Boots – shoes – and leggings
Patent
1994-04-18
1997-03-04
Cosimano, Edward R.
Boots, shoes, and leggings
G06F 1710
Patent
active
056086598
ABSTRACT:
The present invention is a method for identifying a Most-Probable-Point (MPP) in original space obviating the need for a probability transformation, for use in first order/second order reliability analysis. It comprises generating the linear approximation of a limit-state-function, g(x) about the median, mean point, or mode of random variables, x of g(x). g(x) is defined so that g(x)f0 denotes a failure set. The Most-Probable-Point-Locus (MPPL) of g.sub.1, MPPL.sub.1, is constructed by the steps of: i) identifying the mode of x; ii) identifying the MPP of g.sub.1 (x)=c, where c is an arbitrary constant, and iii) constructing said MPPL.sub.1 by connecting said mode of x from step i), above, and the MPPs corresponding to different c's from step ii), above. A quadratic search algorithm is to identify point MPP.sub.1, the intersection of MPPL.sub.1 and g(x)=0, based on the following convergence criteria: ##EQU1## The process is then stopped, unless the convergence criteria are not satisfied. g.sub.2, the linear approximation of the limit-state-function, g(x) about MPP.sub.1 is generated. MPP.sub.21, the Most-Probable-Point of g.sub.2 (x)=0 is located. The approximate MPPL of g.sub.2, MPPL.sub.2, is constructed by connecting the mode and the MPP.sub.21. The quadratic search algorithm is used to identify point MPP.sub.2,, the intersection of MPPL.sub.2 and g(x)=0 based on the convergence criteria. g.sub.f (x) is updated, where j=2, 3, . . . , m, where m is the total number of steps required for convergence.
REFERENCES:
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"A New Most-Probable-Point Search Procedure for Efficient Structural Reliability Analysis" by M. R. Khalessi, Y. T. Wu & T. Y. Torng Proceedings of the 32nd Structures, Structural Dynamics, and Materials Conference, Part 2, AIAA/ASME/ASCE/AHS/ASC, Apr. 191, pp. 1295-1304.
Khalessi Mohammad R.
Lin Hong-Zong
Cosimano Edward R.
Field Harry B.
Ginsberg Lawrence N.
Montanye George A.
Rockwell International Corporation
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