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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

本发明公开一种质子交换膜燃料电池估测方法及计算机可读介质。本发明计算每个时刻的质子交换膜燃料电池的堆叠电压，输入多个时刻的质子交换膜燃料电池的测量堆叠电压；构建堆叠电压优化目标，选取决策变量，构建参数的约束条件；通过改进红狐优化算法进行求解，得到优化后的第一半经验因子、优化后的第二半经验因子、优化后的第三半经验因子、优化后的第四半经验因子、优化后的膜的恒定电阻、优化后的质子交换膜内含水量、优化后的常数因子，进一步实现质子交换膜燃料电池的优化设置。本发明所提出的改进算法具有收敛速度快，结果准确的特点，且输出堆栈电压的理论值与实验输出电压拟合程度较高。

Figure 202310042334

The invention discloses a proton exchange membrane fuel cell estimation method and a computer readable medium. The invention calculates the stack voltage of the proton exchange membrane fuel cell at each moment, and inputs the measured stack voltage of the proton exchange membrane fuel cell at multiple moments; constructs the optimization target of the stack voltage, selects decision variables, and constructs constraint conditions of parameters; Fox optimization algorithm to solve, get the optimized first half empirical factor, optimized second half empirical factor, optimized third half empirical factor, optimized fourth half empirical factor, optimized constant resistance of the film , the optimized water content in the proton exchange membrane, and the optimized constant factor to further realize the optimal setting of the proton exchange membrane fuel cell. The improved algorithm proposed by the invention has the characteristics of fast convergence speed and accurate results, and the theoretical value of the output stack voltage has a high fitting degree with the experimental output voltage.

Figure 202310042334

Description

一种质子交换膜燃料电池估测方法及计算机可读介质A proton exchange membrane fuel cell estimation method and computer readable medium

技术领域Technical Field

本发明涉及燃料电池技术领域，尤其涉及一种质子交换膜燃料电池估测方法及计算机可读介质。The present invention relates to the field of fuel cell technology, and in particular to a proton exchange membrane fuel cell estimation method and a computer-readable medium.

背景技术Background Art

随着社会经济与新能源产业的飞速发展，能源需求逐渐提高，煤炭和石油等化石能源储量日益减少，可再生能源会逐渐替代传统化石能源。氢能作为一种新二次能源，具有燃烧无污染、热值高等优点，并且储量丰富。合理利用氢能源，对缓解化石能源危机有重要意义。推广氢能源的应用，技术创新意义重大。With the rapid development of social economy and new energy industry, energy demand is gradually increasing, and the reserves of fossil energy such as coal and oil are decreasing. Renewable energy will gradually replace traditional fossil energy. Hydrogen energy, as a new secondary energy, has the advantages of pollution-free combustion, high calorific value, and abundant reserves. The rational use of hydrogen energy is of great significance to alleviating the fossil energy crisis. Promoting the application of hydrogen energy and technological innovation are of great significance.

在对氢能源的运用中，燃料电池技术因其能量转化效率高、能量密度高、无污染、噪音小等优点得到了快速发展。燃料电池是一种把燃料所具有的化学能转化为电能的化学装置。在众多燃料电池中，质子交换膜燃料电池是最具有发展前景的燃料电池，对氢能的利用具有重要意义。对于质子交换膜燃料电池相关领域，我国政府给予政策上的支持，以期早日实现氢能源革命。In the application of hydrogen energy, fuel cell technology has developed rapidly due to its advantages of high energy conversion efficiency, high energy density, no pollution, and low noise. A fuel cell is a chemical device that converts the chemical energy of a fuel into electrical energy. Among many fuel cells, proton exchange membrane fuel cells are the most promising fuel cells, which are of great significance to the utilization of hydrogen energy. For the fields related to proton exchange membrane fuel cells, the Chinese government has given policy support in order to realize the hydrogen energy revolution as soon as possible.

在过去的十年里，中外质子交换膜领域相关科研论文不断涌现，每一篇都对燃料电池领域进行了技术突破。现有技术采用改进版阿基米德优化算法估计质子交换膜燃料电池模型参数；并采用基于自洽模型和SCCSA优化算法，实现了对PEM燃料电池参数精确提取；采用混沌博弈优化技术建立了质子交换膜燃料电池模型。若通过智能算法将质子交换膜燃料电池极化曲线精确模拟，将极大节省成本与运算时间。In the past decade, scientific research papers related to the field of proton exchange membranes have continued to emerge in China and abroad, and each of them has made a technological breakthrough in the field of fuel cells. The existing technology uses an improved version of the Archimedean optimization algorithm to estimate the parameters of the proton exchange membrane fuel cell model; and uses a self-consistent model and SCCSA optimization algorithm to achieve accurate extraction of PEM fuel cell parameters; and uses chaos game optimization technology to establish a proton exchange membrane fuel cell model. If the polarization curve of the proton exchange membrane fuel cell is accurately simulated through an intelligent algorithm, it will greatly save costs and computing time.

发明内容Summary of the invention

为了解决上述技术问题，本发明提供一种质子交换膜燃料电池估测方法及计算机可读介质，得出质子交换膜燃料电池参数的最优解，使输出堆栈电压的计算值与测量值尽可能接近，以便于对质子交换膜燃料电池做进一步的预测与动态分析。In order to solve the above technical problems, the present invention provides a proton exchange membrane fuel cell estimation method and a computer-readable medium to obtain the optimal solution of the proton exchange membrane fuel cell parameters, so that the calculated value of the output stack voltage is as close as possible to the measured value, so as to facilitate further prediction and dynamic analysis of the proton exchange membrane fuel cell.

本发明方法的技术方案为一种质子交换膜燃料电池估测方法，具体步骤如下：The technical solution of the method of the present invention is a proton exchange membrane fuel cell estimation method, and the specific steps are as follows:

步骤1：获取多个时刻的能斯特电压、多个时刻的激活电压、多个时刻的电极和膜电阻引起的欧姆压降、多个时刻的浓度电压损失，计算每个时刻的质子交换膜燃料电池的堆叠电压，输入多个时刻的质子交换膜燃料电池的测量堆叠电压；Step 1: Obtain the Nernst voltage at multiple times, the activation voltage at multiple times, the ohmic voltage drop caused by the electrode and membrane resistance at multiple times, and the concentration voltage loss at multiple times, calculate the stack voltage of the proton exchange membrane fuel cell at each time, and input the measured stack voltage of the proton exchange membrane fuel cell at multiple times;

步骤2：构建堆叠电压优化目标，选取第一半经验因子、第二半经验因子、第三半经验因子、第四半经验因子、膜的恒定电阻、质子交换膜内含水量、常数因子作为决策变量，构建参数的约束条件；Step 2: Construct the stack voltage optimization target, select the first semi-empirical factor, the second semi-empirical factor, the third semi-empirical factor, the fourth semi-empirical factor, the constant resistance of the membrane, the water content in the proton exchange membrane, and the constant factor as decision variables, and construct the parameter constraints;

步骤3：结合堆叠电压优化目标、参数的约束条件，将第一半经验因子、第二半经验因子、第三半经验因子、第四半经验因子、膜的恒定电阻、质子交换膜内含水量、常数因子作为待求解变量，通过改进红狐优化算法进行求解，得到优化后的第一半经验因子、优化后的第二半经验因子、优化后的第三半经验因子、优化后的第四半经验因子、优化后的膜的恒定电阻、优化后的质子交换膜内含水量、优化后的常数因子，进一步实现质子交换膜燃料电池的优化设置。Step 3: In combination with the stack voltage optimization objective and parameter constraints, the first semi-empirical factor, the second semi-empirical factor, the third semi-empirical factor, the fourth semi-empirical factor, the constant resistance of the membrane, the water content in the proton exchange membrane, and the constant factor are taken as variables to be solved, and solved by the improved Red Fox optimization algorithm to obtain the optimized first semi-empirical factor, the optimized second semi-empirical factor, the optimized third semi-empirical factor, the optimized fourth semi-empirical factor, the optimized constant resistance of the membrane, the optimized water content in the proton exchange membrane, and the optimized constant factor, thereby further realizing the optimized setting of the proton exchange membrane fuel cell.

作为优选，步骤1所述计算每个时刻的质子交换膜燃料电池的堆叠电压，具体如下：Preferably, the calculation of the stack voltage of the proton exchange membrane fuel cell at each moment in step 1 is as follows:

Figure SMS_1
Figure SMS_1

Figure SMS_2
Figure SMS_2

Figure SMS_3
Figure SMS_3

其中，

Figure SMS_4
表示第k个时刻的质子交换膜燃料电池的堆叠电压，
Figure SMS_5
为每个堆栈中串联燃料电池的数量，
Figure SMS_6
为第k个时刻的单个燃料电池的输出电压，
Figure SMS_7
为第k个时刻的能斯特电压，
Figure SMS_8
为第k个时刻的激活电压，
Figure SMS_9
为第k个时刻的电极和膜电阻引起的欧姆压降，
Figure SMS_10
为第k个时刻的浓度电压损失，n表示时刻的数量；in,
Figure SMS_4
represents the stack voltage of the proton exchange membrane fuel cell at the kth moment,
Figure SMS_5
For the number of fuel cells in series in each stack,
Figure SMS_6
is the output voltage of a single fuel cell at the kth moment,
Figure SMS_7
is the Nernst voltage at the kth moment,
Figure SMS_8
is the activation voltage at the kth moment,
Figure SMS_9
is the ohmic voltage drop caused by the electrode and membrane resistance at the kth moment,
Figure SMS_10
is the concentration voltage loss at the kth moment, n represents the number of moments;

步骤1所述多个时刻的质子交换膜燃料电池的测量堆叠电压，定义为：The measured stack voltage of the proton exchange membrane fuel cell at multiple moments in step 1 is defined as:

Figure SMS_11
，
Figure SMS_12
Figure SMS_11
,
Figure SMS_12

其中，

Figure SMS_13
表示第k个时刻的质子交换膜燃料电池的测量堆叠电压，n表示时刻的数量；in,
Figure SMS_13
represents the measured stack voltage of the proton exchange membrane fuel cell at the kth moment, and n represents the number of moments;

作为优选，步骤2所述构建堆叠电压优化目标，具体如下：Preferably, the stack voltage optimization target is constructed in step 2, specifically as follows:

Figure SMS_14
Figure SMS_14

Figure SMS_15
Figure SMS_15

其中，min表示最小化，

Figure SMS_16
表示第k个时刻的质子交换膜燃料电池的堆叠电压，
Figure SMS_17
表示第k个时刻的质子交换膜燃料电池的测量堆叠电压，n表示时刻的数量，SSE表示质子交换膜燃料电池的电压误差模型；Among them, min means minimization,
Figure SMS_16
represents the stack voltage of the proton exchange membrane fuel cell at the kth moment,
Figure SMS_17
represents the measured stack voltage of the proton exchange membrane fuel cell at the kth moment, n represents the number of moments, and SSE represents the voltage error model of the proton exchange membrane fuel cell;

步骤2所述参数的约束条件，具体如下：The constraints of the parameters described in step 2 are as follows:

Figure SMS_18
Figure SMS_18

Figure SMS_19
Figure SMS_19

其中，

Figure SMS_20
表示第一半经验因子，
Figure SMS_21
表示第一半经验因子的下限，
Figure SMS_22
表示第一半经验因子的上限；in,
Figure SMS_20
represents the first semi-empirical factor,
Figure SMS_21
represents the lower limit of the first half of the empirical factor,
Figure SMS_22
represents the upper limit of the first half of the empirical factor;

Figure SMS_23
表示第二半经验因子，
Figure SMS_24
表示第二半经验因子的下限，
Figure SMS_25
表示第二半经验因子的上限；
Figure SMS_23
represents the second semi-empirical factor,
Figure SMS_24
represents the lower limit of the second half empirical factor,
Figure SMS_25
represents the upper limit of the second half of the empirical factor;

Figure SMS_26
表示第三半经验因子，
Figure SMS_27
表示第三半经验因子的下限，
Figure SMS_28
表示第三半经验因子的上限；
Figure SMS_26
represents the third semi-empirical factor,
Figure SMS_27
represents the lower limit of the third semi-empirical factor,
Figure SMS_28
represents the upper limit of the third semi-empirical factor;

Figure SMS_29
表示第四半经验因子，
Figure SMS_30
表示第四半经验因子的下限，
Figure SMS_31
表示第四半经验因子的上限；
Figure SMS_29
represents the fourth semi-empirical factor,
Figure SMS_30
represents the lower limit of the fourth half empirical factor,
Figure SMS_31
represents the upper limit of the fourth half of the empirical factor;

Figure SMS_32
表示质子交换膜内含水量，
Figure SMS_33
为质子交换膜内含水量的下限，
Figure SMS_34
为质子交换膜内含水量的上限；
Figure SMS_32
represents the water content in the proton exchange membrane,
Figure SMS_33
is the lower limit of water content in the proton exchange membrane,
Figure SMS_34
is the upper limit of water content in the proton exchange membrane;

Figure SMS_35
表示膜的恒定电阻，
Figure SMS_36
为膜的恒定电阻的下限，
Figure SMS_37
为膜的恒定电阻的上限；
Figure SMS_35
represents the constant resistance of the membrane,
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 membrane;

Figure SMS_38
表示常数因子，
Figure SMS_39
为常数因子的下限，
Figure SMS_40
为常数因子的上限。
Figure SMS_38
represents the constant factor,
Figure SMS_39
is the lower limit of the constant factor,
Figure SMS_40
is the upper limit of the constant factor.

作为优选，步骤3所述通过用改进红狐优化算法进行求解，具体过程如下：As a preference, step 3 is solved by using an improved Red Fox optimization algorithm, and the specific process is as follows:

步骤3.1：初始化红狐搜索算法；Step 3.1: Initialize the Red Fox search algorithm;

步骤3.1.1：根据参数的约束条件设置红狐的活动空间

Figure SMS_41
；Step 3.1.1: Set the activity space of the red fox according to the parameter constraints
Figure SMS_41
;

将第一半经验因子的上限、第二半经验因子的下限、第三半经验因子的下限、第四三半经验因子的下限、膜的恒定电阻的下限、质子交换膜内含水量的下限、常数因子的下限逐维存入

Figure SMS_42
中，The upper limit of the first half of the empirical factor, the lower limit of the second half of the empirical factor, the lower limit of the third half of the empirical factor, the lower limit of the fourth half of the empirical factor, the lower limit of the constant resistance of the membrane, the lower limit of the water content in the proton exchange membrane, and the lower limit of the constant factor are stored dimension by dimension.
Figure SMS_42
middle,

具体如下：

Figure SMS_43
为第一半经验因子的下限，
Figure SMS_44
为第二半经验因子的下限，
Figure SMS_45
为第三半经验因子的下限，
Figure SMS_46
为第四半经验因子的下限，
Figure SMS_47
为膜恒定电阻的下限，
Figure SMS_48
为质子交换膜内水含量的下限，
Figure SMS_49
为常数因子下限；The details are as follows:
Figure SMS_43
is the lower limit of the first half of the empirical factor,
Figure SMS_44
is the lower limit of the second half of the 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 membrane,
Figure SMS_48
is the lower limit of water content in the proton exchange membrane,
Figure SMS_49
is the lower limit of the constant factor;

将第一半经验因子的上限、第二半经验因子的上限、第三半经验因子的上限、第四三半经验因子的上限、膜的恒定电阻的上限、质子交换膜内含水量的上限、常数因子的上限逐维存入

Figure SMS_50
中，具体如下：The upper limit of the first half of the empirical factor, the upper limit of the second half of the empirical factor, the upper limit of the third half of the empirical factor, the upper limit of the fourth half of the empirical factor, the upper limit of the constant resistance of the membrane, the upper limit of the water content in the proton exchange membrane, and the upper limit of the constant factor are stored dimension by dimension.
Figure SMS_50
The details are as follows:

Figure SMS_51
为第一半经验因子的上限，
Figure SMS_52
为第二半经验因子的上限，
Figure SMS_53
为第三半经验因子的下上限，
Figure SMS_54
为第四半经验因子的上限，
Figure SMS_55
为膜恒定电阻的上限，
Figure SMS_56
为质子交换膜内水含量的上限，
Figure SMS_57
为常数因子上限；
Figure SMS_51
is the upper limit of the first half of the empirical factor,
Figure SMS_52
is the upper limit of the second half of the empirical factor,
Figure SMS_53
is the lower upper limit of the third semi-empirical factor,
Figure SMS_54
is the upper limit of the fourth semi-empirical factor,
Figure SMS_55
is the upper limit of the membrane constant resistance,
Figure SMS_56
is the upper limit of water content in the proton exchange membrane,
Figure SMS_57
is the upper limit of the constant factor;

设置最大迭代次数为

Figure SMS_58
、种群内红狐数量为
Figure SMS_60
、观察角度为
Figure SMS_62
、天气因子为
Figure SMS_63
、行动判断因子为
Figure SMS_64
、路线判断因子为
Figure SMS_65
、进化判断因子为
Figure SMS_66
、进化个体数量为
Figure SMS_59
、形状控制因子为
Figure SMS_61
；Set the maximum number of iterations to
Figure SMS_58
The number of red foxes in the population is
Figure SMS_60
, the observation angle is
Figure SMS_62
, weather factors are
Figure SMS_63
, the action judgment factor is
Figure SMS_64
, the route judgment factor is
Figure SMS_65
, the evolution judgment factor is
Figure SMS_66
The number of evolved individuals is
Figure SMS_59
The shape control factor is
Figure SMS_61
;

根据步骤2所述质子交换膜燃料电池优化模型中决策变量的数量确定红狐的搜索维度为

Figure SMS_67
；According to the number of decision variables in the proton exchange membrane fuel cell optimization model described in step 2, the search dimension of the red fox is determined as
Figure SMS_67
;

其中，

Figure SMS_69
为
Figure SMS_71
之间的随机数，
Figure SMS_73
为
Figure SMS_75
之间的随机数，
Figure SMS_77
为区间
Figure SMS_78
之间的常数，
Figure SMS_79
、
Figure SMS_68
和
Figure SMS_70
为
Figure SMS_72
之间的常数，
Figure SMS_74
为区间
Figure SMS_76
之间的常数；in,
Figure SMS_69
for
Figure SMS_71
A random number between
Figure SMS_73
for
Figure SMS_75
A random number between
Figure SMS_77
For interval
Figure SMS_78
The constant between
Figure SMS_79
,
Figure SMS_68
and
Figure SMS_70
for
Figure SMS_72
The constant between
Figure SMS_74
For interval
Figure SMS_76
The constant between

在红狐的活动区间内随机生成红狐种群，设置当前迭代次数

Figure SMS_80
；Randomly generate a red fox population within the red fox's activity range and set the current number of iterations
Figure SMS_80
;

其中,初始化红狐种群的定义如下：Among them, the definition of the initial red fox population is as follows:

Figure SMS_81
Figure SMS_81

其中，

Figure SMS_95
表示第
Figure SMS_96
次迭代过程中第
Figure SMS_98
个个体解向量的第一半经验因子，
Figure SMS_99
表示第
Figure SMS_100
次迭代过程中第
Figure SMS_101
个个体解向量的第二半经验因子，
Figure SMS_102
表示第
Figure SMS_82
次迭代过程中第
Figure SMS_85
个个体解向量的第三半经验因子，
Figure SMS_87
表示第
Figure SMS_89
次迭代过程中第
Figure SMS_91
个个体解向量的第四半经验因子，
Figure SMS_92
表示第
Figure SMS_94
次迭代过程中第
Figure SMS_97
个个体解向量的质子交换膜内含水量，
Figure SMS_83
表示第
Figure SMS_84
次迭代过程中第
Figure SMS_86
个个体解向量的质子交换膜恒定电阻，
Figure SMS_88
表示第
Figure SMS_90
次迭代过程中第
Figure SMS_93
个个体解向量的燃料电池常数因子；in,
Figure SMS_95
Indicates
Figure SMS_96
In the iteration process
Figure SMS_98
The first half empirical factor of the individual solution vector,
Figure SMS_99
Indicates
Figure SMS_100
In the iteration process
Figure SMS_101
The second semi-empirical factor of the individual solution vector,
Figure SMS_102
Indicates
Figure SMS_82
In the iteration process
Figure SMS_85
The third semi-empirical factor of the individual solution vector,
Figure SMS_87
Indicates
Figure SMS_89
In the iteration process
Figure SMS_91
The fourth semi-empirical factor of the individual solution vector,
Figure SMS_92
Indicates
Figure SMS_94
In the iteration process
Figure SMS_97
The water content in the proton exchange membrane of each individual solution vector,
Figure SMS_83
Indicates
Figure SMS_84
In the iteration process
Figure SMS_86
The constant resistance of the proton exchange membrane of the individual solution vector,
Figure SMS_88
Indicates
Figure SMS_90
In the iteration process
Figure SMS_93
The fuel cell constant factor of each individual solution vector;

且满足：

Figure SMS_103
And satisfy:
Figure SMS_103

其中，

Figure SMS_104
为解的维度，
Figure SMS_105
表示红狐活动空间中第
Figure SMS_106
维解向量参数的下限，
Figure SMS_107
表示红狐活动空间中第
Figure SMS_108
维解向量参数的上限。in,
Figure SMS_104
is the dimension of the solution,
Figure SMS_105
Indicates the red fox activity space
Figure SMS_106
The lower limit of the solution vector parameter,
Figure SMS_107
Indicates the red fox activity space
Figure SMS_108
An upper limit on the dimensional solution vector parameter.

步骤3.2：搜寻猎物栖息地，采用融入混沌优化算法的小波精英学习策略进行全局搜索；Step 3.2: Search for prey habitats and use a wavelet elite learning strategy integrated with a chaotic optimization algorithm for global search;

根据步骤2所述的质子交换膜燃料电池的电压误差模型的目标函数计算种群内所有红狐个体的适应度，并依据适应度的大小对红狐个体进行排序，挑选出最优红狐个体

Figure SMS_109
；The fitness of all red fox individuals in the population is calculated according to the objective function of the voltage error model of the proton exchange membrane fuel cell described in step 2, and the red fox individuals are sorted according to the size of the fitness to select the best red fox individual
Figure SMS_109
;

采用融入混沌优化算法的小波精英学习策略驱动其余个体向最优个体移动，具体如下：The wavelet elite learning strategy integrated with the chaotic optimization algorithm is used to drive the remaining individuals to move toward the optimal individual, as follows:

Figure SMS_110
Figure SMS_110

其中，

Figure SMS_112
为Morlet小波，
Figure SMS_113
为全局搜索因子，
Figure SMS_115
为SPM混沌映射，
Figure SMS_117
表示第
Figure SMS_120
次迭代过程中第
Figure SMS_121
个更新前的个体，
Figure SMS_124
表示第
Figure SMS_111
次迭代过程中更新前的全局最优解，
Figure SMS_114
为符号函数，
Figure SMS_116
为红狐活动空间的下限，
Figure SMS_118
为红狐活动空间的上限，
Figure SMS_119
表示第
Figure SMS_122
次迭代过程中第
Figure SMS_123
个更新后的个体；in,
Figure SMS_112
is the Morlet wavelet,
Figure SMS_113
is the global search factor,
Figure SMS_115
is the SPM chaotic map,
Figure SMS_117
Indicates
Figure SMS_120
In the iteration process
Figure SMS_121
Individuals before the update,
Figure SMS_124
Indicates
Figure SMS_111
The global optimal solution before updating in the iteration process is
Figure SMS_114
is the symbolic function,
Figure SMS_116
is the lower limit of the red fox's activity space.
Figure SMS_118
The upper limit of the red fox's activity space.
Figure SMS_119
Indicates
Figure SMS_122
In the iteration process
Figure SMS_123
An updated individual;

Figure SMS_125
Figure SMS_125

其中，

Figure SMS_126
为区间
Figure SMS_127
之间的随机数；in,
Figure SMS_126
For interval
Figure SMS_127
A random number between

Figure SMS_128
Figure SMS_128

其中，

Figure SMS_129
为取随机数函数，
Figure SMS_130
为
Figure SMS_131
与
Figure SMS_132
之间的欧氏距离，计算公式如下：in,
Figure SMS_129
To get the random number function,
Figure SMS_130
for
Figure SMS_131
and
Figure SMS_132
The Euclidean distance between them is calculated as follows:

Figure SMS_133
Figure SMS_133

其中，

Figure SMS_134
为质子交换膜燃料电池模型参数个数；in,
Figure SMS_134
is the number of parameters of the proton exchange membrane fuel cell model;

Figure SMS_135
Figure SMS_135

其中，

Figure SMS_136
表示混沌因子，
Figure SMS_138
为区间
Figure SMS_140
之间的随机数，
Figure SMS_142
为取余函数，
Figure SMS_144
表示第t次迭代过程中第
Figure SMS_145
个更新前的个体，
Figure SMS_146
和
Figure SMS_137
为区间
Figure SMS_139
之间的常数；
Figure SMS_141
表示第t次迭代过程中第
Figure SMS_143
个更新前的个体，in,
Figure SMS_136
represents the chaos factor,
Figure SMS_138
For interval
Figure SMS_140
A random number between
Figure SMS_142
is the remainder function,
Figure SMS_144
Indicates the number of iterations in the tth
Figure SMS_145
Individuals before the update,
Figure SMS_146
and
Figure SMS_137
For interval
Figure SMS_139
The constant between
Figure SMS_141
Indicates the number of iterations in the tth
Figure SMS_143
Individuals before the update,

根据步骤2所述的质子交换膜燃料电池的电压误差模型重新计算更新后的红狐适应度，判断更新后的红狐适应度是否优于历史最优个体，若满足保持更新后的位置不变并替换历史最优个体。Recalculate the updated red fox fitness according to the voltage error model of the proton exchange membrane fuel cell described in step 2, and determine whether the updated red fox fitness is better than the historical best individual. If it is satisfied, keep the updated position unchanged and replace the historical best individual.

步骤3.3：遍历栖息地，在猎物栖息地内搜索猎物的准确位置；Step 3.3: Traverse the habitat and search for the exact location of the prey in the prey habitat;

对每只红狐设置伪装因子

Figure SMS_147
以模拟红狐在接近猎物时被注意到的可能性，其中伪装因子
Figure SMS_148
为区间
Figure SMS_149
之间的随机数；Set a camouflage factor for each red fox
Figure SMS_147
To simulate the likelihood of a red fox being noticed when approaching prey, the camouflage factor
Figure SMS_148
For interval
Figure SMS_149
A random number between

判断伪装因子

Figure SMS_150
是否满足
Figure SMS_151
，若不满足则留在原地进行伪装；Determine the camouflage factor
Figure SMS_150
Is it satisfied?
Figure SMS_151
, if not satisfied, stay where you are and pretend;

其中，

Figure SMS_152
为区间
Figure SMS_153
之间的常数；in,
Figure SMS_152
For interval
Figure SMS_153
The constant between

若满足则设置路线影响因子

Figure SMS_154
与局部放缩因子
Figure SMS_155
；If satisfied, set the route impact factor
Figure SMS_154
Local scaling factor
Figure SMS_155
;

其中，路线影响因子

Figure SMS_156
为区间
Figure SMS_157
之间的随机数，局部放缩因子
Figure SMS_158
为区间
Figure SMS_159
之间的随机数；Among them, the route impact factor
Figure SMS_156
For interval
Figure SMS_157
A random number between , a local scaling factor
Figure SMS_158
For interval
Figure SMS_159
A random number between

判断满足

Figure SMS_160
红狐个体的路线影响因子
Figure SMS_161
是否满足
Figure SMS_162
，若满足则依照螺线公式更新红狐种群；其中，
Figure SMS_163
和
Figure SMS_164
为区间
Figure SMS_165
之间的常数；Judgment Satisfaction
Figure SMS_160
Factors affecting the route of individual red foxes
Figure SMS_161
Is it satisfied?
Figure SMS_162
, if satisfied, the red fox population is updated according to the spiral formula; among them,
Figure SMS_163
and
Figure SMS_164
For interval
Figure SMS_165
The constant between

所述螺线公式，具体如下：The spiral formula is as follows:

Figure SMS_166
Figure SMS_166

其中，

Figure SMS_168
表示第一搜索角度，
Figure SMS_169
表示第二搜索角度，
Figure SMS_171
表示第三搜索角度，
Figure SMS_174
表示第四搜索角度，
Figure SMS_175
表示第五搜索角度，
Figure SMS_178
表示第六搜索角度，
Figure SMS_180
表示第七搜索角度，均为
Figure SMS_182
之间的随机数，
Figure SMS_183
为局部放缩因子，
Figure SMS_185
表示第
Figure SMS_188
次迭代过程中第
Figure SMS_190
个个体解向量的第一半经验因子，
Figure SMS_191
表示第
Figure SMS_193
次迭代过程中第
Figure SMS_196
个个体解向量的第二半经验因子，
Figure SMS_197
表示第
Figure SMS_199
次迭代过程中第
Figure SMS_202
个个体解向量的第三半经验因子，
Figure SMS_204
表示第
Figure SMS_205
次迭代过程中第
Figure SMS_207
个个体解向量的第四半经验因子，
Figure SMS_208
表示第
Figure SMS_209
次迭代过程中第
Figure SMS_210
个个体解向量的质子交换膜内含水量，
Figure SMS_211
表示第
Figure SMS_212
次迭代过程中第
Figure SMS_213
个个体解向量的质子交换膜恒定电阻，
Figure SMS_214
表示第
Figure SMS_215
次迭代过程中第
Figure SMS_216
个个体解向量的燃料电池常数因子，
Figure SMS_217
表示第
Figure SMS_167
次迭代过程中第
Figure SMS_170
个个体螺线更新后解向量的第一半经验因子，
Figure SMS_172
表示第
Figure SMS_173
次迭代过程中第
Figure SMS_176
个个体螺线更新后解向量的第二半经验因子，
Figure SMS_177
表示第
Figure SMS_179
次迭代过程中第
Figure SMS_181
个个体螺线更新后解向量的第三半经验因子，
Figure SMS_184
表示第
Figure SMS_186
次迭代过程中第
Figure SMS_187
个个体螺线更新后解向量的第四半经验因子，
Figure SMS_189
表示第
Figure SMS_192
次迭代过程中第
Figure SMS_194
个个体螺线更新后解向量的质子交换膜内含水量，
Figure SMS_195
表示第
Figure SMS_198
次迭代过程中第
Figure SMS_200
个个体螺线更新后解向量的质子交换膜恒定电阻，
Figure SMS_201
表示第
Figure SMS_203
次迭代过程中第
Figure SMS_206
个个体螺线更新后解向量的燃料电池常数因子；in,
Figure SMS_168
represents the first search angle,
Figure SMS_169
represents the second search angle,
Figure SMS_171
represents the third search angle,
Figure SMS_174
represents the fourth search angle,
Figure SMS_175
represents the fifth search angle,
Figure SMS_178
represents the sixth search angle,
Figure SMS_180
Indicates the seventh search angle, both
Figure SMS_182
A random number between
Figure SMS_183
is the local scaling factor,
Figure SMS_185
Indicates
Figure SMS_188
In the iteration process
Figure SMS_190
The first half empirical factor of the individual solution vector,
Figure SMS_191
Indicates
Figure SMS_193
In the iteration process
Figure SMS_196
The second semi-empirical factor of the individual solution vector,
Figure SMS_197
Indicates
Figure SMS_199
In the iteration process
Figure SMS_202
The third semi-empirical factor of the individual solution vector,
Figure SMS_204
Indicates
Figure SMS_205
In the iteration process
Figure SMS_207
The fourth semi-empirical factor of the individual solution vector,
Figure SMS_208
Indicates
Figure SMS_209
In the iteration process
Figure SMS_210
The water content in the proton exchange membrane of each individual solution vector,
Figure SMS_211
Indicates
Figure SMS_212
In the iteration process
Figure SMS_213
The constant resistance of the proton exchange membrane of the individual solution vector,
Figure SMS_214
Indicates
Figure SMS_215
In the iteration process
Figure SMS_216
The fuel cell constant factor for each individual solution vector,
Figure SMS_217
Indicates
Figure SMS_167
In the iteration process
Figure SMS_170
The first half empirical factor of the solution vector after the individual spiral is updated,
Figure SMS_172
Indicates
Figure SMS_173
In the iteration process
Figure SMS_176
The second half empirical factor of the solution vector after the individual spiral is updated,
Figure SMS_177
Indicates
Figure SMS_179
In the iteration process
Figure SMS_181
The third semi-empirical factor of the solution vector after the individual spiral is updated,
Figure SMS_184
Indicates
Figure SMS_186
In the iteration process
Figure SMS_187
The fourth semi-empirical factor of the solution vector after the individual spiral is updated,
Figure SMS_189
Indicates
Figure SMS_192
In the iteration process
Figure SMS_194
The water content in the proton exchange membrane of the solution vector after the individual spiral is updated,
Figure SMS_195
Indicates
Figure SMS_198
In the iteration process
Figure SMS_200
The constant resistance of the proton exchange membrane after the solution vector of each individual spiral is updated,
Figure SMS_201
Indicates
Figure SMS_203
In the iteration process
Figure SMS_206
The fuel cell constant factor of the solution vector after each individual spiral update;

Figure SMS_218
为红狐的视野半径，计算公式如下：
Figure SMS_218
is the field of vision radius of the red fox, and the calculation formula is as follows:

Figure SMS_219
Figure SMS_219

其中，

Figure SMS_220
为观察角度，
Figure SMS_221
为天气因子，
Figure SMS_222
为局部放缩因子；in,
Figure SMS_220
For the observation angle,
Figure SMS_221
For weather factors,
Figure SMS_222
is the local scaling factor;

若不满足路线影响因子

Figure SMS_223
，则采用改进后的阿基米德螺线公式更新红狐种群，
Figure SMS_224
为区间
Figure SMS_225
之间的常数；If the route impact factor is not met
Figure SMS_223
, the improved Archimedean spiral formula is used to update the red fox population.
Figure SMS_224
For interval
Figure SMS_225
The constant between

所述改进后的阿基米德螺线公式，具体如下：The improved Archimedean spiral formula is as follows:

Figure SMS_226
Figure SMS_226

其中，

Figure SMS_227
为表示第
Figure SMS_229
次迭代过程中更新后的第
Figure SMS_231
个个体，
Figure SMS_233
表示调节因子，
Figure SMS_235
为对数螺旋形状常数，
Figure SMS_236
为区间
Figure SMS_238
中的随机数，T表示最大迭代次数，
Figure SMS_228
表示第
Figure SMS_230
次迭代过程中第
Figure SMS_232
个更新前的个体，
Figure SMS_234
表示第
Figure SMS_237
次迭代过程中更新前的全局最优解；in,
Figure SMS_227
To indicate the
Figure SMS_229
After the update in the iteration
Figure SMS_231
Individuals,
Figure SMS_233
represents the adjustment factor,
Figure SMS_235
is the logarithmic spiral shape constant,
Figure SMS_236
For interval
Figure SMS_238
The random number in, T represents the maximum number of iterations,
Figure SMS_228
Indicates
Figure SMS_230
In the iteration process
Figure SMS_232
Individuals before the update,
Figure SMS_234
Indicates
Figure SMS_237
The global optimal solution before updating in the iteration process;

调节因子

Figure SMS_239
的计算公式为：Modulating Factor
Figure SMS_239
The calculation formula is:

Figure SMS_240
Figure SMS_240

其中，

Figure SMS_241
为四舍五入函数；in,
Figure SMS_241
is the rounding function;

重新计算红狐种群适应度，依据适应度对红狐进行重新排序，并选出最优的两只红狐个体；Recalculate the fitness of the red fox population, reorder the red foxes according to their fitness, and select the two best red fox individuals;

步骤3.4：繁殖与放逐，根据红狐个体的适应度选择

Figure SMS_242
个最差个体放逐至栖息地之外或直接猎杀，其中，
Figure SMS_243
为具体操作步骤如下：Step 3.4: Breeding and exile, selection based on individual red fox fitness
Figure SMS_242
The worst individuals are exiled outside their habitats or hunted directly, among which,
Figure SMS_243
The specific steps are as follows:

设置进化因子

Figure SMS_244
，其中
Figure SMS_245
为
Figure SMS_246
之间的随机数；Set the evolution factor
Figure SMS_244
,in
Figure SMS_245
for
Figure SMS_246
A random number between

判断

Figure SMS_247
是否满足
Figure SMS_248
，若满足，则将
Figure SMS_249
个最差个体猎杀，同时最优的两只红狐会在栖息地内繁殖出等量的红狐个体替代被猎杀的红狐，随机分布在当前栖息地内；其中，
Figure SMS_250
为区间
Figure SMS_251
之间的常数。judge
Figure SMS_247
Is it satisfied?
Figure SMS_248
, if satisfied, then
Figure SMS_249
The worst individuals are hunted, and the two best red foxes will breed an equal number of red fox individuals in the habitat to replace the hunted red foxes, which are randomly distributed in the current habitat;
Figure SMS_250
For interval
Figure SMS_251
The constant between .

当前栖息地中心点计算公式如下：The current habitat center point calculation formula is as follows:

Figure SMS_252
Figure SMS_252

其中，

Figure SMS_253
为第
Figure SMS_254
次迭代过程中适应度排序为前2的红狐个体。in,
Figure SMS_253
For the
Figure SMS_254
The red fox individuals ranked in the top 2 in fitness during the iteration.

步骤3.4.2所述栖息地的直径计算公式如下：The diameter of the habitat described in step 3.4.2 is calculated as follows:

Figure SMS_255
Figure SMS_255

若不满足

Figure SMS_256
，则将
Figure SMS_257
个最差红狐个体逐出栖息地，被逐出栖息地的红狐会结合狩猎经验重新寻找新的猎物栖息地；If not satisfied
Figure SMS_256
, then
Figure SMS_257
The worst red foxes are driven out of their habitats. The driven red foxes will find new prey habitats based on their hunting experience.

即采用新型回溯更新策略对被放逐红狐的位置进行更新，更新公式如下：That is, a new backtracking update strategy is used to update the position of the exiled red fox. The update formula is as follows:

Figure SMS_258
Figure SMS_258

Figure SMS_259
Figure SMS_259

其中，

Figure SMS_261
为红狐的初始位置，
Figure SMS_262
为SPM混沌映射，
Figure SMS_263
为第
Figure SMS_264
次迭代过程中进化后的第
Figure SMS_265
个红狐个体，
Figure SMS_266
为幂函数分布值；
Figure SMS_267
为区间
Figure SMS_260
之间的常数，T表示最大迭代次数；in,
Figure SMS_261
is the initial position of the red fox,
Figure SMS_262
is the SPM chaotic map,
Figure SMS_263
For the
Figure SMS_264
After the evolution in the iteration
Figure SMS_265
Red fox individuals,
Figure SMS_266
is the power function distribution value;
Figure SMS_267
For interval
Figure SMS_260
The constant between them, T represents the maximum number of iterations;

计算所有红狐个体的适应度并排序，令

Figure SMS_268
；Calculate the fitness of all red fox individuals and sort them.
Figure SMS_268
;

步骤3.5：重复步骤3.2—步骤3.4，直至

Figure SMS_269
大于T，并输出优化后的第一半经验因子、优化后的第二半经验因子、优化后的第三半经验因子、优化后的第四半经验因子、优化后的膜的恒定电阻、优化后的质子交换膜内含水量、优化后的常数因子。Step 3.5: Repeat steps 3.2 to 3.4 until
Figure SMS_269
Greater than T, and output the optimized first semi-empirical factor, the optimized second semi-empirical factor, the optimized third semi-empirical factor, the optimized fourth semi-empirical factor, the optimized constant resistance of the membrane, the optimized water content in the proton exchange membrane, and the optimized constant factor.

本发明还提供了一种计算机可读介质，所述计算机可读介质存储电子设备执行的计算机程序，当所述计算机程序在电子设备上运行时，使得所述电子设备执行所述质子交换膜燃料电池估测方法的步骤。The present invention also provides a computer-readable medium, which stores a computer program executed by an electronic device. When the computer program runs on the electronic device, the electronic device executes the steps of the proton exchange membrane fuel cell estimation method.

本发明的优点在于：The advantages of the present invention are:

采用融入混沌优化算法的小波精英学习策略驱动红狐个体向最优个体移动，有效地保留了精英解的特性，优化红狐的空间分布，提高算法的全局搜索能力。The wavelet elite learning strategy integrated with the chaotic optimization algorithm is used to drive the red fox individuals to move towards the optimal individual, which effectively retains the characteristics of the elite solution, optimizes the spatial distribution of red foxes, and improves the global search ability of the algorithm.

在算法进行局部搜索时，引入新型阿基米德螺线行动路径，使红狐的行动路线多样化，提高算法的局部搜索能力，帮助算法更快地寻到局部最优解的准确位置。When the algorithm performs local search, a new Archimedean spiral action path is introduced to diversify the red fox's action route, improve the algorithm's local search capability, and help the algorithm find the exact location of the local optimal solution more quickly.

采用新型回溯更新策略对放逐后的红狐个体进行位置更新，帮助被放逐红狐更快寻找到其他栖息地，有助于算法跳出局部最优，避免算法因陷入局部最优而过早收敛。A new backtracking update strategy is used to update the positions of exiled red foxes, helping them to find other habitats faster. This helps the algorithm to escape from the local optimum and avoid premature convergence due to being trapped in the local optimum.

对红狐搜索算法进行改进，提高了算法对复杂模型的适应能力。Improvements have been made to the Red Fox search algorithm to increase the algorithm's adaptability to complex models.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1：本发明实施例的方法流程图；FIG1 is a flow chart of a method according to an embodiment of the present invention;

图2：本发明实施例的改进红狐搜索算法流程图。FIG2 is a flow chart of an improved RedFox search algorithm according to an embodiment of the present invention.

具体实施方式DETAILED DESCRIPTION

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

具体实施时，本发明技术方案提出的方法可由本领域技术人员采用计算机软件技术实现自动运行流程，实现方法的系统装置例如存储本发明技术方案相应计算机程序的计算机可读存储介质以及包括运行相应计算机程序的计算机设备，也应当在本发明的保护范围内。In specific implementation, the method proposed in the technical solution of the present invention can be implemented by technical personnel in this field using computer software technology to realize automatic operation process. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of the present invention and computer equipment running the corresponding computer program, should also be within the protection scope of the present invention.

下面结合图1-图2介绍本发明实施例方法的技术方案为一种质子交换膜燃料电池估测方法，具体如下：The technical solution of the method of the embodiment of the present invention is described below in conjunction with FIG. 1-FIG 2 as a proton exchange membrane fuel cell estimation method, which is as follows:

如图1所示为本发明的方法流程图。FIG. 1 is a flow chart of the method of the present invention.

步骤1：获取多个时刻的能斯特电压、多个时刻的激活电压、多个时刻的电极和膜电阻引起的欧姆压降、多个时刻的浓度电压损失，计算每个时刻的质子交换膜燃料电池的堆叠电压，输入多个时刻的质子交换膜燃料电池的测量堆叠电压；Step 1: Obtain the Nernst voltage at multiple times, the activation voltage at multiple times, the ohmic voltage drop caused by the electrode and membrane resistance at multiple times, and the concentration voltage loss at multiple times, calculate the stack voltage of the proton exchange membrane fuel cell at each time, and input the measured stack voltage of the proton exchange membrane fuel cell at multiple times;

步骤1所述计算每个时刻的质子交换膜燃料电池的堆叠电压，具体如下：The calculation of the stack voltage of the proton exchange membrane fuel cell at each moment in step 1 is as follows:

Figure SMS_270
Figure SMS_270

Figure SMS_271
Figure SMS_271

Figure SMS_272
Figure SMS_272

其中，

Figure SMS_273
表示第k个时刻的质子交换膜燃料电池的堆叠电压，
Figure SMS_274
为每个堆栈中串联燃料电池的数量，
Figure SMS_275
为第k个时刻的单个燃料电池的输出电压，
Figure SMS_276
为第k个时刻的能斯特电压，
Figure SMS_277
为第k个时刻的激活电压，
Figure SMS_278
为第k个时刻的电极和膜电阻引起的欧姆压降，
Figure SMS_279
为第k个时刻的浓度电压损失，n=3600表示时刻的数量；in,
Figure SMS_273
represents the stack voltage of the proton exchange membrane fuel cell at the kth moment,
Figure SMS_274
For the number of fuel cells in series in each stack,
Figure SMS_275
is the output voltage of a single fuel cell at the kth moment,
Figure SMS_276
is the Nernst voltage at the kth moment,
Figure SMS_277
is the activation voltage at the kth moment,
Figure SMS_278
is the ohmic voltage drop caused by the electrode and membrane resistance at the kth moment,
Figure SMS_279
is the concentration voltage loss at the kth moment, n = 3600 represents the number of moments;

步骤1所述多个时刻的质子交换膜燃料电池的测量堆叠电压，定义为：

Figure SMS_280
，
Figure SMS_281
The measured stack voltage of the proton exchange membrane fuel cell at multiple moments in step 1 is defined as:
Figure SMS_280
,
Figure SMS_281

其中，

Figure SMS_282
表示第k个时刻的质子交换膜燃料电池的测量堆叠电压，n表示时刻的数量；in,
Figure SMS_282
represents the measured stack voltage of the proton exchange membrane fuel cell at the kth moment, and n represents the number of moments;

步骤2：构建堆叠电压优化目标，选取第一半经验因子、第二半经验因子、第三半经验因子、第四半经验因子、膜的恒定电阻、质子交换膜内含水量、常数因子作为决策变量，构建参数的约束条件；Step 2: Construct the stack voltage optimization target, select the first semi-empirical factor, the second semi-empirical factor, the third semi-empirical factor, the fourth semi-empirical factor, the constant resistance of the membrane, the water content in the proton exchange membrane, and the constant factor as decision variables, and construct the parameter constraints;

步骤2所述构建堆叠电压优化目标，具体如下：Step 2 constructs the stack voltage optimization target as follows:

Figure SMS_283
Figure SMS_283

Figure SMS_284
Figure SMS_284

其中，min表示最小化，

Figure SMS_285
表示第k个时刻的质子交换膜燃料电池的堆叠电压，
Figure SMS_286
表示第k个时刻的质子交换膜燃料电池的测量堆叠电压，n表示时刻的数量，SSE表示质子交换膜燃料电池的电压误差模型；Among them, min means minimization,
Figure SMS_285
represents the stack voltage of the proton exchange membrane fuel cell at the kth moment,
Figure SMS_286
represents the measured stack voltage of the proton exchange membrane fuel cell at the kth moment, n represents the number of moments, and SSE represents the voltage error model of the proton exchange membrane fuel cell;

步骤2所述参数的约束条件，具体如下：The constraints of the parameters described in step 2 are as follows:

Figure SMS_287
Figure SMS_287

Figure SMS_288
Figure SMS_288

其中，

Figure SMS_289
表示第一半经验因子，
Figure SMS_290
=-1.19969表示第一半经验因子的下限，
Figure SMS_291
=-0.8532表示第一半经验因子的上限，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。in,
Figure SMS_289
represents the first semi-empirical factor,
Figure SMS_290
=-1.19969 represents the lower limit of the first half of the empirical factor,
Figure SMS_291
=-0.8532 represents the upper limit of the first half empirical factor, which is determined through experience. Obviously, this value is only a preferred value among multiple values.

Figure SMS_292
表示第二半经验因子，
Figure SMS_293
=0.001表示第二半经验因子的下限，
Figure SMS_294
=0.005表示第二半经验因子的上限，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。
Figure SMS_292
represents the second semi-empirical 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 semi-empirical factor, and this value is determined through experience. Obviously, this value is only a preferred value among multiple values.

Figure SMS_295
表示第三半经验因子，
Figure SMS_296
=0.000036表示第三半经验因子的下限，
Figure SMS_297
=0.000098表示第三半经验因子的上限，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。
Figure SMS_295
represents the third semi-empirical factor,
Figure SMS_296
=0.000036 represents the lower limit of the third half empirical factor,
Figure SMS_297
=0.000098 represents the upper limit of the third semi-empirical factor, and this value is obtained through experience. Obviously, this value is only a preferred value among multiple values.

Figure SMS_298
表示第四半经验因子，
Figure SMS_299
=-0.00026表示第四半经验因子的下限，
Figure SMS_300
=-0.0000954表示第四半经验因子的上限，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。
Figure SMS_298
represents the fourth semi-empirical factor,
Figure SMS_299
=-0.00026 represents the lower limit of the fourth half empirical factor,
Figure SMS_300
=-0.0000954 represents the upper limit of the fourth semi-empirical factor, which is determined through experience. Obviously, this value is only a preferred value among multiple values.

Figure SMS_301
表示质子交换膜内含水量，
Figure SMS_302
=10为质子交换膜内含水量的下限，
Figure SMS_303
=24为质子交换膜内含水量的上限，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。
Figure SMS_301
represents the water content in the proton exchange membrane,
Figure SMS_302
=10 is the lower limit of water content in the proton exchange membrane,
Figure SMS_303
=24 is the upper limit of the water content in the proton exchange membrane, and this value is determined through experience. Obviously, this value is only a preferred value among multiple values.

Figure SMS_304
表示膜的恒定电阻，
Figure SMS_305
=0.0001为膜的恒定电阻的下限，
Figure SMS_306
=0.0008为膜的恒定电阻的上限，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。
Figure SMS_304
represents the constant resistance of the membrane,
Figure SMS_305
=0.0001 is the lower limit of the constant resistance of the membrane,
Figure SMS_306
=0.0008 is the upper limit of the constant resistance of the membrane, and this value is determined through experience. Obviously, this value is only a preferred value among multiple values.

Figure SMS_307
表示常数因子，
Figure SMS_308
=0.0136为常数因子的下限，
Figure SMS_309
=0.5为常数因子的上限，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。
Figure SMS_307
represents the constant factor,
Figure SMS_308
=0.0136 is the lower limit of the constant factor,
Figure SMS_309
=0.5 is the upper limit of the constant factor, and this value is determined through experience. Obviously, this value is only a preferred value among multiple values.

步骤3：结合堆叠电压优化目标、参数的约束条件，将第一半经验因子、第二半经验因子、第三半经验因子、第四半经验因子、膜的恒定电阻、质子交换膜内含水量、常数因子作为待求解变量，通过改进红狐优化算法进行求解，得到优化后的第一半经验因子、优化后的第二半经验因子、优化后的第三半经验因子、优化后的第四半经验因子、优化后的膜的恒定电阻、优化后的质子交换膜内含水量、优化后的常数因子，进一步实现质子交换膜燃料电池的优化设置。Step 3: In combination with the stack voltage optimization objective and parameter constraints, the first semi-empirical factor, the second semi-empirical factor, the third semi-empirical factor, the fourth semi-empirical factor, the constant resistance of the membrane, the water content in the proton exchange membrane, and the constant factor are taken as variables to be solved, and solved by the improved Red Fox optimization algorithm to obtain the optimized first semi-empirical factor, the optimized second semi-empirical factor, the optimized third semi-empirical factor, the optimized fourth semi-empirical factor, the optimized constant resistance of the membrane, the optimized water content in the proton exchange membrane, and the optimized constant factor, thereby further realizing the optimized setting of the proton exchange membrane fuel cell.

如图2所示，步骤3所述通过用改进红狐优化算法进行求解，具体过程如下：As shown in Figure 2, step 3 is solved by using the improved Red Fox optimization algorithm. The specific process is as follows:

步骤3.1：初始化红狐搜索算法；Step 3.1: Initialize the Red Fox search algorithm;

步骤3.1.1：根据参数的约束条件设置红狐的活动空间

Figure SMS_310
；Step 3.1.1: Set the activity space of the red fox according to the parameter constraints
Figure SMS_310
;

将第一半经验因子的上限、第二半经验因子的下限、第三半经验因子的下限、第四三半经验因子的下限、膜的恒定电阻的下限、质子交换膜内含水量的下限、常数因子的下限逐维存入

Figure SMS_311
中，The upper limit of the first half of the empirical factor, the lower limit of the second half of the empirical factor, the lower limit of the third half of the empirical factor, the lower limit of the fourth half of the empirical factor, the lower limit of the constant resistance of the membrane, the lower limit of the water content in the proton exchange membrane, and the lower limit of the constant factor are stored dimension by dimension.
Figure SMS_311
middle,

具体如下：

Figure SMS_312
为第一半经验因子的下限，
Figure SMS_313
为第二半经验因子的下限，
Figure SMS_314
为第三半经验因子的下限，
Figure SMS_315
为第四半经验因子的下限，
Figure SMS_316
为膜恒定电阻的下限，
Figure SMS_317
为质子交换膜内水含量的下限，
Figure SMS_318
为常数因子下限；The details are as follows:
Figure SMS_312
is the lower limit of the first half of the empirical factor,
Figure SMS_313
is the lower limit of the second half of the 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 membrane,
Figure SMS_317
is the lower limit of water content in the proton exchange membrane,
Figure SMS_318
is the lower limit of the constant factor;

将第一半经验因子的上限、第二半经验因子的上限、第三半经验因子的上限、第四三半经验因子的上限、膜的恒定电阻的上限、质子交换膜内含水量的上限、常数因子的上限逐维存入

Figure SMS_319
中，具体如下：The upper limit of the first half of the empirical factor, the upper limit of the second half of the empirical factor, the upper limit of the third half of the empirical factor, the upper limit of the fourth half of the empirical factor, the upper limit of the constant resistance of the membrane, the upper limit of the water content in the proton exchange membrane, and the upper limit of the constant factor are stored dimension by dimension.
Figure SMS_319
The details are as follows:

Figure SMS_320
为第一半经验因子的上限，
Figure SMS_321
为第二半经验因子的上限，
Figure SMS_322
为第三半经验因子的下上限，
Figure SMS_323
为第四半经验因子的上限，
Figure SMS_324
为膜恒定电阻的上限，
Figure SMS_325
为质子交换膜内水含量的上限，
Figure SMS_326
为常数因子上限；
Figure SMS_320
is the upper limit of the first half of the empirical factor,
Figure SMS_321
is the upper limit of the second half of the empirical factor,
Figure SMS_322
is the lower upper limit of the third semi-empirical factor,
Figure SMS_323
is the upper limit of the fourth semi-empirical factor,
Figure SMS_324
is the upper limit of the membrane constant resistance,
Figure SMS_325
is the upper limit of water content in the proton exchange membrane,
Figure SMS_326
is the upper limit of the constant factor;

设置最大迭代次数为

Figure SMS_327
、种群内红狐数量为
Figure SMS_329
、观察角度为
Figure SMS_331
、天气因子为
Figure SMS_332
、行动判断因子为
Figure SMS_333
、路线判断因子为
Figure SMS_334
、进化判断因子为
Figure SMS_335
、进化个体数量为
Figure SMS_328
、形状控制因子为
Figure SMS_330
；Set the maximum number of iterations to
Figure SMS_327
The number of red foxes in the population is
Figure SMS_329
, the observation angle is
Figure SMS_331
, weather factors are
Figure SMS_332
, the action judgment factor is
Figure SMS_333
, the route judgment factor is
Figure SMS_334
, the evolution judgment factor is
Figure SMS_335
The number of evolved individuals is
Figure SMS_328
The shape control factor is
Figure SMS_330
;

根据步骤2所述质子交换膜燃料电池优化模型中决策变量的数量确定红狐的搜索维度为

Figure SMS_336
；According to the number of decision variables in the proton exchange membrane fuel cell optimization model described in step 2, the search dimension of the red fox is determined as
Figure SMS_336
;

其中，最大迭代次数

Figure SMS_338
=100，种群内红狐数量
Figure SMS_339
=100，
Figure SMS_341
为
Figure SMS_343
之间的随机数，
Figure SMS_345
为
Figure SMS_347
之间的随机数，
Figure SMS_349
=10为区间
Figure SMS_337
之间的常数，
Figure SMS_340
=0.75、
Figure SMS_342
=0.5、
Figure SMS_344
=0.45为
Figure SMS_346
之间的常数，
Figure SMS_348
=-0.8为区间
Figure SMS_350
之间的常数，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。Among them, the maximum number of iterations
Figure SMS_338
=100, the number of red foxes in the population
Figure SMS_339
=100,
Figure SMS_341
for
Figure SMS_343
A random number between
Figure SMS_345
for
Figure SMS_347
A random number between
Figure SMS_349
=10 is the interval
Figure SMS_337
The constant between
Figure SMS_340
=0.75,
Figure SMS_342
=0.5,
Figure SMS_344
=0.45
Figure SMS_346
The constant between
Figure SMS_348
=-0.8 is the interval
Figure SMS_350
The constant between is determined through experience. Obviously, this value is only a preferred value among multiple values.

在红狐的活动区间内随机生成红狐种群，设置当前迭代次数

Figure SMS_351
；Randomly generate a red fox population within the red fox's activity range and set the current number of iterations
Figure SMS_351
;

其中,初始化红狐种群的定义如下：Among them, the definition of the initial red fox population is as follows:

Figure SMS_352
Figure SMS_352

其中，

Figure SMS_367
表示第
Figure SMS_369
次迭代过程中第
Figure SMS_370
个个体解向量的第一半经验因子，
Figure SMS_371
表示第
Figure SMS_372
次迭代过程中第
Figure SMS_373
个个体解向量的第二半经验因子，
Figure SMS_374
表示第
Figure SMS_354
次迭代过程中第
Figure SMS_355
个个体解向量的第三半经验因子，
Figure SMS_357
表示第
Figure SMS_360
次迭代过程中第
Figure SMS_362
个个体解向量的第四半经验因子，
Figure SMS_364
表示第
Figure SMS_365
次迭代过程中第
Figure SMS_368
个个体解向量的质子交换膜内含水量，
Figure SMS_353
表示第
Figure SMS_356
次迭代过程中第
Figure SMS_358
个个体解向量的质子交换膜恒定电阻，
Figure SMS_359
表示第
Figure SMS_361
次迭代过程中第
Figure SMS_363
个个体解向量的燃料电池常数因子；且满足：
Figure SMS_366
in,
Figure SMS_367
Indicates
Figure SMS_369
In the iteration process
Figure SMS_370
The first half empirical factor of the individual solution vector,
Figure SMS_371
Indicates
Figure SMS_372
In the iteration process
Figure SMS_373
The second semi-empirical factor of the individual solution vector,
Figure SMS_374
Indicates
Figure SMS_354
In the iteration process
Figure SMS_355
The third semi-empirical factor of the individual solution vector,
Figure SMS_357
Indicates
Figure SMS_360
In the iteration process
Figure SMS_362
The fourth semi-empirical factor of the individual solution vector,
Figure SMS_364
Indicates
Figure SMS_365
In the iteration process
Figure SMS_368
The water content in the proton exchange membrane of each individual solution vector,
Figure SMS_353
Indicates
Figure SMS_356
In the iteration process
Figure SMS_358
The constant resistance of the proton exchange membrane of the individual solution vector,
Figure SMS_359
Indicates
Figure SMS_361
In the iteration process
Figure SMS_363
The fuel cell constant factor of each individual solution vector; and satisfying:
Figure SMS_366

其中，

Figure SMS_375
为解的维度，
Figure SMS_376
表示红狐活动空间中第
Figure SMS_377
维解向量参数的下限，
Figure SMS_378
表示红狐活动空间中第
Figure SMS_379
维解向量参数的上限。in,
Figure SMS_375
is the dimension of the solution,
Figure SMS_376
Indicates the red fox activity space
Figure SMS_377
The lower limit of the solution vector parameter,
Figure SMS_378
Indicates the red fox activity space
Figure SMS_379
An upper limit on the dimensional solution vector parameter.

步骤3.2：搜寻猎物栖息地，采用融入混沌优化算法的小波精英学习策略进行全局搜索；Step 3.2: Search for prey habitats and use a wavelet elite learning strategy integrated with a chaotic optimization algorithm for global search;

根据步骤2所述的质子交换膜燃料电池的电压误差模型的目标函数计算种群内所有红狐个体的适应度，并依据适应度的大小对红狐个体进行排序，挑选出最优红狐个体

Figure SMS_380
；The fitness of all red fox individuals in the population is calculated according to the objective function of the voltage error model of the proton exchange membrane fuel cell described in step 2, and the red fox individuals are sorted according to the size of the fitness to select the best red fox individual
Figure SMS_380
;

采用融入混沌优化算法的小波精英学习策略驱动其余个体向最优个体移动，具体如下：The wavelet elite learning strategy integrated with the chaotic optimization algorithm is used to drive the remaining individuals to move toward the optimal individual, as follows:

Figure SMS_381
Figure SMS_381

其中，

Figure SMS_383
为Morlet小波，
Figure SMS_385
为全局搜索因子，
Figure SMS_387
为SPM混沌映射，
Figure SMS_389
表示第
Figure SMS_391
次迭代过程中第
Figure SMS_392
个更新前的个体，表示第
Figure SMS_394
次迭代过程中更新前的全局最优解，
Figure SMS_382
为符号函数，
Figure SMS_384
为红狐活动空间的下限，
Figure SMS_386
为红狐活动空间的上限，
Figure SMS_388
表示第
Figure SMS_390
次迭代过程中第
Figure SMS_393
个更新后的个体；in,
Figure SMS_383
is the Morlet wavelet,
Figure SMS_385
is the global search factor,
Figure SMS_387
is the SPM chaotic map,
Figure SMS_389
Indicates
Figure SMS_391
In the iteration process
Figure SMS_392
individuals before the update, indicating the
Figure SMS_394
The global optimal solution before updating in the iteration process is
Figure SMS_382
is the symbolic function,
Figure SMS_384
is the lower limit of the red fox's activity space.
Figure SMS_386
The upper limit of the red fox's activity space.
Figure SMS_388
Indicates
Figure SMS_390
In the iteration process
Figure SMS_393
An updated individual;

Figure SMS_395
Figure SMS_395

其中，

Figure SMS_396
为区间
Figure SMS_397
之间的随机数。in,
Figure SMS_396
For interval
Figure SMS_397
A random number between .

Figure SMS_398
Figure SMS_398

其中，

Figure SMS_399
为取随机数函数，为
Figure SMS_400
与
Figure SMS_401
之间的欧氏距离，计算公式如下：in,
Figure SMS_399
is the random number function,
Figure SMS_400
and
Figure SMS_401
The Euclidean distance between them is calculated as follows:

Figure SMS_402
Figure SMS_402

其中，

Figure SMS_403
为质子交换膜燃料电池模型参数个数；in,
Figure SMS_403
is the number of parameters of the proton exchange membrane fuel cell model;

Figure SMS_404
Figure SMS_404

其中，

Figure SMS_406
表示混沌因子，
Figure SMS_408
为区间
Figure SMS_410
之间的随机数，
Figure SMS_412
为取余函数，
Figure SMS_414
表示第
Figure SMS_416
次迭代过程中第
Figure SMS_417
个更新前的个体，
Figure SMS_405
=0.4和
Figure SMS_407
=0.3为区间
Figure SMS_409
之间的常数；
Figure SMS_411
表示第
Figure SMS_413
次迭代过程中第
Figure SMS_415
个更新前的个体，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。in,
Figure SMS_406
represents the chaos factor,
Figure SMS_408
For interval
Figure SMS_410
A random number between
Figure SMS_412
is the remainder function,
Figure SMS_414
Indicates
Figure SMS_416
In the iteration process
Figure SMS_417
Individuals before the update,
Figure SMS_405
=0.4 and
Figure SMS_407
=0.3 is the interval
Figure SMS_409
The constant between
Figure SMS_411
Indicates
Figure SMS_413
In the iteration process
Figure SMS_415
The value is determined through experience. Obviously, this value is only a preferred value among multiple values.

根据步骤2所述的质子交换膜燃料电池的电压误差模型重新计算更新后的红狐适应度，判断更新后的红狐适应度是否优于历史最优个体，若满足保持更新后的位置不变并替换历史最优个体。Recalculate the updated red fox fitness according to the voltage error model of the proton exchange membrane fuel cell described in step 2, and determine whether the updated red fox fitness is better than the historical best individual. If it is satisfied, keep the updated position unchanged and replace the historical best individual.

步骤3.3：遍历栖息地，在猎物栖息地内搜索猎物的准确位置；Step 3.3: Traverse the habitat and search for the exact location of the prey in the prey habitat;

对每只红狐设置伪装因子

Figure SMS_418
以模拟红狐在接近猎物时被注意到的可能性，其中伪装因子
Figure SMS_419
为区间
Figure SMS_420
之间的随机数；Set a camouflage factor for each red fox
Figure SMS_418
To simulate the likelihood of a red fox being noticed when approaching prey, the camouflage factor
Figure SMS_419
For interval
Figure SMS_420
A random number between

判断伪装因子

Figure SMS_421
是否满足
Figure SMS_422
，若不满足则留在原地进行伪装；Determine the camouflage factor
Figure SMS_421
Is it satisfied?
Figure SMS_422
, if not satisfied, stay where you are and pretend;

其中，

Figure SMS_423
=0.75为区间
Figure SMS_424
之间的常数。in,
Figure SMS_423
=0.75 is the interval
Figure SMS_424
The constant between .

若满足则设置路线影响因子

Figure SMS_425
与局部放缩因子
Figure SMS_426
；If satisfied, set the route impact factor
Figure SMS_425
Local scaling factor
Figure SMS_426
;

其中，路线影响因子

Figure SMS_427
为区间
Figure SMS_428
之间的随机数，局部放缩因子
Figure SMS_429
为区间
Figure SMS_430
之间的随机数；Among them, the route impact factor
Figure SMS_427
For interval
Figure SMS_428
A random number between , a local scaling factor
Figure SMS_429
For interval
Figure SMS_430
A random number between

判断满足

Figure SMS_431
红狐个体的路线影响因子
Figure SMS_432
是否满足
Figure SMS_433
，若满足则依照螺线公式更新红狐种群；其中，
Figure SMS_434
=0.5为区间
Figure SMS_435
之间的常数，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。Judgment Satisfaction
Figure SMS_431
Factors affecting the route of individual red foxes
Figure SMS_432
Is it satisfied?
Figure SMS_433
, if satisfied, the red fox population is updated according to the spiral formula; among them,
Figure SMS_434
=0.5 is the interval
Figure SMS_435
The constant between is determined through experience. Obviously, this value is only a preferred value among multiple values.

所述螺线公式，具体如下：The spiral formula is as follows:

Figure SMS_436
Figure SMS_436

其中，

Figure SMS_438
表示第一搜索角度，
Figure SMS_440
表示第二搜索角度，
Figure SMS_442
表示第三搜索角度，
Figure SMS_443
表示第四搜索角度，
Figure SMS_444
表示第五搜索角度，
Figure SMS_445
表示第六搜索角度，
Figure SMS_447
表示第七搜索角度，均为
Figure SMS_449
之间的随机数，
Figure SMS_451
为局部放缩因子，
Figure SMS_453
表示第
Figure SMS_455
次迭代过程中第
Figure SMS_457
个个体解向量的第一半经验因子，
Figure SMS_459
表示第
Figure SMS_461
次迭代过程中第
Figure SMS_462
个个体解向量的第二半经验因子，
Figure SMS_465
表示第
Figure SMS_466
次迭代过程中第
Figure SMS_468
个个体解向量的第三半经验因子，
Figure SMS_470
表示第
Figure SMS_472
次迭代过程中第
Figure SMS_474
个个体解向量的第四半经验因子，
Figure SMS_476
表示第
Figure SMS_478
次迭代过程中第
Figure SMS_480
个个体解向量的质子交换膜内含水量，
Figure SMS_481
表示第
Figure SMS_482
次迭代过程中第
Figure SMS_483
个个体解向量的质子交换膜恒定电阻，
Figure SMS_484
表示第
Figure SMS_485
次迭代过程中第
Figure SMS_486
个个体解向量的燃料电池常数因子，
Figure SMS_487
表示第
Figure SMS_437
次迭代过程中第
Figure SMS_439
个个体螺线更新后解向量的第一半经验因子，
Figure SMS_441
表示第
Figure SMS_446
次迭代过程中第
Figure SMS_448
个个体螺线更新后解向量的第二半经验因子，
Figure SMS_450
表示第
Figure SMS_452
次迭代过程中第
Figure SMS_454
个个体螺线更新后解向量的第三半经验因子，
Figure SMS_456
表示第
Figure SMS_458
次迭代过程中第
Figure SMS_460
个个体螺线更新后解向量的第四半经验因子，
Figure SMS_463
表示第
Figure SMS_464
次迭代过程中第
Figure SMS_467
个个体螺线更新后解向量的质子交换膜内含水量，
Figure SMS_469
表示第
Figure SMS_471
次迭代过程中第
Figure SMS_473
个个体螺线更新后解向量的质子交换膜恒定电阻，
Figure SMS_475
表示第
Figure SMS_477
次迭代过程中第
Figure SMS_479
个个体螺线更新后解向量的燃料电池常数因子；in,
Figure SMS_438
represents the first search angle,
Figure SMS_440
represents the second search angle,
Figure SMS_442
represents the third search angle,
Figure SMS_443
represents the fourth search angle,
Figure SMS_444
represents the fifth search angle,
Figure SMS_445
represents the sixth search angle,
Figure SMS_447
Indicates the seventh search angle, both
Figure SMS_449
A random number between
Figure SMS_451
is the local scaling factor,
Figure SMS_453
Indicates
Figure SMS_455
In the iteration process
Figure SMS_457
The first half empirical factor of the individual solution vector,
Figure SMS_459
Indicates
Figure SMS_461
In the iteration process
Figure SMS_462
The second semi-empirical factor of the individual solution vector,
Figure SMS_465
Indicates
Figure SMS_466
In the iteration process
Figure SMS_468
The third semi-empirical factor of the individual solution vector,
Figure SMS_470
Indicates
Figure SMS_472
In the iteration process
Figure SMS_474
The fourth semi-empirical factor of the individual solution vector,
Figure SMS_476
Indicates
Figure SMS_478
In the iteration process
Figure SMS_480
The water content in the proton exchange membrane of each individual solution vector,
Figure SMS_481
Indicates
Figure SMS_482
In the iteration process
Figure SMS_483
The constant resistance of the proton exchange membrane of the individual solution vector,
Figure SMS_484
Indicates
Figure SMS_485
In the iteration process
Figure SMS_486
The fuel cell constant factor for each individual solution vector,
Figure SMS_487
Indicates
Figure SMS_437
In the iteration process
Figure SMS_439
The first half empirical factor of the solution vector after the individual spiral is updated,
Figure SMS_441
Indicates
Figure SMS_446
In the iteration process
Figure SMS_448
The second half empirical factor of the solution vector after the individual spiral is updated,
Figure SMS_450
Indicates
Figure SMS_452
In the iteration process
Figure SMS_454
The third semi-empirical factor of the solution vector after the individual spiral is updated,
Figure SMS_456
Indicates
Figure SMS_458
In the iteration process
Figure SMS_460
The fourth semi-empirical factor of the solution vector after the individual spiral is updated,
Figure SMS_463
Indicates
Figure SMS_464
In the iteration process
Figure SMS_467
The water content in the proton exchange membrane of the solution vector after the individual spiral is updated,
Figure SMS_469
Indicates
Figure SMS_471
In the iteration process
Figure SMS_473
The constant resistance of the proton exchange membrane after the solution vector of each individual spiral is updated,
Figure SMS_475
Indicates
Figure SMS_477
In the iteration process
Figure SMS_479
The fuel cell constant factor of the solution vector after each individual spiral update;

Figure SMS_488
为红狐的视野半径，计算公式如下：
Figure SMS_488
is the field of vision radius of the red fox, and the calculation formula is as follows:

Figure SMS_489
Figure SMS_489

其中，

Figure SMS_490
为观察角度，
Figure SMS_491
为天气因子，
Figure SMS_492
为局部放缩因子。in,
Figure SMS_490
For the observation angle,
Figure SMS_491
For weather factors,
Figure SMS_492
is the local scaling factor.

若不满足路线影响因子

Figure SMS_493
，则采用改进后的阿基米德螺线公式更新红狐种群，
Figure SMS_494
=0.5为区间
Figure SMS_495
之间的常数；If the route impact factor is not met
Figure SMS_493
, the improved Archimedean spiral formula is used to update the red fox population.
Figure SMS_494
=0.5 is the interval
Figure SMS_495
The constant between

所述改进后的阿基米德螺线公式，具体如下：The improved Archimedean spiral formula is as follows:

Figure SMS_496
Figure SMS_496

其中，

Figure SMS_498
为表示第
Figure SMS_500
次迭代过程中更新后的第
Figure SMS_501
个个体，
Figure SMS_503
表示调节因子，
Figure SMS_506
=1为对数螺旋形状常数，
Figure SMS_507
为区间
Figure SMS_508
中的随机数，T表示最大迭代次数，
Figure SMS_497
表示第
Figure SMS_499
次迭代过程中第
Figure SMS_502
个更新前的个体，
Figure SMS_504
表示第
Figure SMS_505
次迭代过程中更新前的全局最优解；in,
Figure SMS_498
To indicate the
Figure SMS_500
After the update in the iteration
Figure SMS_501
Individuals,
Figure SMS_503
represents the adjustment factor,
Figure SMS_506
=1 is the logarithmic spiral shape constant,
Figure SMS_507
For interval
Figure SMS_508
The random number in, T represents the maximum number of iterations,
Figure SMS_497
Indicates
Figure SMS_499
In the iteration process
Figure SMS_502
Individuals before the update,
Figure SMS_504
Indicates
Figure SMS_505
The global optimal solution before updating in the iteration process;

调节因子

Figure SMS_509
的计算公式为：Modulating Factor
Figure SMS_509
The calculation formula is:

Figure SMS_510
Figure SMS_510

其中，

Figure SMS_511
为四舍五入函数；in,
Figure SMS_511
is the rounding function;

重新计算红狐种群适应度，依据适应度对红狐进行重新排序，并选出最优的两只红狐个体；Recalculate the fitness of the red fox population, reorder the red foxes according to their fitness, and select the two best red fox individuals;

步骤3.4：繁殖与放逐，根据红狐个体的适应度选择

Figure SMS_512
个最差个体放逐至栖息地之外或直接猎杀，其中，
Figure SMS_513
为具体操作步骤如下：Step 3.4: Breeding and exile, selection based on individual red fox fitness
Figure SMS_512
The worst individuals are exiled outside their habitats or hunted directly, among which,
Figure SMS_513
The specific steps are as follows:

设置进化因子

Figure SMS_514
，其中
Figure SMS_515
为
Figure SMS_516
之间的随机数。Set the evolution factor
Figure SMS_514
,in
Figure SMS_515
for
Figure SMS_516
A random number between .

判断

Figure SMS_517
是否满足
Figure SMS_518
，若满足，则将
Figure SMS_519
个最差个体猎杀，同时最优的两只红狐会在栖息地内繁殖出等量的红狐个体替代被猎杀的红狐，随机分布在当前栖息地内；其中，
Figure SMS_520
=0.45为区间
Figure SMS_521
之间的常数，该取值通过经验取值，显然，该取值仅仅是多种取值中的一种优选取值。judge
Figure SMS_517
Is it satisfied?
Figure SMS_518
, if satisfied, then
Figure SMS_519
The worst individuals are hunted, and the two best red foxes will breed an equal number of red fox individuals in the habitat to replace the hunted red foxes, which are randomly distributed in the current habitat;
Figure SMS_520
=0.45 is the interval
Figure SMS_521
The constant between is determined through experience. Obviously, this value is only a preferred value among multiple values.

当前栖息地中心点计算公式如下：The current habitat center point calculation formula is as follows:

Figure SMS_522
Figure SMS_522

其中，

Figure SMS_523
为第
Figure SMS_524
次迭代过程中适应度排序为前2的红狐个体。in,
Figure SMS_523
For the
Figure SMS_524
The red fox individuals ranked in the top 2 in fitness during the iteration.

步骤3.4.2所述栖息地的直径计算公式如下：The diameter of the habitat described in step 3.4.2 is calculated as follows:

Figure SMS_525
Figure SMS_525

若不满足

Figure SMS_526
，则将
Figure SMS_527
个最差红狐个体逐出栖息地，被逐出栖息地的红狐会结合狩猎经验重新寻找新的猎物栖息地；If not satisfied
Figure SMS_526
, then
Figure SMS_527
The worst red foxes are driven out of their habitats. The driven red foxes will find new prey habitats based on their hunting experience.

即采用新型回溯更新策略对被放逐红狐的位置进行更新，更新公式如下：That is, a new backtracking update strategy is used to update the position of the exiled red fox. The update formula is as follows:

Figure SMS_528
Figure SMS_528

Figure SMS_529
Figure SMS_529

其中，

Figure SMS_531
为红狐的初始位置，
Figure SMS_532
为SPM混沌映射，
Figure SMS_533
为第
Figure SMS_534
次迭代过程中进化后的第
Figure SMS_535
个红狐个体，
Figure SMS_536
为幂函数分布值；
Figure SMS_537
为区间
Figure SMS_530
之间的常数，T表示最大迭代次数；in,
Figure SMS_531
is the initial position of the red fox,
Figure SMS_532
is the SPM chaotic map,
Figure SMS_533
For the
Figure SMS_534
After the evolution in the iteration
Figure SMS_535
Red fox individuals,
Figure SMS_536
is the power function distribution value;
Figure SMS_537
For interval
Figure SMS_530
The constant between them, T represents the maximum number of iterations;

计算所有红狐个体的适应度并排序，令

Figure SMS_538
；Calculate the fitness of all red fox individuals and sort them.
Figure SMS_538
;

步骤3.5：重复步骤3.2—步骤3.4，直至

Figure SMS_539
大于
Figure SMS_540
，并输出优化后的第一半经验因子、优化后的第二半经验因子、优化后的第三半经验因子、优化后的第四半经验因子、优化后的膜的恒定电阻、优化后的质子交换膜内含水量、优化后的常数因子。Step 3.5: Repeat steps 3.2 to 3.4 until
Figure SMS_539
Greater than
Figure SMS_540
, and output the optimized first semi-empirical factor, the optimized second semi-empirical factor, the optimized third semi-empirical factor, the optimized fourth semi-empirical factor, the optimized constant resistance of the membrane, the optimized water content in the proton exchange membrane, and the optimized constant factor.

本发明的具体实施例还提供了一种计算机可读介质。A specific embodiment of the present invention also provides a computer-readable medium.

所述计算机可读介质为服务器工作站；The computer readable medium is a server workstation;

所述服务器工作站存储电子设备执行的计算机程序，当所述计算机程序在电子设备上运行时，使得所述电子设备执行本发明实施例的质子交换膜燃料电池估测方法的步骤。The server workstation stores a computer program executed by an electronic device. When the computer program is executed 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 present invention.

应当理解的是，本说明书未详细阐述的部分均属于现有技术。It should be understood that parts not elaborated in detail in this specification belong to the prior art.

应当理解的是，上述针对较佳实施例的描述较为详细，并不能因此而认为是对本发明专利保护范围的限制，本领域的普通技术人员在本发明的启示下，在不脱离本发明权利要求所保护的范围情况下，还可以做出替换或变形，均落入本发明的保护范围之内，本发明的请求保护范围应以所附权利要求为准。It should be understood that the above description of the preferred embodiment is relatively detailed and cannot be regarded as limiting the scope of patent protection of the present invention. Under the enlightenment of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, which all fall within the scope of protection of the present invention. The scope of protection requested for the present invention shall be based on the attached 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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