Proton exchange membrane fuel cell parameter estimation method and system

Abstract

The present invention relates to a method and system for estimating parameters of a proton exchange membrane fuel cell (PEMFC). The method comprises the following steps: constructing a PEMFC model to obtain unknown parameters to be estimated; constructing an objective function with the sum-of-squares error between the model's output voltage and a measured value as a target; and obtaining the optimal optimization result of the objective function based on a bald eagle search algorithm, which is the desired unknown parameters. The bald eagle search algorithm (BES) is used to extract the optimal parameters from the proton exchange membrane fuel cell (PEMFC) model. The constructed objective function determines the optimal parameters for the model composed of unknown parameters and minimizes the error between the model and the data, thereby converting the parameter estimation process into an iterative function optimization process.

Description

Technical Field

[0001] The present invention relates to the technical field of fuel cells, and in particular to a method and system for estimating parameters of proton exchange membrane fuel cells. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] A fuel cell is a modern energy production system that uses hydrogen as fuel to react with oxygen to generate efficient energy. Among them, the proton exchange membrane fuel cell (PEMFC) that uses polymer as electrolyte is increasingly attractive because its reaction process is the same as the hydrogen combustion process, it does not produce pollutants and noise, and its application diversity is increasingly attractive.

[0004] For example, proton exchange membrane fuel cells are used in marine aquaculture, and their reaction product is water, which will not affect the animal and plant breeding operations in marine ranches.

[0005] Proton exchange membrane fuel cells (PEMFCs) have a short lifespan. To improve their performance, modeling is used to describe the internal chemical reactions based on nonlinear differential equations. These equations contain multiple empirical parameters that cannot be directly measured and require accurate identification to improve model accuracy. Existing technologies make it difficult to achieve ideal identification of the parameters in the model. Summary of the Invention

[0006] In order to solve the technical problems existing in the above-mentioned background technology, the present invention provides a proton exchange membrane fuel cell parameter estimation method and system, which uses the bald eagle search algorithm (BES) to extract the optimal parameters in the proton exchange membrane fuel cell (PEMFC) model. The constructed objective function determines the optimal parameters for the model composed of unknown parameters and minimizes the error between the model and the data, thereby converting the parameter estimation process into an iterative optimization process of the function.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A first aspect of the present invention provides a method for estimating parameters of a proton exchange membrane fuel cell, comprising the following steps:

[0009] Construct a proton exchange membrane fuel cell model and obtain the unknown parameters to be estimated;

[0010] The objective function is constructed with the sum of square errors between the model's output voltage and the measured value as the target;

[0011] The best optimization result of the objective function is obtained based on the bald eagle search algorithm, which is the required unknown parameters.

[0012] The objective function is:

[0013]

[0014] Where M is the data size, V data is the measured data, V model is the model output, and x is a vector containing the required unknown parameters.

[0015] The specific process of solving the objective function is:

[0016] Assign candidate solutions to the model;

[0017] Calculate the error between the model and the measurements;

[0018] The fitness value is evaluated based on the obtained error and the best solution is assigned in this iteration, which is the desired PEMFC parameters.

[0019] Based on the bald eagle search algorithm, the optimal optimization result of the objective function is obtained, which is the required unknown parameters, specifically:

[0020] Select space, the eagle starts from any position to lock the prey space;

[0021] Searching for prey in space, the eagle explores and analyzes the search space selected in the previous stage by flying in a spiral shape, and chooses the best position for hunting;

[0022] Dive: The eagle quickly dives down from the best position searched in the previous stage to hit the prey, and finally obtains the best optimization result.

[0023] Select the space, and the vulture will lock the prey space from any position, as shown below:

[0024] P new =P best +α.r.(P m -P i )

[0025] Where, P new is the new position, P best is the target position (optimal position), P m is the average of all actual positions, and the target position will be at P new Fitness is then updated, P i represents the i-th position of the bald eagle, a has a set value range, and r is an arbitrary gain.

[0026] To search for prey in space, the eagle explores and analyzes the search space selected in the previous stage by flying in a spiral shape, and selects the best position for hunting, as shown in the following formula:

[0027] P new(i)=P(i)+y(i)·(P(i)-P(i+1))+x(i)·(P(i)-P m )

[0028] Where, P new (i) is the eagle's most recent i-th position, and x and y represent the direction coordinates, as follows:

[0029]

[0030]

[0031] θ(i)=a·π·rand; r(i)=θ(i)·R.rand

[0032] Where a is the control gain, which is used to select the angle between the search points on the center point, R is the control gain, which is used to determine the number of search cycles, θ(i) and r(i) represent the polar angle and polar radius of the spiral equation, respectively, and rand is a random number within the set range.

[0033] Dive, the eagle quickly dives down from the best position searched in the previous stage to hit the prey, and finally obtains the best optimization result, as shown in the following formula:

[0034] P new (i) = rand·P best +x1(i)·(P(i)-c1·P mean )+y1(i)·(P(i)-c2·P best )

[0035] Where c1 and c2 are arbitrary gains representing the intensity of the bald eagle's dive; x1 and y1 are defined as:

[0036]

[0037]

[0038] θ(i)=a·π·rand; r(i)=θ(i)

[0039] A second aspect of the present invention provides a system for implementing the above method, comprising:

[0040] A model building module is configured to: build a model of a proton exchange membrane fuel cell to obtain unknown parameters to be estimated;

[0041] An objective function building module is configured to: build an objective function with the sum of square errors between the output voltage of the model and the measured value as a target;

[0042] The result output module is configured to obtain the best optimization result of the objective function based on the bald eagle search algorithm, which is the required unknown parameter.

[0043] A third aspect of the present invention provides a computer-readable storage medium.

[0044] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the above-mentioned method for estimating parameters of a proton exchange membrane fuel cell.

[0045] A fourth aspect of the present invention provides a computer device.

[0046] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps in the above-mentioned method for estimating parameters of a proton exchange membrane fuel cell when executing the program.

[0047] Compared with the existing technology, one or more of the above technical solutions have the following beneficial effects:

[0048] 1. The Bald Eagle Search (BES) algorithm is used to extract the optimal parameters in the proton exchange membrane fuel cell (PEMFC) model. The constructed objective function determines the optimal parameters for the model composed of unknown parameters and minimizes the error between the model and the data, transforming the parameter estimation process into an iterative optimization process of the function.

[0049] 2. The Bald Eagle Search (BES) algorithm is a robust meta-heuristic optimization algorithm that can provide good results for many engineering problems. The convergence mechanism of the algorithm is based on the selection phase, the search phase, and the dive phase. In each phase, the position will be updated according to its update mechanism.

[0050] 3. Introducing the sum of square errors to form the optimization objective function can converge more quickly while ensuring accurate accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0052] Figure 1 is a schematic diagram of a polarization curve of a fuel cell system provided by one or more embodiments of the present invention;

[0053] Figure 2 is a parameter estimation flow chart provided by one or more embodiments of the present invention. DETAILED DESCRIPTION

[0054] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0055] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0056] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0057] As described in the background technology, the lifespan of proton exchange membrane fuel cells (PEMFCs) is relatively short. To improve the performance of PEMFCs, relevant research is conducted through modeling based on nonlinear differential equations to describe the internal chemical reactions. These equations contain multiple empirical parameters that cannot be directly measured and require accurate identification to improve the accuracy of the model. Existing technologies make it difficult to achieve ideal identification of the parameters in the model.

[0058] Example 1:

[0059] A fuel cell system (FC) is an energy conversion device that converts the energy (chemical form) of fuel directly into electrical energy. The reaction can be expressed by formula (1):

[0060] 2H2+O2→H2O+electricity+heat(1)

[0061] The PEMFC polarization curve can be divided into three regions: polarization, concentration and ohmic loss, such as Figure 1 As shown in Figure 1, the polarization loss region represents chemical reactions delayed from the activation barrier. The concentration loss region represents the concentration voltage drop caused by mass transfer. The ohmic loss region represents the ohmic losses resulting from varying internal resistances. Therefore, the electrical behavior of a proton exchange membrane fuel cell can be modeled based on its polarization curve, where the cell output voltage consists of three distinct components.

[0062] V fc =E Nernest -V act -V ohm -V con (2)

[0063] Where V act is the polarization activation voltage, V ohm is the ohmic loss voltage, Vcon is the concentration loss voltage, E Nernest is the Nernst voltage (thermodynamic potential). Temperature <100C.

[0064]

[0065] Where F is the Faraday constant (9.6485333289*10 4 Cmol-1); ΔG represents the change in free Gibbs energy; ΔS represents the entropy change; R is the universal gas constant (8.3145); T is the operating temperature, T ref is the reference temperature (298.15K); P H2 and P O2 are the partial pressures of hydrogen and oxygen, which can be calculated as follows:

[0066]

[0067]

[0068]

[0069] Where R ha and R hc Indicates the positive and negative electrode vapor humidity, P a and P c represents the positive and cathode inlet pressure (atm), A represents the electrode area (cm 2 ), i represents FC output current (A), P H2O represents the water vapor saturation pressure (atm), T c =TT ref .

[0070] The polarization activation voltage (Vact) is calculated as follows

[0071]

[0072] Where ζ1, ζ2, ζ3, ζ4 are semi-empirical coefficients; Describes the O2 concentration (mol.cm -3 ), we can get the following results:

[0073]

[0074] The calculation formula of concentration loss voltage is:

[0075]

[0076] Where β is the diffusion parameter, i lim Limits the current for the fuel cell.

[0077] The ohmic loss voltage can be calculated as follows:

[0078] V ohm =i(R m +R c )(10)

[0079] Where R c is the connector resistance (proton electron transfer impedance), R m is the ohmic film resistance, which can be calculated as follows:

[0080]

[0081] Where l is the thickness of the film (cm), A m is the surface area of ​​the membrane (cm 2 ), ρ m is the specific resistivity of the film (ohm.cm), which can be calculated as:

[0082]

[0083] where λ is the control gain representing the water content of the membrane material (i.e. the water content of the proton exchange membrane).

[0084] The Bald Eagle Search (BES) algorithm is a new metaheuristic algorithm (MA) inspired by the flight and fishing methods of bald eagles. The BES algorithm outperforms other algorithms due to its unique convergence process. Bald eagles are found throughout North America and have sharp eyesight and excellent observation skills during flight. For example, when hunting salmon, a bald eagle first selects a search space based on the concentration of salmon, whether individual or population, and then flies towards a specific area. Then, it searches the water surface within the selected search space until it finds suitable prey. Finally, the bald eagle gradually changes its flight altitude, rapidly diving downward to successfully capture prey such as salmon from the water.

[0085] The Bald Eagle Algorithm model consists of three phases: selection, search, and dive. In the selection phase, the eagle selects the optimal position within the search space by randomly choosing a new search space near the previously explored area. Then, in the next phase, the eagle searches for prey within the selected space, flying in a spiral motion to determine the optimal hunting position. Finally, in the final phase, the eagle strikes the target from the optimal position obtained in the previous phase. All positions are close to the optimal position.

[0086] MATLAB, a combination of the words "matrix" and "laboratory," means "matrix factory" or "matrix laboratory." It is a high-tech computing environment primarily for scientific computing, visualization, and interactive programming. It integrates powerful capabilities such as numerical analysis, matrix calculations, scientific data visualization, and modeling and simulation of nonlinear dynamic systems into an easy-to-use windowing environment. It provides a comprehensive solution for scientific research, engineering design, and numerous other scientific fields requiring efficient numerical computation, significantly moving away from the editing methods of traditional non-interactive programming languages ​​such as C and Fortran.

[0087] This example first applied the BES algorithm to extract the optimal parameters for a PEMFC model. Based on the Bald Eagle Search (BES) algorithm, it can provide excellent results for many engineering problems. The algorithm's convergence mechanism is based on a selection phase, a search phase, and a dive phase. In each phase, the position is updated according to its update mechanism.

[0088] When estimating fuel cell parameters, currently common methods such as particle swarm optimization, genetic algorithms, and sparrow search algorithms all suffer from relatively slow convergence rates due to limitations in the algorithm's population update methods. To overcome this slow convergence problem, a comparison of numerous algorithms revealed that the Bald Eagle algorithm, through its unique three-stage process of selection, search, and dive, can quickly lock onto a target, thereby converging to the desired result. Furthermore, in parameter estimation experiments, the accuracy of its results meets practical requirements, thus effectively resolving the convergence speed issue currently encountered by most common algorithms in the field of fuel cell parameter estimation.

[0089] Use MATLAB to model a proton exchange membrane fuel cell system. Parameter optimization and modeling are performed on the same platform, simplifying data reference and operation.

[0090] Specifically:

[0091] Step 1: Problem Formulation

[0092] The proton exchange membrane fuel cell models include ζ1, ζ2, ζ3, ζ4, R c ,λ, and six unknown parameters, whose ideal values ​​need to be sufficiently accurate. The sum-squared error (SSE) is used to represent the difference between the measured value and the output voltage of the estimated model (i.e., the proton exchange membrane fuel cell mathematical model given in Formula 2-12 above). The measured value represents the actual output voltage value obtained from actual measurement of the proton exchange membrane fuel cell; the estimated model output voltage represents the simulated output voltage value of the mathematical model containing the six unknown parameters.

[0093] The objective function can be constructed as follows:

[0094]

[0095] Where M is the data size, V data is the measured data, V model is the model output, and x is a vector containing 6 unknown parameters:

[0096] χ=[ζ1 ζ2 ζ3 ζ4 R C λ] (14)

[0097] Where ζ1, ζ2, ζ3, and ζ4 are all semi-empirical coefficients, R C is the connector resistance (proton-electron transfer impedance) in Equation 10, and λ is the water content of the proton exchange membrane in Equation 12 (i.e., the control gain of the water content of the membrane material). Each parameter must be limited to its range, and the constraints are:

[0098]

[0099] LB≤x≤UB (16)

[0100] Where LB and UB represent the upper and lower limits of the unknown parameters, respectively.

[0101] The objective function of Equation (13) and the constraints of Equations (14), (15), and (16) form an optimization problem that is minimized using the Bald Eagle Search (BES) algorithm. The key idea is to determine the optimal parameter set x for the unknown model that minimizes the error between the model and the data. First, a candidate solution x is assigned to the model. Then, the error between the model and the measurement is calculated. Finally, the fitness value is evaluated based on this error, and the best solution is assigned in this iteration. The identification strategy is an iterative model that ends with a stopping criterion or a maximum number of iterations.

[0102] Step 2: Bald Eagle Search Algorithm

[0103] 1. Selection space: The eagle starts to lock the prey space from any position, as shown in formula (17):

[0104] P new =P best +ar(P m -P i ) (17)

[0105] Where P new is the new position, P best is the target position (optimal position), α is [1.5, 2], r is an arbitrary gain [0, 1], P m is the average of all actual positions. The target position will be at P new The fitness is then updated. irepresents the i-th position of the bald eagle.

[0106] 2 Searching for prey in space: In this stage, the eagle explores and analyzes the search space selected in the previous stage by flying in a spiral shape, and selects the best position for hunting.

[0107] The search phase is modeled as follows:

[0108] P new (i)=P(i)+y(i)·(P(i)-P(i+1))+x(i)·(P(i)-P m ) (18)

[0109] Where P new (i) is the eagle's most recent i-th position, and x and y represent the direction coordinates calculated as follows:

[0110]

[0111]

[0112] θ(i)=a·π·rand; r(i)=θ(i)·R.rand (21)

[0113] Where a is a control gain [5, 10], used to select the angle between search points on the center point, and R is a control gain [0.5, 2], used to determine the number of search cycles. θ(i) and r(i) represent the polar angle and polar radius of the spiral equation, respectively. rand is a random number in the range (0, 1).

[0114] 3. Dive: The eagle quickly dives down from the position that is easiest to obtain the target in the previous stage, and finally obtains the best optimization result, as shown in the following formula:

[0115] P new (i) = rand·P best +x1(i)·(P(i)-c1·P mean )+y1(i)·(P(i)-c2·P best ) (twenty two)

[0116] Where c1 and c2 are arbitrary gains [1, 2], representing the intensity of the bald eagle's dive; x1 and y1 are defined as:

[0117]

[0118]

[0119] θ(i)=a·π·rand; r(i)=θ(i) (25)

[0120] The best optimization results obtained from the above steps are the six required unknown parameters.

[0121] Example 2:

[0122] A system for implementing the above method includes:

[0123] A model building module is configured to: build a model of a proton exchange membrane fuel cell to obtain unknown parameters to be estimated;

[0124] An objective function building module is configured to: build an objective function with the sum of square errors between the output voltage of the model and the measured value as a target;

[0125] The result output module is configured to obtain the best optimization result of the objective function based on the bald eagle search algorithm, which is the required unknown parameter.

[0126] The system implementation method uses the Bald Eagle Search algorithm (BES) to extract the optimal parameters in the proton exchange membrane fuel cell (PEMFC) model. The constructed objective function determines the optimal parameters for the model composed of unknown parameters and minimizes the error between the model and the data, transforming the parameter estimation process into an iterative optimization process of the function.

[0127] Example 3:

[0128] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps in the method for estimating parameters of a proton exchange membrane fuel cell as described in the first embodiment above are implemented.

[0129] The implementation method uses the Bald Eagle Search algorithm (BES) to extract the optimal parameters in the proton exchange membrane fuel cell (PEMFC) model. The constructed objective function determines the optimal parameters for the model composed of unknown parameters and minimizes the error between the model and the data, transforming the parameter estimation process into an iterative optimization process of the function.

[0130] Example 4:

[0131] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the proton exchange membrane fuel cell parameter estimation method described in the first embodiment are implemented.

[0132] The implementation method uses the Bald Eagle Search algorithm (BES) to extract the optimal parameters in the proton exchange membrane fuel cell (PEMFC) model. The constructed objective function determines the optimal parameters for the model composed of unknown parameters and minimizes the error between the model and the data, transforming the parameter estimation process into an iterative optimization process of the function.

[0133] The steps or modules involved in Examples 2 to 4 above correspond to those in Example 1. For detailed implementations, please refer to the relevant description of Example 1. The term "computer-readable storage medium" should be understood to mean a single medium or multiple media that includes one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and cause the processor to perform any method of the present invention.

[0134] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for estimating parameters of a proton exchange membrane fuel cell, characterized in that: The following steps are involved: Construct a proton exchange membrane fuel cell model and obtain the unknown parameters to be estimated; The objective function is constructed with the sum of square errors between the model's output voltage and the measured value as the target; Based on the bald eagle search algorithm, the best optimization result of the objective function is obtained, which is the required unknown parameters; The objective function is: Where M is the data size, V data is the measured data, V model is the model output, x is the vector containing the required unknown parameters; The specific process of solving the objective function is: Assign candidate solutions to the model; Calculate the error between the model and the measurements; The fitness value is evaluated based on the obtained error and the best solution is assigned in this iteration, which is the desired PEMFC parameters; Based on the bald eagle search algorithm, the optimal optimization result of the objective function is obtained, which is the required unknown parameters, specifically: Select space, the eagle starts from any position to lock the prey space; Searching for prey in space, the eagle explores and analyzes the search space selected in the previous stage by flying in a spiral shape, and chooses the best position for hunting; Dive: The eagle quickly dives down and hits the prey from the best position searched in the previous stage, and finally obtains the best optimization result.

2. The method for estimating parameters of a proton exchange membrane fuel cell according to claim 1, wherein: Select the space, and the vulture will lock the prey space from any position, as shown below: P new =P best +α.r.(P m -P i ) Where, P new is the new position, P best is the target position (optimal position), P m is the average of all actual positions, and the target position will be at P new Fitness is then updated, P i represents the i-th position of the bald eagle, α has a set value range, and r is an arbitrary gain.

3. The method for estimating parameters of a proton exchange membrane fuel cell according to claim 1, wherein: To search for prey in space, the eagle explores and analyzes the search space selected in the previous stage by flying in a spiral shape, and selects the best position for hunting, as shown in the following formula: P new (i)=P(i)+y(i)·(P(i)-P(i+1))+x(i)·(P(i)-P m ) Where, P new (i) is the eagle's most recent i-th position, and x and y represent the direction coordinates, as follows: θ(i)=a·π·rand; r(i)=θ(i)·R.rand Where a is the control gain, which is used to select the angle between the search points on the center point, R is the control gain, which is used to determine the number of search cycles, θ(i) and r(i) represent the polar angle and polar radius of the spiral equation, respectively, and rand is a random number within the set range.

4. The method for estimating parameters of a proton exchange membrane fuel cell according to claim 1, wherein: Dive, the eagle quickly dives down from the best position searched in the previous stage to hit the prey, and finally obtains the best optimization result, as shown in the following formula: P new (i)=rand·P best +x1(i)·(P(i)-c1·P mean )+y1(i)·(P(i)-c2·P best ) Where c1 and c2 are arbitrary gains representing the intensity of the bald eagle's dive; x1 and y1 are defined as: θ(i)=a·π·rand; r(i)=θ(i).

5. A proton exchange membrane fuel cell parameter estimation system, comprising: include: A model building module is configured to: build a model of a proton exchange membrane fuel cell to obtain unknown parameters to be estimated; An objective function building module is configured to: build an objective function with the sum of square errors between the output voltage of the model and the measured value as a target; The result output module is configured to obtain the best optimization result of the objective function based on the bald eagle search algorithm, which is the required unknown parameter.

6. A computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, the steps of the method for estimating parameters of a proton exchange membrane fuel cell according to any one of claims 1 to 4 are implemented.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the method for estimating parameters of a proton exchange membrane fuel cell according to any one of claims 1 to 4 are implemented.

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