How can I perform a four dimensional curve fitting.

There is now a five-dimensional matrix that is calculated by the finite element method.

The resulting matrix Y is affected by the parameter matrices A, B, C, D.

Now I want to get Y=f(A, B, C, D) by means of curve fitting.

The data is in the attachment, the MATLAB code for reading in the data is as follows

%
clear;
clc;

ANG_1teeth = 360 / 23;
RR = 100;
ratio = 0.1:0.05:0.75;
theta_f = 5:1:30;
TangF = 500:500:5000;
NormalF = 0:500:1000;
for i = 1: length(NormalF)
    for j = 1:length(TangF)
        for k = 1: length(theta_f)                                            
            TSEQUENCE = 1;
            filename=['E:\Test\TheLastReasultofHollowRing_SF\RingNf=' num2str(NormalF(i)) 'NTF=' num2str(TangF(j)) 'N' num2str(theta_f(k)) '°.lis'];
            fidin=fopen(filename);
            fidout=fopen('E:\Test\MKMATLAB.txt','wt');              %  MKMATLAB.txt 
            while ~feof(fidin)                                      %                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    % 判断是否为文件末尾
                tline=fgetl(fidin);                                 %  
                tline = strtrim(tline);                             % 
                if double(tline(1))>=48&&double(tline(1))<=57       %  
                    fprintf(fidout,'%s\n',tline);                  %  
                    continue                                         %  
                end
            end
            MK=importdata('E:\Test\MKMATLAB.txt');                          % 
            fclose(fidout);
            fclose(fidin);
            fclose('all');
            MKK = sortrows(MK,4);
            rows = length(ratio);
            columns = 10;                % 总共10列
            for ii = 1:rows
                for jj = 1:columns
                    MKK_4(ii,jj,k,j,i) = MKK(ii,jj);
                end
                MKK_XRatio(ii,4,k,j,i) = MKK_4(ii,5,k,j,i)/MKK_4(ii,4,k,j,i);            % ratio------------Independent variable
                MKK_XTheta(ii,3,k,j,i) = MKK_4(ii,6,k,j,i);                              % theta_f------------Independent variable
                MKK_XFT(ii,1,k,j,i) = MKK_4(ii,2,k,j,i);                          % FT------------Independent variable
                MKK_XFA(ii,2,k,j,i) = MKK_4(ii,3,k,j,i);                          % FA------------Independent variable
                MKK_UYM(ii,1,k,j,i) = MKK_4(ii,7,k,j,i);                            % UY_Max------------This is the dependent variable
            end
        end
    end
end

The curve fitting formula for a single variable is as follows：

%%  
% rational---------------1：ratio 
ratio0 = 0.1:0.01:0.9;
p1_rario = 0.0002103;
q1_rario = 0.04092;
q2_rario = -0.0004491;
y_rational_ratio = (p1_rario) ./ (ratio0.^2 + q1_rario*ratio0 + q2_rario);
figure
plot(ratio0,y_rational_ratio,'r*')
grid on
title('ratio0(rrr/RR)')
% ---------------2：TF
TangF0 = 10:10:30000;
p1_TF =  6.198e-07;
p2_TF =  2.966e-11;
y_TF = p1_TF * TangF0 + p2_TF;
figure
plot(TangF0,y_TF,'r*')
grid on
title('TangF0')
% ---------------3:NF
NormalF0 = 10:10:30000;
p1_NF =  -5.067e-10;
p2_NF =   2.529e-12;
y_NF = p1_NF*NormalF0 + p2_NF;
figure
plot(NormalF0,y_NF,'r*')
grid on
title('NormalF0')
% ---------------4：Theta
theta_f0 = 2:0.1:40;
a_theta_f0 = 0.0002677;
b_theta_f0 = -0.1311;
c_theta_f0 = 0.0005681;
d_theta_f0 = -0.01049;
y_theta_f0 = a_theta_f0*exp(b_theta_f0*theta_f0) + c_theta_f0*exp(d_theta_f0*theta_f0);
%
figure
plot(theta_f0,y_theta_f0,'r*')
grid on
title('theta_f0')

Answer 1

[Liu Yanping]

Why there is NO answers.

Is it because the problem is not clear or because of the difficulty?

Answer 2

[Liu Yanping]

STILL NO ANSWER!

Answer 3

[Liu Yanping]

Any body can do me a help!!!!!!??????

Answer 4

[Liu Yanping]

Any body can do me a help!!!!!!??????

Answer 5

[Daniel Taylor]

Did you ever figure this out as i am currently having the same issue and using the regression forumlae and curve fitting toolbox aren't working