Random Testing and the Power Spectral Density (PSD)

June 25, 2019

Vibrations in the world around us are not repetitive or predictable like sinusoidal waveforms. They are random, so engineers often use random waveforms in vibration testing to ensure their products can withstand a realistic environment.

random acceleration waveform

A random acceleration waveform.

The main reason for performing random vibration testing is to bring a device under test (DUT) to failure. Testing the DUT to failure will expose details about the device’s weaknesses and indicate ways to improve the design.

Power Spectral Density

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

power spectral density graph acceleration waveform

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

Generating a functional PSD is not as simple as pushing a button in the software. Engineers set various parameters to tailor the PSD calculation to specific test requirements. For the parameter settings to be effective, the engineer must understand the underlying calculation of the PSD.

How to Calculate the PSD

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