CN116053536B - Proton exchange membrane fuel cell estimation method and computer readable medium - Google Patents

Proton exchange membrane fuel cell estimation method and computer readable medium Download PDF

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CN116053536B
CN116053536B CN202310042334.4A CN202310042334A CN116053536B CN 116053536 B CN116053536 B CN 116053536B CN 202310042334 A CN202310042334 A CN 202310042334A CN 116053536 B CN116053536 B CN 116053536B
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付波
张万祥
何晗哲
陈登耀
黎祥程
李超顺
范秀香
韩越
姜源
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Abstract

The invention discloses a proton exchange membrane fuel cell estimation method and a computer readable medium. The invention calculates the stacking voltage of the proton exchange membrane fuel cell at each moment, and inputs the measured stacking voltages of the proton exchange membrane fuel cells at a plurality of moments; constructing a stacking voltage optimization target, selecting decision variables and constructing constraint conditions of parameters; the optimized first half empirical factor, the optimized second half empirical factor, the optimized third half empirical factor, the optimized fourth half empirical factor, the optimized constant resistance of the membrane, the optimized water content of the proton exchange membrane and the optimized constant factor are obtained by improving the red fox optimization algorithm for solving, so that the optimized setting of the proton exchange membrane fuel cell is further realized. The improved algorithm provided by the invention has the characteristics of high convergence rate and accurate result, and the fitting degree of the theoretical value of the output stack voltage and the experimental output voltage is higher.

Description

Proton exchange membrane fuel cell estimation method and computer readable medium
Technical Field
The present invention relates to the field of fuel cell technologies, and in particular, to a proton exchange membrane fuel cell estimation method and a computer readable medium.
Background
With the rapid development of social economy and new energy industry, the energy demand is gradually increased, the reserves of fossil energy such as coal and petroleum are gradually reduced, and renewable energy can gradually replace traditional fossil energy. The hydrogen energy is used as a new secondary energy source, has the advantages of no pollution in combustion, high heat value and the like, and has rich reserves. The reasonable utilization of hydrogen energy is of great significance in relieving the crisis of fossil energy. The application of the popularization hydrogen energy source has great significance in technical innovation.
In the application of hydrogen energy, the fuel cell technology has been rapidly developed due to the advantages of high energy conversion efficiency, high energy density, no pollution, low noise and the like. A fuel cell is a chemical device that converts chemical energy possessed by fuel into electric energy. Among the many fuel cells, proton exchange membrane fuel cells are the most promising ones, and have important significance for the utilization of hydrogen energy. For the related field of proton exchange membrane fuel cells, the government of China gives policy support for realizing the hydrogen energy revolution in the early days.
In the past decade, related scientific papers in the field of proton exchange membranes have emerged, each of which has made technical breakthroughs in the field of fuel cells. In the prior art, an improved Archimedes optimization algorithm is adopted to estimate the model parameters of the proton exchange membrane fuel cell; the parameters of the PEM fuel cell are accurately extracted by adopting a self-consistent model and an SCCSA optimization algorithm; and a proton exchange membrane fuel cell model is established by adopting a chaotic game optimization technology. If the polarization curve of the proton exchange membrane fuel cell is accurately simulated by an intelligent algorithm, the cost and the operation time are greatly saved.
Disclosure of Invention
In order to solve the above technical problems, the present invention provides a method for estimating a proton exchange membrane fuel cell and a computer readable medium thereof, which obtain an optimal solution of parameters of the proton exchange membrane fuel cell, so that a calculated value and a measured value of an output stack voltage are as close as possible, thereby facilitating further prediction and dynamic analysis of the proton exchange membrane fuel cell.
The technical scheme of the method is a proton exchange membrane fuel cell estimation method, which comprises the following specific steps:
step 1: acquiring Nernst voltages at a plurality of moments, activation voltages at a plurality of moments, ohmic voltage drops caused by electrodes and membrane resistances at a plurality of moments, concentration voltage losses at a plurality of moments, calculating the stack voltage of the proton exchange membrane fuel cell at each moment, and inputting the measured stack voltage of the proton exchange membrane fuel cell at a plurality of moments;
step 2: constructing a stacking voltage optimization target, selecting a first half empirical factor, a second half empirical factor, a third half empirical factor, a fourth half empirical factor, constant resistance of the membrane, water content of the proton exchange membrane and a constant factor as decision variables, and constructing constraint conditions of parameters;
step 3: and combining constraint conditions of a stacking voltage optimization target and parameters, taking the first half empirical factor, the second half empirical factor, the third half empirical factor, the fourth half empirical factor, the constant resistance of the membrane, the water content of the proton exchange membrane and the constant factor as variables to be solved, and solving by improving a red fox optimization algorithm to obtain an optimized first half empirical factor, an optimized second half empirical factor, an optimized third half empirical factor, an optimized fourth half empirical factor, the constant resistance of the optimized membrane, the water content of the optimized proton exchange membrane and the optimized constant factor, thereby further realizing the optimized setting of the proton exchange membrane fuel cell.
Preferably, the stack voltage of the proton exchange membrane fuel cell at each moment is calculated in the step 1, specifically as follows:
Figure SMS_1
Figure SMS_2
Figure SMS_3
wherein,
Figure SMS_4
stack voltage of proton exchange membrane fuel cell at kth time, < >>
Figure SMS_5
For the number of fuel cells in series in each stack, < >>
Figure SMS_6
For the output voltage of the individual fuel cells at the kth instant,/->
Figure SMS_7
For the Nernst voltage at time k, < >>
Figure SMS_8
For the activation voltage at the kth time, +.>
Figure SMS_9
For ohmic drop due to electrode and membrane resistance at time k, < >>
Figure SMS_10
A concentration voltage loss at the kth time, n representing the number of times;
the measured stack voltages of the proton exchange membrane fuel cells at the multiple moments described in step 1 are defined as:
Figure SMS_11
，/>
Figure SMS_12
wherein,
Figure SMS_13
a measured stack voltage of the proton exchange membrane fuel cell at the kth time is represented, and n represents the number of times;
preferably, the stacking voltage optimization objective is constructed as described in step 2, and specifically as follows:
Figure SMS_14
Figure SMS_15
wherein min represents the minimization of the number of the steps,
Figure SMS_16
stack voltage of proton exchange membrane fuel cell at kth time, < >>
Figure SMS_17
The measured stack voltage of the proton exchange membrane fuel cell at the kth moment is represented, n represents the number of the moments, and SSE represents a voltage error model of the proton exchange membrane fuel cell;
The constraint conditions of the parameters in the step 2 are as follows:
Figure SMS_18
Figure SMS_19
wherein,
Figure SMS_20
representing the first half of the experience factor, ">
Figure SMS_21
Represents the lower limit of the first half empirical factor, +.>
Figure SMS_22
An upper limit representing a first half of the empirical factor;
Figure SMS_23
representing the second half experience factor,/->
Figure SMS_24
Represents the lower limit of the second half empirical factor, < ->
Figure SMS_25
Representing an upper bound of a second half empirical factor;
Figure SMS_26
representing the third half experience factor, ">
Figure SMS_27
Represents the lower limit of the third half empirical factor, < ->
Figure SMS_28
Representing an upper bound of a third half empirical factor;
Figure SMS_29
representing the fourth half experience factor,/->
Figure SMS_30
Represents the lower limit of the fourth half empirical factor, < ->
Figure SMS_31
Representing an upper bound of a fourth half empirical factor;
Figure SMS_32
represents the water content of the proton exchange membrane, < >>
Figure SMS_33
Is the lower limit of the water content of the proton exchange membrane, < + >>
Figure SMS_34
Is the upper limit of the water content in the proton exchange membrane;
Figure SMS_35
representing the constant resistance of the film, +.>
Figure SMS_36
Is the lower limit of the constant resistance of the membrane, +.>
Figure SMS_37
Is the upper limit of the constant resistance of the film;
Figure SMS_38
representing a constant factor->
Figure SMS_39
Is the lower limit of the constant factor, +.>
Figure SMS_40
Is the upper limit of the constant factor.
Preferably, the solution in the step 3 is carried out by using a modified red fox optimization algorithm, and the specific process is as follows:
step 3.1: initializing a red fox search algorithm;
step 3.1.1: setting the activity space of the red fox according to the constraint condition of the parameters
Figure SMS_41
；
Storing the upper limit of the first half empirical factor, the lower limit of the second half empirical factor, the lower limit of the third half empirical factor, the lower limit of the fourth half empirical factor, the lower limit of the constant resistance of the membrane, the lower limit of the water content of the proton exchange membrane and the lower limit of the constant factor in a dimension-by-dimension manner
Figure SMS_42
In the process,
the method comprises the following steps:
Figure SMS_43
is the lower limit of the first half empirical factor, +.>
Figure SMS_44
Is the lower limit of the second half empirical factor, < ->
Figure SMS_45
Is the lower limit of the third half empirical factor, < ->
Figure SMS_46
Is the lower limit of the fourth half empirical factor, < ->
Figure SMS_47
Is the lower limit of the constant resistance of the film, +.>
Figure SMS_48
Is the lower limit of the water content in the proton exchange membrane, < >>
Figure SMS_49
Is a constant factor lower limit;
storing the upper limit of the first half empirical factor, the upper limit of the second half empirical factor, the upper limit of the third half empirical factor, the upper limit of the fourth half empirical factor, the upper limit of the constant resistance of the membrane, the upper limit of the water content of the proton exchange membrane and the upper limit of the constant factor in a dimension-by-dimension manner
Figure SMS_50
The concrete steps are as follows:
Figure SMS_51
is the upper limit of the first half empirical factor, +.>
Figure SMS_52
Is the upper limit of the second half empirical factor, < ->
Figure SMS_53
Is the lower upper limit of the third half experience factor, < ->
Figure SMS_54
Is the upper limit of the fourth half empirical factor, < ->
Figure SMS_55
Is a filmUpper limit of constant resistance, < >>
Figure SMS_56
Is the upper limit of the water content in the proton exchange membrane, < >>
Figure SMS_57
Is a constant factor upper limit;
Setting the maximum iteration number as
Figure SMS_58
The number of red foxes in the population is +.>
Figure SMS_60
The observation angle is +.>
Figure SMS_62
Weather factor->
Figure SMS_63
The action judgment factor is->
Figure SMS_64
Route judgment factor of->
Figure SMS_65
The evolution judgment factor is->
Figure SMS_66
The number of evolved individuals is->
Figure SMS_59
Shape control factor->
Figure SMS_61
；
Determining the search dimension of the red fox as the number of decision variables in the proton exchange membrane fuel cell optimization model in the step 2
Figure SMS_67
；
Wherein,
Figure SMS_69
is->
Figure SMS_71
Random number between->
Figure SMS_73
Is->
Figure SMS_75
Random number between->
Figure SMS_77
For interval->
Figure SMS_78
Constant between->
Figure SMS_79
、/>
Figure SMS_68
And->
Figure SMS_70
Is->
Figure SMS_72
Constant between->
Figure SMS_74
For interval->
Figure SMS_76
A constant therebetween;
randomly generating a population of red foxes in an activity interval of the red foxes, and setting the current iteration times
Figure SMS_80
；
The definition of the initialized red fox population is as follows:
Figure SMS_81
wherein,
Figure SMS_95
indicate->
Figure SMS_96
The->
Figure SMS_98
First half empirical factor of individual solution vector, < ->
Figure SMS_99
Indicate->
Figure SMS_100
The->
Figure SMS_101
A second half-empirical factor of individual solution vectors, < ->
Figure SMS_102
Indicate->
Figure SMS_82
In the second iteration process
Figure SMS_85
Third half empirical factor of individual solution vector, < ->
Figure SMS_87
Indicate->
Figure SMS_89
The->
Figure SMS_91
A fourth half empirical factor of individual solution vectors, < ->
Figure SMS_92
Indicate->
Figure SMS_94
The->
Figure SMS_97
Water content of proton exchange membrane with individual solution vector, < > >
Figure SMS_83
Indicate->
Figure SMS_84
The->
Figure SMS_86
Constant resistance of proton exchange membrane of individual solution vector, < ->
Figure SMS_88
Indicate->
Figure SMS_90
The->
Figure SMS_93
A fuel cell constant factor for each individual solution vector;
and satisfies the following:
Figure SMS_103
wherein,
Figure SMS_104
for the dimension of the solution, <' > for>
Figure SMS_105
Indicating +.f. in the active space of the red fox>
Figure SMS_106
Lower bound of dimension solution vector parameters +.>
Figure SMS_107
Indicating +.f. in the active space of the red fox>
Figure SMS_108
The upper limit of the vector parameters is maintained.
Step 3.2: searching a prey habitat, and performing global searching by adopting a wavelet elite learning strategy integrated with a chaos optimization algorithm;
calculating the fitness of all red fox individuals in the population according to the objective function of the voltage error model of the proton exchange membrane fuel cell in the step 2, sorting the red fox individuals according to the fitness, and selecting the optimal red fox individuals
Figure SMS_109
；
The wavelet elite learning strategy integrated with the chaos optimization algorithm is adopted to drive other individuals to move towards the optimal individuals, and the method specifically comprises the following steps:
Figure SMS_110
wherein,
Figure SMS_112
is Morlet wavelet->
Figure SMS_113
For global search factor, ++>
Figure SMS_115
For SPM chaotic mapping, < >>
Figure SMS_117
Indicate->
Figure SMS_120
The->
Figure SMS_121
Individuals before update->
Figure SMS_124
Indicate->
Figure SMS_111
Before updating in the iterative process, the global optimal solution, < >>
Figure SMS_114
As a function of the sign of the symbol,/>
Figure SMS_116
is the lower limit of the activity space of the red fox, < - >
Figure SMS_118
Is the upper limit of the activity space of the red fox, < ->
Figure SMS_119
Indicate->
Figure SMS_122
The->
Figure SMS_123
-updated individuals;
Figure SMS_125
wherein,
Figure SMS_126
for interval->
Figure SMS_127
Random numbers in between;
Figure SMS_128
wherein,
Figure SMS_129
to take the function of random number +.>
Figure SMS_130
Is->
Figure SMS_131
And->
Figure SMS_132
The Euclidean distance between the two is calculated as follows:
Figure SMS_133
wherein,
Figure SMS_134
the number of the model parameters of the proton exchange membrane fuel cell is the number;
Figure SMS_135
wherein,
Figure SMS_136
representing chaos factor->
Figure SMS_138
For interval->
Figure SMS_140
Random number between->
Figure SMS_142
For the remainder function, ++>
Figure SMS_144
Represents +.>
Figure SMS_145
Individuals before update->
Figure SMS_146
And->
Figure SMS_137
For interval->
Figure SMS_139
A constant therebetween; />
Figure SMS_141
Represents +.>
Figure SMS_143
The individual prior to the update is presented with a list of individuals,
and (3) recalculating the updated fitness of the red fox according to the voltage error model of the proton exchange membrane fuel cell in the step (2), judging whether the updated fitness of the red fox is superior to the historical optimal individual, and if so, keeping the updated position unchanged and replacing the historical optimal individual.
Step 3.3: traversing the habitat, searching for an accurate location of the game within the game habitat;
setting camouflage factors for each red fox
Figure SMS_147
To simulate the possibility of the red fox being noticed when approaching the prey, wherein the camouflage factor +.>
Figure SMS_148
For interval->
Figure SMS_149
Random numbers in between;
judging camouflage factor
Figure SMS_150
Whether or not to meet->
Figure SMS_151
If not, the method is left in place for camouflage;
wherein,
Figure SMS_152
for interval->
Figure SMS_153
A constant therebetween;
if yes, setting a route influencing factor
Figure SMS_154
And local scale factor->
Figure SMS_155
；
Wherein the route influencing factor
Figure SMS_156
For interval->
Figure SMS_157
Random number in between, local scaling factor->
Figure SMS_158
For interval->
Figure SMS_159
Random numbers in between;
judging to satisfy
Figure SMS_160
Route influencing factor of individual red fox->
Figure SMS_161
Whether or not to meet->
Figure SMS_162
If the rule is satisfied, updating the population of the red fox according to a spiral formula; wherein (1)>
Figure SMS_163
And->
Figure SMS_164
For interval->
Figure SMS_165
A constant therebetween;
the spiral formula is specifically as follows:
Figure SMS_166
wherein,
Figure SMS_168
representing a first search angle, +.>
Figure SMS_169
Representing a second search angle, +.>
Figure SMS_171
Representing a third search angle, ++>
Figure SMS_174
Representing a fourth search angle, ++>
Figure SMS_175
Representing a fifth search angle, ++>
Figure SMS_178
Representing a sixth search angle, ++>
Figure SMS_180
Indicating a seventh search angle, all of
Figure SMS_182
Random number between->
Figure SMS_183
For local scale factor->
Figure SMS_185
Indicate->
Figure SMS_188
The->
Figure SMS_190
First half empirical factor of individual solution vector, < ->
Figure SMS_191
Indicate->
Figure SMS_193
The->
Figure SMS_196
A second half-empirical factor of individual solution vectors, < ->
Figure SMS_197
Indicate->
Figure SMS_199
The->
Figure SMS_202
Third half empirical factor of individual solution vector, < ->
Figure SMS_204
Indicate->
Figure SMS_205
The->
Figure SMS_207
A fourth half empirical factor of individual solution vectors, < - >
Figure SMS_208
Indicate->
Figure SMS_209
The->
Figure SMS_210
Water content of proton exchange membrane with individual solution vector, < >>
Figure SMS_211
Indicate->
Figure SMS_212
The->
Figure SMS_213
Constant resistance of proton exchange membrane of individual solution vector, < ->
Figure SMS_214
Indicate->
Figure SMS_215
The->
Figure SMS_216
Fuel cell constant factor of individual solution vector, < ->
Figure SMS_217
Indicate->
Figure SMS_167
The->
Figure SMS_170
First half empirical factor of solution vector after individual spiral update,/->
Figure SMS_172
Indicate->
Figure SMS_173
The->
Figure SMS_176
Second half empirical factor of solution vector after individual spiral update, +.>
Figure SMS_177
Indicate->
Figure SMS_179
The->
Figure SMS_181
Third half empirical factor of solution vector after individual spiral update, +.>
Figure SMS_184
Indicate->
Figure SMS_186
The->
Figure SMS_187
Fourth half empirical factor of solution vector after individual spiral update, +.>
Figure SMS_189
Indicate->
Figure SMS_192
The->
Figure SMS_194
Water content of proton exchange membrane of solution vector after individual spiral update, < >>
Figure SMS_195
Indicate->
Figure SMS_198
The->
Figure SMS_200
Proton exchange membrane constant resistance of solution vector after individual spiral update, +.>
Figure SMS_201
Indicate->
Figure SMS_203
The->
Figure SMS_206
A fuel cell constant factor of the individual spiral updated solution vector;
Figure SMS_218
for the radius of vision of the red fox, the calculation formula is as follows:
Figure SMS_219
wherein,
Figure SMS_220
for the observation angle +.>
Figure SMS_221
Is weather factor (I/O) >
Figure SMS_222
Is a local scaling factor;
if the route influencing factor is not satisfied
Figure SMS_223
Then the improved Archimedes spiral formula is adopted to update the population of the red fox,
Figure SMS_224
for interval->
Figure SMS_225
A constant therebetween;
the improved Archimedes spiral formula is specifically as follows:
Figure SMS_226
wherein,
Figure SMS_227
to express +.>
Figure SMS_229
Updated +.>
Figure SMS_231
Individual(s), fright>
Figure SMS_233
Representing the regulatory factor->
Figure SMS_235
Is logarithmic spiral shape constant +.>
Figure SMS_236
For interval->
Figure SMS_238
T represents the maximum number of iterations, +.>
Figure SMS_228
Indicate->
Figure SMS_230
The->
Figure SMS_232
Individuals before update->
Figure SMS_234
Indicate->
Figure SMS_237
The global optimal solution before updating in the secondary iteration process;
regulatory factor
Figure SMS_239
The calculation formula of (2) is as follows:
Figure SMS_240
wherein,
Figure SMS_241
is a rounding function;
re-calculating the population fitness of the red fox, re-sequencing the red fox according to the fitness, and selecting two optimal red fox individuals;
step 3.4: reproduction and release, according to the adaptability of red fox individual selection
Figure SMS_242
The worst individuals are laid out outside the habitat or directly hunted, wherein the +.>
Figure SMS_243
The method comprises the following specific operation steps:
setting an evolution factor
Figure SMS_244
Wherein->
Figure SMS_245
Is->
Figure SMS_246
Random numbers in between;
judging
Figure SMS_247
Whether or not to meet->
Figure SMS_248
If so, then ∈>
Figure SMS_249
The worst individuals are killed, and two optimal red foxes can reproduce equal amounts of red foxes in the habitat to replace the red foxes killed, and the red foxes are randomly distributed in the current habitat; wherein (1) >
Figure SMS_250
For interval->
Figure SMS_251
Constant of the same.
The calculation formula of the current habitat center point is as follows:
Figure SMS_252
wherein,
Figure SMS_253
is->
Figure SMS_254
And (5) sequencing the fitness of the red fox individuals in the previous 2 in the iterative process.
The diameter calculation formula of the habitat in step 3.4.2 is as follows:
Figure SMS_255
if it does not meet
Figure SMS_256
Will->
Figure SMS_257
The worst red fox individuals evict habitat, and evicted habitatThe red fox will find new game habitat again in combination with hunting experience;
namely, a novel backtracking updating strategy is adopted to update the position of the red fox which is put by the red fox, and the updating formula is as follows:
Figure SMS_258
Figure SMS_259
wherein,
Figure SMS_261
is the initial position of the red fox +.>
Figure SMS_262
For SPM chaotic mapping, < >>
Figure SMS_263
Is->
Figure SMS_264
Post evolution +.>
Figure SMS_265
Individual red fox, ->
Figure SMS_266
Distributing values for a power function; />
Figure SMS_267
For interval->
Figure SMS_260
Constant, T represents the maximum number of iterations;
calculating the fitness of all red foxes and sequencing, and making
Figure SMS_268
；
Step 3.5: repeating the steps 3.2-3.4 until
Figure SMS_269
And outputting the optimized first half empirical factor, the optimized second half empirical factor, the optimized third half empirical factor, the optimized fourth half empirical factor, the optimized constant resistance of the membrane, the optimized water content of the proton exchange membrane and the optimized constant factor, wherein the constant resistance is larger than T.
The present invention also provides a computer readable medium storing a computer program executed by an electronic device, which when run on the electronic device causes the electronic device to perform the steps of the proton exchange membrane fuel cell estimation method.
The invention has the advantages that:
the wavelet elite learning strategy integrated with the chaos optimization algorithm is adopted to drive the red fox individuals to move to the optimal individuals, so that the characteristic of elite solution is effectively reserved, the spatial distribution of the red fox is optimized, and the global searching capability of the algorithm is improved.
When the algorithm performs local search, a novel Archimedes spiral action path is introduced, so that the action path of the red fox is diversified, the local search capability of the algorithm is improved, and the algorithm is helped to find the accurate position of the local optimal solution more quickly.
The novel backtracking updating strategy is adopted to update the positions of the individuals of the red foxes after being put, help the individuals of the red foxes to find other habitats faster, help the algorithm to jump out of the local optimum, and avoid premature convergence of the algorithm due to the fact that the algorithm falls into the local optimum.
The red fox search algorithm is improved, and the adaptability of the algorithm to complex models is improved.
Drawings
Fig. 1: the method of the embodiment of the invention is a flow chart;
fig. 2: the embodiment of the invention provides an improved red fox search algorithm flow chart.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In particular, the method according to the technical solution of the present invention may be implemented by those skilled in the art using computer software technology to implement an automatic operation flow, and a system apparatus for implementing the method, such as a computer readable storage medium storing a corresponding computer program according to the technical solution of the present invention, and a computer device including the operation of the corresponding computer program, should also fall within the protection scope of the present invention.
The following technical scheme of the method of the embodiment of the present invention is described with reference to fig. 1-2, which is a proton exchange membrane fuel cell estimation method, specifically as follows:
a flow chart of the method of the present invention is shown in fig. 1.
Step 1: acquiring Nernst voltages at a plurality of moments, activation voltages at a plurality of moments, ohmic voltage drops caused by electrodes and membrane resistances at a plurality of moments, concentration voltage losses at a plurality of moments, calculating the stack voltage of the proton exchange membrane fuel cell at each moment, and inputting the measured stack voltage of the proton exchange membrane fuel cell at a plurality of moments;
the stack voltage of the proton exchange membrane fuel cell at each moment is calculated in the step 1, and is specifically as follows:
Figure SMS_270
Figure SMS_271
Figure SMS_272
wherein,
Figure SMS_273
indicating the kth timeStack voltage of proton exchange membrane fuel cell, +.>
Figure SMS_274
For the number of fuel cells in series in each stack, < >>
Figure SMS_275
For the output voltage of the individual fuel cells at the kth instant,/->
Figure SMS_276
For the Nernst voltage at time k, < >>
Figure SMS_277
For the activation voltage at the kth time, +.>
Figure SMS_278
For ohmic drop due to electrode and membrane resistance at time k, < >>
Figure SMS_279
For the concentration voltage loss at the kth time, n=3600 indicates the number of times;
the measured stack voltages of the proton exchange membrane fuel cells at the multiple moments described in step 1 are defined as:
Figure SMS_280
，
Figure SMS_281
wherein,
Figure SMS_282
a measured stack voltage of the proton exchange membrane fuel cell at the kth time is represented, and n represents the number of times;
step 2: constructing a stacking voltage optimization target, selecting a first half empirical factor, a second half empirical factor, a third half empirical factor, a fourth half empirical factor, constant resistance of the membrane, water content of the proton exchange membrane and a constant factor as decision variables, and constructing constraint conditions of parameters;
The stacking voltage optimization target is constructed in the step 2, and the method specifically comprises the following steps:
Figure SMS_283
Figure SMS_284
wherein min represents the minimization of the number of the steps,
Figure SMS_285
stack voltage of proton exchange membrane fuel cell at kth time, < >>
Figure SMS_286
The measured stack voltage of the proton exchange membrane fuel cell at the kth moment is represented, n represents the number of the moments, and SSE represents a voltage error model of the proton exchange membrane fuel cell;
the constraint conditions of the parameters in the step 2 are as follows:
Figure SMS_287
Figure SMS_288
wherein,
Figure SMS_289
representing the first half of the experience factor, ">
Figure SMS_290
= -1.19969 represents the lower limit of the first half empirical factor,/->
Figure SMS_291
The upper limit of the first half empirical factor is represented by = -0.8532, which is an empirical value, which is obviously only one preferred value of the plurality of values.
Figure SMS_292
Representing the second half experience factor,/->
Figure SMS_293
=0.001 represents the lower limit of the second half empirical factor, ++>
Figure SMS_294
=0.005 represents the upper limit of the second half empirical factor, which is an empirical value, which is obviously only one preferred value of the plurality of values.
Figure SMS_295
Representing the third half experience factor, ">
Figure SMS_296
= 0.000036 represents the lower limit of the third half empirical factor, ++>
Figure SMS_297
The value of = 0.000098 represents the upper limit of the third half empirical factor, which is an empirical value, which is obviously only one preferred value of the plurality of values.
Figure SMS_298
Representing the fourth half experience factor,/->
Figure SMS_299
= -0.00026 represents the lower limit of the fourth half empirical factor, ++>
Figure SMS_300
The upper limit of the fourth half empirical factor is represented by = -0.0000954, which is an empirical value, which is obviously only one preferred value of the plurality of values.
Figure SMS_301
Represents the water content of the proton exchange membrane, < >>
Figure SMS_302
=10 is the lower limit of the water content in the proton exchange membrane, +.>
Figure SMS_303
The value=24 is the upper limit of the water content in the proton exchange membrane, and is an empirical value, which is obviously only one preferred value among a plurality of values.
Figure SMS_304
Representing the constant resistance of the film, +.>
Figure SMS_305
=0.0001 is the lower limit of the constant resistance of the film, +.>
Figure SMS_306
=0.0008 is the upper limit of the constant resistance of the film, which is an empirical value, which is obviously only one preferred value of the plurality of values.
Figure SMS_307
Representing a constant factor->
Figure SMS_308
=0.0136 is the lower limit of the constant factor, +.>
Figure SMS_309
The value=0.5 is the upper limit of the constant factor, which is empirically valued, and obviously is only one preferred value among a plurality of values.
Step 3: and combining constraint conditions of a stacking voltage optimization target and parameters, taking the first half empirical factor, the second half empirical factor, the third half empirical factor, the fourth half empirical factor, the constant resistance of the membrane, the water content of the proton exchange membrane and the constant factor as variables to be solved, and solving by improving a red fox optimization algorithm to obtain an optimized first half empirical factor, an optimized second half empirical factor, an optimized third half empirical factor, an optimized fourth half empirical factor, the constant resistance of the optimized membrane, the water content of the optimized proton exchange membrane and the optimized constant factor, thereby further realizing the optimized setting of the proton exchange membrane fuel cell.
As shown in fig. 2, the solution is performed by using the improved red fox optimization algorithm in step 3, and the specific process is as follows:
step 3.1: initializing a red fox search algorithm;
step 3.1.1: setting the activity space of the red fox according to the constraint condition of the parameters
Figure SMS_310
；
Storing the upper limit of the first half empirical factor, the lower limit of the second half empirical factor, the lower limit of the third half empirical factor, the lower limit of the fourth half empirical factor, the lower limit of the constant resistance of the membrane, the lower limit of the water content of the proton exchange membrane and the lower limit of the constant factor in a dimension-by-dimension manner
Figure SMS_311
In the process,
the method comprises the following steps:
Figure SMS_312
is the lower limit of the first half empirical factor, +.>
Figure SMS_313
Is the lower limit of the second half empirical factor, < ->
Figure SMS_314
Is the lower limit of the third half empirical factor, < ->
Figure SMS_315
Is the lower limit of the fourth half empirical factor, < ->
Figure SMS_316
Is the lower limit of the constant resistance of the film, +.>
Figure SMS_317
Is the lower limit of the water content in the proton exchange membrane, < >>
Figure SMS_318
Is a constant factor lower limit;
storing the upper limit of the first half empirical factor, the upper limit of the second half empirical factor, the upper limit of the third half empirical factor, the upper limit of the fourth half empirical factor, the upper limit of the constant resistance of the membrane, the upper limit of the water content of the proton exchange membrane and the upper limit of the constant factor in a dimension-by-dimension manner
Figure SMS_319
The concrete steps are as follows:
Figure SMS_320
is the upper limit of the first half empirical factor, +. >
Figure SMS_321
Is the upper limit of the second half empirical factor, < ->
Figure SMS_322
Is the lower upper limit of the third half experience factor, < ->
Figure SMS_323
Is the upper limit of the fourth half empirical factor, < ->
Figure SMS_324
Is the upper limit of the constant resistance of the film, +.>
Figure SMS_325
Is the upper limit of the water content in the proton exchange membrane, < >>
Figure SMS_326
Is a constant factor upper limit;
setting the maximum iteration number as
Figure SMS_327
The number of red foxes in the population is +.>
Figure SMS_329
The observation angle is +.>
Figure SMS_331
Weather factor->
Figure SMS_332
The action judgment factor is->
Figure SMS_333
Route judgment factor of->
Figure SMS_334
The evolution judgment factor is->
Figure SMS_335
The number of evolved individuals is->
Figure SMS_328
Shape control factor->
Figure SMS_330
；
Determining the search dimension of the red fox as the number of decision variables in the proton exchange membrane fuel cell optimization model in the step 2
Figure SMS_336
；
Wherein the maximum number of iterations
Figure SMS_338
=100, number of red foxes in population +.>
Figure SMS_339
=100，/>
Figure SMS_341
Is->
Figure SMS_343
Random number between->
Figure SMS_345
Is->
Figure SMS_347
Random in betweenCount (n)/(l)>
Figure SMS_349
=10 is interval +.>
Figure SMS_337
Constant between->
Figure SMS_340
=0.75、/>
Figure SMS_342
=0.5、/>
Figure SMS_344
=0.45>
Figure SMS_346
Constant between->
Figure SMS_348
= -0.8 is interval +.>
Figure SMS_350
The constant between, this value is empirically chosen, it being evident that this value is only one preferred value of the plurality of values.
Randomly generating a population of red foxes in an activity interval of the red foxes, and setting the current iteration times
Figure SMS_351
；
The definition of the initialized red fox population is as follows:
Figure SMS_352
wherein,
Figure SMS_367
indicate->
Figure SMS_369
The- >
Figure SMS_370
First half empirical factor of individual solution vector, < ->
Figure SMS_371
Indicate->
Figure SMS_372
The->
Figure SMS_373
A second half-empirical factor of individual solution vectors, < ->
Figure SMS_374
Indicate->
Figure SMS_354
In the second iteration process
Figure SMS_355
Third half empirical factor of individual solution vector, < ->
Figure SMS_357
Indicate->
Figure SMS_360
The->
Figure SMS_362
A fourth half empirical factor of individual solution vectors, < ->
Figure SMS_364
Indicate->
Figure SMS_365
The->
Figure SMS_368
Water content of proton exchange membrane with individual solution vector, < >>
Figure SMS_353
Indicate->
Figure SMS_356
The->
Figure SMS_358
Constant resistance of proton exchange membrane of individual solution vector, < ->
Figure SMS_359
Indicate->
Figure SMS_361
The->
Figure SMS_363
A fuel cell constant factor for each individual solution vector; and satisfies the following: />
Figure SMS_366
Wherein,
Figure SMS_375
for the dimension of the solution, <' > for>
Figure SMS_376
Indicating +.f. in the active space of the red fox>
Figure SMS_377
Lower bound of dimension solution vector parameters +.>
Figure SMS_378
Indicating +.f. in the active space of the red fox>
Figure SMS_379
The upper limit of the vector parameters is maintained.
Step 3.2: searching a prey habitat, and performing global searching by adopting a wavelet elite learning strategy integrated with a chaos optimization algorithm;
calculating the fitness of all red fox individuals in the population according to the objective function of the voltage error model of the proton exchange membrane fuel cell in the step 2, sorting the red fox individuals according to the fitness, and selecting the optimal red fox individuals
Figure SMS_380
；
The wavelet elite learning strategy integrated with the chaos optimization algorithm is adopted to drive other individuals to move towards the optimal individuals, and the method specifically comprises the following steps:
Figure SMS_381
wherein,
Figure SMS_383
is Morlet wavelet->
Figure SMS_385
For global search factor, ++>
Figure SMS_387
For SPM chaotic mapping, < >>
Figure SMS_389
Indicate->
Figure SMS_391
The->
Figure SMS_392
Individuals before update, represent +.>
Figure SMS_394
Before updating in the iterative process, the global optimal solution, < >>
Figure SMS_382
As a sign function +.>
Figure SMS_384
Is the lower limit of the activity space of the red fox, < ->
Figure SMS_386
Is the upper limit of the activity space of the red fox, < ->
Figure SMS_388
Indicate->
Figure SMS_390
The->
Figure SMS_393
-updated individuals;
Figure SMS_395
wherein,
Figure SMS_396
for interval->
Figure SMS_397
Random numbers in between.
Figure SMS_398
Wherein,
Figure SMS_399
for taking a random number function, is +.>
Figure SMS_400
And->
Figure SMS_401
The Euclidean distance between the two is calculated as follows:
Figure SMS_402
wherein,
Figure SMS_403
the number of the model parameters of the proton exchange membrane fuel cell is the number;
Figure SMS_404
wherein,
Figure SMS_406
representing chaos factor->
Figure SMS_408
For interval->
Figure SMS_410
Random number between->
Figure SMS_412
For the remainder function, ++>
Figure SMS_414
Indicate->
Figure SMS_416
The->
Figure SMS_417
Individuals before update->
Figure SMS_405
=0.4 and->
Figure SMS_407
=0.3 is interval +.>
Figure SMS_409
A constant therebetween; />
Figure SMS_411
Indicate->
Figure SMS_413
The->
Figure SMS_415
The value is empirically determined for the individual prior to updating, and obviously, the value is only one preferred value of a plurality of values.
And (3) recalculating the updated fitness of the red fox according to the voltage error model of the proton exchange membrane fuel cell in the step (2), judging whether the updated fitness of the red fox is superior to the historical optimal individual, and if so, keeping the updated position unchanged and replacing the historical optimal individual.
Step 3.3: traversing the habitat, searching for an accurate location of the game within the game habitat;
setting camouflage factors for each red fox
Figure SMS_418
To simulate the possibility of the red fox being noticed when approaching the prey, wherein the camouflage factor +.>
Figure SMS_419
For interval->
Figure SMS_420
Random numbers in between; />
Judging camouflage factor
Figure SMS_421
Whether or not to meet->
Figure SMS_422
If not, the method is left in place for camouflage;
wherein,
Figure SMS_423
=0.75 interval +.>
Figure SMS_424
Constant of the same.
If yes, setting a route influencing factor
Figure SMS_425
And local scale factor->
Figure SMS_426
；
Wherein the route influencing factor
Figure SMS_427
For interval->
Figure SMS_428
Random number in between, local scaling factor->
Figure SMS_429
For interval->
Figure SMS_430
Random numbers in between;
judging to satisfy
Figure SMS_431
Route influencing factor of individual red fox->
Figure SMS_432
Whether or not to meet->
Figure SMS_433
If the rule is satisfied, updating the population of the red fox according to a spiral formula; wherein (1)>
Figure SMS_434
=0.5 interval +.>
Figure SMS_435
The constant between, this value is empirically chosen, it being evident that this value is only one preferred value of the plurality of values.
The spiral formula is specifically as follows:
Figure SMS_436
wherein,
Figure SMS_438
representing a first search angle, +.>
Figure SMS_440
Representing a second search angle, +.>
Figure SMS_442
Representing a third search angle, ++>
Figure SMS_443
Representing a fourth search angle, ++>
Figure SMS_444
Representing a fifth search angle, ++>
Figure SMS_445
Representing a sixth search angle, ++>
Figure SMS_447
Indicating a seventh search angle, all of
Figure SMS_449
Random number between->
Figure SMS_451
For local scale factor->
Figure SMS_453
Indicate->
Figure SMS_455
The->
Figure SMS_457
First half empirical factor of individual solution vector, < ->
Figure SMS_459
Indicate->
Figure SMS_461
The->
Figure SMS_462
A second half-empirical factor of individual solution vectors, < ->
Figure SMS_465
Indicate->
Figure SMS_466
The->
Figure SMS_468
Individual solution vectorsThird half experience factor, < >>
Figure SMS_470
Indicate->
Figure SMS_472
The->
Figure SMS_474
A fourth half empirical factor of individual solution vectors, < ->
Figure SMS_476
Indicate->
Figure SMS_478
The->
Figure SMS_480
Water content of proton exchange membrane with individual solution vector, < >>
Figure SMS_481
Indicate->
Figure SMS_482
The->
Figure SMS_483
Constant resistance of proton exchange membrane of individual solution vector, < ->
Figure SMS_484
Indicate->
Figure SMS_485
The->
Figure SMS_486
Fuel cell constant factor of individual solution vector, < ->
Figure SMS_487
Indicate->
Figure SMS_437
Sub-stackIn the course of substitution->
Figure SMS_439
First half empirical factor of solution vector after individual spiral update,/->
Figure SMS_441
Indicate->
Figure SMS_446
The->
Figure SMS_448
Second half empirical factor of solution vector after individual spiral update, +.>
Figure SMS_450
Indicate->
Figure SMS_452
The->
Figure SMS_454
Third half empirical factor of solution vector after individual spiral update, +.>
Figure SMS_456
Indicate->
Figure SMS_458
The->
Figure SMS_460
Fourth half empirical factor of solution vector after individual spiral update, +.>
Figure SMS_463
Indicate- >
Figure SMS_464
The->
Figure SMS_467
Water content of proton exchange membrane of solution vector after individual spiral update, < >>
Figure SMS_469
Indicate->
Figure SMS_471
The->
Figure SMS_473
Proton exchange membrane constant resistance of solution vector after individual spiral update, +.>
Figure SMS_475
Indicate->
Figure SMS_477
The->
Figure SMS_479
A fuel cell constant factor of the individual spiral updated solution vector;
Figure SMS_488
for the radius of vision of the red fox, the calculation formula is as follows:
Figure SMS_489
wherein,
Figure SMS_490
for the observation angle +.>
Figure SMS_491
Is weather factor (I/O)>
Figure SMS_492
Is a local scaling factor.
If the route influencing factor is not satisfied
Figure SMS_493
Then the improved Archimedes spiral formula is adopted to update the population of the red fox,
Figure SMS_494
=0.5 interval +.>
Figure SMS_495
A constant therebetween;
the improved Archimedes spiral formula is specifically as follows:
Figure SMS_496
wherein,
Figure SMS_498
to express +.>
Figure SMS_500
Updated +.>
Figure SMS_501
Individual(s), fright>
Figure SMS_503
Representing the regulatory factor->
Figure SMS_506
=1 is a logarithmic spiral shape constant, +.>
Figure SMS_507
For interval->
Figure SMS_508
T represents the maximum number of iterations, +.>
Figure SMS_497
Indicate->
Figure SMS_499
The->
Figure SMS_502
Individuals before update->
Figure SMS_504
Indicate->
Figure SMS_505
The global optimal solution before updating in the secondary iteration process;
regulatory factor
Figure SMS_509
The calculation formula of (2) is as follows:
Figure SMS_510
wherein,
Figure SMS_511
is a rounding function;
re-calculating the population fitness of the red fox, re-sequencing the red fox according to the fitness, and selecting two optimal red fox individuals;
Step 3.4: reproduction and release, according to the adaptability of red fox individual selection
Figure SMS_512
The worst individuals are laid out outside the habitat or directly hunted, wherein the +.>
Figure SMS_513
The method comprises the following specific operation steps:
setting an evolution factor
Figure SMS_514
Wherein->
Figure SMS_515
Is->
Figure SMS_516
Random numbers in between.
Judging
Figure SMS_517
Whether or not to meet->
Figure SMS_518
If so, then ∈>
Figure SMS_519
The worst individuals are killed, and two optimal red foxes can reproduce equal amounts of red foxes in the habitat to replace the red foxes killed, and the red foxes are randomly distributed in the current habitat; wherein (1)>
Figure SMS_520
=0.45 is interval +.>
Figure SMS_521
The constant between, this value is empirically chosen, it being evident that this value is only one preferred value of the plurality of values.
The calculation formula of the current habitat center point is as follows:
Figure SMS_522
wherein,
Figure SMS_523
is->
Figure SMS_524
And (5) sequencing the fitness of the red fox individuals in the previous 2 in the iterative process.
The diameter calculation formula of the habitat in step 3.4.2 is as follows:
Figure SMS_525
if it does not meet
Figure SMS_526
Will->
Figure SMS_527
The worst red fox individuals evict habitats, and the red fox evicted habitats can find new game habitats again in combination with hunting experience;
namely, a novel backtracking updating strategy is adopted to update the position of the red fox which is put by the red fox, and the updating formula is as follows:
Figure SMS_528
Figure SMS_529
wherein,
Figure SMS_531
is the initial position of the red fox +. >
Figure SMS_532
For SPM chaotic mapping, < >>
Figure SMS_533
Is->
Figure SMS_534
Post evolution +.>
Figure SMS_535
Individual red fox, ->
Figure SMS_536
Distributing values for a power function; />
Figure SMS_537
For interval->
Figure SMS_530
Constant, T represents the maximum number of iterations;
calculating the fitness of all red foxes and sequencing, and making
Figure SMS_538
；
Step 3.5: repeating the steps 3.2-3.4 until
Figure SMS_539
Is greater than->
Figure SMS_540
And outputting the optimized first half empirical factor, the optimized second half empirical factor, the optimized third half empirical factor, the optimized fourth half empirical factor, the optimized constant resistance of the membrane, the optimized water content of the proton exchange membrane and the optimized constant factor.
Particular embodiments of the present invention also provide a computer readable medium.
The computer readable medium is a server workstation;
the server workstation stores a computer program executed by the electronic device, and when the computer program runs on the electronic device, the electronic device executes the steps of the proton exchange membrane fuel cell estimation method according to the embodiment of the invention.
It should be understood that parts of the specification not specifically set forth herein are all prior art.
It should be understood that the foregoing description of the preferred embodiments is not intended to limit the scope of the invention, but rather to limit the scope of the claims, and that those skilled in the art can make substitutions or modifications without departing from the scope of the invention as set forth in the appended claims.

Claims (4)

1. A method for estimating a proton exchange membrane fuel cell, comprising the steps of:
step 1: acquiring Nernst voltages at a plurality of moments, activation voltages at a plurality of moments, ohmic voltage drops caused by electrodes and membrane resistances at a plurality of moments, concentration voltage losses at a plurality of moments, calculating the stack voltage of the proton exchange membrane fuel cell at each moment, and inputting the measured stack voltage of the proton exchange membrane fuel cell at a plurality of moments;
step 2: constructing a stacking voltage optimization target, selecting a first half empirical factor, a second half empirical factor, a third half empirical factor, a fourth half empirical factor, constant resistance of the membrane, water content of the proton exchange membrane and a constant factor as decision variables, and constructing constraint conditions of parameters;
step 3: combining constraint conditions of a stacking voltage optimization target and parameters, taking a first half empirical factor, a second half empirical factor, a third half empirical factor, a fourth half empirical factor, constant resistance of a membrane, water content of a proton exchange membrane and a constant factor as variables to be solved, and solving by improving a red fox optimization algorithm to obtain an optimized first half empirical factor, an optimized second half empirical factor, an optimized third half empirical factor, an optimized fourth half empirical factor, constant resistance of the optimized membrane, water content of the optimized proton exchange membrane and the optimized constant factor, thereby further realizing the optimized setting of the proton exchange membrane fuel cell;
The solving by using the improved red fox optimization algorithm in the step 3 comprises the following steps:
step 3.1: initializing a red fox search algorithm;
step 3.2: searching a prey habitat, and performing global searching by adopting a wavelet elite learning strategy integrated with a chaos optimization algorithm;
step 3.3: traversing habitat, and searching accurate positions of the hunting object in the hunting object habitat by combining a spiral formula and an improved Archimedes spiral formula;
step 3.4: according to the adaptability of the red fox individuals, carrying out propagation updating, and adopting a novel backtracking updating strategy to update the positions of the released red foxes;
step 3.5: repeating the steps 3.2-3.4 until the maximum iteration times are reached, and outputting an optimized first half empirical factor, an optimized second half empirical factor, an optimized third half empirical factor, an optimized fourth half empirical factor, an optimized constant resistance of the membrane, an optimized water content of the proton exchange membrane and an optimized constant factor;
the initialization red fox search algorithm is specifically as follows:
setting the activity space of the red fox according to the constraint condition of the parameters
Figure QLYQS_1
；
Storing the upper limit of the first half empirical factor, the lower limit of the second half empirical factor, the lower limit of the third half empirical factor, the lower limit of the fourth half empirical factor, the lower limit of the constant resistance of the membrane, the lower limit of the water content of the proton exchange membrane and the lower limit of the constant factor in a dimension-by-dimension manner
Figure QLYQS_2
In the process,
the method comprises the following steps:
Figure QLYQS_3
is the lower limit of the first half empirical factor, +.>
Figure QLYQS_4
Is the lower limit of the second half empirical factor, < ->
Figure QLYQS_5
Is the lower limit of the third half empirical factor, < ->
Figure QLYQS_6
Is the lower limit of the fourth half empirical factor, < ->
Figure QLYQS_7
Is the lower limit of the constant resistance of the film, +.>
Figure QLYQS_8
Is the lower limit of the water content in the proton exchange membrane, < >>
Figure QLYQS_9
Is a constant factor lower limit;
storing the upper limit of the first half empirical factor, the upper limit of the second half empirical factor, the upper limit of the third half empirical factor, the upper limit of the fourth half empirical factor, the upper limit of the constant resistance of the membrane, the upper limit of the water content of the proton exchange membrane and the upper limit of the constant factor in a dimension-by-dimension manner
Figure QLYQS_10
The concrete steps are as follows:
Figure QLYQS_11
is the upper limit of the first half empirical factor, +.>
Figure QLYQS_12
Is the upper limit of the second half empirical factor, < ->
Figure QLYQS_13
Is the lower upper limit of the third half experience factor, < ->
Figure QLYQS_14
Is the upper limit of the fourth half empirical factor, < ->
Figure QLYQS_15
Is the upper limit of the constant resistance of the film, +.>
Figure QLYQS_16
Is the upper limit of the water content in the proton exchange membrane, < >>
Figure QLYQS_17
Is a constant factor upper limit;
setting the maximum iteration number as
Figure QLYQS_19
The number of red foxes in the population is +.>
Figure QLYQS_23
The observation angle is +.>
Figure QLYQS_25
Weather factor->
Figure QLYQS_20
The action judgment factor is->
Figure QLYQS_21
Route judgment factor of->
Figure QLYQS_24
The evolution judgment factor is->
Figure QLYQS_26
The number of evolved individuals is->
Figure QLYQS_18
Shape control factor->
Figure QLYQS_22
；
Determining the search dimension of the red fox as the number of decision variables in the proton exchange membrane fuel cell optimization model in the step 2
Figure QLYQS_27
；
Wherein,
Figure QLYQS_29
is->
Figure QLYQS_32
Random number between->
Figure QLYQS_36
Is->
Figure QLYQS_31
Random number between->
Figure QLYQS_33
For interval->
Figure QLYQS_35
A constant of the two-dimensional space between the two-dimensional space,
Figure QLYQS_38
、/>
Figure QLYQS_28
and->
Figure QLYQS_34
Is->
Figure QLYQS_37
Constant between->
Figure QLYQS_39
For interval->
Figure QLYQS_30
A constant therebetween;
randomly generating a population of red foxes in an activity interval of the red foxes, and setting the current iteration times
Figure QLYQS_40
；
The definition of the initialized red fox population is as follows:
Figure QLYQS_41
wherein,
Figure QLYQS_44
indicate->
Figure QLYQS_43
The->
Figure QLYQS_52
First half empirical factor of individual solution vector, < ->
Figure QLYQS_49
Indicate->
Figure QLYQS_56
The->
Figure QLYQS_58
A second half-empirical factor of individual solution vectors, < ->
Figure QLYQS_62
Indicate->
Figure QLYQS_46
The->
Figure QLYQS_53
Third half empirical factor of individual solution vector, < ->
Figure QLYQS_42
Indicate->
Figure QLYQS_50
The->
Figure QLYQS_48
A fourth half empirical factor of individual solution vectors, < ->
Figure QLYQS_60
Indicate->
Figure QLYQS_54
The->
Figure QLYQS_59
Water content of proton exchange membrane with individual solution vector, < >>
Figure QLYQS_45
Indicate->
Figure QLYQS_55
The->
Figure QLYQS_57
Constant resistance of proton exchange membrane of individual solution vector, < ->
Figure QLYQS_61
Indicate->
Figure QLYQS_47
The->
Figure QLYQS_51
A fuel cell constant factor for each individual solution vector;
and satisfies the following:
Figure QLYQS_63
wherein,
Figure QLYQS_64
for the dimension of the solution, <' > for>
Figure QLYQS_65
Indicating +.f. in the active space of the red fox>
Figure QLYQS_66
Lower bound of dimension solution vector parameters +.>
Figure QLYQS_67
Indicating +.f. in the active space of the red fox>
Figure QLYQS_68
Maintaining an upper limit of the vector parameters;
The searching of the prey habitat adopts a wavelet elite learning strategy integrated with a chaos optimization algorithm to perform global searching, and the method is specifically as follows:
calculating the fitness of all red fox individuals in the population according to the objective function of the voltage error model of the proton exchange membrane fuel cell in the step 2, sorting the red fox individuals according to the fitness, and selecting the optimal red fox individuals
Figure QLYQS_69
；
The wavelet elite learning strategy integrated with the chaos optimization algorithm is adopted to drive other individuals to move towards the optimal individuals, and the method specifically comprises the following steps:
Figure QLYQS_70
wherein,
Figure QLYQS_74
is Morlet wavelet->
Figure QLYQS_78
For global search factor, ++>
Figure QLYQS_82
For SPM chaotic mapping, < >>
Figure QLYQS_73
Indicate->
Figure QLYQS_75
The->
Figure QLYQS_79
Individuals before update->
Figure QLYQS_81
Indicate->
Figure QLYQS_71
Before updating in the iterative process, the global optimal solution, < >>
Figure QLYQS_77
As a sign function +.>
Figure QLYQS_83
Is a red foxLower limit of the active space,/->
Figure QLYQS_84
Is the upper limit of the activity space of the red fox, < ->
Figure QLYQS_72
Indicate->
Figure QLYQS_76
In the second iteration process
Figure QLYQS_80
-updated individuals;
Figure QLYQS_85
wherein,
Figure QLYQS_86
for interval->
Figure QLYQS_87
Random numbers in between;
Figure QLYQS_88
wherein,
Figure QLYQS_89
to take the function of random number +.>
Figure QLYQS_90
Is->
Figure QLYQS_91
And->
Figure QLYQS_92
The Euclidean distance between the two is calculated as follows:
Figure QLYQS_93
wherein,
Figure QLYQS_94
the number of the model parameters of the proton exchange membrane fuel cell is the number;
Figure QLYQS_95
wherein,
Figure QLYQS_97
representing chaos factor- >
Figure QLYQS_100
For interval->
Figure QLYQS_103
Random number between->
Figure QLYQS_98
For the remainder function, ++>
Figure QLYQS_101
Represents +.>
Figure QLYQS_104
Individuals before update->
Figure QLYQS_105
And->
Figure QLYQS_96
For interval->
Figure QLYQS_99
A constant therebetween; />
Figure QLYQS_102
Represents +.>
Figure QLYQS_106
The individual prior to the update is presented with a list of individuals,
the updated fitness of the red fox is recalculated according to the voltage error model of the proton exchange membrane fuel cell in the step 2, whether the updated fitness of the red fox is superior to a historical optimal individual is judged, and if the situation that the updated position is unchanged and the historical optimal individual is replaced is met;
the traversing habitat is combined with a spiral formula and an improved Archimedes spiral formula to search the accurate position of the hunting object in the hunting object habitat, and the method is specifically as follows:
setting camouflage factors for each red fox
Figure QLYQS_107
To simulate the possibility of the red fox being noticed when approaching the prey, wherein the camouflage factor +.>
Figure QLYQS_108
For interval->
Figure QLYQS_109
Random numbers in between;
judging camouflage factor
Figure QLYQS_110
Whether or not to meet->
Figure QLYQS_111
If not, the method is left in place for camouflage;
wherein,
Figure QLYQS_112
for interval->
Figure QLYQS_113
A constant therebetween;
if yes, setting a route influencing factor
Figure QLYQS_114
And local scale factor->
Figure QLYQS_115
；
Wherein the route influencing factor
Figure QLYQS_116
For interval->
Figure QLYQS_117
Random number in between, local scaling factor->
Figure QLYQS_118
For interval->
Figure QLYQS_119
Random numbers in between;
Judging to satisfy
Figure QLYQS_120
Route influencing factor of individual red fox->
Figure QLYQS_121
Whether or not to meet->
Figure QLYQS_122
If the rule is satisfied, updating the population of the red fox according to a spiral formula; wherein (1)>
Figure QLYQS_123
And->
Figure QLYQS_124
For interval->
Figure QLYQS_125
A constant therebetween;
the spiral formula is specifically as follows:
Figure QLYQS_126
wherein,
Figure QLYQS_161
representing a first search angle, +.>
Figure QLYQS_166
Representing a second search angle, +.>
Figure QLYQS_171
Representing a third search angle, ++>
Figure QLYQS_162
Representing a fourth search angle, ++>
Figure QLYQS_170
Representing a fifth search angle, ++>
Figure QLYQS_175
Representing a sixth search angle, ++>
Figure QLYQS_177
Representing a seventh search angle, all +.>
Figure QLYQS_131
Random number between->
Figure QLYQS_137
For local scale factor->
Figure QLYQS_143
Indicate->
Figure QLYQS_150
The->
Figure QLYQS_158
First half empirical factor of individual solution vector, < ->
Figure QLYQS_163
Indicate->
Figure QLYQS_169
The->
Figure QLYQS_173
A second half-empirical factor of individual solution vectors, < ->
Figure QLYQS_134
Indicate->
Figure QLYQS_139
The->
Figure QLYQS_151
Third half empirical factor of individual solution vector, < ->
Figure QLYQS_157
Indicate->
Figure QLYQS_130
The->
Figure QLYQS_135
A fourth half empirical factor of individual solution vectors, < ->
Figure QLYQS_140
Indicate->
Figure QLYQS_145
The->
Figure QLYQS_128
Water content of proton exchange membrane with individual solution vector, < >>
Figure QLYQS_141
Indicate->
Figure QLYQS_149
The->
Figure QLYQS_155
Constant resistance of proton exchange membrane of individual solution vector, < ->
Figure QLYQS_160
Indicate->
Figure QLYQS_164
The->
Figure QLYQS_168
Fuel cell constant factor of individual solution vector, < - >
Figure QLYQS_174
Indicate->
Figure QLYQS_132
The->
Figure QLYQS_142
First half empirical factor of solution vector after individual spiral update,/->
Figure QLYQS_148
Indicate->
Figure QLYQS_156
The->
Figure QLYQS_133
After individual spiral updatesSecond half empirical factor of solution vector, +.>
Figure QLYQS_138
Indicate->
Figure QLYQS_144
The->
Figure QLYQS_152
Third half empirical factor of solution vector after individual spiral update, +.>
Figure QLYQS_127
Indicate->
Figure QLYQS_136
The->
Figure QLYQS_146
Fourth half empirical factor of solution vector after individual spiral update, +.>
Figure QLYQS_153
Indicate->
Figure QLYQS_159
The->
Figure QLYQS_167
Water content of proton exchange membrane of solution vector after individual spiral update, < >>
Figure QLYQS_172
Indicate->
Figure QLYQS_176
The->
Figure QLYQS_129
The proton exchange membrane constant resistance of the solution vector after the individual spiral update,/>
Figure QLYQS_147
indicate->
Figure QLYQS_154
The->
Figure QLYQS_165
A fuel cell constant factor of the individual spiral updated solution vector;
Figure QLYQS_178
for the radius of vision of the red fox, the calculation formula is as follows:
Figure QLYQS_179
wherein,
Figure QLYQS_180
for the observation angle +.>
Figure QLYQS_181
Is weather factor (I/O)>
Figure QLYQS_182
Is a local scaling factor;
if the route influencing factor is not satisfied
Figure QLYQS_183
Then the improved Archimedes spiral formula is adopted to update the population of the red fox, the ∈red fox>
Figure QLYQS_184
For interval->
Figure QLYQS_185
A constant therebetween;
the improved Archimedes spiral formula is specifically as follows:
Figure QLYQS_186
wherein,
Figure QLYQS_189
to express +. >
Figure QLYQS_190
Updated +.>
Figure QLYQS_194
Individual, s represents a modulator,/->
Figure QLYQS_188
Is logarithmic spiral shape constant +.>
Figure QLYQS_191
For interval->
Figure QLYQS_193
T represents the maximum number of iterations, +.>
Figure QLYQS_196
Indicate->
Figure QLYQS_187
The->
Figure QLYQS_192
Individuals before update->
Figure QLYQS_195
Indicate->
Figure QLYQS_197
The global optimal solution before updating in the secondary iteration process;
regulatory factor
Figure QLYQS_198
The calculation formula of (2) is as follows:
Figure QLYQS_199
wherein,
Figure QLYQS_200
is a rounding function;
re-calculating the population fitness of the red fox, re-sequencing the red fox according to the fitness, and selecting two optimal red fox individuals;
the breeding and updating are carried out according to the fitness of the red fox individuals, and the positions of the red fox which are put aside are updated by adopting a novel backtracking updating strategy, specifically as follows:
selection according to individual fitness of red fox
Figure QLYQS_201
The worst individuals were placed outside the habitat or were directly hunted, as follows:
setting an evolution factor
Figure QLYQS_202
Wherein->
Figure QLYQS_203
Is->
Figure QLYQS_204
Random numbers in between;
judging
Figure QLYQS_205
Whether or not to meet->
Figure QLYQS_206
If so, then ∈>
Figure QLYQS_207
The worst individuals are killed, and two optimal red foxes can reproduce equal amounts of red foxes in the habitat to replace the red foxes killed, and the red foxes are randomly distributed in the current habitat; wherein (1)>
Figure QLYQS_208
For interval->
Figure QLYQS_209
A constant therebetween;
The calculation formula of the current habitat center point is as follows:
Figure QLYQS_210
wherein,
Figure QLYQS_211
is->
Figure QLYQS_212
The fitness of the red fox individuals in the iterative process is ranked as the first 2;
the diameter calculation formula of the habitat is as follows:
Figure QLYQS_213
if it does not meet
Figure QLYQS_214
Will->
Figure QLYQS_215
The worst red fox individuals evict habitats, and the red fox evicted habitats can find new game habitats again in combination with hunting experience;
namely, a novel backtracking updating strategy is adopted to update the position of the red fox which is put by the red fox, and the updating formula is as follows:
Figure QLYQS_216
Figure QLYQS_217
wherein,
Figure QLYQS_220
is the initial position of the red fox +.>
Figure QLYQS_222
For SPM chaotic mapping, < >>
Figure QLYQS_224
Is->
Figure QLYQS_219
Post evolution +.>
Figure QLYQS_221
Individual red fox, ->
Figure QLYQS_223
Distributing values for a power function; />
Figure QLYQS_225
For interval->
Figure QLYQS_218
Constant, T represents the maximum number of iterations;
calculating the fitness of all red foxes and sequencing, and making
Figure QLYQS_226
。
2. The method for estimating a proton exchange membrane fuel cell as claimed in claim 1, wherein,
the stack voltage of the proton exchange membrane fuel cell at each moment is calculated in the step 1, and is specifically as follows:
Figure QLYQS_227
Figure QLYQS_228
Figure QLYQS_229
wherein,
Figure QLYQS_230
stack voltage of proton exchange membrane fuel cell at kth time, < >>
Figure QLYQS_231
For the number of fuel cells in series in each stack, < >>
Figure QLYQS_232
For the output voltage of the individual fuel cells at the kth instant,/- >
Figure QLYQS_233
For the Nernst voltage at time k, < >>
Figure QLYQS_234
For the activation voltage at the kth time, +.>
Figure QLYQS_235
For ohmic drop due to electrode and membrane resistance at time k, < >>
Figure QLYQS_236
A concentration voltage loss at the kth time, n representing the number of times;
the measured stack voltages of the proton exchange membrane fuel cells at the multiple moments described in step 1 are defined as:
Figure QLYQS_237
，/>
Figure QLYQS_238
wherein,
Figure QLYQS_239
represents the measured stack voltage of the pem fuel cell at time k and n represents the number of times.
3. The method for estimating a proton exchange membrane fuel cell as claimed in claim 2, wherein,
the stacking voltage optimization target is constructed in the step 2, and the method specifically comprises the following steps:
Figure QLYQS_240
Figure QLYQS_241
wherein min represents the minimization of the number of the steps,
Figure QLYQS_242
stack voltage of proton exchange membrane fuel cell at kth time, < >>
Figure QLYQS_243
The measured stack voltage of the proton exchange membrane fuel cell at the kth moment is represented, n represents the number of the moments, and SSE represents a voltage error model of the proton exchange membrane fuel cell;
the constraint conditions of the parameters in the step 2 are as follows:
Figure QLYQS_244
Figure QLYQS_245
wherein,
Figure QLYQS_246
representing the first half of the experience factor, ">
Figure QLYQS_247
Represents the lower limit of the first half empirical factor, +.>
Figure QLYQS_248
An upper limit representing a first half of the empirical factor;
Figure QLYQS_249
representing the second half experience factor,/- >
Figure QLYQS_250
Represents the lower limit of the second half empirical factor, < ->
Figure QLYQS_251
Representing an upper bound of a second half empirical factor;
Figure QLYQS_252
representing the third half experience factor, ">
Figure QLYQS_253
Represents the lower limit of the third half empirical factor, < ->
Figure QLYQS_254
Representing an upper bound of a third half empirical factor;
Figure QLYQS_255
representing the fourth half experience factor,/->
Figure QLYQS_256
Represents the lower limit of the fourth half empirical factor, < ->
Figure QLYQS_257
Representing an upper bound of a fourth half empirical factor;
Figure QLYQS_258
representing the constant resistance of the film, +.>
Figure QLYQS_259
Is the lower limit of the constant resistance of the membrane, +.>
Figure QLYQS_260
Is the upper limit of the constant resistance of the film.
4. A computer readable medium, characterized in that it stores a computer program for execution by an electronic device, which computer program, when run on the electronic device, causes the electronic device to perform the steps of the method according to any of claims 1-3.
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