A method for parameter identification of a proton exchange membrane fuel cell

Abstract

The application discloses a kind of proton exchange membrane fuel cell parameter identification method, belong to fuel cell technical field, comprising: definition is the parameter vector to be identified, with the error between the actual measured terminal voltage corresponding to reference true value working condition data set of predicted voltage as optimization goal, establish objective function, based on Hadamard product introduces multi-dimensional independent random vector to make follower approach adjacent better solution and current global optimal solution, introduce random disturbance term to make leader carry out big step search update, obtain global updated individual position;If the objective function value corresponding to global updated individual position has not occurred decline, then introduce inertia weight with dynamic exponential decay along with iteration number, in the neighborhood of current global updated individual position, carry out local depth search and position update to all individuals, obtain local updated individual position, retain the solution corresponding to smaller objective function value.The application solves the problem that existing technology extracts semi-empirical parameter is not accurate.

Description

Technical Field

[0001] This invention relates to a method for identifying parameters of a proton exchange membrane fuel cell, belonging to the field of fuel cell technology. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) offer advantages such as high energy conversion efficiency, zero emissions, and fast dynamic response, making them promising for applications in portable electronic devices, drones, residential backup power supplies, and fuel cell vehicles. In practical applications, achieving efficient energy management and condition monitoring requires establishing accurate PEMFC output characteristic models. Currently, semi-empirical models are commonly used to describe the output voltage characteristics of PEMFCs. These models contain several highly nonlinear unknown parameters, the values ​​of which directly determine the fitting accuracy between the model output and the actual current-voltage curve.

[0003] However, due to the complexity of actual operating conditions and the non-convex, multi-modal characteristics of the objective function corresponding to the semi-empirical model, traditional gradient-based parameter identification methods are prone to getting trapped in local optima. Existing widely used single heuristic algorithms, such as the standard particle swarm optimization algorithm and the whale optimization algorithm, generally suffer from an imbalance between global exploration and local exploitation capabilities, and are prone to premature convergence when dealing with the aforementioned high-dimensional multi-modal optimization problems. This results in insufficient accuracy of the extracted semi-empirical parameters, making it difficult to provide a reliable basis for the underlying energy management system. Summary of the Invention

[0004] The purpose of this invention is to provide a method for identifying parameters of a proton exchange membrane fuel cell. By dividing the population into leaders and followers, the followers approximate the neighboring better solutions and the current global optimum based on the multidimensional independent random vector introduced by the Hadamard product. The leaders introduce random perturbation terms to perform large-step search updates. When the objective function does not decrease after a preset number of iterations, an inertial weight that dynamically decays exponentially with the number of iterations is introduced to perform local depth search, thereby solving the problem of inaccurate extraction of semi-empirical parameters in the prior art.

[0005] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution.

[0006] This invention provides a method for identifying parameters of a proton exchange membrane fuel cell, comprising:

[0007] Based on the operating data of proton exchange membrane fuel cell stacks under different load conditions, a benchmark true value operating condition dataset is constructed.

[0008] A semi-empirical output voltage prediction model is established in the control unit, and the parameters of the proton exchange membrane fuel cell that cannot be directly measured are defined as parameter vectors to be identified.

[0009] Based on the parameter vector to be identified, a semi-empirical output voltage prediction model is used to predict and output the predicted voltage of the proton exchange membrane fuel cell stack.

[0010] An objective function is established with the error between the predicted voltage and the actual measured terminal voltage corresponding to the reference true operating condition dataset as the optimization objective.

[0011] Within the physical boundary of the parameter vector to be identified, the individual position corresponds to a candidate solution of the parameter vector to be identified. Several individuals are uniformly generated using pseudo-random numbers to construct an initial population, and the position of the individual with the smallest objective function value in the initial population is taken as the initial global optimal solution.

[0012] Repeat the following steps until the preset maximum number of iterations is reached, and extract the optimal solution of the current round as the parameters of the proton exchange membrane fuel cell:

[0013] Leaders and followers are determined based on the objective function values ​​corresponding to the positions of individuals in the current population.

[0014] Based on the Hadamard product, a multidimensional independent random vector is introduced to enable the followers to approach the neighboring better solutions and the current global best solution. A random perturbation term is introduced to enable the leader to perform a large-step search update and obtain the individual position after the global update.

[0015] If the objective function value corresponding to the globally updated individual position does not decrease in a series of iterations with a preset number of iterations, then an inertial weight that dynamically decays exponentially with the number of iterations is introduced. In the neighborhood of the currently globally updated individual position, a local depth search and position update are performed on all individuals to obtain the locally updated individual position.

[0016] The solution with the smaller objective function value among the globally updated and locally updated individual positions is retained as the global optimal solution for the next round.

[0017] Furthermore, the baseline true condition dataset, constructed based on the operating data of the proton exchange membrane fuel cell stack under different load conditions, includes:

[0018] Real-time operating data of proton exchange membrane fuel cell stacks under different load conditions are collected through a sensor network.

[0019] The operating data includes at least the stack operating temperature, anode hydrogen inlet pressure, cathode oxygen inlet pressure, stack output current, and actual measured terminal voltage of the stack.

[0020] By performing operating condition data preprocessing on the operating data, a benchmark true operating condition dataset is constructed.

[0021] Furthermore, the parameter vector to be identified is represented as follows:

[0022] ;

[0023] In the formula, To characterize the fundamental thermodynamic activation coefficient of a proton exchange membrane fuel cell under reference conditions, The temperature-dependent activation coefficient is used to characterize the effect of the operating temperature of a proton exchange membrane fuel cell stack on the activation reaction kinetics. To characterize the effect of cathode reactive gas concentration on activation pressure drop in proton exchange membrane fuel cells, the concentration-dependent activation coefficient is used. The charge transfer activation coefficient is used to characterize the effect of the load current on the activation voltage drop in a proton exchange membrane fuel cell. Indicates the water content inside the membrane. Indicates the equivalent contact resistance. This represents the concentration polarization coefficient.

[0024] Furthermore, the predicted voltage of the proton exchange membrane fuel cell stack is expressed as:

[0025] ;

[0026] In the formula, This represents the predicted voltage of the proton exchange membrane fuel cell stack. Represents the ideal open-circuit voltage. This represents the ohmic polarization voltage drop. This represents the activation polarization voltage drop. Indicates concentration polarization voltage drop;

[0027] The ideal open-circuit voltage is expressed as:

[0028] ;

[0029] In the formula, Indicates the operating temperature of the fuel cell stack. Let e ​​represent the logarithmic function with base e. This indicates the hydrogen inlet pressure at the anode. Indicates the cathode oxygen inlet pressure;

[0030] The ohmic polarization voltage drop is expressed as:

[0031] ;

[0032] ;

[0033] ;

[0034] In the formula, Indicates the output current of the fuel cell stack. This represents the overall equivalent ohmic resistance of the proton exchange membrane. The resistivity of a proton exchange membrane is represented by its resistance. Indicates the thickness of the proton exchange membrane. Indicates the effective area of ​​the membrane. This represents the natural exponential function. Indicates the equivalent contact resistance;

[0035] The activation polarization voltage drop is expressed as:

[0036] ;

[0037] In the formula, Indicates the effective molar concentration of the gas;

[0038] The concentration polarization voltage drop is expressed as:

[0039] ;

[0040] In the formula, This represents the limiting current density.

[0041] Furthermore, the objective function is expressed as:

[0042] ;

[0043] In the formula, Describe the objective function. Indicates the total number of sampling points. Indicates the first The actual measured terminal voltage at each sampling point Based on the parameter vector to be identified The predicted voltage of the proton exchange membrane fuel cell stack was calculated.

[0044] Furthermore, leaders and followers are assigned based on the objective function values ​​of each individual in the current population, including:

[0045] Sort the individuals in the current population in ascending order according to the objective function value, and assign the top 100 individuals as leaders and the remaining individuals as followers.

[0046] Furthermore, based on the Hadamard product, a multidimensional independent random vector is introduced to enable followers to approach neighboring better solutions and the current global optimum. A random perturbation term is introduced to enable the leader to perform large-step search updates, obtaining the globally updated individual positions, including:

[0047] Calculate the average position of the leader in the current iteration based on the leader's position;

[0048] Based on the current position of each follower, the position of the next better individual, the average position of the leader, and the optimal solution of the current round, an independent multidimensional random weight vector is introduced and a Hadamard product is performed to obtain the initial updated position of the follower.

[0049] Based on the current position of each leader and the upper and lower limits of the parameter search space, a random perturbation term is introduced to perform a global jump search to obtain the initial updated position vector of the leader.

[0050] The initial updated position vectors of the followers and the initial updated position vectors of the leader are compared with the physical boundaries of the parameters to be identified, and boundary constraint projection processing is performed on the dimensions that exceed the physical boundaries to obtain the globally updated individual positions.

[0051] Furthermore, the average position of the leader in the current iteration round is represented as:

[0052] ;

[0053] In the formula, Indicates the first The average position of the leader in each iteration round. Indicates the number of leaders. Indicates the first In the nth iteration A leader's position;

[0054] The update formula for the initial position update of the follower is expressed as:

[0055] ;

[0056] In the formula, Indicates the first In the nth iteration The position of a follower Indicates the first In the nth iteration The position of a follower Indicates the first The position of the previous follower adjacent to the current follower in the next iteration. It represents the Hadamah accumulation. This is an independent random vector used to regulate how followers approximate the positions of neighboring, better individuals. Let A be an independent random vector used to adjust the approximation of followers toward the current globally optimal individual position. For the first The optimal position of the leader in the next iteration.

[0057] Furthermore, an inertial weight that dynamically decays exponentially with the number of iterations is introduced. Within the neighborhood of the currently globally updated individual position, a local depth search and position update are performed on all individuals to obtain the locally updated individual positions, including:

[0058] A local search neighborhood is constructed with the current global best individual position as the center. An exponentially decaying inertia weight coefficient is generated based on the current iteration number, and the individual velocity of each individual is initialized.

[0059] Based on the historical best position and the current global best position of each individual, an independent multidimensional random weight vector is introduced to update the individual velocity of each individual, and the individual position is locally searched and updated based on the updated individual velocity to obtain the initial local updated position of the individual.

[0060] The preliminary local update position is compared with the physical boundary of the parameter to be identified, and boundary constraint projection processing is performed on the dimension that exceeds the physical boundary to obtain the locally updated individual position.

[0061] Furthermore, the update formula for the initial local update position of the individual is expressed as:

[0062] ;

[0063] In the formula, For the first The first update in the next iteration The individual position of a leader For the first In the nth iteration The current individual position of a leader Let be an independent random vector used to adjust the intensity of the random perturbation. This is used to generate independent random vectors with random offsets within a search space bounded by upper and lower limits. It represents the Hadamah accumulation. and These are the upper limit and lower limit of the physical boundary of the parameter to be identified, respectively.

[0064] The exponentially decaying inertia weighting coefficient is expressed as:

[0065] ;

[0066] In the formula, For the first The exponentially decaying inertia weight coefficient generated in the next iteration. The inertia weights are preset for the initial iteration. This is the weight decay coefficient;

[0067] The individual velocity is expressed as:

[0068] ;

[0069] In the formula, Indicates the first In the nth iteration The updated velocity vector of each individual Indicates the first The velocity vector of -1 iterations; Individual cognitive learning factors that guide individuals toward their historical best position. A social experience learning factor that guides individuals to approach the optimal position of the group. Individual experience random numbers are used to assign random perturbation weights to individual cognitive items. A globally empirical random number to which random perturbation weights are assigned to the social experience terms. For the first The individual in the first The historical best position in -1 iterations For the group in the first The global historical best position in -1 iterations This is the solution corresponding to the smaller objective function value between the globally updated individual positions and the locally updated individual positions;

[0070] The locally updated individual position is represented as follows:

[0071] ;

[0072] In the formula, This indicates the individual's position after a partial update.

[0073] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0074] 1. This invention constructs a benchmark true value dataset based on the operating data of the fuel cell stack under different load conditions, and establishes a semi-empirical output voltage prediction model. The objective function is constructed with the error between the predicted voltage and the actual measured terminal voltage as the optimization objective. An initial population is randomly generated within the physical boundary of the parameters, and an initial global optimum is determined. A global search is adopted, which introduces multi-dimensional independent random vectors based on the Hadamard product to make the followers approach the adjacent better solutions and the current global optimum. At the same time, a random perturbation term is introduced to make the leader perform large-step search updates. When there is no improvement in continuous iterations, an inertial weight that dynamically decays exponentially with the number of iterations is introduced to perform local depth search. This achieves a dynamic balance between global exploration and local development capabilities, effectively avoids the problems of traditional methods being prone to local optima and premature convergence, and significantly improves the identification accuracy of unknown parameters of the semi-empirical model.

[0075] 2. This invention introduces multidimensional independent random vectors based on the Hadamard product to enable followers to approach neighboring better solutions and the current global optimum. At the same time, it introduces random perturbation terms to enable the leader to perform large-scale search updates. In the global search phase, it achieves collaborative local convergence of followers and large-scale exploration of the leader, avoiding the problem of imbalance between global exploration and local development capabilities in traditional single heuristic algorithms.

[0076] 3. When the objective function value does not decrease in a series of preset iterations, this invention introduces an inertial weight that dynamically decays exponentially with the number of iterations. This weight performs a local depth search and position update on all individuals in the neighborhood of the currently globally updated individual position, so that the algorithm automatically switches to fine search when it gets stuck. This effectively overcomes the defect of premature convergence in traditional methods. Attached Figure Description

[0077] Figure 1 This is a schematic flowchart of a method for identifying parameters of a proton exchange membrane fuel cell provided in an embodiment of the present invention;

[0078] Figure 2 This is a schematic diagram comparing the fitting effects provided in an embodiment of the present invention. Detailed Implementation

[0079] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0080] Example 1

[0081] like Figure 1 As shown in the figure, this embodiment introduces a method for identifying parameters of a proton exchange membrane fuel cell, including:

[0082] Step 1: Based on the operating data of the proton exchange membrane fuel cell stack under different load conditions, construct a benchmark true value operating condition dataset.

[0083] This embodiment constructs a benchmark true value operating condition dataset based on the operating data of the proton exchange membrane fuel cell stack under different load conditions. It can use the measured data of the real stack during the variable load process to form a standard reference system covering the actual working range of the stack, providing a true value comparison basis consistent with the physical characteristics of the stack for parameter identification.

[0084] Step 2: Establish a semi-empirical output voltage prediction model in the control unit, and define the proton exchange membrane fuel cell parameters that cannot be directly measured as parameter vectors to be identified.

[0085] In this embodiment, a semi-empirical output voltage prediction model is established in the control unit, and the parameters of the proton exchange membrane fuel cell that cannot be directly measured are defined as parameter vectors to be identified. Unmeasurable parameters such as membrane water content, catalyst active surface area, and ohmic internal resistance inside the stack can be explicitly expressed as adjustable variables of the model, thus transforming the parameter identification problem into a mathematical matching problem between the model output and the measured data.

[0086] Step 3: Based on the parameter vector to be identified, make a prediction based on the semi-empirical output voltage prediction model, and output the predicted voltage of the proton exchange membrane fuel cell stack.

[0087] This embodiment predicts and outputs the predicted voltage of the proton exchange membrane fuel cell stack based on a semi-empirical output voltage prediction model using the parameter vector to be identified. It can map the changes in the parameters to be identified into the numerical response of the terminal voltage through forward calculation of the model, providing a directly comparable voltage output value for quantitatively evaluating the accuracy of parameter estimation.

[0088] Step 4: Establish an objective function with the error between the predicted voltage and the actual measured terminal voltage corresponding to the reference true operating condition dataset as the optimization objective.

[0089] This embodiment establishes an objective function with the error between the predicted voltage and the actual measured terminal voltage corresponding to the benchmark true operating condition dataset as the optimization objective. This realizes the quantification of the parameter identification task into a single numerical index, so that the advantages and disadvantages of different parameter combinations can be directly sorted by the error magnitude, which facilitates the optimization algorithm to iteratively seek the best.

[0090] Step 5: Within the physical boundary of the parameter vector to be identified, the individual position corresponds to a candidate solution of the parameter vector to be identified. Several individuals are uniformly generated using pseudo-random numbers to construct an initial population, and the position of the individual with the smallest objective function value in the initial population is taken as the initial global optimal solution.

[0091] In this embodiment, within the physical boundary of the parameter vector to be identified, the individual position corresponds to a candidate solution of the parameter vector to be identified. Several individuals are uniformly generated using pseudo-random numbers to construct an initial population, and the position of the individual with the smallest objective function value in the initial population is taken as the initial global optimal solution. This can ensure that the initial search is uniformly covered within the feasible region of the parameters, avoid the bias introduced by artificial initial values, and lock the optimal estimation direction in advance in the initial stage.

[0092] Step Six: Repeat the following steps until the preset maximum number of iterations is reached, and extract the optimal solution of the current round as the parameters of the proton exchange membrane fuel cell:

[0093] Leaders and followers are determined based on the objective function values ​​corresponding to the positions of individuals in the current population.

[0094] Based on the Hadamard product, a multidimensional independent random vector is introduced to enable the followers to approach the neighboring better solutions and the current global best solution. A random perturbation term is introduced to enable the leader to perform a large-step search update and obtain the individual position after the global update.

[0095] If the objective function value corresponding to the globally updated individual position does not decrease in a series of iterations with a preset number of iterations, then an inertial weight that dynamically decays exponentially with the number of iterations is introduced. In the neighborhood of the currently globally updated individual position, a local depth search and position update are performed on all individuals to obtain the locally updated individual position.

[0096] The solution with the smaller objective function value among the globally updated and locally updated individual positions is retained as the global optimal solution for the next round.

[0097] This embodiment repeats the iterative steps until a preset maximum number of iterations is reached, and the optimal solution of the current round is extracted as the parameters of the proton exchange membrane fuel cell. Leaders and followers are set according to the objective function values ​​corresponding to the positions of each individual in the current population. Based on the Hadamard product, a multidimensional independent random vector is introduced to make followers approximate neighboring better solutions and the current global optimal solution. A random perturbation term is introduced to make the leader perform large-scale search updates to obtain the globally updated individual positions. This enables a well-defined adaptive search mechanism among different individuals, where followers perform local refinement and convergence while the leader maintains a large exploration capability, preventing the population from prematurely falling into local optima. If, after a preset number of iterations, the objective function value corresponding to the globally updated individual position is obtained... If the objective function value does not decrease, an inertial weight that dynamically decays exponentially with the number of iterations is introduced. A local depth search and position update are performed on all individuals in the neighborhood of the currently globally updated individual position to obtain the locally updated individual position. When the search stalls, the local development intensity can be automatically enhanced. The search step size is gradually reduced by the decaying inertial weight to deeply explore the region near the optimal solution. The solution with the smaller objective function value between the globally updated individual position and the locally updated individual position is retained as the global optimal solution for the next round. This ensures that the better result of the two update mechanisms is inherited in each iteration, so that the global optimal solution continuously approaches the true parameters and finally outputs high-precision proton exchange membrane fuel cell parameter identification values.

[0098] Example 2

[0099] Based on the same inventive concept as Example 1, this example introduces a method for identifying parameters of a proton exchange membrane fuel cell, including:

[0100] Step 1: Based on the operating data of the proton exchange membrane fuel cell stack under different load conditions, construct a benchmark true condition dataset.

[0101] Step 1.1: Collect real-time operating data of the proton exchange membrane fuel cell stack under different load conditions through a sensor network.

[0102] In this embodiment, the operating data includes at least the stack operating temperature, anode hydrogen inlet pressure, cathode oxygen inlet pressure, stack output current, and actual measured terminal voltage of the stack.

[0103] Step 1.2: Construct a baseline true value operating condition dataset by performing operating condition data preprocessing on the operating data.

[0104] Step 2: Establish a semi-empirical output voltage prediction model in the control unit, and define the proton exchange membrane fuel cell parameters that cannot be directly measured as parameter vectors to be identified.

[0105] In this embodiment, the parameter vector to be identified is represented as:

[0106] ;

[0107] In the formula, To characterize the fundamental thermodynamic activation coefficient of a proton exchange membrane fuel cell under reference conditions, The temperature-dependent activation coefficient is used to characterize the effect of the operating temperature of a proton exchange membrane fuel cell stack on the activation reaction kinetics. To characterize the effect of cathode reactive gas concentration on activation pressure drop in proton exchange membrane fuel cells, the concentration-dependent activation coefficient is used. The charge transfer activation coefficient is used to characterize the effect of the load current on the activation voltage drop in a proton exchange membrane fuel cell. Indicates the water content inside the membrane. Indicates the equivalent contact resistance. This represents the concentration polarization coefficient.

[0108] Step 3: Based on the parameter vector to be identified, make a prediction based on the semi-empirical output voltage prediction model and output the predicted voltage of the proton exchange membrane fuel cell stack.

[0109] In this embodiment, the predicted voltage of the proton exchange membrane fuel cell stack is expressed as:

[0110] ;

[0111] In the formula, This represents the predicted voltage of the proton exchange membrane fuel cell stack. Represents the ideal open-circuit voltage. This represents the ohmic polarization voltage drop. This represents the activation polarization voltage drop. This represents the concentration polarization voltage drop.

[0112] In this embodiment, the ideal open-circuit voltage is expressed as:

[0113] ;

[0114] In the formula, Indicates the operating temperature of the fuel cell stack. Let e ​​represent the logarithmic function with base e. This indicates the hydrogen inlet pressure at the anode. This indicates the oxygen inlet pressure at the cathode.

[0115] In this embodiment, the ohmic polarization voltage drop is expressed as:

[0116] ;

[0117] ;

[0118] ;

[0119] In the formula, Indicates the output current of the fuel cell stack. This represents the overall equivalent ohmic resistance of the proton exchange membrane. The resistivity of a proton exchange membrane is represented by its resistance. Indicates the thickness of the proton exchange membrane. Indicates the effective area of ​​the membrane. This represents the natural exponential function. This represents the equivalent contact resistance.

[0120] In this embodiment, the activation polarization voltage drop is expressed as:

[0121] ;

[0122] In the formula, This indicates the effective molar concentration of the gas.

[0123] In this embodiment, the concentration polarization voltage drop is expressed as:

[0124] ;

[0125] In the formula, This represents the limiting current density.

[0126] Step 4: Establish an objective function with the error between the predicted voltage and the actual measured terminal voltage corresponding to the reference true operating condition dataset as the optimization objective.

[0127] In this embodiment, the objective function is expressed as:

[0128] ;

[0129] In the formula, Describe the objective function. Indicates the total number of sampling points. Indicates the first The actual measured terminal voltage at each sampling point Based on the parameter vector to be identified The predicted voltage of the proton exchange membrane fuel cell stack was calculated.

[0130] Step 5: Within the physical boundary of the parameter vector to be identified, the individual position corresponds to a candidate solution of the parameter vector to be identified. Several individuals are uniformly generated using pseudo-random numbers to construct an initial population, and the position of the individual with the smallest objective function value in the initial population is taken as the initial global optimal solution.

[0131] Step 6: Repeat the following steps until the preset maximum number of iterations is reached, and extract the optimal solution of the current round as the parameters of the proton exchange membrane fuel cell:

[0132] Step 6.1: Determine the leader and followers based on the objective function value corresponding to the position of each individual in the current population.

[0133] In this embodiment, individuals in the current population are sorted in ascending order according to the objective function value. The top-ranked individuals are designated as leaders, and the remaining individuals are designated as followers.

[0134] Step 6.2: Based on the Hadamard product, introduce a multidimensional independent random vector to make the followers approach the neighboring better solutions and the current global best solution. Introduce a random perturbation term to make the leader perform a large-step search update to obtain the global updated individual position.

[0135] Step 6.2.1: Calculate the average position of the leader in the current iteration round based on the leader's position.

[0136] In this embodiment, the average position of the leader in the current iteration round is represented as:

[0137] ;

[0138] In the formula, Indicates the first The average position of the leader in each iteration round. Indicates the number of leaders. Indicates the first In the nth iteration A leader's position.

[0139] Step 6.2.2: Based on the current position of each follower, the position of the next better individual, the average position of the leader, and the optimal solution of the current round, introduce mutually independent multidimensional random weight vectors and perform Hadamard product operation to obtain the initial updated position of the followers.

[0140] In this embodiment, the update formula for the initial position update of the follower is expressed as:

[0141] ;

[0142] In the formula, Indicates the first In the nth iteration The position of a follower Indicates the first In the nth iteration The position of a follower Indicates the first The position of the previous follower adjacent to the current follower in the next iteration. It represents the Hadamah accumulation. This is an independent random vector used to regulate how followers approximate the positions of neighboring, better individuals. Let A be an independent random vector used to adjust the approximation of followers toward the current globally optimal individual position. For the first The optimal position of the leader in the next iteration.

[0143] Step 6.2.3: Based on the current position of each leader and the upper and lower limits of the parameter search space, a random perturbation term is introduced to perform a global jump search to obtain the initial updated position vector of the leaders.

[0144] Step 6.2.4: Compare the initial updated position vectors of the followers and the initial updated position vectors of the leaders with the physical boundaries of the parameters to be identified, and perform boundary constraint projection processing on the dimensions that exceed the physical boundaries to obtain the globally updated individual positions.

[0145] Step 6.3: If the objective function value corresponding to the globally updated individual position does not decrease in the number of consecutive iterations, then an inertial weight that dynamically decays exponentially with the number of iterations is introduced. In the neighborhood of the currently globally updated individual position, a local depth search and position update are performed on all individuals to obtain the locally updated individual position.

[0146] Step 6.3.1: Construct a local search neighborhood centered on the current global best individual position, generate exponentially decaying inertia weight coefficients based on the current iteration number, and initialize the individual velocity of each individual.

[0147] In this embodiment, the individual velocity is expressed as:

[0148] ;

[0149] In the formula, Indicates the first In the nth iteration The updated velocity vector of each individual Indicates the first The velocity vector of -1 iterations; Individual cognitive learning factors that guide individuals toward their historical best position. A social experience learning factor that guides individuals to approach the optimal position of the group. Individual experience random numbers are used to assign random perturbation weights to individual cognitive items. A globally empirical random number to which random perturbation weights are assigned to the social experience terms. For the first The individual in the first The historical best position in -1 iterations For the group in the first The global historical best position in -1 iterations This is the solution corresponding to the smaller objective function value between the globally updated and locally updated individual positions.

[0150] In this embodiment, the exponentially decaying inertia weighting coefficient is expressed as:

[0151] ;

[0152] In the formula, For the first The exponentially decaying inertia weight coefficient generated in the next iteration. The inertia weights are preset for the initial iteration. This is the weight decay coefficient.

[0153] Step 6.3.2: Based on the historical best position and the current global best position of each individual, introduce mutually independent multidimensional random weight vectors to update the individual velocity of each individual, and perform local search update on the individual position based on the updated individual velocity to obtain the preliminary local updated position of the individual.

[0154] In this embodiment, the update formula for the initial local update position of the individual is expressed as:

[0155] ;

[0156] In the formula, For the first The first update in the next iteration The individual position of a leader For the first In the nth iteration The current individual position of a leader Let be an independent random vector used to adjust the intensity of the random perturbation. This is used to generate independent random vectors with random offsets within a search space bounded by upper and lower limits. It represents the Hadamah accumulation. and These are the upper limit and lower limit of the physical boundary of the parameter to be identified, respectively.

[0157] Step 6.3.3: Compare the preliminary local update position with the physical boundary of the parameter to be identified, and perform boundary constraint projection processing on the dimensions that exceed the physical boundary to obtain the locally updated individual position.

[0158] In this embodiment, the locally updated individual position is represented as:

[0159] ;

[0160] In the formula, This indicates the individual's position after a partial update.

[0161] Step 6.4: Retain the solution with the smaller objective function value between the globally updated and locally updated individual positions as the global optimal solution for the next round. Figure 2 This is a schematic diagram comparing the fitting effects provided in an embodiment of the present invention.

[0162] Example 3

[0163] Based on the same inventive concept as other embodiments, this embodiment describes a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the steps of the methods of Embodiment 1 or 2 described above.

[0164] Example 4

[0165] Based on the same inventive concept as other embodiments, this embodiment introduces a computer program product, including computer instructions that, when executed by a processor, implement the steps of the methods described in Embodiment 1 or 2 above.

[0166] In summary, this invention constructs a benchmark true condition dataset based on the operating data of the fuel cell stack under different load conditions, and establishes a semi-empirical output voltage prediction model. The objective function is constructed with the error between the predicted voltage and the actual measured terminal voltage as the optimization objective. An initial population is randomly generated within the physical boundaries of the parameters, and an initial global optimum is determined. A global search is employed, using a multi-dimensional independent random vector based on the Hadamard product to allow followers to approach neighboring better solutions and the current global optimum, while a random perturbation term is introduced to allow the leader to perform large-step search updates. Furthermore, when there is no improvement in continuous iterations, an inertial weight that dynamically decays exponentially with the number of iterations is introduced for local depth search. This achieves a dynamic balance between global exploration and local development capabilities, effectively avoiding the problems of local optima and premature convergence that are common in traditional methods, and significantly improving the identification accuracy of unknown parameters in the semi-empirical model.

[0167] This invention introduces multidimensional independent random vectors based on the Hadamard product to enable followers to approach neighboring better solutions and the current global optimum. At the same time, it introduces random perturbation terms to enable the leader to perform large-scale search updates. In the global search phase, it achieves collaborative local convergence of followers and large-scale exploration of the leader, avoiding the problem of imbalance between global exploration and local development capabilities in traditional single heuristic algorithms.

[0168] When the objective function value does not decrease in a series of preset iterations, this invention introduces an inertial weight that dynamically decays exponentially with the number of iterations. This weight performs a local depth search and position update on all individuals within the neighborhood of the currently globally updated individual position, enabling the algorithm to automatically switch to a fine search when it gets stuck. This effectively overcomes the shortcomings of traditional methods that are prone to premature convergence.

[0169] Those skilled in the art will understand that embodiments of the present invention can be provided as 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.

[0170] 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, and 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 illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0171] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for identifying parameters of a proton exchange membrane fuel cell, characterized in that, include: Based on the operating data of proton exchange membrane fuel cell stacks under different load conditions, a benchmark true value operating condition dataset is constructed. A semi-empirical output voltage prediction model is established in the control unit, and the parameters of the proton exchange membrane fuel cell that cannot be directly measured are defined as parameter vectors to be identified. Based on the parameter vector to be identified, a semi-empirical output voltage prediction model is used to predict and output the predicted voltage of the proton exchange membrane fuel cell stack. An objective function is established with the error between the predicted voltage and the actual measured terminal voltage corresponding to the reference true operating condition dataset as the optimization objective. Within the physical boundary of the parameter vector to be identified, the individual position corresponds to a candidate solution of the parameter vector to be identified. Several individuals are uniformly generated using pseudo-random numbers to construct an initial population, and the position of the individual with the smallest objective function value in the initial population is taken as the initial global optimal solution. Repeat the following steps until the preset maximum number of iterations is reached, and extract the optimal solution of the current round as the parameters of the proton exchange membrane fuel cell: Leaders and followers are determined based on the objective function values ​​corresponding to the positions of individuals in the current population. Based on the Hadamard product, a multidimensional independent random vector is introduced to enable the followers to approach the neighboring better solutions and the current global best solution. A random perturbation term is introduced to enable the leader to perform a large-step search update and obtain the individual position after the global update. If the objective function value corresponding to the globally updated individual position does not decrease in a series of iterations with a preset number of iterations, then an inertial weight that dynamically decays exponentially with the number of iterations is introduced. In the neighborhood of the currently globally updated individual position, a local depth search and position update are performed on all individuals to obtain the locally updated individual position. The solution with the smaller objective function value among the globally updated and locally updated individual positions is retained as the global optimal solution for the next round.

2. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 1, characterized in that, The benchmark true condition dataset, constructed based on the operating data of the proton exchange membrane fuel cell stack under different load conditions, includes: Real-time operating data of proton exchange membrane fuel cell stacks under different load conditions are collected through a sensor network. The operating data includes at least the stack operating temperature, anode hydrogen inlet pressure, cathode oxygen inlet pressure, stack output current, and actual measured terminal voltage of the stack. By performing operating condition data preprocessing on the operating data, a benchmark true operating condition dataset is constructed.

3. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 1, characterized in that, The parameter vector to be identified is represented as follows: ； In the formula, To characterize the fundamental thermodynamic activation coefficient of a proton exchange membrane fuel cell under reference conditions, The temperature-dependent activation coefficient is used to characterize the effect of the operating temperature of a proton exchange membrane fuel cell stack on the activation reaction kinetics. To characterize the effect of cathode reactive gas concentration on activation pressure drop in proton exchange membrane fuel cells, the concentration-dependent activation coefficient is used. The charge transfer activation coefficient is used to characterize the effect of the load current on the activation voltage drop in a proton exchange membrane fuel cell. Indicates the water content inside the membrane. Indicates the equivalent contact resistance. This represents the concentration polarization coefficient.

4. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 3, characterized in that, The predicted voltage of the proton exchange membrane fuel cell stack is expressed as follows: ； In the formula, This represents the predicted voltage of the proton exchange membrane fuel cell stack. Represents the ideal open-circuit voltage. This represents the ohmic polarization voltage drop. This represents the activation polarization voltage drop. Indicates concentration polarization voltage drop; The ideal open-circuit voltage is expressed as: ； In the formula, Indicates the operating temperature of the fuel cell stack. Let e ​​represent the logarithmic function with base e. This indicates the hydrogen inlet pressure at the anode. Indicates the cathode oxygen inlet pressure; The ohmic polarization voltage drop is expressed as: ； ； ； In the formula, Indicates the output current of the fuel cell stack. This represents the overall equivalent ohmic resistance of the proton exchange membrane. The resistivity of a proton exchange membrane is represented by its resistance. Indicates the thickness of the proton exchange membrane. Indicates the effective area of ​​the membrane. This represents the natural exponential function. Indicates the equivalent contact resistance; The activation polarization voltage drop is expressed as: ； In the formula, Indicates the effective molar concentration of the gas; The concentration polarization voltage drop is expressed as: ； In the formula, This represents the limiting current density.

5. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 4, characterized in that, The objective function is expressed as: ； In the formula, Describe the objective function. Indicates the total number of sampling points. Indicates the first The actual measured terminal voltage at each sampling point Based on the parameter vector to be identified The predicted voltage of the proton exchange membrane fuel cell stack was calculated.

6. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 5, characterized in that, Leaders and followers are assigned based on the objective function values ​​of each individual in the current population, including: Sort the individuals in the current population in ascending order according to the objective function value, and assign the top 100 individuals as leaders and the remaining individuals as followers.

7. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 6, characterized in that, The introduction of multidimensional independent random vectors based on the Hadamard product enables followers to approximate neighboring better solutions and the current global optimum. The introduction of random perturbation terms allows the leader to perform large-step search updates, obtaining the globally updated individual positions, including: Calculate the average position of the leader in the current iteration based on the leader's position; Based on the current position of each follower, the position of the next better individual, the average position of the leader, and the optimal solution of the current round, an independent multidimensional random weight vector is introduced and a Hadamard product is performed to obtain the initial updated position of the follower. Based on the current position of each leader and the upper and lower limits of the parameter search space, a random perturbation term is introduced to perform a global jump search to obtain the initial updated position vector of the leader. The initial updated position vectors of the followers and the initial updated position vectors of the leader are compared with the physical boundaries of the parameters to be identified, and boundary constraint projection processing is performed on the dimensions that exceed the physical boundaries to obtain the globally updated individual positions.

8. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 7, characterized in that, The average position of the leader in the current iteration round is represented as: ； In the formula, Indicates the first The average position of the leader in each iteration round. Indicates the number of leaders. Indicates the first In the nth iteration A leader's position; The update formula for the initial position update of the follower is expressed as: ； In the formula, Indicates the first In the nth iteration The position of a follower Indicates the first In the nth iteration The position of a follower Indicates the first The position of the previous follower adjacent to the current follower in the next iteration. It represents the Hadamah accumulation. This is an independent random vector used to regulate how followers approximate the positions of neighboring, better individuals. Let A be an independent random vector used to adjust the approximation of followers toward the current globally optimal individual position. For the first The optimal position of the leader in the next iteration.

9. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 8, characterized in that, Introducing an inertial weight that dynamically decays exponentially with the number of iterations, a local depth search and position update are performed on all individuals within the neighborhood of the currently globally updated individual position to obtain the locally updated individual positions, including: A local search neighborhood is constructed with the current global best individual position as the center. An exponentially decaying inertia weight coefficient is generated based on the current iteration number, and the individual velocity of each individual is initialized. Based on the historical best position and the current global best position of each individual, an independent multidimensional random weight vector is introduced to update the individual velocity of each individual, and the individual position is locally searched and updated based on the updated individual velocity to obtain the initial local updated position of the individual. The preliminary local update position is compared with the physical boundary of the parameter to be identified, and boundary constraint projection processing is performed on the dimension that exceeds the physical boundary to obtain the locally updated individual position.

10. The method for identifying parameters of a proton exchange membrane fuel cell according to claim 9, characterized in that, The update formula for the initial local update position of the individual is expressed as: ； In the formula, For the first The first update in the next iteration The individual position of a leader For the first In the nth iteration The current individual position of a leader. Let be an independent random vector used to adjust the intensity of the random perturbation. This is used to generate independent random vectors with random offsets within a search space bounded by upper and lower limits. It represents the Hadamah accumulation. and These are the upper limit and lower limit of the physical boundary of the parameter to be identified, respectively. The exponentially decaying inertia weighting coefficient is expressed as: ； In the formula, For the first The exponentially decaying inertia weight coefficient generated in the next iteration. The inertia weights are preset for the initial iteration. This is the weight decay coefficient; The individual velocity is expressed as: ； In the formula, Indicates the first In the nth iteration The updated velocity vector of each individual Indicates the first The velocity vector of -1 iterations; Individual cognitive learning factors that guide individuals toward their historical best position. A social experience learning factor that guides individuals to approach the optimal position of the group. Individual experience random numbers are used to assign random perturbation weights to individual cognitive items. A globally empirical random number to which random perturbation weights are assigned to the social experience terms. For the first The individual in the first The historical best position in -1 iterations For the group in the first The global historical best position in -1 iterations This is the solution corresponding to the smaller objective function value between the globally updated individual positions and the locally updated individual positions; The locally updated individual position is represented as follows: ； In the formula, This indicates the individual's position after a partial update.

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