Probability Distribution of Statistical Energy Analysis Model Responses Due to Parameter Randomness

Abstract

The Statistical Energy Analysis (SEA) methodology has been widely used in aerospace, ship and automotive industry for high frequency noise analysis and acoustic designs. SEA models are treated here as baseline representations of a population of models for systems such as automotive vehicles. SEA responses from the population of all possible models for a vehicle have a random distribution because of the unavoidable uncertainty in the physical parameters due to fabrication imperfection, manufacturing and assembly variations. The random characteristics of the SEA responses can be described by the response probability distribution. In this work, SEA energy response probability distributions due to parameter randomness in a small neighborhood of nominal design values in frequency bands are proven through the Central Limit Theorem to be Gaussian for infinite number of design parameters. Mean squared sound pressure and velocity are directly proportional to SEA energy responses, their distributions are also shown to be Gaussian. In engineering applications, the number of design parameters is always finite for any SEA models. A Monte Carlo test and Statistical Hypothesis test on a simple 3-element SEA model show that the theoretical, infinite order, Gaussian distributions are good approximations for response distributions of a finite parameter SEA model.