Fit Model to Data

Hello there,

I have a question regardind fitting model to data. I have 3 models, my problem is with time constant. Time constant parameters that are coming out of time vector, T, rather than parameter vector, P. This effectively gives them fixed values for time constants that are far too low. All of the models should fit the data fairly well. I ccould not figure it out and need help.

Main code is

close all; clear all;

% SET CALIBRATION CONSTANT

CF = 2.1931;

% LOAD DATA FILE

[fname,pname] = uigetfile('*.txt','LOAD DATA FILE');

DAT = dlmread([pname,'\',fname]);

% TIME IS COLUMN 1, DISPLACEMENT IS COLUMN 2

TIME = DAT(:,1);

DISP = CF*DAT(:,2); % APPLY CALIBRATION TO DISPLACEMENT

% CLIP AT 59.9s

IN = find(TIME >= 59.9);

TIME = TIME(IN);

DISP = DISP(IN);

% ZERO INITIAL AND FLIP DISPLACEMENT

TIME = TIME - TIME(1);

DISP = -DISP + DISP(1);

Y=DISP;

% DEFINE FUNCTION

[YM1] = MODEL_1(TIME,Y);

[YM2] = MODEL_2(TIME,Y);

[YM3] = MODEL_3(TIME,Y);

YM=[YM1 YM2 YM3];

My model function is

function [YM1] = MODEL_1(TIME,Y)

MODEL = @(P,T) P(1)+P(2).*(1-exp(-T./T(3)));

P0 = [0,1,1]; % INITIAL GUESS VALUES FOR PARAMETERS

PF = lsqcurvefit(MODEL,P0,TIME,Y);

YM1 = MODEL(PF,TIME);

% CALCULATE ADJUSTED R^2 HERE

Ybar = mean(Y); % AVERAGE OBSERVED

SStot = sum( (Y - Ybar).^2 ); % TOTAL SUM OF SQUARES

SSres = sum( (Y - YM1).^2 ); % RESIDUAL SUM OF SQUARES

R2 = 1 - SSres/SStot; % R SQUARED

n = length(Y); % NUMBER OF OBSERVATIONS

p = length (PF); % NUMBER OF PARAMETERS

Rbar2 = 1 - (1 - R2)*(n - 1)/(n - p - 1);

disp(['R^2 = ',num2str(R2),', ADJUSTED R^2 = ',num2str(Rbar2)])

end

and main code is

close all; clear all;

% SET CALIBRATION CONSTANT

CF = 2.1931;

% LOAD DATA FILE

[fname,pname] = uigetfile('*.txt','LOAD DATA FILE');

DAT = dlmread([pname,'\',fname]);

% TIME IS COLUMN 1, DISPLACEMENT IS COLUMN 2

TIME = DAT(:,1);

DISP = CF*DAT(:,2); % APPLY CALIBRATION TO DISPLACEMENT

% CLIP AT 59.9s

IN = find(TIME >= 59.9);

TIME = TIME(IN);

DISP = DISP(IN);

% ZERO INITIAL AND FLIP DISPLACEMENT

TIME = TIME - TIME(1);

DISP = -DISP + DISP(1);

Y=DISP;

% DEFINE FUNCTION

[YM1] = MODEL_1(TIME,Y);

[YM2] = MODEL_2(TIME,Y);

[YM3] = MODEL_3(TIME,Y);

YM=[YM1 YM2 YM3];

[Image Analyst]

Unfortunately you forgot to attach any .txt files so no one can do anything with that code.

I guess you blew right past the posting guidelines. But luckily you can read them now. They are in the "Community Guidelines" link below or here's another one:

TUTORIAL: How to ask a question (on Answers) and get a fast answer

Make it easy for us to help you, not hard. We'll check back later for the txt file.

[Star Strider]

Here the function lists 2 parameters, however the initial estimat vector is for 3:

MODEL = @(P,T) P(1)+P(2).*(1-exp(-T./T(3))); 
P0 = [0,1,1]; % INITIAL GUESS VALUES FOR PARAMETERS

Should ‘MODEL’ be:

MODEL = @(P,T) P(1)+P(2).*(1-exp(-T./P(3))); 

instead?

Also, 0 is never a good initial choice for a parameter estimate.

Answer 1

[mehtap agirsoy]

Many thanks

Answer 2

[mehtap agirsoy]

Thanks for the quideline. I will update my question and will insert .txt file.