Crossing Statistics of Quadratic Transformations of LMA Processes
Artikel i vetenskaplig tidskrift, 2013

Random loads that exhibit significant non-Gaussianity in terms of asymmetric distributions with high kurtosis can be modeled as Laplace Moving Average (LMA) processes. Examples of such loads are the wave loadings in ships, wind loads on wind turbines, loads arising due to surface roughness in vehicular systems, etc. The focus of this paper is on estimating the crossing statistics of second-order response of structures subjected to LMA loads. Following the Kac–Siegert representation, a second order approximation of the Volterra expansion of the system enables representing the response as a quadratic combination of vector LMA processes. The mean crossing rate of the response is then computed using a hybrid approach. The proposed method is illustrated through two numerical examples.

Kac-Siegert representation

Rice's formula

LMA processes

Crossing statistics

Gamma processes

Quadratic transformation


J. Jith

Indian Institute of Technology, Madras

Sayan Gupta

Indian Institute of Technology, Madras

Igor Rychlik

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Probabilistic Engineering Mechanics

0266-8920 (ISSN)

Vol. 33 9-17


Grundläggande vetenskaper


Sannolikhetsteori och statistik