Dear SciLab Friends:
I have an object consisting of many (~10,000) small components that can fail in
a statistical way during long-term operation at extreme conditions.
My primary failure model is described by PHI(t) going monotonically from zero
to one at times from t=0 to T. In the computer, this is realized in n timesteps.
Mechanism 2: There is a secondary failure mechanism that starts only when a
component has previously failed by mechanism 1 and occurs after some delay. The
delay function is f(t) and final expression for the evolution of the mechanism
2 failure is given by:
F(t) = Int_{0}^{T} PHI(t) . f(T-t) . dt
a classical convolution Faltungsintegral.
In Scilab, I write
F= conv(PHI, f, "same")/ n;
and the resulting function F looks reasonable for most of the time. Under some
conditions, however, I can have
F>PHI
at early stages, but this is physically impossible. Because it comes later, F
must always be below PHI.
What do I do wrong?
Heinz
_________________________
PS: massively simplified code below......
k=1E-7; // corrosion rate(s-1) in mechanism #1
n=100; // number of timesteps
t=(1:n)'; // time in days
ts= 3600*t; // time in seconds
PHI= 1 - exp(-((k*ts)^2)); // failure fraction in mechanism #1
plot("nl", t, PHI, 'r--');
f= 1 - exp(-ts/3E5); // "pure" failure fraction in mechanism #2
F=conv(PHI,f,"same")/length(t); //"convoluted" failure fraction mechanism #2
plot(t,F,'b--');
legend('failure fraction #1','subsequent failure fraction #2',4);
xlabel('time (hours)');
ylabel('failure fraction');
title('Component failure evolution #1 is followed by #2');
_______________________________________________
users mailing list - users@lists.scilab.org
Click here to unsubscribe: <mailto:users-unsubscr...@lists.scilab.org>
https://lists.scilab.org/mailman/listinfo/users
This email and any attachments are intended solely for the use of the
individual or entity to whom it is addressed and may be confidential and/or
privileged.
If you are not one of the named recipients or have received this email in error,
(i) you should not read, disclose, or copy it,
(ii) please notify sender of your receipt by reply email and delete this email
and all attachments,
(iii) Dassault Systèmes does not accept or assume any liability or
responsibility for any use of or reliance on this email.
Please be informed that your personal data are processed according to our data
privacy policy as described on our website. Should you have any questions
related to personal data protection, please contact 3DS Data Protection Officer
https://www.3ds.com/privacy-policy/contact/
