The three conditions for two randomly vibrating processes to be equivalent are:
a) Both are stationary ergodic random vibrations.
b) Their probability density functions follow a Gaussian-normal distribution.
c) They have the same auto-power spectral density function.
The vibration environment experienced by a product in the field is a highly complex time-domain process. To replicate external vibration environment stresses in a laboratory setting, certain necessary assumptions must be made, trimming away some non-mainstream influencing factors, with a certain probability statistical parameter acting as the main condition. Therefore, we can assume:
1) Random vibration processes can satisfy the condition of stationary random vibration. Because the statistical characteristics of stationary random processes do not change over time, we can segment finite-length data from an infinitely long external vibration environment for analysis. Each analysis of the segmented data yields statistically equivalent results, independent of the sampling time points. Similarly, during whole-room testing, random sampling and analysis (FFT) of time-domain data can yield consistent results each time. If a random process lacks stationary characteristics but its statistical properties change slowly over time, the process can sometimes be divided into multiple time segments. Within a certain margin of error, each segment can be considered a stationary random process.