed as:

[0054] (1) Randomly select a portion of samples from the original data set (with replacement sampling) to form a smaller training set.

[0055] (2) Construct a decision tree using the selected samples and feature subsets. The decision tree construction process is based on feature splitting, aiming to divide the samples into subsets with similar target variables. At the same time, for each decision tree construction, a portion of features are randomly selected from all features as candidate features.

[0056] (3) Repeat steps 1 and 2 to build multiple decision trees to form a forest. Each decision tree learns and predicts independently. In regression problems, the most commonly used integration strategy is to take the average of the decision tree prediction results as the final regression prediction result.

[0057] Figure 3 The prediction performance of the surrogate model based on three methods, random forest, support vector machine, and radial basis neural network, is analyzed. The training time of random forest is 0.3s, while the training time of support vector machine and radial basis neural network is 2.2s and 169.2s respectively. The maximum error between the surrogate model based on random forest and the original model is 0.0966, which is 53% and 36% lower than that of support vector machine and radial basis neural network respectively. The mean absolute error, mean square error and coefficient of determination of the random forest algorithm are also lower than those of the other two.

[0058] Step 4: Optimize the prediction results by combining the improved spectral algorithm, and compare the optimization performance of the improved spectral algorithm with the traditional spectral algorithm, particle swarm algorithm and differential evolution algorithm. Predict the maximum power density and the corresponding operating parameter set, and compare the optimization time of the original model and the proxy model.

[0059] The improved spectral algorithm optimizes the input variables of the proxy model (temperature, anode pressure, cathode / anode relative humidity and current density) and substitutes them into the proxy model to compare the output values ​​(power density) of the proxy model. The input corresponding to the optimal output value is the current optimal solution, and the current optimal solution is then fed back into the algorithm for optimization until the final number of iterations is reached.

[0060] Furthermore, the principle of improving the spectral algorithm can be expressed as:

[0061] Initialization: The search process of the improved spectral algorithm starts with random initialization of white light, and the mathematical expression is:

[0062]

[0063] in is the initial white light; X rand is an array of random numbers uniformly distributed between [0, 1]; d is X rand lb and ub are the lower and upper bounds of the search space respectively;

[0064] In the optimization of the power density and operating parameters of the proton exchange membrane fuel cell, lb and ub are the upper and lower limits of the set operating temperature, anode pressure, cathode / anode relative humidity and current density respectively; through the above initialization steps, several (depending on the number of set initial white lights) initial operating parameters are formed, namely The matrix is ​​constructed and the fitness function value of each initial operating parameter is calculated; the current optimal solution is selected, and then the algorithm iteration is entered through the following steps;

[0065] Rainbow ray vector calculation; after initialization, internal refraction Internal reflection External Refraction The normal vector is calculated as:

[0066]

[0067] in is a solution randomly selected from the current population when the number of iterations is g; is the current solution when the number of iterations is g; is the global optimal solution; norm() represents the normalized value of the vector and is calculated according to the following formula:

[0068]

[0069] Where d represents the dimension of the optimization problem; is the input vector of the norm function; used to normalize it; m j is the input vector The jth dimension in ; for the incident ray, the calculation is as follows:

[0070]

[0071] in is the incident ray; M is the average value of the current solution N is the population size;

[0072] Then, the vectors for the inner and outer refracted and reflected rays are calculated as:

[0073]

[0074] in and They are internal refraction, internal reflection and external refraction rays; k r Represents the refractive index:

[0075] k r =X rand (k red -k violet ) (26)

[0076] where k red is the refractive index of red light; k violet is the refractive index of violet light;

[0077] Generation of new colored rays; Generate new colorful rays by designing scaling factors and adaptive control factors:

[0078]

[0079] GI=P-1(a,1) (29)

[0080] GI1=0.2·GI·a (30)

[0081] GI2=10·GI·a (31)

[0082] GI3=GI4=50·GI·a (32)

[0083] GI5=5·GI·a (33)

[0084]

[0085] in is the newly generated candidate solution; is the current candidate solution when the number of iterations is g; and are four solutions randomly selected from the current population; p, q, and X rand是A random number between 0 and 1; g is the current iteration number; G is the maximum iteration number; a and GI are adaptive control factors;

[0086] Scattering of colored light; the mathematical formula for the first scattering stage is as follows:

[0087]

[0088] in is the newly generated candidate solution; This is the best solution so far; and are two solutions randomly selected from the current population; the predetermined probability β helps to move the current solution in the direction of the best solution so far;

[0089] The mathematical formula for the second scattering stage is as follows:

[0090]

[0091] in is the newly generated candidate solution; π is the circumference of a circle; the exchange between the first and second scattering stages is based on a predefined probability P e It is implemented as shown below:

[0092]

[0093] in is the newly generated candidate solution;

[0094] The third scattering phase is based on generating new solutions based on randomly selected solutions from the population and the current solution, and its formula is:

[0095]

[0096] in is the newly generated candidate solution; and are three solutions randomly selected from the current population; is a vector containing random values ​​0 and 1;

[0097]

[0098] Where F is the difference between the fitness value of each solution and the fitness value of the best solution so far; f, f best and f worst Respectively represent the fitness values ​​of the current solution, the best solution so far, and the worst solution;

[0099]

[0100] in is the newly generated candidate solution; P s is a predefined probability.

[0101] The improved spectrum optimization algorithm is based on the refraction phenomenon that occurs when light propagates through materials with different refractive indices. When sunlight propagates from one material to another, it is refracted and dispersed into Figure 4 The rainbow spectrum shown.

[0102] Figure 5 The figure shows the performance comparison between the improved spectral algorithm and other algorithms. The convergence curve of the improved spectral algorithm is better than that of the traditional spectral algorithm. This is because the different data ranges of the five characteristic variables lead to poor population differences in the traditional spectral algorithm. The improved method of the present invention can improve the differences between populations and find the optimal solution more quickly. The improved spectral algorithm completed convergence in the 57th iteration, which is 50.4% and 33.8% faster than the differential evolution algorithm and the particle swarm algorithm, and the best fitness value is also higher than these two.

[0103] Figure 6 The figure shows the optimization time comparison between the random forest-based proxy model and the original model. The combination of the number of iterations and the number of rays is shown in Table 1. Figure 6 As shown in Figure 2, the optimization time increases with the number of iterations and rays. The average optimization time of the proxy model is 1716.3s, which is 44.8% less than the original model (3110.3s).

[0104] Table 1 Combinations of iteration times and number of rays.

[0105]

[0106] Figure 7 The power density curves of the proxy model based on random forest and the original model are shown. The relative error between the proxy model and the original model is kept within 2.5%, and the current density at the optimal power density point is 1.77A / cm 2 .

[0107] The present invention uses five different target powers of 5, 10, 15, 20 and 25 kW as objective functions, and predicts their corresponding operating parameters as shown in Table 2.

[0108] To deal with this changing target power optimization problem, the fitness function of the improved spectral algorithm is as follows:

[0109]

[0110] Among them, Pr is the predicted value, TP is the target power value, A active is the activation area of ​​PEMFC. The relative errors between the five predicted values ​​and the target power density value are kept below 0.16%, which ensures the accuracy of the present invention.

[0111] Table 2 Prediction parameters under different target powers

[0112]

[0113] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0114] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A method for optimizing the power density and operating parameters of a proton exchange membrane fuel cell, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of electrochemical reaction of proton exchange membrane fuel cell stack; Step 2: Taking the power density of the battery stack as the target quantity, the operating temperature, anode pressure, cathode / anode relative humidity and current density as decision variables, the data set is obtained using matlab / simulink software; Step 3: Use the random forest algorithm to train and predict the data set to obtain the proxy model. At the same time, compare the mean absolute error, mean square error and determination coefficient of the three machine learning proxy models of random forest, support vector machine and radial basis neural network; Step 4: Optimize the prediction results by combining the improved spectral algorithm, and compare the optimization performance of the improved spectral algorithm with the traditional spectral algorithm, particle swarm algorithm and differential evolution algorithm; predict the maximum power density and the corresponding operating parameter set, and compare the optimization time of the original model and the proxy model.

2. The method according to claim 1, characterized in that In the Step 1, establishing a mathematical model of electrochemical reaction of a proton exchange membrane fuel cell stack includes the following contents: In the electrochemical reaction process of proton exchange membrane fuel cells, there are the following unavoidable losses, which are activation loss, ohmic loss and concentration loss; the actual voltage output voltage V cell It can be expressed as: V cell =E Nernst -V act -V ohm -V con ; Where E Nernst is the open circuit voltage; V act 、V ohm and V con represent activation loss, ohmic loss and concentration loss respectively; E Nernst Calculated by the Nernst equation: Where T st is the operating temperature of the battery stack; is the effective partial pressure of anode hydrogen; is the effective partial pressure of cathode oxygen; RH an and Rh ca are the relative humidity of the anode and cathode respectively; P an and P ca are the inlet pressures of the anode and cathode, respectively; is the saturated vapor pressure of water, which can be described by the following formula: The expression of activation loss is: Among them, ξ1, ξ2, ξ3, ξ4 are empirical parameters; I st is the operating current of the battery stack; is the dissolved oxygen concentration, which can be calculated by Henry's theorem, namely: Ohmic loss can be expressed as: V ohm =I st ·R m ; Where R m is the membrane impedance of a single cell; A is the active area of ​​a single cell in the stack; l is the thickness of the membrane (cm); ρ m is the resistivity of the proton exchange membrane; m It represents the water content of proton exchange membrane, and its specific function expression is as follows: where a an and a ca are the anode and cathode water activities respectively; a m is the average water activity; The concentration loss expression is: Where b is a parameter determined by the system; i and i max are the actual current density and the maximum current density respectively; the output voltage and power of the battery stack can be described as: V st =V cell ·N cell ; P st =V st ·I st ; Where V cell is the voltage of a single cell; N cell It is the number of single cells in the battery stack.

3. The method according to claim 1, characterized in that In Step 3, The random forest algorithm performs prediction and regression analysis by building multiple decision trees and integrating them.

4. The method according to claim 1, characterized in that In Step 4, The principle of the improved spectral algorithm is expressed as: Initialization: The search process of the improved spectral algorithm starts with random initialization of white light, and the mathematical expression is: in is the initial white light; X rand is a row vector of random numbers uniformly distributed between [0,1]; d is X rand lb and ub are the lower and upper limits of the search space respectively; In the optimization of the power density and operating parameters of the proton exchange membrane fuel cell, lb and ub are the upper and lower limits of the set operating temperature, anode pressure, cathode / anode relative humidity and current density respectively; through the above initialization steps, several (depending on the number of set initial white lights) initial operating parameters are formed, namely The matrix is ​​constructed and the fitness function value of each initial operating parameter is calculated; the current optimal solution is selected, and then the algorithm iteration is entered through the following steps; Rainbow ray vector calculation; after initialization, internal refraction Internal reflection External Refraction The normal vector is calculated as: in is a solution randomly selected from the current population when the number of iterations is g; is the current solution when the number of iterations is g; is the global optimal solution; norm() represents the normalized value of the vector and is calculated according to the following formula: Where d represents the dimension of the optimization problem; is the input vector of the norm function, used to normalize it; m j is the input vector The jth dimension in ; for the incident ray, it is calculated as follows: in is the incident ray; M is the average value of the current solution N is the population size; The vectors for internal and external refraction and reflection rays are calculated as: in and They are internal refraction, internal reflection and external refraction rays; k r Represents the refractive index: k r =X rand (k red -k violet ); where k red is the refractive index of red light; k violet is the refractive index of violet light; Generation of new colored light; Generate new colorful light by designing scaling factor and adaptive control factor: GI=P -1 (a,1); GI1 = 0.2 GI a; GI2 = 10 GI a; GI3=GI4=50·GI·a; GI5 = 5 GI a; in is the newly generated candidate solution; is the current candidate solution when the number of iterations is g; and are four solutions randomly selected from the current population; p, q, and X rand is a random number between 0 and 1; g is the current iteration number; G is the maximum iteration number; a and GI are adaptive control factors; Scattering of colored light; the mathematical formula for the first scattering stage is as follows: in is the newly generated candidate solution; This is the best solution so far; and are two solutions randomly selected from the current population; the predetermined probability β helps to move the current solution in the direction of the best solution so far; The mathematical formula for the second scattering stage is as follows: in is the newly generated candidate solution; π is the circumference of a circle; the exchange between the first and second scattering stages is based on a predefined probability P e It is implemented as shown below: in is the newly generated candidate solution; The third scattering phase is based on generating new solutions based on randomly selected solutions from the population and the current solution, and its formula is: in is the newly generated candidate solution; and are three solutions randomly selected from the current population; is a vector containing random values ​​0 and 1; Where F is the difference between the fitness value of each solution and the fitness value of the best solution so far; f, f best and f worst Respectively represent the fitness values ​​of the current solution, the best solution so far, and the worst solution; in is the newly generated candidate solution; P s is a predefined probability.

5. The method according to claim 1, characterized in that The input is the operating temperature, pressure, cathode / anode relative humidity and current density of the proton exchange membrane fuel cell stack, and the output is power density.

6. The method according to claim 1, characterized in that The improved spectral algorithm optimizes the input variables of the proxy model and substitutes them into the proxy model, compares the output values ​​of the proxy model, and the input corresponding to the optimal output value is the current optimal solution, which is then fed back into the algorithm for optimization; when the current number of iterations g is less than the maximum number of iterations G, g=g+1, and the above operations continue to loop; otherwise, the operation is terminated.

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