Grazing incidence small angle scattering data fitting method and system

Abstract

The invention provides a grazing incidence small-angle scattering data fitting method and system, and the method comprises the steps: constructing a grazing incidence small-angle scattering model, and obtaining a target function; preprocessing experimental data and inputting a target function; according to the preprocessed experimental data, determining the nanoparticles by adopting a Pood fitting method; determining a target function according to a judgment result, performing Monte Carlo fitting, and outputting an optimal parameter; iteratively optimizing the optimal parameter by adopting a gradient descent method, and outputting a fitting parameter result; and post-processing the fitting parameter result, and outputting and evaluating a visual fitting result. According to the method, a multi-stage optimization process is introduced, so that the characterization deviation problems that the traditional data processing process depends on manual operation, the result is obviously influenced by subjective factors and model selection, and the stability is relatively poor are solved; the processing efficiency of GISAS experimental data and the quantitative characterization capacity of the microstructure are remarkably improved, the efficient processing requirement of multiple groups of experimental data can be met, and more reliable technical support is provided for subsequent material research.

Description

Technical Field

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

[0002] In the application of multiphase dense flow system, one phase is usually dispersed in the matrix phase with a very low volume fraction, such as protein distributed in water or metal precipitate phase in the matrix of alloy. Grazing incidence small angle scattering technology can extract some structural parameters of the target phase, including particle morphology, size distribution, surface roughness and volume fraction. Since the scattering signals between particles in the dense flow system will 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 a specific selected model 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 seem to 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 models and parameters, which are highly subjective and difficult to effectively cope with the processing needs of complex large-scale data.

[0004] The research results presented in the paper "Application of GISAXS in the Investigation of Three-Dimensional Lattices of Nanostructures" (Crystals 9.9 (2019): 479.) published in the journal "Crystals" in 2019 by Lovro Basioli et al. 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 requires the selection of corresponding models for different materials to describe the arrangement characteristics of nano-objects. Moreover, the study did not achieve automation of data fitting, and the fitting efficiency and result stability were limited by the experience of the researchers.

[0005] The patent document "Method and System for Automatic Fitting of Small-angle Scattering Data" (CN111159847A) discloses that the automatic fitting of small-angle scattering data is achieved by combining heuristic algorithms, gradient descent methods, and grid search methods, thereby greatly reducing the impact of human subjectivity in the data processing process. However, its coarse optimization is too simple, has poor robustness, and low adaptability, which leads to the easy loss of microstructure characterization information.

[0006] Therefore, there is an urgent need for an automated fitting method based on GISAS data that does not rely on additional model selection, can realize automatic search and fitting of model parameters, and avoid errors caused by human adjustments. Summary of the invention

[0007] In view of the defects in the prior art, an object of the present invention is to provide a grazing incidence small-angle scattering data fitting method and system.

[0008] A grazing incidence small angle scattering data fitting method provided by the present invention comprises: Step S1: construct a grazing incidence small angle scattering model to obtain the objective function; Step S2: preprocessing experimental data and inputting objective function; Step S3: using the Porod fitting method to determine the nanoparticles according to 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: Adopting gradient descent method to iteratively optimize the best parameters and output the fitting parameter results; Step S6: Post-process the fitting parameter results, output the visual fitting results and evaluate them.

[0009] Preferably, the step S1 comprises: Step S1.1: According to the actual geometric structure of the sample being tested, select the buried model or the support model and set the distribution density function of the spherical particle model. And the scattering intensity of the spherical particle grazing incidence small angle scattering model , together as the objective function; Construct a fitting function and set the parameters to be fitted ( )and( , ); in, Represents the average radius of spherical particles; represents the average variance of the radius of spherical particles; represents the radius of a single spherical particle; Represents the average variance of the radius of a single spherical particle; represents the volume fraction coefficient of spherical particles; K represents the structural parameter; represents the in-plane incidence angle; represents the minimum in-plane incidence angle; represents the maximum in-plane incidence angle; () represents the grazing incidence small-angle scattered light intensity of a single spherical particle radius; represents the incident wave vector; represents the outgoing wave vector; represents the angle of incidence; represents the exit angle; q represents the small-angle scattering vector; Step S1.2: Input the parameter range q to be fitted according to objective rules min ,q max Construct the parameter space for parameter search.

[0010] The step S2 comprises: Step S2.1: normalize the experimental data; Step S2.2: Set the upper and lower limits of the parameter space according to the parameter range to be fitted and the set resolution.

[0011] The step S3 comprises: Step S3.1: Calculate small angle scattering intensity , ; in, represents the Porod constant; represents the Laue scattering intensity; Step S3.2: Draw is the horizontal axis, The curve with vertical axis is n Within the range of , judge the relationship of the scattering curve. If it shows an obvious linear relationship, it means At this time, it is a constant, and it is determined that there are no nanoparticles, and the fitting is terminated. If no obvious linear relationship is presented, it is determined that there are nanoparticles, and step S4 is continued.

[0012] Preferably, the step S4 comprises: Initial parameter setting step: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ; in, Represents a combination parameter; , Respectively represent the minimum and maximum values ​​of the combined parameters.

[0013] Random sampling step: Generate a set of parameters from random distribution Input the objective function to get the model scattering intensity .

[0014] Loss function calculation steps: 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 perform the random sampling step; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; Represents the model scattering intensity.

[0015] Fitting termination step: judgment and the number of sampling times, if Or the upper limit of the sampling frequency is reached, the result output step is executed. If the upper limit is not reached, the random sampling step and the loss function calculation step are performed to continue fitting.

[0016] Result output step: Output the optimal parameters , and let the starting point Pass in the gradient descent optimization algorithm.

[0017] Preferably, step S5 comprises: Initialization parameter step: According to the optimal parameters The starting point obtained , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as .

[0018] Calculate the gradient step: Loss function under parameters Calculate the gradient of the loss function with respect to the parameters , ; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; represents the model scattering intensity; represents the parameter value of the tth iteration, .

[0019] Parameter update step: Update for , .

[0020] Abort inspection and result output step: flush calculation of the loss function for the t+1th iteration And the loss function of the tth iteration Compare, if or the maximum number of iterations is reached , then terminate the iteration and execute the step of verifying the fitting quality. If And the maximum number of iterations has not been reached , then the gradient calculation step and parameter update step are executed and the iteration continues.

[0021] Verify the fit quality step: Output the fit parameter results , , and let the gradient descend to the optimal solution ,judge ,like , then the fitting quality is judged to be up to standard and retained ,like , then the fitting quality is judged to be unsatisfactory and discarded .

[0022] Preferably, step S6 comprises: Step S6.1: Perform statistical processing on the fitting parameter results and output the final fitting results , and combined with other characterization methods to compare and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions; Step S6.2: The matching between the fitting data obtained according to the final fitting result and the experimental data is output as a one-dimensional and two-dimensional table to obtain a visual fitting result.

[0023] A grazing incidence small angle scattering data fitting system provided by the present invention comprises: Module M1: Construct a grazing incidence small-angle scattering model and obtain the objective function; Module M2: Preprocessing experimental data and inputting 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: Use gradient descent method to iteratively optimize the best parameters and output the fitting parameter results; Module M6: Post-process the fitting parameter results, output the visual fitting results and evaluate them.

[0024] Preferably, the module M1 comprises: Module M1.1: Select the buried model or the support model according to the actual geometric structure of the sample to be tested, and set the distribution density function of the spherical particle model And the scattering intensity of the spherical particle grazing incidence small angle scattering model , together as the objective function; Construct a fitting function and set the parameters to be fitted ( )and( , ); in, Represents the average radius of spherical particles; represents the average variance of the radius of spherical particles; represents the radius of a single spherical particle; Represents the average variance of the radius of a single spherical particle; represents the volume fraction coefficient of spherical particles; K represents the structural parameter; represents the in-plane incidence angle; represents the minimum in-plane incidence angle; represents the maximum in-plane incidence angle; () represents the grazing incidence small-angle scattered light intensity of a single spherical particle radius; represents the incident wave vector; represents the outgoing wave vector; represents the angle of incidence; represents the exit angle; q represents the small-angle scattering vector; Module M1.2: Input the parameter range q to be fitted according to objective laws min ,q max Construct the parameter space for parameter search.

[0025] The module M2 comprises: Module M2.1: Normalize the experimental data; Module M2.2: Set the upper and lower limits of the parameter space according to the parameter range to be fitted and the set resolution.

[0026] The module M3 comprises: Module M3.1: Calculation of small angle scattering intensity , ; in, represents the Porod constant; represents the Laue scattering intensity; Module M3.2: Draw is the horizontal axis, The curve with the vertical axis is Within the range of , judge the relationship of the scattering curve. If it shows an obvious linear relationship, it means At this time, it is a constant, and it is determined that there are no nanoparticles, and the fitting is terminated. If there is no obvious linear relationship, it is determined that there are nanoparticles, and the module M4 is triggered continuously.

[0027] Preferably, the module M4 comprises: Initial parameter setting module: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ; in, Represents a combination parameter; , Respectively represent the minimum and maximum values ​​of the combined parameters.

[0028] Random sampling module: Generate parameter sets from random distribution Input the objective function to get the model scattering intensity .

[0029] 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; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; Represents the model scattering intensity.

[0030] 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.

[0031] Result output module: output the best parameters , and let the starting point Pass in the gradient descent optimization algorithm.

[0032] Preferably, the module M5 comprises: Initialization parameter module: according to the optimal parameters The starting point obtained , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as .

[0033] Calculate gradient module: Loss function under parameters Calculate the gradient of the loss function with respect to the parameters , ; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; represents the model scattering intensity; represents the parameter value of the tth iteration, .

[0034] Parameter update module: Update for , .

[0035] Abort inspection and result output module: flush calculation of the loss function of the t+1th iteration And the loss function of the tth iteration Compare, if or the maximum number of iterations is reached , the iteration is terminated and the verification fitting quality module is triggered. If And the maximum number of iterations has not been reached , then the gradient calculation module and parameter update module are triggered to continue the iteration.

[0036] Verify Fitting Quality Module: Output Fitting Parameter Results , , and let the gradient descend to the optimal solution ,judge ,like , then the fitting quality is judged to be up to standard and retained ,like , then the fitting quality is judged to be unsatisfactory and discarded .

[0037] Preferably, module M6 comprises: Module M6.1: Perform statistical processing on the fitting parameter results and output the final fitting results , and combined with other characterization methods to compare and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions; Module M6.2: The matching between the fitting data and the experimental data obtained according to the final fitting results is output as one-dimensional and two-dimensional tables to obtain visual fitting results.

[0038] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention introduces a multi-stage optimization process to achieve fully automated processing from data preprocessing, model construction to parameter fitting, solving the problem of characterization deviation in which the traditional data processing process relies on manual operation, the results are significantly affected by subjective factors and model selection, and the stability is poor.

[0039] 2. The present invention combines Monte Carlo optimization with precise adjustment to achieve efficient processing of grazing-incidence small-angle scattering data, accurate fitting of model parameters, and quantitative characterization of material microstructure, which greatly improves the fitting accuracy. The fitting process is time-saving and can meet the needs of efficient processing of multiple sets of experimental data.

[0040] 3. The present invention solves the problem of loss of microstructure characterization information caused by insufficient adaptability of the data fitting model by adopting a multi-level optimization algorithm that combines Monte Carlo optimization with gradient descent, significantly improves the processing efficiency of GISAS experimental data and the quantitative characterization capability of microstructure, and provides more reliable technical support for subsequent material research. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings: Figure 1 This is a schematic diagram of the grazing incidence small angle scattering fitting process; Figure 2 This is a schematic diagram of grazing incidence small angle scattering geometry; Figure 3 This is a schematic diagram of the original data of the RPV high-energy iron ion 300℃ irradiation sample experiment; Figure 4 This is a schematic diagram of one-dimensional data of the RPV high-energy iron ion 300℃ irradiation sample experiment; Figure 5 This is a schematic diagram of the fitting results of the RPV high-energy iron ion 300℃ irradiation sample experiment; Figure 6 This is a schematic diagram of the original data of the RPV low-energy iron ion 200℃ irradiation sample experiment; Figure 7 This is a schematic diagram of one-dimensional data of the RPV low-energy iron ion 200℃ irradiation sample experiment; Figure 8 This is a schematic diagram of the fitting results of the RPV low-energy iron ion 200℃ irradiation sample experiment; Fig. 9 This is a schematic diagram of the original data of the RPV medium-energy proton room-temperature irradiation sample experiment; Fig.10 This is a schematic diagram of one-dimensional data of the RPV medium-energy proton room-temperature irradiation sample experiment; Fig.11 Schematic diagram of the fitting results of the RPV medium-energy proton room-temperature irradiation sample experiment. DETAILED DESCRIPTION

[0042] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0043] The present invention is based on automated processing and fitting technology to solve the shortcomings of traditional methods in GISAS experimental data processing due to human intervention and model limitations. By introducing a multi-stage optimization process, fully automated processing from data preprocessing, model construction to parameter fitting is achieved.

[0044] According to a grazing incidence small angle scattering data fitting method provided by the present invention, Figure 1 For example, starting from the normalization and filtering of experimental data, multi-dimensional fitting optimization of the material microstructure is performed, and advanced optimization algorithms (such as Monte Carlo fitting and gradient descent) and error analysis methods are combined to ensure the high accuracy and repeatability of the final results. The specific steps include: Step S1: Establishing a grazing incidence small-angle scattering model (Model Selection).

[0045] 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; The grazing incidence small angle scattering (GISAS) burial model is selected, where the structure factor depends not only on the scattering vector, but also on the incident and outgoing vectors. Each term is weighted by the corresponding Fresnel reflection coefficient and refraction coefficient, which are defined at the reflection or refraction stage, respectively, to obtain the shape factor of the modified grazing incidence small angle scattering burial model.

[0046] Spherical particles are one of the most common forms of precipitation phases and are widely found in a variety of material systems, such as metal alloys, polymers, and nanocomposites. The formation of such particles is usually closely related to the heat treatment or phase change process of the material, and their size, distribution, and morphology have a significant impact on the microstructure and macroscopic properties of the material.

[0047] Spherical particles usually have a certain embedding depth and rotation angle in the surface layer. For spherical particles, the rotation angle does not affect the vector distribution because the spherical particles are assumed to be isotropic. The rotation matrix of the combined scattering vector under burial is obtained. In order to simplify the model to a certain extent and to match the actual experimental results (most of the spherical particles in RPV and other samples have no embedding depth), it is assumed that the embedding depth , from which we can further derive the calculation formula for the single-particle spherical grazing-incidence small-angle scattering intensity.

[0048] In the spherical particle model setting stage, first of all, it is necessary to confirm whether the location of the nanoparticles is embedded in the substrate based on the actual geometric structure of the sample being tested. If so, a buried model needs to be selected; otherwise, a supported model needs to be selected.

[0049] Secondly, in the precipitated nanoparticles of metal alloy samples, the size often follows a log-Gaussian distribution. Here, we can assume that any structural parameter It follows a logarithmic Gaussian distribution, and its distribution density function is , then there is a corresponding parameter ( ) makes:

[0050] The corresponding fitting parameters and the expressions of their intensity in grazing incidence small angle scattering of spherical particles;

[0051] In summary, in the model setting stage, ( The parameters are intermediate phases in the simulation fitting process and have no effect on the significance of the overall fitting experiment.

[0052] The parameters to be fitted are selected into two categories: the first category is the parameters that need to be fitted for the logarithmic Gaussian distribution model, which is ( ); The second type is the parameters that need to be fitted for the scattering intensity of spherical particles, which are ( , ).

[0053] in, Represents the average radius of spherical particles; represents the average variance of the radius of spherical particles; represents the radius of a single spherical particle; Represents the average variance of the radius of a single spherical particle; represents the volume fraction coefficient of spherical particles; K represents the structural parameter; represents the in-plane incidence angle; represents the minimum in-plane incidence angle; represents the maximum in-plane incidence angle; () represents the grazing incidence small-angle scattered light intensity of a single spherical particle radius; represents the incident wave vector; represents the outgoing wave vector; represents the angle of incidence; represents the exit angle; q represents the small-angle scattering vector.

[0054] A larger parameter range is selected based on objective laws, for example, the nanoparticle range is 0.1nm–100nm.

[0055] Step S1.2: Input range according to experimental data (such as q min ,q max ) to construct a parameter search space.

[0056] Step S2: Experimental data preprocessing (Input Pre-processing).

[0057] Step S2.1: Normalize the experimental data to ensure the balance of the data in terms of error weight and distribution; Step S2.2: Set the upper and lower limits of the search space according to the experimental data range and resolution.

[0058] Step S3: using the Porod fitting method to determine the nanoparticles.

[0059] 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:

[0060] in, is called the Porod constant, represents the Laue scattering intensity, The value is between 3 and 4, reflecting the geometric characteristics of the scattering surface. When it is close to 4, the surface of the sample can be considered to be relatively smooth, while smaller It represents a rough or diverse surface. represents the Laue scattering intensity; In the fitting of grazing incidence small angle scattering data, the surface is relatively smooth, so we use .

[0061] Draw with is the horizontal axis, The curve with the vertical axis is If the scattering curve shows an obvious linear relationship within the range of It is a constant in this region, while the linear relationship corresponds to the dominant contribution of the sample surface or interface characteristics rather than the contribution of the granular structure to the scattering. The above judgment method can effectively identify whether there are small nano-precipitated phase particles in the sample, especially in the research of processing irradiated samples. It can 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 first judgment step after VGISAS data preprocessing, so as to optimize the subsequent fitting process after confirming the existence of small-scale structures.

[0062] Step S4: Monte Carlo fitting (Coarse Tuning).

[0063] This process aims to confirm whether the global 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 area in the parameter space, effectively explore the parameter space, and improve the accuracy of the fitting results through higher-precision local optimization, providing high-quality initial parameters for subsequent gradient descent optimization, thereby improving optimization accuracy and efficiency.

[0064] The Monte Carlo method divides the parameter space into high-dimensional grids and generates random combinations of parameters. To calculate the scattering intensity After each sampling, the performance of its parameter combination in the loss function is evaluated and its chi-square value is calculated ( ), ; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; Represents the model scattering intensity.

[0065] Specifically, the steps include: Initial parameter setting steps: Set the parameter range in the parameter space , the scope is reasonably defined through empirical data or prior knowledge; Random sampling step: Generate a set of parameters using a random distribution , the generated parameters are used to calculate the model scattering intensity ; Loss function calculation steps: Calculate the corresponding loss function value according to each set of random parameters , compare it with the optimal value and judge ,like , then let ,like , then perform the random sampling step; Fitting termination step: judgment and the number of sampling times, if Or the upper limit of the sampling number is reached, the fitting is terminated. If the upper limit is not reached, the fitting continues; Result output step: Output the optimal parameters , and order Pass in the gradient descent optimization algorithm as a starting point.

[0066] Compared with traditional methods, the Monte Carlo fitting and gradient descent algorithms can realize automatic search and fitting of model parameters, avoiding errors caused by manual adjustments. At the same time, it can efficiently process multiple sets of GISAS data and integrate the results under different experimental conditions, significantly improving analysis efficiency.

[0067] Step S5: Adopting the gradient descent method to iteratively update the parameters and gradually approach the global optimal solution; The gradient descent optimization method is a classic iterative optimization algorithm. Its core idea is to gradually adjust the parameters by calculating the gradient information of the objective function (such as the loss function or the chi-square statistic) so that it approaches the optimal solution along the direction where the objective function decreases fastest. In the VGISAS fitting algorithm, the gradient descent method uses the gradient information to achieve efficient local optimization, which is an important supplement to the global search of the Monte Carlo method.

[0068] In the gradient descent method, the objective function is assumed to be the loss function ,in is the optimal solution after Monte Carlo fitting, which represents the set of fitting parameters. Then the gradient descent adjusts the parameters by updating the following formula:

[0069] in, represents the parameter value of the tth iteration, is the learning rate, which controls the step size of each update, is the gradient of the loss function to the parameter, indicating the changing trend of the current parameter to the objective function value. Therefore, in VGISAS fitting, the objective function chi-square statistic The gradient of can be expressed as:

[0070] The specific application steps of the gradient optimization algorithm in VGISAS are as follows: 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 , record the initial gradient as ; Gradient calculation step: loss function under current parameters Computing Gradients ; Parameter update step: Update for ; 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; 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.

[0071] 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.

[0072] 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.

[0073] Step S6: Data post-processing (Post-process).

[0074] 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; 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.

[0075]

[0076] In the table, It represents the average radius of spherical particles of sample number RPV-HE-300T-1.0dpa, It represents the average variance of the radius of a single spherical particle of sample number RPV-HE-300T-1.0dpa.

[0077] These differences are reasonable because: APT mainly collects atoms on the surface of the tip sample, and there may be a "truncation effect" in 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, which is because the grazing incidence method is more sensitive to the nanostructure of the sample surface and near-surface area, and under high-energy particle irradiation conditions, the irradiation effect is often concentrated on the surface or near-surface area of ​​the material, resulting in accelerated atomic migration and rearrangement in the surface area, thereby forming a larger precipitate phase.

[0078] Step S6.2: Provide confidence intervals and optimization reports for the fitting results, including confidence interval estimates for each fitting parameter and quantitative analysis of the overall performance of the fitting model. At the same time, the chi-square test ( ) and mean square error test ( ), quantitatively evaluate the accuracy and consistency of the fitting results to determine whether the model is statistically consistent with the experimental data; Step S6.3: Visualize the fitting results, intuitively present the matching between the fitting data and the experimental data through one-dimensional and two-dimensional tables, and perform distribution analysis on the fitting residuals through images to enhance the intuitive understanding of the fitting quality.

[0079] Since there is no need to rely on additional model selection, the complete information in the original two-dimensional scattering image can be retained, and the anisotropy and complex arrangement characteristics of the microstructure can be accurately characterized.

[0080] In more preferred examples, the samples in the sample list are experimentally fitted. Under the set conditions, all samples are subjected to the action of specific irradiation energy and temperature, resulting in the formation of precipitates in the internal microstructure, which are specifically manifested as spherical particles. Such precipitates are common damage products of various steel alloy materials in nuclear irradiation environments. Their size distribution, density and phase structure characteristics are characterized by Figure 2 For example, the grazing incidence small angle scattering (GISAXS) technique accurately captures

[0081] Table 1. Experimental sample list:

[0082] The experimental data of the samples were processed and analyzed. For RPV steel, the high-energy iron ion irradiation intensity was 300℃, and the irradiation damage was 1.0dpa, with 50μm uniform damage on the front and back sides. The original data of the grazing incidence small angle scattering experiment was as follows: Figure 3 As shown, the experimental one-dimensional data is Figure 4 The fitting results are shown in Figure 5 As shown. I is the abbreviation of intensity, q xy Indicates the amount of radiation damage.

[0083] Table 2. Fitting results of RPV high energy iron ion irradiation samples at 300℃:

[0084] In more preferred examples, for RPV steel, low-energy iron ions are irradiated at 200°C with an irradiation damage amount of 1.0 dpa. The raw data of the grazing incidence small angle scattering experiment are as follows: Figure 6 As shown, the experimental one-dimensional data is Figure 7 The fitting results are shown in Figure 8 shown.

[0085] Table 3. Fitting results of RPV low energy iron ion 200℃ irradiated samples:

[0086] In more preferred examples, for RPV medium energy protons at room temperature, the irradiation intensity is 0.35 dpa, and the raw data of the grazing incidence small angle scattering experiment is as follows: Fig. 9 As shown, the experimental one-dimensional data is Fig.10 The fitting results are shown in Fig.11 shown.

[0087] Table 4. Fitting results of RPV medium energy proton room temperature irradiation samples:

[0088] The present invention also provides a grazing incidence small-angle scattering data fitting system, which can be implemented 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 a preferred implementation of the grazing incidence small-angle scattering data fitting system.

[0089] A grazing incidence small angle scattering data fitting system provided by the present invention comprises: Module M1: Construct a grazing incidence small-angle scattering model and obtain the objective function; Module M2: Preprocessing experimental data and inputting 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: Use gradient descent method to iteratively optimize the best parameters and output the fitting parameter results; Module M6: Post-process the fitting parameter results, output the visual fitting results and evaluate them.

[0090] In more preferred embodiments, the module M1 includes: Module M1.1: Select the buried model or the support model according to the actual geometric structure of the sample to be tested, and set the distribution density function of the spherical particle model And the scattering intensity of the spherical particle grazing incidence small angle scattering model , together as the objective function; Construct a fitting function and set the parameters to be fitted ( )and( , ); in, Represents the average radius of spherical particles; represents the average variance of the radius of spherical particles; represents the radius of a single spherical particle; Represents the average variance of the radius of a single spherical particle; represents the volume fraction coefficient of spherical particles; K represents the structural parameter; represents the in-plane incidence angle; represents the minimum in-plane incidence angle; represents the maximum in-plane incidence angle; () represents the grazing incidence small-angle scattered light intensity of a single spherical particle radius; represents the incident wave vector; represents the outgoing wave vector; represents the angle of incidence; represents the exit angle; q represents the small-angle scattering vector; Module M1.2: Input the parameter range q to be fitted according to objective laws min ,q max Construct the parameter space for parameter search.

[0091] The module M2 comprises: Module M2.1: Normalize the experimental data; Module M2.2: Set the upper and lower limits of the parameter space according to the parameter range to be fitted and the set resolution.

[0092] The module M3 comprises: Module M3.1: Calculation of small angle scattering intensity , ; in, represents the Porod constant; represents the Laue scattering intensity; Module M3.2: Draw is the horizontal axis, The curve with the vertical axis is Within the range of , judge the relationship of the scattering curve. If it shows an obvious linear relationship, it means At this time, it is a constant, and it is determined that there are no nanoparticles, and the fitting is terminated. If there is no obvious linear relationship, it is determined that there are nanoparticles, and the module M4 is triggered continuously.

[0093] In more preferred embodiments, the 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 ; in, Represents a combination parameter; , Respectively represent the minimum and maximum values ​​of the combined parameters.

[0094] Random sampling module: Generate parameter sets from random distribution Input the objective function to get the model scattering intensity .

[0095] 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; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; Represents the model scattering intensity.

[0096] 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.

[0097] Result output module: output the best parameters , and let the starting point Pass in the gradient descent optimization algorithm.

[0098] In more preferred embodiments, the module M5 includes: Initialization parameter module: according to the optimal parameters The starting point obtained , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as .

[0099] Calculate gradient module: Loss function under parameters Calculate the gradient of the loss function with respect to the parameters , ; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; represents the model scattering intensity; represents the parameter value of the tth iteration, .

[0100] Parameter update module: Update for , .

[0101] Abort inspection and result output module: flush calculation of the loss function of the t+1th iteration And the loss function of the tth iteration Compare, if or the maximum number of iterations is reached , the iteration is terminated and the verification fitting quality module is triggered. If And the maximum number of iterations has not been reached , then the gradient calculation module and parameter update module are triggered to continue the iteration.

[0102] Verify Fitting Quality Module: Output Fitting Parameter Results , , and let the gradient descend to the optimal solution ,judge ,like , then the fitting quality is judged to be up to standard and retained ,like , then the fitting quality is judged to be unsatisfactory and discarded .

[0103] In more preferred embodiments, module M6 includes: Module M6.1: Perform statistical processing on the fitting parameter results and output the final fitting results , and combined with other characterization methods to compare and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions; Module M6.2: The matching between the fitting data and the experimental data obtained according to the final fitting results is output as one-dimensional and two-dimensional tables to obtain visual fitting results.

[0104] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0105] The above describes the specific embodiments of the present invention. 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. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A grazing incidence small angle scattering data fitting method, characterized in that: include: Step S1: construct a grazing incidence small angle scattering model to obtain the objective function; Step S2: preprocessing experimental data and inputting objective function; Step S3: using the Porod fitting method to determine the nanoparticles according to 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: Adopting gradient descent method to iteratively optimize the best parameters and output the fitting parameter results; Step S6: Post-process the fitting parameter results, output the visual fitting results and evaluate them.

2. The grazing incidence small angle scattering data fitting method according to claim 1, characterized in that: The step S1 comprises: Step S1.1: According to the actual geometric structure of the sample being tested, select the buried model or the support model and set the distribution density function of the spherical particle model. And the scattering intensity of the spherical particle grazing incidence small angle scattering model , together as the objective function; Construct a fitting function and set the parameters to be fitted ( )and( , ); in, Represents the average radius of spherical particles; represents the average variance of the radius of spherical particles; represents the radius of a single spherical particle; Represents the average variance of the radius of a single spherical particle; represents the volume fraction coefficient of spherical particles; K represents the structural parameter; represents the in-plane incidence angle; represents the minimum in-plane incidence angle; represents the maximum in-plane incidence angle; () represents the grazing incidence small angle scattered light intensity of a single spherical particle radius; represents the incident wave vector; represents the outgoing wave vector; represents the angle of incidence; represents the exit angle; q represents the small-angle scattering vector; Step S1.2: Input the parameter range q to be fitted according to objective rules min ,q max Construct parameter space for parameter search; The step S2 comprises: Step S2.1: normalize the experimental data; Step S2.2: according to the range of parameters to be fitted and the set resolution, set the upper and lower limits of the parameter space; The step S3 comprises: Step S3.1: Calculate small angle scattering intensity , ; in, represents the Porod constant; represents the Laue scattering intensity; Step S3.2: Draw is the horizontal axis, The curve with the vertical axis is Within the range of , judge the relationship of the scattering curve. If it shows an obvious linear relationship, it means At this time, it is a constant, and it is determined that there are no nanoparticles, and the fitting is terminated. If no obvious linear relationship is presented, it is determined that there are nanoparticles, and step S4 is continued.

3. The grazing incidence small angle scattering data fitting method according to claim 1, characterized in that: The step S4 comprises: Initial parameter setting step: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ; in, Represents a combination parameter; , Respectively represent the minimum and maximum values ​​of the combined parameters; Random sampling step: Generate a set of parameters from random distribution Input the objective function to get the model scattering intensity ; Loss function calculation steps: 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 perform the random sampling step; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; represents the model scattering intensity; Fitting termination step: judgment and the number of sampling times, if Or the upper limit of the sampling frequency is reached, the result output step is executed. If the upper limit is not reached, the random sampling step and the loss function calculation step are performed to continue fitting; Result output step: Output the optimal parameters , and let the starting point Pass in the gradient descent optimization algorithm.

4. The grazing incidence small angle scattering data fitting method according to claim 1, characterized in that: The step S5 comprises: Initialization parameter step: According to the optimal parameters The starting point obtained , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as ; Calculate the gradient step: Loss function under parameters Calculate the gradient of the loss function with respect to the parameters , ； Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; represents the model scattering intensity; represents the parameter value of the tth iteration, ; Parameter update step: Update for , ; Abort inspection and result output step: flush calculation of the loss function for the t+1th iteration And the loss function of the tth iteration Compare, if or the maximum number of iterations is reached , then terminate the iteration and execute the step of verifying the fitting quality. If And the maximum number of iterations has not been reached , then execute the gradient calculation step and parameter update step, and continue iterating; Verify the fit quality step: Output the fit parameter results , , and let the gradient descend to the optimal solution ,judge ,like , then the fitting quality is judged to be up to standard and retained ,like , then the fitting quality is judged to be unsatisfactory and discarded .

5. The grazing incidence small angle scattering data fitting method according to claim 1, characterized in that: Step S6 includes: Step S6.1: Perform statistical processing on the fitting parameter results and output the final fitting results , and combined with other characterization methods to compare and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions; Step S6.2: The matching between the fitting data obtained according to the final fitting result and the experimental data is output as a one-dimensional and two-dimensional table to obtain a visual fitting result.

6. A grazing incidence small angle scattering data fitting system, characterized in that: include: Module M1: Construct a grazing incidence small-angle scattering model and obtain the objective function; Module M2: Preprocessing experimental data and inputting 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: Use gradient descent method to iteratively optimize the best parameters and output the fitting parameter results; Module M6: Post-process the fitting parameter results, output the visual fitting results and evaluate them.

7. The grazing incidence small angle scattering data fitting system according to claim 6, characterized in that: The module M1 comprises: Module M1.1: Select the buried model or the support model according to the actual geometric structure of the sample to be tested, and set the distribution density function of the spherical particle model And the scattering intensity of the spherical particle grazing incidence small angle scattering model , together as the objective function; Construct a fitting function and set the parameters to be fitted ( )and( , ); in, Represents the average radius of spherical particles; represents the average variance of the radius of spherical particles; represents the radius of a single spherical particle; Represents the average variance of the radius of a single spherical particle; represents the volume fraction coefficient of spherical particles; K represents the structural parameter; represents the in-plane incidence angle; represents the minimum in-plane incidence angle; represents the maximum in-plane incidence angle; () represents the grazing incidence small angle scattered light intensity of a single spherical particle radius; represents the incident wave vector; represents the outgoing wave vector; represents the angle of incidence; represents the exit angle; q represents the small-angle scattering vector; Module M1.2: Input the parameter range q to be fitted according to objective laws min ,q max Construct parameter space for parameter search; The module M2 comprises: Module M2.1: Normalize the experimental data; Module M2.2: Set the upper and lower limits of the parameter space according to the parameter range to be fitted and the resolution to be set; The module M3 comprises: Module M3.1: Calculation of small angle scattering intensity , ; in, represents the Porod constant; represents the Laue scattering intensity; Module M3.2: Draw is the horizontal axis, The curve with the vertical axis is Within the range of , judge the relationship of the scattering curve. If it shows an obvious linear relationship, it means At this time, it is a constant, and it is determined that there are no nanoparticles, and the fitting is terminated. If there is no obvious linear relationship, it is determined that there are nanoparticles, and the module M4 is triggered continuously.

8. The grazing incidence small angle scattering data fitting system according to claim 6, characterized in that: The module M4 comprises: Initial parameter setting module: Set the parameter range in the parameter space of the objective function through empirical data or prior knowledge ; in, Represents a combination parameter; , Respectively represent the minimum and maximum values ​​of the combined parameters; Random sampling module: Generate parameter sets from random distribution Input the objective function to get the model scattering intensity ; 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; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; represents the model scattering intensity; 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 upper limit is not reached, the random sampling module and loss function calculation module are triggered to continue fitting; Result output module: output the best parameters , and let the starting point Pass in the gradient descent optimization algorithm.

9. The grazing incidence small angle scattering data fitting system according to claim 6, characterized in that: The module M5 comprises: Initialization parameter module: according to the optimal parameters The starting point obtained , , set the initial learning rate and the maximum number of iterations , , calculate the initial loss function , record the initial gradient as ; Calculate gradient module: Loss function under parameters Calculate the gradient of the loss function with respect to the parameters , ; Where 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; represents the scattering intensity of grazing incidence small-angle scattering in the experiment; represents the small-angle scattering intensity error in the experiment; represents the model scattering intensity; represents the parameter value of the tth iteration, ; Parameter update module: Update for , ; Abort inspection and result output module: flush calculation of the loss function of the t+1th iteration And the loss function of the tth iteration Compare, if or the maximum number of iterations is reached , the iteration is terminated and the verification fitting quality module is triggered. If And the maximum number of iterations has not been reached , then the gradient calculation module and parameter update module are triggered to continue iteration; Verify Fitting Quality Module: Output Fitting Parameter Results , , and let the gradient descend to the optimal solution ,judge ,like , then the fitting quality is judged to be up to standard and retained ,like , then the fitting quality is judged to be unsatisfactory and discarded .

10. The grazing incidence small angle scattering data fitting system according to claim 6, characterized in that: Module M6 includes: Module M6.1: Perform statistical processing on the fitting parameter results and output the final fitting results , and combined with other characterization methods to compare and evaluate the physical meaning of the fitting parameters and their rationality under experimental conditions; Module M6.2: The matching between the fitting data and the experimental data obtained according to the final fitting results is output as one-dimensional and two-dimensional tables to obtain visual fitting results.

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