A semi-empirical model parameter optimization method and system for air-cooled pemfc

Abstract

The application provides a semi-empirical model parameter optimization method and system for air-cooled PEMFC, and belongs to the technical field of fuel cell model optimization, which comprises the following steps: inputting multiple groups of operating condition input parameters of a target air-cooled PEMFC into a parameter prediction model, and outputting multiple prediction parameters of the semi-empirical model of the air-cooled PEMFC; each group of operating conditions comprises the temperature, hydrogen pressure and current of the air-cooled PEMFC during operation; substituting the multiple prediction parameters into the corresponding semi-empirical model of the air-cooled PEMFC, and outputting multiple simulation voltages; comparing the multiple simulation voltages with the measured voltages, calculating the mean square error (MSE) of the voltages according to the comparison results, and screening out the parameter group with the minimum MSE, wherein the parameter group with the minimum MSE is the optimal semi-empirical model parameter. After the complex coupling law between the operating conditions and the model parameters is learned by the offline training of the BP neural network, only the real-time operating conditions need to be input during online application, and the corresponding model parameters can be directly output, so that the efficient parameter prediction in the millisecond level is realized.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell model optimization technology, specifically relating to a semi-empirical model parameter optimization method and system for air-cooled PEMFCs. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) are widely recognized as one of the most promising clean energy conversion devices due to their significant advantages, including high energy conversion efficiency, high specific power, rapid start-up, and zero pollution. In low-power applications such as drones and forklifts, air-cooled PEMFCs are widely used due to their simple and compact structure. The accuracy of the voltage model for these fuel cells directly affects the accuracy of system performance evaluation and the effectiveness of control strategies, making it a crucial factor that cannot be ignored in their practical application.

[0003] To better study and apply PEMFCs, semi-empirical models of proton exchange membrane hydrogen fuel cells play a crucial role. These models possess both clear physical meaning and high computational efficiency, thus occupying a core position in system simulation and control strategy design. However, to truly realize the value of this model, the accurate identification of its key parameters (such as activation coefficient, ohmic resistance, concentration polarization parameter, and water content) is a pressing problem. Currently, parameter identification faces three fundamental challenges: First, the model itself exhibits strong nonlinear dynamic characteristics, making traditional optimization methods prone to getting trapped in local optima and struggling to find the global optimum. Second, the complex coupling effects of multiple physical field variables such as temperature, pressure, and current density significantly increase the dimensionality of the parameter solution space, further complicating identification. Third, unavoidable noise interference during experimental measurements further reduces the robustness of parameter estimation, affecting the reliability of the identification results.

[0004] Among existing parameter identification methods, the traditional least squares method is prone to getting trapped in local optima under dynamic conditions, making it difficult to meet the requirements for accurate identification. While genetic algorithms (GA) possess global search capabilities and can avoid the problem of local optima to some extent, they still have fundamental limitations that are difficult to overcome: First, they are computationally inefficient, requiring tens of thousands of population iterations for a single identification, often taking minutes or even hours, which is difficult to match the rapid response required by real-time control; second, the optimization results are extremely sensitive to hyperparameters such as crossover rate and mutation rate, requiring repeated adjustments based on experience, increasing the complexity of practical applications; third, their random evolution mechanism makes it impossible to effectively control the convergence speed and stability, and in the presence of noise interference, the parameter identification error fluctuates greatly, affecting the consistency and reliability of the results.

[0005] In summary, although genetic algorithms have the advantage of global search, their population iteration mechanism requires repeated execution of complete electrochemical model simulations, resulting in inherent defects such as low computational efficiency, high hyperparameter sensitivity, and large convergence randomness. This makes it difficult to meet the millisecond-level response requirements of real-time control systems and prevents them from playing a full role in the precise optimization of parameters in PEMFC. Summary of the Invention

[0006] To address the issue of more accurate semi-empirical equation coefficients for PEMFCs, this invention provides a method for optimizing semi-empirical model parameters for air-cooled PEMFCs. This method effectively identifies the semi-empirical coefficients of air-cooled PEMFCs, while improving computational efficiency and being easy to implement.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A semi-empirical model parameter optimization method for air-cooled PEMFC includes the following steps:

[0009] Multiple sets of operating conditions of the target air-cooled PEMFC are input into the parameter prediction model, and multiple predicted parameters of the corresponding semi-empirical model of the air-cooled PEMFC are output. Specifically, the operating conditions of the air-cooled PEMFC and the output voltage of the semi-empirical model of the air-cooled PEMFC are used as inputs, and the parameters of the semi-empirical model of the air-cooled PEMFC are used as outputs to train a double-hidden-layer BP network, learn the coupling law between the operating conditions and the model parameters, and obtain the parameter prediction model. Each set of operating conditions includes the temperature, hydrogen pressure and current of the air-cooled PEMFC during operation.

[0010] Substitute multiple predicted parameters into the corresponding air-cooled PEMFC semi-empirical model to output multiple simulated voltages;

[0011] Multiple simulated voltages are compared with measured voltages, and the mean square error (MSE) of the voltage is calculated based on the comparison results. The parameter group with the smallest MSE is then selected as the optimal semi-empirical model parameter group.

[0012] Preferably, the double-hidden-layer BP network is constructed using the newff function; wherein, the first hidden layer of the double-hidden-layer BP network uses the tan-sigmoid activation function to achieve nonlinear transformation of the input features; the second hidden layer of the double-hidden-layer BP network uses a linear activation function to continuously output prediction parameters.

[0013] Preferably, before constructing the double-hidden-layer BP network using the newff function, the optimal hyperparameters of the BP neural network are searched through a double-layer loop. The optimal hyperparameters include the learning rate η and the number of hidden layer nodes. The learning rate ranges from [0.05, 1.05], and the number of hidden layer nodes is 4-18.

[0014] Based on the number of hidden layer nodes, a double-hidden-layer BP network is constructed using the newff function.

[0015] Preferably, the Levenberg-Marquardt second-order optimization algorithm is used to train the two-hidden-layer BP network based on the learning rate η.

[0016] Preferably, before training the dual-hidden-layer BP network, the operating conditions of the air-cooled PEMFC and the output voltage of the air-cooled PEMFC semi-empirical model are used as inputs and the parameters of the air-cooled PEMFC semi-empirical model are used as outputs. The normalization process is also included for the temperature, hydrogen pressure and current of the air-cooled PEMFC during operation.

[0017] Preferably, the semi-empirical model of the air-cooled PEMFC is:

[0018] (1)

[0019] In the formula, Represents the output voltage of a single battery cell. Represents Nernst voltage. Represents activation loss, Represents ohmic loss, Represents concentration loss;

[0020] in,

[0021] (2)

[0022] (3)

[0023] (4)

[0024] (5)

[0025] (6)

[0026] (7)

[0027] In the formula, , , and The activation coefficient is... For membrane impedance, For moisture content, For concentration polarization parameters, For limiting current density, R For gas molar constants, n The number of electrons transferred in the reaction. F It is Faraday's constant. T Operating temperature I This is the operating current. The equivalent resistivity of the proton exchange membrane. The thickness of the proton exchange membrane. A To activate the current area, J For current density, The equivalent impedance at the load end. p For the pressure of each component, Oxygen concentration; H 2 represents hydrogen gas. The total impedance within the fuel cell, For the partial pressure of oxygen, H 2 O For water;

[0028] in, , , , , , , and These are the eight semi-empirical model parameters that need to be identified.

[0029] This invention also proposes a semi-empirical model parameter identification system for air-cooled PEMFCs, comprising:

[0030] The prediction parameter acquisition module is used to input multiple sets of operating conditions of the target air-cooled PEMFC into the parameter prediction model and output multiple prediction parameters of the corresponding air-cooled PEMFC semi-empirical model. Specifically, the operating conditions of the air-cooled PEMFC and the output voltage of the air-cooled PEMFC semi-empirical model are used as inputs, and the parameters of the air-cooled PEMFC semi-empirical model are used as outputs to train a double-hidden-layer BP network, learning the coupling relationship between the operating conditions and the model parameters to obtain the parameter prediction model. Each set of operating conditions includes the temperature, hydrogen pressure, and current during the operation of the air-cooled PEMFC.

[0031] The simulation voltage acquisition module is used to substitute multiple predicted parameters into the corresponding air-cooled PEMFC semi-empirical model and output multiple simulation voltages.

[0032] The parameter optimization module is used to compare multiple simulated voltages with measured voltages, calculate the mean square error (MSE) of the voltage based on the comparison results, and select the parameter group with the smallest MSE. The parameter group with the smallest MSE is the optimal semi-empirical model parameter.

[0033] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement any of the steps in the semi-empirical model parameter optimization method for air-cooled PEMFC.

[0034] The present invention also provides a computer-readable storage medium storing a computer program that, when loaded by a processor, can execute any of the steps in the semi-empirical model parameter optimization method for air-cooled PEMFC.

[0035] The semi-empirical model parameter optimization method for air-cooled PEMFCs provided by this invention has the following beneficial effects:

[0036] The BP neural network proposed in this invention, after offline training to learn the complex coupling relationship between operating conditions and model parameters, allows for direct output of corresponding model parameters during online applications, requiring only real-time operating conditions as input. Unlike traditional methods such as genetic algorithms, it eliminates the need for iterative simulations, avoiding the inherent hyperparameter sensitivity and convergence randomness issues of genetic algorithms. This achieves millisecond-level efficient parameter prediction, meeting real-time control requirements. The predicted parameters are substituted into a semi-empirical model to obtain the simulated voltage, which is then compared with the measured voltage to calculate the mean square error (MSE). The parameter set with the smallest MSE is selected to determine the optimal semi-empirical model parameters, ensuring parameter accuracy. Attached Figure Description

[0037] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of the semi-empirical model parameter optimization method for air-cooled PEMFC according to Embodiment 1 of the present invention;

[0039] Figure 2 Schematic diagram of parameter identification using a BP neural network;

[0040] Figure 3 This is a diagram of the internal structure of a BP neural network.

[0041] Figure 4 Train the regression curve for the BP neural network;

[0042] Figure 5 The training performance graph of the BP neural network;

[0043] Figure 6 This is a training state diagram for a BP neural network.

[0044] Figure 7 This is a comparison chart of experimental voltage and simulated voltage. Detailed Implementation

[0045] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0046] Example 1

[0047] This invention provides a semi-empirical model parameter optimization method for air-cooled PEMFCs, specifically a method for parameter identification of semi-empirical models of air-cooled PEMFCs based on BP neural network regression prediction. In this invention, identification means finding the optimal parameters, such as... Figure 1 and Figure 2 As shown, the method includes the following steps:

[0048] S1 is modeled using semi-empirical equations based on the air-cooled PEMFC battery stack model.

[0049] In step S1, the air-cooled PEMFC battery stack model of the present invention adopts semi-empirical equation modeling to reflect the relationship between operating parameters and battery stack output voltage.

[0050] Due to its fast computation speed and high accuracy, the semi-empirical model of air-cooled PEMFC is often used in simulation studies at the PEMFC system level. The semi-empirical model of air-cooled PEMFC is used to obtain the output voltage of a single cell. The expression for the output voltage of a single cell in the semi-empirical model of air-cooled PEMFC is:

[0051] (1)

[0052] In the formula, Represents the output voltage of a single battery cell. Represents Nernst voltage. Represents activation loss, Represents ohmic loss, This represents concentration loss.

[0053] in,

[0054] (2)

[0055] (3)

[0056] (4)

[0057] (5)

[0058] (6)

[0059] (7)

[0060] In the formula, , , and The activation coefficient is... For membrane impedance, For moisture content, For concentration polarization parameters, For limiting current density, R For gas molar constants, n The number of electrons transferred in the reaction. F It is Faraday's constant. T Operating temperature I This is the operating current. The equivalent resistivity of the proton exchange membrane. The thickness of the proton exchange membrane. A To activate the current area, J For current density, The equivalent impedance at the load end. p For the pressure of each component, Oxygen concentration; H 2 represents hydrogen gas. The total impedance within the fuel cell, For the partial pressure of oxygen, H 2 O It is water. , , , , , , , There are 8 coefficients, which are the 8 parameters of the air-cooled PEMFC semi-empirical model. The optimal values ​​of these parameters need to be searched for later.

[0061] S2. Based on the semi-empirical model of air-cooled PEMFC established in S1, design the training and test sets for the BP neural network.

[0062] In step S2, the test set data was obtained from the polarization experiment of the air-cooled PEMFC stack. Since the training process of the BP neural network needs to cover the entire range of inputs and outputs, the range of the coefficients of the semi-empirical equation was first defined, and four sets of coefficients were selected as outputs through interpolation. The ranges of temperature, pressure, and current in the input were defined and evenly divided to obtain more data. The voltage value was determined as the input based on the semi-empirical equation in S1, thus establishing the training set of the BP neural network. The permutations and combinations of the input and output variables can yield thousands of training samples, ensuring the accuracy of the BP neural network training effect. The coefficient ranges of the semi-empirical model are shown in Table 1.

[0063] Table 1. Range of coefficients for semi-empirical equations

[0064]

[0065] The training regression curve of a BP neural network is as follows Figure 4 As shown, after 1000 training iterations, R=0.9713 was obtained, which is very close to 1, indicating a good training effect. The training performance of the BP neural network is shown in the figure below. Figure 5 As shown, after 1000 training iterations, the residual converged to 0.03, indicating that it has reached a stable stage. The training state diagram of the BP neural network is shown below. Figure 6 As shown, Figure 6 It reflects the tortuous descent of the gradient during the iteration process, the changing trend of the damping factor (mu), and checks and verifies the error rate of the training process in 1000 iterations, ensuring the effectiveness of the training.

[0066] The set temperature values ​​are 11 sets: 22℃, 26℃, 30℃, 34℃, 38℃, 42℃, 46℃, 50℃, 54℃, 58℃, and 62℃.

[0067] The hydrogen pressure was set to eight values: 40 kPa, 45 kPa, 50 kPa, 55 kPa, 60 kPa, 65 kPa, 70 kPa, and 75 kPa.

[0068] The current is set to 20 values: 2 A, 4 A, 6 A, 8 A, 10 A, 12 A, 14 A, 16 A, 18 A, 20 A, 22 A, 24 A, 26 A, 28 A, 30 A, 32 A, 34 A, 36 A, 38 A, and 40 A. Ignoring the low-temperature operating conditions under high current, 1184 input combinations can be obtained.

[0069] Given the coefficients of four sets of hypothetical semi-empirical equations, the voltage values ​​can be calculated as inputs based on the semi-empirical equation of S1, thus establishing the training set for the BP neural network, consisting of 4736 sets of data, ensuring the accuracy of the BP neural network training effect. (Based on the calculation of the corresponding voltage values ​​using the four sets of coefficients, a training set of 4736 sets of data is formed).

[0070] S3. Design the structure and internal parameters of a double-hidden-layer BP neural network, train the BP neural network using the training set, and obtain the semi-empirical coefficients using the test set.

[0071] Specifically, the double-hidden-layer BP network is trained using the operating conditions of the air-cooled PEMFC and the output voltage of the semi-empirical model of the air-cooled PEMFC as inputs and the parameters of the semi-empirical model of the air-cooled PEMFC as outputs. The coupling law between the operating conditions and the model parameters is learned to obtain the parameter prediction model. Each set of operating conditions includes the temperature, hydrogen pressure and current of the air-cooled PEMFC during operation.

[0072] In step S3, the specific construction of the BP neural network includes three parts: data preprocessing and network initialization, network search and network training, and training evaluation and testing verification. The internal structure diagram of the BP neural network is shown below. Figure 3 As shown.

[0073] The data preprocessing section normalizes the inputs and outputs of the training set, as well as the input of the test set.

[0074] (8)

[0075] This operation compresses the operating conditions of different dimensions into the [0,1] interval, eliminating the differences caused by the dimensions, laying the foundation for efficient training in the future, and avoiding training bias caused by different scales of dependent variables.

[0076] The core of the network search employs a two-layer loop for hyperparameter optimization: the learning rate η∈[0.05,1.05] is used to adjust the gradient descent step size, and the number of hidden layer nodes is adjusted by... Sure, For the number of input variables, To output the number of variables, The present invention selects a positive integer. The learning rate is ∈[1,15], therefore the number of hidden layer neurons is selected from 4 to 18 to explore the optimal structure. The values ​​of the learning rate and the number of hidden layer nodes will affect the fitting effect during the training process. Too small a value will lead to underfitting, while too large a value will lead to overfitting. It is necessary to continuously adjust to achieve a balance between model capacity and generalization. By optimizing the learning rate and the number of hidden layer nodes (4-18) through a double loop, the model capacity and generalization are balanced to avoid underfitting or overfitting, which directly affects the accuracy of parameter prediction.

[0077] The learning rate η and the number of hidden layer nodes are key parameters affecting the training performance of a backpropagation (BP) neural network. The learning rate η is a crucial hyperparameter used to adjust the gradient descent step size during BP neural network training, directly impacting the network's training efficiency and convergence performance. The learning rate η ranges from [0.05, 1.05] and is used to adjust the gradient descent step size. Its value directly affects the network's convergence speed and stability: too small a value may lead to slow training and getting stuck in local optima (underfitting); too large a value may lead to oscillating parameter updates and failure to converge (overfitting).

[0078] The number of hidden layer nodes is determined by the number of input variables (m), the number of output variables (n), and a positive integer a (a∈[1,15]), ultimately selecting 4 to 18 nodes. The number of nodes needs to be balanced between model capacity (the ability to fit complex relationships) and generalization (the ability to adapt to new data): too few nodes make it difficult to capture the coupling relationships between variables (underfitting); too many nodes may overfit the training data (overfitting).

[0079] In network training, a BP network with two hidden layers is constructed using the newff function: the first layer uses the tan-sigmoid activation function to achieve nonlinear feature transformation, and the newff function is obtained from equation (9):

[0080] (9)

[0081] The second layer uses linear activation to ensure parameter continuity, and the sample output value is obtained from equation (10):

[0082] (10)

[0083] In the formula, The weight matrix, For hidden layer input, This is the offset.

[0084] The training process uses the Levenberg-Marquardt algorithm:

[0085] (11)

[0086] In the formula, For the updated weight matrix; The Jacobian matrix reflects the sensitivity of the function output to changes in parameters; It is the damping factor; It is the identity matrix; This is the error vector, reflecting the error in the model's predictions.

[0087] A second-order Levenberg-Marquardt optimization method is employed to combine the stability of gradient descent with the fast convergence of Newton's method, with a target error of 10. -7 It efficiently solves weight updates under the condition of a maximum of 1000 iterations, ensuring the efficiency and accuracy of parameter identification.

[0088] Training evaluation and testing validation are the detection phases after training is completed. The sim function is used to perform forward propagation to calculate the predicted output. After inverse normalization, the mean square error (MSE) was calculated. train。 Next, the normalized test set data is loaded, and the resulting output parameters are denormalized. This innovatively introduces a parameter integration strategy: averaging the outputs of 20 test samples. The average value of the test sample output is taken to reduce the impact of random fluctuations, improve the parameter stability under small sample size, and further enhance the robustness of the identification results.

[0089] Backpropagation (BP) neural networks demonstrate significant advantages in PEMFC parameter identification, with their core value stemming from the breakthrough of traditional optimization paradigms through end-to-end nonlinear mapping mechanisms. Compared to iterative methods such as genetic algorithms, which require repeated solutions to high-dimensional nonconvex optimization problems, BP networks construct direct functional relationships between operating conditions (temperature, pressure, current, voltage) and model parameters (activation coefficient, proton membrane resistance, water content, etc.) through offline training. Online inference is simplified to millisecond-level forward propagation. This computation is achieved through 1000 iterations using the Levenberg-Marquardt second-order optimization algorithm, overcoming the premature convergence (getting trapped in local optima) problem caused by random evolution in genetic algorithms.

[0090] In terms of identification accuracy, the BP network combines normalization and implicit regularization techniques (structure search + early stopping mechanism) to suppress parameter identification fluctuations over a wide operating range of 22~62℃ and 40~75 kPa. Specifically, its dual-hidden-layer structure (4-18 node adaptive) accurately fits the electrochemical-thermodynamic coupling effect through the tan-sigmoid activation function. After substituting the output parameters into the semi-empirical equation, the mean square error (MSE) of voltage prediction is small, resulting in accurate identification.

[0091] S4: Find the group with the best recognition effect among multiple neural networks to achieve the best recognition of PEMFC.

[0092] Specifically, multiple sets of operating conditions of the target air-cooled PEMFC are input into the parameter prediction model, and multiple predicted parameters of the corresponding air-cooled PEMFC semi-empirical model are output. The multiple predicted parameters are substituted into the corresponding air-cooled PEMFC semi-empirical model to output multiple simulated voltages. The multiple simulated voltages are compared with the measured voltages, and the mean square error (MSE) of the voltage is calculated based on the comparison results. The parameter group with the smallest MSE is selected, and the parameter group with the smallest MSE is the optimal semi-empirical model parameter.

[0093] In step S4, the output parameters of the neural network are substituted into the semi-empirical model described in step S1 to calculate the simulated voltage of a single cell. Since the experimental stack is composed of 50 cells, multiplying this by the number of cells in the stack yields the predicted total voltage. The mean square error between the predicted voltage and the measured voltage is obtained from equation (12):

[0094] (12)

[0095] Experimental voltage With simulated voltage Comparative analysis chart as follows Figure 7 As shown, by Figure 7 It can be seen that the maximum voltage error identified by BP is 0.235 V, the maximum relative error is 0.6%, and the minimum relative error is 0.019%, which shows that it has a very good identification effect.

[0096] This allows for physical consistency verification of network performance. Finally, among the multiple neural networks optimized in two layers, the group with the smallest MSE value is selected, which represents the optimal learning rate and number of hidden layers for parameter identification, resulting in the best identification performance. The eight parameters with the best identification performance and their MSE values ​​are shown in Table 2.

[0097] Table 2 Optimal Parameter Table

[0098]

[0099] This invention transforms the traditional "simulation-based iterative optimization" paradigm into a highly efficient "offline training-online table lookup" architecture by constructing an end-to-end nonlinear mapping from operating conditions to model parameters. This method leverages the powerful function approximation capabilities of neural networks to autonomously learn multivariate coupling relationships, combining this with the LM optimization algorithm to achieve rapid convergence and effectively avoid local optima traps. Its advantages are concentrated in three aspects: In terms of computational efficiency, the forward propagation mechanism reduces online computational complexity to constant levels, achieving millisecond-level real-time response; in terms of accuracy, the fine-grained search characteristics of gradient descent combined with regularization techniques significantly improve parameter stability under noisy environments.

[0100] To address the problems of existing parameter identification methods, the backpropagation BP neural network parameter identification method proposed in this invention exhibits significant advantages, as detailed below:

[0101] Significantly improved computational efficiency: The BP neural network transforms the high-dimensional parameter identification problem into efficient forward propagation computation through an end-to-end nonlinear mapping mechanism. By utilizing normalized preprocessing, regularized training and its alternatives, as well as the LM optimization algorithm, a direct mapping from operating conditions to model parameters is established during the offline training phase. The forward propagation mechanism of the BP neural network reduces the online computational complexity to the constant level, achieving millisecond-level real-time response, meeting real-time control requirements, and solving the problem of low computational efficiency of genetic algorithms.

[0102] Significantly improved identification accuracy: The BP network, combined with normalization and implicit regularization techniques (structure search plus early stopping mechanism), effectively suppresses parameter identification fluctuations within a wide operating range of 22-62℃ and 40-75kPa. Its dual-hidden-layer structure (4-18 node adaptive) accurately fits the electrochemical-thermodynamic coupling effect through the tan-sigmoid activation function, resulting in a smaller mean square error (MSE) of voltage prediction after the output parameters are substituted into the semi-empirical equation, leading to more accurate identification and overcoming the low identification accuracy problem caused by nonlinearity and multi-physics field variable coupling in traditional methods.

[0103] Robustness Enhancement: By normalizing the data and introducing a parameter ensemble strategy (averaging the output of the test samples), the impact of random fluctuations is reduced, the parameter stability under small sample sizes is improved, the robustness of the identification results is enhanced, and the impact of noise interference on parameter estimation is reduced to some extent.

[0104] Avoiding hyperparameter sensitivity and convergence randomness: BP neural networks avoid the inherent hyperparameter sensitivity and convergence randomness problems of genetic algorithms. Their fixed weights and thresholds can be directly embedded in the controller, providing a reliable solution for high-precision identification of multi-physics coupling parameters of hydrogen fuel cells and advancing the engineering practice of digital modeling and real-time optimization control of systems.

[0105] Genetic algorithms require iterative execution of full electrochemical model simulations at the population scale, resulting in a computational efficiency difference of four orders of magnitude. Meanwhile, BP neural networks, with their gradient descent-based local fine-search capabilities, achieve higher-precision parameter identification across a wide operating range (22~62℃ / 40~75kPa) for fuel cells, avoiding the inherent hyperparameter sensitivity and convergence randomness issues of genetic algorithms. Their fixed weights and thresholds can be directly embedded into the controller, meeting the millisecond-level response requirements of real-time model predictive control (MPC). Therefore, BP neural networks, with their efficient nonlinear mapping capabilities, regularization mechanisms, and millisecond-level online response characteristics, significantly surpass genetic algorithms in computational efficiency, identification accuracy, and engineering practicality. They provide a reliable solution for high-precision identification of multi-physics coupling parameters in hydrogen fuel cells, significantly advancing the engineering practice of system digital modeling and real-time optimization control.

[0106] Based on the same inventive concept, this invention also proposes a semi-empirical model parameter identification system for air-cooled PEMFCs, comprising:

[0107] The prediction parameter acquisition module is used to input multiple sets of operating conditions of the target air-cooled PEMFC into the parameter prediction model and output multiple prediction parameters of the corresponding air-cooled PEMFC semi-empirical model. Specifically, the operating conditions of the air-cooled PEMFC and the output voltage of the air-cooled PEMFC semi-empirical model are used as inputs, and the parameters of the air-cooled PEMFC semi-empirical model are used as outputs to train a double-hidden-layer BP network, learn the coupling law between the operating conditions and the model parameters, and obtain the parameter prediction model. Each set of operating conditions includes the temperature, hydrogen pressure and current of the air-cooled PEMFC during operation.

[0108] The simulation voltage acquisition module is used to substitute multiple predicted parameters into the corresponding air-cooled PEMFC semi-empirical model and output multiple simulation voltages.

[0109] The parameter optimization module is used to compare multiple simulated voltages with measured voltages, calculate the mean square error (MSE) of the voltage based on the comparison results, and select the parameter group with the smallest MSE. The parameter group with the smallest MSE is the optimal semi-empirical model parameter.

[0110] The modules in the aforementioned semi-empirical model parameter identification system for air-cooled PEMFCs can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of a computer device in hardware form or independent of it, or stored in the memory of the computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0111] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps in the embodiment of the semi-empirical model parameter optimization method for air-cooled PEMFCs. Specific implementation methods can be found in the method embodiments, and will not be repeated here.

[0112] Furthermore, the present invention also provides a non-transitory computer-readable storage medium containing instructions on which a computer program is stored. For example, a memory containing instructions that can be executed by a processor of a computer device to perform the above-described method. For example, the non-transitory computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage device, etc. When the computer program is executed by the processor, it can implement the steps in the embodiment of the semi-empirical model parameter optimization method for air-cooled PEMFCs. Specific implementation methods can be found in the method embodiments, which will not be repeated here.

[0113] Those skilled in the art will understand that embodiments of the present invention can provide methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0114] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0115] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0116] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0117] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail in this specification and embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention; and all technical solutions and improvements that do not depart from the spirit and scope of the present invention are covered within the protection scope of the present invention patent. No reference numerals in the claims should be construed as limiting the scope of the claims. Any simple variations or equivalent substitutions of technical solutions that can be readily obtained by those skilled in the art within the scope of the technology disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A semi-empirical model parameter optimization method for air-cooled PEMFC, characterized in that, Includes the following steps: Multiple sets of operating conditions of the target air-cooled PEMFC are input into the parameter prediction model, and multiple predicted parameters of the corresponding semi-empirical model of the air-cooled PEMFC are output. Specifically, the operating conditions of the air-cooled PEMFC and the output voltage of the semi-empirical model of the air-cooled PEMFC are used as inputs, and the parameters of the semi-empirical model of the air-cooled PEMFC are used as outputs to train a double-hidden-layer BP network, learn the coupling law between the operating conditions and the model parameters, and obtain the parameter prediction model. Each set of operating conditions includes the temperature, hydrogen pressure and current of the air-cooled PEMFC during operation. Substitute multiple predicted parameters into the corresponding air-cooled PEMFC semi-empirical model to output multiple simulated voltages; Multiple simulated voltages are compared with measured voltages, and the mean square error (MSE) of the voltage is calculated based on the comparison results. The parameter group with the smallest MSE is then selected as the optimal semi-empirical model parameter group.

2. The method for parameter optimization of semi-empirical model for air-cooled PEMFC according to claim 1, characterized in that, The double-hidden-layer BP network is constructed using the newff function; wherein, the first hidden layer of the double-hidden-layer BP network uses the tan-sigmoid activation function to achieve non-linear transformation of the input features; the second hidden layer of the double-hidden-layer BP network uses a linear activation function to continuously output prediction parameters.

3. The method for parameter optimization of semi-empirical model for air-cooled PEMFC according to claim 2, characterized in that, Before constructing the double-hidden-layer BP network using the newff function, the optimal hyperparameters of the BP neural network are searched through a double-layer loop. The optimal hyperparameters include the learning rate η and the number of hidden layer nodes. The learning rate ranges from [0.05, 1.05], and the number of hidden layer nodes is 4-18. Based on the number of hidden layer nodes, a double-hidden-layer BP network is constructed using the newff function.

4. The method according to claim 3, wherein, Based on the learning rate η, the Levenberg-Marquardt second-order optimization algorithm is used to train the two-hidden-layer BP network.

5. The method of claim 4, wherein, Before training the dual-hidden-layer BP network, the operating conditions of the air-cooled PEMFC and the output voltage of the semi-empirical model of the air-cooled PEMFC are used as inputs and the parameters of the semi-empirical model of the air-cooled PEMFC are used as outputs. The normalization process is also included for the temperature, hydrogen pressure and current of the air-cooled PEMFC during operation.

6. The semi-empirical model parameter optimization method for air-cooled PEMFCs according to claim 1, characterized in that, The semi-empirical model for the air-cooled PEMFC is as follows: （1） In the formula, Represents the output voltage of a single battery cell. Represents Nernst voltage. Represents activation loss, Represents ohmic loss, Represents concentration loss; in, （2） （3） （4） （5） （6） （7） In the formula, , , and The activation coefficient is... The membrane impedance, For moisture content, For concentration polarization parameters, For limiting current density, R For gas molar constants, n The number of electrons transferred in the reaction. F It is Faraday's constant. T Operating temperature I This is the operating current. The equivalent resistivity of the proton exchange membrane. The thickness of the proton exchange membrane. A To activate the current area, J For current density, The equivalent impedance at the load end. p For the pressure of each component, Oxygen concentration, H 2 represents hydrogen gas. The total impedance within the fuel cell, For the partial pressure of oxygen, H 2 O For water; in, , , , , , , and These are the eight semi-empirical model parameters that need to be identified.

7. A semi-empirical model parameter identification system for air-cooled PEMFC, characterized in that, include: The prediction parameter acquisition module is used to input multiple sets of operating conditions of the target air-cooled PEMFC into the parameter prediction model and output multiple prediction parameters of the corresponding air-cooled PEMFC semi-empirical model. Specifically, the operating conditions of the air-cooled PEMFC and the output voltage of the air-cooled PEMFC semi-empirical model are used as inputs, and the parameters of the air-cooled PEMFC semi-empirical model are used as outputs to train a double-hidden-layer BP network, learning the coupling relationship between the operating conditions and the model parameters to obtain the parameter prediction model. Each set of operating conditions includes the temperature, hydrogen pressure, and current during the operation of the air-cooled PEMFC. The simulation voltage acquisition module is used to substitute multiple predicted parameters into the corresponding air-cooled PEMFC semi-empirical model and output multiple simulation voltages. The parameter optimization module is used to compare multiple simulated voltages with measured voltages, calculate the mean square error (MSE) of the voltage based on the comparison results, and select the parameter group with the smallest MSE. The parameter group with the smallest MSE is the optimal semi-empirical model parameter.

8. A computer device comprising a memory, a processor, and a computer program stored on the memory, wherein the computer program comprises instructions that, when executed by the processor, cause the processor to perform the method of any one of claims 1-7. The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

9. A computer readable storage medium having stored thereon a computer program, characterized in that, When the computer program is loaded by the processor, it is able to perform the steps of the method according to any one of claims 1 to 6.

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