A Design Method for Solar Thermal Radiation Selective Absorbing Materials

Abstract

The present invention relates to the field of solar thermal radiation selective absorption materials, and particularly to a design method for solar thermal radiation selective absorption materials. The present invention fully considers the complex relationship between material structure parameters and spectral response in the design process of solar thermal radiation selective absorption materials. By constructing a multi-objective double annealing algorithm and accelerating it with a deep learning network, iterative and time-consuming calculations are eliminated. The combination of multi-objective and global and local double annealing greatly speeds up the design process, greatly saving the design time of micro-nano photon structure parameters and hardware costs; this design method also provides various candidate materials, enabling the selection of suitable materials and the thickness of each layer to meet the required optical requirements. Finally, the present invention effectively solves the problems of high design time cost, low applicability of high-dimensional design, and poor multi-objective design effect existing in the current design process of solar thermal radiation selective absorption materials.

Description

Technical Field

[0001] The present invention relates to the field of solar thermal radiation selective absorption materials, and specifically relates to a design method for solar thermal radiation selective absorption materials, which is a multi-objective dual annealing algorithm accelerated by deep learning. Background Art

[0002] Solar energy, as one of the most promising renewable resources, has attracted great interest. In various studies in this field, solar thermal radiation selective absorption materials have shown great potential in converting solar energy into available energy.

[0003] To maximize the utilization of solar energy, it is crucial to design an ideal solar thermal radiation selective absorption material. According to Wien's displacement law, an ideal solar thermal radiation selective absorption material should have a high absorption rate within the solar radiation spectrum range (0.3 - 2.5 micrometers) and a low emissivity in the infrared region (2.5 - 25 micrometers), so as to reduce heat leakage while efficiently absorbing solar thermal radiation. Based on Kirchhoff's law of thermodynamics, the emissivity of a material is equal to the absorption rate of the material. Therefore, a low emissivity in the infrared region is equivalent to a low absorption rate.

[0004] Micro-nano photon structures provide numerous advantages for the development of solar thermal radiation selective absorption materials, including a variety of patterned structures and the flexibility to combine different materials. Currently, intelligent design algorithms such as genetic algorithms and particle swarm algorithms are applied to design such micro-nano photon structures for solar thermal radiation selective absorption. However, these existing intelligent design algorithms have several problems: First, intelligent design algorithms rely on electromagnetic simulation calculations for data acquisition, and higher-dimensional designs require larger simulation calculations, thus significantly increasing the time cost of the design process; Second, popular intelligent design algorithms are prone to falling into local optimal solutions when facing high-dimensional design problems; Finally, existing intelligent design algorithms mainly focus on achieving single-objective designs and have poor effects when facing multi-objective design problems. Therefore, there is still a great demand for a powerful design solution to accelerate the development of ideal solar thermal radiation selective absorption materials. Such a solution will help overcome the problems existing in current intelligent design algorithms and achieve better results in a short time. Summary of the Invention

[0005] In view of the above existing problems or deficiencies, to solve the problems such as high design time cost, low applicability for high-dimensional designs, and poor effects in multi-objective designs in the current design process of solar thermal radiation selective absorption materials, the present invention provides a design method for solar thermal radiation selective absorption materials, which is a multi-objective dual annealing algorithm accelerated by deep learning.

[0006] A design method for solar thermal radiation selective absorption materials, based on a multi-objective dual annealing algorithm accelerated by deep learning, includes the following steps:

[0007] S1: Using FDTD (Finite Difference Time Domain method), within the given structural parameter range, calculate the physical model of the micro-nano photon structure for solar thermal radiation selective absorption to generate data samples. The data samples are the absorption spectra of the physical model in the solar radiation spectral range to the infrared region (within 0.3 - 25 microns), and randomly divide the data samples into a training set and a test set.

[0008] The physical model of the micro-nano photon structure is rich and can be a multi-layer thin film stacked with metal-dielectric materials, a two-dimensional grating structure, or other three-dimensional structures (such as cuboids, cubes, spheres, or cylinders, etc.). The corresponding types of structural parameters include the material composition of the micro-nano photon structure (usually two, the type of metal material and the type of dielectric material), and the corresponding structural size parameters (such as period, length, width, height, or diameter, etc.), which are adjusted accordingly according to the different micro-nano photon structures in use. The structural parameter range is a numerical range for dimension units such as length, width, and height (such as 10 - 100 nm); for types of material composition and other units, it is the type range in the material library, such as selected from within [magnesium fluoride, aluminum oxide, silicon dioxide]. Among them, both metal and dielectric materials have great degrees of freedom: they can be noble metal materials such as gold, silver, and platinum, or high-loss materials such as titanium, chromium, and tungsten; the dielectric can be various natural or artificially synthesized dielectric materials such as magnesium fluoride, aluminum oxide, and silicon dioxide.

[0009] S2: Construct a deep learning network for accelerating the multi-objective dual annealing algorithm. The model of the deep learning network includes an input layer, a hidden layer, and an output layer.

[0010] The length of the input layer is n, the number of types of structural parameters of the micro-nano photon structure described in S1. The hidden layer is constructed by m fully connected layers, which perform a non-linear transformation on the structural parameters of the micro-nano photon structure in the input layer and extract fitting features.

[0011] The number m of fully connected layers in the hidden layer and the size of each fully connected layer are not unique and are usually designed by empirical selection or open-source deep learning network model optimization algorithms such as Optuna.

[0012] The length of the output layer is 2501, corresponding to 2501 absorption spectrum points in the solar radiation spectral range to the infrared region (0.3 - 25 microns).

[0013] Initialize the structural parameters of the deep learning network, including setting the batch size, the total number of learning epochs, and the initial learning rate, using Nadam as the gradient descent optimizer, using the mean squared error (MSE) as the loss function, and using the Swish function as the activation function of the deep learning network.

[0014] S3: Use the training set obtained in S1 as the input layer and input it into the deep learning network constructed in S2 for training, and use the test set obtained in S1 to verify the accuracy performance of the deep learning network to obtain the trained deep learning network.

[0015] S4: Construct a multi-objective double annealing algorithm. The present invention uses a multi-objective double annealing algorithm for design, and the double annealing algorithm combines a global search algorithm and a local search algorithm.

[0016] Global search algorithms are generally good at identifying regions (basins in the search space) where the best solution might be found, but they often have difficulty finding the best solution within the basin. On the other hand, local search algorithms perform excellently in determining the ideal value within the basin.

[0017] The multi-objective double annealing algorithm proposed by the present invention can perform simultaneous design for two objectives; where the objective function FOM1 is the main design objective, and the constraint condition FOM2 is the limiting factor for FOM1, that is, the design logic of the multi-objective double annealing algorithm proposed by the present invention is:

[0018]

[0019] That is, while satisfying the constraint condition of FOM2 (FOM2 ≤ 0.1), maximize FOM1; FOM1 and FOM2 are respectively:

[0020]

[0021] In the formula, I AM1.5 (λ) represents the normal irradiance of solar thermal radiation at wavelength λ, α(λ) and ε(λ) respectively represent the normal absorptance of the solar thermal radiation selective absorption material in the solar radiation spectrum range and the infrared region at wavelength λ, and dλ represents the integration with respect to the wavelength.

[0022] The working logic of the multi-objective double annealing algorithm is:

[0023] 1), Randomly initialize the parameters of the multi-objective double annealing algorithm, set the initial temperature value T of the global annealing temperature, the Markov chain progress N = 0, and the Markov chain length is M;

[0024] 2), Set the currently randomly initialized parameters as the optimal parameter solution;

[0025] 3) Generate a new parameter solution by applying a random perturbation to the optimal parameter solution during the iteration process;

[0026] 4) Determine whether the new parameter solution satisfies the constraint conditions, specifically including:

[0027] Calculate whether the absorption rate spectrum of the new parameter solution satisfies the constraint condition FOM2 through FDTD: If it is satisfied, retain the new parameter solution and proceed to step 5, where N = N + 1; if it is not satisfied, repeat step 3 until a new parameter solution whose absorption rate spectrum satisfies the constraint condition FOM2 is found;

[0028] 5) Compare the new parameter solution with the optimal parameter solution, specifically including:

[0029] Calculate the difference df of FOM1 corresponding to the absorption rate spectra of the new parameter solution and the optimal parameter solution respectively through FDTD:

[0030] If df > 0, update the optimal parameter solution with the current new parameter solution and proceed to step 6;

[0031] If df ≤ 0, make a judgment with probability P, where probability P is expressed as e is the base of the natural logarithm function, and rand is a random number uniformly distributed in the interval (0, 1): If P > rand, update the optimal parameter solution with the current new parameter solution and proceed to step 6; if P ≤ rand, retain the optimal parameter solution and proceed to step 8;

[0032] 6) Perform local annealing on the optimal parameter solution updated in step 5, specifically including:

[0033] 6-1) Set the initial temperature value T of the local annealing L , the length of the local Markov chain is M L , the progress N of the local Markov chain L ;

[0034] 6-2) Set the optimal parameter solution as the local optimal parameter solution of the local annealing;

[0035] 6-3) Generate a local new parameter solution by applying a random perturbation to the local optimal parameter solution during the iteration process;

[0036] 6-4) Determine whether the local new parameter solution satisfies the constraint conditions, specifically including: Calculate whether the absorption rate spectrum of the local new parameter solution satisfies the constraint condition FOM2 through FDTD; if it is satisfied, retain the local new parameter solution and proceed to step 6-5, where N L = N L + 1; if it is not satisfied, repeat step 6-3 until a local new parameter solution whose absorption rate spectrum satisfies the constraint condition FOM2 is found;

[0037] 6-5), Compare the locally new parameter solution and the locally optimal parameter solution obtained in step 6-4, specifically including: Calculate the difference df of FOM1 corresponding to the absorption rate spectra of the locally new parameter solution and the locally optimal parameter solution respectively by FDTD:

[0038] If df > 0, update the locally optimal parameter solution with the current locally new parameter solution and go to step 6-6;

[0039] If df ≤ 0, make a judgment with probability P: If P > rand, update the locally optimal parameter solution with the current locally new parameter solution and go to step 6-6; If P ≤ rand, retain the locally optimal parameter solution and go to step 6-6;

[0040] 6-6), Determine whether the local Markov chain length, i.e., N L = M L : If the local Markov chain length is not reached, repeat step 6-3; If the local Markov chain length M L is reached, update the local annealing temperature T L at the local annealing attenuation rate K L ;

[0041] 6-7), Determine whether the local annealing temperature T L has dropped to the local termination temperature. If it has dropped to the local termination temperature, output the locally optimal parameter solution to step 7; If it has not dropped to the local termination temperature, enter step 6-3 with the updated local annealing temperature T L and the locally optimal parameter solution until T L drops to the local termination temperature.

[0042] 7), Update the optimal parameter solution with the locally optimal parameter solution;

[0043] 8), Determine whether the Markov chain length, i.e., N = M, is reached; If the Markov chain length is not reached, repeat step 3; If the Markov chain length M is reached, update the global annealing temperature T at the global attenuation rate K;

[0044] 9), Determine whether the global annealing temperature T has dropped to the global termination temperature. If it has dropped to the global termination temperature, output the optimal parameter solution as the final solution and calculate the FOM1 corresponding to the final solution by FDTD; If it has not dropped to the global termination temperature, enter step 3 with the updated annealing temperature T and the optimal parameter solution until it drops to the global termination temperature.

[0045] S5: Combine the deep learning network trained in S3 with the multi-objective double annealing algorithm in S4 to accelerate the calculation of the multi-objective double annealing algorithm by the deep learning network. Specifically: Replace the FDTD calculation part in the multi-objective double annealing algorithm in S4 with the deep learning network trained in S3; Input the parameter solution in the multi-objective double annealing algorithm into the trained deep learning network and output the corresponding absorption rate spectrum, and calculate FOM1 and FOM2 used in the multi-objective double annealing algorithm according to the absorption rate spectrum. Thus, all the parameters of the solar thermal radiation selective absorption material are obtained.

[0046] In summary, the present invention combines a global search algorithm and a local search algorithm to construct a multi-objective double annealing algorithm, and accelerates the multi-objective double annealing algorithm with a deep learning network. The addition of the deep learning network overcomes the cumbersome and time-consuming physical calculation processes of traditional numerical simulation methods and intelligent design algorithms, greatly saving the design time of micro-nano photon structure parameters and hardware costs. The present invention effectively solves the problems of high design time cost, poor applicability of high-dimensional design, and inability to handle multiple objectives existing in the current design process of solar thermal radiation selective absorption materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a schematic flow chart of the present invention;

[0048] Figure 2 is a schematic cross-sectional view of the physical model of the thin film photon structure in the embodiment;

[0049] Figure 3 is the parameter range of the data set generated by the thin film photon structure in the embodiment;

[0050] Figure 4 is a schematic structural view of the deep learning network in the embodiment;

[0051] Figure 5 is the MSE corresponding to the training set and test set of the trained deep learning network in the embodiment;

[0052] Figure 6 is the absorption rate spectrum predicted by the trained deep learning network in the embodiment and the absorption rate spectrum calculated by FDTD;

[0053] Figure 7 is the historical record of designing FOM1 in the embodiment when randomly selecting three different initial values;

[0054] Figure 8 is the final design result of the given physical model of the thin film photon structure in the embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0055] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0056] A design method for a solar thermal radiation selective absorption material is as Figure 1 shown, and specifically includes the following steps:

[0057] S1: Using FDTD, within a given range of structural parameters, calculate the physical model of the micro-nano photon structure for solar thermal radiation selective absorption to generate data samples. In this embodiment, the micro-nano photon structure is a thin-film photon structure stacked with metal-dielectric materials. Figure 2 is a schematic cross-sectional view of the physical model of the thin-film photon structure of this embodiment. In the embodiment, an 8-layer thin-film photon structure is selected, and the structure is composed of alternately stacked metal-dielectric layers; the top and bottom are fixed as magnesium fluoride antireflection layers and metal chromium layers respectively, and the metal of the remaining layers is any one of iron, titanium, tungsten, and chromium, and the material of the dielectric is any one of magnesium fluoride, alumina, and silica. The structural parameters of the thin-film photon structure used in the embodiment include T = [h1, h2, h3, h4, h5, h6, h7, n m , n i , where h1 - h7 are the thicknesses of each thin film from top to bottom, and the thickness of the bottom Cr layer is fixed at 200 nm; n m and n i are the material types of the metal and the dielectric respectively.

[0058] Figure 3 shows the given range of structural parameters used in the embodiment; the data sample is the absorption rate spectrum of the physical model in the range of 0.3 - 25 microns, where 2201 absorption rate spectrum points are equally spaced in the wavelength range of 0.3 - 2.5 microns, and 300 absorption rate spectrum points are equally spaced in the range of 2.5 - 25 microns. Finally, each set of sample data includes 2501 spectral rate spectrum points, and a total of 30000 sets of sample data are obtained. The data samples are randomly divided into a training set (80%, 24000 sets) and a test set (20%, 6000 sets) according to a ratio.

[0059] S2: Construct a deep learning network used to accelerate the multi-objective double annealing algorithm in the embodiment, as Figure 4 shown, including an input layer, a hidden layer, and an output layer.

[0060] The length of the input layer is 9, which is the type of structural parameters of the thin-film photon structure in the embodiment described in S1; the hidden layer is constructed by 6 fully connected layers with lengths of 32, 64, 128, 256, 512, and 1024 respectively, performing non-linear transformation on the structural parameters of the input layer and extracting fitting features; the length of the output layer is 2501, corresponding to 2501 absorption rate spectrum points in the solar radiation spectrum range to the infrared region (0.3 - 25 microns).

[0061] Initialize the structural parameters of the deep learning network, including setting the batch size to 32, the total number of learning epochs to 800, and the initial learning rate to 0.0001. Use Nadam as the gradient descent optimizer, mean squared error (MSE) as the loss function, and the Swish function as the activation function of the deep learning network.

[0062] S3: Use the training set obtained in S1 as the input layer and input it into the deep learning network constructed in S2 for training, and use the test set obtained in S1 to verify the performance of the deep learning network, obtaining a trained deep learning network. Figure 5 Shows the MSE corresponding to the training set and test set of the trained deep learning network in the embodiment. After 800 epochs, the epochs of the training set and test set tend to be stable and are both less than 10 -2 ; Figure 6 Shows that the trained deep learning network in the embodiment is used to predict the absorption rate spectrum. The absorption rate spectrum predicted by the deep learning network is in good agreement with the absorption rate spectrum calculated by FDTD, demonstrating the excellent prediction accuracy and generalization ability of the trained deep learning network used in the embodiment.

[0063] S4: Construct a multi-objective double annealing algorithm for the embodiment. The multi-objective double annealing algorithm proposed by the present invention can perform simultaneous design on two objectives; where the objective function FOM1 is used as the main design objective, and the constraint condition FOM2 is used as a limiting factor for FOM1. While satisfying the constraint condition of FOM2 (FOM2 ≤ 0.1), maximize FOM1.

[0064]

[0065] For the working logic of the multi-objective double annealing algorithm in the embodiment, please refer to the detailed description part of the invention. The details are as follows:

[0066] Set the initial value of the global annealing temperature T = 100, the global annealing decay rate K = 0.99, and the global annealing termination temperature is the global annealing temperature after decaying 2000 times by K (T × K 2000 ); The Markov chain progress N = 0, and the length of the Markov chain is M = 1000; Set the initial value of the local annealing temperature T L = 50, the local annealing decay rate K L = 0.9, and the local annealing termination temperature is the local annealing temperature after decaying 500 times by K L (T L × K L 500 ); The local Markov chain progress N L = 0, and the length of the local Markov chain is ML = 100.

[0067] S5: Combine the deep learning network trained in S3 with the multi-objective double annealing algorithm in S4 to accelerate the calculation of the multi-objective double annealing algorithm by the deep learning network. Specifically: Replace the FDTD calculation part in the multi-objective double annealing algorithm with the trained deep learning network; Input the parameter solution in the multi-objective double annealing algorithm into the trained deep learning network and predict the corresponding absorption rate spectrum, and calculate FOM1 and FOM2 used in the multi-objective double annealing algorithm according to the absorption rate spectrum. In this embodiment, as Figure 7 shown, the deep learning accelerated multi-objective double annealing algorithm proposed by the present invention is used for three design calculations on the thin film photon structure. While satisfying the constraint condition FOM2, the same FOM1 = 0.981 is obtained, indicating that the deep learning accelerated multi-objective double annealing algorithm proposed by the present invention has strong global search and design capabilities. The final design structure in the embodiment is as Figure 8 shown.

[0068] As can be seen from the above embodiments, compared with the traditional intelligent design algorithm, the present invention fully considers the relationship between the complex material structure parameters and the spectral response in the design process of the solar thermal radiation selective absorption material. By constructing a multi-objective double annealing algorithm and accelerating it with a deep learning network, iteration and time-consuming calculations are eliminated. The combination of multi-objective and global / local double annealing greatly speeds up the design process, saving a great deal of time for designing the parameters of the micro-nano photon structure and hardware costs; the present invention also has great extensibility and is applicable to the physical models of various micro-nano photon structures. Combined with various candidate materials, it is possible to select suitable material types and structure parameters (such as the thickness in the embodiment) to meet the required optical requirements; the present invention effectively solves the problems such as high design time cost, low applicability of high-dimensional design, and poor multi-objective design effect existing in the current design process of solar thermal radiation selective absorption materials.

Claims

1. A design method for a solar thermal radiation selective absorption material, characterized in that, It includes the following steps: S1: Using the finite-difference time-domain (FDTD) method, within the given structural parameter range, calculate the physical model of the micro-nano photon structure for selective absorption of solar thermal radiation to generate data samples. The data samples are the absorption spectra of the physical model in the solar radiation spectral range to the infrared region of 0.3 - 25 μm. Randomly divide the data samples into a training set and a test set; The physical model of the micro-nano photon structure is a multi-layer thin film structure stacked with metal-dielectric materials, a two-dimensional grating structure, or a three-dimensional structure. The corresponding structural parameters include the material composition of the micro-nano photon structure and the corresponding structural size parameters; S2: Construct a deep learning network for accelerating the multi-objective double annealing algorithm. The model of the deep learning network includes an input layer, a hidden layer, and an output layer; The length of the input layer is n, the number of types of structural parameters of the micro-nano photon structure in S1. The hidden layer is constructed by m fully connected layers, which perform non-linear transformation on the structural parameters of the micro-nano photon structure in the input layer and extract fitting features; The length of the output layer is 2501, corresponding to 2501 absorption spectrum points in the solar radiation spectral range to the infrared region; Initialize the structural parameters of the constructed deep learning network, including setting the batch size, the total number of learning epochs, and the initial learning rate. Use Nadam as the gradient descent optimizer, use the mean squared error (MSE) as the loss function, and use the Swish function as the activation function of the deep learning network; S3: Use the training set obtained in S1 as the input to the deep learning network constructed in S2 for training, and use the test set obtained in S1 to verify the accuracy performance of the deep learning network, obtaining a trained deep learning network; S4: Combine the global search algorithm and the local search algorithm to construct a multi-objective double annealing algorithm; The design logic of the multi-objective double annealing algorithm is: That is, while satisfying the constraint condition of FOM2, FOM2 ≤ 0.1, maximize FOM1; FOM1 and FOM2 are respectively: where I AM1.5 (λ) represents the normal emittance of solar thermal radiation at wavelength λ, α(λ) and ε(λ) respectively represent the normal absorptances of the solar thermal radiation selective absorption material in the solar radiation spectrum range and the infrared region, and dλ represents the integration with respect to wavelength; S5: Combine the deep learning network trained in S3 with the multi-objective double annealing algorithm in S4 to accelerate the calculation of the multi-objective double annealing algorithm by the deep learning network. Specifically: use the deep learning network trained in S3 to replace the FDTD calculation part in the multi-objective double annealing algorithm in S4; input the parameter solution in the multi-objective double annealing algorithm into the trained deep learning network and output the corresponding absorption spectrum, and calculate FOM1 and FOM2 used in the multi-objective double annealing algorithm according to the absorption spectrum.

2. The design method of the solar thermal radiation selective absorption material according to claim 1, characterized in that: The metal is a noble metal material or a high-loss metal material; the dielectric material is magnesium fluoride, aluminum oxide, or silicon dioxide.

3. The design method of the solar thermal radiation selective absorption material according to claim 1, characterized in that The working logic of the multi-objective double annealing algorithm constructed in S4 is: 1), Randomly initialize the parameters of the multi-objective double annealing algorithm, set the initial temperature value T0 of the global annealing temperature, the Markov chain progress N = 0, and the length of the Markov chain is M; 2), Set the currently randomly initialized parameters as the optimal parameter solution; 3), During the iteration process, apply a random perturbation to the optimal parameter solution to generate a new parameter solution; 4) Determine whether the new parameter solution satisfies the constraint conditions, specifically including: Calculate through FDTD whether the absorption rate spectrum of the new parameter solution satisfies the constraint condition FOM2; if it satisfies, retain the new parameter solution and proceed to step 5, where N = N + 1; if it does not satisfy, repeat step 3 until a new parameter solution whose absorption rate spectrum satisfies the constraint condition FOM2 is found; 5) Compare the new parameter solution with the optimal parameter solution, specifically including: Calculate through FDTD the difference df of FOM1 corresponding to the absorption rate spectra of the new parameter solution and the optimal parameter solution respectively: If df > 0, update the optimal parameter solution with the current new parameter solution and proceed to step 6; If df ≤ 0, then make a judgment with probability P, and the probability P is expressed as e is the base of the natural logarithm function, and rand is a random number uniformly distributed in the interval (0, 1): If P > rand, then update the optimal parameter solution with the current new parameter solution and go to step 6; if P ≤ rand, then retain the optimal parameter solution and go to step 8; 6) Perform local annealing on the optimal parameter solution updated in step 5, specifically including: 6-1), Set the initial temperature value T of local annealing L , the length of the local Markov chain is M L , the progress N of the local Markov chain L ; 6-2) Set the optimal parameter solution as the local optimal parameter solution for local annealing; 6-3) Apply a random perturbation to the local optimal parameter solution during the iteration process to generate a local new parameter solution; 6-4), determine whether the local new parameter solution satisfies the constraint conditions, specifically including: calculating whether the absorption rate spectrum of the local new parameter solution satisfies the constraint condition FOM2 through FDTD; if it is satisfied, retain the local new parameter solution and proceed to step 6-5, where N L = N L + 1; if it is not satisfied, repeat step 6-3 until a local new parameter solution whose absorption rate spectrum satisfies the constraint condition FOM2 is found; 6-5) Compare the local new parameter solution obtained in step 6-4 with the local optimal parameter solution, specifically including: Calculate through FDTD the difference df of FOM1 corresponding to the absorption rate spectra of the local new parameter solution and the local optimal parameter solution respectively: If df > 0, update the local optimal parameter solution with the current local new parameter solution and proceed to step 6-6; If df ≤ 0, make a judgment with probability P: if P > rand, update the local optimal parameter solution with the current local new parameter solution and proceed to step 6-6; if P ≤ rand, retain the local optimal parameter solution and proceed to step 6-6; 6-6), determine whether the local Markov chain length, i.e., N L = M L : If the local Markov chain length is not reached, repeat step 6-3; if the local Markov chain length M L is reached, then update the local annealing temperature T at the local annealing decay rate K L ; L ; 6 - 7), determine whether the local annealing temperature T L has dropped to the local termination temperature. If it has dropped to the local termination temperature, output the local optimal parameter solution to step 7; if it has not dropped to the local termination temperature, enter step 6 - 3 with the updated local annealing temperature T L and the local optimal parameter solution until T L drops to the local termination temperature; 7) Update the optimal parameter solution with the local optimal parameter solution; 8) Determine whether the Markov chain length is reached, i.e., N = M; if the Markov chain length is not reached, repeat step 3; if the Markov chain length M is reached, update the global annealing temperature T at the global decay rate K; 9) Determine whether the global annealing temperature T has dropped to the global termination temperature. If it has dropped to the global termination temperature, output the optimal parameter solution as the final solution, and calculate the FOM1 corresponding to the final solution through FDTD; if it has not dropped to the global termination temperature, enter step 3 with the updated global annealing temperature T and the optimal parameter solution until it drops to the global termination temperature.

Images