A System Parameter Identification Method Integrating Adaptive Collaboration and Elite Guidance

Abstract

This invention discloses a system parameter identification method integrating adaptive cooperative and elite-guided approaches, belonging to the field of system parameter identification. The method includes the following steps: establishing a system parameter identification model and determining the system parameters to be identified; acquiring a set of measurable operational variables of the system; randomly generating initial population individuals based on a reasonable range of the system parameters to be identified; performing a first-stage iterative update identification of the system parameters based on an adaptive cooperative strategy; performing a second-stage iterative update identification of the system parameters based on an elite-guided strategy; and using the system parameters at the end of the iteration as the final parameter identification result, thereby outputting the system parameter identification result. This invention effectively considers the combined influence of population diversity and population fitness, and can achieve rapid global convergence of the system parameter identification process while ensuring effective coverage of the parameter identification space by a small population size.

Description

Technical Field

[0001] This invention belongs to the field of system parameter identification technology, specifically relating to a system parameter identification method that integrates adaptive collaboration and elite guidance. Background Technology

[0002] With the continuous development of society and the economy, the state monitoring, analysis, and control of modern industrial systems place higher demands on the accuracy of system models. Accurate system models are a crucial foundation for achieving observable and controllable critical states in industrial systems. Reasonable and accurate identification of equivalent system parameters is a vital step in system modeling and a crucial prerequisite for further model-driven state observation and control of industrial systems. However, achieving reliable system parameter identification remains a significant challenge.

[0003] Currently, various nature-inspired swarm intelligence methods have been proposed for parameter identification of equivalent system models, including particle swarm optimization (PSO) and ant colony optimization (ACO). The effectiveness of these nature-inspired swarm intelligence methods in parameter identification depends primarily on two aspects: first, they rely on a large population size to ensure effective coverage of the parameter identification space by the initial population; second, the entire parameter identification process is dominated by the population's optimal fitness, easily leading to local optima and failing to achieve a globally optimal result. Therefore, existing nature-inspired swarm intelligence methods typically perform poorly in parameter identification with small population sizes and are unsuitable for rapid and accurate parameter identification in industrial systems with limited performance and resource allocation. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a system parameter identification method that integrates adaptive collaboration and elite guidance. This method effectively considers the combined effects of population diversity and population fitness, and can achieve rapid global convergence of the system parameter identification process while ensuring effective coverage of the parameter identification space by a small population size.

[0005] The technical solution of the present invention is as follows:

[0006] A system parameter identification method integrating adaptive collaboration and elite guidance includes the following steps:

[0007] S1. Establish a system parameter identification model and determine the system parameters to be identified;

[0008] S2. Obtain the set of measurable operating variables of the system, including the set of measurable input / output variables and the set of measurable state variables;

[0009] S3. Randomly generate initial population individuals based on a reasonable range of system parameters to be identified;

[0010] S4. The first stage of iterative update and identification of system parameters is based on an adaptive cooperative strategy. The termination condition of this stage is that the variance of the population difference of the identified parameters is stable or the set number of iterations is reached.

[0011] S5. The second stage of iterative update and identification of system parameters is based on the elite-guided strategy. The termination condition of this stage is that the fitness of the elite individuals in the population with the identified parameters is lower than the set fitness threshold or the set number of iterations is reached.

[0012] S6. Use the system parameters at the end of the iteration as the final parameter identification result, and then output the system parameter identification result.

[0013] Furthermore, in step S1, the system parameter identification model takes the form shown in equation (1).

[0014]

[0015] Where y represents the output of the system parameter identification model, x1, x2, ..., x m The m input variables, u1, u2, ..., u, represent the system parameter identification model. n The n state variables, a1, a2, ..., a, represent the system parameter identification model. d f represents the d parameters to be identified in the model. i This represents the functional relationship expressed by the input quantity and the unknown parameter to be identified.

[0016] Furthermore, the specific process of step S2 is as follows:

[0017] S201. Identify the state variables and input / output variables in the model based on the system parameters, and determine the measurable state variables and measurable input / output variables of the system.

[0018] S202. Obtain the set of operating condition data of the measurable input / output variables and the measurable state variables through actual operating condition testing of the system.

[0019] Furthermore, the specific process of step S3 is as follows:

[0020] S301. Determine the reasonable range of parameters for the system to be identified:

[0021] Based on existing publicly available data or empirical values, the range of system parameters to be identified is given, as shown in equation (2).

[0022]

[0023] Where a is the parameter to be identified, lb represents the lower bound of the parameter to be identified, and ub represents the upper bound of the parameter to be identified.

[0024] S302, Randomly generate population individuals;

[0025] Each individual is a candidate solution, containing d-dimensional variables, representing d parameters that need to be identified; the variable of the d-th dimension of each candidate solution is given by equation (3).

[0026] x d =lb d +(ub d -lb d rand (3)

[0027] Where, x d Let d be the variable of the d-th dimension of the candidate solution, and rand is a random number in the range [0,1].

[0028] Furthermore, the specific process of step S4 is as follows:

[0029] S401. Adaptive cooperative strategy initialization: Set the basic parameters of the adaptive cooperative strategy;

[0030] Set the population size to NP, which is the number of individuals in the population; randomly generate NP individuals x, each candidate solution contains d-dimensional variables, representing d parameters that need to be identified;

[0031] S402. Calculate the fitness performance P of all individuals. f and difference performance P d The specific process is as follows:

[0032] The root mean square error (RMSE) between the measured output and the model output is used as the fitness function f. fitness (x k As shown in equation (4), the fitness of each individual is calculated.

[0033]

[0034] Where, x k Let k represent an individual, h be the number of sample points in the measured data sequence, and y be the measured output. Output for the model;

[0035] The difference function f is defined using Euclidean distance. diversity (x k As shown in equation (5), the degree of difference for each individual is calculated.

[0036]

[0037] Where, x k Let k represent an individual, NP represent the number of individuals in the population, and ||x k -x w|| represents the Euclidean distance between individual k and individual w, which is calculated using equation (6).

[0038]

[0039] and Representing individual x k and x w The coordinates in the i-th dimension, where d is the number of dimensions;

[0040] Individual fitness and diversity are sorted in descending order to obtain the fitness ranking R of the individuals. fitness And the difference ranking R diversity As shown in equations (7) and (8),

[0041] R fitness (x k )=NP+1-i k i k =1,2,...,NP (7)

[0042] R diversity (x k )=NP+1-j k ,j k =1,2,...,NP (8)

[0043] The fitness performance P of each individual is calculated using equations (9) and (10). f and difference performance P d ,

[0044]

[0045]

[0046] Here, we introduce the collaborative performance P. s As an evaluation index for individual k, its definition is given by equation (11).

[0047] P s =P d ·c k,s +P f ·(1-c k,s (11)

[0048] Among them, P f With P d As given by equations (9) and (10), c k,s The coordination coefficient is a random number in the range [0,1].

[0049] S403, Adaptive Cooperative Iterative Update of System Parameters:

[0050] In each iteration of adaptive collaborative optimization, the fitness performance and diversity performance of each individual are first calculated, and the individuals with the best and worst fitness, x, are given. fbest and x fworst ;

[0051] Furthermore, for each individual x k Determine if x is the individual with the lowest fitness. k For the individual with the lowest fitness, the optimal solution is updated according to equation (12).

[0052]

[0053] Where the superscript R represents two randomly selected individuals, The one with better fitness among the randomly selected individuals. Let x′ be the randomly selected individual with the worst fitness, v represents the variable of the v-th dimension. fbest,v For the updated x fbest,v r 1,fbest,v A random number in the range [0,1];

[0054] If x k If the individual is not the one with the lowest fitness, then a cooperability coefficient c is randomly generated. k,s The synergistic performance P of all individuals is calculated using equation (11). s And identify the individuals with the best and worst cooperative performance. and

[0055] Then randomly select two different individuals x l1 and x l2 Compare their synergistic performance P s Choose P s Larger individuals, if P s If they are the same, then compare the diversity performance P. d Choose P d Larger individuals, if P d Similarly, comparing the fitness performance P... f Choose P f Larger individuals, if P s P d P f If all are the same, then select the first individual and denote the selected individual as x. l Comparison of individual x l With individual x k Synergistic performance P s If x l P sIf the value is large, then update individual x according to equation (13). k Otherwise, update individual x according to equation (14). k ,

[0056]

[0057]

[0058] Where the subscript v represents the variable of the v-th dimension, and the superscript s indicates that the individual is selected based on cooperative performance. and R represents the individuals with the best and worst collaborative performance in the v-th dimension. 1,v and r 2,v It is a random number in the range [0,1].

[0059] S404. Calculate the updated individual x′ k,v fitness performance P f It is then compared with the current optimal solution. If the solution is better than the optimal solution, the optimal solution is updated; otherwise, the optimal solution is kept unchanged.

[0060] The iterative update termination condition of the adaptive collaborative strategy is to satisfy at least one of the following iterative update termination conditions: Condition 1 is that the number of parameter update iterations is equal to the specified maximum number of iterations, as shown in Equation (15); Condition 2 is that the rate of change of the variance of the population difference is less than a set threshold, as shown in Equation (16).

[0061] t < t max (15)

[0062]

[0063] in, It is the variance of population diversity in the t-th iteration. It is the variance of the population diversity in the (t-1)th iteration, defined as D i For the degree of variability of individual i, D i =||x i -x w ||Calculated, NP represents the average difference among all individuals in the population, where NP is the number of individuals in the population. To set a threshold.

[0064] Furthermore, the specific process of step S5 is as follows:

[0065] S501. Divide the population obtained in step S4 into two populations, population 1 and population 2, with the number of individuals in each population being NP / 2. Generate the paths of random walks of individuals in population 1. Each path contains d-dimensional variables, representing the d parameters that need to be identified. The paths of random walks of individuals in population 1 are given by equation (17).

[0066] X(t)=[0,cumsum(2r(t1)-1),cumsum(2r(t2)-1),...,cumsum(2r(t) n )-1)](17)

[0067] Where t represents the number of random steps, cumsum represents the cumulative sum, n is the maximum number of iterations, and r(t) is a random function, given by equation (18):

[0068]

[0069] In the formula, rand is a random number in the interval [0,1].

[0070] Considering that the search space for the system's identification parameters is bounded, equation (17) is normalized using equation (19).

[0071]

[0072] Where i represents the i-th dimension, a i b i These are the minimum and maximum values ​​of the random walk path for the i-th dimension variable before normalization, respectively, where t represents the current iteration number. These are the lower and upper bounds of the i-th dimension variable at the t-th iteration, respectively.

[0073] S502. Calculate and rank the fitness of individuals in the population.

[0074] The fitness of all individuals is calculated using formula (4) in S402. The individual with the best fitness in population 2 is selected as the elite individual. For each individual in population 1, a corresponding individual in population 2 is selected using roulette wheel selection.

[0075] Equation (20) indicates that the random walking radius of an individual in population 1 around an individual in population 2 decreases adaptively.

[0076]

[0077] Among them, lb t and ub t These are the lower and upper bounds of the variable in the t-th iteration, respectively. t represents the current iteration number, and T represents the maximum iteration number;

[0078] The selected individuals in population 2 will affect the random walks of the corresponding individuals in population 1. Equation (21) is used to represent the update of the random walk boundary of the corresponding individuals in population 1.

[0079]

[0080] Where t represents the current iteration number, and These are the lower and upper bounds of the variable for the i-th individual in population 1, respectively, lb t and ub t These are the lower and upper bounds of the variable in the t-th iteration, respectively. This represents the position of the j-th selected individual in population 2 during the t-th iteration;

[0081] Elite individuals will influence the movement of all individuals in population 1 in subsequent iterations, and this influence is expressed by equation (22).

[0082]

[0083] Where t represents the current iteration number; It is the random walking path around the selected individual in population 2 at the t-th iteration; It is the random walking path around the elite individual at the t-th iteration; This represents the position of the i-th individual in population 1 during the t-th iteration.

[0084] S503. After updating all individuals in population 1, if the fitness of an individual in population 1 becomes less than the fitness of the corresponding individual in population 2, then the position of the corresponding individual in population 2 is updated using the position of the individual in population 1, i.e., equation (23).

[0085]

[0086] Where t represents the current iteration number; This represents the position of the j-th individual in population 2 at the t-th iteration; This represents the position of the i-th individual in population 1 at the t-th iteration.

[0087] The individual with the best fitness in population 2 obtained in each iteration is taken as the elite individual, and the system identification parameters are updated in the (t+1)th iteration based on the elite guidance strategy.

[0088] S504. When the system parameter identification iteration process based on the elite guidance strategy reaches the iteration termination condition, the update iteration of the system parameter identification based on the elite guidance strategy is stopped.

[0089] The iteration termination condition of the system parameter identification iteration process based on the elite guidance strategy is to satisfy at least one of the following iteration update termination conditions: condition one is that the number of parameter update iterations is equal to the specified maximum number of iteration updates; condition two is that the fitness of the elite individual is less than a specified threshold.

[0090] The beneficial technical effects of this invention are as follows:

[0091] Based on existing swarm intelligence optimization algorithms, this paper takes into account the impact of population diversity on the system parameter identification process. In the first stage, an adaptive cooperative strategy is used to ensure a large population diversity and achieve a fast initial global search in the parameter identification process. In the second stage, an elite-guided strategy is used to achieve accurate optimization in the later stage of the system parameter identification process while reducing the strategy complexity and the number of iterations required for system parameter identification in small-scale populations. Attached Figure Description

[0092] Figure 1 This is a flowchart of a system parameter identification method that integrates adaptive collaboration and elite guidance according to the present invention;

[0093] Figure 2 This is a flowchart of the parameter optimization identification of a proton exchange membrane electrolyzer system using a system parameter identification method that integrates adaptive collaboration and elite guidance in Embodiment 1 of the present invention. Detailed Implementation

[0094] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0095] like Figure 1 As shown, a system parameter identification method integrating adaptive collaboration and elite guidance includes the following steps:

[0096] S1. Establish a system parameter identification model and determine the system parameters to be identified;

[0097] The general form of the system parameter identification model is shown in equation (1).

[0098]

[0099] Where y represents the output of the system parameter identification model, x1, x2, ..., x m The m input variables, u1, u2, ..., u, represent the system parameter identification model. n The n state variables, a1, a2, ..., a, represent the system parameter identification model. d f represents the d parameters to be identified in the model. i This represents the functional relationship expressed by the input quantity and the unknown parameter to be identified.

[0100] S2. Obtain the set of measurable operational variables of the system, including the set of measurable input / output variables and the set of measurable state variables; the specific process is as follows:

[0101] S201. Identify the state variables and input / output variables in the model based on the system parameters, and determine the measurable state variables and measurable input / output variables of the system.

[0102] S202. Obtain the set of operating condition data of the measurable input / output variables and the measurable state variables through actual operating condition testing of the system.

[0103] S3. Randomly generate initial population individuals based on a reasonable range of system parameters to be identified; the specific process is as follows:

[0104] S301. Determine the reasonable range of parameters for the system to be identified:

[0105] Based on existing publicly available data or empirical values, the range of system parameters to be identified is given, as shown in equation (2).

[0106]

[0107] Where a is the parameter to be identified, lb represents the lower bound of the parameter to be identified, and ub represents the upper bound of the parameter to be identified.

[0108] S302, Randomly generate population individuals;

[0109] Each individual is a candidate solution, containing d-dimensional variables, representing d parameters that need to be identified; the variable of the d-th dimension of each candidate solution is given by equation (3).

[0110] x d =lb d +(ub d -lb d rand (3)

[0111] Where, x d Let d be the variable of the d-th dimension of the candidate solution, and rand is a random number in the range [0,1].

[0112] S4. The first stage of iterative update and identification of system parameters is based on an adaptive cooperative strategy. The termination condition for this stage is that the variance of the population difference of the identified parameters is stable or the set number of iterations is reached. The specific process is as follows:

[0113] S401. Adaptive cooperative strategy initialization: Set the basic parameters of the adaptive cooperative strategy;

[0114] Set the population size to NP, which is the number of individuals in the population; randomly generate NP individuals x (candidate solutions), each candidate solution contains d-dimensional variables, representing d parameters that need to be identified.

[0115] S402. Calculate the fitness performance P of all individuals. f and difference performance P d The specific process is as follows:

[0116] The root mean square error (RMSE) between the measured output and the model output is used as the fitness function f. fitness (x k As shown in equation (4), the fitness of each individual is calculated.

[0117]

[0118] Where, x k Let k represent an individual, h be the number of sample points in the measured data sequence, and y be the measured output. Output for the model;

[0119] The difference function f is defined using Euclidean distance. diversity (x k As shown in equation (5), the degree of difference for each individual is calculated.

[0120]

[0121] Where, x k Let k represent an individual, NP represent the number of individuals in the population, and ||x k -x w || represents the Euclidean distance between individual k and individual w, which is calculated using equation (6).

[0122]

[0123] and Representing individual x k and x w The coordinates in the i-th dimension, where d is the number of dimensions;

[0124] Individual fitness and diversity are sorted in descending order to obtain the fitness ranking R of the individuals. fitness And the difference ranking R diversity As shown in equations (7) and (8),

[0125] R fitness (x k )=NP+1-i k i k =1,2,...,NP (7)

[0126] R diversity (x k )=NP+1-j k ,j k =1,2,...,NP (8)

[0127] The fitness performance P of each individual is calculated using equations (9) and (10). f and difference performance P d ,

[0128]

[0129]

[0130] Here, we introduce the collaborative performance P. s As an evaluation index for individual k, its definition is given by equation (11).

[0131] P s =P d ·c k,s +P f ·(1-c k,s (11)

[0132] Among them, P f With P d As given by equations (9) and (10), c k,s The synergy coefficient is a random number in the range [0,1].

[0133] S403, Adaptive Cooperative Iterative Update of System Parameters:

[0134] In each iteration of adaptive collaborative optimization, the fitness performance and diversity performance of each individual are first calculated, and the individuals with the best and worst fitness, x, are given. fbest and x fworst ;

[0135] Furthermore, for each individual x k Determine if x is the individual with the lowest fitness. k For the individual with the lowest fitness, the optimal solution is updated according to equation (12).

[0136]

[0137] Where the superscript R represents two randomly selected individuals, The one with better fitness among the randomly selected individuals. Let x′ be the randomly selected individual with the worst fitness, v represents the variable of the v-th dimension. fbest,v For the updated x fbest,v r1,fbest,v A random number in the range [0,1];

[0138] If x k If the individual is not the one with the lowest fitness, then a cooperability coefficient c is randomly generated. k,s The synergistic performance P of all individuals is calculated using equation (11). s And identify the individuals with the best and worst cooperative performance. and

[0139] Then randomly select two different individuals x l1 and x l2 Compare their synergistic performance P s Choose P s Larger individuals, if P s If they are the same, then compare the diversity performance P. d Choose P d Larger individuals, if P d Similarly, comparing the fitness performance P... f Choose P f Larger individuals, if P s P d P f If all are the same, then select the first individual and denote the selected individual as x. l Comparison of individual x l With individual x k Synergistic performance P s If x l P s If the value is large, then update individual x according to equation (13). k Otherwise, update individual x according to equation (14). k ,

[0140]

[0141]

[0142] Where the subscript v represents the variable of the v-th dimension, and the superscript s indicates that the individual is selected based on cooperative performance. and R represents the individuals with the best and worst collaborative performance in the v-th dimension. 1,v and r 2,v It is a random number in the range [0,1].

[0143] S404. Calculate the updated individual x′ k,v fitness performance P f It is then compared with the current optimal solution. If the solution is better than the optimal solution, the optimal solution is updated; otherwise, the optimal solution is kept unchanged.

[0144] The iterative update termination condition of the adaptive collaborative strategy is to satisfy at least one of the following iterative update termination conditions: Condition 1 is that the number of parameter update iterations is equal to the specified maximum number of iterations, as shown in Equation (15); Condition 2 is that the rate of change of the variance of the population difference is less than a set threshold, as shown in Equation (16).

[0145] t < t max (15)

[0146]

[0147] in, It is the variance of population diversity in the t-th iteration. It is the variance of the population diversity in the (t-1)th iteration, defined as D i For the degree of variability of individual i, D i =||x i -x w ||Calculated, NP represents the average difference among all individuals in the population, where NP is the number of individuals in the population. To set a threshold.

[0148] S5. The second stage of system parameter identification based on the elite-guided strategy is iterative update identification. The termination condition for this stage is that the fitness of the elite individuals in the identified parameters is lower than the set fitness threshold or the set number of iterations is reached. The specific process is as follows:

[0149] S501. Divide the population obtained in step S4 into two populations, population 1 and population 2, with NP / 2 individuals in each population. Generate the paths of random walks of individuals in population 1. Each path contains d-dimensional variables, representing the d parameters that need to be identified. The paths of random walks of individuals in population 1 are given by equation (17).

[0150] X(t)=[0,cumsum(2r(t1)-1),cumsum(2r(t2)-1),...,cumsum(2r(t) n )-1)](17)

[0151] Where t represents the number of random steps (the current iteration number in this algorithm), cumsum represents the cumulative sum, n is the maximum iteration number, and r(t) is a random function, given by equation (18):

[0152]

[0153] In the formula, rand is a random number in the interval [0,1].

[0154] Considering that the search space for the system's identification parameters is bounded, equation (17) is normalized using equation (19).

[0155]

[0156] Where i represents the i-th dimension, a i b i These are the minimum and maximum values ​​of the random walk path for the i-th dimension variable before normalization, respectively, where t represents the current iteration number. These are the lower and upper bounds of the i-th dimension variable at the t-th iteration, respectively.

[0157] S502. Calculate and rank the fitness of individuals in the population.

[0158] The fitness of all individuals is calculated using formula (4) in S402. The individual with the best fitness in population 2 is selected as the elite individual. For each individual in population 1, a corresponding individual in population 2 is selected using roulette wheel selection.

[0159] Equation (20) indicates that the random walking radius of an individual in population 1 around an individual in population 2 decreases adaptively.

[0160]

[0161] Among them, lb t and ub t These are the lower and upper bounds of the variable in the t-th iteration, respectively. t represents the current iteration number, and T represents the maximum iteration number.

[0162] The selected individuals in population 2 will affect the random walks of the corresponding individuals in population 1. Equation (21) is used to represent the update of the random walk boundary of the corresponding individuals in population 1.

[0163]

[0164] Where t represents the current iteration number, and These are the lower and upper bounds of the variable for the i-th individual in population 1, respectively, lb t and ub t These are the lower and upper bounds of the variable in the t-th iteration, respectively. This represents the position of the j-th selected individual in population 2 during the t-th iteration;

[0165] Elite individuals will influence the movement of all individuals in population 1 in subsequent iterations, and this influence is expressed by equation (22).

[0166]

[0167] Where t represents the current iteration number, The t-th iteration is the random walking path around the selected individual in population 2. It is the random walking path around the elite individual in the t-th iteration. Let be the position of the i-th individual in population 1 during the t-th iteration.

[0168] S503. After updating all individuals in population 1, if the fitness of an individual in population 1 becomes less than the fitness of the corresponding individual in population 2, then the position of the corresponding individual in population 2 is updated using the position of the individual in population 1, i.e., equation (23).

[0169]

[0170] Where t represents the current iteration number, This represents the position of the j-th individual in population 2 at the t-th iteration. This represents the position of the i-th individual in population 1 at the t-th iteration.

[0171] The individual with the best fitness in population 2 obtained in each iteration is taken as the elite individual, and the system identification parameters based on the elite guidance strategy are updated in the (t+1)th iteration.

[0172] S504. When the system parameter identification iteration process based on the elite-guided strategy reaches the iteration termination condition, the update iteration of the system parameter identification based on the elite-guided strategy is stopped.

[0173] The iteration termination condition of the system parameter identification iteration process based on the elite guidance strategy is to satisfy at least one of the following iteration update termination conditions: condition one is that the number of parameter update iterations is equal to the specified maximum number of iteration updates; condition two is that the fitness of the elite individual is less than a specified threshold.

[0174] S6. Use the system parameters at the end of the iteration as the final parameter identification result, and then output the system parameter identification result.

[0175] Example 1

[0176] In one or more of the technical solutions disclosed in the embodiments, inspired by the proton exchange membrane fuel cell model, a mathematical model containing multiple unknown parameters is constructed as a proton exchange membrane electrolyzer model. The parameters in the model can be obtained by parameter identification using measured experimental data. A two-stage parameter optimization algorithm that integrates adaptive collaborative and elite-guided optimization is used to identify the parameters of the established proton exchange membrane electrolyzer model, thereby achieving parameter estimation of the proton exchange membrane electrolyzer.

[0177] like Figure 2As shown, the implementation process of the above-mentioned electrolytic cell parameter identification and optimization method specifically includes the following steps:

[0178] S1. Based on the experimental data of the electrolyzer and the correlation of various parameters, determine the unknown parameters required for the electrolyzer model, and establish a mathematical model of the electrolyzer based on the above parameters; the specific process is as follows:

[0179] A proton exchange membrane electrolyzer consists of several units, each with an operating voltage u. cell It can be expressed as open-circuit voltage u Ocv Activation overvoltage η act Ohmic overvoltage η ohm With concentration overvoltage η conc The sum of the four is as shown in equation (24).

[0180] u cell =u OCv +η act +η ohm +η conc (twenty four)

[0181] Open circuit voltage u Ocv As given by equation (25),

[0182]

[0183] Where T is the thermodynamic temperature scale, in K, obtained experimentally; R is the gas constant, typically taken as 8.3145 J / (mol·K); F is the Faraday constant, typically taken as 96485 C / mol; p H2O p H2 p O2 Given by equations (26)(27)(28),

[0184]

[0185] p H2 =P ca -p H2O (27)

[0186] p O2 =P an -p H2O (28)

[0187] Among them, P ca and P an These are the absolute pressures measured by the hydrogen separator and the oxygen separator, respectively.

[0188] Activation overvoltage η act As given by equation (29),

[0189]

[0190] Where, α an The anode charge transfer coefficient, i, needs to be identified. 0,an The anode current density is given by equation (30).

[0191]

[0192] i 0,an,std E represents the anode current density under standard conditions. exc The activation energy required for anodic electron transport needs to be identified.

[0193] Ohmic overvoltage η ohm As given by equation (31),

[0194]

[0195] Where, σ mem As expressed by equation (32),

[0196]

[0197] σ mem,std E represents the film resistivity under standard conditions. pro The activation energy required for proton transport in the membrane needs to be identified.

[0198] Because the rated operating current density in the experiment will not be high enough to generate concentration overvoltage η. conc Therefore, it has been omitted.

[0199] From the above equations, a mathematical model for a proton exchange membrane electrolyzer can be determined. The five parameters that need to be identified are: the anode charge transfer coefficient α... an Anode current density i under standard conditions 0,an,std The activation energy E required for anodic electron transport exc The membrane resistivity σ under standard conditions mem,std And the activation energy E required for proton transport in the membrane pro .

[0200] S2. Obtain experimental data on the measurable parameters and corresponding working states of the electrolytic cell through actual working condition testing of the electrolytic cell system, that is, record the experimental data on voltage, current, temperature and pressure when the electrolytic cell is in operation.

[0201] S3. Randomly generate initial population individuals based on a reasonable range of system parameters to be identified; the specific process is as follows:

[0202] S301. Determine the reasonable range of the parameters to be identified in the electrolytic cell system:

[0203] Based on existing publicly available data or empirical values, the range of parameters for the electrolytic cell system is given, as shown in equation (33).

[0204]

[0205] Where a represents the parameter to be identified in the electrolytic cell, lb represents the lower bound of the parameter to be identified, and ub represents the upper bound of the parameter to be identified.

[0206] S302, Randomly generate population individuals

[0207] Each individual is a candidate solution, containing d-dimensional variables, representing d parameters that need to be identified; the variable of the d-th dimension of each candidate solution is given by equation (34).

[0208] x d =lb d +(ub d -lb d rand (34)

[0209] Where, x d For the candidate solution, the variable of the d-th dimension is rand, which is a random number in the range [0,1].

[0210] S4. The first stage of iterative update and identification of system parameters is based on an adaptive cooperative strategy. The termination condition for this stage is that the variance of the population difference of the identified parameters is stable or the set number of iterations is reached. The specific process is as follows:

[0211] S401. Adaptive cooperative strategy initialization: Set the basic parameters of the adaptive cooperative strategy;

[0212] Set the population size to NP, which is the number of individuals in the population; randomly generate NP individuals x (candidate solutions), each candidate solution contains d-dimensional variables, representing d parameters that need to be identified.

[0213] S402. Calculate the fitness performance P of all individuals. f and difference performance P d The specific process is as follows:

[0214] The root mean square error (RMSE) between the measured output and the model output is used as the fitness function f. fitness (x k As shown in equation (35), the fitness of each individual is calculated.

[0215]

[0216] Where, x k Let k represent an individual, h be the number of sample points in the measured data sequence, and y be the measured output. Output for the model;

[0217] The difference function f is defined using Euclidean distance. diversity (x k As shown in equation (36), the degree of difference for each individual is calculated.

[0218]

[0219] Where, x k Let k represent an individual, NP represent the number of individuals in the population, and ||x k -x w || represents the Euclidean distance between individual k and individual w, which is calculated using equation (37).

[0220]

[0221] and Representing individual x k and x w The coordinates in the i-th dimension, where d is the number of dimensions.

[0222] Individual fitness and diversity are sorted in descending order to obtain the fitness ranking R of the individuals. fitness And the difference ranking R diversity As shown in equations (38) and (39),

[0223] R fitness (x k )=NP+1-i k i k =1,2,...,NP (38)

[0224] R diversity (x k )=NP+1-j k ,j k =1,2,...,NP (39)

[0225] The fitness performance P of each individual is calculated using equations (40) and (41). f and difference performance P d ,

[0226]

[0227]

[0228] Here, we introduce the collaborative performance P. s As an evaluation index for individual k, its definition is given by equation (42).

[0229] P s =Pd ·c k,s +P f ·(1-c k,s (42)

[0230] Among them, P f With P d As given by equations (40) and (41), c k,s The synergy coefficient is a random number in the range [0,1].

[0231] S403, Adaptive Cooperative Iterative Update of System Parameters:

[0232] In each iteration of adaptive collaborative optimization, the fitness performance and diversity performance of each individual are first calculated, and the individuals with the best and worst fitness, x, are given. fbest and x fworst ;

[0233] Furthermore, for each individual x k Determine if x is the individual with the lowest fitness. k For the individual with the lowest fitness, the optimal solution is updated according to equation (43).

[0234]

[0235] Where the superscript R represents two randomly selected individuals, The one with better fitness among the randomly selected individuals. Let x′ be the randomly selected individual with the worst fitness, v represents the variable of the v-th dimension. fbest,v For the updated x fbest,v r 1,fbest,v A random number in the range [0,1];

[0236] If x k If the individual is not the one with the lowest fitness, then a cooperability coefficient c is randomly generated. k,s The synergistic performance P of all individuals is calculated using equation (42). s And identify the individuals with the best and worst cooperative performance. and

[0237] Then randomly select two different individuals x l1 and x l2 Compare their synergistic performance P s Choose P s Larger individuals, if P s If they are the same, then compare the diversity performance P. d Choose P d Larger individuals, if P dSimilarly, comparing the fitness performance P... f Choose P f Larger individuals, if P s P d P f If all are the same, then select the first individual and denote the selected individual as x. l ;

[0238] Comparing individual x l With individual x k Synergistic performance P s If x l P s If the value is large, then update individual x according to equation (44). k Otherwise, update individual x according to equation (45). k ,

[0239]

[0240]

[0241] Where the subscript v represents the variable of the v-th dimension, and the superscript s indicates that the individual is selected based on cooperative performance. and R represents the individuals with the best and worst collaborative performance in the v-th dimension. 1,v and r 2,v It is a random number in the range [0,1].

[0242] S404. Calculate the updated individual x′ k,v fitness performance P f It is then compared with the current optimal solution. If the solution is better than the optimal solution, the optimal solution is updated; otherwise, the optimal solution is kept unchanged.

[0243] After updating all individuals in the population, increment the iteration count by 1 and continue to the next adaptive collaborative optimization iteration until the iteration termination condition is met.

[0244] The iterative update termination condition of the adaptive collaborative strategy is to satisfy at least one of the following iterative update termination conditions: Condition 1 is that the number of parameter update iterations is equal to the specified maximum number of iterations, as shown in Equation (46); Condition 2 is that the rate of change of the variance of the population difference is less than a set threshold, as shown in Equation (47).

[0245] t < t max (46)

[0246]

[0247] in, It is the variance of population diversity in the t-th iteration. It is the variance of the population diversity in the (t-1)th iteration, defined as D i For the degree of variability of individual i, D i =||x i -x w ||Calculated, NP represents the average difference among all individuals in the population, where NP is the number of individuals in the population. To set a threshold.

[0248] S5. The second stage of system parameter identification based on the elite-guided strategy is iterative update identification. The termination condition for this stage is that the fitness of the elite individuals in the identified parameters is lower than the set fitness threshold or the set number of iterations is reached. The specific process is as follows:

[0249] S501. Divide the population obtained in step S4 into two populations, population 1 and population 2, with NP / 2 individuals in each population. Generate the paths of random walks of individuals in population 1. Each path contains d-dimensional variables, representing the d parameters that need to be identified. The paths of random walks of individuals in population 1 are given by equation (48).

[0250] X(t)=[0,cumsum(2r(t1)-1),cumsum(2r(t2)-1),...,cumsum(2r(t) n )-1)](48)

[0251] Where t represents the number of random steps (the current iteration number in this algorithm), cumsum represents the cumulative sum, n is the maximum iteration number, and r(t) is a random function, given by equation (49):

[0252]

[0253] In the formula, rand is a random number in the interval [0,1].

[0254] Considering that the search space for the system's identification parameters is bounded, equation (48) is normalized using equation (50).

[0255]

[0256] Where i represents the i-th dimension, a i b i These are the minimum and maximum values ​​of the random walk path for the i-th dimension variable before normalization, respectively, where t represents the current iteration number. These are the lower and upper bounds of the i-th dimension variable at the t-th iteration, respectively.

[0257] S502, calculate and sort the fitness of individuals in the population. Use formula (35) in S402 to calculate and sort the fitness of all individuals. Select the individual with the best fitness in population 2 as the elite individual. For each individual in population 1, use roulette wheel to select a corresponding individual in population 2.

[0258] Equation (51) indicates that the random walking radius of an individual in population 1 around an individual in population 2 decreases adaptively.

[0259]

[0260] Among them, lb t and ub t These are the lower and upper bounds of the variable in the t-th iteration, respectively. t represents the current iteration number, and T represents the maximum iteration number.

[0261] The selected individuals in population 2 will affect the random walks of the corresponding individuals in population 1. Equation (52) is used to represent the update of the random walk boundary of the corresponding individuals in population 1.

[0262]

[0263] Where t represents the current iteration number, and These are the lower and upper bounds of the variable for the i-th individual in population 1, respectively, lb t and ub t These are the lower and upper bounds of the variable in the t-th iteration, respectively. This represents the position of the j-th selected individual in population 2 during the t-th iteration;

[0264] Elite individuals will influence the movement of all individuals in population 1 in subsequent iterations, and this influence is expressed by equation (53).

[0265]

[0266] Where t represents the current iteration number, It is the random walking path around the selected individual in population 2 at the t-th iteration. It is the random walking path around the elite individual in the t-th iteration. Let be the position of the i-th individual in population 1 during the t-th iteration.

[0267] S503. After updating all individuals in population 1, if the fitness of an individual in population 1 becomes less than the fitness of the corresponding individual in population 2, then the position of the corresponding individual in population 2 is updated using the position of the individual in population 1.

[0268]

[0269] Where t represents the current iteration number, This represents the position of the j-th individual in population 2 at the t-th iteration. This represents the position of the i-th individual in population 1 at the t-th iteration.

[0270] The individual with the best fitness in population 2 obtained in each iteration is taken as the elite individual, and the system identification parameters based on the elite guidance strategy are updated in the (t+1)th iteration.

[0271] S504. When the system parameter identification iteration process based on the elite-guided strategy reaches the iteration termination condition, the update iteration of the system parameter identification based on the elite-guided strategy is stopped.

[0272] The iteration termination condition of the system parameter identification iteration process based on the elite guidance strategy is to satisfy at least one of the following iteration update termination conditions: condition one is that the number of parameter update iterations is equal to the specified maximum number of iteration updates; condition two is that the fitness of the elite individual is less than a specified threshold.

[0273] S6. The final parameter identification result output is the system parameter corresponding to the elite individual at the time when the system parameter identification iteration process based on the elite guidance strategy terminates.

[0274] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A system parameter identification method integrating adaptive collaboration and elite guidance, characterized in that, For proton exchange membrane electrolyzers, a mathematical model containing multiple unknown parameters is constructed as the proton exchange membrane electrolyzer model. A two-stage parameter optimization algorithm integrating adaptive collaborative and elite-guided optimization is used to identify the parameters of the established proton exchange membrane electrolyzer model, thereby achieving parameter estimation of the proton exchange membrane electrolyzer. The specific steps include the following: S1. Establish a system parameter identification model and determine the system parameters to be identified; For a proton exchange membrane electrolyzer, the system parameter identification model is specifically a proton exchange membrane electrolyzer model; Based on the experimental data of the electrolyzer and the correlation of various parameters, the unknown parameters required for the electrolyzer model are determined, and a proton exchange membrane electrolyzer model based on the above parameters is established; the specific establishment process is as follows: A proton exchange membrane electrolyzer consists of several units, each with an operating voltage u. cell Represented as open-circuit voltage u Ocv Activation overvoltage η act Ohmic overvoltage η ohm With concentration overvoltage η conc The sum of the four is as shown in equation (24). you cell =u OCv +n act +n ohm +n conc (24) Open circuit voltage u Ocv As given by equation (25), Where T is the thermodynamic temperature scale, obtained experimentally; R is the gas constant; F is the Faraday constant; p H2O p H2 p O2 Given by equations (26)(27)(28), p H2 =P ca -p H2O (27) p O2 =P an -p H2O (28) Among them, P ca and P an These are the absolute pressures measured by the hydrogen separator and the oxygen separator, respectively. Activation overvoltage η act As given by equation (29), Where, α an i is the anode charge transfer coefficient; 0,an The anode current density is given by equation (30). i 0,an,std E represents the anode current density under standard conditions. exc The activation energy required for anodic electron transport; Ohmic overvoltage η ohm As given by equation (31), Where, σ mem As expressed by equation (32), σ mem,std E represents the film resistivity under standard conditions. pro The activation energy required for proton transport in the membrane; The above equations determine a mathematical model for a proton exchange membrane electrolyzer, where five parameters need to be identified: the anode charge transfer coefficient α. an Anode current density i under standard conditions 0,an,std The activation energy E required for anodic electron transport exc The membrane resistivity σ under standard conditions mem,std And the activation energy E required for proton transport in the membrane pro ; S2. Obtain the set of measurable operating variables of the system, including the set of measurable input / output variables and the set of measurable state variables; for the proton exchange membrane electrolyzer, obtain experimental data that records the measurable parameters of the electrolyzer and the corresponding working state through actual operating condition testing of the electrolyzer system, that is, record the experimental data of voltage, current, temperature and pressure when the electrolyzer is in operation. S3. Randomly generate initial population individuals based on a reasonable range of system parameters to be identified; for a proton exchange membrane electrolyzer, the system parameters to be identified are specifically the electrolyzer system parameters to be identified. S4. The first stage of iterative update and identification of system parameters is based on an adaptive cooperative strategy. The termination condition of this stage is that the variance of the population difference of the identified parameters is stable or the set number of iterations is reached. S5. The second stage of iterative update and identification of system parameters is based on the elite-guided strategy. The termination condition of this stage is that the fitness of the elite individuals in the population with the identified parameters is lower than the set fitness threshold or the set number of iterations is reached. S6. Take the system parameters at the end of the iteration as the final parameter identification result, and then output the system parameter identification result.

2. The system parameter identification method integrating adaptive collaboration and elite guidance according to claim 1, characterized in that, in step S1, the system parameter identification model is in the form of equation (1). Where y represents the output of the system parameter identification model, x1, x2, ..., x m The m input variables, u1, u2, ..., u, represent the system parameter identification model. n The n state variables, a1, a2, ..., a, represent the system parameter identification model. d f represents the d parameters to be identified in the model. i This represents the functional relationship expressed by the input quantity and the unknown parameter to be identified.

3. The system parameter identification method integrating adaptive collaboration and elite guidance according to claim 2, characterized in that, The specific process of step S2 is as follows: S201. Identify the state variables and input / output variables in the model based on the system parameters, and determine the measurable state variables and measurable input / output variables of the system. S202. Obtain the set of operating condition data of the measurable input / output variables and the measurable state variables through actual operating condition testing of the system.

4. The system parameter identification method integrating adaptive collaboration and elite guidance according to claim 3, characterized in that, The specific process of step S3 is as follows: S301. Determine the reasonable range of parameters for the system to be identified: Based on existing publicly available data or empirical values, the range of system parameters to be identified is given, as shown in equation (2). Where a is the parameter to be identified, lb represents the lower bound of the parameter to be identified, and ub represents the upper bound of the parameter to be identified. S302, Randomly generate population individuals; Each individual is a candidate solution, containing d-dimensional variables, representing d parameters that need to be identified; the variable of the d-th dimension of each candidate solution is given by equation (3). x d =lb d +(ub d -lb d )·rand (3) Where, x d Let d be the variable of the d-th dimension of the candidate solution, and rand is a random number in the range [0,1].

5. The system parameter identification method integrating adaptive collaboration and elite guidance according to claim 4, characterized in that, The specific process of step S4 is as follows: S401. Adaptive cooperative strategy initialization: Set the basic parameters of the adaptive cooperative strategy; Set the population size to NP, which is the number of individuals in the population; randomly generate NP individuals x, each candidate solution contains d-dimensional variables, representing d parameters that need to be identified; S402. Calculate the fitness performance P of all individuals. f and difference performance P d The specific process is as follows: The root mean square error (RMSE) between the measured output and the model output is used as the fitness function f. fitness (x k As shown in equation (4), the fitness of each individual is calculated. Where, x k Let k represent an individual, h be the number of sample points in the measured data sequence, and y be the measured output. Output for the model; The difference function f is defined using Euclidean distance. diversity (x k As shown in equation (5), the degree of difference for each individual is calculated. Where, x k Let k represent an individual, NP represent the number of individuals in the population, and ||x k -x w || represents the Euclidean distance between individual k and individual w, which is calculated using equation (6). and Representing individual x k and x w The coordinates in the i-th dimension, where d is the number of dimensions; Individual fitness and diversity are sorted in descending order to obtain the fitness ranking R of the individuals. fitness And the difference ranking R diversity As shown in equations (7) and (8), R fitness (x k )=NP+1-i k ,i k =1,2,…,NP (7) R diversity (x k )=NP+1-j k ,j k =1,2,…,NP (8) The fitness performance P of each individual is calculated using equations (9) and (10). f and difference performance P d , Here, we introduce the collaborative performance P. s As an evaluation index for individual k, its definition is given by equation (11). P s =P d ·c k,s +P f ·(1-c k,s ) (11) Among them, P f With P d As given by equations (9) and (10), c k,s The coordination coefficient is a random number in the range [0,1]. S403, Adaptive Cooperative Iterative Update of System Parameters: In each iteration of adaptive collaborative optimization, the fitness performance and diversity performance of each individual are first calculated, and the individuals with the best and worst fitness, x, are given. fbest and x fworst ; Furthermore, for each individual x k Determine if x is the individual with the lowest fitness. k For the individual with the lowest fitness, the optimal solution is updated according to equation (12). Where the superscript R represents two randomly selected individuals, The one with better fitness among the randomly selected individuals. Let x′ be the randomly selected individual with the worst fitness, v represents the variable of the v-th dimension. fbest,v For the updated x fbest,v r 1,fbest,v A random number within the range [0,1]; If x k If the individual is not the one with the lowest fitness, then a cooperability coefficient c is randomly generated. k,s The synergistic performance P of all individuals is calculated using equation (11). s And identify the individuals with the best and worst cooperative performance. and Then randomly select two different individuals x l1 and x l2 Compare their synergistic performance P s Choose P s Larger individuals, if P s If they are the same, then compare the diversity performance P. d Choose P d Larger individuals, if P d Similarly, comparing the fitness performance P... f Choose P f Larger individuals, if P s P d P f If all are the same, then select the first individual and denote the selected individual as x. l Comparison of individual x l With individual x k Synergistic performance P s If x l P s If the value is large, then update individual x according to equation (13). k Otherwise, update individual x according to equation (14). k , Where the subscript v represents the variable of the v-th dimension, and the superscript s indicates that the individual is selected based on cooperative performance. and r represents the individuals with the best and worst collaborative performance in the v-th dimension. 1,v and r 2,v It is a random number in the range [0,1]. S404. Calculate the updated individual x′ k,v fitness performance P f It is then compared with the current optimal solution. If the solution is better than the optimal solution, the optimal solution is updated; otherwise, the optimal solution is kept unchanged. The iterative update termination condition of the adaptive collaborative strategy is to satisfy at least one of the following iterative update termination conditions: Condition 1 is that the number of parameter update iterations is equal to the specified maximum number of iterations, as shown in Equation (15); Condition 2 is that the rate of change of the variance of the population difference is less than a set threshold, as shown in Equation (16). t<t max (15) in, It is the variance of population diversity in the t-th iteration. It is the variance of the population diversity in the (t-1)th iteration, defined as D i For the degree of variability of individual i, D i =||x i -x w ||Calculated, NP represents the average difference among all individuals in the population, where NP is the number of individuals in the population. To set a threshold.

6. The system parameter identification method integrating adaptive collaboration and elite guidance according to claim 5, characterized in that, The specific process of step S5 is as follows: S501. Divide the population obtained in step S4 into two populations, population 1 and population 2, with the number of individuals in each population being NP / 2. Generate the paths of random walks of individuals in population 1. Each path contains d-dimensional variables, representing the d parameters that need to be identified. The paths of random walks of individuals in population 1 are given by equation (17). X(t)=[0,cumsum(2r(t1)-1),cumsum(2r(t2)-1),…,cumsum(2r(t n )-1)] (17) Where t represents the number of random steps, cumsum represents the cumulative sum, n is the maximum number of iterations, and r(t) is a random function, given by equation (18): In the formula, rand is a random number in the interval [0,1]. Considering that the search space for the system's identification parameters is bounded, equation (17) is normalized using equation (19). Where i represents the i-th dimension, a i b i These are the minimum and maximum values ​​of the random walk path for the i-th dimension variable before normalization, respectively, where t represents the current iteration number. These are the lower and upper bounds of the i-th dimension variable at the t-th iteration, respectively. S502. Calculate and rank the fitness of individuals in the population. Use equation (4) in S402 to calculate the fitness of all individuals. Select the individual with the best fitness in population 2 as the elite individual. For each individual in population 1, use roulette wheel to select a corresponding individual in population 2. Use equation (20) to indicate that the random walking radius of an individual in population 1 around an individual in population 2 is adaptively reduced. Among them, lb t and ub t These are the lower and upper bounds of the variable in the t-th iteration, respectively. t represents the current iteration number, and T represents the maximum iteration number; The selected individuals in population 2 will affect the random walks of the corresponding individuals in population 1. Equation (21) is used to represent the update of the random walk boundary of the corresponding individuals in population 1. Where t represents the current iteration number, and These are the lower and upper bounds of the variable for the i-th individual in population 1, respectively, lb t and ub t These are the lower and upper bounds of the variable in the t-th iteration, respectively. This represents the position of the j-th selected individual in population 2 during the t-th iteration; Elite individuals will influence the movement of all individuals in population 1 in subsequent iterations, and this influence is expressed by equation (22). Where t represents the current iteration number; It is the random walking path around the selected individual in population 2 at the t-th iteration; It is the random walking path around the elite individual at the t-th iteration; This represents the position of the i-th individual in population 1 during the t-th iteration. S503. After updating all individuals in population 1, if the fitness of an individual in population 1 becomes less than the fitness of the corresponding individual in population 2, then the position of the corresponding individual in population 2 is updated using the position of the individual in population 1, i.e., equation (23). Where t represents the current iteration number; This represents the position of the j-th individual in population 2 at the t-th iteration; This represents the position of the i-th individual in population 1 at the t-th iteration. The individual with the best fitness in population 2 obtained in each iteration is taken as the elite individual, and the system identification parameters are updated in the (t+1)th iteration based on the elite guidance strategy. S504. When the system parameter identification iteration process based on the elite guidance strategy reaches the iteration termination condition, the update iteration of the system parameter identification based on the elite guidance strategy is stopped. The iteration termination condition of the system parameter identification iteration process based on the elite guidance strategy is to satisfy at least one of the following iteration update termination conditions: Condition 1 is that the number of parameter update iterations is equal to the specified maximum number of iteration updates; Condition 2 is that the fitness of the elite individual is less than a specified threshold.

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