Multiple population adaptive differential evolution parameter identification method for ground heat exchanger model

Abstract

The application provides a multi-population adaptive differential evolution parameter identification method for a ground heat exchanger model, and belongs to the technical field of ground heat exchanger parameter identification. The method solves the problems of the traditional modeling method, such as over-reliance on the internal mechanism of the ground heat exchanger, complex model structure, large amount of identification parameters, and the need to consider unstable factors such as rock-soil thermal properties and seasonal changes in the identification process. The technical scheme comprises the following steps: step 1) establishing a Wiener-Hammerstein model of the ground heat exchanger to describe the input-output relationship; and step 2) constructing an identification process of a multi-population adaptive differential evolution algorithm. The application has the advantages of good identification accuracy and convergence speed, and can be well applied to the parameter identification of the ground heat exchanger heat transfer process.

Description

Technical Field

[0001] This invention relates to the field of parameter identification technology for buried pipe heat exchangers, and in particular to a multi-population adaptive differential evolution parameter identification method for buried pipe heat exchanger models. Background Technology

[0002] Ground source heat pumps utilize the relatively stable temperature of underground soil to exchange heat with the building's interior through a pipeline system buried deep around the building. They provide heating and cooling, are highly efficient and energy-saving, and truly meet low-carbon and environmental protection requirements, leading to their widespread application in today's society. The buried pipe heat exchanger is the device in the ground source heat pump system that exchanges heat with the soil; its heat exchange performance significantly impacts the reliability of the entire system. The heat transfer system of a buried pipe heat exchanger is a highly complex nonlinear system. Traditionally, heat transfer analysis of buried pipe heat exchangers requires establishing a mathematical model based on energy conservation. While this theoretical approach offers high computational accuracy, it suffers from numerous parameters to be identified, requires consideration of unstable factors such as soil thermal properties and seasonal variations, and faces various obstacles during implementation, making it uneconomical. Wiener-Hammerstein nonlinear systems consist of a dynamic linear subsystem and a static nonlinear subsystem connected in series. They can accurately describe most nonlinear systems using only the system's input and output data, and are widely used in electrical, mechanical, chemical, and aerospace fields. Using the Wiener-Hammerstein system simplifies the modeling of buried pipe heat exchangers, thereby ensuring the reliability, energy efficiency, and sustainability of soil source heat pump systems. To date, many scholars have proposed different identification methods for this system, such as the least squares method, stochastic gradient method, Gauss-Newton method, and gradient descent method.

[0003] Traditional identification algorithms often suffer from low accuracy and slow convergence speed when identifying complex nonlinear systems. Therefore, this paper proposes a Multi-Group Adaptive Differential Evolution (MPSADE) algorithm based on the differential evolution algorithm, incorporating the concepts of multi-population and parameter adaptation.

[0004] How to solve the above-mentioned technical problems is the challenge facing this invention. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-population adaptive differential evolution parameter identification method for a buried pipe heat exchanger model. Strong nonlinearity exists in the heat transfer process. The Wiener-Hammerstein model used in this invention consists of two linear subsystems and one nonlinear subsystem connected in series. Its nonlinear part uses Volterra series, which can accurately express the inherent nonlinear characteristics of the system during the buried pipe heat transfer process. Colored noise is also added at the output to represent existing external interference factors. The multi-population adaptive differential evolution algorithm proposed in this invention is an algorithm that combines multi-population thinking, parameter adaptive strategy, and differential evolution thinking. Compared with traditional algorithms, this algorithm has better identification accuracy and convergence speed, and can be well applied to parameter identification in the buried pipe heat transfer process.

[0006] This invention is achieved through the following measures: a multi-population adaptive differential evolution parameter identification method for a buried pipe heat exchanger model, characterized by comprising the following steps:

[0007] Step 1) Establish a Wiener-Hammerstein model of the buried pipe heat exchanger to describe its input-output relationship;

[0008] Step 2) Construct the identification process of multi-population adaptive differential evolution algorithm.

[0009] As a multi-population adaptive differential evolution parameter identification method for a buried pipe heat exchanger model proposed in this invention, step 1) includes the following steps:

[0010] Step 1-1) Establish the Wiener-Hammerstein model of the buried pipe heat exchanger:

[0011] The model of the buried pipe heat exchanger is represented by the Wiener-Hammerstein model.

[0012]

[0013]

[0014]

[0015] ω(t)=E(z)v(t) (4)

[0016]

[0017] Where t is time, u(t) and y(t) are the system input and output, respectively, and v(t) is the system noise. The system's noiseless output is ω(t), which is colored noise. x(t), ω(t) is an unmeasurable intermediate variable. In the above equation, A(z), B(z), C(z), D(z), and E(z) are represented by the following polynomials, where z -1 It is a shift operator and z -1 u(t) = u(t-1);

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] Describes a polynomial function consisting of Volterra series, i.e.

[0024]

[0025] Where N represents the maximum nonlinear order of the Volterra series, and M n It is the length of memory, τ n =0,1,…,M n -1,h n (τ1,τ2,…,τ n ) is the Volterra kernel function. Assume n a n b n c n d n e Given that when t≤0, the values ​​of input u(t) and output y(t) are 0, and u(t) is a continuous excitation signal, in order to obtain a unique parameter estimate, the value of h1(0) in the nonlinear component is set to 1, that is:

[0026]

[0027] Step 1-2) Based on equations (1)-(11), the output y(t) and input u(t), intermediate variables can be derived. x(t), The relationship between system noise v(t) is shown in the following equation;

[0028]

[0029] The parameter vectors a, b, c, d in the linear subsystem and the parameter vector e of the noise component are defined as follows:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] The parameter vector h in the nonlinear subsystem is defined as follows:

[0036]

[0037]

[0038] Parameter vectors α,β,θ,θ s and information vectors ψ(t), ξ(t), ζ(t), η(t), The definition is as follows:

[0039]

[0040]

[0041]

[0042]

[0043] D = n a +n b +n c +n d +n h +n e

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] Then equations (1) to (3) are reformulated as follows:

[0052]

[0053] x(t)=η T (t)β (13)

[0054]

[0055] Equation (5) is reformulated as

[0056]

[0057] As a multi-population adaptive differential evolution parameter identification method for a buried pipe heat exchanger model proposed in this invention, step 2) includes the following steps:

[0058] Step 2-1) Set the control parameters required for the multi-population adaptive differential evolution algorithm: population size, mutation factor, crossover probability, mutation strategy, and termination condition;

[0059] Step 2-2) Given the upper and lower bounds of the solution range of the optimization problem, randomly initialize the population.

[0060]

[0061] in Let θ represent the i-th individual in the population after k iterations, and j represent the j-th parameter in the vector. After each iteration, the individual with the best fitness value is selected as the parameter estimate of θ. The definition method is as follows:

[0062] make Let be the estimated values ​​of the parameter vectors a, b, c, d, e, h, respectively, defined as:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Then the parameter vector α,β,θ,θ s Estimate Defined respectively

[0070]

[0071]

[0072]

[0073]

[0074] Step 2-3) Define the fitness function as follows:

[0075]

[0076] Where l is the data length. for The estimated value for the k-th iteration is defined as follows:

[0077] make These are vectors ψ(t), ξ(t), ζ(t), and η(t), respectively. Estimates, unknown variables x(ti) and v(ti) are respectively derived from their iterative estimates. replace.

[0078]

[0079] u(t-1), u(t-2), …, u(tn) b )] T

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] in k-iteration estimates of x(ti), v(ti) It is expressed as follows:

[0087]

[0088]

[0089]

[0090]

[0091] Steps 2-4) Evaluate the fitness values ​​of individuals and divide the original population into elite subpopulations, general subpopulations and worst subpopulations based on the fitness values, and use three different mutation strategies for evolution respectively;

[0092] Mutation strategy:

[0093] 1)DE / best / 1:

[0094]

[0095] 2)DE / rand-to-best / 1:

[0096]

[0097] 3) DE / rand / 2:

[0098]

[0099] Where 'best' indicates that the individual with the best fitness value is the best individual in the population, and 'i,r1,r2,r3,r4,r5' indicates that the individual is the i,r1,r2,r3,r4,r5th individual in the population. The r1,r2,r3,r4,r5th individuals are random and, under the same mutation strategy, they are all different. i (k+1) represents the i-th mutated individual, also known as the mutation vector, and j represents p. i,j (k+1) is p i The j-th parameter of (k+1) is F, which is the mutation factor.

[0100] The DE / rand / 2 strategy randomly selects all individuals participating in mutation. It randomly chooses a new search direction, and the search is unbiased. It has two sets of difference vectors, resulting in better perturbation than the DE / rand / 1 strategy, which has only one set, generating more diverse trial vectors. The DE / rand-to-best / 1 algorithm coordinates both local and global search capabilities. DE / best / 1 is characterized by strong local search capability, high search accuracy, and fast convergence speed. The DE / best / 1 strategy is used to evolve the elite subpopulation, the DE / rand-to-best / 1 strategy is used to evolve the general subpopulation, and the DE / rand / 2 strategy is used to evolve the worst subpopulation.

[0101] Steps 2-5) Crossover operation: Each individual in the population undergoes a crossover operation with its corresponding mutation vector. The specific operation is as follows:

[0102]

[0103] randl i,jIt is a random decimal number between [0,1], m i (k+1) represents the i-th experimental individual, and CR represents the crossover probability, which controls the degree of exchange among individuals in the population. During the crossover process, if the randomly generated value is less than or equal to the crossover probability, the population individuals are exchanged; otherwise, the original individuals are retained.

[0104] Steps 2-6) Selection Operation: After the k-th crossover mutation, the population produces NP individuals, called test individuals. The test individuals are evaluated and compared with the original individuals in the population. If the fitness value of the test individual is worse than that of the original individuals, the original individuals are retained; otherwise, the original individuals will be replaced by the test individuals in the next generation. These selected individuals form a new population and enter the next iteration.

[0105]

[0106] Step 2-7) Determine if the termination condition is met. If it is met, stop; otherwise, go to step 2-4).

[0107] For each individual in the population, its crossover probability CR is independently generated according to a normal distribution with a standard deviation of 0.1 and a mean of μCR. Similarly, its factor of variation F is independently generated according to a normal distribution with a mean of μF and a standard deviation of 0.1. The factor of variation F and the crossover probability CR take values ​​between 0 and 1, as shown in the following equation:

[0108] CR i =randn i (μCR, 0.1)

[0109] F i =randn i (μF, 0.1)

[0110] Among them, CR i and F i Let F represent the crossover probability and mutation factor of the i-th individual. i >1, F i Set to 1, otherwise, if F i ≤0, F i Then a new value will be generated; similarly, if CR i >1, CR i Set to 1, if CR i ≤0, CR i Then a new value will be generated;

[0111] S CR and S FμCR and μF are defined as the sets of crossover probabilities and mutation factors, respectively, during the evolution of experimental individuals that successfully enter the next generation after a selection operation. Both μCR and μF are initialized to 0.5 and are updated after each generation using the following formula;

[0112] μCR=(1-q)μCR+q·mean(S CR )

[0113] μF=(1-q)μF+q·mean(S F )

[0114] Where q is a positive number between 0 and 1, mean(S CR ) and mean(S F The following represent the Lehmer average values:

[0115]

[0116]

[0117] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0118] (1) The present invention establishes a Wiener-Hammerstein model for buried pipe heat exchangers and uses a multi-group adaptive differential evolution algorithm to identify the parameters of buried pipe heat exchangers, thereby improving the convergence speed and estimation accuracy.

[0119] (2) Compared with differential evolution algorithm, adaptive differential evolution algorithm and some other traditional algorithms, multi-population adaptive differential evolution algorithm has higher estimation accuracy and faster convergence speed, which shows that the identification method has good applicability to parameter identification of buried pipe heat exchangers. Attached Figure Description

[0120] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0121] Figure 1 This is a schematic diagram of the basic structure of a buried pipe heat exchanger.

[0122] Figure 2 This is a schematic diagram of the Wiener-Hammerstein output error system.

[0123] Figure 3 This is a flowchart of a multi-population adaptive differential evolution algorithm.

[0124] Figure 4 This is a schematic diagram illustrating the error between the identification parameters and the true values ​​in this invention. Detailed Implementation

[0125] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0126] Example 1

[0127] This example illustrates the Wiener-Hammerstein output error system for buried pipe heat exchangers, such as... Figure 2 As shown, u(t) is the inlet water temperature T of the buried pipe heat exchanger. in (°C), y(t) is its outlet water temperature T out (°C).

[0128] See Figures 1 to 4 The present invention provides a technical solution for identifying multi-population adaptive differential evolution parameters of a buried pipe heat exchanger model, the specific steps of which are as follows:

[0129] Step 1) Establish a Wiener-Hammerstein model of the buried pipe heat exchanger to describe its input-output relationship;

[0130] Step 2) Construct the identification process of multi-population adaptive differential evolution algorithm.

[0131] As a multi-population adaptive differential evolution parameter identification method for a buried pipe heat exchanger model proposed in this invention, step 1) includes the following steps:

[0132] Step 1-1) Establish the Wiener-Hammerstein model of the buried pipe heat exchanger:

[0133] The model of a buried pipe heat exchanger can be used Figure 2 The Wiener-Hammerstein model shown is expressed as follows:

[0134]

[0135]

[0136]

[0137] ω(t)=E(z)v(t) (4)

[0138]

[0139] Where t is time, u(t) and y(t) are the system input and output, respectively, and v(t) is the system noise. The system's noiseless output is ω(t), which is colored noise. x(t), ω(t) is an unmeasurable intermediate variable. In the above equation, A(z), B(z), C(z), D(z), and E(z) are represented by the following polynomials, where z -1 It is a shift operator and z -1 u(t) = u(t-1);

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] Describes a polynomial function consisting of Volterra series, i.e.

[0146]

[0147] Where N represents the maximum nonlinear order of the Volterra series, and M n It is the length of memory, τ n =0,1,…,M n -1,h n (τ1,τ2,…,τ n ) is the Volterra kernel function. Assume n a n b n c n d n e Given that when t ≤ 0, the values ​​of input u(t) and output y(t) are 0, and u(t) is a continuous excitation signal. To obtain a unique parameter estimate, the value of h1(0) in the nonlinear component is set to 1, i.e.:

[0148]

[0149] Step 1-2) Based on equations (1)-(11), the output y(t) and input u(t), intermediate variables can be derived. x(t), The relationship between system noise v(t) is shown in the following equation;

[0150]

[0151] The parameter vectors a, b, c, d in the linear subsystem and the parameter vector e of the noise component are defined as follows:

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] The parameter vector h in the nonlinear subsystem is defined as follows:

[0158]

[0159]

[0160] Parameter vectors α,β,θ,θ s and information vectors ψ(t), ξ(t), ζ(t), η(t), The definition is as follows:

[0161]

[0162]

[0163]

[0164]

[0165] D = n a +n b +n c +n d +n h +n e

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173] Then equations (1)-(3) are rewritten as

[0174]

[0175] x(t)=η T (t)β (13)

[0176]

[0177] Equation (5) is reformulated as

[0178]

[0179] Based on the Wiener-Hammerstein model mentioned above, the following Wiener-Hammerstein output error model can be established for this example:

[0180]

[0181]

[0182]

[0183] w(t)=(1+e1z -1 +e2z -2 v(t)

[0184] =(1-0.08748z) -1 -0.07621z -2 v(t)

[0185] Based on step 1, the parameters to be identified are as follows:

[0186] θ=[a1,a2,b1,b2,h1(1),h2(0,0),h2(0,1),h2(1,1),c1,c2,d1,d2,e1,e2]=[0.44229,0.65269,0.77873,0 .99995,-0.03003,-0.09991,0.99994,0.52370,0.32814,0.26828,0.99771,0.20500,-0.08748,-0.07621]

[0187] As a multi-population adaptive differential evolution parameter identification method for a buried pipe heat exchanger model proposed in this invention, step 2) includes the following steps:

[0188] Step 2-1) Set the control parameters required for the multi-population adaptive differential evolution algorithm: population size, mutation factor, crossover probability, mutation strategy, and termination condition;

[0189] Step 2-2) Given the upper and lower bounds of the solution range of the optimization problem, randomly initialize the population.

[0190]

[0191] in Let θ represent the i-th individual in the population after k iterations, and j represent the j-th parameter in the vector. After each iteration, the individual with the best fitness value is selected as the parameter estimate of θ. The definition method is as follows:

[0192] make Let be the estimated values ​​of the parameter vectors a, b, c, d, e, h, respectively, defined as:

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199] Then the parameter vector α,β,θ,θ s Estimate Defined respectively

[0200]

[0201]

[0202]

[0203]

[0204] Step 2-3) Define the fitness function as follows:

[0205]

[0206] Where l is the data length. for The estimated value for the k-th iteration is defined as follows:

[0207] make These are vectors ψ(t), ξ(t), ζ(t), and η(t), respectively. Estimates, unknown variables x(ti) and v(ti) are respectively derived from their iterative estimates. replace.

[0208]

[0209] u(t-1), u(t-2), …, u(tn) b )] T

[0210]

[0211]

[0212]

[0213]

[0214]

[0215]

[0216] in k-iteration estimates of x(ti), v(ti) It is expressed as follows:

[0217]

[0218]

[0219]

[0220]

[0221] Steps 2-4) Evaluate the fitness values ​​of individuals and divide the original population into elite subpopulations, general subpopulations and worst subpopulations based on the fitness values, and use three different mutation strategies for evolution respectively;

[0222] Mutation strategy:

[0223] 1)DE / best / 1:

[0224]

[0225] 2)DE / rand-to-best / 1:

[0226]

[0227] 3) DE / rand / 2:

[0228]

[0229] Where 'best' indicates that the individual with the best fitness value is the best individual in the population, and 'i,r1,r2,r3,r4,r5' indicates that the individual is the i,r1,r2,r3,r4,r5th individual in the population. The r1,r2,r3,r4,r5th individuals are random and, under the same mutation strategy, they are all different. i (k+1) represents the i-th mutated individual, also known as the mutation vector, and j represents p. i,j (k+1) is p i The j-th parameter of (k+1) is F, which is the mutation factor.

[0230] The DE / rand / 2 strategy randomly selects all individuals participating in mutation. It randomly chooses a new search direction, and the search is unbiased. It has two sets of difference vectors, resulting in better perturbation than the DE / rand / 1 strategy, which has only one set, generating more diverse trial vectors. The DE / rand-to-best / 1 algorithm coordinates both local and global search capabilities. DE / best / 1 is characterized by strong local search capability, high search accuracy, and fast convergence speed. The DE / best / 1 strategy is used to evolve the elite subpopulation, the DE / rand-to-best / 1 strategy is used to evolve the general subpopulation, and the DE / rand / 2 strategy is used to evolve the worst subpopulation.

[0231] Steps 2-5) Crossover operation: Each individual in the population undergoes a crossover operation with its corresponding mutation vector. The specific operation is as follows:

[0232]

[0233] randl i,j It is a random decimal number between [0,1], m i (k+1) represents the i-th experimental individual, and CR represents the crossover probability, which controls the degree of exchange among individuals in the population. During the crossover process, if the randomly generated value is less than or equal to the crossover probability, the population individuals are exchanged; otherwise, the original individuals are retained.

[0234] Steps 2-6) Selection Operation: After the k-th crossover mutation, the population produces NP individuals, called test individuals. The test individuals are evaluated and compared with the original individuals in the population. If the fitness value of the test individual is worse than that of the original individuals, the original individuals are retained; otherwise, the original individuals will be replaced by the test individuals in the next generation. These selected individuals form a new population and enter the next iteration.

[0235]

[0236] Step 2-7) Determine if the termination condition is met. If it is met, stop; otherwise, go to step 2-4).

[0237] For each individual in the population, its crossover probability CR is independently generated according to a normal distribution with a standard deviation of 0.1 and a mean of μCR. Similarly, its factor of variation F is independently generated according to a normal distribution with a mean of μF and a standard deviation of 0.1. The factor of variation F and the crossover probability CR take values ​​between 0 and 1, as shown in the following equation:

[0238] CR i =randn i (μCR, 0.1)

[0239] F i =randn i (μF, 0.1)

[0240] Among them, CR i and F i Let F represent the crossover probability and mutation factor of the i-th individual. i >1, F i Set to 1, otherwise, if F i ≤0, F i Then a new value will be generated; similarly, if CR i >1, CR i Set to 1, if CR i ≤0, CR i Then a new value will be generated;

[0241] S CR and S F μCR and μF are defined as the sets of crossover probabilities and mutation factors, respectively, during the evolution of experimental individuals that successfully enter the next generation after a selection operation. Both μCR and μF are initialized to 0.5 and are updated after each generation using the following formula;

[0242] μCR=(1-q)μCR+q·mean(S CR )

[0243] μF=(1-q)μF+q·mean(S F )

[0244] Where q is a positive number between 0 and 1, mean(S CR ) and mean(S F The following represent the Lehmer average values:

[0245]

[0246]

[0247] Excellent parameters tend to produce individuals more likely to survive. The successful crossover probability (CR) and successful mutation factor (F) of the previous generation are instructive for generating the crossover probability (CR) and mutation factor (F) of the next generation. Therefore, the values ​​of μCR and μF are based on the following criteria, with the successful crossover probability (CR) and successful mutation factor (F) of the previous generation recorded on S. CR and S F In this process, it is easier to generate population individuals with better fitness values ​​under the guidance of the parameters successfully controlled by the previous generation.

[0248] The multi-population adaptive differential evolution parameter identification results using a buried pipe heat exchanger model of the present invention are as follows: Figure 4 As shown in the figure, the method has high identification accuracy, the estimated values ​​of the parameters to be identified are very close to the true values, and its convergence speed is relatively fast; at the same time, it also shows that the method has good applicability to parameter identification of buried pipe heat exchangers.

[0249] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying multi-population adaptive differential evolution parameters of a buried pipe heat exchanger model, characterized in that, Includes the following steps: Step 1) Establish a Wiener-Hammerstein model of the buried pipe heat exchanger to describe its input-output relationship; Step 2) Constructing the identification process of multi-population adaptive differential evolution algorithm; Step 2) includes the following steps: Step 2-1) Set the control parameters required for the multi-population adaptive differential evolution algorithm: population size, mutation factor, crossover probability, mutation strategy, and termination condition; Step 2-2) Given the upper and lower bounds of the solution range of the optimization problem, randomly initialize the population as follows: ； in Let represent the i-th individual in the population after k iterations, and j represent the j-th parameter in the vector. After each iteration, the individual with the best fitness value is selected as the [i-th individual]. Parameter estimation , The definition method is as follows: make , , , , , They are parameter vectors , , , , , The estimated value is defined as: ； ； ； ； ； ； Then the parameter vector , , , Estimate , , , They are defined as follows: ； ； ； ； Step 2-3) Define the fitness function as follows: ； Where l is the data length. for The estimated value for the k-th iteration is defined as follows: make , , , , , , They are vectors , , , , , , Estimates, unknown variables , , , Their iterative estimates , , , replace; ； ； ； ； ； ； ； in , , , k-th iteration estimate , , , It is expressed as follows: ； ； ； ； Steps 2-4) Evaluate the fitness values ​​of individuals and divide the original population into elite subpopulations, general subpopulations and worst subpopulations based on the fitness values, and use three different mutation strategies for evolution respectively; Mutation strategy: 1)DE / best / 1: ； 2)DE / rand-to-best / 1: ； 3) DE / rand / 2: ； Where "best" indicates that the individual with the best fitness value is the best-ranked individual in the population. This indicates that the individual is the [number]th [unit] in the population. The individual, the first Each individual is random, and within the same mutation strategy, they are all distinct. Let j represent the i-th mutated individual, also known as the mutation vector. for The j-th parameter, F is the mutation factor; Steps 2-5) Crossover operation: Each individual in the population undergoes a crossover operation with its corresponding mutation vector. The specific operation is as follows: ； in It is a random decimal number between [0,1]. It is the i-th experimental individual, and CR represents the crossover probability, which is used to control the degree of exchange of individuals in the population. During the crossover process, when the randomly generated value is less than or equal to the crossover probability, the operation of exchanging individuals in the population is performed; otherwise, the original individuals are retained. Steps 2-6) Selection operation: After the k-th crossover mutation, the population produces NP individuals, called test individuals. The test individuals are evaluated and compared with the original individuals in the population. If the fitness value of the test individual is worse than that of the original individual, the original individual is retained. Otherwise, the original individual will be replaced by the test individual in the next generation. These selected individuals form a new population and enter the next iteration. ； Step 2-7) Determine if the termination condition is met. If it is, stop; otherwise, go to step 2-4. For each individual in the population, the crossover probability CR is calculated based on a standard deviation of 0.1 and a mean of 0.

1. The normal distribution is formed independently, and similarly, its variation factor F is based on the mean. The distribution is generated independently of a normal distribution with a standard deviation of 0.1, and the variation factor F and crossover probability CR take values ​​between 0 and 1, as shown in the following equation: ； ； in, and Represents the crossover probability and mutation factor of the i-th individual, if , Set to 1, otherwise, if , Then a new value will be generated; similarly, if , Set to 1, if , Then a new value will be generated; Will and These are defined as the sets of crossover probabilities and mutation factors in the evolutionary process of experimental individuals that successfully enter the next generation after a selection operation. and They are all initialized to 0.5, and after each generation, they are updated using the following formula; ； ； Where q is a positive number between 0 and 1. and The Lehmer average values ​​are shown below: ； 。 2. The method for identifying multi-population adaptive differential evolution parameters of the buried pipe heat exchanger model according to claim 1, characterized in that, Step 1) includes the following steps: Step 1-1) Establish the Wiener-Hammerstein model of the buried pipe heat exchanger: The model of the buried pipe heat exchanger, represented by the Wiener-Hammerstein model, is as follows: ； ； ； ； ； Where t is time. and These are the system's input and output, respectively. It's system noise. It is a noiseless output of the system. It is colored noise. , , , It is an unmeasurable intermediate variable in the above formula. , , , , This is represented here by the following polynomial, where It is a shift operator and ; ； ； ； ； ； Let denote a polynomial function consisting of Volterra series, i.e.: ； in This represents the maximum nonlinear order of the Volterra series. It is the length of memory. , It is the Volterra kernel function; assuming , , , , Given all, when When, input Output The value is 0. For a continuous excitation signal, in order to obtain a unique parameter estimate, the nonlinear component is... The value is set to 1, that is: ； Steps 1-2) Derive the output based on equations (1) to (11). With input intermediate variables , , System noise The relationship between them is shown in the following formula; ； Define the parameter vector in a linear subsystem , , , and the parameter vector of the noise part. as follows: ； ； ； ； ； Define the parameter vector in a nonlinear subsystem as follows: ； Parameter vector , , , and information vector , , , , , , The definition is as follows: ； ； ； ； ； ； ； ； ； ； ； Equations (1) to (3) are then restated as follows: ； ； ； Equation (5) is reformulated as: 。

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