# Definitions for Random Vibration Analysis

## Random or Stochastic Process

A stochastic process is generally viewed as a family of random variables, or a collection of a large number of records that describe a physical phenomenon. The records can be a function of time {xk(t)} or frequency {xk(f)}. Each record is somewhat different from any other record. It is impossible therefore to include all possible records in the analysis. Instead, a random process is described in terms of statistical properties. Each load in a random vibration study is a random process. The response of a model to these loads is also a random process described in statistical terms.

## Autocorrelation Function

The autocorrelation function of a random process describes the correlation between the values in a record at different instants of time. It is defined as the expected value of the product of a random variable x(t) with a time-shifted version of itself.

(Eq.1)

## Root Mean Square (rms)

The mean square value provides a measure of the energy associated with the random process.

It is defined as the value of the autocorrelation function for τ = 0

(Eq.2)

where E is called the expectation operator. The positive square root of the mean value is known as the root mean square, or rms.

## Variance

The mean square value of a random process about its mean μx.

(Eq.3)

The positive square root of the variance is known as standard deviation.

## Power Spectral Density (psd)

The power spectral density is defined as the Fourier transform of the autocorrelation function of a random process.

(Eq.4)

Power spectral density describes how the energy of the random process is distributed in the frequency domain.

## White Noise

A white noise signal has a uniform power spectral density in all frequencies. In other words, the signal's energy is distributed equally in all frequencies.

Provide feedback on this topic

* Required

 *Email: Subject: Feedback on Help Topics Page: Definitions for Random Vibration Analysis *Comment: * I acknowledge I have read and I hereby accept the privacy policy under which my Personal Data will be used by Dassault Systèmes

Print Topic

Select the scope of content to print:

x

We have detected you are using a browser version older than Internet Explorer 7. For optimized display, we suggest upgrading your browser to Internet Explorer 7 or newer.

Never show this message again
x

Web Help Content Version: SOLIDWORKS 2016 SP05

To disable Web help from within SOLIDWORKS and use local help instead, click Help > Use SOLIDWORKS Web Help.

To report problems encountered with the Web help interface and search, contact your local support representative. To provide feedback on individual help topics, use the “Feedback on this topic” link on the individual topic page.