Glancing Incidence Small Angle Scattering Data Fitting Method and System

Abstract

The present invention provides a grazing incidence small angle scattering data fitting method and system, including: constructing a grazing incidence small angle scattering model to obtain an objective function; preprocessing experimental data and inputting it into the objective function; determining nanoparticles by using the Porod fitting method according to the preprocessed experimental data; confirming the objective function according to the judgment result, performing Monte Carlo fitting, and outputting the optimal parameters; using the gradient descent method to iteratively optimize the optimal parameters and output the fitting parameter result; post-processing the fitting parameter result to output a visual fitting result and evaluate. By introducing a multi-stage optimization process, the present invention solves the problems of characterization deviation in the traditional data processing process that relies on manual operation, the results are significantly affected by subjective factors and model selection, and the stability is poor; significantly improves the processing efficiency of GISAS experimental data and the quantitative characterization ability of the microstructure, can meet the high-efficiency processing requirements of multiple groups of experimental data, and provides more reliable technical support for subsequent material research.

Description

Technical Field

[0001] The present invention belongs to the field of data processing, and specifically, relates to a grazing incidence small angle scattering data fitting method and system. Background Art

[0002] In applications in multiphase dense flow systems, one phase is usually dispersed in the base phase at a very low volume fraction. For example, proteins are distributed in water or metal precipitation phases exist in the alloy base. The grazing incidence small angle scattering technique can extract partial structural parameters of the target phase, including the morphology, size distribution, surface roughness, and volume fraction of particles, etc. Since the scattering signals between particles in the dense flow system do not interfere with each other, the total scattering signal can be regarded as a simple superposition of the scattering contributions of each particle.

[0003] Currently, existing grazing incidence small angle scattering fitting methods rely on selected specific models to describe the arrangement characteristics of nano-objects. However, if the model is not selected accurately, even if the experimental data and the fitting results seemingly match, the obtained structural parameters may have serious deviations. In addition, the existing data analysis and fitting processes usually require researchers to manually adjust the model and parameters, which is highly subjective and difficult to effectively meet the processing requirements of complex large-scale data.

[0004] The research results presented in the literature "Application of GISAXS in the Investigation of Three-Dimensional Lattices of Nanostructures" (Crystals 9.9(2019):479.) published by Lovro Basioli et al. in the journal Crystals in 2019 demonstrated the application of GISAS technology in nanostructure analysis and developed the GisaxsStudio software, which can be used to simulate and fit GISAXS data. However, this method still needs to select corresponding models for different materials to describe the arrangement characteristics of nano-objects. Moreover, this research did not achieve the automation of data fitting, and the fitting efficiency and result stability are limited by the experience of researchers.

[0005] The patent document "Method and System for Automatically Fitting Small Angle Scattering Data" (CN111159847A) discloses that by combining heuristic algorithms, gradient descent methods, and grid search methods, the automation of small angle scattering data fitting is achieved, thereby greatly reducing the influence caused by human subjectivity in the data processing process. However, its coarse optimization is too brief, with poor robustness and low adaptability, resulting in the easy loss of microscopic structure characterization information.

[0006] Therefore, there is an urgent need for an automated fitting method based on GISAS data, which can achieve automatic search and fitting of model parameters without relying on additional model selection and avoid errors caused by manual adjustment. Summary of the Invention

[0007] Aiming at the defects in the prior art, the purpose of the present invention is to provide a grazing incidence small angle scattering data fitting method and system.

[0008] According to a grazing incidence small angle scattering data fitting method provided by the present invention, it includes:

[0009] Step S1: Construct a grazing incidence small angle scattering model to obtain an objective function;

[0010] Step S2: Preprocess the experimental data and input it into the objective function;

[0011] Step S3: Determine nanoparticles by using the Porod fitting method according to the preprocessed experimental data;

[0012] Step S4: Confirm the objective function according to the judgment result, perform Monte Carlo fitting, and output the optimal parameters;

[0013] Step S5: Iteratively optimize the optimal parameters by using the gradient descent method and output the fitting parameter results;

[0014] Step S6: Post-process the fitting parameter results, output the visual fitting results and evaluate.

[0015] Preferably, the step S1 includes:

[0016] Step S1.1: According to the geometric structure of the actual sample to be measured, select a buried model or a support model, and set the distribution density function of the spherical particle model and the scattering intensity of the grazing incidence small angle scattering model of the spherical particle , which are jointly used as the objective function;

[0017] Construct a fitting function and set the parameters to be fitted ( ) and ( , );

[0018] Among them, represents the average value of the spherical particle radius;

[0019] represents the average variance of the spherical particle radius;

[0020] represents the radius of a single spherical particle;

[0021] represents the average variance of the radius of a single spherical particle;

[0022] represents the volume fraction coefficient of spherical particles;

[0023] K represents the structural parameter;

[0024] represents the in-plane emission angle;

[0025] represents the minimum in-plane emission angle;

[0026] represents the maximum in-plane emission angle;

[0027] () represents the grazing-incidence small-angle scattering light intensity of the radius of a single spherical particle;

[0028] represents the incident wave vector;

[0029] represents the outgoing wave vector;

[0030] represents the incident angle;

[0031] represents the outgoing angle;

[0032] q represents the small-angle scattering vector;

[0033] Step S1.2: Input the range of parameters to be fitted q min 、q max to construct the parameter space for parameter search.

[0034] The said step S2 includes:

[0035] Step S2.1: Normalize the experimental data;

[0036] Step S2.2: Set the upper and lower limits of the parameter space according to the range of parameters to be fitted and the set resolution.

[0037] The said step S3 includes:

[0038] Step S3.1: Calculate the small-angle scattering intensity , ;

[0039] Among them, represents the Porod constant;

[0040] represents the Laue scattering intensity;

[0041] Step S3.2: Plot with as the horizontal axis, A curve with the vertical axis, where n is within the range of, judge the relationship of the scattering curve. If an obvious linear relationship appears, it indicates that is a constant at this time, determine that there are no nanoparticles, and end the fitting. If no obvious linear relationship appears, determine that there are nanoparticles, and continue to execute step S4.

[0042] Preferably, the step S4 includes:

[0043] Initial parameter setting step: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ;

[0044] Among them, represents the combined parameter;

[0045] , respectively represent the minimum and maximum values of the combined parameter.

[0046] Random sampling step: Generate a parameter set with a random distribution Input it into the objective function to obtain the model scattering intensity .

[0047] Loss function calculation step: Set the chi-square value of the initial best parameter , and calculate the corresponding loss function chi-square value according to the parameter set , judge , if , then let , if , then execute the random sampling step;

[0048] Among them, N represents the number of grazing incidence small angle scattering experimental points;

[0049] n represents the number of fitting parameters;

[0050] represents the i-th small angle scattering vector;

[0051] represents the scattering intensity of grazing incidence small angle scattering in the experiment;

[0052] represents the small angle scattering intensity error in the experiment;

[0053] represents the model scattering intensity.

[0054] Fitting termination step: Judge and the sampling times. If Or reach the upper limit of the set number of samplings, then execute the result output step. If And do not reach the set upper limit, then execute the random sampling step and the loss function calculation step, and continue fitting.

[0055] Result output step: Output the optimal parameters , and let the starting point Be passed into the gradient descent optimization algorithm.

[0056] Preferably, the step S5 includes:

[0057] Initialization parameter step: According to the optimal parameters Obtained starting point , , set the initial learning rate And the maximum number of iterations , , calculate the initial loss function , record the initial gradient as .

[0058] Gradient calculation step: For The loss function under the parameters Calculate the gradient of the loss function with respect to the parameters , ;

[0059] Among them, N represents the number of grazing incidence small angle scattering experiment points;

[0060] n represents the number of fitting parameters;

[0061] Represents the i-th small angle scattering vector;

[0062] Represents the scattering intensity of grazing incidence small angle scattering in the experiment;

[0063] Represents the small angle scattering intensity error in the experiment;

[0064] Represents the model scattering intensity;

[0065] Represents the parameter value of the t-th iteration, .

[0066] Parameter update step: Update To , .

[0067] Abort check and result output step: Flush and calculate the loss function of the (t + 1)-th iteration And compare it with the loss function of the t-th iteration Compare. If or the maximum number of iterations is reached , terminate the iteration and execute the step of verifying the fitting quality. If and the maximum number of iterations is not reached , execute the step of calculating the gradient and the step of updating the parameters, and continue the iteration.

[0068] Step of verifying the fitting quality: Output the result of the fitting parameters , , and let the optimal solution of gradient descent , judge , if , it is determined that the fitting quality meets the standard, and retain , if , it is judged that the fitting quality does not meet the standard, and discard .

[0069] Preferably, step S6 includes:

[0070] Step S6.1: Statistically process the result of the fitting parameters, output the final fitting result , and compare and evaluate the physical meaning of the fitting parameters and their rationality under the experimental conditions in combination with other characterization methods;

[0071] Step S6.2: Output the matching situation between the fitting data obtained according to the final fitting result and the experimental data as one-dimensional and two-dimensional tables to obtain a visual fitting result.

[0072] According to a grazing incidence small angle scattering data fitting system provided by the present invention, it includes:

[0073] Module M1: Construct a grazing incidence small angle scattering model to obtain an objective function;

[0074] Module M2: Preprocess the experimental data and input it into the objective function;

[0075] Module M3: Determine nanoparticles by using the Porod fitting method according to the preprocessed experimental data;

[0076] Module M4: Confirm the objective function according to the judgment result, perform Monte Carlo fitting, and output the optimal parameters;

[0077] Module M5: Iteratively optimize the optimal parameters by using the gradient descent method and output the result of the fitting parameters;

[0078] Module M6: Post-process the result of the fitting parameters, output a visual fitting result and evaluate it.

[0079] Preferably, the module M1 includes:

[0080] Module M1.1: Select a burial model or a support model according to the geometric structure of the actual sample to be measured, and set the distribution density function of the spherical particle model and the scattering intensity of the grazing-incidence small-angle scattering model of spherical particles as the objective function together;

[0081] Construct a fitting function and set the parameters to be fitted ( ) and ( , );

[0082] Among them, represents the average value of the spherical particle radius;

[0083] represents the mean variance of the spherical particle radius;

[0084] represents the radius of a single spherical particle;

[0085] represents the mean variance of the radius of a single spherical particle;

[0086] represents the spherical particle volume fraction coefficient;

[0087] K represents the structure parameter;

[0088] represents the in-plane emission angle;

[0089] represents the minimum in-plane emission angle;

[0090] represents the maximum in-plane emission angle;

[0091] () represents the grazing-incidence small-angle scattering light intensity of the radius of a single spherical particle;

[0092] represents the incident wave vector;

[0093] represents the outgoing wave vector;

[0094] represents the incident angle;

[0095] represents the emission angle;

[0096] q represents the small-angle scattering vector;

[0097] Module M1.2: Input the range of parameters to be fitted q according to objective laws min 、q maxConstruct the parameter space for parameter search.

[0098] The module M2 includes:

[0099] Module M2.1: Normalize the experimental data;

[0100] Module M2.2: Set the upper and lower limits of the parameter space according to the range of parameters to be fitted and the set resolution.

[0101] The module M3 includes:

[0102] Module M3.1: Calculate the small-angle scattering intensity , ;

[0103] Wherein, represents the Porod constant;

[0104] represents the Laue scattering intensity;

[0105] Module M3.2: Plot a curve with as the horizontal axis and as the vertical axis. In the range of , judge the relationship of the scattering curve. If an obvious linear relationship is presented, it indicates that is a constant at this time, determine that there are no nanoparticles, end the fitting. If no obvious linear relationship is presented, determine that there are nanoparticles and continue to trigger module M4.

[0106] Preferably, the module M4 includes:

[0107] Initial parameter setting module: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ;

[0108] Wherein, represents the combined parameter;

[0109] , respectively represent the minimum and maximum values of the combined parameter.

[0110] Random sampling module: Generate a parameter set with a random distribution input into the objective function to obtain the model scattering intensity .

[0111] Loss function calculation module: Set the chi-square value of the initial best parameter , calculate the corresponding loss function chi-square value according to the parameter set , judge , if , then let , if , then trigger the random sampling module;

[0112] Among them, N represents the number of grazing incidence small angle scattering experiment points;

[0113] n represents the number of fitting parameters;

[0114] represents the i-th small angle scattering vector;

[0115] represents the scattering intensity of grazing incidence small angle scattering in the experiment;

[0116] represents the small angle scattering intensity error in the experiment;

[0117] represents the model scattering intensity.

[0118] Fitting termination module: Judge and the number of sampling times. If or reach the set upper limit of the number of sampling times, then trigger the result output module. If and do not reach the set upper limit, then trigger the random sampling module and the loss function calculation module to continue fitting.

[0119] Result output module: Output the optimal parameters , and let the starting point be passed into the gradient descent optimization algorithm.

[0120] Preferably, the module M5 includes:

[0121] Initialization parameter module: According to the optimal parameters to obtain the starting point , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as .

[0122] Calculate gradient module: For the loss function under the parameters calculate the gradient of the loss function with respect to the parameters , ;

[0123] Among them, N represents the number of grazing incidence small angle scattering experiment points;

[0124] n represents the number of fitting parameters;

[0125] represents the i-th small-angle scattering vector;

[0126] represents the scattering intensity of grazing-incidence small-angle scattering in the experiment;

[0127] represents the small-angle scattering intensity error in the experiment;

[0128] represents the model scattering intensity;

[0129] represents the parameter value of the t-th iteration, .

[0130] Parameter update module: Update to , .

[0131] Abort check and result output module: Flush and calculate the loss function of the (t + 1)-th iteration and compare it with the loss function of the t-th iteration . If or the maximum number of iterations is reached, terminate the iteration and trigger the verification fitting quality module. If and the maximum number of iterations is not reached, trigger the calculation gradient module and the parameter update module to continue the iteration.

[0132] Verification fitting quality module: Output the fitting parameter results , , and set the gradient descent optimal solution . Judge . If , it is determined that the fitting quality meets the standard, and is retained. If , it is determined that the fitting quality does not meet the standard, and is discarded.

[0133] Preferably, module M6 includes:

[0134] Module M6.1: Statistically process the fitting parameter results, output the final fitting results , and compare and evaluate the physical meaning of the fitting parameters and their rationality under the experimental conditions in combination with other characterization methods;

[0135] Module M6.2: Output the matching situation between the fitting data obtained from the final fitting results and the experimental data as one-dimensional and two-dimensional tables to obtain the visualized fitting results.

[0136] Compared with the prior art, the present invention has the following beneficial effects:

[0137] 1. By introducing a multi-stage optimization process, the present invention realizes fully automated processing from data preprocessing, model construction to parameter fitting, and solves the problem of significant characterization deviation in traditional data processing, which depends on manual operations, and the results are significantly affected by subjective factors and model selection, resulting in poor stability.

[0138] 2. The present invention combines Monte Carlo optimization and fine-tuning to achieve efficient processing of grazing incidence small angle scattering data, accurate fitting of model parameters, and quantitative characterization of material microstructure, greatly improving the fitting accuracy, with a short time-consuming fitting process, and can meet the efficient processing requirements of multiple sets of experimental data.

[0139] 3. By adopting a multi-level optimization algorithm combining Monte Carlo optimization and gradient descent, the present invention solves the problem of loss of microstructure characterization information caused by insufficient adaptability of the data fitting model, significantly improves the processing efficiency of GISAS experimental data and the quantitative characterization ability of the microstructure, and provides more reliable technical support for subsequent material research. BRIEF DESCRIPTION OF THE DRAWINGS

[0140] Other features, objects, and advantages of the present invention will become more apparent by reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0141] Figure 1 It is a schematic diagram of the fitting process for grazing incidence small angle scattering;

[0142] Figure 2 It is a schematic diagram of the geometry of grazing incidence small angle scattering;

[0143] Figure 3 It is a schematic diagram of the original experimental data of the RPV high-energy iron ion irradiated sample at 300°C;

[0144] Figure 4 It is a schematic diagram of the one-dimensional data of the RPV high-energy iron ion irradiated sample at 300°C;

[0145] Figure 5 It is a schematic diagram of the fitting result of the RPV high-energy iron ion irradiated sample at 300°C;

[0146] Figure 6 It is a schematic diagram of the original experimental data of the RPV low-energy iron ion irradiated sample at 200°C;

[0147] Figure 7 It is a schematic diagram of the one-dimensional data of the RPV low-energy iron ion irradiated sample at 200°C;

[0148] Figure 8 It is a schematic diagram of the fitting result of the RPV low-energy iron ion irradiated sample at 200°C;

[0149] Figure 9 Schematic diagram of the original data of the experiment on the room-temperature irradiation of samples with medium-energy protons in the RPV;

[0150] Figure 10 Schematic diagram of the one-dimensional data of the experiment on the room-temperature irradiation of samples with medium-energy protons in the RPV;

[0151] Figure 11 Schematic diagram of the fitting results of the experiment on the room-temperature irradiation of samples with medium-energy protons in the RPV. Specific implementation manners

[0152] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those of ordinary skill in the art can make several changes and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0153] Based on the automated processing and fitting technology, the present invention solves the deficiencies brought by traditional methods due to human intervention and model limitations in the processing of GISAS experimental data, and realizes the full automation processing from data preprocessing, model construction to parameter fitting by introducing a multi-stage optimization process.

[0154] According to a grazing-incidence small-angle scattering data fitting method provided by the present invention, taking Figure 1 as an example, starting from the normalization and filtering of experimental data, multi-dimensional fitting optimization of the material microstructure is carried out, and combined with advanced optimization algorithms (such as Monte Carlo fitting and gradient descent) and error analysis methods to ensure the high accuracy and repeatability of the final result, which specifically includes the following steps:

[0155] Step S1: Establish a grazing-incidence small-angle scattering model (Model Selection).

[0156] Step S1.1: Determine the material model (such as a spherical model) of the small-angle scattering experimental data and the distribution function of its structural parameters, construct a fitting function and set the parameters to be fitted;

[0157] Select a grazing-incidence small-angle scattering (GISAS) buried model, where the structure factor depends not only on the scattering vector but also on the incident vector and the outgoing vector. Each term is weighted by the corresponding Fresnel reflection coefficient and refraction coefficient, which are defined in the reflection or refraction stage respectively, so as to obtain the shape factor of the modified grazing-incidence small-angle scattering buried model.

[0158] Spherical particles are one of the most common forms of precipitated phases and widely exist in various material systems, such as metal alloys, polymers, and nanocomposites. The formation of such particles is usually closely related to the heat treatment or phase transformation process of the material, and their size, distribution, and morphological characteristics have a significant impact on the microstructure and macroscopic properties of the material.

[0159] Spherical particles usually have a certain embedding depth and rotation angle on the surface layer. For spherical particles, the rotation angle does not affect the vector distribution because spherical particles are assumed to be isotropic, and a rotation matrix combining the scattering vector is obtained under burial. To simplify the model to a certain extent and be consistent with the actual experimental results (most of the spherical particles in samples such as RPV do not have an embedding depth), the embedding depth is therefore assumed. , from which the calculation formula for the intensity of single-particle spherical grazing-incidence small-angle scattering can be further derived.

[0160] In the spherical particle model setting section, first, according to the geometric structure of the actual sample to be measured, it is necessary to confirm whether the position where the nanoparticles exist is embedded in the substrate. If so, the burial model needs to be selected; if not, the supported model needs to be selected.

[0161] Secondly, among the precipitated-phase nanoparticles in metal alloy samples, the size often follows a log-normal distribution. Here, it can be assumed that any structural parameter follows a log-normal distribution, and its distribution density function is , then there are corresponding parameters ( ) such that:

[0162]

[0163] Correspondingly, the fitting parameters and their expressions for the intensity in the grazing-incidence small-angle scattering of spherical particles are set;

[0164]

[0165] To sum up, in the model setting section, ( The parameter is an intermediate phase in the simulation fitting process and has no impact on the significance of the overall fitting experiment.

[0166] The two types of parameters to be fitted are selected as follows: The first type is the parameters that need to be fitted in the log-normal distribution model, which are ( ); The second type is the parameters that need to be fitted for the scattering intensity of spherical particles, which are ( , ).

[0167] Among them, represents the average value of the spherical particle radius;

[0168] represents the average variance of the spherical particle radius;

[0169] represents the radius of a single spherical particle;

[0170] represents the mean variance of the radius of a single spherical particle;

[0171] represents the volume fraction coefficient of spherical particles;

[0172] K represents the structural parameter;

[0173] represents the in-plane emission angle;

[0174] represents the minimum in-plane emission angle;

[0175] represents the maximum in-plane emission angle;

[0176] () represents the grazing-incidence small-angle scattering light intensity of the radius of a single spherical particle;

[0177] represents the incident wave vector;

[0178] represents the outgoing wave vector;

[0179] represents the incident angle;

[0180] represents the emission angle;

[0181] q represents the small-angle scattering vector.

[0182] Select a larger parameter range according to objective laws. For example, the range of nanoparticles is 0.1 nm - 100 nm.

[0183] Step S1.2: Construct a parameter search space according to the experimental data input range (such as q min , q max ).

[0184] Step S2: Experimental data preprocessing link (Input Pre-processing).

[0185] Step S2.1: Normalize the experimental data to ensure the balance of data in terms of error weight and distribution;

[0186] Step S2.2: Set the upper and lower limits of the search space according to the experimental data range and resolution.

[0187] Step S3: Use the Porod fitting method to determine nanoparticles.

[0188] Specifically, the Porod method is used to determine whether there are small-scale nanoparticle structures in the sample. In the Porod method, the small-angle scattering intensity can be expressed by a specific formula as follows:

[0189]

[0190] where is called the Porod constant, represents the Laue scattering intensity, ranges from 3 to 4, reflecting the geometric characteristics of the scattering surface. When is close to 4, it can be considered that the surface of the sample is relatively smooth, while a smaller represents a rough or diverse surface morphology. represents the Laue scattering intensity;

[0191] In the grazing-incidence small-angle scattering data fitting, the surface is relatively smooth, so is adopted.

[0192] Plot a curve with as the horizontal axis and as the vertical axis. In the range of , if the scattering curve shows an obvious linear relationship, it indicates that is a constant in this region, and the linear relationship corresponds to the dominance of the sample surface or interface characteristics rather than the contribution of the particulate structure to the scattering. Through the above judgment method, especially in the study of irradiated samples, it is possible to effectively identify whether there are small nano-precipitate phase particles in the sample, not only quickly judge the structural characteristics of the sample, but also significantly reduce the dependence on complex fitting processes and improve the efficiency of data analysis. Therefore, this method is used as the primary judgment step after VGISAS data preprocessing to optimize the subsequent fitting process after confirming the existence or non-existence of small-scale structures.

[0193] Step S4: Monte Carlo fitting (Coarse Tuning).

[0194] This process aims to confirm whether the globally optimal solution inferred by the Monte Carlo method is true and reliable. This strategy can ensure that the subsequent optimization process focuses on the most promising regions in the parameter space, effectively explore the parameter space, and at the same time improve the accuracy of the fitting result through higher-precision local optimization, providing high-quality initial parameters for the subsequent gradient descent optimization, thereby improving the optimization accuracy and efficiency.

[0195] The Monte Carlo method divides the parameter space into high-dimensional grids and calculates the scattering intensity by randomly generating combined parameters , after each sampling, its parameter combination is evaluated for its performance in the loss function, and its chi-square value ( ) is calculated, ;

[0196] where N represents the number of grazing-incidence small-angle scattering experimental points;

[0197] n represents the number of fitting parameters;

[0198] represents the i-th small-angle scattering vector;

[0199] represents the scattering intensity of grazing-incidence small-angle scattering in the experiment;

[0200] represents the small-angle scattering intensity error in the experiment;

[0201] represents the model scattering intensity.

[0202] Specifically, it includes the following steps:

[0203] Initial parameter setting step: Set the parameter range in the parameter space , and reasonably define the range through empirical data or prior knowledge;

[0204] Random sampling step: Use a random distribution to generate a set of parameters , and the generated parameters are used to calculate the model scattering intensity ;

[0205] Loss function calculation step: Calculate the corresponding loss function value according to each set of random parameters , compare it with the optimal value, and judge , if , then let , if , then execute the random sampling step;

[0206] Fitting termination step: Judge and the number of sampling times, if or reach the upper limit of the set number of sampling times, then terminate the fitting, if and have not reached the set upper limit, then continue the fitting;

[0207] Result output step: Output the best parameters , and let be passed into the gradient descent optimization algorithm as the starting point.

[0208] Compared with traditional methods, the automatic search and fitting of model parameters are achieved through Monte Carlo fitting and gradient descent algorithms, avoiding errors caused by manual adjustment. At the same time, it can efficiently process multiple sets of GISAS data and integrate the results under different experimental conditions, significantly improving the analysis efficiency.

[0209] Step S5: Use the Gradient Method to iteratively update the parameters and gradually approach the global optimal solution;

[0210] The gradient descent optimization method is a classic iterative optimization algorithm. Its core idea is to calculate the gradient information of the objective function (such as the loss function or chi-square statistic), and gradually adjust the parameters to approach the optimal solution along the direction where the objective function decreases fastest. In the VGISAS fitting algorithm, the gradient descent method realizes efficient local optimization by using gradient information and is an important supplementary means after the global search by the Monte Carlo method.

[0211] In the gradient descent method, assume the objective function is the loss function , where is the optimal solution after Monte Carlo fitting, representing the set of fitting parameters. Then, the gradient descent adjusts the parameters by updating the following formula:

[0212]

[0213] where, represents the parameter value at the t-th iteration, is the learning rate, controlling the step size of each update, is the gradient of the loss function with respect to the parameters, representing the change trend of the current parameters on the objective function value. Therefore, in the VGISAS fitting, the gradient of the objective function chi-square statistic can be expressed as:

[0214]

[0215] The specific application steps of the gradient optimization algorithm in VGISAS are as follows:

[0216] Initialization parameter step: According to the initial parameter set provided by the Monte Carlo method, set the initial learning rate and the maximum number of iterations ; Calculate the initial loss function , and record the initial gradient as ;

[0217] Gradient calculation step: Calculate the gradient of the loss function under the current parameters;

[0218] Parameter update step: Update for ;

[0219] Abort check and result output step: After each iteration, flush the loss function calculation And compare, if or the maximum number of iterations is reached Then terminate the iteration and output the result; if And the maximum number of iterations has not been reached , then continue to iterate;

[0220] Verify the fitting quality step: After the optimization is completed, output the fitting parameter set , and order As the optimal solution of gradient descent, judge Is it true? Evaluate the fitting quality. , then the fitting quality is judged to be up to standard and the fitting result is retained. , the fitting quality is judged to be substandard and the fitting result is discarded.

[0221] The advantage of the gradient optimization algorithm is that it can accurately fit and control the error within a very small range. The disadvantage is that it is easy to fall into the local optimum for the calculation of complex functions. Based on the global initial parameters provided by the Monte Carlo method, the gradient descent optimization algorithm is further used to fine-tune the fitting results. The Monte Carlo fitting and gradient descent optimization results are combined to give full play to the respective advantages of the gradient descent and Monte Carlo methods, and comprehensively evaluate the reliability and consistency of each fitting parameter.

[0222] Specifically, the Monte Carlo method is used to provide initial parameters for global search, and gradient descent is used to make fine adjustments based on this. The final fitting parameter value is selected through the chi-square distribution test, and an optimization result report containing fitting accuracy, error distribution and parameter confidence interval is generated, achieving an effective combination of global and local optimization. The optimized parameter results are finally output , which is used for subsequent experimental analysis and result verification. This hybrid strategy ensures the efficiency and accuracy of the fitting and provides a reliable solution for the analysis of grazing-incidence small-angle scattering data of complex systems.

[0223] Step S6: Data post-processing (Post-process).

[0224] Step S6.1: Perform statistical processing on the fitting parameter results and output the final fitting results , and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions;

[0225] The main content of the evaluation is to evaluate whether it is consistent with the actual information of the sample, combined with comparison with other characterization methods.

[0226]

[0227] In the table, represents the average radius of spherical particles of sample number RPV-HE-300T-1.0dpa, represents the mean variance of the radius of individual spherical particles of sample number RPV-HE-300T-1.0dpa.

[0228] These differences are reasonable because: APT mainly collects the surface atoms of the tip sample, and there may be a "truncation effect" during the collection process, that is, only a part of the particle is measured, resulting in a slightly smaller measured particle size; the measurement result of SANS is slightly larger than that of APT, reflecting its more objective characterization of the overall particle size of the sample; the particle size measured by GISAXS is the largest, because the grazing incidence method is more sensitive to the nanostructure of the sample surface and near-surface area, and under the condition of high-energy particle irradiation, the irradiation effect often concentrates on the surface or near-surface area of the material, resulting in accelerated atomic migration and rearrangement on the surface area, thus forming larger precipitation phases.

[0229] Step S6.2: Provide the confidence interval and optimization report of the fitting result, including the confidence space estimation of each fitting parameter and the quantitative analysis of the overall performance of the fitting model. At the same time, introduce the chi-square test ( ) and the mean square error test ( ) to quantitatively evaluate the accuracy and consistency of the fitting result, and judge whether the model conforms to the experimental data in a statistical sense;

[0230] Step S6.3: Visualize the fitting result, intuitively present the matching situation between the fitting data and the experimental data through one-dimensional and two-dimensional tables, and analyze the distribution of the fitting residuals through images to enhance the intuitive understanding of the fitting quality.

[0231] Since it does not need to rely on additional model selection, it can retain the complete information in the original two-dimensional scattering image and accurately characterize the anisotropy and complex arrangement characteristics of the microstructure.

[0232] In more preferred examples, experimental fitting is performed on the samples in the sample list. Under the set conditions, all samples have experienced the action of specific irradiation energy and temperature, resulting in the formation of precipitation phases in the internal microstructure, specifically manifested as the morphology of spherical particles. Such precipitation phases are common damage products in various steel alloy materials in a nuclear irradiation environment, and their size distribution, density, and phase structure characteristics are accurately captured by the grazing incidence small angle scattering (GISAXS) technology taking Figure 2 as an example.

[0233] Table 1. Experimental sample list:

[0234]

[0235] The experimental data of the sample are processed and analyzed. For the RPV steel, under the irradiation intensity of high-energy iron ions at 300 °C, an irradiation damage dose of 1.0 dpa is adopted, and the front and back sides are uniformly damaged by 50 μm. The original data of the grazing incidence small angle scattering experiment are as Figure 3 shown, and the one-dimensional experimental data are as Figure 4 shown, and the fitting results are as Figure 5 shown. I is the abbreviation of intensity, and q xy represents the irradiation damage dose.

[0236] Table 2. Fitting results of the RPV high-energy iron ion irradiated sample at 300 °C:

[0237]

[0238] In more preferred examples, for the RPV steel, under the irradiation intensity of low-energy iron ions at 200 °C, an irradiation damage dose of 1.0 dpa is adopted for damage. The original data of the grazing incidence small angle scattering experiment are as Figure 6 shown, and the one-dimensional experimental data are as Figure 7 shown, and the fitting results are as Figure 8 shown.

[0239] Table 3. Fitting results of the RPV low-energy iron ion irradiated sample at 200 °C:

[0240]

[0241] In more preferred examples, for the RPV medium-energy protons, under the irradiation intensity at room temperature, an irradiation damage dose of 0.35 dpa is adopted for damage. The original data of the grazing incidence small angle scattering experiment are as Figure 9 shown, and the one-dimensional experimental data are as Figure 10 shown, and the fitting results are as Figure 11 shown.

[0242] Table 4. Fitting results of the RPV medium-energy proton irradiated sample at room temperature:

[0243]

[0244] The present invention also provides a grazing incidence small angle scattering data fitting system, which can be realized by executing the process steps of the grazing incidence small angle scattering data fitting method. That is, those skilled in the art can understand the grazing incidence small angle scattering data fitting method as the preferred implementation manner of the grazing incidence small angle scattering data fitting system.

[0245] According to the grazing incidence small angle scattering data fitting system provided by the present invention, it includes:

[0246] Module M1: Construct a grazing-incidence small-angle scattering model to obtain an objective function;

[0247] Module M2: Preprocess the experimental data and input it into the objective function;

[0248] Module M3: Determine nanoparticles using the Porod fitting method based on the preprocessed experimental data;

[0249] Module M4: Confirm the objective function based on the judgment result, perform Monte Carlo fitting, and output the optimal parameters;

[0250] Module M5: Iteratively optimize the optimal parameters using the gradient descent method and output the fitting parameter results;

[0251] Module M6: Post-process the fitting parameter results, output the visual fitting results, and evaluate.

[0252] In more preferred examples, the module M1 includes:

[0253] Module M1.1: Select a buried model or a support model according to the geometric structure of the actual sample to be measured, and set the distribution density function of the spherical particle model and the scattering intensity of the grazing-incidence small-angle scattering model of the spherical particle , which are jointly used as the objective function;

[0254] Construct a fitting function and set the parameters to be fitted ( ), and ( , );

[0255] Among them, represents the average value of the spherical particle radius;

[0256] represents the mean variance of the spherical particle radius;

[0257] represents the radius of a single spherical particle;

[0258] represents the mean variance of the radius of a single spherical particle;

[0259] represents the volume fraction coefficient of the spherical particle;

[0260] K represents the structure parameter;

[0261] represents the in-plane emission angle;

[0262] represents the minimum in-plane emission angle;

[0263] represents the maximum in-plane emission angle;

[0264] () represents the grazing-incidence small-angle scattering light intensity of the radius of a single spherical particle;

[0265] represents the incident wave vector;

[0266] represents the outgoing wave vector;

[0267] represents the incident angle;

[0268] represents the emission angle;

[0269] q represents the small-angle scattering vector;

[0270] Module M1.2: Input the range of parameters q to be fitted according to objective laws min 、q max Construct the parameter space for parameter search.

[0271] The said module M2 includes:

[0272] Module M2.1: Normalize the experimental data;

[0273] Module M2.2: Set the upper and lower limits of the parameter space according to the range of parameters to be fitted and the set resolution.

[0274] The said module M3 includes:

[0275] Module M3.1: Calculate the small-angle scattering intensity , ;

[0276] Among them, represents the Porod constant;

[0277] represents the Laue scattering intensity;

[0278] Module M3.2: Draw a curve with as the horizontal axis and as the vertical axis. In the range of , judge the relationship of the scattering curve. If an obvious linear relationship appears, it indicates that is a constant at this time, determine that there are no nanoparticles, end the fitting. If no obvious linear relationship appears, determine that there are nanoparticles and continue to trigger module M4.

[0279] In more preferred examples, the said module M4 includes:

[0280] Initial parameter setting module: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ;

[0281] in, Represents a combination parameter;

[0282] , Respectively represent the minimum and maximum values of the combination parameters.

[0283] Random sampling module: Generate parameter sets from random distribution Input the objective function to get the model scattering intensity .

[0284] Loss function calculation module: Setting the chi-square value of the initial optimal parameter , according to the parameter set Calculate the corresponding loss function chi-square value ,judge ,like , then let ,like , then the random sampling module is triggered;

[0285] Where N represents the number of grazing incidence small-angle scattering experimental points;

[0286] n represents the number of fitting parameters;

[0287] represents the i-th small-angle scattering vector;

[0288] represents the scattering intensity of grazing incidence small-angle scattering in the experiment;

[0289] represents the small-angle scattering intensity error in the experiment;

[0290] Represents the model scattering intensity.

[0291] Fitting termination module: judgment and the number of sampling times, if Or the upper limit of the sampling times is reached, the result output module is triggered. If the set upper limit is not reached, the random sampling module and the loss function calculation module are triggered to continue fitting.

[0292] Result output module: output the best parameters , and let the starting point Pass in the gradient descent optimization algorithm.

[0293] In more preferred embodiments, the module M5 includes:

[0294] Initialization parameter module: According to the optimal parameters The obtained starting point , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as .

[0295] Gradient calculation module: For the loss function under the parameters calculate the gradient of the loss function with respect to the parameters , ;

[0296] where N represents the number of grazing-incidence small-angle scattering experimental points;

[0297] n represents the number of fitting parameters;

[0298] represents the i-th small-angle scattering vector;

[0299] represents the scattering intensity of grazing-incidence small-angle scattering in the experiment;

[0300] represents the small-angle scattering intensity error in the experiment;

[0301] represents the model scattering intensity;

[0302] represents the parameter value at the t-th iteration, .

[0303] Parameter update module: Update to , .

[0304] Abort check and result output module: Flush and calculate the loss function for the (t + 1)-th iteration and compare it with the loss function for the t-th iteration , if or the maximum number of iterations is reached , then terminate the iteration and trigger the verification fitting quality module, if and the maximum number of iterations is not reached , then trigger the gradient calculation module and the parameter update module to continue the iteration.

[0305] Verification fitting quality module: Output the fitting parameter results , , and let the optimal solution of gradient descent , judge , if , then it is determined that the fitting quality meets the standard, and is retained; if , then it is judged that the fitting quality does not meet the standard, and is discarded.

[0306] In more preferred examples, module M6 includes:

[0307] Module M6.1: Statistically process the fitting parameter results and output the final fitting result , and compare and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions in combination with other characterization methods;

[0308] Module M6.2: Output the matching situation between the fitting data obtained according to the final fitting result and the experimental data as one-dimensional and two-dimensional tables to obtain a visual fitting result.

[0309] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program codes, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc. to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be regarded as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structure within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as either software modules for implementing the method or the structure within the hardware component.

[0310] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined arbitrarily with each other.

Claims

1. A grazing incidence small angle scattering data fitting method, characterized in that, Including: Step S1: Construct a grazing-incidence small-angle scattering model to obtain an objective function; Step S2: Preprocess the experimental data and input it into the objective function; Step S3: Determine nanoparticles using the Porod fitting method based on the preprocessed experimental data; Step S4: Confirm the objective function according to the judgment result, perform Monte Carlo fitting, and output the optimal parameters; Step S5: Iteratively optimize the optimal parameters using the gradient descent method and output the fitting parameter results; Step S6: Post-process the fitting parameter results, output the visualized fitting results and evaluate; The said Step S4 includes: Initial parameter setting step: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ; Among them, represents a combined parameter; , represent the minimum and maximum values of the combined parameters respectively; Random sampling step: Generate a set of parameters for random distribution Input the objective function to obtain the model scattering intensity ; Loss function calculation steps: Set the chi-square value of the initial optimal parameters , according to the parameter set Calculate the corresponding chi-square value of the loss function , judge , if , then let , if , then perform the random sampling step; Wherein, N represents the number of grazing-incidence small-angle scattering experimental points; n represents the number of fitting parameters; represents the small-angle scattering vector of the i-th; Indicates the scattering intensity of grazing incidence small angle scattering in the experiment; Indicates the small-angle scattering intensity error in the experiment; Represents the scattering intensity of the model; Fitting termination step: Determine and the number of sampling times. If or the set upper limit of the number of sampling times is reached, then execute the result output step. If and the set upper limit is not reached, then execute the random sampling step and the loss function calculation step, and continue fitting; Result output step: Output the optimal parameters , and let the starting point be input into the gradient descent optimization algorithm.

2. The grazing incidence small angle scattering data fitting method according to claim 1, wherein The said Step S1 includes: Step S1.1: Select a burial model or a support model according to the geometric structure of the actual sample to be measured, and set the distribution density function of the spherical particle model and the scattering intensity of the grazing-incidence small-angle scattering model of the spherical particle , which are jointly used as the objective function; Construct a fitting function and set the parameters to be fitted ( ), and ( , ); Among them, represents the average value of the spherical particle radius; Represents the mean variance of the radius of spherical particles; Denote the radius of a single spherical particle; represents the mean variance of the radius of a single spherical particle; Represents the volume fraction coefficient of spherical particles; K represents the structural parameter; Indicates the in-plane emission angle; Indicates the minimum in-plane emission angle; Indicates the maximum in-plane emission angle; () represents the grazing-incidence small-angle scattering light intensity of the radius of a single spherical particle; denote the incident wave vector; Denote the outgoing wave vector; Indicates the incident angle; Indicates the exit angle; q represents the small-angle scattering vector; Step S1.2: Input the range q of the parameters to be fitted according to objective laws min , q max Construct the parameter space for parameter search; The said Step S2 includes: Step S2.1: Normalize the experimental data; Step S2.2: Set the upper and lower limits of the parameter space according to the range of parameters to be fitted and the set resolution; The said Step S3 includes: Step S3.1: Calculate the small-angle scattering intensity , ; Among them, represents the Porod constant; Indicates the Laue scattering intensity; Step S3.2: Draw a curve with as the horizontal axis and as the vertical axis. In the range of , judge the relationship of the scattering curve. If an obvious linear relationship appears, it indicates that is a constant at this time, determine that there are no nanoparticles, end the fitting. If no obvious linear relationship appears, determine that there are nanoparticles and continue to execute Step S4.

3. The grazing incidence small angle scattering data fitting method according to claim 1, wherein The said Step S5 includes: Initialization parameter steps: According to the optimal parameters The obtained starting point , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as ; Steps for calculating the gradient: For the loss function under the parameters, calculate the gradient of the loss function with respect to the parameters , ; Wherein, N represents the number of grazing-incidence small-angle scattering experimental points; n represents the number of fitting parameters; represents the small-angle scattering vector of the i-th; Indicates the scattering intensity of grazing-incidence small-angle scattering in the experiment; Indicates the small-angle scattering intensity error in the experiment; Represents the scattering intensity of the model; denotes the parameter value at the t-th iteration, ; Parameter update step: Update For , ; Abort Check and Result Output Step: Flush and calculate the loss function for the (t + 1)-th iteration and compare it with the loss function of the t-th iteration If or the maximum number of iterations is reached , terminate the iteration and execute the verification fitting quality step. If and the maximum number of iterations is not reached , execute the calculation gradient step and the parameter update step, and continue the iteration; Steps for verifying the fitting quality: Output the results of the fitting parameters , , and set the optimal solution of gradient descent , and judge . If , it is determined that the fitting quality meets the standard, and is retained. If , it is determined that the fitting quality does not meet the standard, and is discarded.

4. The grazing incidence small angle scattering data fitting method according to claim 1, wherein Step S6 includes: Step S6.1: Statistically process the fitting parameter results and output the final fitting result , and compare and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions in combination with other characterization methods; Step S6.2: Output the matching situation between the fitting data and the experimental data obtained from the final fitting result as one-dimensional and two-dimensional tables to obtain the visualized fitting results.

5. A grazing incidence small angle scattering data fitting system, characterized in that Including: Module M1: Construct a grazing-incidence small-angle scattering model to obtain an objective function; Module M2: Preprocess the experimental data and input it into the objective function; Module M3: Determine nanoparticles using the Porod fitting method based on the preprocessed experimental data; Module M4: Confirm the objective function according to the judgment result, perform Monte Carlo fitting, and output the optimal parameters; Module M5: Iteratively optimize the optimal parameters using the gradient descent method and output the fitting parameter results; Module M6: Post-process the fitting parameter results, output the visualized fitting results and evaluate; The said Module M4 includes: Initial parameter setting module: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ; Among them, represents a combined parameter; , respectively represent the minimum and maximum values of the combined parameters; Random sampling module: Generate a set of parameters for random distribution Input the objective function to obtain the model scattering intensity ; Loss function calculation module: Set the chi-square value of the initial optimal parameters , according to the parameter set Calculate the corresponding chi-square value of the loss function , judge , if , then let , if , then trigger the random sampling module; Wherein, N represents the number of grazing-incidence small-angle scattering experimental points; n represents the number of fitting parameters; represents the i-th small-angle scattering vector; Indicates the scattering intensity of grazing-incidence small-angle scattering in the experiment; Indicates the small-angle scattering intensity error in the experiment; Represents the scattering intensity of the model; Fitting termination module: Determine and the number of sampling times. If or the upper limit of the set number of sampling times is reached, trigger the result output module. If and the upper limit is not reached, trigger the random sampling module and the loss function calculation module to continue fitting; Result output module: Output the optimal parameters , and let the starting point be input into the gradient descent optimization algorithm.

6. The grazing incidence small angle scattering data fitting system according to claim 5, characterized in that The said Module M1 includes: Module M1.1: Select a buried model or a support model according to the geometric structure of the actual sample to be measured, and set the distribution density function of the spherical particle model and the scattering intensity of the grazing-incidence small-angle scattering model of spherical particles to be used together as the objective function; Construct a fitting function and set the parameters to be fitted ( ), and ( , ); Among them, represents the average value of the spherical particle radius; Indicates the mean variance of the spherical particle radius; Represents the radius of a single spherical particle; Represents the mean variance of the radius of a single spherical particle; Represents the volume fraction coefficient of spherical particles; K represents the structural parameter; Indicates the in-plane emission angle; Indicates the minimum in-plane emission angle; Indicates the maximum in-plane emission angle; () represents the grazing-incidence small-angle scattering light intensity of the radius of a single spherical particle; denotes the incident wave vector; Denote the outgoing wave vector; Indicates the incident angle; Denote the exit angle; q represents the small-angle scattering vector; Module M1.2: Input the range q of parameters to be fitted according to objective laws min , q max Construct the parameter space for parameter search; The said Module M2 includes: Module M2.1: Normalize the experimental data; Module M2.2: Set the upper and lower limits of the parameter space according to the range of parameters to be fitted and the set resolution; The said Module M3 includes: Module M3.1: Calculate small-angle scattering intensity , ; Among them, represents the Porod constant; Indicates the Laue scattering intensity; Module M3.2: Draw a curve with as the horizontal axis and as the vertical axis. Within the range of , judge the relationship of the scattering curve. If an obvious linear relationship appears, it indicates that is a constant at this time, determine that there are no nanoparticles, and end the fitting. If no obvious linear relationship appears, determine that there are nanoparticles and continue to trigger Module M4.

7. The grazing incidence small angle scattering data fitting system according to claim 5, wherein The said Module M5 includes: Initialization parameter module: According to the optimal parameters The obtained starting point , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as ; Calculation gradient module: For the loss function under the parameters, calculate the gradient of the loss function with respect to the parameters , ; Wherein, N represents the number of grazing-incidence small-angle scattering experimental points; n represents the number of fitting parameters; Denote the small-angle scattering vector of the i-th; Indicates the scattering intensity of grazing-incidence small-angle scattering in the experiment; Indicates the small-angle scattering intensity error in the experiment; Indicates the scattering intensity of the model; denotes the parameter value at the t-th iteration, ; Parameter update module: Update to , ; Suspension Check and Result Output Module: Flush and calculate the loss function for the (t + 1)-th iteration of the rinse and compare it with the loss function of the t-th iteration If or the maximum number of iterations is reached , terminate the iteration and trigger the verification fitting quality module. If and the maximum number of iterations is not reached , trigger the calculation gradient module and the parameter update module to continue the iteration; Verification fitting quality module: Output the fitting parameter results , , and set the optimal solution of gradient descent , judge , if , then it is determined that the fitting quality meets the standard, and retain , if , then it is judged that the fitting quality does not meet the standard, and discard .

8. The grazing incidence small angle scattering data fitting system according to claim 5, characterized in that, Module M6 includes: Module M6.1: Statistically process the fitting parameter results and output the final fitting results , and compare and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions in combination with other characterization methods; Module M6.2: Output the matching situation between the fitting data and the experimental data obtained from the final fitting result as one-dimensional and two-dimensional tables to obtain the visualized fitting results.

Images