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Asymptotic Approximations for Multinormal Integrals
Abstract
The problem of deriving approximations for multinormal integrals is examined using results of asymptotic analysis. The boundary of the integration domain given by g(x¯)=0 is simplified by replacing g(x¯) by its Taylor expansion at the points on the boundary with minimal distance to the origin. Two approximations which are obtained by using a linear or quadratic Taylor expansion are compared. It is shown that, applying a quadratic Taylor expansion, an asymptotic approximation for multinormal integrals can be obtained, whereas using linear approximations large relative errors may occur.
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Cited by
Chojaczyk, A. A., Teixeira, A. P., Neves, L. C., Cardoso, J. B., & Guedes Soares, C. (2015) · Structural Safety · doi:10.1016/j.strusafe.2014.09.002 · Cited by 391
Distribution of Quadratic Forms in Normal Space—Application to Structural Reliability
Tvedt, L. (1990) · Journal of Engineering Mechanics · doi:10.1061/(asce)0733-9399(1990)116:6(1183 · Cited by 313
Updating robust reliability using structural test data
Papadimitriou, C., Beck, J. L., & Katafygiotis, L. S. (2001) · Probabilistic Engineering Mechanics · doi:10.1016/s0266-8920(00)00012-6 · Cited by 287
Efficient Reliability Assessment With the Conditional Probability Method
Mansour, R., & Olsson, M. (2018) · Journal of Mechanical Design · doi:10.1115/1.4040170 · Cited by 12
Structural Seismic Reliability Analysis
Sankararaman, S. (2014) · Encyclopedia of Earthquake Engineering · doi:10.1007/978-3-642-36197-5_280-1 · Cited by 2
Metadata
- Authors
- Breitung, K.
- Venue
- Journal of Engineering Mechanics
- Published
- 1984-03
- Volume
- 110
- Issue
- 3
- Pages
- 357-366
- ISSN
- 0733-9399 (ISSN-L)
- 1943-7889
- DOI
- 10.1061/(asce)0733-9399(1984)110:3(357
- OpenAlex
- W1963649399
- Cited by
- 912
- References
- 0
- FWCI
- 4.37
- Type
- journal article
- Language
- en
- Open access
- closed
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- Breitung, K. (1984). Asymptotic Approximations for Multinormal Integrals. Journal of Engineering Mechanics. https://doi.org/10.1061/(asce)0733-9399(1984)110%3A3(357
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