View Full Version : time dependent curves

Marco Viceconti
05-28-1993, 12:21 AM
Originally posted on Tue, 23 Mar 93 18:17:47 SET

Some time ago I have posted the following question:

Can anyone help with this problem:
I am writing a computer simulation to determine the forces acting on the
prosthetic head in different hip joint simulators (devices which generate in
vitro wear in prosthetic joints). My model generate a time curve for every
force component which I compare with the physiological curves propesed by
Paul. Which sintetic descriptor can I use to compare those curves, to say that
one simulator is generating a force history which is more close to the
physiological pattern than another? The method should give more importance to
short time force drifts and less to eventual small time shifts.

Here below there is the collection of the answer I've received;
it must be noted that the number of request for info was more
than the answers. Maybe the question was unclear, or maybe I've hit
a common problem. In any case, I feel that further discussion would needed.

From: jill mcnitt

Please let us know responses to your time curve comparison question. We've
tried cross correlation techniques.
Jill McNitt-Gray
USC Biomechanics Lab

From: "Maury A. Nussbaum"

I am sending you a message because I am curious as to the responses to
the message you posted on Biomech-L regarding comparisons of force
histories. I would like to request that you post a summary of the
responses as I think many people would be interested.


Dear Marco,
Might I suggest that you model your force curves as a Fourier series and use
the coefficients to compare the similarity of the curves. This would also
allow you to priortise the frequency components in terms of wear potential.
McNeill Alexander use such a modelling approach some years back and reported
his work in the Journal of Biomechanics I believe.
Hope this quick comment is helpful.


Graeme A. Wood, PhD
Human Movement Department
The University of Western Australia

Beside the suggestion of G. Wood, which was probably interesting but
we refused for computational reasons, non of the suggestions fitted
our problem. So, we had to find the way by ourselves. Finally we found
useful a cost function definition used on trajectory tracing problem,
tipical of automatic controls. The cost function is defined as:
J = K * Integral (eT Q e) dt
J = dimensionless cost function
K = normalization factor; we choosen it such that the biggest J in our
study became equal to 100. K dimensions in our problem were
e = instantaneous error vector between the two curves; here is
Q = weight positive definite matrix; here was choose the identity matrix
in a spatial problem like our, e is a 3x1 vector and Q is a 3x3 matrix.
The integral on time is extended from initial to final time.

Thank to anybody for the suggestions. I'll be glad to receive any comment
on this idea; due to the reduced discussion, this can also be considered as
a reposting of the question itself.

|marco viceconti lk1boq72 @ icineca.cineca.it|
|laboratorio di tecnologia dei materiali tel. 0039-51-6366864 |
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