Power Spectral Density (PSD) and Random Testing

June 25, 2019

A random waveform is inherently irregular, non-deterministic, and non-repetitive. A measured point in a random time-history graph cannot be used to predict any point before or after it. A random waveform can be analyzed and understood from a statistical standpoint, but any specific point is unknown until it occurs.

Random waveforms are commonly used in vibration testing because they are reflective of the end-use environment. Real-world vibrational events are random, and products should be tested using realistic test profiles.

The PSD and Random Waveforms

The power spectral density (PSD) is the most common tool for analyzing random vibration. Resonances and harmonics hidden in a time-history graph are visible in a PSD graph. In practice, generating a PSD is usually the first step in examining and analyzing a random waveform.

power spectral density graph acceleration waveform

Power spectral density (above) compared to a random time-history graph (below).

Generating a useful PSD is not as simple as pushing a button. Test engineers and technicians set various parameters to tailor the PSD calculations to specific test requirements. For the parameter settings to be effective, however, the engineer must understand the PSD.

How to Calculate the PSD

The subsequent lessons provide the steps to calculate the PSD. The lessons will communicate critical concepts without equations first and then move into a mathematically rigorous description of the PSD and related calculations.