Contact US

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Clarification needed on Jacobian for Levenberg Marquardt Least Squares function

Clarification needed on Jacobian for Levenberg Marquardt Least Squares function

Clarification needed on Jacobian for Levenberg Marquardt Least Squares function


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,


RE: Clarification needed on Jacobian for Levenberg Marquardt Least Squares function

OK, after a bit more thinking I believe the Jacobian should actually be J = [F(P,K)/dK1; F(P,K)/dK2; ...; F(P,K)/dK22] where F(P,K) is the fit function I have written in MATLAB, P are the input parameters for spool speed, temperature and pressure. It was confusing me how to take the derivative of the individual parameters w.r.t. the coefficients because they wouldn't change. However I am still unsure how to take the derivative of the function w.r.t. values I only have one initial guess for. Any hints or prods in the right direction would be much appreciated.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login


Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close