Fitting modeling results of a coupled thermal-mechanical numerical model in COMSOL Multiphysics to field data requires solving a least squared objective function which compares temperature and elevation data to find optimized values of certain parameters.
I need to assign a weight to temperature and settlement data under 'column contribution factor'. Units of Temperature are in K, and those of settlement are in m.
What will be the adjustment factor? 1 K ~ ___ m?
Both values are rounded off to 4 decimal digits.
Thanks,
Simran
Dear Simran,
I think this problem can be treated within the frame of the differentiation process.
That is assume that you have a function z in x and y.
Then
z= f(x,y)
dz= ( pdf/dx) dx + (p df/dy) dy = w1 dx + w2 dy
where p stands for partial differentiation.
So to get the total error in z , dz is the sum of two errors dx and dy with weights w1 for x and w2 for y. where w1 is the first partial derivative of z with respect to x and w2 is the same for y.
If the two error distributions are independent of each other then you square the terms and get
signa^2 z= W1^2 sigma ^2x + W2^2 sigm^2y
This proposal needs to be elaborated but it may give you an approach.
If it works please tell me.
Best wishes
For clarity: I need to calculate an appropriate weighting factor for temperature (K) and elevation (m).
The weight you assign to the different fitted variables depends on which is the variable you want to fit better - the higher the weight, the better the fit on that variable. In lack of any indication, I would suggest to use the relative squared error, that is, to set the weight as inversely proportional to the expected order of magnitude of the variable to be fitted. This would allow larger errors on variables with larger values, and vice versa.
Dear Simran,
I think this problem can be treated within the frame of the differentiation process.
That is assume that you have a function z in x and y.
Then
z= f(x,y)
dz= ( pdf/dx) dx + (p df/dy) dy = w1 dx + w2 dy
where p stands for partial differentiation.
So to get the total error in z , dz is the sum of two errors dx and dy with weights w1 for x and w2 for y. where w1 is the first partial derivative of z with respect to x and w2 is the same for y.
If the two error distributions are independent of each other then you square the terms and get
signa^2 z= W1^2 sigma ^2x + W2^2 sigm^2y
This proposal needs to be elaborated but it may give you an approach.
If it works please tell me.
Best wishes
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