2) Random vibration processes can satisfy the condition of ergodic random vibration. Because ergodic random processes have statistical properties in each sub-sample that encompass the characteristics of the entire population, an infinitely long time-domain random process can be substituted with statistical properties derived from a finite time length. In practice, it is impossible to obtain extensive data on infinitely long random vibration time histories, so we always assume that the random vibration under study is an ergodic random process.
With the assumptions of stationary and ergodic states, we can replicate the statistical parameter characteristics of external field data using laboratory analysis results based on limited (preferably abundant) data volumes. This also allows for the random selection of a time-domain data frame during laboratory testing to represent the statistical properties of the random vibration.
3) The probability density functions of random vibration processes are essentially Gaussian-normal distributions.
In practical engineering, within a certain margin of error, most random vibration processes satisfy the above three assumptions.
Therefore, when determining the equivalence of two random vibration processes, the primary focus often lies in whether their auto-power spectral density functions are identical, while assuming that they both satisfy the “stationary ergodic random vibration” and “probability density functions follow Gaussian-normal distribution” conditions as implicit equivalence criteria by default.