Numerical and experimental validation of variance prediction in the statistical energy analysis of built-up systems

Ranking paths in statistical energy analysis models with non-deterministic loss factors

“…For instance, if N ¼3 we get Φðp ij Þ ¼ μw i…j À 3σw i…j and it is guaranteed that for a path weightwðp n ij Þ having a Gaussian distribution, the probability P of the weight lying between μw i…j 73σw i…j is greater than 0.99. The cost function in (11) provides one way to compare paths, so that a path p ij;1 is said to be more dominant than p ij;2 whenever Φðp ij;1 Þ 4 Φðp ij;2 Þ.…”

“…(9). The connection between a clone t i and the virtual target vt is then weighted with the value of the variance term of the cost function in (11), i.e., w t i vt ¼ ϕðiÞ, to be added to its mean value to get the cost of the path Φ (see Fig. 2(c)).…”

“…Random variances ranging from 0.5 to 3 dB are assigned to the edges of the stochastic SEA graph for illustrative purposes. Besides, the cost function in (11) is defined again to follow the three sigma rule, ϕðσ 2 Þ ¼ À3σ. As mentioned, the negative sign is used to consider the most restrictive situation [23].…”

“…Since then, both nonparametric and parametric approaches have been followed to deal with uncertainties. Recently, some closed formulas have been derived for the former based on the Gaussian orthogonal ensemble [10,11] (see also the work in [12]). Analytic [3] as well as parametric methods to evaluate subsystem energy variability due to loss factor and input power uncertainties have been also developed [13].…”

Accurate extreme-value-based frequency response bounding for structures with a small number of highly random parameters

“…Importance or Line Sampling [19][20] can speed-up the process (as available in the software COSSAN [21]) but accuracy is not guaranteed. High frequency methods apply to structures with vibration wavelengths much shorter than component dimensions for which SEA is most successful [22][23][24][25][26]. SEA takes no account of differing levels of parameter variability because randomness is assumed to be sufficiently high for knowledge of variability not to be needed.…”