Clarification needed on Jacobian for Levenberg Marquardt Least Squares function
Clarification needed on Jacobian for Levenberg Marquardt Least Squares function
(OP)
Hi,
I am trying to write a MATLAB script to estimate the damage to a turbofan engine component based on key engine parameters; spool speed (NH), high pressure compressor inlet pressure (P30) and high pressure compressor inlet temperature (T30). I have an empirical formula to base the fit on, contained in a function AlgoFit.m. This function has 22 coefficients, stored in a vector K.
As my university did not focus much on numerical analysis or statistics this is all fairly new to me and I am having a hard time understanding descriptions online. What I want to do is fit the AlgoFit.m function to experimental data I have by altering all 22 coefficients in K to reduce the residuals, but I cannot get clear in my head what I am doing.
I have read that I want the Jacobian, and i think this should be of the form J = [dNH/dK1,dP30/dK1,dT30/dK1; dNH/dK2,dP30/dK2,...,dT30/dK22], but i am not sure how to compute this jacobian from my parameters P = [NH(:),P30(:),T30(:)], coefficients K = [K1 K2 ... K22], experimental data SA40 = [time(:) Stress(:) temp(:)] and fitted approximation/residuals from AlgoFit.m.
If anyone can clear up how to get the Jacobian then hopefully that will be all I need to get going on this. I do have plenty more data as this is a small part of a larger project, i've given all that i think is relevant but if i need anything else I can probably find it quite easily.
Thank you,
Steve
I am trying to write a MATLAB script to estimate the damage to a turbofan engine component based on key engine parameters; spool speed (NH), high pressure compressor inlet pressure (P30) and high pressure compressor inlet temperature (T30). I have an empirical formula to base the fit on, contained in a function AlgoFit.m. This function has 22 coefficients, stored in a vector K.
As my university did not focus much on numerical analysis or statistics this is all fairly new to me and I am having a hard time understanding descriptions online. What I want to do is fit the AlgoFit.m function to experimental data I have by altering all 22 coefficients in K to reduce the residuals, but I cannot get clear in my head what I am doing.
I have read that I want the Jacobian, and i think this should be of the form J = [dNH/dK1,dP30/dK1,dT30/dK1; dNH/dK2,dP30/dK2,...,dT30/dK22], but i am not sure how to compute this jacobian from my parameters P = [NH(:),P30(:),T30(:)], coefficients K = [K1 K2 ... K22], experimental data SA40 = [time(:) Stress(:) temp(:)] and fitted approximation/residuals from AlgoFit.m.
If anyone can clear up how to get the Jacobian then hopefully that will be all I need to get going on this. I do have plenty more data as this is a small part of a larger project, i've given all that i think is relevant but if i need anything else I can probably find it quite easily.
Thank you,
Steve
Talk To Other Members
RE: Clarification needed on Jacobian for Levenberg Marquardt Least Squares function