I'm lost with the cost function to be evaluated when carrying out a sensitivity analysis

I'm trying to carry out a sensitivity analysis on my simulink model that represents the Penman-Monteith equation and estimates Evapotranspiration (ETo) values. Well, I want to find out how any of the parameters I need to estimate ETo influences ETo. Everything went well until I had to evaluate the cost function for any of the samples previously created. It is here wher I get stuck. What's actually a cost function, what does it do, and what would be the most appropiate cost function in my case? I can provide more information about my model, inputs or whatever. Thanks to those who answer me.

[monika dixit]

how did you model the Penman-Montieth equation in Simulink. Could you please guide?

Answer 1

[Star Strider]

A ‘cost function’ measures the variation from the actual performance of your model and the ideal performance. I don’t know what you’re doing, but one example of a cost function is a sum-squared-error function that in nonlinear regression measures the squared difference between the value of the function with a given set of parameter values and the data it is desired to approximate. The optimization of the function adjusts the parameter values to minimise the cost function.

A sensitivity function is the Jacobian of the cost function, the partial derivatives of the cost function with respect to each parameter. This allows you easily to see the effect — or ‘sensitivity’ — of each parameter on the behaviour of the function.

This is a simplified explanation to get you started. An Internet search or any book on optimisation or nonlinear regression will provide you with a much more detailed — and mathematically rigourous — discussion.

[Alberto Benito]

Uauuuuuuuu, I got it!!! thank you sooooooo much Star Strider. So I wasn't that lost because I was thinking of something similar to what you explained. I recently worked on Neural Networks and we needed some ways to calculate the differences between the measured and the predicted values and we finally used MSE and others. Well I followed the path you showed me hoping to solve the issue out. I really appreciate your explanation and help.

PS: Can I get back to you If I need something else about sensitivity analysis??

[Star Strider]

My pleasure!

P.S.: Of course!