Workflow Overview
graph TB
node1(Load Variables From Workspace)
click node1 "#1"
node1(Load Variables From Workspace) --> node2(Obtain 2-Point Statistics)
click node2 "#2"
node2(Obtain 2-Point Statistics) --> node3(PCA)
click node3 "#3"
node3(PCA) --> node4(Function Estimation)
click node4 "#4"
Obtain the direct to Project-Pages publish function here.
Load Variables From Workspace
Loading the microstructures and the effective property.
load GDL200Volumes.mat
load MPL290Volumes.mat
load EffectiveProperty290MPL200GDLinThatOrder.matObtain 2-Point Statistics
GG = zeros(490,49^3);
for i=1:290
current = MPL{i};
GGcurrent = TwoPointMaster('full','auto',25,current);
GG(i,:) = GGcurrent(:)/numel(current);
PP(i)=GGcurrent(25,25,25)/numel(current);
end
for i=1:200
current = GDL{i};
GGcurrent = TwoPointMaster('full','auto',25,current);
GG(i+290,:) = GGcurrent(:)/numel(current);
PP(i+290)=GGcurrent(25,25,25)/numel(current);
endPCA
Via SVD:
[PC1,Var1,Basis1]=PCAConstruct(GG,10);
scatter(PC1(:,1),PC1(:,2),30,[ones(290,1);2*ones(200,1)],'filled'); colormap jet;
Function Estimation
Using Multivariate Polynomial Regression
reg = MultiPolyRegress(PC1(:,1:2),R,3,'figure')reg =
FitParameters: '-----------------'
PowerMatrix: [10x2 double]
Scores: [490x10 double]
PolynomialExpression: [10x2 table]
Coefficients: [10x1 double]
yhat: [490x1 double]
Residuals: [490x1 double]
GoodnessOfFit: '-----------------'
RSquare: 0.9572
MAE: 0.0571
MAESTD: 0.0561
Normalization: '1-to-1 (Default)'
LOOCVGoodnessOfFit: '-----------------'
CVRSquare: 0.9556
CVMAE: 0.0583
CVMAESTD: 0.0570
CVNormalization: '1-to-1 (Default)'