CN115954504A - PEMFC model parameter optimization method based on CGSASA algorithm - Google Patents
PEMFC model parameter optimization method based on CGSASA algorithm Download PDFInfo
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- 239000000446 fuel Substances 0.000 claims abstract description 13
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- 230000005484 gravity Effects 0.000 claims abstract description 8
- 238000010845 search algorithm Methods 0.000 claims abstract description 5
- 239000012528 membrane Substances 0.000 claims description 18
- 230000010287 polarization Effects 0.000 claims description 17
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Abstract
The invention provides a PEMFC model parameter optimization method based on a CGSASA algorithm. The parameters are preferably an important step in the modeling of the fuel cell. Aiming at the problems that the basic gravity search algorithm is low in convergence speed and easy to fall into local optimum, the algorithm combines the ergodicity of chaotic mapping and the advantage that the SA algorithm has progressive convergence, the gravity search algorithm, the chaotic mapping and the simulated annealing are organically combined by introducing two parameters of a population grouping coefficient and a mixed evolution algebra, the CGSASA algorithm is provided, so that the respective advantages of the three algorithms are expected to be exerted, and the solving precision and the convergence speed of the standard GSA algorithm are improved.
Description
Technical Field
The invention relates to the technical field of PEMFCs, in particular to a PEMFC model parameter optimization method based on a CGSASA algorithm.
Background
Proton exchange membrane fuel cells have the advantages of high energy conversion efficiency, quick start at low temperature, zero emission, complementarity between the energy and solar energy and wind energy, and the like, and have attracted more and more attention in the field of new energy. The establishment of a steady-state model reflecting the output performance of the PEMFC is the basis for system structure optimization and performance analysis, and has important significance for further improving the process control performance of the PEMFC and improving the operation and running level of the system. In the modeling process of the PEMFC, besides the requirement of reasonable structure of a model, the simulation effect and the prediction accuracy of the model depend on the selection of model parameters to a great extent. The parameter estimation problem usually translates it into a minimization problem of the deviation of the empirical observations from the estimated values. Because the internal reaction mechanism of the fuel cell is very complex, the PEMFC model has the characteristics of nonlinear structure and numerous parameters, and high correlation and remarkable nonlinear interference exist among the parameters, so that the parameter estimation becomes a complex high-dimensional nonlinear optimization problem, and the solution of the optimization problem faces great challenges.
Most of traditional gradient-based classical optimization methods adopt local search and are sensitive to initial values, the solution of the PEMFC model parameter optimization problem is large in workload and low in solution precision, and a global optimal solution is difficult to obtain.
Disclosure of Invention
In view of this, the present invention aims to provide a PEMFC model parameter optimization method based on a CGSASA algorithm, which can improve the solution accuracy and convergence rate of a standard PSO algorithm, has higher simulation accuracy, and has obvious superiority for optimizing a polarization curve model parameter of a PEMFC.
In order to achieve the purpose, the invention adopts the following technical scheme: a PEMFC model parameter optimization method based on a CGSASA algorithm comprises the following specific steps:
step S1, initializing CGSASA algorithm parameters: population size m, maximum number of iterations G max SA initial temperature T 0 Termination temperature Tf, cooling rate ρ; mixed algebra Mg and population grouping coefficient Pd;
s2, initializing GSA population individuals: initializing a position value and a speed value of a population individual according to a Logistic chaotic mapping equation, namely formula (1), and setting the current iteration number to be G =0; GG =1;
x n ＝u·(1-x n ) x n ∈(0,1) (1)
in the formula: x is a radical of a fluorine atom n The position value of the population individual corresponding to the iteration value of the variable x at the nth time; u is the value x of the variable x at the nth iteration n The corresponding speed value of the population individual; x is more than or equal to 0 and less than or equal to 1 and is a bifurcation parameter of the Logistic chaotic mapping;
s3, judging an iteration condition, and if G is less than or equal to G max If not, turning to step6, otherwise, turning to step S4;
s4, evaluating the individual fitness evaluation, carrying out individual adjustment on the race, if GG is less than Mg, turning to S5, otherwise, using the current optimal position of each individual
Forming a new population, sequencing according to the fitness value, dividing the new population into two groups according to a population grouping coefficient Pd, and executing simulated annealing operation on Pd m superior individuals:
(1) In that
Field generating a new solution>
/>
(2) Evaluation of
And &>
Has an fitness value>
And &>
And calculates Δ f: />
(3) If Δ f < 0, then accept
As a new solution; otherwise accepts with probability exp (- Δ f/T) < >>
As a new solution;
(4) Update the temperature T k+1 ＝ρ·T k (ii) a For (1-Pd) × m poor individuals, performing global disturbance by using chaotic mapping;
step S5: calculating the mass, gravity and acceleration of each individual in the new population according to the following formulas (2) to (5):
step S6: push type
And/or>
Updating individual speed and position, and enabling G = G +1Step S3 is executed;
step S7: the algorithm is terminated and the optimal value is output
In a preferred embodiment: passing each individual through
Is mapped to the chaotic variable->
Hybrid variable>
Warp formula x n ＝u·(1-x n )x n The element belongs to (0, 1) to do chaotic motion to obtain a new position point->
Will be/are>
Pass-through type>
Transform, map to (g) i,max ,g i,min ) Is based on a common variable->
Then, two parts of elite individuals obtained by performing simulated annealing and chaotic mapping are combined into a new population again, and GG =0 is set.
In a preferred embodiment: the principle of the CGSASA algorithm is as follows:
the principle of the CGSASA hybrid algorithm is: generating a large number of initial populations by utilizing the ergodicity of chaotic mapping, selecting the initial population of the GSA from the initial populations, setting parameters, and recording the current optimal position of each individual; when the GSA runs to a certain algebra, a new population is formed by the optimal positions of the current individuals and is sorted according to the fitness value; dividing the sorted new population into two parts including a better individual and a worse individual according to a preset grouping coefficient, and performing local search on each better individual by using an SA (SA) algorithm; for each poor individual, performing global disturbance by using chaotic mapping to increase the diversity of the population; and finally, mixing the two parts of individuals which are subjected to the local search and the global disturbance to form a new population, and continuing to carry out the GSA evolution operation, and alternating the steps until the termination condition of the algorithm is met.
In a preferred embodiment: the PEMFC model is specifically as follows:
the essential reaction of the PEM fuel cell is the oxidation-reduction of hydrogen and oxygen to produce water and the direct conversion of the chemical energy stored in the fuel and oxidant into electrical and thermal energy; the method comprises the following specific steps:
anode H 2 →2H + +2e-
Cathode electrode
General reaction
The two polar reactions are separated by a proton exchange membrane, which is a cation exchange membrane with selective permeability, allowing only protons H + Passing; therefore, the protons generated at the anode permeate the proton exchange membrane to migrate to the cathode, and the electrons are attracted by the protons diffused to the cathode to reach the cathode through an external circuit, so as to form current;
the PEMFC fuel cell stack dynamic physical model comprises a steady-state electrochemical model, dynamic models of a cathode and an anode and a temperature model;
1) The steady-state electrochemical model satisfies:
V cell ＝E Nernst -η act -η ohmic -η con (6)
in the formula, E Nernst Is a thermodynamic electromotive force; eta act Is an activation overvoltage; eta ohmic Is an ohmic over-currentPressing; eta con Is a concentration overvoltage;
2) Thermodynamic electromotive force E Nernst Is the thermodynamic equilibrium reversible electromotive force when the single cell is open-circuited and no load, and is expressed as:
in the formula: Δ G is gibbs free energy; f is a Faraday constant; Δ S is enthalpy change; r is a universal gas constant;
is the effective partial pressure of hydrogen; />
Is the effective partial pressure of oxygen; t is the working environment temperature; t is a unit of 0 Is a reference temperature;
3) Active polarization overvoltage E act Is the voltage drop due to the polarization of the cathode and anode of the electrode, and is a measure of the polarization voltage drop to the electrode, expressed as:
η act ＝-[ξ 1 +ξ 2 T+ξ 3 Tln(CO2)+ξ 4 Tln(I)] (8)
in the formula, coefficient xi 1 、ξ 2 、ξ 3 And xi 4 Determined by experimental data and a parameter optimization method;
4) Ohmic polarization overvoltage E ohmic Comprising a voltage drop caused by the impedance of the two cells, i.e. the equivalent membrane impedance resistance R of the protons across the PEM M And the resistance R of the electrons passing through the external circuit C The resulting voltage loss, expressed according to ohm's law, is:
V ohmic ＝I(R M +R C ) (9)
wherein the equivalent film resistance R M Represented by the formula:
R M ＝ρ M ·l/A (10)
in the formula, ρ M Is the resistivity of the film to electron flow; l is the thickness of the film;
ρ M is obtained by the following formula:
in the formula, lambda is the water content of the proton exchange membrane;
5) Concentration polarization overvoltage E con Is a reaction gas H 2 And O 2 The voltage drop induced by the mass transfer process of (1) is represented by the following formula:
V con ＝-bln(1-I/I max ) (12)
in the formula, b is a system parameter; i is the actual current density of the battery; i is max Is the maximum current density of the cell;
in the above PEMFC steady-state model, there are (xi) 1 ,ξ 2 ,ξ 3 ,ξ 4 ,λ,R c And b) the values of the 7 parameters are not determined.
In a preferred embodiment: the specific principle of the gravity search algorithm GSA is as follows:
in the space of the D-dimension,
and &>
The position and the speed of the ith individual are respectively initialized, the fitness value of each individual is calculated, and the quality of the corresponding individual is expressed as an expression (13):
wherein t is the number of iterations; fit i (t) and M i (t) are each an individual x i Fitness and quality of; best (t) and worst (t) are respectively an optimal solution and a worst solution of the t iteration;
the attractive force between the two bodies is then equation (14):
(i, j ∈ {1,2, \ 8230;, N }, and i ≠ j; D =1,2 \8230;, D) (14)
The total force acting on the individual i at the t-th iteration is formula (15):
wherein G (t) is a universal gravitation constant which is changed along with the iteration number t, and G (t) = G 0 e -αt/T In the formula G 0 And alpha is a constant, T is the maximum iteration number; epsilon is a constant such that the denominator is not zero; r ij (t) is the Euclidean distance between the two bodies; further, according to newton's second law, the acceleration is defined as formula (16):
the individual velocity and position updates are respectively equations (17), (18):
in a preferred embodiment: the specific principle of the simulated annealing algorithm is as follows:
the algorithm adopts a heuristic random search process based on a Monte Carlo iterative solution method; the algorithm repeats iteration of 'generating new solution, calculating target function difference, accepting or abandoning' on the current solution from the initial solution x and the temperature parameter T, gradually attenuates the value T, and the current solution when the algorithm is terminated is the obtained approximate optimal solution; the probability that the current new solution is accepted or rejected in the iterative process is determined by the Metropolis criterion;
wherein
And E (x) are expressed as objective function values corresponding to the new solution and the old solution, respectively.
In a preferred embodiment: the individual fitness function in step S4 is specifically as follows:
applying the proposed CGSASA algorithm to the PEMFC battery model to obtain ([ xi ]) 1 ,ξ 2 ,ξ 3 ,ξ 4 λ, rc, b); the fitness function in the parameter optimization process is defined as:
in the formula, S is a fitness function; v i And V i sim Respectively an ith experimental value and a model simulation output value; n is the number of data points.
Compared with the prior art, the invention has the following beneficial effects: compared with the traditional algorithm, the CGSASA has the advantages that the square error obtained by parameter optimization is smaller, the model precision performance is better, and the convergence speed is higher; the PEMFC polarization curve optimized based on the CGSASA algorithm has the best fitting effect with the experimental value and higher precision, and can accurately reflect the change trend of the voltage of the proton exchange membrane fuel cell along with the current; by combining the chaotic mapping and the annealing search strategy, the premature convergence phenomenon is effectively avoided, and higher convergence precision is obtained. Thereby laying a foundation for the optimization design and control of the PEMFC system.
Drawings
FIG. 1 is a flow chart of a method of a preferred embodiment of the present invention.
Detailed Description
The invention is further explained by the following embodiments in conjunction with the drawings.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application; as used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
A PEMFC model parameter optimization method based on CGSASA algorithm refers to FIG. 1, and comprises the following specific steps:
step S1, initializing CGSASA algorithm parameters: population size m, maximum number of iterations G max SA initial temperature T 0 End temperature T f The cooling rate ρ; mixed algebra Mg and population grouping coefficient Pd;
s2, initializing GSA population individuals: initializing a position value and a speed value of a population individual according to a Logistic chaotic mapping equation, namely formula (1), and setting the current iteration number to be G =0; GG =1;
x n ＝u·(1-x n ) x n ∈(0,1) (1)
in the formula: x is the number of n The position value of the population individual corresponding to the iteration value of the variable x at the nth time; u is the value x of the variable x at the nth iteration n The corresponding speed value of the individual population; x is more than or equal to 0 and less than or equal to 1 and is a bifurcate parameter of the Logl sic chaotic mapping;
s3, judging an iteration condition, and if G is less than or equal to G max If not, turning to step6, otherwise, turning to step S4;
s4, evaluating the individual fitness evaluation, carrying out individual adjustment on the race, if GG is less than Mg, turning to S5, otherwise, using the current optimal position of each individual
Forming a new population, sequencing according to the fitness value, dividing the new population into two groups according to a population grouping coefficient Pd, and executing simulated annealing operation on Pd m superior individuals:
(1) In that
The field generates a new solution>
(2) Evaluation of
And &>
Is based on the fitness value->
And &>
And calculates Δ f: />
(3) If Δ f < 0, then accept
As a new solution; otherwise it is accepted with a probability exp (- Δ f/T)>
As a new solution; />
(4) Update temperature Tk +1= ρ · T k (ii) a For (1-Pd) m poor individuals, performing global disturbance by using chaotic mapping;
step S5: calculating the mass, gravity and acceleration of each individual in the new population according to the following formulas (2) to (5):
step S6: push type
And/or>
Updating the individual speed and position, enabling G = G +1, and turning to the step S3;
step S7: the algorithm is terminated and the optimal value is output
Passing each individual through
Is mapped to the chaotic variable->
Mix the variable->
Warp formula x n ＝u·(1-x n )x n The element belongs to (0, 1) to do chaotic motion to obtain a new position point->
Will->
Passing through type
Transform, map to (gi, max, g) i,min ) Is based on a common variable->
Then, two parts of elite individuals obtained by performing simulated annealing and chaotic mapping are grouped into a new population again, and GG =0.
The specific values of the control parameters are as follows:
the settings of the test function are: dimension D =30, the number of groups is set to N =50, and the maximum number of iterations Max _ it =2000. The parameters of the CGSASA algorithm are set as: the annealing initiation temperature T0=92, and the cooling rate k =0.98.
The principle of the CGSASA algorithm is as follows:
the principle of the CGSASA hybrid algorithm is: generating a large number of initial populations by utilizing the ergodicity of chaotic mapping, selecting the initial population of the GSA from the initial populations, setting parameters, and recording the current optimal position of each individual; when the GSA runs to a certain algebra, a new population is formed by the optimal positions of the current individuals and is sorted according to the fitness value; dividing the sorted new population into two parts including a better individual and a worse individual according to a preset grouping coefficient, and performing local search on each better individual by using an SA algorithm; for each poor individual, performing global disturbance by using chaotic mapping to increase the diversity of the population; and finally, mixing the two parts of individuals which are subjected to the local search and the global disturbance to form a new population, and continuing the GSA evolution operation, and alternating the steps until the termination condition of the algorithm is met.
The PEMFC model is specifically as follows:
the essential reaction of the PEM fuel cell is the oxidation-reduction of hydrogen and oxygen to produce water and the direct conversion of the chemical energy stored in the fuel and oxidant into electrical and thermal energy; the method comprises the following specific steps:
anode H 2 →2H + +2e -
Cathode electrode
General reaction
The two polar reactions are separated by a proton exchange membrane, which is a cation exchange membrane with selective permeability, allowing only protons H + Passing; therefore, the protons generated at the anode permeate the proton exchange membrane to migrate to the cathode, and the electrons are attracted by the protons diffused to the cathode to reach the cathode through an external circuit, so as to form current;
the PEMFC fuel cell stack dynamic physical model comprises a steady-state electrochemical model, dynamic models of a cathode and an anode and a temperature model;
1) The steady-state electrochemical model satisfies:
V ce ll＝EN ernst -η act -η ohmic -η con (6)
in the formula, E Nernst Is a thermodynamic electromotive force; eta act Is an activation overvoltage; eta ohmic Is an ohmic overvoltage; eta con Is a concentration overvoltage;
2) Thermodynamic electromotive force E Nernst Is the thermodynamic equilibrium reversible electromotive force when a single cell is open-circuited and no load, and is expressed as:
in the formula: Δ G is gibbs free energy; f is a Faraday constant; Δ S is enthalpy change; r is a universal gas constant;
is an effective partial pressure of hydrogen; />
Is the effective partial pressure of oxygen; t is the working environment temperature; t is 0 Is a reference temperature;
3) Activating polarization overvoltage E act Is the voltage drop due to the polarization of the cathode and anode of the electrode, and is a measure of the polarization voltage drop to the electrode, expressed as:
in the formula, coefficient xi 1 、ξ 2 、ξ 3 And xi 4 Determined by experimental data and a parameter optimization method;
4) Ohmic polarization overvoltage E ohmic Involving a voltage drop due to the impedance of the two-part cell, i.e. the equivalent membrane impedance resistance R of the protons across the proton exchange membrane M And the resistance R of the electrons passing through the external circuit C The resulting voltage loss, expressed according to ohm's law, is:
V ohmic ＝I(R M +R C ) (9)
wherein the equivalent film resistance R M Represented by the formula:
R M ＝ρ M ·l/A (10)
in the formula, ρ M Is the resistivity of the film to electron flow; l is the thickness of the film;
ρ M is obtained by the following formula:
in the formula, lambda is the water content of the proton exchange membrane;
5) Concentration polarization overvoltage E con Is a reaction gas H 2 And O 2 The voltage drop induced by the mass transfer process of (a) is represented by the following formula:
V con ＝-bln(1-I/I max ) (12)
in the formula, b is a system parameter; i is electricityThe actual current density of the cell; i is max Is the maximum current density of the battery;
in the above PEMFC steady-state model, there are (xi) 1 ,ξ 2 ,ξ 3 ,ξ 4 ,λ,R c And b) the values of the 7 parameters are not determined. The specific principle of the gravity search algorithm GSA is as follows:
in the space of the D-dimension,
and &>
The position and the speed of the ith individual are respectively initialized, the fitness value of each individual is calculated, and the quality of the corresponding individual is expressed as an expression (13):
wherein t is the number of iterations; fit (Fit) i (t) and M i (t) are each an individual x i Fitness and quality of; best (t) and worst (t) are respectively an optimal solution and a worst solution of the t iteration;
the attractive force between the two bodies is then equation (14):
(i, j ∈ {1,2, \ 8230;, N }, and i ≠ j; D =1,2 \8230;, D) (14)
The total force at the t iteration on individual i is formula (15):
wherein G (t) is a universal gravitation constant which is transformed with the iteration number t, and G (t) = G 0 e -αt/T In the formula G 0 And alpha is a constant, T is the maximum iteration number; epsilon is a constantMaking the denominator not zero; r ij (t) is the Euclidean distance between the two bodies; further, according to newton's second law, the acceleration is defined as formula (16):
the individual velocity and position updates are equations (17), (18), respectively:
the specific principle of the simulated annealing algorithm is as follows:
the algorithm adopts a heuristic random search process based on a Monte Carlo iterative solution method; the algorithm repeats iteration of 'generating new solution, calculating target function difference, accepting or abandoning' on the current solution from the initial solution x and the temperature parameter T, gradually attenuates the value T, and the current solution when the algorithm is terminated is the obtained approximate optimal solution; the probability that the current new solution is accepted or rejected in the iterative process is determined by the Metropolis criterion;
wherein
And E (x) are expressed as objective function values corresponding to the new solution and the old solution, respectively.
The individual fitness function of step S4 is specifically as follows:
applying the proposed CGSASA algorithm to the PEMFC battery model to obtain ([ xi ]) 1 ,ξ 2 ,ξ 3 ,ξ 4 ,λ,R c The set of optimal parameter combinations of b); in the process of parameter optimizationThe fitness function is defined as:
in the formula, S is a fitness function; v i And V i sim Respectively an ith experimental value and a model simulation output value; n is the number of data points.
The test selects 5 representative standard test functions to verify the optimizing performance of the proposed CGSASA algorithm, and compares the optimizing performance with two optimization algorithms of GSA and PSO. Table 1 lists 5 criteria functions and their search spaces. The dimension of the test function is set to D =30, the population is set to N =50, and the maximum number of iterations Max _ it =2000. In order to eliminate the influence of randomness, each algorithm was independently run 20 times on each standard test function, and the results of the optimal values, mean values and variances obtained by the operation are shown in table 2.
TABLE 1 Standard test function
TABLE 2 Algorithm optimization results
The above description is only a preferred embodiment of the present invention, and all the equivalent changes and modifications made according to the claims of the present invention should be covered by the present invention.
Claims (7)
1. A PEMFC model parameter optimization method based on CGSASA algorithm is characterized in that: the method comprises the following specific steps:
step S1, initializing CGSASA algorithm parameters: population size m, maximum number of iterations G max SA initial temperature T 0 End temperature T f The cooling rate ρ; mixed algebra Mg and population grouping coefficient Pd;
s2, initializing GSA population individuals: initializing a position value and a speed value of a population individual according to a Logistic chaotic mapping equation, namely formula (1), and setting the current iteration number to be G =0; GG =1;
x n ＝u·(1-x n )x n ∈(0,1) (1)
in the formula: x is the number of n The position value of the population individual corresponding to the iteration value of the variable x at the nth time; u is the value x of the variable x at the nth iteration n The corresponding speed value of the individual population; x is more than or equal to 0 and less than or equal to 1 and is a bifurcate parameter of the Logic chaotic mapping;
s3, judging an iteration condition, and if G is less than or equal to G max If not, turning to step6, otherwise, turning to step S4;
s4, evaluating the individual fitness evaluation, carrying out individual adjustment on the race, if GG is less than Mg, turning to the step S5, or else, taking the current optimal position of each individual
Forming a new population, sequencing according to the fitness value, dividing the new population into two groups according to a population grouping coefficient Pd, and executing simulated annealing operation on Pd m superior individuals:
(1) In that
The field generates a new solution>
(2) Evaluation of
And &>
Is based on the fitness value->
And &>
And calculates Δ f: />
(3) If Δ f < 0, then accept
As a new solution; otherwise accepts with probability exp (- Δ f/T) < >>
As a new solution;
(4) Update the temperature T k+1 ＝ρ·T k (ii) a For (1-Pd) × m poor individuals, performing global disturbance by using chaotic mapping;
step S5: calculating the mass, gravity and acceleration of each individual in the new population according to the following formulas (2) to (5):
(i, j ∈ {1,2, \ 8230;, N }, and i ≠ j; D =1,2 \8230;, D)
Step S6: push type
And &>
Updating the individual speed and position, enabling G = G +1, and turning to a step S3;
step S7: the algorithm is terminated and the optimal value is output
2. The PEMFC model parameter optimization method based on CGSASA algorithm of claim 1, wherein: passing each individual through
Is mapped to the chaotic variable->
Mix the variable->
Warp formula x n ＝u·(1-x n )x n The element belongs to (0, 1) to do chaotic motion to obtain a new position point->
Will->
Passing type->
Transform, map to (g) i,max, g i,min ) Is based on a common variable->
Then, the simulated annealing and chaos mapping are performedThe two elite individuals that came in again constituted a new population and were given GG =0.
3. The method of claim 1 for PEMFC model parameter optimization based on CGSASA algorithm, wherein: the principle of the CGSASA algorithm is as follows:
the principle of the CGSASA hybrid algorithm is: generating a large number of initial populations by utilizing the ergodicity of chaotic mapping, selecting the initial population of the GSA from the initial populations, setting parameters, and recording the current optimal position of each individual; when the GSA runs to a certain algebra, a new population is formed by the optimal positions of the current individuals and is sorted according to the fitness value; dividing the sorted new population into two parts including a better individual and a worse individual according to a preset grouping coefficient, and performing local search on each better individual by using an SA algorithm; for each poor individual, performing global disturbance by using chaotic mapping to increase the diversity of the population; and finally, mixing the two parts of individuals which are subjected to the local search and the global disturbance to form a new population, and continuing to carry out the GSA evolution operation, and alternating the steps until the termination condition of the algorithm is met.
4. The PEMFC model parameter optimization method based on CGSASA algorithm of claim 1, wherein: the PEMFC model is specifically as follows:
the essential reaction of the PEM fuel cell is the oxidation-reduction of hydrogen and oxygen to produce water and the direct conversion of the chemical energy stored in the fuel and oxidant into electrical and thermal energy; the method comprises the following specific steps:
anode H 2 →2H + +2e -
Cathode electrode
General reaction
The bipolar reaction being carried out by proton exchangeMembrane separation which is a cation exchange membrane with selective permeability allowing only protons H + Passing; therefore, the protons generated at the anode permeate the proton exchange membrane to migrate to the cathode, and the electrons are attracted by the protons diffused to the cathode to reach the cathode through an external circuit, so as to form current;
the PEMFC fuel cell stack dynamic physical model comprises a steady-state electrochemical model, dynamic models of a cathode and an anode and a temperature model;
1) The steady-state electrochemical model satisfies:
V cell ＝E Nernst -η act -η ohmic -η con (6)
in the formula, E Nernst Is a thermodynamic electromotive force; eta act Is an activation overvoltage; eta ohmic Is an ohmic overvoltage; eta con Is a concentration overvoltage;
2) Thermodynamic electromotive force E Nernst Is the thermodynamic equilibrium reversible electromotive force when a single cell is open-circuited and no load, and is expressed as:
in the formula: Δ G is gibbs free energy; f is a Faraday constant; Δ S is enthalpy change; r is a universal gas constant;
is an effective partial pressure of hydrogen; />
Is the effective partial pressure of oxygen; t is the working environment temperature; t is 0 Is a reference temperature;
3) Activating polarization overvoltage E act Is the voltage drop due to the polarization of the cathode and anode of the electrode, and is a measure of the polarization voltage drop to the electrode, expressed as:
in the formula, coefficient xi 1 、ξ 2 、ξ 3 And xi 4 Determined by experimental data and a parameter optimization method;
4) Ohmic polarization overvoltage E ohmic Involving a voltage drop due to the impedance of the two-part cell, i.e. the equivalent membrane impedance resistance R of the protons across the proton exchange membrane M And the resistance R of the electrons passing through the external circuit C The voltage loss caused is expressed according to ohm's law as:
V ohmic ＝I(R M +R C ) (9)
wherein the equivalent film resistance R M Represented by the formula:
R M ＝ρ M ·l/A (10)
in the formula, ρ M Is the resistivity of the film to electron flow; l is the thickness of the film;
ρ M is obtained by the following formula:
in the formula, lambda is the water content of the proton exchange membrane;
5) Concentration polarization overvoltage E con Is a reaction gas H 2 And O 2 The voltage drop induced by the mass transfer process of (1) is represented by the following formula:
V con ＝-bln(1-I/I max ) (12)
in the formula, b is a system parameter; i is the actual current density of the battery; i is max Is the maximum current density of the cell;
in the above PEMFC steady-state model, xi is still 1 ,ξ 2 ,ξ 3 ,ξ 4 ,λ,R c And b) the values of the 7 parameters are not determined.
5. The method of claim 3 for PEMFC model parameter optimization based on CGSASA algorithm, wherein: the specific principle of the gravity search algorithm GSA is as follows:
in the space of the D-dimension,
and &>
The position and the speed of the ith individual are respectively initialized, the fitness value of each individual is calculated, and the quality of the corresponding individual is expressed as an expression (13):
wherein t is the number of iterations; fit (Fit) i (t) and M i (t) are each an individual x i Fitness and quality of (2); best (t) and worst (t) are respectively an optimal solution and a worst solution of the t iteration;
the attractive force between the two bodies is then equation (14):
the total force acting on the individual i at the t-th iteration is formula (15):
wherein G (t) is a universal gravitation constant which is changed along with the iteration number t, and G (t) = G 0 e -αt/T In the formula G 0 And alpha is a constant, T is the maximum iteration number; epsilon is a constant such that the denominator is not zero; r ij (t) is the Euclidean distance between the two bodies; further, according to newton's second law, the acceleration is defined as formula (16):
the individual velocity and position updates are respectively equations (17), (18):
6. the method of claim 3 for PEMFC model parameter optimization based on CGSASA algorithm, wherein: the specific principle of the simulated annealing algorithm is as follows:
the algorithm adopts a heuristic random search process based on a Monte Carlo iterative solution; the algorithm repeats iteration of 'generating new solution, calculating target function difference, accepting or abandoning' on the current solution from the initial solution x and the temperature parameter T, gradually attenuates the value T, and the current solution when the algorithm is terminated is the obtained approximate optimal solution; the probability that the current new solution is accepted or rejected in the iterative process is determined by the Metropolis criterion;
wherein
And E (x) are respectively expressed as objective function values corresponding to the new solution and the old solution.
7. The PEMFC model parameter optimization method based on CGSASA algorithm of claim 1, wherein: the individual fitness function of step S4 is specifically as follows:
applying the proposed CGSASA algorithm to the PEMFC battery model to obtain ([ xi ]) 1 ,ξ 2 ,ξ 3 ,ξ 4 ,λ,R c The set of optimal parameter combinations of b); the fitness function in the parameter optimization process is defined as:
in the formula, S is a fitness function; v i And V i sim Respectively an ith experimental value and a model simulation output value; n is the number of data points.
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