Estimation of Tail Distribution of Structural Response
Using a Technique of Moving Domain of Taylor Expansion
Jong Seo Kim
This paper presents a estimation technique of tail distribution of structural response using not sampling based method but analytic one. Tail region is defined from nearby reliability index 3.75 to infinite as engineering concern in this paper.
To estimate the tail distribution of response from random variable distribution, analytic distribution of response is employed. Analytic distribution of response is a result of integrating the joint probability distribution of random variables. It is considered that the random variables are statistically independent in this paper.
To integrate the joint probability distribution, response function is necessary. So, the Taylor Expansion is employed to approximate the structural response function, which is the result of differential of structural stiffness matrix in term of variables.
It is assessed that the consequences of 1st Order Taylor Expansion and 2nd Order Taylor Expansion in terms of necessity of numerical integral and precision of tail.
To reduce the quantity of calculation, Mean Value 1st Order Taylor Expansion is employed to approximate the response function and tail distribution is estimated using that. To enhance the preciseness of tail distribution, Method of Moving Domain of Taylor Expansion(MMD) is proposed to move the domain from mean to tail sequentially. In the middle of moving domain, for the purpose of determining new combination of random variables, Rackwitz Algorithm is employed.
The validity of proposed method will be verified through numerical exercises of cable-supported bridge from normally distributed single random variable to multi-random variables. And the validity will be extended to the non-normally distributed random variables using Rack Fiessler Transform.
Estimation of tail distribution, Analytic response distribution, Response function, Joint probability distribution, Taylor Expansion, Method of moving domain