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PONon linear function parameter estimation - matlab, lsqnonlin, fzero
 

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  1. PONon linear function parameter estimation - matlab, lsqnonlin, fzero
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    <p>I'm having difficulty with a fitting problem. From the errors that I get I imagine that the boundaries are not defined correctly and I haven't managed to find a solution. Any help would be very much appreciated.</p> <p>Alternative methods for the solution of the same problem are also accepted.</p> <h1>Description</h1> <p>I have to estimate the parameters of a non-linear function of the type:</p> <pre><code>A*y(x) + B*EXP(C*y(x)) + g(x,D) = 0 </code></pre> <p>subjected to the parameters <code>PAR = [A,B,C,D]</code> being within the range </p> <pre><code>LB &lt; PAR &lt; UB </code></pre> <h1>Code</h1> <p>To solve the problem I'm using the Matlab functions <code>lsqnonlin</code> and <code>fzero</code>. The simplified code used is reported below.</p> <p>The problem is divided in four functions:</p> <ol> <li><code>parameterEstimation</code> - (a wrapper for the lsqnonlin function)</li> <li><code>objectiveFunction_lsq</code> - (the objective function for the param estimation)</li> <li><code>yFun</code> - (the function returing the value of the variable y)</li> <li><code>objectiveFunction_zero</code> - (the objective function of the non-linear equation used to calculate y)</li> </ol> <h1>Errors</h1> <p>Running the code on the data I get the this waring</p> <blockquote> <p>Warning: Length of lower bounds is > length(x); ignoring extra bounds</p> </blockquote> <p>and this error</p> <blockquote> <p>Failure in initial user-supplied objective function evaluation. LSQNONLIN cannot continue</p> </blockquote> <p>This makes me to think that the boundaries are not correctly used or not correctly called, but maybe the problem is elsewhere.</p> <hr> <pre><code>function Done = parameterEstimation() %read inputs Xmeas = xlsread('filepath','worksheet','range'); Ymeas = xlsread('filepath','worksheet','range'); %inital values and boundary conditions initialGuess = [1,1,1,1]; %model parameters initial guess LB = [0,0,0,0]; %model parameters lower boundaries UB = [2,2,2,2]; %model parameters upper boundaries %parameter estimation calcParam = lsqnonlin(@objectiveFunction_lsq_2,initialGuess,LB,UB,[],Xmeas,Ymeas); Done = calcParam; function diff = objectiveFunction_lsq_2(PAR,Xmeas,Ymeas) y_calculated = yFun(PAR,Xmeas); diff = y_calculated-Ymeas; function result = yFun(PAR,X) y_0 = 2; val = fzero(@(y)objfun_y(y,PAR,X),y_0); result = val; function result = objfun_y(y,PAR,X) A = PAR(1); B = PAR(2); A = PAR(3); C = PAR(4); D = PAR(5); val = A*y+B*exp(y*C)+g(D,X); result = val; </code></pre>
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    1. USAndrew Strathclyde
    1. USAndrew Strathclyde
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    1. COBefore you call `lsqnonlin` what are the sizes of your input variables?
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      1. USslayton
    2. COIn your objfun_y function why are you setting 'A' twice, what is 'CONST', is g() something that can be accessed by this function, and what is 'd' (maybe should be D)?
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    3. CO@ slayton: Xmeas and Ymeas are arrays of vimension 40 (44 to be precise), I don't think it's a "large" dataset @ ioums: pardon, errors done in simplifying the function to show th problem, I'm correcting them.
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      1. USAndrew Strathclyde
 

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