In mechanical engineering, random vibration is motion which is non-deterministic, meaning that the exact behavior at a future point in time cannot be predicted, but general trends and statistical properties can be known.
Some common examples include an automobile riding on a rough road, wave height on the water, or the load induced on an airplane wing during flight.
Structural response to random vibration is usually treated using statistical or probabilistic approaches.
The Grms value is typically used to express the overall energy of a particular random vibration event and is a statistical value used in mechanical engineering for structural design and analysis purposes.
While the term power spectral density (PSD) is commonly used to specify a random vibration event, ASD is more appropriate when acceleration is being measured and used in structural analysis and testing.