A method and system for predicting the microstructure of a material by materializing a two-point correlation function

Abstract

The present invention discloses a method and system for material microstructure prediction by materializing the two-point correlation function. The method first initializes the microstructure image and calculates the Fourier amplitude from the target two-point autocorrelation function; applies Fourier constraints, support domain constraints, and characteristic microstructure constraints to the microstructure image; then performs image processing operations; adjusts the microstructure image by stage-wise phase volume fraction to optimize the microstructure morphology stage-wise; and finally obtains the materialized predicted microstructure. The microstructure materialization prediction method disclosed by the present invention is close to the classical simulated annealing algorithm in terms of calculation accuracy and is comparable to the traditional hybrid input-output algorithm in terms of calculation efficiency. It has strong generalization ability and broad application prospects and can provide technical support for process-structure-property relationship modeling, microstructure optimization, new material design, etc.

Description

Technical Field

[0001] The present invention belongs to the technical field of material microstructure informatics, and in particular relates to a method and system for materializing and predicting material microstructure from a two-point correlation function. Background Art

[0002] Identifying and understanding the microstructural information of materials plays a key role in promoting the forward prediction and reverse search of process-structure-performance (PSP), leading to the flourishing of many advanced technologies and algorithms in the field of materials, such as machine learning, neural network series methods, two-point correlation function methods, dimensionality reduction algorithms, etc. Among them, the two-point correlation function method has been proven to be one of the best solutions. Although coupling the structural information of the two-point correlation function statistics can accelerate PSP modeling, it is still a huge challenge to instantiate the microstructure from the two-point correlation function information predicted by the model, which hinders the normal implementation of a series of scientific tasks such as direct verification of the accuracy of the PSP model and optimization design of the microstructure. Therefore, the instantiation and prediction of the microstructure from the two-point correlation function is an urgent and challenging scientific problem to be solved.

[0003] Driven by the fourth data-driven paradigm, it has become an inevitable trend to carry out materials science research with high efficiency and low cost, which requires relevant research in the field of PSP modeling to consider both the high efficiency and high precision of calculation or experiment at the same time. The classical simulated annealing method can achieve the goal of accurately materializing the prediction of the microstructure from the two-point correlation function, but its computational efficiency is low. Usually, it takes more than 10 hours to calculate on a numerical picture with a 200×200 grid. The literature [Yuksel C. Yabansu, Almambet Iskakov, Anna Kapustina, Sudhir Rajagopalan, Surya R. Kalidindi, Application of Gaussian process regression models for capturing the evolution of microstructure statistics in aging of nickel-based superalloys, Acta Materialia, 178 (2019) 45-58] also reported a method for predicting the materialization of microstructure developed based on image processing technology. This method has an extremely high computational speed (<10s), but its universality is poor. The literature [David T. Fullwood, Stephen R. Niezgoda, Surya R. Kalidindi, Microstructure reconstructions from 2-point statistics using phase-recovery algorithms, Acta Materialia, 56 (2008) 942-948] reported another fast method for predicting the materialization of microstructure based on Fourier transform. Compared with the methods in the above two literatures, this method has the advantages of both high efficiency and high precision. However, due to the special requirement of all-lossless two-point correlation function input, this method cannot be extended to the actual PSP modeling process. Although the above various methods have their own advantages, none of them provide a technical solution that combines high efficiency, reliability and universality for materializing the prediction of microstructure from two-point correlation functions. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above-mentioned disadvantages of the prior art and provide a method and system for materializing the prediction of the microstructure of materials from two-point correlation functions, so as to solve the problem that it is difficult for the prior art methods for predicting the microstructure to have high efficiency, reliability and universality at the same time.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions:

[0006] A method for predicting the microstructure of a material by materializing a two-point correlation function, comprising the following steps:

[0007] Step 1, obtaining an initial microstructure image, obtaining a Fourier amplitude based on a target two-point autocorrelation function, and a target volume fraction of a target phase in the initial microstructure image;

[0008] Step 2, after performing a Fourier transform and an inverse Fourier transform on the initial microstructure image, applying a support domain constraint and a characteristic microstructure constraint to the microstructure image after the inverse Fourier transform to obtain a constrained microstructure image;

[0009] Step 3, processing the constrained microstructure image through image processing operations;

[0010] Step 4, through a cross-species pixel nearest neighbor base pixel exchange rule, performing a staged adjustment on the original volume fraction of a target processed phase in the image obtained in Step 3 until the difference between the adjusted volume fraction of the target phase and the target volume fraction of the target phase is less than a set threshold, or the number of times of adjusting the volume fraction of the target phase reaches the maximum number of loop times, obtaining an image with the volume fraction of the target phase adjusted, and then performing Step 5;

[0011] Step 5, through a cross-species pixel nearest neighbor base pixel exchange rule, determining the number of pixel points exchanged between two phases in the image with the volume fraction adjusted and exchanging pixels to optimize the microstructure morphology, obtaining an optimized microstructure image;

[0012] Step 6, determining whether the optimized microstructure image meets a termination condition. If it meets, perform Step 7. If it does not meet, return to Step 3;

[0013] Step 7, outputting the materialized predicted microstructure of the microstructure image.

[0014] A further improvement of the present invention lies in:

[0015] Preferably, in Step 2, the initial Fourier transform is:

[0016]

[0017] The image obtained by Fourier-transforming with a Fourier amplitude constraint is:

[0018] G' k = |M|·e iφ

[0019] The process of the inverse Fourier transform is:

[0020]

[0021] where g kis the initial microstructure image, M is the Fourier amplitude, and the calculation formula is:

[0022]

[0023] Among them, S is The number of grids, yes The Fourier transform of is the target two-point autocorrelation function.

[0024] Preferably, in step 2, the constraints of the inverse Fourier transformed image include support region constraints and characteristic microstructure constraints:

[0025]

[0026] where β is a constant in the range of 0.5-1, γ is the support domain, and EM is the characteristic microstructural constraint, ensuring that g' k The array contains only the numbers 0 or 1.

[0027] Preferably, in step 3, the image processing operation includes a morphological opening operation and a morphological closing operation.

[0028] Preferably, in step 4, the process of adjusting the volume fraction in stages comprises the following steps:

[0029] S41, obtaining the two-point autocorrelation function and phase volume fraction of the image obtained in step 3, obtaining the difference between the volume fraction of the target phase and the target volume fraction of the target phase, and calculating the error value;

[0030] S42, determining whether the error value is less than a critical threshold, if so, executing step 5; otherwise, executing step S43;

[0031] S43, calculating the pixel values ​​of the image obtained in step 3 and the number of pixels to be exchanged, exchanging the pixel values ​​according to the heterogeneous pixel neighbor-based pixel exchange rule, updating the image, and calculating the two-point autocorrelation function, phase volume fraction and error value of the updated image;

[0032] S44, determining whether the error value obtained in S43 is reduced, if reduced, executing step S45, otherwise returning to step S43;

[0033] S45, recording the updated image and error value;

[0034] S46, determining whether the number of cycles of the current volume fraction adjustment reaches the preset maximum number of cycles, if so, inputting the updated image and error value, if not, returning to S43.

[0035] Preferably, the specific process of step 5 is:

[0036] S51. Calculate the two-point autocorrelation function and the error value of the image with adjusted volume fraction, and determine the number of pixels to be exchanged.

[0037] S52. Exchange pixels according to the rule of exchanging neighboring base pixels of different types of pixels to obtain the image after pixel exchange, and calculate the two-point autocorrelation function and the error value of the pixel image after exchange.

[0038] S53. Determine whether the topography optimization condition is satisfied. If it is satisfied, execute S54; if not, return to S52.

[0039] S54. Determine whether the number of loops for the current microstructure topography optimization has reached the preset maximum number of loops. If it is satisfied, output the optimized microstructure image; otherwise, execute S52.

[0040] Preferably, in S53, the topography optimization condition is whether the error value is less than 0.

[0041] Preferably, in step 6, the termination condition is that the number of iterations reaches the set maximum number, or the error value is less than the set value.

[0042] Preferably, the calculation formula of the error value is:

[0043]

[0044] where is the two-point autocorrelation function of the materialized predicted microstructure.

[0045] A system for materializing and predicting the microstructure of materials from the two-point correlation function includes:

[0046] An initialization module, configured to obtain an initial microstructure image, obtain the Fourier amplitude based on the target two-point autocorrelation function, and the target volume fraction of the target phase in the initial microstructure image.

[0047] A constraint application module, configured to perform Fourier transform and inverse Fourier transform on the initial microstructure image, and then apply a support domain constraint and a characteristic microstructure constraint to the microstructure image after inverse Fourier transform to obtain a constrained microstructure image.

[0048] An image processing module, configured to process the constrained microstructure image through image processing operations.

[0049] A stepwise error reduction module is used to perform stepwise adjustment on the original volume fraction of the target processing phase in the image obtained by the image processing module through the heterogeneous pixel neighboring base pixel exchange rule until the difference between the volume fraction of the adjusted target phase and the target volume fraction of the target phase is less than the set threshold, or the number of times of adjusting the volume fraction of the target phase reaches the maximum number of cycles, so as to obtain an image with the volume fraction of the target phase adjusted;

[0050] A morphology optimization module determines the number of pixel points exchanged between two phases in the image with the volume fraction adjusted through the heterogeneous pixel neighboring base pixel exchange rule, exchanges pixels, optimizes the microstructure morphology, and obtains an optimized microstructure image;

[0051] A judgment module judges whether the optimized microstructure image meets the termination condition. If it meets, the physical prediction output module is executed. If it does not meet, it returns to the image processing module;

[0052] The physical prediction output module outputs the physically predicted microstructure of the microstructure image.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] The present invention discloses a method for physically predicting the microstructure of a material from a two-point correlation function. The method includes: 1) initializing a microstructure picture and calculating the Fourier amplitude from the target two-point autocorrelation function; 2) applying Fourier constraints, support domain constraints, and characteristic microstructure constraints; 3) performing image processing operations; 4) stepwise adjusting the phase volume fraction to quickly reduce errors; 5) stepwise optimizing the microstructure morphology; 6) repeating steps 2-5. When the termination condition is met, the physically predicted microstructure is obtained. The microstructure physical prediction method disclosed by the present invention is close to the classical simulated annealing algorithm in terms of calculation accuracy and equivalent to the traditional hybrid input-output algorithm in terms of calculation efficiency. It has strong generalization ability and broad application prospects, and can provide technical support for process-structure-property relationship modeling, microstructure optimization, new material design, etc.

[0055] The present invention also discloses a system for predicting the microstructure of materials by materializing the two-point correlation function. First, by introducing the fast Fourier transform and the inverse Fourier transform, the phase lost in the calculation process of the two-point autocorrelation function is quickly restored in the form of matrix operations, significantly improving the calculation efficiency during the microstructure materialization prediction. Then, an image processing module is added to quickly eliminate the noise pixels in the microstructure image and smooth the boundaries of the target phase region, significantly accelerating the convergence process of the method and the microstructure materialization prediction effect. Furthermore, by stagewise selecting the optimal pixel exchange results to adjust the volume fraction of the target phase, and optimizing the morphology of the target phase by accepting or rejecting the pixel exchange results, the prediction error is quickly reduced, ensuring the reliability of the microstructure materialization prediction. Finally, the present invention does not introduce constraints on the material system and the microstructure morphology characteristics, and has the technical effect of universality for the microstructures of different materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flowchart of the method for predicting the microstructure of materials by materializing the two-point correlation function according to the present invention.

[0057] Figure 2 It is a flowchart of stagewise adjusting the volume fraction of the target phase in the method for predicting the microstructure of materials by materializing the two-point correlation function according to the present invention.

[0058] Figure 3 It is a flowchart of optimizing the morphology of the target phase in the method for predicting the microstructure of materials by materializing the two-point correlation function according to the present invention.

[0059] Figure 4 It is a system structure diagram of the system for predicting the microstructure of materials by materializing the two-point correlation function according to the present invention.

[0060] Figure 5 It is a comparison diagram of the original microstructure and the materialized predicted microstructure provided by the embodiment of the present invention.

[0061] Figure 6 It is a change curve diagram of the error with the number of iterations when removing the support domain constraint provided by the embodiment of the present invention.

[0062] Figure 7 It is a change curve diagram of the error with the number of iterations when adding the support domain constraint provided by the embodiment of the present invention.

[0063] Figure 8 It is a comparison diagram of the method for predicting the microstructure of materials by materializing the two-point correlation function provided by the embodiment of the present invention with the classical simulated annealing and the hybrid input-output method in terms of calculation efficiency and accuracy. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0064] The following further describes the present invention in detail with reference to the accompanying drawings:

[0065] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention; the terms "first", "second", "third" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance; in addition, unless otherwise clearly specified and defined, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it can be a fixed connection or a detachable connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0066] The present invention first provides a method for predicting the microstructure of a material from the materialization of a two-point correlation function, and the method includes:

[0067] Step S1: Preset an initial microstructure g k , input the target two-point autocorrelation function Calculate the Fourier amplitude and the target volume fraction V of the target phase f :

[0068] where S is the number of grids of is the Fourier transform of

[0069] Step S2: Perform a Fourier transform on the initial microstructure g k , where e iφ is the phase of g k in the Fourier space; apply a Fourier constraint through G' k =|M|·e iφ ; perform an inverse Fourier transform on G' k where , is the phase of G' k in the real space, and g' k is the microstructure after the inverse Fourier transform; as shown in the following formula (1), apply a support domain constraint and a characteristic microstructure constraint to g' k :

[0070]

[0071] Among them, β is a constant within the range of 0.5 - 1, γ is the support domain, and EM is the characteristic microstructure constraint to ensure g' k The array only contains the numbers 0 or 1.

[0072] Step S3: Every 10 iterations, perform image processing on g' k and update g' k .

[0073] The image processing operations include: morphological opening operation and morphological closing operation to remove noise and smooth the boundary; if image processing is continuously used, the phase volume fraction will be overly changed, increasing the error. Therefore, processing is performed once after 10 iterations here.

[0074] Step S4: Based on the dissimilar pixel nearest neighbor base (DPN) pixel exchange rule, perform a staged adjustment on the original volume fraction of the target phase in g' k to quickly reduce the solidification prediction error and update g' k . If the difference between the volume fraction of g' k and the target volume fraction V of the target phase f is less than the set threshold, skip this step.

[0075] The staged phase volume fraction adjustment includes:

[0076] Step S41: Calculate the two-point autocorrelation function k of g' and the phase volume fraction Calculate the difference ΔV from the target volume fraction V of the target phase f and calculate the current error ER using formula (2).

[0077] Step S42: Judge whether ΔV is less than the set critical threshold. If the condition is satisfied, skip steps S43 - S46 and execute "Step S5"; if the condition is not satisfied, continue to execute steps S43 - S47.

[0078] Step S43: Select the target processing phase, whose pixel value is φ = (ΔV + |ΔV|) / 2|ΔV|; set the number of pixel points n swap = S × dV, where dV is a preset proportional constant. Exchange the pixel value φ = 1 - φ using the DPN pixel exchange rule and update g' k .

[0079] Step S44: Calculate the two-point autocorrelation function k of g' and the phase volume fraction Calculate the difference from the target volume fraction v fThe difference ΔV is used to calculate ER through formula (2), and it is determined whether the current error ER decreases. If ER decreases, step S45 is executed; if ER does not decrease, return to step S43.

[0080] Step S45: Record g' k and ER;

[0081] Step S46: Determine whether the condition to terminate "Step S4" is satisfied. If the condition is satisfied, output g' corresponding to the minimum ER k ; if the condition is not satisfied, return to "Step S43". The "termination condition is: the number of cycles of the current volume fraction adjustment reaches the preset maximum number of cycles.

[0082] Step S5: Based on the DPN pixel exchange rule, determine the number of pixel points exchanged between the two phases within g' k , exchange pixels, optimize the microstructure morphology, update g' k , and mark g' k as g k .

[0083] The optimization of the microstructure morphology includes:

[0084] Step S51: Calculate the two-point autocorrelation function of g' k Calculate the current error ER using formula (2); determine the number of pixels to be exchanged where r is a proportionality constant.

[0085] Step S52: Exchange pixels using the DPN pixel exchange rule to obtain g' k '; calculate the two-point autocorrelation function of g' k ' Calculate the current error ER using formula (2).

[0086] Step S53: Determine whether the morphology optimization condition is satisfied. If the condition is satisfied, update g' k ' to g' k , and update ER; if the condition is not satisfied, return to "Step S52". The condition for determining whether the morphology is optimized is: the calculated ER is less than 0.

[0087] Step S54: Determine whether the termination condition is satisfied. If the condition is satisfied, output g' k ; if the condition is not satisfied, return to "Step S52".

[0088] The termination condition is:

[0089] The number of cycles of the current microstructure morphology optimization reaches the preset maximum number of cycles.

[0090] Step S6: Determine whether the termination condition is satisfied. If the condition is satisfied, execute "Step S7"; if the condition is not satisfied, return to "Step S2".

[0091] The termination condition is any of the following cases:

[0092] (1) The number of iterations reaches the set maximum number;

[0093] (2) The materialization prediction error ER is less than the set threshold value.

[0094]

[0095] where, is the two-point autocorrelation function of the microstructure of the materialization prediction.

[0096] Step S7: Crop the picture and output the microstructure g of the materialization prediction k .

[0097] The present invention also provides a system for materializing and predicting the microstructure of a material from a two-point correlation function. The system includes:

[0098] An initialization module for initializing system parameters, presetting an initial microstructure numerical picture, inputting a two-point autocorrelation function, and calculating the Fourier amplitude and the target phase volume fraction;

[0099] A constraint application module: for replacing the Fourier amplitude of the microstructure map by Fourier transform and inverse Fourier transform, making the larger pixel values decrease rapidly by using the support domain constraint, and adjusting the pixel values to 0 or 1 by using the characteristic microstructure constraint for subsequent exchange and two-point autocorrelation function calculation;

[0100] An image processing module: for rapidly converging pixels by using image processing operations, removing noise, and smoothing the interface;

[0101] A stagewise error reduction module: for stagewise adjusting the volume fraction of the target phase by using the DPN pixel exchange rule to rapidly reduce the error of the materialized microstructure;

[0102] A morphology optimization module: for optimizing the morphology of the current microstructure by using the DPN pixel exchange rule;

[0103] A judgment module: for judging whether the termination condition is satisfied. If the condition is satisfied, execute the "constraint application module"; if the condition is not satisfied, execute the "materialization prediction output module";

[0104] A materialization prediction output module: for cropping the picture and outputting the finally materialized and predicted microstructure.

[0105] Example 1

[0106] As shown Figure 1 in the figure, the present invention discloses a method for predicting the microstructure of a material from the materialization of a two-point correlation function, and the method includes:

[0107] Step S1: Preset an initial microstructure g k , calculate the Fourier amplitude and the target volume fraction V of the target phase from the input target two-point autocorrelation function f .

[0108] Step S2: Apply Fourier constraints to g k : Perform Fourier transform on g k , replace the amplitude through G' k =|M|·e iφ ; perform inverse Fourier transform on G' k , apply support domain constraints and characteristic microstructure constraints to g' k using formula (#1) to obtain an updated numerical picture g' k .

[0109] Step S3: Perform image processing on g' k during the set iteration to update g' k , and skip this step in other iteration steps.

[0110] Step S4: Based on the DPN pixel exchange rule, perform a staged adjustment on the phase volume fraction in g' k to quickly reduce the materialization prediction error and update g' k . If the difference between the volume fraction of g' k and the target volume fraction V f is less than the set threshold, then skip this step.

[0111] Step S5: Based on the DPN pixel exchange rule, determine the number of pixel points for the exchange of two phases within g' k , exchange pixels, optimize the microstructure morphology, update g' k , and mark g' k as g k .

[0112] Step S6: Determine whether the termination condition is satisfied. If the condition is satisfied, then execute "Step S7"; if the condition is not satisfied, then return to "Step S2".

[0113] Step S7: Crop the picture and output the materialized predicted microstructure g k .

[0114] The following is a detailed description of other steps:

[0115] The image processing operations in "Step S3" include: morphological erosion operation; morphological dilation operation; morphological opening operation and morphological closing operation.

[0116] The termination conditions in "Step S6" are: the number of iterations reaches the set maximum number; the materialized prediction error ER calculated using formula (#2) is less than the set threshold.

[0117] As Figure 2 shown, the stepwise phase volume fraction adjustment in "Step S4" can be subdivided into the following steps:

[0118] Step S41: Calculate the two-point autocorrelation function of g' k and the phase volume fraction and calculate the difference ΔV between and the target volume fraction V of the target phase f , and calculate the current error ER using formula (#2).

[0119] Step S42: Determine whether the condition for skipping "Steps S43 - S47" is satisfied. If the condition is satisfied, skip "Steps S43 - S47" and execute "Step S5" described in claim 1; if the condition is not satisfied, continue to execute "Steps S43 - S47". The skipping condition here is that the ΔV calculated in "Step S41" is less than the set critical threshold.

[0120] Step S43: Determine the pixel value φ of the phase to be processed as φ = (ΔV + |ΔV|) / 2|ΔV|; determine the number of pixel points n swap = S × dV, where dV is a preset proportional constant. Exchange the pixel value φ = 1 - φ using the DPN pixel exchange rule and update g' k .

[0121] Step S44: Determine whether the current error ER decreases. If ER decreases, execute "Step S45"; if ER does not decrease, return to "Step S43".

[0122] Step S45: Record g' k and ER;

[0123] Step S46: Determine whether the condition for terminating "Step S4" in claim 1 is satisfied. If the condition is satisfied, output g' k corresponding to the minimum ER; if the condition is not satisfied, return to "Step S43". The termination condition here is that the number of loops of the current volume fraction adjustment reaches the preset maximum number of loops.

[0124] AsFigure 3 As shown in the figure, the optimization of the microstructure morphology in "Step S5" can be subdivided into the following steps:

[0125] Step S51: Calculate the two-point autocorrelation function of g' k and use formula (#2) to calculate the current error ER; determine the number of pixels to be exchanged where r is a proportionality constant.

[0126] Step S52: Exchange pixels using the DPN pixel exchange rule to obtain g'; calculate the two-point autocorrelation function of g' k ' and use formula (#2) to calculate the current error ER. k

[0127] Step S53: Determine whether the morphology optimization condition is satisfied. If the condition is satisfied, update g' k ' to g' k , update ER; if the condition is not satisfied, return to "Step S52". The morphology optimization condition here is that the ER calculated in "Step S52" is less than 0.

[0128] Step S54: Determine whether the termination condition is satisfied. If the condition is satisfied, output g' k ; if the condition is not satisfied, return to "Step S52". The termination condition here is that the number of cycles of the current microstructure morphology optimization reaches the preset maximum number of cycles.

[0129] A method for predicting the microstructure of materials from the materialization of the two-point correlation function provided in Embodiment 1 absorbs the scientific properties of the Fourier transform, advanced image processing techniques, and the DPN pixel exchange rule, demonstrating the technical completeness of the method and the originality of the invention.

[0130] Embodiment 2

[0131] As Figure 4 shown, the present invention discloses a system for predicting the microstructure of materials from the materialization of the two-point correlation function, and the system includes:

[0132] Initialization module 201: Initialize system parameters, preset an initial microstructure numerical picture, and initialize the Fourier amplitude and the target volume fraction of the target phase;

[0133] Constraint application module 202: Replace the Fourier amplitude of the microstructure map using the Fourier transform and the inverse Fourier transform, make the larger pixel values decrease rapidly using the support domain constraint, and adjust the pixel values to 0 or 1 using the characteristic microstructure constraint;

[0134] Image processing module 203: Use image processing to quickly converge pixels, remove noise, and smooth the interface;​​​

[0135] Stepwise error reduction module 204: Using the DPN pixel exchange rule, stepwise adjust the volume fraction of the target phase to quickly reduce the error of the materialized microstructure;

[0136] Morphology optimization module 205: Using the DPN pixel exchange rule, optimize the morphology of the current microstructure;

[0137] Judgment module 206: Used to judge whether the termination condition is satisfied. If the condition is satisfied, execute the "constraint application module"; if the condition is not satisfied, execute the "materialization prediction output module";

[0138] Materialization prediction output module 207: Output the finally materialized predicted microstructure.

[0139] The content of the system provided in Embodiment 2 that is the same as that in Embodiment 1 will not be repeated here one by one.

[0140] Embodiment 3

[0141] The technical effects of a method and a system for materializing and predicting the microstructure of a material from a two-point correlation function provided by the present invention are illustrated by examples. The two original sample microstructures are from the literature [Lalit M. Pant, Sushanta K. Mitra, and Marc Secane, Stochastic reconstruction using multiple correlation functions with different-phase-neighbor-based pixel selection, 90(2014)023306] and the literature [David T. Fullwood, Stephen R. Niezgoda, Surya R. Kalidindi, Microstructure reconstructions from 2-point statistics using phase-recovery algorithms, Acta Materialia, 56(2008)942 - 948]. The two samples are processed into binary images of 200×200 pixels. Through the erosion and dilation operations of different square and disk-shaped kernels in image processing, 14 derivative samples are generated by expanding the two samples. All samples are processed into one-dimensional arrays to construct a sample matrix D (size 16×40000); for each sample in the matrix, solve the two-point autocorrelation function under the condition of no support domain to obtain the lossless matrix F (size 16×40000); use the principal component analysis method (PCA) to reduce the dimension of F to obtain the reduced-dimension matrix F PCA(with a size of 16×3), and then use the PCA method to reversely recover the two-point autocorrelation function matrix (with a size of 16×40000); then use the methods and system entities provided in Example 1 and Example 2 to materialize the prediction matrix F and two samples in. The specific steps will not be elaborated one by one. Under the condition of the support domain, the calculation steps are the same as above and will not be elaborated one by one.

[0142] From Figure 5 it can be seen that the microstructure materialized and predicted by the method and system provided by the present invention from the lossless two-point autocorrelation function is close to the original microstructure in morphology and has the same volume fraction; the microstructure materialized and predicted by the two-point autocorrelation function recovered from PCA also has similar structural characteristics to the original microstructure and has the same volume fraction. The results preliminarily verify the practicability and effectiveness of the method and system provided by the present invention.

[0143] Figure 6 shows the change curve of the error of the materialized prediction with the number of iterations of the method provided by the present invention under the condition of no support domain constraint. It can be seen that the error drops rapidly in the early stage of the method operation, reaches the minimum at about 50 steps and then maintains a fluctuating and stable trend, and the method converges. The final error of the materialized prediction of the two-point autocorrelation function recovered from PCA is slightly higher than that of the lossless two-point autocorrelation function, but within an acceptable range. The example results prove the reliability of the method and system provided by the present invention in materializing and predicting the microstructure from the lossy or lossless two-point autocorrelation function under the condition of no support domain constraint.

[0144] Figure 7 shows the change curve of the error of the materialized prediction with the number of iterations of the method provided by the present invention under the condition of support domain constraint. It can be seen that the error drops rapidly in the first 10 steps of the method, maintains a slow fluctuating downward trend before 450 steps, drops rapidly for the second time at 450 steps, and then maintains a slow downward trend until it finally converges. The final error of the materialized prediction of the two-point autocorrelation function recovered from PCA is slightly higher than that of the lossless two-point autocorrelation function, but within an acceptable range. Under the condition of support domain constraint, whether materializing and predicting the microstructure from the lossy or lossless two-point autocorrelation function, the example results prove the reliability of the method and system provided by the present invention.

[0145] Example 4

[0146] The technical effects of a method and system for predicting the microstructure of materials by materializing two-point correlation functions provided by the present invention are further demonstrated by comparison with classical methods. The classical methods for comparison are respectively from the literature [T. TANG, Q. TENG, X. HE & D. LUO, A pixel selection rule based on the number of different-phase neighbours for the simulated annealing reconstruction of sandstonemicrostructure, Journal of Microscopy, 234(2009)262-268], the literature [Lalit M. Pant, Sushanta K. Mitra, and Marc Secane, Stochastic reconstruction using multiplecorrelation functions with different-phase-neighbor-based pixel selection, 90(2014)023306] and the literature [David T. Fullwood, Stephen R. Niezgoda, Surya R. Kalidindi, Microstructure reconstructions from 2-point statistics using phase-recoveryalgorithms, Acta Materialia, 56(2008)942-948], and the three classical methods are respectively named PSA DPN , PSA random and HIO. In Example 3, lossy and lossless two-point autocorrelation functions are obtained under support constraint conditions and without support domain constraint conditions as the inputs of the three methods, and the error (ΔE) and the consumed time t at the final convergence are evaluated. The accuracy and computational efficiency of all methods are evaluated by |log(ΔE)| and 1 / t.

[0147] As can be seen from Figure 8 it, PSA DPN and PSA random methods have ideal accuracy but low computational efficiency, while the HIO method has high computational efficiency and low accuracy. The method and system provided by the present invention have the advantages of both high computational accuracy and fast running speed.

[0148] Examples 1-4 illustrate that the method and system provided by the present invention overcome the challenges of material microstructure prediction from two-point correlation function materialization, and have the advantages of high efficiency, high precision and universality, providing technical support for the solution of scientific problems such as the verification of the PSP relationship model and the optimization design of microstructure.

[0149] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the microstructure of a material from the instantiation of a two-point correlation function, characterized in that, The following steps are involved: Step 1, obtaining an initial microstructure image, obtaining a Fourier amplitude based on a target two-point autocorrelation function, and a target volume fraction of a target phase in the initial microstructure image; Step 2, after Fourier transform and inverse Fourier transform are performed on the initial microstructure image, support domain constraints and characteristic microstructure constraints are applied to the inverse Fourier transformed microstructure image to obtain a constrained microstructure image; Step 3, processing the constrained microscopic tissue image through image processing operations; Step 4, by using the heterogeneous pixel neighbor-based pixel exchange rule, the original volume fraction of the target processing phase in the image obtained in step 3 is adjusted in stages until the difference between the adjusted volume fraction of the target phase and the target volume fraction of the target phase is less than a set threshold, or the number of times the volume fraction of the target phase is adjusted reaches a maximum number of cycles, an image after the volume fraction of the target phase is adjusted is obtained, and then step 5 is executed; Step 5, by using the heterogeneous pixel neighbor-based pixel exchange rule, determine the number of pixels exchanged between the two phases in the image after the volume fraction adjustment and exchange the pixels, optimize the microstructure morphology, and obtain an optimized microstructure image; Step 6, judging whether the optimized microstructure image meets the termination condition, if so, executing step 7, if not, returning to step 3; Step 7: Output the materialized predicted microstructure of the microstructure image.

2. The method for predicting the microstructure of a material by materializing a two-point correlation function according to claim 1, wherein In step 2, the initial Fourier transform is: The image of Fourier transform through Fourier amplitude constraint is: The process of the inverse Fourier transform is: ； Among them, is the initial microstructure image, is the Fourier amplitude, is the Fourier transform of and is the phase in the Fourier space; The calculation formula is as follows: Among them, is the number of grids of, is the Fourier transform of, being the autocorrelation function of the target two points.

3. A method for predicting the microstructure of a material from the materialization of a two-point correlation function according to claim 2, characterized in that, In step 2, the constraints of the inverse Fourier transformed image include support domain constraints and characteristic microstructure constraints: （1） Among them, is a constant within the range of 0.5 - 1, is the support domain, and EM is the characteristic microstructure constraint, ensuring that the array only contains the numbers 0 or 1.

4. A method for predicting the microstructure of a material by materializing a two-point correlation function according to claim 1, characterized in that In step 3, the image processing operation includes a morphological opening operation and a morphological closing operation.

5. A method for predicting the microstructure of a material by materializing a two-point correlation function according to claim 1, characterized in that, In step 4, the process of adjusting the volume fraction in stages includes the following steps: S41, obtaining the two-point autocorrelation function and phase volume fraction of the image obtained in step 3, obtaining the difference between the volume fraction of the target phase and the target volume fraction of the target phase, and calculating the error value; S42, determining whether the error value is less than a critical threshold, if so, executing step 5; otherwise, executing step S43; S43, calculating the pixel values ​​of the image obtained in step 3 and the number of pixels to be exchanged, exchanging the pixel values ​​according to the heterogeneous pixel neighbor-based pixel exchange rule, updating the image, and calculating the two-point autocorrelation function, phase volume fraction and error value of the updated image; S44, determining whether the error value obtained in S43 is reduced, if reduced, executing step S45, otherwise returning to step S43; S45, recording the updated image and error value; S46, determining whether the number of cycles of the current volume fraction adjustment reaches the preset maximum number of cycles, if so, inputting the updated image and error value, if not, returning to S43.

6. A method for predicting the microstructure of a material by materializing a two-point correlation function according to claim 1, characterized in that, The specific process of step 5 is: S51, calculating the two-point autocorrelation function and error value of the image after the volume fraction is adjusted, and determining the number of pixels to be exchanged; S52, exchanging pixels according to a heterogeneous pixel neighbor-based pixel exchange rule to obtain an image after the pixels are exchanged, and calculating a two-point autocorrelation function and an error value of the pixel image after the pixels are exchanged; S53, judging whether the morphology optimization conditions are met, if so, executing S54, if not, returning to S52; S54, judging whether the number of cycles of the current microstructure morphology optimization reaches the preset maximum number of cycles, if it is satisfied, outputting the optimized microstructure image, otherwise executing S52.

7. A method for predicting the microstructure of a material by materializing a two-point correlation function according to claim 6, characterized in that, In S53, the shape optimization condition is whether the error value is less than 0.

8. A method for predicting the microstructure of a material by materializing a two-point correlation function according to claim 1, characterized in that, In step 6, the termination condition is that the number of iterations reaches a set maximum number, or the error value is less than a set value.

9. A method for predicting the microstructure of a material from the materialization of a two-point correlation function according to claim 5 or 6 or 8, characterized in that, The calculation formula of the error value is: Among them, is the two-point autocorrelation function of the microstructures predicted by the materialization.

10. A system for predicting the microstructure of a material by materializing a two-point correlation function, characterized in that, include: An initialization module, used to obtain an initial microstructure image, obtain a Fourier amplitude based on a target two-point autocorrelation function, and a target volume fraction of a target phase in the initial microstructure image; A constraint applying module is used for applying support domain constraints and characteristic microstructure constraints to the microstructure image after the inverse Fourier transformation after Fourier transformation to obtain a constrained microstructure image; An image processing module, used for processing the constrained microscopic tissue image through image processing operations; The staged error reduction module is used to perform staged adjustment on the original volume fraction of the target processing phase in the image obtained by the image processing module through the heterogeneous pixel neighbor-based pixel exchange rule, until the difference between the adjusted volume fraction of the target phase and the target volume fraction of the target phase is less than a set threshold, or the number of times the volume fraction of the target phase is adjusted reaches a maximum number of cycles, thereby obtaining an image after the volume fraction of the target phase is adjusted; The morphology optimization module determines the number of pixels exchanged between the two phases in the image after the volume fraction adjustment and exchanges the pixels through the heterogeneous pixel neighbor-based pixel exchange rule, optimizes the microstructure morphology, and obtains the optimized microstructure image; A judgment module is used to judge whether the optimized microstructure image meets the termination condition. If so, the entity prediction output module is executed. If not, the image processing module is returned. The materialized prediction output module outputs the materialized predicted microstructure of the microstructure image.

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