Power Spectral Density (PSD)

June 25, 2019

Importance of Power Spectral Density (PSD) in Vibration Testing

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. A 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 must be tested against realistic situations.

Power spectral density (PSD) is the most common tool used to analyze random vibration. Resonances and harmonics that are 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 next two lessons present the steps to calculate the PSD. Each step is a mathematical process, but the following lessons communicate the critical concepts without equations. For a mathematically rigorous description of PSD and related calculations, you can navigate to the Converting Recorded Data section of this course.