Powell dynamic identification of displacement parameters of indeterminate thin-walled curve box based on FCSE theory

Abstract

The FCSE controlling equation of pinned thinwalled curve box was derived and the indeterminate problem of continuous thin-walled curve box with diaphragm was solved based on flexibility theory. With Bayesian statistical theory, dynamic Bayesian error function of displacement parameters of indeterminate curve box was founded. The corresponding formulas of dynamic Bayesian expectation and variance were deduced. Combined with one-dimensional Fibonacci automatic search scheme of optimal step size, the Powell optimization theory was utilized to research the stochastic identification of displacement parameters of indeterminate thin-walled curve box. Then the identification steps were presented in detail and the corresponding calculation procedure was compiled. Through some classic examples, it is obtained that stochastic performances of systematic parameters and systematic responses are simultaneously deliberated in dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step size is solved by adopting Fibonacci search method. And the Powell identification of displacement parameters of indeterminate thin-walled curve box has satisfied numerical stability and convergence, which demonstrates that the presented method and the compiled procedure are correct and reliable.During parameters' iterative processes, the Powell theory is irrelevant with the calculation of finite curve strip element (FCSE) partial differentiation, which proves high computation efficiency of the studied method.

Accumulative Bayesian detection of displacement constants of a hybrid indeterminate box girder with variable scale gradient theory

“…Substituting the agglomerated redundant force vector R obtained from equation (24) into equation 23, the vector r of the redundant forces of the hybrid indeterminate box is gained. Then let the redundant force vector r added on the basic system and the displacement field of the hybrid indeterminate curvilinear box can be achieved by equations (18) and (19).…”

Updated Bayes identification of displacement constants of curve indeterminate box girder with variable scale theory

“…where D is the elastic matrix and B is the strain matrix determined by substituting equation (14) into equation (13). In equation (15), it can be achieved as…”

“…12 Generally, the direct search methods are comparatively inferior to the gradient search methods for the lower computational efficiency because of its only simply depending on the revision of the objective function. 13,14 Variable-scale optimal method ceaselessly alters the spatial matrix scale to produce new search directions during the iterative processes and optimizes the objective function efficiently. During the variable scale steps of displacement constants of curve indeterminate box girder, determination of the optimal step size is involved, which belongs to a fairly complicated question in constant identification analysis.…”

“…In identification of research achievements such as identification of models performance of fracture toughness of polymeric particle nanocomposites, identification of material interfaces in piezoelectric structures, and identification of typical flaws in piezoelectric structures using extended finite element method (FEM), [20][21][22] Bayes theory is widely applied because one of the superiorities lies in its taking the stochastic property of systematic parameters and systematic responses into account efficiently; however, a much more efficient Bayes objective function in this article is derived below. From Bayes theorem, 13 it can be attained as…”

“…12 In Powell iterative processes, the improvement of the displacement constants only depends on the revision of the objective function without any search direction, which consequentially leads to lower computational efficiency. 13 In Zhang et al, 14 one-dimensional optimization method called Fibonacci series search method is employed to improve the computational efficiency, but it cannot conquer the inherent disadvantage of the Powell direct optimization method. The gradient optimization methods such as the variable-scale optimization method can smooth over the defect just disserted to a certain extent.…”