How can I estimate time constants in a Prony series without trial and error?

[nellierd]

Hi,

I am trying to fit a prony series to set of data(modulus and time). I want to use curve fitting to fit the experimental data set. I am confused about the time constants. Is there a way I can find the time constants without having to do it by hit and trial method. Is there a way by which I can estimate the time constants? Any help is appreciated.

 

[hotvette]

The pdf in the below link describes a least squares method based on measured and calculated stress.

http://www.osti.gov/bridge/purl.cov...A94E1C94ACE4?purl=/469147-jdOZBI/webviewable/

In your case, it sounds like you have ordered pairs $(G_i,t_i)$ and want to fit the data to a function that looks something like:

$$G(t) = G_0 + \sum_{i=1}^n G_i e^{t/\tau_i}$$

where $G_0$ is known and you want to obtain estimates for the [tex]G_i[/itex] and $\tau_i$. Since the number of unknowns is 2*n, you need at least 2*n data points.