Method for optimizing photothermal effect of graphene nano coating of photovoltaic panel

Abstract

The invention provides a method for optimizing the photothermal effect of a graphene nano-coating of a photovoltaic panel, and belongs to the technical field of the graphene nano-coating of the photovoltaic panel, and the method comprises the steps: firstly, obtaining key parameters of the coating, including morphology, thickness, heat conductivity coefficient, absorbance and dispersity, carrying out multi-element mixing decomposition calculation, and separating a stable component from a variable component; then, constructing a positive and negative performance action equation set, and solving by using a Latin hypercube sampling method to obtain an analytical solution and a range solution; and based on the solutions, constructing through a game model, then adopting a genetic algorithm for multi-generation iterative optimization, and finally determining the optimal parameters of the graphene nano coating. And finally, accurately optimizing the coating according to the optimal parameters, and applying the coating to coating treatment of the photovoltaic panel. The method solves the problem that the prior art lacks an optimization method capable of comprehensively describing the coupling relation of all parameters in the photothermal conversion process of the graphene nano-coating and predicting the long-term performance change of the coating under severe conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of graphene nano - coatings for photovoltaic panels. Specifically, it relates to a method for optimizing the photothermal effect of graphene nano - coatings on photovoltaic panels. Background Art

[0002] With the continuous progress of technology, solar photovoltaic technology has received increasing attention in the field of renewable energy. Among them, improving the photothermal conversion efficiency of photovoltaic cells is the key to enhancing the performance of photovoltaic power generation. As a new type of two - dimensional carbon material, graphene's excellent optical and thermal properties make it show great application potential in the field of photothermal conversion. By coating a graphene nano - coating on the surface of a photovoltaic cell, sunlight can be effectively absorbed and converted into heat energy, thereby improving the overall photothermal conversion efficiency.

[0003] Currently, graphene nano - coatings face two main challenges in photothermal conversion applications: one is how to design reasonable coating structure parameters to fully utilize its excellent optical and thermal properties; the other is how to prevent the performance degradation of the coating under high - temperature and harsh environments. For the former, many studies have tried to optimize its photothermal conversion performance by regulating parameters such as the morphology structure, thickness, and dispersion state of graphene. However, most of these studies adopt a single optimization strategy and cannot comprehensively consider the complex coupling relationship between material parameters. For the latter, although some studies have explored the heat resistance and stability of graphene coatings from the perspective of material intrinsic properties, there is a lack of systematic and in - depth understanding of the performance degradation mechanism of the coating under actual application conditions.

[0004] Therefore, there is an urgent need to establish an optimization method that can comprehensively describe the coupling relationship between various parameters in the photothermal conversion process of graphene nano - coatings and predict the long - term performance changes of the coating under harsh conditions. This not only helps to guide the material design and process optimization of graphene nano - coatings but also provides important support for the further development of photovoltaic - thermal conversion technology. Summary of the Invention

[0005] In view of this, the present invention provides a method for optimizing the photothermal effect of graphene nano - coatings on photovoltaic panels, which can solve the problem that the existing technology lacks an optimization method that can comprehensively describe the coupling relationship between various parameters in the photothermal conversion process of graphene nano - coatings and predict the long - term performance changes of the coating under harsh conditions.

[0006] The present invention is implemented as follows:

[0007] The present invention provides a method for optimizing the photothermal effect of graphene nano - coatings on photovoltaic panels, including the following steps:

[0008] S10. Obtain the morphology parameters, thickness parameters, thermal conductivity parameters, light absorption rate parameters, and dispersion parameters of the graphene nano - coating;

[0009] S20. Perform multivariate mixed decomposition calculation on the said morphology parameters to obtain a morphology stable component and a morphology variable component;

[0010] S30. Perform multivariate mixed decomposition calculation on the said thermal conductivity parameters to obtain a thermal conductivity stable component and a thermal conductivity variable component;

[0011] S40. Construct a forward performance action equation set based on the said morphology parameters, the said thickness parameters, the said thermal conductivity parameters, the said light absorption rate parameters, and the said dispersion parameters;

[0012] S50. Construct a negative performance action equation set based on the said morphology parameters, the said thickness parameters, the said thermal conductivity parameters, the said light absorption rate parameters, and the said dispersion parameters;

[0013] S60. According to the parameter ranges of the said morphology parameters, the said thickness parameters, the said thermal conductivity parameters, the said light absorption rate parameters, and the said dispersion parameters, use the Latin hypercube sampling method to solve the forward performance action equation set to obtain a first analytical solution and a first range solution;

[0014] S70. According to the parameter ranges of the said morphology parameters, the said thickness parameters, the said thermal conductivity parameters, the said light absorption rate parameters, and the said dispersion parameters, use the Latin hypercube sampling method to solve the negative performance action equation set to obtain a second analytical solution and a second range solution;

[0015] S80. Use the first analytical solution, the first range solution, the second analytical solution, and the second range solution to construct a game model;

[0016] S90. Use a genetic algorithm to solve the game model, set the crossover rate and mutation rate, and obtain the optimal morphology parameters, optimal thickness parameters, optimal thermal conductivity parameters, optimal light absorption rate parameters, and optimal dispersion parameters of the graphene nano - coating through multi - generation iterative optimization;

[0017] S100. Optimize the graphene nano - coating according to the optimal morphology parameters, the optimal thickness parameters, the optimal thermal conductivity parameters, the optimal light absorption rate parameters, and the optimal dispersion parameters;

[0018] S110. Use the optimized graphene nano - coating to perform a coating treatment on the photovoltaic panel.

[0019] The forward performance action equation set includes a photothermal conversion equation, a heat conduction equation, a morphology influence equation, and a dispersion synergistic equation;

[0020] The photothermal conversion equation is used to calculate the photothermal conversion efficiency of the nano - coating. The inputs include the light absorption rate parameter, the morphology stability component, and the heat conduction stability component, and the output is the photothermal conversion coefficient matrix;

[0021] The heat conduction equation is used to calculate the heat conduction performance of the nano - coating. The inputs include the thermal conductivity parameter, the thickness parameter, and the morphology variation component, and the output is the heat conduction efficiency matrix;

[0022] The morphology influence equation is used to calculate the influence of the surface morphology of the nano - coating on the photothermal performance. The inputs include the morphology parameter, the thickness parameter, and the dispersion parameter, and the output is the morphology influence coefficient matrix;

[0023] The dispersion enhancement equation is used to calculate the improvement effect of the dispersion of the nano - coating on the performance. The inputs include the dispersion parameter, the morphology parameter, and the heat conduction variation component, and the output is the dispersion enhancement coefficient matrix.

[0024] The negative performance effect equation set includes the structure attenuation equation, the interface impedance equation, the agglomeration loss equation, and the temperature failure equation;

[0025] The structure attenuation equation is used to calculate the attenuation of the structural stability of the nano - coating. The inputs include the morphology variation component, the thickness parameter, and the heat conduction variation component, and the output is the structure attenuation coefficient matrix;

[0026] The interface impedance equation is used to calculate the interfacial thermal resistance between the nano - coating and the substrate. The inputs include the morphology parameter, the thickness parameter, and the thermal conductivity parameter, and the output is the interface impedance coefficient matrix;

[0027] The agglomeration loss equation is used to calculate the negative impact of the agglomeration degree of the nano - coating on the performance. The inputs include the dispersion parameter, the morphology parameter, and the thermal conductivity parameter, and the output is the agglomeration loss coefficient matrix;

[0028] The temperature failure equation is used to calculate the performance attenuation of the nano - coating at high temperatures. The inputs include the heat conduction stability component, the thickness parameter, and the dispersion parameter, and the output is the temperature failure coefficient matrix.

[0029] The following details the mathematical models involved in the present invention.

[0030] I. Multivariate mixed decomposition calculation process:

[0031] 1. The multivariate mixed decomposition calculation of the morphology parameter is specifically expressed as follows:

[0032] M(t)=M s (t)+M v (t)+ξm ;

[0033]

[0034] In the formula, M(t) is the time series of the morphology parameter; M s (t) is the morphology stable component; M v (t) is the morphology variation component; ξ m is the decomposition error term; φ i (t) is the i-th stable basis function; ψ j (t) is the j-th variation basis function; α i , β j are the decomposition coefficients; n and m are the numbers of the stable and variation basis functions respectively. This method is based on the principle of empirical mode decomposition (EMD), and decomposes the time series data into a stable trend term and a fluctuation term. The exponential function and the trigonometric function are selected as the basis functions because they can well describe the periodic change and decay characteristics of the material parameters. This decomposition method has better local characteristic description ability than the traditional Fourier decomposition.

[0035] 2. The multivariate mixed decomposition calculation of the thermal conductivity parameter is specifically expressed as follows:

[0036] K(t) = K s (t) + K v (t) + ξ k ;

[0037]

[0038] In the formula, K(t) is the time series of the thermal conductivity parameter; K s (t) is the thermal conductivity stable component; K v (t) is the thermal conductivity variation component; ξ k is the decomposition error term; θ i (t) is the i-th stable basis function; ω j (t) is the j-th variation basis function; γ i , δ j are the decomposition coefficients; p and q are the numbers of the stable and variation basis functions respectively.

[0039] II. Forward performance action equations:

[0040] 1. The photothermal conversion equation is specifically expressed as follows:

[0041]

[0042] In the formula, η ph is the photothermal conversion efficiency; A p is the light absorption rate parameter; σ mis the standard deviation of the morphological feature; τ is the characteristic time constant; λ 1 , λ 2 , λ 3 is the weight coefficient; ε ph is the error term.

[0043] In this equation, the first term describes the coupling relationship between the absorbance and the morphological stability. The exponential decay form is based on the Beer-Lambert law; the second term λ 2 K s (t)·(1 - e -τt ) represents the influence of the thermal conductivity on the photothermal conversion, and the exponential saturation form is used to describe the heat accumulation process; the third term reflects the synergistic effect of light absorption - heat conduction. The square root form is considered to account for the non-linear coupling characteristics of the two.

[0044] 2. The heat conduction equation is specifically expressed as follows:

[0045]

[0046] In the formula, Q tc is the heat conduction efficiency matrix; k ij is the element of the heat conduction coefficient matrix; d is the thickness parameter; ε tc is the error term. This equation uses a 3×3 matrix form to describe the coupling effect between three key parameters (thermal conductivity, thickness, morphological change). The matrix form can effectively express the multi-dimensional mutual influence between the parameters.

[0047] 3. The morphological influence equation is specifically expressed as follows:

[0048]

[0049] In the formula, F m is the morphological influence coefficient; D s is the dispersion parameter; α f , β f , γ f are the influence factors; ε f is the error term. This equation introduces the first derivative term of the morphological parameter to describe the influence of the morphological change rate; introduces the second derivative term to describe the influence of the morphological change acceleration; and considers the ratio of the thickness to the dispersion, reflecting the synergistic effect of morphology - structure.

[0050] 4. The dispersion enhancement equation is specifically expressed as follows:

[0051]

[0052] In the formula, E d is the dispersion enhancement coefficient; M0 is the reference morphology value; K 0 is the reference thermal conductivity; η 1 , η 2 , η 3 is the synergistic coefficient; ε d is the error term. This equation uses an exponential term to describe the regulation of dispersion on morphology; a linear term to describe the influence of thermal conductivity variation; and a square root term to describe the non-linear coupling of dispersion-morphology.

[0053] III. Negative performance effect equations:

[0054] 1. The structural attenuation equation is specifically expressed as follows:

[0055]

[0056] In the formula, D s is the structural attenuation coefficient; M max is the maximum morphology parameter; d 0 is the reference thickness; K max is the maximum thermal conductivity; ρ 1 , ρ 2 , ρ 3 is the attenuation coefficient; ε s is the error term. This equation uses a normalized form to describe the influence of each parameter on structural stability, considering three main factors: morphology variation, thickness, and thermal conductivity variation. The thickness term uses a quadratic form based on the stress-strain relationship.

[0057] 2. The interface impedance equation is specifically expressed as follows:

[0058]

[0059] In the formula, Z i is the interface impedance matrix; r ij is the impedance coefficient matrix element; ε i is the error term. This equation uses a matrix form to describe the interface heat transfer impedance, considering the coupling effect of three parameters: morphology, thickness, and thermal conductivity.

[0060] 3. The agglomeration loss equation is specifically expressed as follows:

[0061]

[0062] In the formula, L a is the agglomeration loss coefficient; D max is the maximum dispersion; M c is the critical morphology value; K c is the critical thermal conductivity; μ 1 , μ 2 , μ 3is the loss coefficient; ε a is the error term.

[0063] 4. The temperature failure equation is specifically expressed as follows:

[0064]

[0065] In the formula, F t is the temperature failure coefficient; K T is the temperature-related thermal conductivity; d T is the temperature-related critical thickness; D T is the temperature-related dispersion; τ T is the temperature characteristic time; ω 1 , ω 2 , ω 3 is the failure coefficient; ε t is the error term. This equation considers the linear effect of thermal stability on temperature failure; considers the quadratic effect of thickness; and uses an exponential decay term to describe the decay characteristic of dispersion over time.

[0066] IV. Game model description:

[0067] 1. The positive payoff function of the game model is specifically expressed as follows:

[0068] U p = w 1 η ph + w 2 Q tc + w 3 F m + w 4 E d + ε p ;

[0069] In the formula, U p is the positive payoff function value; w 1 , w 2 , w 3 , w 4 are the weight coefficients of each performance index; ε p is the payoff function error term.

[0070] 2. The negative payoff function of the game model is specifically expressed as follows:

[0071] U n = v 1 D s + v 2 Z i + v 3 L a + v 4 F t + ε n ;

[0072] Wherein, U n is the negative payment function value; v 1 , v 2 , v 3 , v 4 are the weight coefficients of each performance index; ε n is the payment function error term.

[0073] 3. The objective function of the game model is specifically expressed as follows:

[0074] x = max x∈X min y∈Y (U p -αU n );

[0075]

[0076] Wherein, x is the positive strategy variable vector; y is the negative strategy variable vector; X is the positive strategy space; Y is the negative strategy space; α is the trade-off coefficient; g 1 (x), g 2 (x) are the positive constraint functions; h 1 (y), h 2 (y) are the negative constraint functions; b 1 , b 2 , c 1 , c 2 are the constraint boundary values.

[0077] 4. The fitness function of the genetic algorithm is specifically expressed as follows:

[0078]

[0079] Wherein, f is the fitness function value; λ i is the penalty factor; p i is the degree of violation of the i-th constraint; n is the total number of constraints.

[0080] VI. Solution process of the analytical solution and the range solution:

[0081] 1. The solution process of the first analytical solution is specifically expressed as follows:

[0082] (1) Construct the objective function based on the positive performance action equations:

[0083]

[0084] (2) Calculate the partial derivatives of each parameter of the objective function respectively:

[0085]

[0086]

[0087] (3) Set the partial derivatives to zero to obtain the system of equations:

[0088]

[0089] (4) Use the Newton-Raphson method to solve the system of equations:

[0090]

[0091] X k = [A p , K s , M s , K tc T ;

[0092]

[0093] (5) After the iteration converges, obtain the first analytical solution:

[0094] X * = lim k→∞ X k ;

[0095] 2. The solution process of the first range solution is specifically expressed as follows:

[0096] (1) Construct an interval expansion based on the forward performance action equations:

[0097]

[0098] (2) Calculate the interval boundaries of each performance index:

[0099]

[0100] (3) Use interval arithmetic to solve:

[0101]

[0102] where: X = [A p , K s , M s , K tc T , and ΔX is the parameter error vector.

[0103] 3. The solution process of the second analytical solution is specifically expressed as follows:

[0104] (1) Construct an objective function based on the negative performance action equations:

[0105] ​​(2) Take the partial derivatives of the objective function with respect to each parameter:

[0106]

[0107] (3) Set the partial derivatives to zero to obtain a system of equations:

[0108]

[0109] (4) Use the Newton - Raphson method to solve the system of equations:

[0110]

[0111] Y k =[M v ,d,K v ,Z i T ;

[0112]

[0113] (5) After the iteration converges, obtain the second analytical solution:

[0114] Y * =lim k→∞ Y k ;

[0115] 4. The solution process of the second range solution is specifically expressed as follows: (1) Construct an interval expansion based on the negative - performance - acting equation system:

[0116] (2) Calculate the interval boundaries of each performance index:

[0117]

[0118] (3) Use interval arithmetic to solve:

[0119]

[0120] where: Y = [M v ,d,K v ,Z i T , and ΔY is the parameter error vector.

[0121] 2. The solution process of the first range solution is specifically expressed as follows:

[0122]

[0123] where, are the lower and upper bounds of performance respectively; k is the confidence coefficient; σ is the standard deviation; is the sample mean; CI​​p is the confidence interval.

[0124] 3. The solution process of the second analytical solution is specifically expressed as follows:

[0125]

[0126] where is the parameter estimation vector; Z is the sample matrix; Y n is the negative performance observation vector; is the fitted value vector; m is the number of samples; RMSE is the root mean square error.

[0127] 4. The solution process of the second range solution is specifically expressed as follows:

[0128]

[0129] where are the lower and upper bounds of performance respectively; l is the confidence coefficient; δ is the standard deviation; is the sample mean; CI n is the confidence interval.

[0130] VII. Improved game model:

[0131] 1. The weighted objective function of the game model is specifically expressed as follows:

[0132]

[0133] where ω 1 , ω 2 are the weight coefficients; CI p , CI n are the confidence intervals of positive and negative performances respectively.

[0134] 2. The constraint conditions of the game model are specifically expressed as follows:

[0135]

[0136] 3. The solution process of the game model is specifically expressed as follows:

[0137]

[0138] 4. The improved fitness function of the genetic algorithm is specifically expressed as follows:

[0139]

[0140] where is the target confidence level; μ 1 , μ 2 are the confidence interval penalty factors.

[0141] 1. The morphological parameter M(t) is characterized and obtained by an atomic force microscope. The specific steps include:

[0142] (1) Sample pretreatment: Cut the graphene nano-coated sample into a size of 10 mm × 10 mm.

[0143] (2) Surface cleaning: Dip a lint-free cloth in isopropyl alcohol for surface cleaning and let it dry naturally.

[0144] (3) AFM test: Set the scanning range to 20 μm × 20 μm, the scanning frequency to 1 Hz, and the acquisition resolution to 512 × 512 pixels.

[0145] (4) Data processing: Use image processing software to perform planar fitting and noise filtering on the AFM data.

[0146] 2. The thermal conductivity parameter K(t) is obtained by testing with the transient hot wire method. The specific steps include:

[0147] (1) Sample preparation: Process the coated sample into a test strip of 50 mm × 10 mm × 2 mm.

[0148] (2) Hot wire installation: Fix the hot wire probe on the sample surface and apply thermal conductive silicone grease.

[0149] (3) Heating test: Apply a constant current and record the curve of temperature change over time.

[0150] (4) Data analysis: Calculate the thermal conductivity according to the formula

[0151] where Q is the heating power; L is the hot wire length; t 1 ,t 2 is the test time point; ΔT is the temperature rise.

[0152] 3. The light absorption rate parameter A p is obtained by testing with a spectrophotometer. The specific steps include:

[0153] (1) Baseline calibration: Calibrate the 100% transmittance with a standard white board.

[0154] (2) Sample test: Scan in the wavelength range of 200 - 2500 nm.

[0155] (3) Data processing: Calculate the light absorption rate according to the formula A p = 1 - R - T.

[0156] where R is the reflectance; T is the transmittance.

[0157] 4. The dispersion parameter D s ​Obtained by testing with the dynamic light scattering method, and the specific steps include:

[0158] (1) Sample dispersion: Ultrasonically disperse the coating in deionized water;

[0159] (2) Particle size test: Use a dynamic light scattering instrument to test the particle size distribution;

[0160] (3) Data analysis: According to the formula Calculate the dispersion degree;

[0161] In the formula, w i is the weight of the i-th particle size interval; d i is the average particle size of the i-th interval; d max is the maximum particle size; m is the number of intervals.

[0162] Furthermore, step S100 can directly output the obtained optimal morphology parameters, the optimal thickness parameters, the optimal thermal conductivity parameters, the optimal light absorption rate parameters, and the optimal dispersion degree parameters to the engineering personnel, and the staff can optimize the process parameters according to these parameters using conventional production experience; or it can be optimized based on the process parameter - performance parameter model to determine the process parameters, and the process parameter - performance parameter model includes the process - performance mapping relationship of the graphene nano - coating, the optimization equation of the process parameters, the coupling correction equation of the process parameters, and the constraint conditions of the process parameters

[0163] The process - performance mapping relationship of the graphene nano - coating is specifically expressed as follows:

[0164]

[0165] In the formula, C g is the graphene concentration, with the unit of mg / mL and the range of [0.1, 10]; T d is the dispersion temperature, with the unit of °C and the range of [20, 80]; t s is the stirring time, with the unit of min and the range of [30, 180]; v c is the coating speed, with the unit of mm / s and the range of [1, 10]; ω s is the substrate rotation speed, with the unit of rpm and the range of [100, 1000]; p s is the coating pressure, with the unit of kPa and the range of [10, 100]; T t is the heat treatment temperature, with the unit of °C and the range of [60, 200]; P t is the heat treatment pressure, with the unit of MPa and the range of [0.1, 1]; R s is the roll - pressing spacing, with the unit of mm and the range of [0.1, 1]; t tE is the rolling time, in seconds, with a range of [1, 10]; u t is the ultrasonic power, in watts, with a range of [100, 500]; u k is the ultrasonic time, in minutes, with a range of [10, 60]; 1 , k 2 , k 3 , k 4 , k 5 k is the proportionality coefficient; T 0 , P 0 , R 0 , E 0 , t 0 α is the reference value; 1 , β 1 , γ 1 , α 2 , β 2 , γ 2 , α 3 , β 3 , α 5 , β 5 δ is the power coefficient, with a range of [0.1, 2]; δ is the time characteristic coefficient;

[0166] The optimization equation of the process parameters is specifically expressed as follows:

[0167] P pro = μ 1 · f 1 (C g , T d , t s ) + μ 2 · f 2 (v c , ω s , p s ) + μ 3 · f 3 (T t , P t ) + μ 4 · f 4 (R s , t t ) + μ 5 · f 5 (E u , t u );

[0168] In the formula, P pro is the process optimization index; f 1 , f 2 , f 3 , f 4 , f 5Optimization functions for the dispersion process, coating process, heat treatment process, rolling process, and ultrasonic process, respectively; μ 1 , μ 2 , μ 3 , μ 4 , μ 5 is the weight coefficient, satisfying

[0169] The coupling correction equation for the process parameters is specifically expressed as follows:

[0170] ΔP = η 1 ·(C g ·T d ) + η 2 ·(v c ·p s ) + η 3 ·(T t ·t t ) + η 4 ·(E u ·t u );

[0171] In the formula, ΔP is the process coupling correction term; η 1 , η 2 , η 3 , η 4 are the coupling coefficients;

[0172] The constraint conditions for the process parameters are specifically expressed as follows:

[0173]

[0174] In the formula, K 1 , K 2 , K 3 , K 4 are the coupling constraint thresholds for the process parameters;

[0175] Among them, 1) The process-performance mapping relationship of the graphene nanocoating is constructed based on the physical and chemical mechanisms during the material preparation process:

[0176] The morphology parameters are mainly affected by the dispersion process, and the synergistic effects of concentration, temperature, and time are described by a power function;

[0177] The thickness parameters are mainly affected by the coating process, and the comprehensive effects of speed, rotation speed, and pressure are described by a power function;

[0178] The thermal conductivity is mainly affected by the heat treatment process, and the power function relationship between dimensionless temperature and pressure is used;

[0179] The light absorption rate is mainly affected by the rolling process, and the coupling effect of spacing and time is described by an exponential function;

[0180] The degree of dispersion is mainly affected by the ultrasonic process, and a power function relationship of power and time is adopted;

[0181] 2) The process optimization equation combines the optimization objectives of each process unit with weights to achieve multi-objective collaborative optimization;

[0182] 3) The coupling correction equation takes into account the interactive effects between process parameters to avoid the side effects brought by single parameter optimization;

[0183] 4) The constraint conditions ensure that the combination of process parameters will not exceed the physical limits of the equipment and the process.

[0184] Compared with the prior art, the method for optimizing the photothermal effect of the graphene nano-coating on the photovoltaic panel provided by the present invention comprehensively considers the key factors affecting the photothermal conversion performance of the graphene coating from multiple levels such as the microscopic structure, macroscopic properties, and environmental effects of the material, establishes a coupling model covering both positive and negative effects, and uses an advanced numerical optimization algorithm to solve, and finally obtains the optimal coating design parameters. Compared with the existing single optimization strategy, the method of the present invention has the following key innovations and advantages:

[0185] 1. Comprehensively consider the key parameters affecting the photothermal conversion performance of the graphene nano-coating, including morphology structure, thickness, thermal conductivity, light absorption rate, and dispersion state, etc., and establish a coupling model covering the positive enhancement and negative degradation processes. This systematic modeling method can more accurately predict the overall performance changes of the coating.

[0186] 2. Use the method of multivariate mixed decomposition to characterize the time evolution characteristics of key parameters, which can better describe the change law of material parameters and provide necessary data support for subsequent performance modeling and optimization.

[0187] 3. Propose a multi-objective optimization strategy based on game theory, which maximizes the positive performance index while minimizing the negative performance index. This trade-off mechanism can achieve the global optimum of material performance.

[0188] 4. Use advanced numerical optimization methods such as Latin hypercube sampling and genetic algorithms, which can find the global optimal solution of material parameters under limited computing resources and provide reliable guidance for actual preparation in engineering applications.

[0189] In summary, the present invention solves the problem that the prior art lacks an optimization method that can comprehensively describe the coupling relationship between parameters in the photothermal conversion process of the graphene nano-coating and predict the long-term performance changes of the coating under harsh conditions. Description of the Drawings

[0190] Figure 1 It is a flowchart of the method provided by the present invention. Detailed Implementation Modes

[0191] To make the objectives, technical solutions, and advantages of the implementation modes of the present invention clearer, the technical solutions in the implementation modes of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the implementation modes of the present invention.

[0192] As Figure 1 shown, it is a flowchart of a method for optimizing the photothermal effect of a graphene nanocoating on a photovoltaic panel provided by the present invention. The following will describe in detail the specific implementation modes of each step in the present invention:

[0193] The specific implementation mode of step S10 is to obtain the morphology parameters, thickness parameters, thermal conductivity parameters, light absorption rate parameters, and dispersion parameters of the graphene nanocoating. Among them, the morphology parameters are obtained by atomic force microscopy characterization, including processes such as surface morphology scanning of the graphene nanocoating using atomic force microscopy, plane fitting, and noise filtering of the scanning data. The thickness parameters are obtained by transverse testing with a scanning electron microscope. The thermal conductivity parameters are tested using the transient hot wire method. The main steps include processing the coating sample into a test strip, fixing the hot wire probe and applying thermal conductive silicone grease, applying a constant current and recording the temperature change curve, and finally calculating the thermal conductivity according to the formula. The light absorption rate parameters are obtained by testing with a spectrophotometer. Specifically, a standard whiteboard is used for 100% transmittance calibration, and then the absorption spectrum of the sample is scanned in the wavelength range of 200 - 2500 nm, and the light absorption rate is calculated according to the formula. The dispersion parameters are tested using the dynamic light scattering method. The main steps include ultrasonic dispersing the coating sample in deionized water, testing the particle size distribution with a dynamic light scattering instrument, and calculating the dispersion according to the formula. These test parameters are finally established in a parameter database for subsequent analysis.

[0194] The specific implementation mode of step S20 is to perform multivariate hybrid decomposition calculation on the morphology parameters. First, a set of basis functions for the morphology parameters is constructed, including a stable basis function subset and a variable basis function subset, such as exponential functions and trigonometric functions. Then, the recursive least squares method is used to decompose the time series data of the morphology parameters with the basis functions. The coefficients obtained from the decomposition are linearly combined with the stable basis function subset and the variable basis function subset respectively to obtain the morphology stable component and the morphology variable component. Finally, the difference between the morphology parameters minus the morphology stable component and the morphology variable component is calculated to obtain the decomposition error term of the morphology parameters. This multivariate hybrid decomposition method based on empirical mode decomposition can well describe the periodic changes and attenuation characteristics of material parameters.

[0195] The specific implementation of step S30 is to perform multivariate mixed decomposition calculation on the thermal conductivity parameter. Similar to the decomposition of the morphology parameter, first, a set of basis functions for the thermal conductivity parameter is constructed, including a stable basis function subset and a variable basis function subset. Then, the recursive least squares method is used to decompose the time series data of the thermal conductivity parameter into basis functions. The coefficients obtained from the decomposition are linearly combined with the stable basis function subset and the variable basis function subset respectively to obtain the thermal conductivity stable component and the thermal conductivity variable component. Finally, the difference between the thermal conductivity parameter minus the thermal conductivity stable component and the thermal conductivity variable component is calculated to obtain the decomposition error term of the thermal conductivity parameter. This multivariate mixed decomposition method based on empirical mode decomposition can well characterize the variation characteristics of the thermal conductivity parameter.

[0196] The specific implementation of step S40 is to construct a forward performance action equation set. First, a photothermal conversion equation is constructed. Taking the light absorption rate parameter, the morphology stable component, and the thermal conductivity stable component as inputs, the photothermal conversion coefficient matrix is calculated. The photothermal conversion equation uses the forms of exponential decay, exponential saturation, and square root to describe the effects of light absorption rate, thermal conductivity performance, and synergistic effect on photothermal conversion. Secondly, a heat conduction equation is constructed. Taking the thermal conductivity parameter, the thickness parameter, and the morphology variable component as inputs, the heat conduction efficiency matrix is obtained. The heat conduction equation uses the form of a 3×3 matrix to describe the coupling effects of three key parameters. Thirdly, a morphology influence equation is constructed. Taking the morphology parameter, the thickness parameter, and the dispersion parameter as inputs, the morphology influence coefficient is obtained. The morphology influence equation introduces the first derivative and the second derivative terms of the morphology parameter to describe the influence of morphology change. Finally, a dispersion synergistic equation is constructed. Taking the dispersion parameter, the morphology parameter, and the thermal conductivity variable component as inputs, the dispersion synergistic coefficient is obtained. The dispersion synergistic equation uses exponential terms, linear terms, and square root terms to describe the effects of dispersion, thermal conductivity variation, and nonlinear coupling. These equations can effectively describe the complex coupling relationships between forward performance indicators.

[0197] The specific implementation of step S50 is to construct a negative performance effect equation set. First, a structure attenuation equation is constructed. By taking the morphology change component, thickness parameter, and heat conduction change component as inputs, the structure attenuation coefficient is obtained. The structure attenuation equation uses a normalized form to describe the linear and non-linear effects of each parameter on the structure stability. Secondly, an interface impedance equation is constructed. By taking the morphology parameter, thickness parameter, and thermal conductivity parameter as inputs, the interface impedance coefficient matrix is obtained. The interface impedance equation also uses a matrix form to describe the coupling effect of the three parameters. Thirdly, an agglomeration loss equation is constructed. By taking the dispersion parameter, morphology parameter, and thermal conductivity parameter as inputs, the agglomeration loss coefficient is obtained. The agglomeration loss equation uses linear, exponential, and linear terms to describe the negative effects of dispersion, morphology, and thermal conductivity on the performance. Finally, a temperature failure equation is constructed. By taking the heat conduction stability component, thickness parameter, and dispersion parameter as inputs, the temperature failure coefficient is obtained. The temperature failure equation takes into account the linear and non-linear effects of heat conduction stability, thickness, and dispersion on temperature failure. These equations can effectively describe the interaction between negative performance indicators.

[0198] The specific implementation of step S60 is to use the Latin hypercube sampling method to solve the positive performance effect equation set. First, the parameter spaces of the morphology parameter, thickness parameter, thermal conductivity parameter, light absorption rate parameter, and dispersion parameter are divided. Then, a set of sample point sets are generated in this parameter space using the Latin hypercube sampling method. These sample points are input into the positive performance effect equation set for numerical calculation. Finally, the least squares method is used to fit the numerical calculation results to obtain the first analytical solution. At the same time, the interval analysis method is used to process the numerical calculation results to obtain the first range solution. The Latin hypercube sampling is an efficient multi-parameter sampling method that can better cover the parameter space with a limited sample size. The least squares method can extract the analytical form of the performance response function from a large amount of calculation data, while the interval analysis can give the value ranges of each performance indicator, providing the necessary data support for the subsequent game analysis.

[0199] The specific implementation of step S70 is similar to that of step S60. It also uses the Latin hypercube sampling method to solve the negative performance effect equation set. First, the parameter spaces of the morphology parameter, thickness parameter, thermal conductivity parameter, light absorption rate parameter, and dispersion parameter are divided. Then, a set of sample point sets are generated in this parameter space using the Latin hypercube sampling method. These sample points are input into the negative performance effect equation set for numerical calculation. Finally, the least squares method is used to fit the numerical calculation results to obtain the second analytical solution. At the same time, the interval analysis method is used to process the numerical calculation results to obtain the second range solution. The purpose of this step is to obtain the analytical function expression describing the negative performance indicators and the value ranges of each indicator, laying the foundation for the subsequent game analysis.

[0200] The specific implementation of step S80 is to construct a game model. First, a positive game payoff function is constructed based on the first analytical solution, and positive performance indicators such as the photothermal conversion efficiency, heat conduction efficiency, morphology influence coefficient, and dispersion enhancement coefficient are combined into a weighted function. Secondly, a negative game payoff function is constructed based on the second analytical solution, and negative performance indicators such as the structural attenuation coefficient, interface impedance coefficient, agglomeration loss coefficient, and temperature failure coefficient are combined into a weighted function. Then, positive and negative game constraint conditions are constructed based on the first range solution and the second range solution respectively. Finally, these payoff functions and constraint conditions are combined into a game model. The purpose of this step is to establish a game relationship between two entities, positive and negative, providing a basis for subsequent optimal design.

[0201] The specific implementation of step S90 is to solve the game model using a genetic algorithm. First, the parameters of the genetic algorithm are initialized, including the population size, crossover rate, mutation rate, and number of iterations, etc. Then, an initial population is generated, and each individual contains morphology parameters, thickness parameters, thermal conductivity parameters, light absorption rate parameters, and dispersion parameters. The initial population is input into the game model to calculate the fitness. Next, selection, crossover, and mutation operations are performed on the population to generate a new population. This process is repeated until the convergence condition is met. Finally, the obtained optimal parameter solutions are output, including the optimal morphology parameters, optimal thickness parameters, optimal thermal conductivity parameters, optimal light absorption rate parameters, and optimal dispersion parameters. The genetic algorithm is a stochastic optimization algorithm based on biological evolution, with strong global search ability, and can effectively solve the multi-objective optimization problem in the game problem.

[0202] The specific implementation of step S100 has been described in detail above and will not be elaborated here. The specific implementation of step S110 is merely to coat the photovoltaic panel with the optimized graphene nano-coating, which also does not need to be elaborated in detail.

[0203] In summary, the present invention proposes an optimization method for the photothermal effect of graphene nano-coatings based on multi-physical field coupling. First, a variety of characterization means are used to obtain key parameters, and the parameters are subjected to multivariate mixed decomposition. Then, positive and negative performance action equation sets are constructed to describe the complex coupling relationship between material parameters. Next, the Latin hypercube sampling and genetic algorithm are used to solve the game model to obtain the optimal design parameters. This method fully considers the multi-scale characteristics of the material, establishes a comprehensive coupling model from microscopic mechanism to macroscopic performance, and can provide effective guidance for the actual preparation and application of graphene nano-coatings.

[0204] A specific embodiment 1 of the present invention is provided below. The specific implementation of steps S10 - S90 in this embodiment 1 is described in detail as follows: The specific implementation of step S10 is to obtain the morphology parameters, thickness parameters, thermal conductivity parameters, light absorption rate parameters, and dispersion parameter D of the graphene nano-coatings Among them, the morphological parameter M(t) is obtained by characterization with an atomic force microscope, and the following steps are adopted:

[0205] (1) Cut the graphene nano-coating sample into a size of 10 mm × 10 mm and perform surface cleaning treatment.

[0206] (2) Use an atomic force microscope (AFM) to scan the surface of the sample. The scanning range is 20 μm × 20 μm, the scanning frequency is 1 Hz, and the acquisition resolution is 512 × 512 pixels.

[0207] (3) Use image processing software to perform plane fitting and noise filtering on the AFM scan data to obtain the time series of the morphological parameter M(t) of the sample.

[0208] The thickness parameter d is obtained by lateral testing with a scanning electron microscope (SEM). The thermal conductivity parameter K(t) is tested by the transient hot wire method. The main steps are as follows:

[0209] (4) Process the coating sample into a test strip with dimensions of 50 mm × 10 mm × 2 mm.

[0210] (5) Fix the hot wire probe on the surface of the sample and apply thermal conductive silicone grease.

[0211] (6) Apply a constant current and record the curve of the surface temperature of the sample changing with time.

[0212] (7) According to the formula Calculate the thermal conductivity parameter, where Q is the heating power, L is the length of the hot wire, t 1 ,t 2 is the test time point, and ΔT is the temperature rise.

[0213] The light absorption rate parameter A p is obtained by testing with a spectrophotometer. The specific steps are as follows:

[0214] (8) Calibrate the 100% transmittance with a standard white board.

[0215] (9) Perform an absorption spectrum scan on the sample in the wavelength range of 200 - 2500 nm.

[0216] (10) According to the formula A p = 1 - R - T to calculate the light absorption rate, where R is the reflectance and T is the transmittance.

[0217] The dispersion parameter D s is tested by the dynamic light scattering method. The main steps include:

[0218] (11) Ultrasonically disperse the coating sample in deionized water.

[0219] (12) The particle size distribution of the sample was measured using a dynamic light scattering instrument.

[0220] (13) According to the formula the dispersity was calculated, where w i is the weight of the i-th particle size interval, d i is the average particle size of the i-th interval, d max is the maximum particle size, and m is the number of intervals.

[0221] Finally, the obtained morphology parameters, thickness parameters, thermal conductivity parameters, light absorption rate parameters, and dispersity parameters were established in a parameter database to provide data support for subsequent analysis and calculation.

[0222] The specific implementation of step S20 is to perform a multivariate mixed decomposition calculation on the morphology parameter M(t) to obtain the morphology stable component M s (t) and the morphology variation component M v (t). The specific process is as follows:

[0223] (1) Construct a set of basis functions for the morphology parameter M(t), including a stable basis function subset {φ i (t)} and a variation basis function subset {ψ j (t)}, such as exponential functions and trigonometric functions.

[0224] (2) Use the recursive least squares method to decompose the time series data of the morphology parameter M(t) with basis functions to obtain:

[0225] M(t) = K s (t) + M v (t) + ξ m ;

[0226]

[0227] where α i , β j are decomposition coefficients, ξ m is the decomposition error term, and n and m are the numbers of stable and variation basis functions respectively.

[0228] (3) Linearly combine the obtained decomposition coefficients α i , β j with the stable basis function subset {φ i (t)} and the variation basis function subset {ψ j (t)} respectively to obtain the morphology stable component M s (t) and the morphology variation component M v (t).

[0229] (4) Calculate the morphology parameter M(t) minus the morphology stable component M s(t) and the morphological change component M v The difference between (t) to obtain the decomposition error term ξ of the morphological parameter m .

[0230] This multivariate hybrid decomposition method based on empirical mode decomposition (EMD) can well describe the periodic variation and attenuation characteristics of material parameters.

[0231] The specific implementation of step S30 is to perform multivariate hybrid decomposition calculation on the thermal conductivity parameter K(t) to obtain the thermal conductivity stable component K s (t) and the thermal conductivity change component K v (t). The specific process is as follows:

[0232] (1) Construct a set of basis functions for the thermal conductivity parameter K(t), including a stable basis function subset {θ i (t)} and a change basis function subset {ω j (t)}.

[0233] (2) Use the recursive least squares method to perform basis function decomposition on the time series data of the thermal conductivity parameter K(t) to obtain:

[0234] K(t) = K s (t) + K v (t) + ξ k ;

[0235]

[0236] In the formula, γ i , δ j are decomposition coefficients, ξ k is the decomposition error term, and p and q are the numbers of stable and change basis functions respectively.

[0237] (3) Linearly combine the obtained decomposition coefficients γ i , δ j with the stable basis function subset {θ i (t)} and the change basis function subset {ω j (t)} respectively to obtain the thermal conductivity stable component K s (t) and the thermal conductivity change component K v (t).

[0238] (4) Calculate the difference between the thermal conductivity parameter K(t) minus the thermal conductivity stable component K s (t) and the thermal conductivity change component K v (t) to obtain the decomposition error term ξ k .

[0239] This EMD-based multi-component hybrid decomposition method can well characterize the variation characteristics of the thermal conductivity parameter.

[0240] The specific implementation of step S40 is to construct a forward performance action equation set, including a photothermal conversion equation, a heat conduction equation, a morphology influence equation, and a dispersion synergistic equation.

[0241] The photothermal conversion equation describes the influence of the light absorption rate A p , the morphology stable component M s (t), and the thermal conductivity stable component K s (t) on the photothermal conversion efficiency η ph , and is specifically expressed as:

[0242]

[0243] Among them, λ 1 , λ 2 , λ 3 are weight coefficients, σ m is the morphology feature standard deviation, τ is the characteristic time constant, and ε ph is the error term. The first term describes the coupling relationship between the light absorption rate and the morphology stability, the second term represents the influence of the thermal conductivity on the photothermal conversion, and the third term reflects the synergistic effect of light absorption-thermal conduction.

[0244] The heat conduction equation describes the influence of the thermal conductivity parameter K(t), the thickness parameter d, and the morphology variation component M v (t) on the heat conduction efficiency Q tc , and is expressed in the form of a 3×3 matrix:

[0245]

[0246] In the formula, k ij is the heat conduction coefficient matrix element, and ε tc is the error term. This matrix form can effectively describe the multi-dimensional coupling effect among the three key parameters.

[0247] The morphology influence equation describes the influence of the morphology parameter M(t), the thickness parameter d, and the dispersion parameter D s on the photothermal performance, and is specifically expressed as:

[0248]

[0249] In the formula, α f , β f , γ f are influence factors, and ε f is the error term. This equation introduces the first-order derivative and second-order derivative of the morphology parameter, as well as the ratio of the thickness to the dispersion, and describes the influence of the morphology change rate, acceleration, and morphology-structure synergy.

[0250] The dispersion enhancement equation describes the influence of the dispersion parameter D s , the morphology parameter M(t), and the thermal conductivity variation component K v (t) on the performance improvement, specifically expressed as:

[0251]

[0252] In the formula, η 1 , η 2 , η 3 are the enhancement coefficients, M 0 , K 0 are the reference values, and ε d is the error term. This equation uses exponential terms, linear terms, and square root terms to describe the regulation of dispersion on morphology, the influence of thermal conductivity variation, and their non-linear coupling.

[0253] By constructing these forward performance effect equations, the multi-physical field coupling relationship between the key parameters of the material can be effectively described, providing a basis for subsequent optimization design.

[0254] The specific implementation of step S50 is to construct a negative performance effect equation set, including a structure attenuation equation, an interface impedance equation, an agglomeration loss equation, and a temperature failure equation.

[0255] The structure attenuation equation describes the influence of the morphology variation component M v (t), the thickness parameter d, and the thermal conductivity variation component K v (t) on the structure attenuation coefficient D s , specifically expressed as:

[0256]

[0257] Among them, ρ 1 , ρ 2 , ρ 3 are the attenuation coefficients, M max , d 0 , K max are the maximum values of the morphology parameter, thickness, and thermal conductivity respectively, and ε s is the error term. This equation uses a normalized form to describe the influence of each parameter on the structure stability.

[0258] The interface impedance equation describes the influence of the morphology parameter M(t), the thickness parameter d, and the thermal conductivity parameter K(t) on the interface thermal resistance Z i , expressed in the form of a 3×3 matrix:

[0259]

[0260] In the formula, r ijis the impedance coefficient matrix element, ε i is the error term. This equation also describes the coupling effect of the three parameters in matrix form.

[0261] The agglomeration loss equation describes the dispersity parameter D s , the morphology parameter M(t), and the thermal conductivity parameter K(t) on the agglomeration loss coefficient L a , and is specifically expressed as:

[0262]

[0263] where μ 1 , μ 2 , μ 3 is the loss coefficient, D max , M c , K c are the critical values of dispersity, morphology, and thermal conductivity respectively, and ε a is the error term. This equation reflects the negative impacts of reduced dispersity, deteriorated morphology, and decreased thermal conductivity on performance.

[0264] The temperature failure equation describes the thermal conductivity stable component K s (t), the thickness parameter d, and the dispersity parameter D s on the temperature failure coefficient F t , and is specifically expressed as:

[0265]

[0266] In the formula, ω 1 , ω 2 , ω 3 is the failure coefficient, K T , d T , D T , τ T are the temperature-related thermal conductivity, critical thickness, dispersity, and characteristic time respectively, and ε t is the error term. This equation considers the linear and non-linear effects of thermal conductivity stability, thickness, and dispersity on temperature failure.

[0267] By constructing these negative performance effect equations, the interaction between the key parameters of the material can be effectively described, laying a foundation for subsequent game analysis.

[0268] The specific implementation of step S60 is to use the Latin hypercube sampling method to solve the forward performance effect equations to obtain the first analytical solution and the first range solution. The specific process is as follows:

[0269] (1) Divide the morphology parameter M(t), the thickness parameter d, the thermal conductivity parameter K(t), the light absorption rate parameter A p and the dispersity parameter Ds parameter space

[0270] (2) Generate a set of sample point sets {M, d, K, A p , D s} in this parameter space by using the Latin hypercube sampling method

[0271] (3) Input these sample points into the forward performance function equations for numerical calculation to obtain a series of performance index values, such as {η ph , Q tc , F m , E d}

[0272] (4) Fit the numerical calculation results by using the least squares method to obtain the first analytical solution

[0273] (5) Process the numerical calculation results by using the interval analysis method to obtain the first range solution

[0274] Latin hypercube sampling is an efficient multi-parameter sampling method that can better cover the parameter space with a limited sample size. The least squares method can extract the analytical performance response function from a large amount of calculation data, while the interval analysis can give the value ranges of various performance indicators, providing the necessary data support for subsequent game analysis

[0275] The specific implementation of step S70 is similar to that of step S60. It also uses the Latin hypercube sampling method to solve the negative performance function equations to obtain the second analytical solution and the second range solution. The specific process is as follows

[0276] (1) Divide the parameter space of the morphology parameter M(t), thickness parameter d, thermal conductivity parameter K(t), light absorption rate parameter A p and dispersion parameter D s

[0277] (2) Generate a set of sample point sets {M, d, K, A p , D s} in this parameter space by using the Latin hypercube sampling method

[0278] (3) Input these sample points into the negative performance function equations for numerical calculation to obtain a series of performance index values, such as {D s , Z i , L a , F t}

[0279] (4) Fit the numerical calculation results by using the least squares method to obtain the second analytical solution​

[0280] (5) The interval analysis method is used to process the numerical calculation results and obtain the second range solution

[0281] The purpose of this step is to obtain the analytical function expression describing the negative performance indicators and the value range of each indicator, laying the foundation for subsequent game analysis.

[0282] The specific implementation method of step S80 is to construct a game model. First, a forward game payment function is constructed based on the first analytical solution:

[0283] U p =w 1 η ph +w 2 Q tc +w 3 F m +w 4 E d +ε p ;

[0284] Where, w 1 ,w 2 ,w 3 ,w 4 is the weight coefficient of each performance index, ε p is the error term of the payment function.

[0285] Secondly, based on the second analytical solution, the negative game payment function is constructed:

[0286] U n =v 1 D s +v 2 Z i +v 3 L a +v 4 F t +ε n ;

[0287] In the formula, v 1 ,v 2 ,v 3 ,v 4 is the weight coefficient of each performance index, ε n is the error term of the payment function.

[0288] Then construct positive and negative game constraints based on the first range solution and the second range solution respectively:

[0289]

[0290] where x is the positive policy variable vector, y is the negative policy variable vector, and g 1 , g 2 is the positive constraint function, h 1 , h 2 is the negative constraint function, b 1 , b 2 , c 1 , c 2 are the constraint boundary values.

[0291] Finally, combine these payoff functions and constraints into a game model:

[0292] x = max x∈X min y∈Y (U p - αU n );

[0293] where α is the trade-off coefficient. The purpose of this step is to establish the game relationship between the positive and negative agents and provide a basis for subsequent optimal design.

[0294] The specific implementation of step S90 is to use the genetic algorithm to solve the game model and obtain the optimal parameter solution. The specific process is as follows:

[0295] (1) Initialize the parameters of the genetic algorithm, including the population size N, the crossover rate p c , the mutation rate p m and the number of iterations T.

[0296] (2) Generate the initial population X 0 = {x 1 , x 2 ,..., x N}, and each individual x i = {M, d, K, A p , D s} contains all the parameters to be optimized.

[0297] (3) Input the initial population into the game model to calculate the fitness function value:

[0298]

[0299] where λ i is the penalty factor, p i is the violation degree of the i-th constraint, and n is the total number of constraints.

[0300] (4) Perform selection, crossover, and mutation operations on the population to generate a new population X t+1 .

[0301] (5) Repeat steps (3)-(4) until the convergence condition t = T is satisfied, and output the optimal parameter solution X * ={M opt ,d opt ,K opt ,A opt ,D opt}}。

[0302] The genetic algorithm is a stochastic optimization algorithm based on biological evolution, with strong global search ability, and can effectively solve the multi-objective optimization problem in the game problem. Through this step, the optimal design parameters of the graphene nano-coating are finally obtained.

[0303] The specific principle of this Embodiment 1 includes:

[0304] 1. Multi-parameter characterization and time-evolution analysis

[0305] Firstly, a variety of characterization means are used to obtain the key parameters of the graphene nano-coating, including the morphology parameter M(t), the thickness parameter d, the thermal conductivity parameter K(t), and the light absorption rate parameter A p and the dispersion parameter D s . These parameters reflect the microscopic structure characteristics, macroscopic performance indicators, and environmental effect of the material.

[0306] To better describe the variation law of these parameters, the present invention adopts a multi-variable hybrid decomposition method based on empirical mode decomposition (EMD) to divide the morphology parameter and the thermal conductivity parameter into stable components and variable components respectively. This decomposition method can effectively capture the periodic evolution and non-linear change characteristics in the material parameters, providing necessary data support for subsequent performance modeling and optimization.

[0307] 2. Forward performance coupling modeling

[0308] Based on the obtained key parameters, the present invention constructs a forward performance action equation set including a photothermal conversion equation, a heat conduction equation, a morphology influence equation, and a dispersion enhancement equation. These equations describe the complex coupling relationship between the material parameters and can comprehensively predict the photothermal conversion performance of the coating.

[0309] The photothermal conversion equation reflects the influence of the light absorption rate A p , the stable component M s (t) of the morphology, and the stable component K s (t) of the thermal conductivity on the photothermal conversion efficiency η ph . The heat conduction equation describes the coupling effect of the thermal conductivity parameter K(t), the thickness parameter d, and the variable component M v (t) of the morphology on the heat conduction efficiency Q tc . The morphology influence equation depicts the morphology parameter M(t), the thickness parameter d, and the dispersion parameter Ds Influence on photothermal performance. The dispersion enhancement equation reflects the influence of the dispersion parameter D s , the morphology parameter M(t), and the thermal conductivity variation component K v (t) on performance improvement. These equations can effectively capture the multi-physical field coupling relationships between material parameters.

[0310] 3. Negative performance coupling modeling

[0311] In addition to the positive performance, the present invention also constructs a set of equations for negative performance effects, including the structure attenuation equation, the interface impedance equation, the agglomeration loss equation, and the temperature failure equation. These equations describe the influence of material parameters on the attenuation of coating performance and provide the necessary data support for subsequent game analysis.

[0312] The structure attenuation equation reflects the influence of the morphology variation component M v (t), the thickness parameter d, and the thermal conductivity variation component K v (t) on the structural stability. The interface impedance equation describes the coupling effect of the morphology parameter M(t), the thickness parameter d, and the thermal conductivity parameter K(t) on the interface thermal resistance. The agglomeration loss equation depicts the influence of the dispersion parameter D s , the morphology parameter M(t), and the thermal conductivity parameter K(t) on performance attenuation. The temperature failure equation reflects the influence of the thermal conductivity stable component K s (t), the thickness parameter d, and the dispersion parameter D s on performance under high-temperature conditions.

[0313] 4. Game theory optimization strategy

[0314] Based on the constructed sets of equations for positive and negative performance effects, the present invention proposes an optimization strategy based on game theory. First, a positive game payoff function and constraint conditions are constructed according to the first analytical solution and the first range solution, and at the same time, a negative game payoff function and constraint conditions are constructed according to the second analytical solution and the second range solution. Then, these payoff functions and constraint conditions are combined into a game model, and a genetic algorithm is used for multi-objective optimization solution. This game mechanism can maximize the positive performance index while minimizing the negative performance index, thus achieving the global optimum of material performance.

[0315] As a stochastic optimization algorithm based on biological evolution, the genetic algorithm has strong global search ability and can effectively solve the multi-objective optimization problem in the game problem. The present invention uses the genetic algorithm to optimize the game model and finally obtains the optimal design parameters of the graphene nano-coating, including the morphology parameter M opt , the thickness parameter d opt , the thermal conductivity parameter K opt , the light absorption rate parameter A opt and the dispersion parameter Dopt These parameter values can not only maximize the photothermal conversion performance but also minimize various negative effects, providing a reliable theoretical basis for the actual preparation in engineering applications.

[0316] To better understand and implement the present invention, the following provides Example 2 of a specific application scenario of the present invention: A certain photovoltaic enterprise desires to improve the photothermal conversion performance of its photovoltaic cell modules and decides to coat a graphene nano-coating on the surface of the cells. To maximize the photothermal conversion efficiency of the coating and at the same time ensure its long-term stability in a high-temperature environment, the enterprise uses the optimization method proposed by the present invention to design and optimize the key parameters of the coating.

[0317] First, the enterprise purchased a batch of graphene nano-materials and conducted a comprehensive characterization on them. By using an atomic force microscope (AFM) to scan the morphology of the coating samples, the variation curve of the morphology parameter M(t) with time was obtained, as shown in Table 1. At the same time, the thermal conductivity parameter K(t) of the coating was measured by the transient hot wire method, and the test results are shown in Table 2. In addition, the light absorption rate parameter A p was obtained through a spectrophotometer test, as shown in Table 3; the dispersion parameter D was measured by a dynamic light scattering instrument s , as shown in Table 4; finally, the sample was horizontally tested by a scanning electron microscope (SEM) to obtain the thickness parameter d, as shown in Table 5.

[0318] Table 1 Test data of the morphology parameter M(t)

[0319] Time (h) M(t) (μm); 0 0.35 100 0.37 300 0.40 500 0.43 700 0.45 900 0.47 1100 0.48

[0320] Table 2 Test data of the thermal conductivity parameter K(t)

[0321]

[0322]

[0323] Table 3 Light absorption rate parameter A p Test data

[0324] Wavelength (nm) <![CDATA[A p ;]]> 300 0.92 500 0.90 700 0.88 900 0.86 1100 0.84 1300 0.82 1500 0.80

[0325] Table 4 Dispersion parameter D s Test data

[0326] Time (h) <![CDATA[D s ;]]> 0 0.85 100 0.82 300 0.79 500 0.76 700 0.73 900 0.70 1100 0.67

[0327] Table 5 Test data of the thickness parameter d

[0328] Sample d (μm); 1 3.2 2 3.5 3 3.8 4 4.1 5 4.4 6 4.7 7 5.0

[0329] With these basic test data, the enterprise then carried out parameter decomposition and coupling relationship modeling. First, the empirical mode decomposition (EMD) method was used to perform multivariate mixed decomposition on the morphology parameter M(t) and the thermal conductivity parameter K(t), obtaining their stable components and variable components:

[0330] Morphology parameter decomposition:

[0331] M(t) = M s (t) + M v (t) + ξ m ;

[0332]

[0333] Thermal conductivity parameter decomposition:

[0334] K(t) = K s (t) + K v (t) + ξ k ;

[0335]

[0336]

[0337] Among them, φ i (t), ψ j (t) are the stable and variable basis functions of the morphology parameter, and θ i (t), ω j (t) are the stable and variable basis functions of the thermal conductivity parameter. The coefficients α i , β j , γ i , δ j and the decomposition error terms ξ m , ξ k will be used as the key inputs for subsequent model construction.

[0338] Next, the enterprise constructed a forward performance action equation set to describe the influence of each parameter on the photothermal conversion performance:

[0339] Photothermal conversion equation:

[0340]

[0341] Heat conduction equation:

[0342]

[0343] Morphology influence equation:

[0344]

[0345] Dispersion synergistic equation:

[0346]

[0347] Meanwhile, the enterprise also constructed a system of equations for negative performance effects, which describes the influence of each parameter on the attenuation of coating performance:

[0348] Structure attenuation equation:

[0349]

[0350] Interface impedance equation:

[0351]

[0352] Agglomeration loss equation:

[0353]

[0354] Temperature failure equation:

[0355]

[0356] Then, the enterprise generated 200 sample points in the parameter space using the Latin hypercube sampling method and substituted them into the above-mentioned forward and negative performance effect equations for numerical calculation, obtaining a series of performance index values.

[0357] Based on these calculation results, the enterprise used the least squares method to fit and obtained the first analytical solution:

[0358]

[0359] Meanwhile, the interval analysis method was used to obtain the first range solution:

[0360]

[0361] Next, the enterprise generated 150 sample points in the parameter space using the Latin hypercube sampling method and substituted them into the negative performance effect equations for numerical calculation, obtaining a series of negative performance index values.

[0362] Based on these calculation results, the enterprise used the least squares method to fit and obtained the second analytical solution:

[0363] d * = 4.0,

[0364] Meanwhile, the interval analysis method was used to obtain the second range solution:

[0365] [d L,d U = [3.6, 4.4],

[0366] With these analytical solutions and range solutions, the enterprise constructed a game model:

[0367] Positive payment function:

[0368] U p = 0.4η ph + 0.3Q tc + 0.2F m + 0.1E d + ε p ;

[0369] Negative payment function:

[0370] U n = 0.3D s + 0.3Z i + 0.2L a + 0.2F t + ε n ;

[0371] Game model objective function:

[0372] J = max x∈X min y∈Y (U p - 0.8U n );

[0373]

[0374] Finally, the enterprise used the genetic algorithm to solve the above game model and obtained the optimal coating design parameters:

[0375] M opt = 0.42, d opt = 4.0, K opt = 7.8, a opt = 0.90, D opt = 0.75;

[0376] According to these optimal parameters, the enterprise optimized the design and preparation of the graphene nano - coating.

[0377] The specific process is as follows:

[0378] (1) Preparation of graphene raw materials: Dissolve graphene powder in deionized water, ultrasonically disperse for 10 min, then add an appropriate amount of surfactant and stir for 30 min to obtain a graphene dispersion with a concentration of 5 mg / mL.

[0379] (2) Coating preparation: The backplane of the photovoltaic cell is subjected to surface cleaning treatment, and then a graphene dispersion liquid is coated on the cell surface by the brushing method. The coating speed is 5 mm / s and the coating pressure is 50 kPa.

[0380] (3) Heat treatment process: The coated sample is placed in a vacuum oven, heated to 150 °C and held for 1 h, and then naturally cooled to room temperature.

[0381] (4) Surface rolling: The coated sample is rolled using a double-roll press. The rolling spacing is 0.5 mm and the rolling speed is 3 mm / s.

[0382] For the graphene nano-coating sample prepared by the above optimized process, its performance indicators are as follows: Photothermal conversion efficiency η ph : 0.88; Thermal conduction efficiency Q tc : 0.72; Morphology influence coefficient F m : 0.65; Dispersion enhancement coefficient E d : 0.78; Structure attenuation coefficient D s : 0.72; Interface impedance coefficient Z i : 0.75; Agglomeration loss coefficient L a : 0.65; Temperature failure coefficient F t : 0.70.

[0383] It can be seen from the above performance indicators that compared with the unoptimized coating, the optimized coating of the present invention has been significantly improved in terms of photothermal conversion efficiency, thermal conduction performance, and environmental stability. Specifically:

[0384] 1. Photothermal conversion efficiency η ph It has increased from 0.82 before optimization to 0.88, an increase of 7.3%. This is mainly due to the fact that the optimized coating has a higher light absorption rate and more optimized morphology-thermal conductivity characteristics.

[0385] 2. Thermal conduction efficiency Q tc It has increased from 0.65 before optimization to 0.72, an increase of 10.8%. This is mainly because the optimized coating is thinner and has better thermal conductivity, improving the heat transfer efficiency.

[0386] 3. Structure attenuation coefficient D s It has decreased from 0.85 before optimization to 0.72, a decrease of 15.3%. This is attributed to the better control of the morphology change, thickness, and thermal conductivity of the optimized coating, improving the structural stability.

[0387] 4. Temperature failure coefficient F tIt is reduced from 0.80 before optimization to 0.70, a reduction of 12.5%. This is mainly due to the optimized coating having higher thermal conductivity stability, a thinner thickness, and a better dispersion state, effectively suppressing the performance decay at high temperatures.

[0388] It should be noted that the detailed explanations of the variables involved in the description of the present invention are shown in Table 6 below.

[0389] Table 6 Explanation of Variables

[0390]

[0391]

[0392] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention.

Claims

1. A method for optimizing the photothermal effect of graphene nano-coating of photovoltaic panels, characterized in that: The following steps are involved: S10, obtaining morphology parameters, thickness parameters, thermal conductivity parameters, absorbance parameters and dispersion parameters of the graphene nanocoating; S20, performing multivariate mixed decomposition calculation on the morphology parameters to obtain a morphology stable component and a morphology variable component; S30, performing multivariate mixed decomposition calculation on the thermal conductivity coefficient parameter to obtain a thermal conductivity stable component and a thermal conductivity variable component; S40, constructing a group of forward performance action equations based on the morphology parameter, the thickness parameter, the thermal conductivity parameter, the absorbance parameter, and the dispersion parameter; S50, constructing a negative performance action equation group based on the morphology parameter, the thickness parameter, the thermal conductivity parameter, the absorbance parameter and the dispersion parameter; S60, solving the forward performance action equations by using a Latin hypercube sampling method according to the parameter range of the morphology parameter, the thickness parameter, the thermal conductivity parameter, the absorbance parameter, and the dispersion parameter to obtain a first analytical solution and a first range solution; S70, solving the negative performance action equations using a Latin hypercube sampling method according to the parameter range of the morphology parameter, the thickness parameter, the thermal conductivity parameter, the absorbance parameter, and the dispersion parameter to obtain a second analytical solution and a second range solution; S80, constructing a game model using the first analytical solution, the first range solution, the second analytical solution, and the second range solution; S90, solving the game model using a genetic algorithm, setting a crossover rate and a mutation rate, and obtaining an optimal morphology parameter, an optimal thickness parameter, an optimal thermal conductivity parameter, an optimal absorbance parameter, and an optimal dispersion parameter of the graphene nanocoating through multi-generation iterative optimization; S100, optimizing the graphene nanocoating according to the optimal morphology parameter, the optimal thickness parameter, the optimal thermal conductivity parameter, the optimal absorbance parameter, and the optimal dispersion parameter; S110, coating the photovoltaic panel with the optimized graphene nano-coating.

2. The method according to claim 1, characterized in that The step S10 specifically includes: Step 101, using an atomic force microscope to characterize the surface morphology of the graphene nanocoating to obtain the morphology parameters; Step 102: Using a hot wire method testing device to test the thermal conductivity of the graphene nano coating to obtain the thermal conductivity parameter; Step 103: using a laser thermal conductivity system to test the thermal conductivity of the graphene nano coating to obtain the absorbance parameter; Step 104: using a dynamic light scattering instrument to perform a dispersion test on the graphene nanocoating to obtain the dispersion parameter; Step 105: Use a scanning electron microscope to perform a transverse test on the graphene nanocoating to obtain the thickness parameter; Step 106: Establish a parameter database of the morphology parameter, the thermal conductivity parameter, the absorbance parameter, the dispersion parameter, and the thickness parameter.

3. The method according to claim 1, characterized in that The step S20 specifically includes: Step 201, constructing a basis function set of the morphology parameters, including a stable basis function subset and a variable basis function subset; Step 202, using recursive least square method to perform basis function decomposition on the morphology parameters; Step 203, linearly combining the decomposed coefficients with the stable basis function subset to obtain the morphology stable component; Step 204, linearly combining the decomposed coefficients with the variation basis function subset to obtain the morphology variation component; Step 205: Calculate the difference between the morphology parameter and the morphology stable component and the morphology variable component to obtain the morphology parameter decomposition error term.

4. The method according to claim 1, characterized in that The step S30 specifically includes: Step 301, constructing a basis function set of the thermal conductivity parameter, including a stable basis function subset and a variable basis function subset; Step 302: using recursive least square method to perform basis function decomposition on the thermal conductivity parameter; Step 303, linearly combining the decomposed coefficients with the stable basis function subset to obtain the thermally conductive stable component; Step 304, linearly combining the decomposed coefficients with the variable basis function subset to obtain the thermal conductivity variable component; Step 305: Calculate the difference between the thermal conductivity parameter and the thermal conductivity variable component to obtain a decomposition error term of the thermal conductivity parameter.

5. The method according to claim 1, characterized in that The step S40 specifically includes: Step 401, constructing the light-to-heat conversion equation, inputting the absorbance parameter, the morphology stability component and the thermal conductivity stability component into the light-to-heat conversion equation to obtain the light-to-heat conversion coefficient; Step 402, constructing the heat conduction equation, inputting the thermal conductivity parameter, the thickness parameter and the morphology variation component into the heat conduction equation to obtain a heat conduction efficiency matrix; Step 403, constructing the morphology influence equation, inputting the morphology parameter, the thickness parameter and the dispersion parameter into the morphology influence equation to obtain the morphology influence coefficient; Step 404: construct the dispersion enhancement equation, input the dispersion parameter, the morphology parameter and the thermal conductivity variation component into the dispersion enhancement equation to obtain the dispersion enhancement coefficient.

6. The method according to claim 1, characterized in that The step S50 specifically includes: Step 501, constructing the structural attenuation equation, inputting the morphology variation component, the thickness parameter and the thermal conductivity variation component into the structural attenuation equation to obtain the structural attenuation coefficient; Step 502, constructing the interface impedance equation, inputting the morphology parameter, the thickness parameter and the thermal conductivity parameter into the interface impedance equation to obtain the interface impedance coefficient; Step 503, constructing the agglomeration loss equation, inputting the dispersion parameter, the morphology parameter and the thermal conductivity parameter into the agglomeration loss equation to obtain the agglomeration loss coefficient; Step 504: construct the temperature failure equation, input the thermal stability component, the thickness parameter and the dispersion parameter into the temperature failure equation to obtain a temperature failure coefficient.

7. The method according to claim 1, characterized in that The step S60 specifically includes: Step 601, dividing the parameter space of the morphology parameter, the thickness parameter, the thermal conductivity parameter, the absorbance parameter and the dispersion parameter; Step 602: Generate a set of sample points in the parameter space using a Latin hypercube sampling method; Step 603: input the sample point set into the forward performance action equation group for numerical calculation; Step 604: Use the least square method to fit the numerical calculation result to obtain the first analytical solution; Step 605: Use an interval analysis method to process the numerical calculation result to obtain the first range solution.

8. The method according to claim 1, characterized in that The step S70 specifically includes: Step 701, dividing the parameter space of the morphology parameter, the thickness parameter, the thermal conductivity parameter, the absorbance parameter and the dispersion parameter; Step 702: Generate a set of sample points in the parameter space using a Latin hypercube sampling method; Step 703: input the sample point set into the negative performance action equation group for numerical calculation; Step 704: Use the least square method to fit the numerical calculation result to obtain the second analytical solution; Step 705: Use an interval analysis method to process the numerical calculation result to obtain the second range solution.

9. The method according to claim 1, characterized in that: The step S80 specifically includes: Step 801: construct a forward game payment function based on the first analytical solution; Step 802: construct a negative game payment function based on the second analytical solution; Step 803: constructing forward game constraint conditions based on the first range solution; Step 804: construct a negative game constraint condition based on the second range solution; Step 805: Combine the positive game payment function, the negative game payment function, the positive game constraint condition and the negative game constraint condition to form the game model.

10. The method according to claim 1, characterized in that The step S90 specifically includes: Step 901, initializing genetic algorithm parameters, including population size, crossover rate, mutation rate, and number of iterations; Step 902, generating an initial population, each individual comprising the morphology parameter, the thickness parameter, the thermal conductivity parameter, the absorbance parameter and the dispersion parameter; Step 903: input the initial population into the game model to calculate fitness; Step 904: performing selection, crossover and mutation operations on the initial population to generate a new population; Step 905: determine whether the new population meets the convergence condition, and if so, output the optimal solution; otherwise, return to step 903.

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