Neutron Diffraction Experiment Strain Field Reconstruction Method and System Based on Gaussian Mixture Model

Abstract

The present invention provides a method and system for reconstructing the strain field of a neutron diffraction experiment based on a Gaussian mixture model, comprising: step S1: establishing a diffraction geometry relationship that takes into account the diffraction volume; step S2: using the diffraction image to obtain a probabilistic sampling model corresponding to the diffraction geometry; step S3: using the sampling model, using the Gaussian mixture model to separate the diffraction images corresponding to different crystal plane orientations; step S4: solving the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material; and step S5: solving the mean strain corresponding to each point in the diffraction volume to reconstruct the strain field information corresponding to a single diffraction measurement. The present invention proposes a method for reconstructing the strain field of a neutron diffraction experiment based on a Gaussian mixture model, which can conveniently, efficiently, and accurately establish the relationship between the neutron diffraction image and the strain field. The present invention does not require dimensionality reduction and compression of the original experimental data, and does not need to ignore information such as the diffraction volume and texture intensity to study the strain field.

Description

Technical Field

[0001] The present invention relates to the field of measurement technology, and in particular to a method and system for reconstructing a strain field in a neutron diffraction experiment based on a Gaussian mixture model. Background Art

[0002] Neutron diffraction experiment is one of the common methods of material characterization. Due to its good penetration and statistical significance of experimental results, it is widely used to measure stress and texture inside materials. A common stress reconstruction method is to numerically integrate the neutron intensity of the diffraction image, and determine the diffraction angle corresponding to the maximum value of the neutron intensity through a fitting method to determine the lattice spacing under the Bragg law. When the fitting method is selected, the accuracy of the numerical integration is one of the most critical factors in determining the value of the diffraction angle. However, the general integration method is limited by the low pixel resolution and unclear integration path. In addition, the method itself performs dimensionality reduction and compression on the neutron diffraction experimental data, resulting in errors. Therefore, in order to ensure the reconstruction quality of the strain field inside the material, it is necessary to directly process the two-dimensional detection data and establish a connection between the image and the strain field.

[0003] Considering that the diffraction experimental data has statistical significance for the lattice size, and the intensity changes on the image reflect the density changes of each crystal plane orientation to a certain extent, the strain field reconstruction should perform separate lattice strain estimation for each point where diffraction occurs. In practice, the average lattice strain inside the material is the weighted average of the strain of each crystal plane orientation with respect to the texture. Therefore, in order to achieve accurate estimation of the strain field, it is necessary to establish a probability distribution sampling model for the diffraction experimental data and to separate the diffraction images of each crystal plane. At present, most methods for strain field reconstruction use the least squares method, which has defects such as rough data processing methods, ignoring the diffraction volume, and ignoring the influence of texture, which affects the reconstruction accuracy and efficiency. Therefore, a high-precision and efficient reconstruction method based on the Gaussian mixture model is proposed, which is of great significance and prospect for improving the accuracy of strain field reconstruction and explaining the relationship between strain and texture. Summary of the Invention

[0004] In view of the defects in the prior art, the purpose of the present invention is to provide a method and system for reconstructing the strain field of a neutron diffraction experiment based on a Gaussian mixture model.

[0005] According to the present invention, a method for reconstructing a strain field from a neutron diffraction experiment based on a Gaussian mixture model is provided, comprising:

[0006] Step S1: establishing a diffraction geometry relationship considering the diffraction volume;

[0007] Step S2: using the diffraction image, obtaining a probability sampling model corresponding to the diffraction geometry;

[0008] Step S3: Under the sampling model, the Gaussian mixture model is used to separate the diffraction images corresponding to different crystal plane orientations;

[0009] Step S4: Calculate the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material;

[0010] Step S5: Calculate the strain mean corresponding to each point in the diffraction volume and reconstruct the strain field information corresponding to a single diffraction measurement.

[0011] Preferably, in step S1:

[0012] The neutron counting intensity at the center of a pixel Q on the detector is I(Q), and the direction of the neutron beam after diffraction is The crystal plane orientation is The neutron counting intensity produced by a single orientation on the detector is I g (p), the area inside the sample where diffraction occurs is is the sum of the diffraction points M, W = ∪ M, The neutron counting intensity generated by a single diffraction point is I g,M ;

[0013] For a single crystal plane orientation, the neutron counting intensity is the sum of all the points where diffraction occurs, which is:

[0014]

[0015] in,

[0016]

[0017] The diffracted neutrons generated by all possible crystal plane orientations in the material sample are superimposed on each other to form the neutron counting intensity on the detection plane, which is:

[0018]

[0019] Preferably, in step S2:

[0020] The actual size of a single pixel is S = d × d mm 2 , pixel center Q i =[q ix ,q iy ] T , a single neutron j falls at position q within the pixel i,j Using random variables express:

[0021]

[0022] For a single measurement, the positions of all neutrons falling on the detection plane are obtained by weighting the positions of each point and the sampling frequency:

[0023]

[0024] Where i is the subscript of the pixel center of the detection plane;

[0025] The neutrons that fall on the detection plane from a specific orientation are represented by the random variable X g If it is expressed as follows:

[0026]

[0027] Preferably, in step S3:

[0028] The probability model distribution corresponding to the random variable X is expressed by Gaussian mixture distribution, which is:

[0029]

[0030] Where x represents the position of the neutron on the detector, μ k ,∑ k are the mean and covariance matrix of the kth Gaussian distribution, π k is the mixing coefficient, N is the normal distribution, and K is the number of multivariate Gaussian distributions;

[0031] Use the EM algorithm to optimize the parameters of the Gaussian mixture model:

[0032] In step E, according to the current π k ,μ k ,∑ k Calculate the posterior probability distribution γ(z nk ):

[0033]

[0034] Among them, x n is the position of the nth detected neutron in the detection plane;

[0035] In the M step, the new π is calculated based on the posterior probability distribution k ,μ k ,∑ k ,in:

[0036]

[0037]

[0038]

[0039]

[0040] Among them, N x is the total number of neutrons, Nk is the number of neutrons belonging to the kth Gaussian distribution after clustering.

[0041] Repeat the above steps until the estimated likelihood function value converges. The expression of the log-likelihood function is:

[0042]

[0043] Preferably, in step S4:

[0044] According to the obtained k multivariate Gaussian distributions in the mixed Gaussian model, the mean values of each are calculated under the detection plane coordinate system {D}. D μ k =( D x k , D y k ,0) T The position of the diffraction enhancement point in the sample coordinate system {S} is obtained to obtain the depression angle and elevation angle (γ k ,η k ), where η k is the angle corresponding to the crystal plane orientation, γ k =2θ k ,θ k is the neutron diffraction angle, satisfying Bragg's law:

[0045] nλ k =2d k sin(θ k ) (50)

[0046] Where λ is the wavelength of the neutron beam, d is the lattice spacing of the material sample, and n is a positive integer;

[0047] Based on the probability density function corresponding to the multivariate Gaussian distribution, the ODF function of each crystal plane orientation at each diffraction point is expressed. For the diffraction point μ=(x,y,z) T , the ODF function value corresponding to the kth crystal plane orientation is:

[0048]

[0049] Among them, Σ' k =R∑ k R T , R is the rotation matrix of the reference frame {D} relative to {S},

[0050] Among them, R y The rotation matrix corresponding to the rotation around the y-axis of the {S} reference frame, γ k is the corresponding rotation angle, R z is the rotation matrix corresponding to the rotation around the z-axis of the {S} reference frame, ηk is the corresponding rotation angle.

[0051] Preferably, in step S5:

[0052] According to the Bragg angle corresponding to each crystal plane orientation, the mean lattice strain ε corresponding to each crystal plane is calculated. k :

[0053]

[0054]

[0055] Among them, d k is the lattice spacing after loading, d0 is the in-situ lattice spacing;

[0056] The mean strain value of each point in the diffraction volume is calculated as the weighted average of the mean strain value of each crystal plane with respect to the ODF function:

[0057]

[0058] Among them, f k (x,y,z) is the point where the diffraction occurs (x,y,z) T The ODF function value corresponding to the upper orientation k.

[0059] According to the present invention, a neutron diffraction experimental strain field reconstruction system based on a Gaussian mixture model is provided, comprising:

[0060] Module M1: Establishing diffraction geometry considering diffraction volume;

[0061] Module M2: Using the diffraction image, obtain the probability sampling model corresponding to the diffraction geometry;

[0062] Module M3: Under the sampling model, the Gaussian mixture model is used to separate the diffraction images corresponding to different crystal plane orientations;

[0063] Module M4: Determine the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material;

[0064] Module M5: Calculate the mean strain value corresponding to each point in the diffraction volume and reconstruct the strain field information corresponding to a single diffraction measurement.

[0065] Preferably, in the module M1:

[0066] The neutron counting intensity at the center of a pixel Q on the detector is I(Q), and the direction of the neutron beam after diffraction is The crystal plane orientation is The neutron counting intensity produced by a single orientation on the detector is I g (p), the area inside the sample where diffraction occurs is is the sum of the diffraction points M, W = ∪ M, The neutron counting intensity generated by a single diffraction point is I g,M ;

[0067] For a single crystal plane orientation, the neutron counting intensity is the sum of all the points where diffraction occurs, which is:

[0068]

[0069] in,

[0070]

[0071] The diffracted neutrons generated by all possible crystal plane orientations in the material sample are superimposed on each other to form the neutron counting intensity on the detection plane, which is:

[0072]

[0073] In the module M2:

[0074] The actual size of a single pixel is S = d × d mm 2 , pixel center Q i =[q ix ,q iy ] T , a single neutron j falls at position q within the pixel i,j Using random variables express:

[0075]

[0076] For a single measurement, the positions of all neutrons falling on the detection plane are obtained by weighting the positions of each point and the sampling frequency:

[0077]

[0078] Where i is the subscript of the pixel center of the detection plane;

[0079] The neutrons that fall on the detection plane from a specific orientation are represented by the random variable X g If it is expressed as follows:

[0080]

[0081] Preferably, in the module M3:

[0082] The probability model distribution corresponding to the random variable X is expressed by Gaussian mixture distribution, which is:

[0083]

[0084] Where x represents the position of the neutron on the detector, μ k ,∑ k are the mean and covariance matrix of the kth Gaussian distribution, π k is the mixing coefficient, N is the normal distribution, and K is the number of multivariate Gaussian distributions;

[0085] Use the EM algorithm to optimize the parameters of the Gaussian mixture model:

[0086] In step E, according to the current π k ,μ k ,∑ k Calculate the posterior probability distribution γ(z nk ):

[0087]

[0088] Among them, x n is the position of the nth detected neutron in the detection plane;

[0089] In the M step, the new π is calculated based on the posterior probability distribution k ,μ k ,∑ k ,in:

[0090]

[0091]

[0092]

[0093]

[0094] Among them, N x is the total number of neutrons, N k is the number of neutrons belonging to the kth Gaussian distribution after clustering.

[0095] Repeat the above steps until the estimated likelihood function value converges. The expression of the log-likelihood function is:

[0096]

[0097] Preferably, in the module M4:

[0098] According to the obtained k multivariate Gaussian distributions in the mixed Gaussian model, the mean values of each are calculated under the detection plane coordinate system {D}. D μ k =( D x k , D y k ,0) TThe position of the diffraction enhancement point in the sample coordinate system {S} is obtained to obtain the depression angle and elevation angle (γ k ,η k ), where η k is the angle corresponding to the crystal plane orientation, γ k =2θ k ,θ k is the neutron diffraction angle, satisfying Bragg's law:

[0099] nλ k =2d k sin(θ k ) (68)

[0100] Where λ is the wavelength of the neutron beam, d is the lattice spacing of the material sample, and n is a positive integer;

[0101] Based on the probability density function corresponding to the multivariate Gaussian distribution, the ODF function of each crystal plane orientation at each diffraction point is expressed. For the diffraction point μ=(x,y,z) T , the ODF function value corresponding to the kth crystal plane orientation is:

[0102]

[0103] Among them, Σ' k =R∑ k R T , R is the rotation matrix of the reference frame {D} relative to {S},

[0104] Among them, R y The rotation matrix corresponding to the rotation around the y-axis of the {S} reference frame, γ k is the corresponding rotation angle, R z is the rotation matrix corresponding to the rotation around the z-axis of the {S} reference frame, η k is the corresponding rotation angle;

[0105] In the module M5:

[0106] According to the Bragg angle corresponding to each crystal plane orientation, the mean lattice strain ε corresponding to each crystal plane is calculated. k :

[0107]

[0108]

[0109] Among them, d k is the lattice spacing after loading, d0 is the in-situ lattice spacing;

[0110] The mean strain value of each point in the diffraction volume is calculated as the weighted average of the mean strain value of each crystal plane with respect to the ODF function:

[0111]

[0112] Among them, f k (x,y,z) is the point where the diffraction occurs (x,y,z) T The ODF function value corresponding to the upper orientation k.

[0113] Compared with the prior art, the present invention has the following beneficial effects:

[0114] 1. This invention proposes a strain field reconstruction method for neutron diffraction experiments based on a Gaussian mixture model, which can conveniently, efficiently, and accurately establish the relationship between the neutron diffraction image and the strain field;

[0115] 2. In terms of modeling, the present invention combines the inherent probabilistic model characteristics of the neutron diffraction phenomenon and uses a mixed Gaussian model to establish the relationship between the diffraction spots of each crystal plane orientation in the diffraction volume and the diffraction image. This eliminates the need to perform dimensionality reduction compression on the original experimental data and does not require ignoring information such as the diffraction volume and texture intensity to study the strain field.

[0116] 3. In terms of reconstruction, the present invention accurately establishes the corresponding relationship between the diffraction volume and the diffraction image without considering the specific shape of the diffraction volume, thereby realizing accurate reconstruction of the internal strain field of the material, making it feasible to reconstruct the strain field taking into account the diffraction volume and texture information, greatly improving the quality of neutron diffraction strain field reconstruction and improving measurement efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0118] Figure 1 Schematic diagram of the realization and principle of neutron diffraction strain field reconstruction;

[0119] Figure 2 This is the corresponding sampling image after neutron diffraction experiment image processing;

[0120] Figure 3 Schematic diagram of the maximum likelihood optimization of model parameters for the GMM model and EM algorithm;

[0121] Figure 4 The GMM method is used to separate the diffraction patterns of each crystal plane orientation, where the origin represents the mean of each multivariate Gaussian distribution and the ellipse represents the covariance matrix of each distribution;

[0122] Figure 5 This is the reconstruction effect of this reconstruction method under actual experimental data. DETAILED DESCRIPTION

[0123] The present invention will be described in detail below with reference to specific embodiments. The following examples 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 skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0124] Example 1:

[0125] The present invention relates to material characterization, neutron diffraction, and strain field reconstruction, and provides a strain field reconstruction method based on a Gaussian mixture model. The method comprises: establishing a diffraction geometry relationship that takes into account the diffraction volume based on the statistical characteristics of the neutron diffraction experiment; obtaining a probability model sampling corresponding to the diffraction geometry using the diffraction image obtained from the detection plane; separating the diffraction images corresponding to different crystal plane orientations using the Gaussian mixture model under a given sampling model; calculating the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material sample using the mean and variance corresponding to the multivariate Gaussian distribution; calculating the strain mean corresponding to each point in the diffraction volume, and reconstructing the strain field information corresponding to a single diffraction measurement. Compared with other similar methods, the present invention does not require approximate calculations on the original measurement data, and the model assumptions are closer to reality, resulting in good measurement accuracy and high efficiency. The model is directly used to process neutron diffraction experimental data, thereby achieving accurate reconstruction of the material strain field, making it feasible to reconstruct multi-point strain information obtained in a single experiment, and greatly improving the quality of material characterization.

[0126] According to the present invention, a neutron diffraction experimental strain field reconstruction method based on a Gaussian mixture model is provided. Figure 1-Figure 5 Shown, including:

[0127] Step S1: establishing a diffraction geometry relationship considering the diffraction volume;

[0128] Specifically, in step S1:

[0129] The neutron counting intensity at the center of a pixel Q on the detector is I(Q), and the direction of the neutron beam after diffraction is The crystal plane orientation is The neutron counting intensity produced by a single orientation on the detector is I g (p), the area inside the sample where diffraction occurs is is the sum of the diffraction points M, W = ∪ M, The neutron counting intensity generated by a single diffraction point is I g,M ;

[0130] For a single crystal plane orientation, the neutron counting intensity is the sum of all the points where diffraction occurs, which is:

[0131]

[0132] in,

[0133]

[0134] The diffracted neutrons generated by all possible crystal plane orientations in the material sample are superimposed on each other to form the neutron counting intensity on the detection plane, which is:

[0135]

[0136] Step S2: using the diffraction image, obtaining a probability sampling model corresponding to the diffraction geometry;

[0137] Specifically, in step S2:

[0138] The actual size of a single pixel is S = d × d mm 2 , pixel center Q i =[q ix ,q iy ] T , a single neutron j falls at position q within the pixel i,j Using random variables express:

[0139]

[0140] For a single measurement, the positions of all neutrons falling on the detection plane are obtained by weighting the positions of each point and the sampling frequency:

[0141]

[0142] Where i is the subscript of the pixel center of the detection plane;

[0143] The neutrons that fall on the detection plane from a specific orientation are represented by the random variable X g If it is expressed as follows:

[0144]

[0145] Step S3: Under the sampling model, the Gaussian mixture model is used to separate the diffraction images corresponding to different crystal plane orientations;

[0146] Specifically, in step S3:

[0147] The probability model distribution corresponding to the random variable X is expressed by Gaussian mixture distribution, which is:

[0148]

[0149] Where x represents the position of the neutron on the detector, μ k ,∑ kare the mean and covariance matrix of the kth Gaussian distribution, π k is the mixing coefficient, N is the normal distribution, and K is the number of multivariate Gaussian distributions;

[0150] Use the EM algorithm to optimize the parameters of the Gaussian mixture model:

[0151] In step E, according to the current π k ,μ k ,∑ k Calculate the posterior probability distribution γ(z nk ):

[0152]

[0153] Among them, x n is the position of the nth detected neutron in the detection plane;

[0154] In the M step, the new π is calculated based on the posterior probability distribution k ,μ k ,∑ k ,in:

[0155]

[0156]

[0157]

[0158]

[0159] Among them, N x is the total number of neutrons, N k is the number of neutrons belonging to the kth Gaussian distribution after clustering.

[0160] Repeat the above steps until the estimated likelihood function value converges. The expression of the log-likelihood function is:

[0161]

[0162] Step S4: Calculate the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material;

[0163] Specifically, in step S4:

[0164] According to the obtained k multivariate Gaussian distributions in the mixed Gaussian model, the mean values of each are calculated under the detection plane coordinate system {D}. D μ k =( D x k , D y k ,0) TThe position of the diffraction enhancement point in the sample coordinate system {S} is obtained to obtain the depression angle and elevation angle (γ k ,η k ), where η k is the angle corresponding to the crystal plane orientation, γ k =2θ k ,θ k is the neutron diffraction angle, satisfying Bragg's law:

[0165] nλ k =2d k sin(θ k ) (86)

[0166] Where λ is the wavelength of the neutron beam, d is the lattice spacing of the material sample, and n is a positive integer;

[0167] Based on the probability density function corresponding to the multivariate Gaussian distribution, the ODF function of each crystal plane orientation at each diffraction point is expressed. For the diffraction point μ=(x,y,z) T , the ODF function value corresponding to the kth crystal plane orientation is:

[0168]

[0169] Among them, Σ' k =R∑ k R T , R is the rotation matrix of the reference frame {D} relative to {S},

[0170] Among them, R y The rotation matrix corresponding to the rotation around the y-axis of the {S} reference frame, γ k is the corresponding rotation angle, R z is the rotation matrix corresponding to the rotation around the z-axis of the {S} reference frame, η k is the corresponding rotation angle.

[0171] Step S5: Calculate the strain mean corresponding to each point in the diffraction volume and reconstruct the strain field information corresponding to a single diffraction measurement.

[0172] Specifically, in step S5:

[0173] According to the Bragg angle corresponding to each crystal plane orientation, the mean lattice strain ε corresponding to each crystal plane is calculated. k :

[0174]

[0175]

[0176] Among them, d kis the lattice spacing after loading, d0 is the in-situ lattice spacing;

[0177] The mean strain value of each point in the diffraction volume is calculated as the weighted average of the mean strain value of each crystal plane with respect to the ODF function:

[0178]

[0179] Among them, f k (x,y,z) is the point where the diffraction occurs (x,y,z) T The ODF function value corresponding to the upper orientation k.

[0180] Example 2:

[0181] Example 2 is a preferred example of Example 1 and is used to illustrate the present invention in more detail.

[0182] The present invention also provides a neutron diffraction experiment strain field reconstruction system based on a Gaussian mixture model. The neutron diffraction experiment strain field reconstruction system based on a Gaussian mixture model can be implemented by executing the process steps of the neutron diffraction experiment strain field reconstruction method based on a Gaussian mixture model, that is, those skilled in the art can understand the neutron diffraction experiment strain field reconstruction method based on a Gaussian mixture model as a preferred embodiment of the neutron diffraction experiment strain field reconstruction system based on a Gaussian mixture model.

[0183] According to the present invention, a neutron diffraction experimental strain field reconstruction system based on a Gaussian mixture model is provided, comprising:

[0184] Module M1: Establishing diffraction geometry considering diffraction volume;

[0185] Specifically, in the module M1:

[0186] The neutron counting intensity at the center of a pixel Q on the detector is I(Q), and the direction of the neutron beam after diffraction is The crystal plane orientation is The neutron counting intensity produced by a single orientation on the detector is I g (p), the area inside the sample where diffraction occurs is is the sum of the diffraction points M, W = ∪ M, The neutron counting intensity generated by a single diffraction point is I g,M ;

[0187] For a single crystal plane orientation, the neutron counting intensity is the sum of all the points where diffraction occurs, which is:

[0188]

[0189] in,

[0190]

[0191] The diffracted neutrons generated by all possible crystal plane orientations in the material sample are superimposed on each other to form the neutron counting intensity on the detection plane, which is:

[0192]

[0193] Module M2: Using the diffraction image, obtain the probability sampling model corresponding to the diffraction geometry;

[0194] In the module M2:

[0195] The actual size of a single pixel is S = d × d mm 2 , pixel center Q i =[q ix ,q iy ] T , a single neutron j falls at position q within the pixel i,j Using random variables express:

[0196]

[0197] For a single measurement, the positions of all neutrons falling on the detection plane are obtained by weighting the positions of each point and the sampling frequency:

[0198]

[0199] Where i is the subscript of the pixel center of the detection plane;

[0200] The neutrons that fall on the detection plane from a specific orientation are represented by the random variable X g If it is expressed as follows:

[0201]

[0202] Module M3: Under the sampling model, the Gaussian mixture model is used to separate the diffraction images corresponding to different crystal plane orientations;

[0203] Specifically, in the module M3:

[0204] The probability model distribution corresponding to the random variable X is expressed by Gaussian mixture distribution, which is:

[0205]

[0206] Where x represents the position of the neutron on the detector, μ k ,∑ k are the mean and covariance matrix of the kth Gaussian distribution, π k is the mixing coefficient, N is the normal distribution, and K is the number of multivariate Gaussian distributions;

[0207] Use the EM algorithm to optimize the parameters of the Gaussian mixture model:

[0208] In step E, according to the current π k ,μ k ,∑ k Calculate the posterior probability distribution γ(z nk ):

[0209]

[0210] Among them, x n is the position of the nth detected neutron in the detection plane;

[0211] In the M step, the new π is calculated based on the posterior probability distribution k ,μ k ,∑ k ,in:

[0212]

[0213]

[0214]

[0215]

[0216] Among them, N x is the total number of neutrons, N k is the number of neutrons belonging to the kth Gaussian distribution after clustering.

[0217] Repeat the above steps until the estimated likelihood function value converges. The expression of the log-likelihood function is:

[0218]

[0219] Module M4: Determine the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material;

[0220] Specifically, in the module M4:

[0221] According to the obtained k multivariate Gaussian distributions in the mixed Gaussian model, the mean values of each are calculated under the detection plane coordinate system {D}. D μ k =( D x k , D y k ,0) T The position of the diffraction enhancement point in the sample coordinate system {S} is obtained to obtain the depression angle and elevation angle (γ k ,η k ), where ηk is the angle corresponding to the crystal plane orientation, γ k =2θ k ,θ k is the neutron diffraction angle, satisfying Bragg's law:

[0222] nλ k =2d k sin(θ k ) (104)

[0223] Where λ is the wavelength of the neutron beam, d is the lattice spacing of the material sample, and n is a positive integer;

[0224] Based on the probability density function corresponding to the multivariate Gaussian distribution, the ODF function of each crystal plane orientation at each diffraction point is expressed. For the diffraction point μ=(x,y,z) T , the ODF function value corresponding to the kth crystal plane orientation is:

[0225]

[0226] Among them, Σ' k =R∑ k R T , R is the rotation matrix of the reference frame {D} relative to {S},

[0227] Among them, R y The rotation matrix corresponding to the rotation around the y-axis of the {S} reference frame, γ k is the corresponding rotation angle, R z is the rotation matrix corresponding to the rotation around the z-axis of the {S} reference frame, η k is the corresponding rotation angle;

[0228] Module M5: Calculate the mean strain value corresponding to each point in the diffraction volume and reconstruct the strain field information corresponding to a single diffraction measurement.

[0229] In the module M5:

[0230] According to the Bragg angle corresponding to each crystal plane orientation, the mean lattice strain ε corresponding to each crystal plane is calculated. k :

[0231]

[0232]

[0233] Among them, d k is the lattice spacing after loading, d0 is the in-situ lattice spacing;

[0234] The mean strain value of each point in the diffraction volume is calculated as the weighted average of the mean strain value of each crystal plane with respect to the ODF function:

[0235]

[0236] Among them, f k (x,y,z) is the point where the diffraction occurs (x,y,z) T The ODF function value corresponding to the upper orientation k.

[0237] Example 3:

[0238] Example 3 is a preferred example of Example 1 and is used to illustrate the present invention in more detail.

[0239] In response to the above-mentioned deficiencies in the prior art, the present invention provides a strain field reconstruction method based on a Gaussian mixture model. This method combines the inherent probabilistic model characteristics of the neutron diffraction phenomenon, uses a mixed Gaussian model to establish the relationship between the diffraction spots and the diffraction images of each crystal plane orientation in the diffraction volume, optimizes the model parameters using the EM algorithm, and uses the optimized multivariate Gaussian distribution mean and covariance to reconstruct the diffraction angle and texture information of the main diffraction crystal plane. The strain and texture information are used to perform weighted mean calculation on each point inside the diffraction volume. Therefore, without considering the specific shape of the diffraction volume, the corresponding relationship between the diffraction volume and the diffraction image is accurately established, and the accurate reconstruction of the strain field inside the material is achieved, making it feasible to reconstruct the strain field taking into account the diffraction volume and texture information, greatly improving the quality of neutron diffraction strain field reconstruction and improving measurement efficiency.

[0240] Specifically, this embodiment provides a method for reconstructing the strain field of a neutron diffraction experiment based on a Gaussian mixture model, comprising the following steps:

[0241] Step 1: Based on the statistical characteristics of the neutron diffraction experiment, establish the diffraction geometry relationship considering the diffraction volume;

[0242] Step 2: Using the diffraction image obtained from the detection plane, obtain the probability model sampling corresponding to the diffraction geometry;

[0243] Step 3: Under a given sampling model, use the Gaussian mixture model to separate the diffraction images corresponding to different crystal plane orientations;

[0244] Step 4: Use the mean and variance corresponding to the multivariate Gaussian distribution to solve the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material sample;

[0245] Step 5: Calculate the strain mean corresponding to each point in the diffraction volume and reconstruct the strain field information corresponding to a single diffraction measurement;

[0246] Preferably, the step 1 is specifically:

[0247] Considering that the diffraction area of the neutron diffraction experiment is at the millimeter level, it has statistical significance for the measured lattice spacing. Assuming that the neutron counting intensity at the center of a pixel Q on the detector is I(Q), the direction of the neutron beam after diffraction is The crystal plane orientation is The neutron counting intensity produced by a single orientation on the detector is I g (p), the area inside the sample where diffraction occurs is is the sum of the diffraction points M, W = ∪ M, The neutron counting intensity generated by a single diffraction point is I g,M For a single crystal plane orientation, the neutron counting intensity is the sum of all the points where diffraction occurs, which is:

[0248]

[0249] in,

[0250]

[0251] The diffracted neutrons generated by all possible crystal plane orientations in the material sample are superimposed on each other, ultimately forming the neutron counting intensity on the detection plane, which is:

[0252]

[0253] Preferably, the step 2 is specifically:

[0254] Consider the actual size of a single pixel to be S = d × d mm 2 , pixel center Q i =[q ix ,q iy ] T , a single neutron j falls at position q within the pixel i,j Available random variables express:

[0255]

[0256] For a single measurement, the positions of all neutrons falling on the detection plane are obtained by weighting the positions of each point and the sampling frequency:

[0257]

[0258] Where i is the subscript of the center of the pixel on the detection plane

[0259] Considering that the detection plane image is a superposition of various orientations, it is assumed that the neutrons that fall on the detection plane in a specific orientation are represented by the random variable X g Expressed as follows:

[0260]

[0261] Preferably, the step 3 is specifically:

[0262] Consider the random variable X in step 2. Its corresponding probability model distribution can be expressed by Gaussian mixture distribution, which is:

[0263]

[0264] Where x represents the position of the neutron on the detector, μ k ,∑ k are the mean and covariance matrix of the kth Gaussian distribution, π k is the mixing coefficient, N is the normal distribution, and K is the number of multivariate Gaussian distributions.

[0265] For a given measurement x and initial k,π k ,μ k ,∑ k , the EM algorithm is used to optimize the parameters of the Gaussian mixture model.

[0266] In step E, according to the current π k ,μ k ,∑ k Calculate the posterior probability distribution γ(z nk ):

[0267]

[0268] Among them, x n is the position of the nth detected neutron in the detection plane.

[0269] In the M step, the new π is calculated based on the posterior probability distribution in the previous step k ,μ k ,∑ k ,in:

[0270]

[0271]

[0272]

[0273]

[0274] Among them, N x is the total number of neutrons, N k is the number of neutrons belonging to the kth Gaussian distribution after clustering.

[0275] Repeat the above steps until the estimated likelihood function value converges. The expression of the log-likelihood function is:

[0276]

[0277] Preferably, the step 4 is specifically:

[0278] According to the k multivariate Gaussian distributions in the mixed Gaussian model obtained in step 3, the mean values of each are calculated in the detection plane coordinate system {D}. D μ k =( D x k , D y k ,0) T The position of the diffraction enhancement point in the sample coordinate system {S} is obtained to obtain the depression angle and elevation angle (γ k ,η k ), where η k is the angle corresponding to the crystal plane orientation, γ k =2θ k ,θ k is the neutron diffraction angle, satisfying Bragg's law:

[0279] nλ k =2d k sin(θ k ) (122)

[0280] Where λ is the wavelength of the neutron beam, d is the lattice spacing of the material sample, and n is a positive integer.

[0281] Based on the probability density function corresponding to the multivariate Gaussian distribution, the ODF function of each crystal plane orientation at each diffraction point is expressed. For the diffraction point μ=(x,y,z) T , the ODF function value corresponding to the kth crystal plane orientation is:

[0282]

[0283] where Σ' k =R∑ k R T

[0284] Where R is the rotation matrix of the reference frame {D} relative to {S},

[0285] Among them, R y The rotation matrix corresponding to the rotation around the y-axis of the {S} reference frame, γ k is the corresponding rotation angle, R z is the rotation matrix corresponding to the rotation around the z-axis of the {S} reference frame, η k is the corresponding rotation angle.

[0286] Preferably, the step 5 is specifically:

[0287] According to the Bragg angle corresponding to each crystal plane orientation calculated in step 4, calculate the lattice strain mean ε corresponding to each crystal plane k :

[0288]

[0289]

[0290] where d k is the lattice spacing after loading, and d0 is the in-situ lattice spacing.

[0291] The mean strain value of each point in the diffraction volume is calculated as the weighted average of the mean strain value of each crystal plane with respect to the ODF function:

[0292]

[0293] Among them, f k (x,y,z) is the point where the diffraction occurs (x,y,z) T The ODF function value corresponding to the upper orientation k.

[0294] Directly applying this model to strain field reconstruction in neutron diffraction experiments can combine diffraction information on lattice strain and texture intensity to accurately reconstruct the lattice strain at each point in the diffraction volume. Because a single diffraction image reflects the strain and texture information of a specific responsive crystal plane within the sample, multiple diffraction measurements in space and sample rotation can further refine the lattice information within the sample. Assuming accurate experimental measurements, theoretically, the more diffraction information measured, the more accurate the reconstruction of the material's strain field.

[0295] The specific implementation scheme of the present invention is described below with reference to specific physical examples. According to steps 1-2 in the content of the invention, a probabilistic statistical model of diffraction geometry is established in combination with the neutron diffraction image to obtain a sampled image corresponding to the model. According to step 3, a Gaussian mixture model is used in combination with the EM algorithm to perform parameter optimization and separate the sampled images corresponding to each crystal plane orientation in the diffraction volume. According to step 4, the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane are solved. The weighted mean of the strain at each point is calculated through step 5 to obtain the reconstruction effect of the strain field using the Gaussian mixture model. The results show that the strain field reconstruction method for neutron diffraction experiments based on the Gaussian mixture model has high reconstruction accuracy.

[0296] Those skilled in the art will appreciate that, in addition to implementing the system, device, and various modules provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like by logically programming the method steps. Therefore, the system, device, and various modules provided by the present invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; the modules for implementing various functions can also be considered both software programs for implementing the method and structures within the hardware component.

[0297] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A method for reconstructing strain fields from neutron diffraction experiments based on a Gaussian mixture model, characterized in that: include: Step S1: establishing a diffraction geometry relationship considering the diffraction volume; Step S2: using the diffraction image, obtaining a probability sampling model corresponding to the diffraction geometry; Step S3: Under the sampling model, the Gaussian mixture model is used to separate the diffraction images corresponding to different crystal plane orientations; Step S4: Calculate the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material; Step S5: Calculate the strain mean corresponding to each point in the diffraction volume and reconstruct the strain field information corresponding to a single diffraction measurement; In step S2: The actual size of a single pixel is S = d × d mm 2 , pixel center Q i =[q ix ,q iy ] T , a single neutron j falls at position q within the pixel i,j Using random variables express: X qi,j ~(X i,j ,Y i,j ) T (4) For a single measurement, the positions of all neutrons falling on the detection plane are obtained by weighting the positions of each point and the sampling frequency: Where i is the subscript of the pixel center on the detection plane; the neutron counting intensity at the center Q of a pixel on the detector is I(Q); The neutrons that fall on the detection plane from a specific orientation are represented by the random variable X g If it is expressed as follows: In step S3: The probability model distribution corresponding to the random variable X is expressed by Gaussian mixture distribution, which is: Where x represents the position of the neutron on the detector, μ k ,∑ k are the mean and covariance matrix of the kth Gaussian distribution, π k is the mixing coefficient, N is the normal distribution, and K is the number of multivariate Gaussian distributions; Use the EM algorithm to optimize the parameters of the Gaussian mixture model: In step E, according to the current π k ,μ k ,∑ k Calculate the posterior probability distribution γ(z nk ): Among them, x n is the position of the nth detected neutron in the detection plane; In the M step, the new π is calculated based on the posterior probability distribution k ,μ k ,∑ k ,in: Among them, N x is the total number of neutrons, N k is the number of neutrons belonging to the kth Gaussian distribution after clustering; Repeat the above steps until the estimated likelihood function value reaches convergence. The expression of the log-likelihood function is:

2. The method for reconstructing the strain field of a neutron diffraction experiment based on a Gaussian mixture model according to claim 1, characterized in that: In step S1: The neutron counting intensity at the center of a pixel Q on the detector is I(Q), and the direction of the neutron beam after diffraction is The crystal plane orientation is The neutron counting intensity produced by a single orientation on the detector is I g (p), the area inside the sample where diffraction occurs is is the sum of the diffraction points M, W = ∪ M, The neutron counting intensity generated by a single diffraction point is I g,M ; For a single crystal plane orientation, the neutron counting intensity is the sum of all the points where diffraction occurs, which is: in, The diffracted neutrons generated by all possible crystal plane orientations in the material sample are superimposed on each other to form the neutron counting intensity on the detection plane, which is:

3. The method for reconstructing the strain field of a neutron diffraction experiment based on a Gaussian mixture model according to claim 1, characterized in that: In step S4: According to the obtained k multivariate Gaussian distributions in the mixed Gaussian model, the mean values of each are calculated under the detection plane coordinate system {D}. D μ k =( D x k , D y k ,0) T The position of the diffraction enhancement point in the sample coordinate system {S} is obtained to obtain the depression angle and elevation angle (γ k ,η k ), where η k is the angle corresponding to the crystal plane orientation, γ k =2θ k ,θ k is the neutron diffraction angle, satisfying Bragg's law: nλ k =2d k sin(θ k ) (14) Where λ is the wavelength of the neutron beam, d is the lattice spacing of the material sample, and n is a positive integer; Based on the probability density function corresponding to the multivariate Gaussian distribution, the ODF function of each crystal plane orientation at each diffraction point is expressed. For the diffraction point μ=(x,y,z) T , the ODF function value corresponding to the kth crystal plane orientation is: Among them, Σ' k =R∑ k R T , R is the rotation matrix of the reference frame {D} relative to {S}, Among them, R y The rotation matrix corresponding to the rotation around the y-axis of the {S} reference frame, γ k is the corresponding rotation angle, R z is the rotation matrix corresponding to the rotation around the z-axis of the {S} reference frame, η k is the corresponding rotation angle.

4. The method for reconstructing the strain field of a neutron diffraction experiment based on a Gaussian mixture model according to claim 1, characterized in that: In step S5: According to the Bragg angle corresponding to each crystal plane orientation, the mean lattice strain ε corresponding to each crystal plane is calculated. k : Among them, d k is the lattice spacing after loading, d0 is the in-situ lattice spacing; The mean strain value of each point in the diffraction volume is calculated as the weighted average of the mean strain value of each crystal plane with respect to the ODF function: Among them, f k (x,y,z) is the point where the diffraction occurs (x,y,z) T The ODF function value corresponding to the upper orientation k.

5. A neutron diffraction experimental strain field reconstruction system based on a Gaussian mixture model, characterized in that: include: Module M1: Establishing diffraction geometry considering diffraction volume; Module M2: Using the diffraction image, obtain the probability sampling model corresponding to the diffraction geometry; Module M3: Under the sampling model, the Gaussian mixture model is used to separate the diffraction images corresponding to different crystal plane orientations; Module M4: Determine the diffraction angle, orientation normal, and volume fraction corresponding to each crystal plane in the material; Module M5: Calculate the mean strain value corresponding to each point in the diffraction volume and reconstruct the strain field information corresponding to a single diffraction measurement; In the module M2: The actual size of a single pixel is S = d × d mm 2 , pixel center Q i =[q ix ,q iy ] T , a single neutron j falls at position q within the pixel i,j Using random variables express: For a single measurement, the positions of all neutrons falling on the detection plane are obtained by weighting the positions of each point and the sampling frequency: Where i is the subscript of the pixel center on the detection plane; the neutron counting intensity at the center Q of a pixel on the detector is I(Q); The neutrons that fall on the detection plane from a specific orientation are represented by the random variable X g If it is expressed as follows: In the module M3: The probability model distribution corresponding to the random variable X is expressed by Gaussian mixture distribution, which is: Where x represents the position of the neutron on the detector, μ k ,∑ k are the mean and covariance matrix of the kth Gaussian distribution, π k is the mixing coefficient, N is the normal distribution, and K is the number of multivariate Gaussian distributions; Use the EM algorithm to optimize the parameters of the Gaussian mixture model: In module E, according to the current π k ,μ k ,∑ k Calculate the posterior probability distribution γ(z nk ): Among them, x n is the position of the nth detected neutron in the detection plane; In the M module, the new π is calculated based on the posterior probability distribution k ,μ k ,∑ k ,in: Among them, N x is the total number of neutrons, N k is the number of neutrons belonging to the kth Gaussian distribution after clustering; Repeat the above modules until the estimated likelihood function value reaches convergence. The expression of the log-likelihood function is:

6. The neutron diffraction experiment strain field reconstruction system based on Gaussian mixture model according to claim 5, characterized in that: In the module M1: The neutron counting intensity at the center of a pixel Q on the detector is I(Q), and the direction of the neutron beam after diffraction is The crystal plane orientation is The neutron counting intensity produced by a single orientation on the detector is I g (p), the area inside the sample where diffraction occurs is is the sum of the diffraction points M, W = ∪ M, The neutron counting intensity generated by a single diffraction point is I g,M ; For a single crystal plane orientation, the neutron counting intensity is the sum of all the points where diffraction occurs, which is: in, The diffracted neutrons generated by all possible crystal plane orientations in the material sample are superimposed on each other to form the neutron counting intensity on the detection plane, which is:

7. The neutron diffraction experiment strain field reconstruction system based on Gaussian mixture model according to claim 5, characterized in that: In the module M4: According to the obtained k multivariate Gaussian distributions in the mixed Gaussian model, the mean values of each are calculated under the detection plane coordinate system {D}. D μ k =( D x k , D y k ,0) T The position of the diffraction enhancement point in the sample coordinate system {S} is obtained to obtain the depression angle and elevation angle (γ k ,η k ), where η k is the angle corresponding to the crystal plane orientation, γ k =2θ k ,θ k is the neutron diffraction angle, satisfying Bragg's law: nλ k =2d k sin(θ k ) (14) Where λ is the wavelength of the neutron beam, d is the lattice spacing of the material sample, and n is a positive integer; Based on the probability density function corresponding to the multivariate Gaussian distribution, the ODF function of each crystal plane orientation at each diffraction point is expressed. For the diffraction point μ=(x,y,z) T , the ODF function value corresponding to the kth crystal plane orientation is: Among them, Σ' k =R∑ k R T , R is the rotation matrix of the reference frame {D} relative to {S}, Among them, R y The rotation matrix corresponding to the rotation around the y-axis of the {S} reference frame, γ k is the corresponding rotation angle, R z is the rotation matrix corresponding to the rotation around the z-axis of the {S} reference frame, η k is the corresponding rotation angle; In the module M5: According to the Bragg angle corresponding to each crystal plane orientation, the mean lattice strain ε corresponding to each crystal plane is calculated. k : Among them, d k is the lattice spacing after loading, d0 is the in-situ lattice spacing; The mean strain value of each point in the diffraction volume is calculated as the weighted average of the mean strain value of each crystal plane with respect to the ODF function: Among them, f k (x,y,z) is the point where the diffraction occurs (x,y,z) T The ODF function value corresponding to the upper orientation k.

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