Air cooling PEMFC temperature control method based on NSGAIII

Abstract

The invention discloses an air cooling PEMFC temperature control method based on NSGAIII, and relates to the technical field of fuel cell thermal management, and the method comprises the following steps: obtaining a plurality of adjustment parameters, overshoot, temperature identification errors and temperature control errors when an RBF-PID controller controls a thermal management system model; establishing a single-target optimization problem, and solving the single-target optimization problem; establishing a multi-objective optimization problem, and solving the multi-objective optimization problem through NSGAIII to obtain a plurality of optimal adjustment parameters; and the multiple optimal adjustment parameters are input into an RBF-PID controller, and the temperature of the air cooling PEMFC is controlled through the RBF-PID controller with the multiple optimal control parameters. According to the method, it can be ensured that the obtained optimization result is at the Pareto frontier, accurate control over the temperature of the air cooling PEMFC is achieved, meanwhile, multiple optimal solutions are provided for different design requirements, and the solving efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of fuel cell thermal management, and particularly to a temperature control method for air-cooled PEMFC based on NSGAIII. Background Technique

[0002] Proton Exchange Membrane Fuel Cell (PEMFC) has the advantages of low operating temperature, high power density, high energy conversion efficiency, clean and pollution-free, etc., and is considered to be the most promising clean energy conversion device. The operating temperature is one of the most important factors affecting the output performance of PEMFC. Too high temperature will cause the exchange membrane to dehydrate and even cause irreversible damage to the battery, and too low temperature will reduce the electrochemical reaction and even cause problems such as flooding. Therefore, controlling the PEMFC at an appropriate operating temperature is crucial for the efficient and stable operation of the PEMFC system.

[0003] Air-cooled PEMFC is widely used in scenarios with low power requirements such as unmanned aerial vehicles and forklifts due to its simple and compact structure. In the temperature control of air-cooled PEMFC, the most widely used method is still the classical PID (Proportional-Integral-Derivative) control. However, the air-cooled PEMFC temperature control system is a strongly nonlinear system. Applying the classical PID control will result in problems such as low adjustment accuracy, slow adjustment time, and large overshoot. The main reason is that the three parameters of the classical PID controller , and are fixed and cannot be applied to the entire operating range of the air-cooled PEMFC temperature control system with a set of fixed parameters. Therefore, researchers have developed many adaptive PID algorithms, such as the RBF-PID (Radial Basis Function-Proportional-Integral-Derivative) algorithm combined with neural networks.

[0004] When the RBF-PID algorithm is used for temperature control, its controller parameters will affect the control effect and identification effect, that is, multiple objectives need to be optimized. Therefore, a suitable method is needed to optimize these parameters to comprehensively improve the performance of RBF-PID.

[0005] Currently, the PSO (Particle Swarm Optimization) algorithm is used to optimize the controller parameters of RBF-PID. The PSO algorithm generally focuses on unilateral optimization, and its objective function is generally a single-objective function. Even if it is constructed as the sum of multiple sub-objectives, it still cannot ensure that multiple sub-objectives are on the Pareto front. The obtained controller parameters are not the best, and the temperature of the air-cooled PEMFC cannot be accurately controlled. At the same time, the single-objective optimization algorithm can only obtain one feasible solution each time it is optimized. If the design requirements change, the weights of multiple sub-objectives need to be changed and optimized again, resulting in low solution efficiency. Summary of the Invention

[0006] Based on the defects existing in the above-mentioned prior art, the present invention provides an air-cooled PEMFC temperature control method based on NSGAIII, which solves the problems that the existing PSO algorithm cannot accurately control the temperature of the air-cooled PEMFC and has low solution efficiency.

[0007] The present invention adopts the following technical solutions: In the first aspect, the present invention provides an air-cooled PEMFC temperature control method based on NSGAIII, including the following steps: Obtain multiple adjustment parameters, temperature control error, overshoot, and temperature identification error when the RBF-PID controller controls the thermal management system model of the air-cooled proton exchange membrane fuel cell PEMFC; integrate the temperature control error to obtain the first sub-objective; average the overshoot to obtain the second sub-objective; integrate the temperature identification error to obtain the third sub-objective; Taking multiple adjustment parameters as decision variables, and minimizing the sum of the standardized first sub-objective, standardized second sub-objective, and standardized third sub-objective as a single optimization objective, establish a single-objective optimization problem, solve the single-objective optimization problem, and obtain optimized adjustment parameters, the first optimized sub-objective, the second optimized sub-objective, and the third optimized sub-objective; Taking multiple optimized adjustment parameters as decision variables, constructing a multi-optimization objective based on the first optimized sub-objective, the second optimized sub-objective, and the third optimized sub-objective, establish a multi-objective optimization problem, and solve the multi-objective optimization problem through NSGAIII to obtain multiple optimal adjustment parameters; Input multiple optimal adjustment parameters into the RBF-PID controller, and control the temperature of the air-cooled PEMFC through the RBF-PID controller with multiple optimal control parameters.

[0008] Preferably, the obtaining of multiple adjustment parameters, temperature control error, overshoot, and temperature identification error when the RBF-PID controller controls the thermal management system model of the air-cooled proton exchange membrane fuel cell PEMFC specifically includes the following steps: Input the control quantity of the thermal management system model at the previous moment, the actual temperature at the current moment, and the actual temperature at the previous moment into the RBF neural network; Perform forward propagation on the RBF neural network to obtain the temperature identification error; establish a performance index function of the RBF neural network based on the temperature identification error; the RBF neural network includes an input layer, a hidden layer, and an output layer; Based on the performance index function, perform error backpropagation on the RBF neural network to obtain the weights between the layers of the RBF neural network and the parameters of the hidden layer; during the error backpropagation process, obtain the first inertia weight, the second inertia weight, and the learning rate for controlling the weights between the layers of the RBF neural network and the parameters of the hidden layer; Obtain the Jacobian information of the thermal management system model through the RBF neural network after error backpropagation; Obtain the temperature control error of the RBF-PID controller based on the given temperature and the actual temperature at the current moment; establish a performance index function of the RBF-PID controller based on the temperature control error; Based on the performance index function, perform online adjustment of the control parameters of proportional, integral, and derivative through the Jacobian information; during the online adjustment, obtain the adjustment rates of proportional, integral, and derivative for controlling the control parameters of proportional, integral, and derivative; Control the proportional, integral, and derivative gains of the RBF-PID controller through the control parameters of proportional, integral, and derivative after online adjustment to obtain the control quantity at the current moment; Control the temperature of the air-cooled PEMFC through the control quantity at the current moment.

[0009] Preferably, the performing error backpropagation on the RBF neural network based on the performance index function specifically includes: According to the gradient descent method, the learning algorithm for the weights from the hidden layer to the output layer is as follows: ; where ; In the formula, is the first inertia weight, is the second inertia weight, is k the weight from the j th hidden layer to the output layer at time is k the weight from the j th hidden layer to the output layer at time is k the weight from the j th hidden layer to the output layer at time is k-3 moment, the weight from the j th hidden layer to the output layer, is the weight at the change amount at the k th moment, is the learning rate, is the performance index function of the RBF neural network.

[0010] Preferably, the online adjustment of the proportional, integral, and derivative control parameters through the Jacobian information includes: Using the gradient descent method to online adjust the control parameters: ; ; ; In the formula, is the proportional gain at the th moment, k is the change amount of the proportional gain at the th moment, is the adjustment rate of the proportional gain, is the k change amount of the integral gain at the th moment, is the integral gain at the th moment, k is the adjustment rate of the integral gain, is the change amount of the derivative gain at the th moment,

[0011] Preferably, the multiple adjustment parameters include the learning rate, the first inertia weight, the second inertia weight, the adjustment rate of the proportional gain, the adjustment rate of the integral gain, and the adjustment rate of the derivative gain.

[0012] Preferably, the first sub-goal, the second sub-goal, and the third sub-goal are specifically as follows: ; ; ; In the formula, is the first sub-goal, t is the time, is the temperature control error, is the second sub-goal, n is the number of current step disturbances, is the temperature overshoot under each disturbance, is the third sub-goal, is the i th temperature identification error under the continuous domain.

[0013] Preferably, the sum of the standardized first sub-goal, the standardized second sub-goal, and the standardized third sub-goal is minimized as a single optimization goal, where the standardized first sub-goal, the standardized second sub-goal, and the standardized third sub-goal are specifically as follows: fit1 = ITAE / ITAE0; fit2 = / 0; fit3 = IAIE / IAIE0; In the formula, fit1 is the standardized first sub-goal, fit2 is the standardized second sub-goal, fit3 is the standardized third sub-goal, ITAE0 = 10706.5951, 0 = 1.0358, IAIE0 = 0.87998.

[0014] Preferably, the PSO algorithm is used to solve the single-objective optimization problem to obtain the first optimized sub-goal ITAE1, the second optimized sub-goal 1, and the third optimized sub-goal IAIE1.

[0015] Preferably, the multi-optimization goal is constructed based on the first optimized sub-goal, the second optimized sub-goal, and the third optimized sub-goal. The multi-optimization goal is specifically as follows: fit4 = ITAE / ITAE1; fit5 = / 1; fit6 = IAIE / IAIE1; In the formula, fit4 is the standardized fourth sub-goal, fit5 is the standardized fifth sub-goal, and fit6 is the standardized sixth sub-goal.

[0016] Compared with the prior art, the above at least one technical solution adopted by the present invention can achieve the following beneficial effects: The present invention first obtains multiple adjustment parameters, overshoot, temperature identification error, and temperature control error when the RBF-PID controller controls the thermal management system model, and constructs multiple optimization objectives through the overshoot, temperature identification error, and temperature control error. Then, a single-objective optimization problem is constructed and preliminarily solved by the PSO algorithm. Finally, a multi-objective optimization problem is established and solved by the NSGAIII algorithm. The NSGAIII algorithm further performs multi-objective optimization on the basis of PSO optimization, improving the control effect and identification effect of PSO-RBF-PID. It can ensure that the obtained optimization results are on the Pareto front, achieve precise control of the temperature of the air-cooled PEMFC, and at the same time provide multiple optimal solutions for different design requirements, improving the solution efficiency. Description of the Drawings

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0018] Figure 1 It is the structure diagram of the air-cooled fuel cell PEMFC thermal management system of the present invention; Figure 2 It is the schematic diagram of the NSGAIII-RBF-PID controller of the present invention; Figure 3 It is the iterative curve diagram of the PSO optimization of the present invention; Figure 4 It is the program flow chart of the controller of the present invention; Figure 5 It is the flow chart of the NSGAIII algorithm of the present invention; Figure 6 It is the Pareto front solution obtained by the NSGAIII algorithm of the present invention; Figure 7 It is the current perturbation diagram applied to the fuel cell in the present invention; Figure 8 It is the comparison diagram of the temperature control effect of the present invention; Figure 9 It is the RBF-PID temperature identification diagram of the present invention; Figure 10 It is the PSO-RBF-PID temperature identification diagram of the present invention; Figure 11 It is the NSGAIII-RBF-PID temperature identification diagram of the present invention; Figure 12 It is the comparison diagram of the temperature identification effect of the present invention; Figure 13 This is the adaptive change diagram of the NSGAIII-RBF-PID control parameters of the present invention. Specific implementation manner

[0019] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0020] I. Explanation of the embodiment. This part is an explanatory embodiment that expands and explains the technical solution of the claim in order to enable those skilled in the art to fully understand how the present invention is specifically implemented.

[0021] A method for controlling the temperature of an air-cooled PEMFC based on the NSGAIII (Non-dominated Sorting Genetic Algorithm III) provided by an embodiment of the present invention specifically includes the following steps: S1: Based on the physical characteristics of the fuel cell stack and auxiliary equipment in the air-cooled PEMFC system, an air-cooled PEMFC thermal management system model is built on the MATLAB / Simulink simulation platform.

[0022] The present invention builds an air-cooled PEMFC thermal management system model. Based on the physical characteristics of the fuel cell stack and auxiliary equipment in the air-cooled PEMFC system, an air-cooled PEMFC thermal management system model is built on the MATLAB / Simulink simulation platform, which can reflect the dynamic changes in the temperature of the fuel cell stack. Its specific structure is shown in Figure 1 and mainly includes a cooling fan model, a thermal management model, and a PEMFC fuel cell stack model.

[0023] The PEMFC fuel cell stack model uses a semi-empirical equation model to calculate the output voltage. The semi-empirical equation model is often used in the simulation research at the PEMFC system level because of its fast calculation speed and high accuracy. The specific PEMFC fuel cell stack model is as follows:

[0024] (1); In the formula, represents the output voltage, represents the Nernst voltage, represents the activation loss, represents the ohmic loss, represents the concentration loss.

[0025] The specific formulas for each item are as follows: (2); (3); (4); (5); (6); (7); (8); In the formula, , , , , , , λ , b and are nine coefficients that can be calibrated through experimental data. is the reaction entropy, is the number of electrons transferred in the reaction, is the Faraday constant, is the standard temperature, is the gas constant, is the battery temperature, is the partial pressure of hydrogen, is the partial pressure of oxygen, is the partial pressure of water vapor, is the oxygen concentration, is the working current, is the total current, is the reaction active area, is the total internal resistance, is the ohmic internal resistance, is the resistivity, is the concentration loss coefficient, is the thickness of the exchange membrane, is the current density.

[0026] In the thermal management model, the energy conservation equation is used to calculate the temperature change rate of the PEMFC. The temperature change is related to the energy absorbed by the fuel cell, specifically, the total energy released by the fuel cell minus the energy output by the electrical load, the heat dissipated by the coolant, and the energy dissipated from the surface. The temperature change rate of the PEMFC is as follows: (9); In the formula, represents the total input energy of the PEMFC, represents the electrical energy output by the PEMFC, represents the heat carried away by the cooling air, Represents the heat loss due to radiation and natural convection. Represents the heat capacity of PEMFC. t is the time.

[0027] The total input energy of the fuel cell is the total energy obtained from the combustion of hydrogen, and the hydrogen consumption is related to the current and the number of single cells. The calculation of is as follows: (10); In the formula, represents the hydrogen consumption. F represents the Faraday constant. is the enthalpy of hydrogen combustion. represents the number of single cells.

[0028] The output electrical energy is the product of the fuel cell stack voltage and the current. The calculation of is as follows: (11); In the formula, represents the fuel cell stack voltage.

[0029] Define the forced convection term of air as the heat taken away by the cooling air: (12); In the formula, is the surface heat transfer coefficient. is the ambient temperature. is the total area of the cathode flow channel.

[0030] Define the natural convection and radiation heat transfer of air as the surface heat dissipation of the fuel cell stack: (13); In the formula, is the equivalent thermal resistance.

[0031] S2: Design a temperature control strategy according to the air-cooled PEMFC thermal management model established in step S1 and use PID for temperature control.

[0032] The air-cooled PEMFC temperature control strategy is to change the air flow rate by adjusting the fan PWM so as to change the surface heat transfer coefficient of the cathode flow channel, and finally achieve precise control of the temperature of the PEMFC fuel cell stack and control the temperature of the fuel cell stack to a given value.

[0033] Assume that the air flow rate is linearly related to the duty cycle PWM Then the following expression can be obtained: (14); In the formula, V represents the air flow rate, PWM It represents the duty cycle, generally expressed as a percentage.

[0034] Since the convective heat transfer of air in the cathode channel is equivalent to the laminar tube flow heat transfer, the Ziegle-Tate formula is used to calculate the surface heat transfer coefficient: (15); In the formula, represents the Nusselt number of the cathode flow channel, represents the Reynolds number, represents the Prandtl number, represents the characteristic dimension, represents the pipe diameter, represents the dynamic viscosity of air, represents the dynamic viscosity of the wall surface.

[0035] The reference temperature of formula (15) is the average fluid temperature, and the characteristic length is the pipe diameter. The applicable range of its correlation formula is:

[0036] ; .

[0037] Taking the controlled temperature of PEMFC as 60 °C and the reference temperature of cathode air as 40 °C, by referring to the air thermophysical property table, we can obtain: ; .

[0038] According to the Reynolds number calculation formula: (16).

[0039] It can be obtained that when PWM = 100%, the corresponding Reynolds number is 752.97 < 2300, meeting the laminar condition, and the Ziegle-Tate formula can be used to calculate the surface heat transfer coefficient.

[0040] PID is the most widely used controller in practical engineering, with the characteristics of simple structure, easy implementation, and strong robustness. The present invention first uses a PID controller to achieve the temperature control of the air-cooled PEMFC. The PID controller will calculate the control quantity according to the temperature control error according to the following formula:

[0041] (17); In the formula, is the control quantity, is the temperature control error, , and They are the proportional, integral, and derivative gains respectively. By adjusting the parameters of the PID controller, the temperature of the PEMFC is controlled to ensure that the temperature of the fuel cell stack is stable at a given value.

[0042] S3: Optimize the PID controller in S2 using an RBF neural network to obtain an RBF-PID temperature controller.

[0043] Establish an RBF (Radial Basis Function) neural network to accurately identify the operating temperature of the air-cooled PEMFC, obtain the Jacobian information of the system, and transmit the obtained system Jacobian information to the self-tuning PID algorithm to adaptively update the control parameters of the PID through the gradient descent method. The RBF neural network includes an input layer, a hidden layer, and an output layer.

[0044] Set the number of input layer nodes of the RBF neural network to 3, where the input data of the first input node is the control quantity at time , the input data of the second input node is the actual temperature , and the input data of the third input node is the actual temperature at time .

[0045] The hidden layer of the RBF neural network includes 4 nodes, and its activation function is the Gaussian function basis function. The Gaussian function basis function is: (18); In the formula, is the center point of the j th basis function, and , n is the number of input nodes, T is the transpose, is a parameter that can be freely selected, which determines the width of the basis function around the center point, m is the number of hidden layer nodes, x is the input of the RBF neural network.

[0046] The derivative of the Gaussian function basis function is: (19); (20); In the formula, is the input of the RBF neural network at time k . In the present invention, x ([[]] k ) = u ([[]] k - 1), y( k ), y ( k -1)], is the k center point of the j th basis function at time is k the j th component of the center point of the i th basis function at time

[0047] The output layer of the RBF neural network includes 1 node, and the output is the temperature identified by the air-cooled PEMFC temperature control system .

[0048] The output of the RBF neural network is: (21); In the formula, is the weight value from the j th hidden layer node to the output layer node at time

[0049] The forward propagation process of the signals in the RBF neural network includes: The output of the input layer nodes of the RBF neural network is: (22); In the formula, and are the input layer nodes.

[0050] The output of the hidden layer nodes of the RBF neural network is: (23).

[0051] The output of the output layer nodes of the RBF neural network is: (24); The temperature identification error of the RBF neural network in the discrete domain is: (25).

[0052] The performance index function of the RBF neural network is: (26).

[0053] The error backpropagation process of the RBF neural network adopts the δ learning algorithm to adjust the weight values between the layers of the RBF neural network. According to the gradient descent method, the learning algorithm for the weight values from the hidden layer to the output layer is as follows:

[0054] (27); In the formula, is the first inertial weight, is the second inertial weight, is k the weight from the j th hidden layer to the output layer at time is k the weight from the j th hidden layer to the output layer at time -1, is k the weight from the j th hidden layer to the output layer at time -2, is k the weight from the j th hidden layer to the output layer at time -3, is the change in the weight at time k .

[0055] From equations (25) and (26), we have: (28).

[0056] Substituting equation (21) into the above equation, we get: (29); then 's learning algorithm is: (30); where, is the learning rate.

[0057] Similarly, the learning algorithms for the high - order Gaussian function parameters and of the hidden layer are: (31); (32).

[0058] From equations (21) and (28), we have: (33).

[0059] Substituting equations (19) and (20) into equation (33), we get: (34); (35).

[0060] then and 's learning algorithms are: (36); (37).

[0061] In the present invention, the RBF-PID controller adjusts based on the RBF neural network identification 、 and . The performance index function of RBF-PID is defined as:

[0062] (38); where r ( k ) is the given temperature, y ( k ) is the actual temperature, is k the temperature control error at time, and the RBF-PID controller adopts incremental PID, as follows: (39).

[0063] In order to reduce , the self-tuning PID algorithm uses the gradient descent method to adjust the control parameters online: (40); (41); (42); where 、 and are 、 and adjustment rates.

[0064] Therefore, the control parameters of RBF-PID can be adjusted to: (43); (44); (45).

[0065] It can be found from the above equations that the Jacobian information of the system needs to be calculated, but this information cannot be obtained directly and can be approximated as follows: (46); where is the output of the RBF in equation (15). And can be obtained through the RBF neural network:

[0066] (47).

[0067] Therefore, accurate online identification ( ) can ensure that the RBF neural network can provide accurate Jacobian information.

[0068] Through the accurate online temperature identification of the RBF neural network and the adaptive adjustment of PID parameters, the temperature control effect of the air-cooled PEMFC is improved, which is applicable to the temperature control requirements under different complex working conditions.

[0069] S4: Use the PSO algorithm to perform single-objective optimization on the parameters of the RBF-PID controller in S3, and assign the optimized parameters to the RBF-PID.

[0070] The particle swarm optimization algorithm (PSO algorithm) is an optimization algorithm based on swarm intelligence. It finds the optimal solution to the problem by simulating the movement and position adjustment of particles in the search space. Its basic principle is: in a multi-dimensional search space, the particle swarm finds the optimal solution by iteratively updating the position and velocity of each particle. Each particle has a position and a velocity, and the update of the particle is affected by three factors, namely: its own best position, that is, the optimal position that the particle itself has ever visited; the global best position, that is, the optimal position of all particles in the particle swarm; velocity adjustment, that is, the velocity of the particle is adjusted by its historical experience and the behavior of other particles. The state of each particle consists of a position and a velocity. The position represents the specific value of the solution, usually represented by a vector, and the velocity represents the change rate of the particle in the current dimension.

[0071] Specifically, use the velocity update formula and position update formula of the PSO to update the state of each particle.

[0072] First is the velocity update formula: (48); Among them, the velocity of particle a at time , is the velocity of particle a at time t ; is the inertia coefficient, which controls the degree of maintaining the particle velocity; and are acceleration constants, which control the pulling force of the particle towards the individual and group optimal solutions; and are random numbers between [0,1]; is the own best position of the particle; is the global best position, is particle a 's position at time t.

[0073] Secondly is the position update formula: (49); wherein, is the position of the particle at time t +1, and the updated position is the current position plus the velocity.

[0074] In the specific iteration process, the PSO algorithm is mainly divided into four steps. First, the positions and velocities of the particle swarm are randomly generated for initialization. Then, the fitness of each particle's current position is evaluated and calculated. Subsequently, according to the fitness, the personal best position and the global best position of each particle are updated. Finally, before meeting the termination condition, the particle swarm iterates according to the velocity and position update rules.

[0075] The process of the PSO algorithm for single-objective optimization of the parameters of the RBF-PID controller in S3 is as follows: First, the particle swarm is initialized. In the present invention, the particle represents the values of 6 decision variables, and the 6 decision variables are the learning rate ( ), the first inertia weight ( ), the second inertia weight ( ), and the PID adjustment rate ( , and ). The population size is set to 20, and the number of iterations is set to 100 times. Then, a single-objective fitness function is defined for optimization, and this function is composed of three sub-objectives. The specific meanings of the three sub-objectives are as follows: the integral of time multiplied by the absolute error ITAE (Integral of Absolute Error), that is, the first sub-objective. The control average overshoot , that is, the second sub-objective. The integral of the absolute identification error IAIE (Integral of Absolute Identification Error), that is, the third sub-objective.

[0076] ; ; In the formula, represents the temperature control error, represents the temperature overshoot under each perturbation, represents the temperature identification error in the continuous domain. The overshoot is obtained by calculating the ratio of the instantaneous maximum deviation value of the temperature to the steady-state value under each current perturbation.

[0077] ITAE measures the control effect of the controller by integrating the absolute error of the temperature of the air-cooled PEMFC. The smaller the ITAE, the smaller the integral of the system error, and the better the corresponding control effect. The average overshoot reflects the dynamic performance of the RBF-PID control process. The smaller the overshoot, the better the dynamic performance. IAIE measures the identification performance of the controlled RBF neural network. The smaller the IAIE means the more accurate the identification of the RBF neural network.

[0078] To avoid the influence of different orders of magnitude, the sub-goals are normalized: fit1 = ITAE / ITAE0, fit2 = / 0, fit3 = IAIE / IAIE0, where ITAE0 = 10706.5951, 0 = 1.0358, IAIE0 = 0.87998, which are the results before optimization. The single-objective fitness function is fitness = fit1 + fit2 + fit3, where fit1 is the normalized first sub-goal, fit2 is the normalized second sub-goal, and fit3 is the normalized third sub-goal.

[0079] According to the update rules of the PSO algorithm, the inertia coefficient and acceleration constants are used to adjust the position and velocity of the particles. Each particle updates its velocity according to its own best position and the global best position, so as to search in the direction of a better parameter combination and then continuously iterate and update. Figure 3 shows the iteration curve diagram optimized by the PSO algorithm. After 100 iterations, the algorithm stops, and the PSO converges at about 70 times. The global best position of the particle is the final optimization result. The optimized fitness function is fitness = 1.8995. When running the obtained PSO-RBF-PID, the three optimized sub-goals can be calculated respectively as: fit1 = 0.44071, fit2 = 0.67754, fit3 = 0.78129.

[0080] S5: Use the NSGAⅢ algorithm to further multi-objective optimize the parameters of the PSO-RBF-PID controller in S4, and assign the optimized parameters to the RBF-PID.

[0081] Appendix Figure 2 shows the structure of the NSGAIII-RBF-PID controller proposed in the present invention. First, a group of initial optimized parameters are obtained through the PSO, and then further multi-objective optimization is carried out through the NSGAIII on the basis of the PSO-RBF-PID obtained in S4. After obtaining the Pareto front solution, the optimized parameters are selected according to the design requirements and assigned to the RBF-PID controller.

[0082] The PSO algorithm outputs fit1 = 0.44071, fit2 = 0.67754, and fit3 = 0.78129. The purpose of optimization is to reduce these three objectives.

[0083] In the present invention, the RBF-PID (with 6 decision variables) is first optimized by PSO, and then two-stage optimization is carried out by NSGAIII.

[0084] NSGAIII (Non-dominated Sorting Genetic Algorithm III) is an evolutionary algorithm designed to solve multi-objective optimization problems, especially high-dimensional problems. Its operation process is based on the genetic algorithm framework. By introducing the concept of reference points, the uniform distribution of solutions is maintained during the optimization process, thereby improving the search efficiency and the diversity of results. NSGA-III realizes the efficient solution of multi-objective problems through population initialization, non-dominated sorting, reference point allocation, and selection operations.

[0085] The algorithm first randomly initializes a population and a set of reference points in the objective space . The reference points represent the desired uniform distribution of solutions in the objective space and are used to guide the diversity of the solution set. In each generation, the current population generates a sub-population through selection, crossover, and mutation operations . The parent and offspring are combined to form an intermediate population = ∪ . Subsequently, non-dominated sorting is performed on , which is divided into multiple front layers , ,…, where represents the Pareto front solutions.

[0086] To construct the next generation population , the algorithm sequentially selects solutions from the front layers until the population size reaches the upper limit . If the addition of a certain front layer causes the population to exceed the limit, the reference point allocation mechanism is used to select the individuals to be retained. Specifically, each individual in the population is allocated according to its Euclidean distance between the normalized objective vector and the reference point. The formula is as follows:

[0087] (35); where is the ideal point, is the normalized distance from the objective vector to the reference point. By selecting the individuals closest to the reference point, the algorithm ensures the uniform distribution of the population solutions, avoids the over-concentration of solutions on certain objectives, and effectively improves the diversity of solutions.

[0088] NSGAIII is particularly suitable for solving high-dimensional multi-objective optimization problems. It can avoid the agglomeration of solutions when the objective dimension is high, and provide rich and balanced Pareto front solutions, so as to meet the diverse design requirements in practical engineering.

[0089] Similar to the PSO optimization, the decision variables selected for NSGAⅢ optimization are: learning rate ( ), the first inertia weight ( ), the second inertia weight ( ), and the PID adjustment rate ( , and ). The optimization objectives are selected as: the standardized fourth sub-objective fit4 (ITAE / ITAE1), the standardized fifth sub-objective fit5 ( / 1), and the standardized sixth sub-objective fit6 (IAIE / IAIE1), where ITAE1, 1, and IAIE1 are the results obtained from the operation of PSO-RBF-PID, that is, it means that NSGAⅢ in S5 is further optimized based on the results of PSO-RBF-PID in S4. The optimization results obtained in this way can reflect the advantages of the multi-objective optimization algorithm compared with the currently popular single-objective optimization algorithms.

[0090] By effectively exploring and finding multiple Pareto front solutions in the solution space through the NSGAIII algorithm, it can ensure that the final NSGAⅢ-RBF-PID controller reaches the Pareto front in three objectives: ITAE, and IAIE, thus obtaining better control and identification effects.

[0091] As shown in the appendix Figure 4 , this figure shows the application process of an RBF-PID control method based on the NSGAIII multi-objective optimization algorithm in the temperature control of an air-cooled PEMFC fuel cell. The core of the process is to first perform single-objective optimization on the parameters of the RBF-PID controller through the PSO algorithm to obtain a set of initial optimized parameters, and the optimization objectives are the sum of ITAE (Integral of Time multiplied by the Absolute Error), the average overshoot ( ), and IAIE (Integral of the Absolute Identification Error). Then, through the NSGAⅢ algorithm, further multi-objective optimization is carried out on the basis of PSO-RBF-PID, and the same parameters as those of PSO are selected for optimization, but the optimization objectives are 3, namely ITAE, and IAIE. Specifically, the PSO algorithm and the NSGAIII algorithm calculate the fitness, apply the optimized parameters to the RBF-PID controller, and continuously evaluate the fitness through the feedback of the control effect to search for better parameters, thus forming a closed-loop iterative optimization process.

[0092] In multi-objective optimization problems, the relationship between optimal solutions is usually non-dominant, and there is rarely an optimal solution that dominates all other feasible solutions. Therefore, the optimal solutions of optimization problems are usually a set of solution sets, commonly known as the Pareto optimal solution set. The present invention uses the NSGAIII algorithm to obtain the Pareto optimal solution set, and the specific process is as shown in the appendix Figure 5 as follows

[0093] During the optimization process, NSGAIII first sets the parameters, randomly initializes the population, and generates a set of uniformly distributed reference points in the objective space to guide population diversity and calculate the objective function. After the population undergoes selection, crossover, and mutation operations, offspring individuals are generated. The parent and offspring are combined to form an intermediate population, and then non-dominated sorting is performed on it, which is divided into multiple front layers according to Pareto superiority and inferiority. Among them, the solutions in the Pareto front layer represent a better balance in multi-objective optimization. To construct the next-generation population, the algorithm screens individuals through a reference point allocation mechanism (based on reference point selection), calculates the distance between the normalized objective vector of each individual in the population and the reference point, and preferentially selects the individual with the closest distance to ensure the uniform distribution of solutions in the objective space, thereby avoiding the over-concentration of the solution set on certain objectives and improving the diversity and distribution quality of the solutions

[0094] The iterative optimization process of NSGAIII will continue until the Pareto front solution set of the population is stable or the preset maximum number of iterations is reached. As shown in the appendix Figure 6 The Pareto front finally output by NSGAIII provides multiple optimal solutions, and different optimization schemes can be selected according to different design requirements. The present invention selects the Pareto optimal solutions with all three optimization objectives less than 1. Since the optimization objectives are normalized (fit1 = ITAE / ITAE1, fit2 = / 1, fit3 = IAIE / IAIE1), that is, the corresponding NSGAⅢ-RBF-PID is superior to PSO-RBF-PID in all three objectives

[0095] S6: Compare the temperature control and identification effects of NSGAⅢ-RBF-PID and PSO-RBF-PID, and analyze the advantages of multi-objective optimization over single-objective optimization

[0096] Among all the Pareto front solutions obtained by NSGAIII in S5, an optimal solution with each objective less than the initial value is selected and substituted into the RBF-PID temperature controller. The running effects of PSO-RBF-PID obtained in S4 are compared. The experimental results are shown in the specific implementation manners. A main reason why NSGAⅢ-RBF-PID is superior to PSO-RBF-PID is that NSGAⅢ is a multi-objective optimization algorithm, which can ensure that the obtained optimal solution lies on the Pareto front. PSO is a single-objective optimization algorithm. Although the sum of 3 objectives is taken as the fitness function at the same time, it cannot ensure that the 3 sub-objectives lie on the Pareto front.

[0097] At the same time, NSGAⅢ can obtain multiple Pareto front solutions in one run, providing a large number of optimization choices for different design requirements. However, PSO can only obtain a set of solutions in one run, with limited choices.

[0098] The 6 decision values before optimization: 0.25, 0.05, 0.01, 100000, 10, 10000.

[0099] The 6 decision variable values after PSO optimization: 0.410009415071648, 0.192497876357553, 0.0259715677144086, 199752.045841515, 61.8291225741132, 79581.8319029502.

[0100] The 6 decision variable values after NSGAⅢ optimization: 0.4100100000000000, 209121868376257, 0.0259720000000000, 359228.714940697, 57.0156253742567, 86551.7857141860.

[0101] As shown in the Figure 7 appendix, this experiment adopts a step input current perturbation design to simulate the operation of the air-cooled PEMFC system under different working conditions.

[0102] As shown in the Figure 8 appendix, it can be seen from the curves of this chart that the control effect of RBF-PID is significantly better than that of the traditional PID, thanks to its control parameters , and adapting to changes with the system state. After single-objective optimization by PSO, the temperature control effect of RBF-PID has been improved. On the basis of PSO-RBF-PID, NSGAⅢ is further optimized, and the obtained NSGAⅢ-RBF-PID realizes a faster adjustment time and a smaller overshoot, achieving the best temperature control effect among the four.

[0103] As shown in the appendix Figures 9 - 11 As shown, RBF-PID, PSO-RBF-PID, and NSGAIII-RBF-PID can all achieve accurate identification of the actual temperature, with their maximum relative errors not exceeding 0.06%, 0.05%, and 0.05% respectively, thus ensuring the accuracy of the system Jacobian information.

[0104] As shown in the appendix Figure 12 As shown, the experiment compared the temperature identification effects of three controllers: RBF-PID, PSO-RBF-PID, and NSGAIII-RBF-PID. It can be seen that the NSGAIII-RBF-PID controller is more accurate in temperature identification. Especially in a period of time when each current disturbance starts to be applied, its relative identification error is significantly smaller than that of the unoptimized RBF-PID controller and slightly smaller than that of the PSO-RBF-PID. It can be concluded that NSGAIII-RBF-PID has achieved the best temperature identification effect among the three, and can provide more accurate system Jacobian information ( ) for the self-tuning PID algorithm.

[0105] Appendix Figure 13 shows the control parameters of NSGAⅢ-RBF-PID , and changing conditions. It can be seen that the PID control parameters have achieved adaptive changes, especially in a period of time when each current disturbance starts to be applied, the changes are obvious. The adaptive changes of the PID parameters can make the air-cooled PEMFC system adapt to different working conditions, thereby improving the control effect.

[0106] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they know the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0107] Obviously, those skilled in the art can make various changes and deformations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and deformations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these changes and deformations.

Claims

1. An air-cooled PEMFC temperature control method based on NSGAIII, characterized in that, The method includes the following steps: Obtain multiple adjustment parameters, temperature control error, overshoot, and temperature identification error when the RBF-PID controller controls the thermal management system model of an air-cooled proton exchange membrane fuel cell (PEMFC); integrate the temperature control error to obtain a first sub-goal; average the overshoot to obtain a second sub-goal; integrate the temperature identification error to obtain a third sub-goal; With the multiple adjustment parameters as decision variables, and minimizing the sum of the normalized first sub-goal, normalized second sub-goal, and normalized third sub-goal as a single optimization goal, establish a single-objective optimization problem, solve the single-objective optimization problem to obtain optimized adjustment parameters, a first optimized sub-goal, a second optimized sub-goal, and a third optimized sub-goal; With the multiple optimized adjustment parameters as decision variables, construct a multi-objective optimization goal based on the first optimized sub-goal, second optimized sub-goal, and third optimized sub-goal, establish a multi-objective optimization problem, and solve the multi-objective optimization problem through NSGAIII to obtain multiple optimal adjustment parameters; Input the multiple optimal adjustment parameters into the RBF-PID controller, and control the temperature of the air-cooled PEMFC through the RBF-PID controller with multiple optimal control parameters.

2. The air-cooled PEMFC temperature control method based on NSGAIII according to claim 1, characterized in that, The obtaining of the multiple adjustment parameters, temperature control error, overshoot, and temperature identification error when the RBF-PID controller controls the thermal management system model of the air-cooled proton exchange membrane fuel cell (PEMFC) specifically includes the following steps: Input the control quantity of the thermal management system model at the previous moment, the actual temperature at the current moment, and the actual temperature at the previous moment into the RBF neural network; Perform forward propagation on the RBF neural network to obtain the temperature identification error; establish a performance index function of the RBF neural network based on the temperature identification error; the RBF neural network includes an input layer, a hidden layer, and an output layer; Perform error backpropagation on the RBF neural network based on the performance index function to obtain the weights between the layers of the RBF neural network and the parameters of the hidden layer; during the error backpropagation process, obtain the first inertia weight, second inertia weight, and learning rate for controlling the weights between the layers of the RBF neural network and the parameters of the hidden layer; Obtain the Jacobian information of the thermal management system model through the RBF neural network after error backpropagation; Obtain the temperature control error of the RBF-PID controller based on the given temperature and actual temperature at the current moment; establish a performance index function of the RBF-PID controller based on the temperature control error; Based on the performance index function, online adjust the control parameters of proportional, integral, and differential through the Jacobian information; during the online adjustment, obtain the adjustment rates of proportional, integral, and differential for controlling the control parameters of proportional, integral, and differential; Control the proportional, integral, and differential gains of the RBF-PID controller through the online-adjusted control parameters of proportional, integral, and differential to obtain the control quantity at the current moment; Control the temperature of the air-cooled PEMFC through the control quantity at the current moment.

3. The air-cooled PEMFC temperature control method based on NSGAIII according to claim 2, wherein The performing of error backpropagation on the RBF neural network based on the performance index function specifically includes: According to the gradient descent method, the learning algorithm for the weights from the hidden layer to the output layer is as follows: ； wherein, ； Wherein, is the first inertia weight, is the second inertia weight, is k the weight from the j -th hidden layer to the output layer at time is k the weight from the j -th hidden layer to the output layer at time is k the weight from the j -th hidden layer to the output layer at time is k the weight from the j -th hidden layer to the output layer at time is the change amount of the weight at time k , is the learning rate, is the performance index function of the RBF neural network.

4. The air-cooled PEMFC temperature control method based on NSGAIII according to claim 2, characterized in that the online adjustment of the control parameters of the proportional, integral, and differential through the Jacobi information includes: using the gradient descent method to online adjust the control parameters: ； ； ； In the formula, is the proportional gain at time is k the change amount of the proportional gain at time is the performance index function of RBF-PID, is the adjustment rate of the proportional gain, is k the change amount of the integral gain at time is the integral gain at time is the adjustment rate of the integral gain, is k the change amount of the derivative gain at time is the derivative gain at time is the adjustment rate of the derivative gain.

5. The air-cooled PEMFC temperature control method based on NSGAIII according to claim 2, characterized in that the multiple adjustment parameters include the learning rate, the first inertia weight, the second inertia weight, the adjustment rate of the proportional gain, the adjustment rate of the integral gain, and the adjustment rate of the differential gain.

6. The air-cooled PEMFC temperature control method based on NSGAIII according to claim 1, characterized in that The specific forms of the first sub-goal, the second sub-goal, and the third sub-goal are as follows: ； ； ； Wherein, is the first sub-goal, t is the time, is the temperature control error, is the second sub-goal, n is the number of current step disturbances, is the temperature overshoot under each disturbance, is the third sub-goal, is the i th temperature identification error in the continuous domain.

7. The air-cooled PEMFC temperature control method based on NSGAIII according to claim 6, characterized in that taking the minimization of the sum of the normalized first sub-goal, the normalized second sub-goal, and the normalized third sub-goal as a single optimization goal, wherein the specific forms of the normalized first sub-goal, the normalized second sub-goal, and the normalized third sub-goal are as follows: fit1 = ITAE / ITAE0; fit2= / 0; fit3 = IAIE / IAIE0; Wherein, fit1 is the normalized first sub-goal, fit2 is the normalized second sub-goal, fit3 is the normalized third sub-goal, ITAE0 = 10706.5951, 0 = 1.0358, IAIE0 = 0.87998.

8. The temperature control method of an air-cooled PEMFC based on NSGAIII according to claim 7, wherein Solve the single-objective optimization problem through the PSO algorithm to obtain the first optimization sub-objective ITAE1, the second optimization sub-objective 1 and the third optimization sub-objective IAIE1.

9. The temperature control method of an air-cooled PEMFC based on NSGAIII according to claim 8, wherein constructing a multi-optimization goal based on the first optimization sub-goal, the second optimization sub-goal, and the third optimization sub-goal, and the specific form of the multi-optimization goal is as follows: fit4 = ITAE / ITAE1; fit5= / 1; fit6 = IAIE / IAIE1; In the formula, fit4 is the normalized fourth sub-goal, fit5 is the normalized fifth sub-goal, and fit6 is the normalized sixth sub-goal.

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