Powell’s optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

Abstract

A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell's optimization theory is used to perform the stochastic identification of material constants of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell's identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element (FCSE) method. Some classical examples show that Powell's identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell's theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses are simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.

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.…”

“…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.…”

Stochastic Gradient Optimization Method of Mechanical Parameters of Prestressed Concrete U Shaped Girder with Gaussian Objective Function

“…The bridge integrates into urban landscape better. The present study is aimed to implement the stochastic Gaussian optimized estimation of mechanical parameters of the reinforced concrete U shaped girder [8][9]. Gaussian objective function of mechanical parameters of the reinforced concrete U shaped girder is founded and the corresponding formulas are derived.…”

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

“…For example, based on conjugate gradient theory and other methods, the analysis of continuous box girder is carried out in Refs. [6,7]. The spatial finite element research of box girder is completed by establishing different element formations in Refs.…”