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Fitting to a Prony series

  1. Mar 27, 2010 #1
    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.
     
  2. jcsd
  3. Mar 27, 2010 #2

    hotvette

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    Homework Helper

    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 [itex](G_i,t_i)[/itex] and want to fit the data to a function that looks something like:

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

    where [itex]G_0[/itex] is known and you want to obtain estimates for the [tex]G_i[/itex] and [itex]\tau_i[/itex]. Since the number of unknowns is 2*n, you need at least 2*n data points.
     
    Last edited: Mar 28, 2010
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