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test_stress_activation.m
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test_stress_activation.m
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function test_stress_activation
clc;
clear all;
dir = 'C:\Users\steve\OneDrive\Tribcorrosion\Matlab Scripts\Tribo-Model\'; %HoldOutputs\
kb = 1.38e-23; %
T = 298;
Na = 6.02e23;
conv_m3_A3 = 1.0e-10*1.0e-10*1.0e-10;
v_act_test = [(0.277*conv_m3_A3),(0.277*conv_m3_A3),(0.261*conv_m3_A3)];
%=====================================================================
% Experimental data files to be loaded - must be in same folder as the
% execution code
%=====================================================================
exp_files = {'Baseline58GPa.csv', 'Baseline86GPa.csv', ...
'Baseline103GPa.csv', 'Baseline1125GPa.csv', 'Baseline1295GPa.csv'};
%=====================================================================
% Names of the CSV output files. Will be stored in the same folder as
% the execution code
%=====================================================================
output_files = {'Model58GPa.csv', 'Model86GPa.csv', ...
'Model103GPa.csv', 'Model1125GPa.csv', 'Model1259GPa.csv'};
%=====================================================================
nfiles = length(exp_files);
I_avg = zeros(1,nfiles);
I_avg_with_cutoff = zeros(1,nfiles);
for i = 1:nfiles
data = csvread(strcat(dir,char(exp_files(i))));
I_avg(1,i) = mean(data(:,2));
mdl_res = csvread(strcat(dir,char(output_files(i))));
I_avg_with_cutoff(1,i) = mean(mdl_res(:,2));
end
%=====================================================================
% Plot formatting
tick_label_size = 16;
axis_label_size = 18;
title_label_size = 20;
plot_line_width = 3;
axis_line_width = 2;
marker_size = 7;
font_weight = 'bold';
color_range = {'b','b','b','b','b','b','b','b','b', ...
'r','r','r','r','r','r','r','r','r', ...
'g','g','g','g','g', ...
'k','k','k','k','k', ...
'c'};
marker_vals_data = {'s','o','+','s','o','+','s','o','+','s','o','+', ...
's','o','+','s','o','+','s','o','+'};
%=====================================================================
% stress = [5.8, 8.6, 10.3, 11.25, 12.59].*1.0e9; %GPa %
stress = [8.61, 9.36, 9.53, 9.77, 10.49].*1.0e9; %GPa %
stress_no86 = [5.8, 10.3, 11.25, 12.59].*1.0e9; %GPa
% I_avg = [33.03812, 54.12765, 56.66675, 80.4581, 122.44677].*1.0e-15; %A Experimental Data
% I_avg = I_avg.*1.0e-15; %A Experimental Data
% I_avg = I_avg .* 1.0e-15; %[37.5, 89.75, 86.6, 104.57, 155.18].*1.0e-15; %A Experimental Data
% I_avg_model_nocutoff = [32.4623, 64.77407, 73.97724, 94.48909].*1.0e-15; %A Tribo Model - no cutoff
%
I_avg_with_cutoff_top = I_avg_with_cutoff.*1.0e-15; %[29.86840232, 100.2, 114.8, 124.5, 139.9]; %A Tribo Model - t_cutoff = 32s
% I_avg_with_cutoff = I_avg_with_cutoff.*1.0e-15; %A Tribo Model - t_cutoff = 32s
% I_avg_with_cutoff = [33.82, 100.71, 115.37, 125.19, 140.78].*1.0e-15; %A Tribo Model - t_cutoff = 48s
fn = @lntest; %@exptest2;
x1 = 7.0:0.1:11.0; %13.0;
x = x1; %x1.*1.0e9;
%=====================================================================
% Fit the exp data
%=====================================================================
% b0 = [10.0e-15, v_act_test(1) 0.3];
% sp = [stress(1), stress(2), stress(3), stress(4)];
% ip = [I_avg(1),I_avg(2), I_avg(3), I_avg(4)];
% mdl_tbc_600_data = fitnlm(sp,ip,fn,b0);
%
% disp(mdl_tbc_600_data)
% y = feval(mdl_tbc_600_data,x);
%=====================================================================
%=====================================================================
% Fit the cutoff top model
b1 = [2.0e-14, -0.5, 0.9e-30]; %[14.485e-15 v_act_test(2) -0.1]; ((0.01/Na)*1000)/(kb*T)
sp = [stress(2), stress(3), stress(4), stress(5)]; %
ip = [I_avg_with_cutoff_top(2), I_avg_with_cutoff_top(3), I_avg_with_cutoff_top(4), I_avg_with_cutoff_top(5)]; %
mdl_tbc_600_cutoff_top = fitnlm(sp,log(ip),fn,b1);
disp(mdl_tbc_600_cutoff_top)
y2 = feval(mdl_tbc_600_cutoff_top,x);
%=====================================================================
%=====================================================================
% Fit the cutoff model
%=====================================================================
% b2 = [1.0e-15 1.4474e-30 0.00040393];
% sp = [ stress(1), stress(2), stress(3), stress(4), stress(5)]; %
% ip = [I_avg_with_cutoff(1), I_avg_with_cutoff(2), I_avg_with_cutoff(3), I_avg_with_cutoff(4), I_avg_with_cutoff(5)]; %
% mdl_tbc_600_cutoff32 = fitnlm(sp,ip,fn,b2);
%
% disp(mdl_tbc_600_cutoff32)
% y3 = feval(mdl_tbc_600_cutoff32,x);
%=====================================================================
%=====================================================================
% Linear fit
% p = polyfit(sp,ip,1);
% y4 = polyval(p,x);
%=====================================================================
% exp_fit_Ea_coeff = mdl_tbc_600_data.Coefficients.Estimate(3);
% exp_fit_Va_coeff = mdl_tbc_600_data.Coefficients.Estimate(2);
% %
% % mdl_nocutoff_fit_Ea_coeff = mdl_tbc_600_cutoff_top.Coefficients.Estimate(3);
% % mdl_nocutoff_fit_Va_coeff = mdl_tbc_600_cutoff_top.Coefficients.Estimate(2);
%
% mdl_cutoff_fit_Ea_coeff = mdl_tbc_600_cutoff32.Coefficients.Estimate(3);
% mdl_cutoff_fit_Va_coeff = mdl_tbc_600_cutoff32.Coefficients.Estimate(2);
%
% exp_fits = [(-exp_fit_Ea_coeff*Na)/1000, (exp_fit_Va_coeff/conv_m3_A3)/(kb*T)].*(kb*T); %kJ/mol A3
% % mdl_nocutoff_fits = [(-mdl_nocutoff_fit_Ea_coeff*Na)/1000, mdl_nocutoff_fit_Va_coeff/conv_m3_A3].*(kb*T); %kJ/mol A3
% v_act_fit = (mdl_cutoff_fit_Va_coeff/conv_m3_A3)/(kb*T);
% mdl_cutoff_fits = [(-mdl_cutoff_fit_Ea_coeff*Na)/1000, v_act_fit].*(kb*T); %kJ/mol A3
% i0_mdl = 1.0e-14;
% v_act_mdl = 9.0e-31;
% e_act_act = ((0.01/Na)*1000)/(kb*T);
% s_term = (x.*v_act_mdl)./(kb*T);
% e_term = (-e_act_act + s_term);
% expval = exp(e_term);
% i_mdl_guess_red = i0_mdl.*expval;
i0_mdl = 0.4468; %0.0319; %2.1434e-15; %1.0e-15;
% v_act_mdl = 17.0e-31; %1.822e-30;
% e_act_act = 1.0e-4; %0.00040393; %((0.01/Na)*1000)/(kb*T);
% s_term = (x.*v_act_mdl)./(kb*T);
% e_term = (-e_act_act + s_term);
e_term = 0.5505.*x; %0.8182.*x; %3.4310E-10.*x;
expval = exp(e_term);
i_mdl_guess_blue = i0_mdl.*expval;
%=====================================================================
% Setup the output matrices
MatrixOutput1 = zeros(length(stress),4);
MatrixOutput1(:,1) = stress;
MatrixOutput1(:,2) = I_avg;
MatrixOutput1(:,3) = stress;
MatrixOutput1(:,4) = I_avg_with_cutoff;
writematrix(MatrixOutput1,'BestFitExpMdl.xls','Sheet',1)
MatrixOutput2 = zeros(length(x), 2);
MatrixOutput2(:,1) = x;
MatrixOutput2(:,2) = i_mdl_guess_blue;
% Create the output file and write the output matrix to it
writematrix(MatrixOutput2,'BestFitExpMdl.xls','Sheet',2)
%=====================================================================
% i_exp_str = strcat('i_{fit, Exp}, E_{a} = ', num2str(exp_fits(1)), ' kJ/mol; V_{a} = ', num2str(exp_fits(2)), 'A^{3}');
% i_mdl1_str = strcat('i_{fit, Model 1}, E_{a} = ', num2str(mdl_nocutoff_fits(1)), ' kJ/mol; V_{a} = ', num2str(mdl_nocutoff_fits(2)), 'A^{3}');
% i_mdl2_str = strcat('i_{fit, Model 2}, E_{a} = ', num2str(mdl_cutoff_fits(1)), ' kJ/mol; V_{a} = ', num2str(mdl_cutoff_fits(2)), 'A^{3}');
figure(20)
hold on
% plot(stress,I_avg,'r+', 'MarkerSize',marker_size+2,'LineWidth',plot_line_width)
% plot(stress_no86,I_avg_model_nocutoff,'r^', 'MarkerSize',marker_size,'LineWidth',plot_line_width)
plot(stress,I_avg_with_cutoff.*1.0e-15,'bo', 'MarkerSize',marker_size,'LineWidth',plot_line_width)
% plot(stress,I_avg_with_cutoff_top,'g^','MarkerSize',marker_size,'LineWidth',plot_line_width)
% plot(x,y,':k', 'MarkerSize',marker_size,'LineWidth',plot_line_width)
plot(x.*1.0e9,exp(y2),'-g', 'MarkerSize',marker_size,'LineWidth',plot_line_width)
% plot(x,y4,'-.b','MarkerSize',marker_size,'LineWidth',plot_line_width)
% plot(x,i_mdl_guess_red,'-r', 'MarkerSize',marker_size,'LineWidth',plot_line_width)
% plot(x,i_mdl_guess_blue,'-b', 'MarkerSize',marker_size,'LineWidth',plot_line_width)
axis square
% legend('i_{avg}, Measured','i_{avg}, Model 1 - no cutoff', 'i_{avg}, Model 2 - \tau_{cutoff} = 48 s', ...
% i_exp_str,i_mdl1_str,i_mdl2_str,'Location','northwest')
% legend('i_{avg}, Measured','i_{avg}, Model 2 - \tau_{cutoff} = 7500 s', ...
% i_exp_str,i_mdl2_str, 'i_{linear}','i_{guess}','Location','northwest')
xlabel('Stress (Pa)', 'FontSize', axis_label_size,'FontWeight',font_weight)
ylabel('I (A)', 'FontSize', axis_label_size,'FontWeight',font_weight)
% title('i_{0,passive}', 'FontSize', title_label_size,'FontWeight',font_weight)
box on
ax = gca;
ax.FontSize = tick_label_size;
ax.FontWeight = font_weight;
ax.LineWidth = axis_line_width;
ax.XMinorTick = 'on';
% legend boxoff
hold off
end
function y = exptest(b,s)
b(1) = 14.485e-15; %A
b(3) = 0.1/(1.0e-10*1.0e-10*1.0e-10);
kb = 1.38e-23;
T = 298; %K
den = kb * T;
exp_term = b(3).*s;
exp_term4 = b(2) + exp_term;
exp_term2 = exp_term4./den;
exp_term3 = exp(exp_term2);
y = b(1) * exp_term3;
end
function y = exptest2(b,x)
i0 = b(1); %14.485e-15; %A
kb = 1.38e-23; %
T = 298;
v_act = b(2); %(0.1*conv_m3_A3);
stress_effect = (v_act.* x)./(kb*T);
E_act = b(3);
y = i0.*exp(stress_effect + E_act);
end
function y = lntest(b,x)
kb = 1.38e-23; %
T = 298;
y = log(b(1)) - (b(2)/(kb * T)) + ((b(3)/(kb * T)).*x);
end