# Poisson Square Wave (PSW) and Filtered Poisson Process (FP)

• Apr 5th 2010, 11:29 AM
sorm
Poisson Square Wave (PSW) and Filtered Poisson Process (FP)
I am currently studying a paper from Prof. Armen Kiureghian regarding stochastic load modeling (reliability engineering). I have come across Poisson Square Wave (PSW) and Filtered Poisson Process (FP) as load modeling types. does anyone know anything about them and their properties?

In that paper the author has used PSW for sustained loads and FP for transient load types. It is a mystery for me!!

thanks
• Apr 5th 2010, 12:56 PM
Anonymous1
Quote:

Originally Posted by sorm
I am currently studying a paper from Prof. Armen Kiureghian regarding stochastic load modeling (reliability engineering). I have come across Poisson Square Wave (PSW) and Filtered Poisson Process (FP) as load modeling types. does anyone know anything about them and their properties?

In that paper the author has used PSW for sustained loads and FP for transient load types. It is a mystery for me!!

thanks

Well I would assume FP is just a special case of Poisson process...

A Poisson process is a way of counting independent exponential arrivals.

For definiteness:

Suppose posters arrive at this thread in independent exponential times $\displaystyle t_i$ with rate $\displaystyle \lambda$ per hour.

Set $\displaystyle T_i = t_1 +...+t_i =$ the time of the $\displaystyle i^{th}$ arrival.

Then the number of arrivals by time $\displaystyle t,$ is a poisson process $\displaystyle N(t) = \{\max\{i\}:T_i \leq t\}.$

There are many interesting properties about this counting process, but ultimatley it is used to count the number of arrivals of independent exponentials.