CN106934453A - A kind of determination method of cubic System Material parent phase and sub alternate orientation relationship - Google Patents
A kind of determination method of cubic System Material parent phase and sub alternate orientation relationship Download PDFInfo
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Abstract
The present invention provides a kind of cubic System Material parent phase and the determination method of sub alternate orientation relationship, can exactly calculate cubic System Material parent phase with sub alternate orientation relationship.Methods described includes：The Eulerian angles of population Pop and the orientation point for obtaining are substituted into default orientation relationship formula to calculate, the matrix popfit of generation storage minimum θ values；Mutation operation is carried out to population Pop, matrix U is obtained；Crossover operation is carried out to population Pop and matrix U, matrix T is obtained；The Eulerian angles of matrix T and the orientation point for obtaining are substituted into default orientation relationship formula to calculate, the matrix tempfit of generation storage minimum θ values；Matrix popfit and tempfit are done into selection operation, the minimum θ values in matrix popfit and tempfit are selected, the corresponding individuality of minimum θ values is selected in population and is entered next iteration；If reaching maximum iteration, the minimum θ values and orientation relationship to be asked in the matrix popfit of last time grey iterative generation are obtained.The present invention is applied to material crystals technical field.
Description
Technical field
The present invention relates to material crystals technical field, a kind of cubic System Material parent phase is particularly related to sub- phase meta to pass
The determination method of system.
Background technology
In recent years, due to EBSD (Electron Backscattered Diffraction, EBSD) skill
It is more and more that art and its related system occur, and makes it possible to return the orientation of original parent phase tissue before phase transformation, and this
The process of kind is also increasingly paid close attention to by everybody.Recurrence to original parent phase orientation needs to know the orientation of the sub- phase of its phase-change product
Information and the parent phase orientation relationship alternate with son, it follows that the acquisition of orientation relationship is extremely important.
But, in the prior art, do not there is also method exactly to calculate cubic System Material parent phase with sub- phase meta to pass
System.
The content of the invention
The technical problem to be solved in the present invention is to provide the determination of a kind of cubic System Material parent phase and sub alternate orientation relationship
Method, to solve exactly calculate asking for cubic System Material parent phase and sub alternate orientation relationship existing for prior art
Topic.
In order to solve the above technical problems, the embodiment of the present invention provides a kind of cubic System Material parent phase and sub alternate orientation relationship
Determination method, including：
S1, obtains the orientation point data of cubic system Steel material, wherein, the orientation point data include：The Euler of orientation point
Angle；
S2, initializes population Pop, and the Eulerian angles of population Pop and the orientation point for obtaining are substituted into default orientation relationship
Formula is calculated, the matrix popfit of generation storage minimum θ values, wherein, θ represents the theoretical orientation and actual orientation of all orientation points
Orientation declinate；
S3, mutation operation is carried out to population Pop, obtains matrix U；
S4, crossover operation is carried out to population Pop and matrix U, obtains matrix T；
Whether S5, the element in judgment matrix T exceeds default span；
S6, if the element in matrix T is without departing from default span, by matrix T and the Europe of the orientation point for obtaining
Draw angle to substitute into default orientation relationship formula to calculate, the matrix tempfit of generation storage minimum θ values；
S7, if the element in matrix T exceeds default span, using default transformation for mula to surpassing in matrix T
The element for going out default span is converted, and the Eulerian angles of the matrix T after conversion and the orientation point for obtaining is substituted into default
Orientation relationship formula is calculated, the matrix tempfit of generation storage minimum θ values；
S8, selection operation is done by matrix popfit and matrix tempfit, selects matrix popfit and matrix tempfit
In minimum θ values, the corresponding individuality of minimum θ values is selected in population and enters next iteration；
S9, judges whether to reach maximum iteration；If being not reaching to maximum iteration, return and perform S3；If reaching
To maximum iteration, then the minimum θ values in the matrix popfit of last time grey iterative generation are obtained, by last time iteration
Position where the minimum θ values for obtaining, obtains orientation relationship to be asked.
Further, before initialization population Pop, methods described also includes：
Arrange parameter, the parameter includes：Population scale, zoom factor, crossover probability, maximum iteration MAX, complete zero
Matrix vmin, maximum value matrix vmax；
Wherein, full null matrix vminSize be 1*6, full null matrix vminThe first three columns default orientation relationship formula of correspondence in
Orientation relationship V, full null matrix vminThe rear three row default orientation relationship formula of correspondence in parent phase orientation information M, maximum
Matrix vmaxSize be 1*6.
Further, the default orientation relationship formula is expressed as：
Wherein, θ represents the theoretical orientation of all orientation points and the orientation declinate of actual orientation, and N is the number of orientation point,
Arccos () represents inverse cosine function, and trace () represents and matrix track taking is operated that V represents orientation relationship, and M represents parent phase
Orientation information, MM represents the Eulerian angles of orientation point, SjAnd SkRespectively parent phase and the corresponding crystallographic symmetry factor of son
Equivalent matrix, j and k represent the crystallographic symmetry factor of parent phase and sub- phase respectively.
Further, the initialization population Pop includes：
By full null matrix vminWith maximum value matrix vmaxThe matrix of Np*6 is separately converted to, and using random generation one
The matrix R of Np*6, wherein, Np represents population scale；
Using formula Pop=vmin+R*(vmax-vmin), generation initial population Pop.
Further, described to carry out mutation operation to population Pop, obtaining matrix U includes：
Population Pop is assigned to matrix U；
In the t times iteration, when i is in 1~Np, the 3 number x of random generation in Np1、x2、x3；
Using formula Ui=Popx1+F*(Popx2-Popx3) mutation operation is carried out, matrix U is updated；
Wherein, F represents zoom factor, x1、x2、x3The xth in population Pop is represented respectively1、x2、x3OK, Popx1、Popx2、
Popx3The xth in population Pop is represented respectively1、x2、x3Capable data, UiThe i-th row data in representing matrix U.
Further, described to carry out crossover operation to population Pop and matrix U, obtaining matrix T includes：
Population Pop is assigned to matrix T；
One matrix R of Np*6 of generation, each element and crossover probability CR in matrix R are compared at random, wherein,
Np represents population scale；
If the element in matrix R is less than crossover probability CR, the element of relevant position in matrix U is assigned in matrix T
The element of same position.
Further, the default span is：More than or equal to default lower boundary and less than or equal on default
Border, wherein, the default lower boundary is full null matrix vmin, the default coboundary is maximum value matrix vmax；
Whether the element in the judgment matrix T includes beyond default span：
By each element and v in matrix TminAnd vmaxIn corresponding element be compared.
Further, if the element in the matrix T exceeds default span, using default transformation for mula pair
Element in matrix T beyond default span does conversion to be included：
If the element in matrix T exceeds default span, at random one matrix R of Np*6 of generation, and using pre-
If transformation for mula to being converted beyond the element of default span in matrix T, wherein, the default transformation for mula table
It is shown as：
T (i)=vmin(i)+R(i)*(vmax(i)-vmin(i))
Wherein, Np represents population scale, vminRepresent full null matrix, vmaxMaximum value matrix is represented, is surpassed in i representing matrixs T
Go out the element position of default span.
Further, it is described that matrix popfit and matrix tempfit are done into selection operation, select matrix popfit and square
Minimum θ values in battle array tempfit, the corresponding individual next iteration that enters of minimum θ values is selected in population to be included：
Element on relevant position in element and tempfit in matrix popfit is compared；
If the element in matrix popfit is more than the element on relevant position in matrix tempfit, by matrix tempfit
The element of middle relevant position is assigned to the element of same position in matrix popfit, updates matrix popfit；
The minimum θ values in the matrix popfit after updating are obtained, and the corresponding individuality of minimum θ values is selected in population
Into next iteration.
Above-mentioned technical proposal of the invention has the beneficial effect that：
In such scheme, by obtaining the orientation point data of cubic system Steel material, wherein, the orientation point data include：
The Eulerian angles of orientation point；Initialization population Pop, and by the Eulerian angles of population Pop and the orientation point for obtaining substitute into default position to
Relational expression is calculated, the matrix popfit of generation storage minimum θ values, wherein, θ represents the theoretical orientation of all orientation points and actually takes
To orientation declinate；Mutation operation is carried out to population Pop, matrix U is obtained；Crossover operation is carried out to population Pop and matrix U, is obtained
To matrix T；Whether the element in judgment matrix T exceeds default span；If the element in matrix T is without departing from default
Span, then substitute into the Eulerian angles of matrix T and the orientation point for obtaining default orientation relationship formula and calculate, and generation storage is minimum
The matrix tempfit of θ values；If the element in matrix T exceeds default span, using default transformation for mula to matrix
Element in T beyond default span is converted, and the Eulerian angles of the matrix T after conversion and the orientation point for obtaining is substituted into pre-
If orientation relationship formula calculate, generation storage minimum θ values matrix tempfit；Matrix popfit and matrix tempfit are selected
Operation is selected, the minimum θ values in matrix popfit and matrix tempfit are selected, selected in population corresponding to minimum θ values
Individuality enters next iteration；Judge whether to reach maximum iteration；If being not reaching to maximum iteration, return and perform
Mutation operation is carried out to population Pop, the step of obtain matrix U；If reaching maximum iteration, the life of last time iteration is obtained
Into matrix popfit in minimum θ values, by the position where the minimum θ values that last time iteration is obtained, obtain to be asked
Orientation relationship.So, by using differential evolution algorithm, i.e., using variation, intersection, selection operation, and by successive ignition, choosing
Select out the corresponding individuality of minimum θ values and enter next iteration, so as to retain defect individual, eliminate worst individual, guiding position to
θ values in relation are gradually approached to globally optimal solution, when θ reaches minimum value, can obtain orientation relationship to be asked.
Brief description of the drawings
Fig. 1 is the flow of cubic System Material parent phase provided in an embodiment of the present invention and the determination method of sub alternate orientation relationship
Schematic diagram；
Fig. 2 is cubic System Material parent phase provided in an embodiment of the present invention detailed with the determination method of sub alternate orientation relationship
Schematic flow sheet；
Fig. 3 is crossover operation schematic diagram provided in an embodiment of the present invention.
Specific embodiment
To make the technical problem to be solved in the present invention, technical scheme and advantage clearer, below in conjunction with accompanying drawing and tool
Body embodiment is described in detail.
The present invention is directed to the existing problem that can not exactly calculate cubic System Material parent phase and sub alternate orientation relationship,
A kind of determination method of cubic System Material parent phase and sub alternate orientation relationship is provided
Referring to shown in Fig. 1, the determination side of cubic System Material parent phase provided in an embodiment of the present invention and sub alternate orientation relationship
Method, including：
S1, obtains the orientation point data of cubic system Steel material, wherein, the orientation point data include：The Euler of orientation point
Angle；
S2, initializes population Pop, and the Eulerian angles of population Pop and the orientation point for obtaining are substituted into default orientation relationship
Formula is calculated, the matrix popfit of generation storage minimum θ values, wherein, θ represents the theoretical orientation and actual orientation of all orientation points
Orientation declinate；
S3, mutation operation is carried out to population Pop, obtains matrix U；
S4, crossover operation is carried out to population Pop and matrix U, obtains matrix T；
Whether S5, the element in judgment matrix T exceeds default span；
S6, if the element in matrix T is without departing from default span, by matrix T and the Europe of the orientation point for obtaining
Draw angle to substitute into default orientation relationship formula to calculate, the matrix tempfit of generation storage minimum θ values；
S7, if the element in matrix T exceeds default span, using default transformation for mula to surpassing in matrix T
The element for going out default span is converted, and the Eulerian angles of the matrix T after conversion and the orientation point for obtaining is substituted into default
Orientation relationship formula is calculated, the matrix tempfit of generation storage minimum θ values；
S8, selection operation is done by matrix popfit and matrix tempfit, selects matrix popfit and matrix tempfit
In minimum θ values, the corresponding individuality of minimum θ values is selected in population and enters next iteration；
S9, judges whether to reach maximum iteration；If being not reaching to maximum iteration, return and perform S3；If reaching
To maximum iteration, then the minimum θ values in the matrix popfit of last time grey iterative generation are obtained, by last time iteration
Position where the minimum θ values for obtaining, obtains orientation relationship to be asked.
Cubic System Material parent phase and the determination method of sub alternate orientation relationship described in the embodiment of the present invention, are stood by obtaining
Side is the orientation point data of Steel material, wherein, the orientation point data include：The Eulerian angles of orientation point；Initialization population Pop,
And the Eulerian angles of population Pop and the orientation point for obtaining are substituted into default orientation relationship formula calculating, the square of generation storage minimum θ values
Battle array popfit, wherein, θ represents the theoretical orientation of all orientation points and the orientation declinate of actual orientation；Row variation is entered to population Pop
Operation, obtains matrix U；Crossover operation is carried out to population Pop and matrix U, matrix T is obtained；Whether the element in judgment matrix T surpasses
Go out default span；If the element in matrix T is without departing from default span, by matrix T and the orientation for obtaining
The Eulerian angles of point substitute into default orientation relationship formula and calculate, the matrix tempfit of generation storage minimum θ values；If the unit in matrix T
Element exceeds default span, then the element in matrix T beyond default span is done using default transformation for mula
The Eulerian angles of the matrix T after conversion and the orientation point for obtaining are substituted into default orientation relationship formula and calculated by conversion, and generation storage is most
The matrix tempfit of small θ values；Matrix popfit and matrix tempfit are done into selection operation, matrix popfit and matrix is selected
Minimum θ values in tempfit, the corresponding individuality of minimum θ values are selected in population and enter next iteration；Judge whether to reach
To maximum iteration；If being not reaching to maximum iteration, return to perform carries out mutation operation to population Pop, obtains square
The step of battle array U；If reaching maximum iteration, the minimum θ values in the matrix popfit of last time grey iterative generation are obtained, led to
Position where crossing the minimum θ values that last time iteration is obtained, obtains orientation relationship to be asked.So, enter by with difference
Change algorithm, i.e., using variation, intersection, selection operation, and by successive ignition, select the corresponding individual entrance of minimum θ values
Next iteration, so as to retain defect individual, eliminates worst individual, and the θ values in guiding orientation relationship are gradually to globally optimal solution
Approach, when θ reaches minimum value, orientation relationship to be asked can be obtained.
In the embodiment of the present invention, due to requiring that θ is minimum in orientation relationship formula, it is absorbed in order to avoid it Premature Convergence occurs
The situation of locally optimal solution, in order to obtain a globally optimal solution as much as possible, the embodiment of the present invention uses differential evolution algorithm
To ask for orientation relationship to be asked；The differential evolution algorithm can be minimized to non-linear non-differentiability continuous space function,
Its general principle is simple, and controlled parameter is less, and in artificial intelligence, the multiple fields such as pattern-recognition are obtained for extensive use；Institute
State differential evolution algorithm three have main steps that variation, intersection, selection.
In the present embodiment, the method that cubic System Material parent phase and sub alternate orientation relationship are determined using differential evolution algorithm,
As shown in Fig. 2 specifically may comprise steps of：
Step one：The orientation point data of cubic system Steel material is obtained, the every a line in the data represents an orientation point, should
Every data line in data represents an orientation information for orientation point, and the orientation information of the orientation point includes：Orientation point
Three Eulerian angles, the present embodiment mainly does computing, the orientation point of use using the orientation information (i.e. three Eulerian angles) of orientation point
Data volume (i.e. orientation point number) up to 300,000.
Step 2：Arrange parameter, the parameter includes：Population scale Np, zoom factor F, crossover probability 0.4, maximum changes
Generation number MAX, full null matrix vmin, maximum value matrix vmax, full null matrix besttr；It is assumed that population scale Np be 30, scaling because
Sub- F and crossover probability CR are 0.4, and maximum iteration MAX is 100；Full null matrix vminSize be 1*6, full null matrix
vminThe first three columns default orientation relationship formula of correspondence in orientation relationship V, full null matrix vminThe default position of rear three row correspondence
To the orientation information M of the parent phase in relational expression；Maximum value matrix vmaxSize be 1*6, maximum value matrix v can be setmaxFor
[90,90,90,360,90,90], the size of full null matrix besttr is 100*1, and full null matrix besttr is used for storing every generation
Minimum θ values.
Step 3：Population (during first time iteration, need to initialize, the kind of first time grey iterative generation to population for initialization
Group Pop is properly termed as initial population Pop), by full null matrix vminWith maximum value matrix vmaxRepmat () function is utilized respectively to turn
The matrix of 30*6 is turned to, then a matrix R of 30*6 is generated at random with rand () function, using formula (1)
Pop=vmin+R*(vmax-vmin) (1)
Generation initial population Pop, wherein, the information of population Pop is stored with a matrix type；
Then, population Pop is assigned to matrix U；Then by the Euler of the orientation point of every a line value and acquisition of population Pop
Angle is calculated in substituting into orientation relationship formula (2), wherein, the variable MM in the Eulerian angles correspondence orientation relationship formula of orientation point, square
Every a line of battle array Pop has 6 column datas, and preceding 3 column data corresponds to the variable V in orientation relationship formula, afterwards 3 column datas correspondence orientation relationship
Variable M in formula, wherein, the orientation relationship formula is expressed as：
In formula (2), θ represents that the theoretical orientation of all orientation points is poor with the misorientation average deviation (orientation) of actual orientation
Angle, trace () represents and matrix track taking is operated that arccos () represents inverse cosine function, and V represents orientation relationship, and N is orientation
The number of point, j and k represents the crystallographic symmetry factor of parent phase and sub- phase respectively, and span is [1,24], SjAnd SkPoint
Not Wei parent phase and the corresponding crystallographic symmetry factor of son equivalent matrix, M is the orientation information of parent phase, and MM represents orientation point
Eulerian angles.
Because the span of j, k is [1,24], therefore the calculating of 24*24 times will be carried out for each orientation point i,
For each orientation point, the minimum value θ in all values is finally takenminI () stores, right after all orientation points have all been calculated
The all θ for obtainingminValue summation is averaged, and obtains the corresponding average theta of corresponding line data in populationmin.Population Pop has 30 line numbers
According to, therefore a matrix of 1*30 can be obtained after the completion of all calculating, each columns value represents the every data line using population Pop
The average theta for calculatingmin, this matrix is defined as popfit, be after the step of use.
In the present embodiment, used as an alternative embodiment, the initialization population Pop includes：
By full null matrix vminWith maximum value matrix vmaxThe matrix of Np*6 is separately converted to, and using random generation one
The matrix R of Np*6, wherein, Np represents population scale；
Using formula Pop=vmin+R*(vmax-vmin), generation initial population Pop.
Step 4：Mutation operation；In the t times iteration, when i is in 1~Np, the 3 number x of random generation in Np1、x2、
x3, using formula (3)：
Ui=Popx1+F*(Popx2-Popx3) (3)
Mutation operation is carried out, matrix U is updated；
Wherein, F represents zoom factor, x1、x2、x3The xth in population Pop is represented respectively1、x2、x3OK, Popx1、Popx2、
Popx3The xth in population Pop is represented respectively1、x2、x3Capable data, UiThe i-th row data in representing matrix U.
Step 5：Crossover operation；Population Pop is assigned to matrix T, the square with matrix T and by being obtained after mutation operation
Battle array U carries out crossover operation.Detailed process is：A matrix R of 30*6 is generated at random with rand () function, will be every in matrix R
Individual element and crossover probability CR are compared, if the element in matrix R is more than or equal to crossover probability CR, in matrix T, with
The element position identical element value is constant in matrix R；If the element in matrix R is less than crossover probability CR, by phase in matrix U
Answer the element of position to be assigned to the element of same position in matrix T, so as to complete crossover operation, realize that code is：T(R<CR)=
U(R<CR), the schematic diagram of crossover operation as indicated at 3, in Fig. 3, riRepresent i-th element in an individual, xiG () represents i-th
The individual value in the g times iteration, vi(g+1) value of i-th individuality in the g+1 times iteration, u are representedi(g+1) i-th is represented
Individuality is in the g+1 times iteration by the result after crossover operation.
It is described that crossover operation is carried out to population Pop and matrix U as an alternative embodiment in the present embodiment, obtain matrix
T includes：
Population Pop is assigned to matrix T；
One matrix R of Np*6 of generation, each element and crossover probability CR in matrix R are compared at random, wherein,
Np represents population scale；
If the element in matrix R is less than crossover probability CR, the element of relevant position in matrix U is assigned in matrix T
The element of same position.
Step 6：Bounds checking；The default span is：More than or equal to default lower boundary and less than or equal to pre-
If coboundary, wherein, the default lower boundary be full null matrix vmin, the default coboundary is maximum value matrix
vmax；Check whether it meets the span for setting at first for the matrix T by being obtained after crossover operation, that is, check matrix T
In element whether exceeded border vminAnd vmax.A matrix R of 30*6 is generated at random again first, then by matrix T
Each element and vminAnd vmaxIn corresponding element be compared, if element is without departing from border in matrix T, in matrix T
Element value is constant, if element exceeds boundary value in matrix T, respective element in matrix T is done using default transformation for mula (4)
Conversion：
T (i)=vmin(i)+R(i)*(vmax(i)-vmin(i)) (4)
Matrix T after being updated after bounds checking, by the Eulerian angles of the orientation point of every a line value and acquisition of matrix T again
Calculated in substitution orientation relationship formula (2), finally given a matrix for storing 30 minimum θ values, be designated as matrix
tempfit。
In the present embodiment, as an alternative embodiment, if the element in the matrix T exceeds default span,
Doing conversion to the element in matrix T beyond default span using default transformation for mula includes：
If the element in matrix T exceeds default span, at random one matrix R of Np*6 of generation, and using pre-
If transformation for mula to being converted beyond the element of default span in matrix T, wherein, the default transformation for mula table
It is shown as：
T (i)=vmin(i)+R(i)*(vmax(i)-vmin(i))
Wherein, Np represents population scale, vminRepresent full null matrix, vmaxMaximum value matrix is represented, is surpassed in i representing matrixs T
Go out the element position of default span.
Step 7：Selection operation；The matrix tempfit that the matrix popfit and step 6 that step 3 is obtained are obtained is carried out
Selection operation, selects the minimum θ values in matrix popfit and matrix tempfit, minimum θ values is selected in population corresponding
Individuality enter next iteration.Detailed process is：By on relevant position in the element in matrix popfit and matrix tempfit
Element be compared, if element in matrix popfit is less than or equal to the element on relevant position in tempfit, popfit
In the position element value keep it is constant；If the element in matrix popfit is more than the element on relevant position in tempfit,
The element of the position in tempfit is assigned to the element of same position in popfit, matrix popfit is updated, code is realized
For：popfit(popfit>Tempfit)=tempfit (popfit>tempfit)；Due to, matrix popfit and matrix
Tempfit is calculated by the element in matrix Pop and matrix T, i.e., in matrix popfit and matrix tempfit
I element, is respectively the i-th row data gained in matrix Pop and matrix T, therefore if i-th element in matrix popfit is by more
Newly, correspondingly, the i-th row data in matrix Pop should also be updated according to matrix T, that is to say, that by matrix popfit and square
Individuality in battle array tempfit corresponding to optimal value (minimum θ values) is screened and allows it to enter the next generation, i.e.,：After renewal
The individuality corresponding to minimum θ values in matrix popfit is screened and allows it to enter the next generation, realizes that code is：Pop(popfit
>tempfit,:)=T (popfit>tempfit,:)；
Wherein, Pop (popfit>tempfit,:)=T (popfit>tempfit,:) in "：" be matlab code,
“：" represent all of row.Additionally, the minimum value in the matrix popfit after renewal to be taken out the matrix for being stored in and setting at first
In besttr (t), besttr (t) represents that this is the optimal solution of generation after the t times iteration.
Step 8：Repeat step four, five, six, seven, until reaching maximum iteration.
Step 9：After iteration terminates, storage is exactly the minimum θ values for finally giving in besttr (100), and the value is also most
The minimum value in a matrix popfit for grey iterative generation, by the position where the value, just can obtain calculating the value afterwards
It is which data in matrix Pop, and the orientation relationship of first three column data of the row exactly our final requirements.
In sum, the present embodiment main thought is exactly to use differential evolution algorithm, by successive ignition, retains excellent
Body, eliminates worst individual, and the θ values in guiding orientation relationship are gradually approached to globally optimal solution, and when minimum value is reached, position is to pass
It is that the variable V calculated used by this value in formula is exactly orientation relationship to be asked.For the selection of parameter in the algorithm, it is first
Population scale Np, from computation complexity analysis, general population scale is bigger, and the possibility of the globally optimal solution for searching is bigger,
But amount of calculation and calculating time can also increase.And when Np increases to a certain number of, the precision of solution occurs reduction on the contrary
Situation, Np can not be less than 3, cannot thus carry out mutation operation.Ordinary circumstance, under given maximum iteration, plants
Group scale Np can well keep the balance of population diversity and convergence rate between 15~50, therefore the embodiment of the present invention is chosen
30 is population scale size.For zoom factor F, if F is larger, larger disturbance will be produced, to keeping the various of population
Property is favourable；If F is smaller, disturbance is also small, and F can play a part of local fineization search.But if F is too big, although energy
Population diversity is kept, but search efficiency can be caused low, the globally optimal solution precision tried to achieve is low；If F is too small, population is various
Property cannot be protected, the easy Premature Convergence of algorithm and be absorbed in locally optimal solution.General zoom factor in the range of 0~1, root
According to above-mentioned analysis, it is 0.4 that the embodiment of the present invention chooses zoom factor F.For crossover probability CR, if CR is smaller, convergence rate
Slowly still success rate is higher for meeting, and algorithm stability might as well；If CR is larger, convergence can be accelerated, be susceptible to precocious phenomenon, success
Rate and stability can all be reduced.In order to ensure success rate higher and faster convergence rate, generally for unimodal function, CR takes
Between 0.6~0.8, for complicated, Solving Multimodal Function, CR values want smaller to value, between 0.1~0.5, according to asking for being solved
Topic, the value of embodiment of the present invention selection CR is 0.4.
The embodiment of the present invention preferably solves the problem of Material Field with computer technology, for the position tried to achieve to pass
System, during can applying to parent phase orientation recurrence, makes Material Field be orientated on the road of regression technique research to parent phase
Gone a step further before again, this is that computer is combined well with one of Material Field, is also in domestic this respect research
Innovation.
The above is the preferred embodiment of the present invention, it is noted that for those skilled in the art
For, on the premise of principle of the present invention is not departed from, some improvements and modifications can also be made, these improvements and modifications
Should be regarded as protection scope of the present invention.
Claims (9)
1. a kind of determination method of cubic System Material parent phase and sub alternate orientation relationship, it is characterised in that including：
S1, obtains the orientation point data of cubic system Steel material, wherein, the orientation point data include：The Eulerian angles of orientation point；
S2, initializes population Pop, and the Eulerian angles of population Pop and the orientation point for obtaining are substituted into default orientation relationship formula meter
Calculate, the matrix popfit of generation storage minimum θ values, wherein, θ represents the theoretical orientation of all orientation points and the orientation of actual orientation
Declinate；
S3, mutation operation is carried out to population Pop, obtains matrix U；
S4, crossover operation is carried out to population Pop and matrix U, obtains matrix T；
Whether S5, the element in judgment matrix T exceeds default span；
S6, if the element in matrix T is without departing from default span, by matrix T and the Eulerian angles of the orientation point for obtaining
Substitute into default orientation relationship formula to calculate, the matrix tempfit of generation storage minimum θ values；
S7, it is pre- to exceeding in matrix T using default transformation for mula if the element in matrix T exceeds default span
If the element of span convert, by the Eulerian angles of the matrix T after conversion and the orientation point for obtaining substitute into default position to
Relational expression is calculated, the matrix tempfit of generation storage minimum θ values；
S8, selection operation is done by matrix popfit and matrix tempfit, in selecting matrix popfit and matrix tempfit
Minimum θ values, the corresponding individuality of minimum θ values are selected in population and enter next iteration；
S9, judges whether to reach maximum iteration；If being not reaching to maximum iteration, return and perform S3；If reaching most
Big iterations, then obtain the minimum θ values in the matrix popfit of last time grey iterative generation, is obtained by last time iteration
Minimum θ values where position, obtain orientation relationship to be asked.
2. the determination method of cubic System Material parent phase according to claim 1 and sub alternate orientation relationship, it is characterised in that
Before initialization population Pop, methods described also includes：
Arrange parameter, the parameter includes：Population scale, zoom factor, crossover probability, maximum iteration MAX, full null matrix
vmin, maximum value matrix vmax；
Wherein, full null matrix vminSize be 1*6, full null matrix vminThe first three columns default orientation relationship formula of correspondence in position
To relation V, full null matrix vminThe rear three row default orientation relationship formula of correspondence in parent phase orientation information M, maximum value matrix
vmaxSize be 1*6.
3. the determination method of cubic System Material parent phase according to claim 1 and 2 and sub alternate orientation relationship, its feature exists
In the default orientation relationship formula is expressed as：
Wherein, θ represents the theoretical orientation of all orientation points and the orientation declinate of actual orientation, and N is the number of orientation point, arccos
() represents inverse cosine function, and trace () represents and matrix track taking is operated that V represents orientation relationship, and M represents the orientation of parent phase
Information, MM represents the Eulerian angles of orientation point, SjAnd SkThe respectively equivalent square of parent phase and the corresponding crystallographic symmetry factor of son
Battle array, j and k represents the crystallographic symmetry factor of parent phase and sub- phase respectively.
4. the determination method of cubic System Material parent phase according to claim 1 and sub alternate orientation relationship, it is characterised in that
The initialization population Pop includes：
By full null matrix vminWith maximum value matrix vmaxThe matrix of Np*6 is separately converted to, and using random one Np*6's of generation
Matrix R, wherein, Np represents population scale；
Using formula Pop=vmin+R*(vmax-vmin), generation initial population Pop.
5. the determination method of cubic System Material parent phase according to claim 1 and sub alternate orientation relationship, it is characterised in that
Described to carry out mutation operation to population Pop, obtaining matrix U includes：
Population Pop is assigned to matrix U；
In the t times iteration, when i is in 1~Np, the 3 number x of random generation in Np1、x2、x3；
Using formula Ui=Popx1+F*(Popx2-Popx3) mutation operation is carried out, matrix U is updated；
Wherein, F represents zoom factor, x1、x2、x3The xth in population Pop is represented respectively1、x2、x3OK, Popx1、Popx2、Popx3
The xth in population Pop is represented respectively1、x2、x3Capable data, UiThe i-th row data in representing matrix U.
6. the determination method of cubic System Material parent phase according to claim 1 and sub alternate orientation relationship, it is characterised in that
Described to carry out crossover operation to population Pop and matrix U, obtaining matrix T includes：
Population Pop is assigned to matrix T；
One matrix R of Np*6 of generation, each element and crossover probability CR in matrix R are compared at random, wherein, Np tables
Show population scale；
If element in matrix R is less than crossover probability CR, the element of relevant position in matrix U is assigned to identical in matrix T
The element of position.
7. the determination method of cubic System Material parent phase according to claim 1 and sub alternate orientation relationship, it is characterised in that
The default span is：More than or equal to default lower boundary and less than or equal to default coboundary, wherein, it is described default
Lower boundary be full null matrix vmin, the default coboundary is maximum value matrix vmax；
Whether the element in the judgment matrix T includes beyond default span：
By each element and v in matrix TminAnd vmaxIn corresponding element be compared.
8. the determination method of cubic System Material parent phase according to claim 1 and sub alternate orientation relationship, it is characterised in that
It is default to exceeding in matrix T using default transformation for mula if the element in the matrix T exceeds default span
The element of span does conversion to be included：
If the element in matrix T exceeds default span, at random one matrix R of Np*6 of generation, and using default
Transformation for mula is converted to the element in matrix T beyond default span, wherein, the default transformation for mula is represented
For：
T (i)=vmin(i)+R(i)*(vmax(i)-vmin(i))
Wherein, Np represents population scale, vminRepresent full null matrix, vmaxMaximum value matrix is represented, beyond pre- in i representing matrixs T
If span element position.
9. the determination method of cubic System Material parent phase according to claim 1 and sub alternate orientation relationship, it is characterised in that
It is described that matrix popfit and matrix tempfit are done into selection operation, select the minimum in matrix popfit and matrix tempfit
θ values, the corresponding individual next iteration that enters of minimum θ values is selected in population to be included：
Element on relevant position in element and tempfit in matrix popfit is compared；
If the element in matrix popfit is more than the element on relevant position in matrix tempfit, by phase in matrix tempfit
Answer the element of position to be assigned to the element of same position in matrix popfit, update matrix popfit；
The minimum θ values in the matrix popfit after updating are obtained, and the corresponding individual entrance of minimum θ values is selected in population
Next iteration.
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