How to find unknown constants from exponential equation

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Niharika_dc
Niharika_dc 2021-8-11
评论： Niharika_dc 2021-8-12
I am trying to find the value of the unknown constants a,b,c from the equation, . Here x and t are variables, the data points of which are available to me.
The equation available with me is a complex one, so to simplify it I have considered the combination of the unknown constants as a,b and c and have tried to find the final constants by solving a, b and c. I have tried solving it like this. For the initial parameters, I used the curve fitting toolbox to get approximate values of a,b and c. Is the approach I used correct? Is there any other way to solve this problem?
clc
clear
v = xlsread('Book1.xlsx');
x=v(:,2);
t=v(:,1);
x = @(p,v) p(1).*v(:,1)-p(2)*exp(-p(3).*v(:,1))+p(2);
p0=[0.2493;155.4;382.4]; %initial parameter
SSECF = @(p) sum((v(:,2) - creep(p,v)).^2);
[abc, SSE] = fminsearch(SSECF, p0);
a = abc(1)
b = abc(2)
c = abc(3)
syms e n1 n2
eqns=[6/(n1+n2)==a;6*n2^(2)/(e*(n1+n2)^2)==b;e*(n1+n2)/(n1*n2)==c];
S=vpasolve(eqns,[e n1 n2]);
E=S.e
N1=S.n1
N2=S.n2
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Niharika_dc
Niharika_dc 2021-8-11
编辑：Niharika_dc 2021-8-11
@Star Strider In my case, there are 3 unknown constants. I did not understand how p0(1),p0(2),p0(3) in this case was estimated and how I can estimate p0(1),p0(2),p0(3) and p0(4) in my case
p0(1) = sigma0/x(end); % Estimate 'E' (Asymptote = 'x(end)')
p0(2) = tau; % Extimate 'eta'
p0(3) = min(x) % Offset

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回答（1 个）

Wan Ji
Wan Ji 2021-8-11
Your code is ok, but the nonlinear model function may not so well selected!
clear
v = xlsread('Book1.xlsx');
x=v(:,2);
t=v(:,1);
creep = @(p,v) p(1).*v(:,1)-p(2)*exp(-p(3).*v(:,1))+p(2);
p0=[1.2493;155.4;382.4]; %initial parameter
SSECF = @(p) sum((v(:,2) - creep(p,v(:,1))).^2);
[abc, SSE] = fminsearch(SSECF, p0);
a = abc(1)
b = abc(2)
c = abc(3)
vfit = creep(abc,v(:,1));
plot(v(:,1),v(:,2)); hold on
plot(v(:,1), vfit)
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Wan Ji
Wan Ji 2021-8-12
As you know the constant item b should be independent (but indeed in your equation it is dependent), so linear item is therefore not necessary here. That's why I change to a.@sakura w （In order to keep the completeness of primary functions [1, , nonlinear constant c ]）

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