Study On Numerical Methods Of Structural Reliability Index

Solving nonlinear algebraic equations is a basic and important question, because in engineering practice, economics, information security, and dynamics have a large number of practical issues eventually be transformed into algebraic equations (in particular, multiple nonlinear algebraic equations) to solve the real roots of the problem.Classical algorithms of solving nonlinear equations, such as Newton's method and its improved form, have fast convergence speed, but the algorithm is sensitive to initial value, if the initial value of a given area is not convergence, then the algorithm does not converge, it can only local search. Such methods are a lot of very good quality, but they also have a common limitation that it is required ( )f xi( i = 1,2,,n) has some kind of monotonicity. Unfortunately, in most practical problems, they don't have the nature that we need, or we can not determine whether it has this kind of nature. It makes Newton-type algorithm difficult to solve the problem.For solving multiple nonlinear equations, N-group of nonlinear equations will be transformed into N-component one-element equations with the same solution, then one-element equation will be easy to solve with dichotomy. Taking use of dichotomy flow of solving one-element equation to extend to N-group of nonlinear equations, then dichotomy flow of solving N-group of nonlinear equations is given. And based on flows, binary, ternary and quaternary non-linear equations of the VB computer program are given. The method avoids the derivation and convergence problems in traditional method. It only takes use of the feature of function value opposite to each other at both ends of the root zone. The method with this feature can be widely used in engineering practice and the computer program given even more increased project efficiency. In solving the reliability index calculation process, for the case of some traditional methods can not find or difficult to find the results, this dichotomy has a very good application effect.