CN106934453B - Method for determining cubic material parent phase and child phase orientation relation - Google Patents
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Abstract
The invention provides a method for determining the orientation relation between a parent phase and a child phase of a cubic material, which can accurately calculate the orientation relation between the parent phase and the child phase of the cubic material. The method comprises the following steps: substituting the population Pop and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation to generate a matrix popfit for storing a minimum theta value; carrying out mutation operation on the population Pop to obtain a matrix U; performing cross operation on the population Pop and the matrix U to obtain a matrix T; substituting the matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation to generate a matrix tempfit storing the minimum theta value; selecting the matrices popfit and tempfit, selecting the minimum theta value in the matrices popfit and tempfit, and selecting the individual corresponding to the minimum theta value in the population to enter the next iteration; and if the maximum iteration times is reached, acquiring the minimum theta value in the matrix popfit generated by the last iteration and the to-be-solved orientation relation. The invention is suitable for the technical field of material crystallography.
Description
Technical Field
The invention relates to the technical field of material crystallography, in particular to a method for determining the direction relation between a parent phase and a child phase of a cubic material.
Background
In recent years, as Electron Back Scattering Diffraction (EBSD) technology and its related systems have been increasing, the orientation regression of the original mother phase structure before phase transformation has become possible, and this process has also been receiving increased attention. The regression of the original parent phase orientation requires to know the orientation information of the child phase of the phase change product and the orientation relationship between the parent phase and the child phase, so that the acquisition of the orientation relationship is very important.
However, in the prior art, no method is available for accurately calculating the orientation relationship between the parent phase and the child phase of the cubic material.
Disclosure of Invention
The invention aims to provide a method for determining the orientation relation between a parent phase and a child phase of a cubic system material, so as to solve the problem that the orientation relation between the parent phase and the child phase of the cubic system material cannot be accurately calculated in the prior art.
In order to solve the above technical problem, an embodiment of the present invention provides a method for determining a directional relationship between a parent phase and a child phase of a cubic system material, including:
s1, obtaining orientation point data of the cubic steel material, wherein the orientation point data comprises: the Euler angle of the orientation point;
s2, initializing a population Pop, substituting the population Pop and the Euler angles of the acquired orientation points into a preset orientation relational expression for calculation, and generating a matrix popfit storing a minimum theta value, wherein theta represents orientation difference angles between theoretical orientations and actual orientations of all orientation points;
s3, performing mutation operation on the population Pop to obtain a matrix U;
s4, performing cross operation on the population Pop and the matrix U to obtain a matrix T;
s5, judging whether the elements in the matrix T exceed a preset value range;
s6, if the elements in the matrix T do not exceed the preset value range, substituting the matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix tempfit storing the minimum theta value;
s7, if the elements in the matrix T exceed the preset value range, transforming the elements in the matrix T exceeding the preset value range by using a preset transformation formula, substituting the transformed matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix tempfit storing the minimum theta value;
s8, selecting the matrix popfit and the matrix tempfit, selecting the minimum theta value in the matrix popfit and the matrix tempfit, and selecting the individual corresponding to the minimum theta value in the population to enter the next iteration;
s9, judging whether the maximum iteration number is reached; if the maximum iteration number is not reached, returning to execute S3; and if the maximum iteration times is reached, acquiring the minimum theta value in the matrix popfit generated by the last iteration, and acquiring the to-be-solved orientation relation according to the position of the minimum theta value obtained by the last iteration.
Further, before initializing the population Pop, the method further comprises:
setting parameters, wherein the parameters comprise: population size, scaling factor, crossover probability, maximum iteration number MAX, and all-zero matrix vminMaximum value matrix vmax；
Wherein the size of the all-zero matrix vmin is 1 x 6, and the all-zero matrix vminThe first three columns of (A) correspond to the orientation relation V in the preset orientation relation, and the all-zero matrix VminThe last three columns of (A) correspond to the orientation information M of the parent phase in the preset orientation relation, and the maximum value matrix vmaxIs 1 x 6.
Further, the preset orientation relation is expressed as:
wherein, theta represents the orientation difference angle between the theoretical orientation and the actual orientation of all the orientation points, N is the number of the orientation points, arccos (·) represents an inverse cosine function, trace (·) represents the trace operation on the matrix, V represents a bit direction relation, M represents the orientation information of the parent phase, MM represents the Euler angle of the orientation points, and S represents the number of the orientation pointsjAnd SkThe equivalent matrixes are the crystallography symmetry factors corresponding to the parent phase and the child phase respectively, and j and k represent the crystallography symmetry factors of the parent phase and the child phase respectively.
Further, the initializing population Pop includes:
will all zero matrix vminAnd a maximum value matrix vmaxRespectively converting the Np matrix into Np 6 matrixes, and randomly generating an Np 6 matrix R, wherein Np represents the size of the population;
using the formula Pop ═ vmin+R*(vmax-vmin) And generating an initial population Pop.
Further, the performing mutation operation on the population Pop to obtain the matrix U includes:
assigning the population Pop to a matrix U;
in the t-th iteration, when i is in the range of 1 to Np, 3 numbers x are randomly generated in Np1、x2、x3；
Using formula Ui＝Popx1+F*(Popx2-Popx3) Performing mutation operation to update the matrix U;
where F denotes a scaling factor, x1、x2、x3Respectively represent the x-th in the population Pop1、x2、x3Line, Popx1、Popx2、Popx3Respectively represent the x-th in the population Pop1、x2、x3Data of a line, UiRepresenting the ith row of data in matrix U.
Further, the performing a cross operation on the population Pop and the matrix U to obtain the matrix T includes:
assigning the population Pop to a matrix T;
randomly generating a matrix R of Np x 6, and comparing each element in the matrix R with a cross probability CR, wherein Np represents the size of the population;
and if the elements in the matrix R are smaller than the cross probability CR, assigning the elements at the corresponding positions in the matrix U to the elements at the same positions in the matrix T.
Further, the preset value range is as follows: greater than or equal to a preset lower boundary and less than or equal to a preset upper boundary, wherein the preset lower boundary is an all-zero matrix vminThe preset upper boundary is a maximum value matrix vmax；
The judging whether the elements in the matrix T exceed the preset value range includes:
each element in the matrix T is added to vminAnd vmaxThe corresponding elements in (a) are compared.
Further, if the elements in the matrix T exceed the preset value range, transforming the elements in the matrix T that exceed the preset value range by using a preset transformation formula includes:
if the elements in the matrix T exceed the preset value range, randomly generating a matrix R of Np × 6, and transforming the elements exceeding the preset value range in the matrix T by using a preset transformation formula, wherein the preset transformation formula is represented as:
T(i)＝vmin(i)+R(i)*(vmax(i)-vmin(i))
wherein Np denotes the size of the population, vminRepresenting all-zero matrices, vmaxAnd (3) representing a maximum value matrix, and i represents the element position exceeding a preset value range in the matrix T.
Further, the selecting operation of the matrix popfit and the matrix tempfit, the minimum θ value in the matrix popfit and the matrix tempfit is selected, and the selecting of the individual corresponding to the minimum θ value in the population to enter the next iteration includes:
comparing the elements in the matrix popfit with the elements at the corresponding positions in tempfit;
if the elements in the matrix popfit are larger than the elements at the corresponding positions in the matrix tempfit, assigning the elements at the corresponding positions in the matrix tempfit to the elements at the same positions in the matrix popfit, and updating the matrix popfit;
and obtaining the minimum theta value in the updated matrix popfit, and selecting the individual corresponding to the minimum theta value from the population to enter next iteration.
The technical scheme of the invention has the following beneficial effects:
in the above scheme, orientation point data of the cubic steel material is obtained, wherein the orientation point data includes: the Euler angle of the orientation point; initializing a population Pop, substituting the population Pop and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix popfit storing a minimum theta value, wherein theta represents orientation difference angles between theoretical orientations and actual orientations of all the orientation points; carrying out mutation operation on the population Pop to obtain a matrix U; performing cross operation on the population Pop and the matrix U to obtain a matrix T; judging whether the elements in the matrix T exceed a preset value range or not; if the elements in the matrix T do not exceed the preset value range, substituting the matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation to generate a matrix tempfit storing the minimum theta value; if the elements in the matrix T exceed the preset value range, transforming the elements exceeding the preset value range in the matrix T by using a preset transformation formula, substituting the transformed matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix tempfit storing the minimum theta value; selecting the matrix popfit and the matrix tempfit, selecting the minimum theta value in the matrix popfit and the matrix tempfit, and selecting the individual corresponding to the minimum theta value in the population to enter next iteration; judging whether the maximum iteration times is reached; if the maximum iteration times are not reached, returning to the step of executing mutation operation on the population Pop to obtain a matrix U; and if the maximum iteration times is reached, acquiring the minimum theta value in the matrix popfit generated by the last iteration, and acquiring the to-be-solved orientation relation according to the position of the minimum theta value obtained by the last iteration. In this way, by applying a differential evolution algorithm, namely, by using mutation, intersection and selection operations and by carrying out multiple iterations, the individual corresponding to the minimum theta value is selected to enter next iteration, so that good individuals are reserved, poor individuals are eliminated, the theta value in the orientation relationship is guided to gradually approach to the global optimal solution, and when the theta reaches the minimum value, the orientation relationship to be solved can be obtained.
Drawings
Fig. 1 is a schematic flow chart of a method for determining an orientation relationship between a parent phase and a child phase of a cubic system material according to an embodiment of the present invention;
fig. 2 is a detailed flowchart of a method for determining the orientation relationship between a parent phase and a child phase of a cubic system material according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a crossover operation according to an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
The invention provides a method for determining the cubic material parent-phase and child-phase orientation relation, aiming at the problem that the existing cubic material parent-phase and child-phase orientation relation cannot be accurately calculated
Referring to fig. 1, a method for determining an orientation relationship between a parent phase and a child phase of a cubic system material according to an embodiment of the present invention includes:
s1, obtaining orientation point data of the cubic steel material, wherein the orientation point data comprises: the Euler angle of the orientation point;
s2, initializing a population Pop, substituting the population Pop and the Euler angles of the acquired orientation points into a preset orientation relational expression for calculation, and generating a matrix popfit storing a minimum theta value, wherein theta represents orientation difference angles between theoretical orientations and actual orientations of all orientation points;
s3, performing mutation operation on the population Pop to obtain a matrix U;
s4, performing cross operation on the population Pop and the matrix U to obtain a matrix T;
s5, judging whether the elements in the matrix T exceed a preset value range;
s6, if the elements in the matrix T do not exceed the preset value range, substituting the matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix tempfit storing the minimum theta value;
s7, if the elements in the matrix T exceed the preset value range, transforming the elements in the matrix T exceeding the preset value range by using a preset transformation formula, substituting the transformed matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix tempfit storing the minimum theta value;
s8, selecting the matrix popfit and the matrix tempfit, selecting the minimum theta value in the matrix popfit and the matrix tempfit, and selecting the individual corresponding to the minimum theta value in the population to enter the next iteration;
s9, judging whether the maximum iteration number is reached; if the maximum iteration number is not reached, returning to execute S3; and if the maximum iteration times is reached, acquiring the minimum theta value in the matrix popfit generated by the last iteration, and acquiring the to-be-solved orientation relation according to the position of the minimum theta value obtained by the last iteration.
The method for determining the parent-phase and child-phase orientation relationship of the cubic system material comprises the following steps of obtaining orientation point data of the cubic system material, wherein the orientation point data comprises: the Euler angle of the orientation point; initializing a population Pop, substituting the population Pop and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix popfit storing a minimum theta value, wherein theta represents orientation difference angles between theoretical orientations and actual orientations of all the orientation points; carrying out mutation operation on the population Pop to obtain a matrix U; performing cross operation on the population Pop and the matrix U to obtain a matrix T; judging whether the elements in the matrix T exceed a preset value range or not; if the elements in the matrix T do not exceed the preset value range, substituting the matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation to generate a matrix tempfit storing the minimum theta value; if the elements in the matrix T exceed the preset value range, transforming the elements exceeding the preset value range in the matrix T by using a preset transformation formula, substituting the transformed matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix tempfit storing the minimum theta value; selecting the matrix popfit and the matrix tempfit, selecting the minimum theta value in the matrix popfit and the matrix tempfit, and selecting the individual corresponding to the minimum theta value in the population to enter next iteration; judging whether the maximum iteration times is reached; if the maximum iteration times are not reached, returning to the step of executing mutation operation on the population Pop to obtain a matrix U; and if the maximum iteration times is reached, acquiring the minimum theta value in the matrix popfit generated by the last iteration, and acquiring the to-be-solved orientation relation according to the position of the minimum theta value obtained by the last iteration. In this way, by applying a differential evolution algorithm, namely, by using mutation, intersection and selection operations and by carrying out multiple iterations, the individual corresponding to the minimum theta value is selected to enter next iteration, so that good individuals are reserved, poor individuals are eliminated, the theta value in the orientation relationship is guided to gradually approach to the global optimal solution, and when the theta reaches the minimum value, the orientation relationship to be solved can be obtained.
In the embodiment of the invention, because the requirement theta in the orientation relation is minimum, in order to avoid the situation that the orientation relation falls into a local optimal solution due to premature convergence, in order to obtain a global optimal solution as much as possible, the embodiment of the invention adopts a differential evolution algorithm to solve the orientation relation to be solved; the differential evolution algorithm can minimize a nonlinear non-differentiable continuous space function, has a simple basic principle and fewer controlled parameters, and is widely applied to multiple fields of artificial intelligence, pattern recognition and the like; the three main steps of the differential evolution algorithm are mutation, crossover and selection.
In this embodiment, the method for determining the direction relationship between the parent phase and the child phase of the cubic system material by using the differential evolution algorithm, as shown in fig. 2, may specifically include the following steps:
the method comprises the following steps: acquiring orientation point data of a cubic system steel material, wherein each line in the data represents one orientation point, each line in the data represents orientation information of one orientation point, and the orientation information of the orientation points comprises: in the present embodiment, the orientation information (i.e., three euler angles) of the orientation points is mainly used for calculation, and the data amount (i.e., the number of the orientation points) of the orientation points can reach thirty-one thousand.
Step two: setting parameters, wherein the parameters comprise: population size Np, scaling factor F, crossover probability 0.4, maximum iteration number MAX, all-zero matrix vminMaximum value matrix vmaxAll-zero matrix bestrr; supposing that the population size Np is 30, the scaling factor F and the cross probability CR are both 0.4, and the maximum iteration number MAX is 100; all-zero matrix vminIs 1 x 6, the all-zero matrix vminThe first three columns of (A) correspond to the orientation relation V in the preset orientation relation, and the all-zero matrix VminThe last three columns of the three-dimensional space correspond to orientation information M of a parent phase in a preset orientation relation; maximum matrix vmaxIs 1 x 6, a maximum matrix v can be setmaxIs [90, 90, 90, 360, 90, 90 ]]The size of the all-zero matrix bestrr is 100 x 1, and the all-zero matrix bestrr is used to store the minimum θ value for each generation.
Step three: initializing a population (when the first iteration is performed, the population needs to be initialized, and the population Pop generated by the first iteration can be called as initial population Pop), and performing all-zero matrix vminAnd maximum momentMatrix vmaxRespectively using repmat () function to convert into 30 x 6 matrix, then using rand () function to randomly generate a 30 x 6 matrix R, using formula (1)
Pop＝vmin+R*(vmax-vmin) (1)
Generating an initial population Pop, wherein the information of the population Pop is stored in a matrix form;
then, assigning the population Pop to a matrix U; then, substituting each row value of the population Pop and the obtained euler angle of the orientation point into a direction relation formula (2) for calculation, wherein the euler angle of the orientation point corresponds to a variable MM in the direction relation formula, each row of the matrix Pop has 6 columns of data, the first 3 columns of data correspond to a variable V in the direction relation formula, and the last 3 columns of data correspond to a variable M in the direction relation formula, wherein the direction relation formula is expressed as:
in the formula (2), θ represents the average deviation (orientation) difference angle of the orientation difference between the theoretical orientation and the actual orientation of all the orientation points, trace (·) represents the tracing operation on the matrix, arccos (·) represents the inverse cosine function, V represents the orientation relation, N is the number of the orientation points, j and k represent the crystallographic symmetry factors of the parent phase and the child phase respectively, and the value ranges are [1, 24 ]]，SjAnd SkThe matrix is an equivalent matrix of the corresponding crystallography symmetry factors of the parent phase and the child phase, M is the orientation information of the parent phase, and MM represents the Euler angle of the orientation point.
Because the value ranges of j and k are both [1, 24 ]]Therefore, for each orientation point i, 24 × 24 calculations are performed, and for each orientation point, the minimum value θ of all the values is finally obtainedmin(i) Storing, calculating all orientation points, and obtaining all thetaminThe values are summed and averaged to obtain the average theta corresponding to the corresponding row of data in the populationmin. The population Pop has 30 rows of data, so that all calculations are completed to obtain a 1 x 30 matrix, and each column number represents the average θ calculated using each row of data of the population PopminWill beThis matrix is defined as popfit and is used for the next steps.
In this embodiment, as an optional embodiment, the initializing population Pop includes:
will all zero matrix vminAnd a maximum value matrix vmaxRespectively converting the Np matrix into Np 6 matrixes, and randomly generating an Np 6 matrix R, wherein Np represents the size of the population;
using the formula Pop ═ vmin+R*(vmax-vmin) And generating an initial population Pop.
Step four: performing mutation operation; in the t-th iteration, when i is in the range of 1 to Np, 3 numbers x are randomly generated in Np1、x2、x3Using equation (3):
Ui＝Popx1+F*(Popx2-Popx3) (3)
performing mutation operation to update the matrix U;
where F denotes a scaling factor, x1、x2、x3Respectively represent the x-th in the population Pop1、x2、x3Line, Popx1、Popx2、Popx3Respectively represent the x-th in the population Pop1、x2、x3Data of a line, UiRepresenting the ith row of data in matrix U.
Step five: performing cross operation; and assigning the population Pop to a matrix T, and performing cross operation by using the matrix T and a matrix U obtained after mutation operation. The specific process is as follows: randomly generating a 30 x 6 matrix R by using a rand () function, comparing each element in the matrix R with the cross probability CR, and if the element in the matrix R is more than or equal to the cross probability CR, keeping the element value which is the same as the element in the matrix R in the position in the matrix T unchanged; if the elements in the matrix R are smaller than the crossover probability CR, assigning the elements at the corresponding positions in the matrix U to the elements at the same positions in the matrix T, thereby completing the crossover operation, and realizing the code as follows: t (R)<CR)＝U(R<CR), the schematic diagram of the crossover operation is shown in FIG. 3, riRepresenting the ith element, x, in an individuali(g) Indicating that the ith individual is inValue at g iterations, vi(g +1) denotes the value of the ith individual at the g +1 iteration, ui(g +1) represents the result of the i-th individual after the crossover operation at the g +1 th iteration.
In this embodiment, as an optional embodiment, the performing a cross operation on the population Pop and the matrix U to obtain the matrix T includes:
assigning the population Pop to a matrix T;
randomly generating a matrix R of Np x 6, and comparing each element in the matrix R with a cross probability CR, wherein Np represents the size of the population;
and if the elements in the matrix R are smaller than the cross probability CR, assigning the elements at the corresponding positions in the matrix U to the elements at the same positions in the matrix T.
Step six: checking a boundary; the preset value range is as follows: greater than or equal to a preset lower boundary and less than or equal to a preset upper boundary, wherein the preset lower boundary is an all-zero matrix vminThe preset upper boundary is a maximum value matrix vmax(ii) a For the matrix T obtained after the cross operation, whether the matrix T meets the value range set firstly is checked, namely whether the elements in the matrix T exceed the boundary vminAnd vmax. Firstly, a 30 x 6 matrix R is randomly generated, and then each element in the matrix T and v are combinedminAnd vmaxComparing the corresponding elements in the matrix T, if the elements in the matrix T do not exceed the boundary, keeping the values of the elements in the matrix T unchanged, and if the elements in the matrix T exceed the boundary, transforming the corresponding elements in the matrix T by using a preset transformation formula (4):
T(i)＝vmin(i)+R(i)*(vmax(i)-vmin(i)) (4)
and after the boundary check, obtaining an updated matrix T, substituting each row value of the matrix T and the obtained Euler angle of the orientation point into the orientation relational expression (2) for calculation, and finally obtaining a matrix storing 30 minimum theta values and recording as a matrix tempfit.
In this embodiment, as an optional embodiment, if the elements in the matrix T exceed the preset value range, the transforming the elements exceeding the preset value range in the matrix T by using a preset transformation formula includes:
if the elements in the matrix T exceed the preset value range, randomly generating a matrix R of Np × 6, and transforming the elements exceeding the preset value range in the matrix T by using a preset transformation formula, wherein the preset transformation formula is represented as:
T(i)＝vmin(i)+R(i)*(vmax(i)-vmin(i))
wherein Np denotes the size of the population, vminRepresenting all-zero matrices, vmaxAnd (3) representing a maximum value matrix, and i represents the element position exceeding a preset value range in the matrix T.
Step seven: selecting operation; and selecting the matrix popfit obtained in the third step and the matrix tempfit obtained in the sixth step, selecting the minimum theta value in the matrix popfit and the matrix tempfit, and selecting the individual corresponding to the minimum theta value in the population to enter next iteration. The specific process is as follows: comparing elements in the matrix popfit with elements at corresponding positions in the matrix tempfit, and if the elements in the matrix popfit are less than or equal to the elements at the corresponding positions in the tempfit, keeping the element values of the positions in the popfit unchanged; if the elements in the matrix popfit are larger than the elements in the corresponding positions in the tempfit, assigning the elements in the positions in the tempfit to the elements in the same positions in the popfit, updating the matrix popfit, and realizing the code as follows: popfit (popfit > tempfit) ═ tempfit (popfit > tempfit); since the matrix popfit and the matrix tempfit are calculated from the elements in the matrix Pop and the matrix T, respectively, that is, the ith element in the matrix popfit and the matrix tempfit are obtained from the ith row of data in the matrix Pop and the matrix T, respectively, if the ith element in the matrix popfit is updated, correspondingly, the ith row of data in the matrix Pop should also be updated according to the matrix T, that is, the individual corresponding to the optimal value (the minimum θ value) in the matrix popfit and the matrix tempfit should be screened out to enter the next generation, that is: the individual corresponding to the minimum θ value in the updated matrix popfit is screened out to enter the next generation, and the implementation code is as follows: pop (popfit > tempfit,: T ═ T (popfit > tempfit,: T);
wherein, Pop (popfit > tempfit: ═ of T (popfit > tempfit: ": "is the code of matlab,": "indicates all columns. In addition, the minimum value in the updated matrix popfit is extracted and stored in the matrix bestrr (t) which is set firstly, and bestrr (t) represents that the minimum value is the optimal solution generated after the t-th iteration.
Step eight: and repeating the fourth step, the fifth step, the sixth step and the seventh step until the maximum iteration times is reached.
Step nine: after the iteration is finished, the finally obtained minimum value theta is stored in bestrr (100), the value is also the minimum value in the matrix popfit generated by the last iteration, and through the position of the value, which row of data in the matrix Pop is calculated, and the first three rows of data in the row are the final required orientation relation.
In summary, the main idea of this embodiment is to use a differential evolution algorithm, through multiple iterations, retain good individuals, eliminate poor individuals, guide the θ value in the orientation relationship to gradually approach to the global optimal solution, and when the minimum value is reached, the variable V used for calculating the value in the orientation relationship is the orientation relationship to be solved. For the selection of parameters in the algorithm, firstly, the population size Np is selected, and from the analysis of computational complexity, the larger the general population size is, the higher the possibility of the searched global optimal solution is, but the computational load and the computational time are also increased. When Np increases to a certain number, the accuracy of the solution may decrease, and Np cannot be smaller than 3, so that the mutation operation cannot be performed. Generally, under the given maximum iteration number, the population size Np is 15-50, and the balance between the population diversity and the convergence rate can be well maintained, so that 30 is selected as the population size in the embodiment of the invention. For the scaling factor F, if the F is larger, larger disturbance can be generated, which is beneficial to keeping the diversity of the population; if F is small, the disturbance is small, and F can play a role in local fine search. If F is too large, although the population diversity can be kept, the searching efficiency is low, and the obtained global optimal solution has low precision; if F is too small, the population diversity cannot be guaranteed, and the algorithm is easy to converge too early and falls into a local optimal solution. Typical scaling factors are in the range of 0 to 1, and according to the above analysis, the embodiment of the present invention selects the scaling factor F to be 0.4. For the cross probability CR, if CR is smaller, the convergence rate is slow but the success rate is higher, and the stability of the algorithm is good; if CR is large, convergence is accelerated, premature aging easily occurs, and success rate and stability are reduced. In order to ensure a high success rate and a high convergence rate, generally, for a unimodal function, the value of CR is between 0.6 and 0.8, and for a complex and multimodal function, the value of CR is small, between 0.1 and 0.5, and according to the problem to be solved, the value of CR is selected to be 0.4 in the embodiment of the invention.
The embodiment of the invention uses the computer technology to better solve the problem of the material field, and the obtained orientation relation can be applied to the process of the parent phase orientation regression, so that the material field advances on the way of researching the parent phase orientation regression technology, which is a good combination of the computer and the material field and is an innovation in the research of the aspect in China.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A method for determining the orientation relation between a parent phase and a child phase of a cubic material is characterized by comprising the following steps:
s1, obtaining orientation point data of the cubic steel material, wherein the orientation point data comprises: the Euler angle of the orientation point;
s2, initializing a population Pop, substituting the population Pop and the Euler angles of the acquired orientation points into a preset orientation relational expression for calculation, and generating a matrix popfit storing a minimum theta value, wherein theta represents orientation difference angles between theoretical orientations and actual orientations of all orientation points;
s3, performing mutation operation on the population Pop to obtain a matrix U;
s4, performing cross operation on the population Pop and the matrix U to obtain a matrix T;
s5, judging whether the elements in the matrix T exceed a preset value range;
s6, if the elements in the matrix T do not exceed the preset value range, substituting the matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix tempfit storing the minimum theta value;
s7, if the elements in the matrix T exceed the preset value range, transforming the elements in the matrix T exceeding the preset value range by using a preset transformation formula, substituting the transformed matrix T and the obtained Euler angles of the orientation points into a preset orientation relational expression for calculation, and generating a matrix tempfit storing the minimum theta value;
s8, selecting the matrix popfit and the matrix tempfit, selecting the minimum theta value in the matrix popfit and the matrix tempfit, and selecting the individual corresponding to the minimum theta value in the population to enter the next iteration;
s9, judging whether the maximum iteration number is reached; if the maximum iteration number is not reached, returning to execute S3; if the maximum iteration times is reached, acquiring the minimum theta value in the matrix popfit generated by the last iteration, and acquiring the to-be-solved orientation relation through the position of the minimum theta value obtained by the last iteration;
wherein the preset orientation relation is expressed as:
wherein, theta represents the orientation difference angle between the theoretical orientation and the actual orientation of all the orientation points, N is the number of the orientation points, arccos (·) represents an inverse cosine function, trace (·) represents the trace operation on the matrix, V represents a bit direction relation, M represents the orientation information of the parent phase, MM represents the Euler angle of the orientation points, and S represents the number of the orientation pointsjAnd SkThe equivalent matrixes are the corresponding crystallography symmetry factors of the parent phase and the child phase respectively, and j and k represent the crystallography symmetry factors of the parent phase and the child phase respectively;
before initializing the population Pop, the method further comprises:
setting parameters, wherein the parameters comprise: population size, scaling factor, crossover probability, maximum iteration number MAX, and all-zero matrix vminMaximum value matrix vmax；
Wherein, the all-zero matrix vminIs 1 x 6, the all-zero matrix vminThe first three columns of (A) correspond to the orientation relation V in the preset orientation relation, and the all-zero matrix VminThe last three columns of (A) correspond to the orientation information M of the parent phase in the preset orientation relation, and the maximum value matrix vmaxThe size of (a) is 1 x 6;
the initializing population Pop includes:
will all zero matrix vminAnd a maximum value matrix vmaxRespectively converting the Np matrix into Np 6 matrixes, and randomly generating an Np 6 matrix R, wherein Np represents the size of the population;
using the formula Pop ═ vmin+R*(vmax-vmin) Generating an initial population Pop;
wherein, the Euler angle of the orientation point corresponds to the variable MM in the orientation relation, each row of the matrix Pop has 6 columns of data, the first 3 columns of data correspond to the variable V in the orientation relation, and the last 3 columns of data correspond to the variable M in the orientation relation;
selecting the matrix popfit and the matrix tempfit, selecting the minimum theta value in the matrix popfit and the matrix tempfit, and selecting the individual corresponding to the minimum theta value in the population to enter the next iteration, wherein the step of selecting the matrix popfit and the matrix tempfit comprises the following steps:
comparing the elements in the matrix popfit with the elements at the corresponding positions in tempfit;
if the elements in the matrix popfit are larger than the elements at the corresponding positions in the matrix tempfit, assigning the elements at the corresponding positions in the matrix tempfit to the elements at the same positions in the matrix popfit, and updating the matrix popfit;
and obtaining the minimum theta value in the updated matrix popfit, and selecting the individual corresponding to the minimum theta value from the population to enter next iteration.
2. The method for determining the orientation relationship between parent phases and child phases of cubic system material according to claim 1, wherein the performing a mutation operation on the population Pop to obtain the matrix U comprises:
assigning the population Pop to a matrix U;
in the t-th iteration, when i is in the range of 1 to Np, 3 numbers x are randomly generated in Np1、x2、x3；
Using formula Ui＝Popx1+F*(Popx2-Popx3) Performing mutation operation to update the matrix U;
where F denotes a scaling factor, x1、x2、x3Respectively represent the x-th in the population Pop1、x2、x3Line, Popx1、Popx2、Popx3Respectively represent the x-th in the population Pop1、x2、x3Data of a line, UiRepresenting the ith row of data in matrix U.
3. The method for determining the orientation relationship between a parent phase and a child phase of a cubic system material according to claim 1, wherein the step of performing a crossover operation on the population Pop and a matrix U to obtain a matrix T comprises:
assigning the population Pop to a matrix T;
randomly generating a matrix R of Np x 6, and comparing each element in the matrix R with a cross probability CR, wherein Np represents the size of the population;
and if the elements in the matrix R are smaller than the cross probability CR, assigning the elements at the corresponding positions in the matrix U to the elements at the same positions in the matrix T.
4. The method for determining the azimuthal relationship between a parent phase and a child phase of a cubic system material according to claim 1, wherein the preset value range is as follows: greater than or equal to a preset lower boundary and less than or equal to a preset upper boundary, wherein the preset lower boundary is an all-zero matrix vminThe preset upper boundary is a maximum value matrix vmax；
The judging whether the elements in the matrix T exceed the preset value range includes:
each element in the matrix T is added to vminAnd vmaxThe corresponding elements in (a) are compared.
5. The method for determining the azimuthal relationship between a parent phase and a child phase of a cubic system material according to claim 1, wherein if the elements in the matrix T exceed a preset value range, transforming the elements in the matrix T exceeding the preset value range by using a preset transformation formula comprises:
if the elements in the matrix T exceed the preset value range, randomly generating a matrix R of Np × 6, and transforming the elements exceeding the preset value range in the matrix T by using a preset transformation formula, wherein the preset transformation formula is represented as:
T(i)＝vmin(i)+R(i)*(vmax(i)-vmin(i))
wherein Np denotes the size of the population, vminRepresenting all-zero matrices, vmaxAnd (3) representing a maximum value matrix, and i represents the element position exceeding a preset value range in the matrix T.
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