Abstract
With general Bayesian theory, the accumulative Bayesian objective function of displacement constants of a hybrid indeterminate box girder was found. The gradient matrix of accumulative Bayesian objective function to displacement constants and the calculative covariance matrix were both derived. The finite curvilinear strip controlling equation of a pinned box girder was derived and the hybrid indeterminate problem of a continuous curvilinear box girder with diaphragm was solved based on agglomeration theory. Combined with one-dimensional (1D) Fibonacci automatic search scheme of optimal step length, the variable scale gradient theory was utilized to research the stochastic detection of displacement constants of the hybrid indeterminate curvilinear box girder. Then the detection steps of displacement constants of the hybrid indeterminate curvilinear box girder were presented in detail and the detection procedure was developed. Through some classic examples, it is achieved that the accumulative Bayesian detection of displacement constants of the hybrid indeterminate curvilinear box girder has perfect numerical stability and convergence, which demonstrates that the derived detection model is correct and reliable. The stochastic performances of displacement constants and structural responses are simultaneously deliberated in an accumulative Bayesian objective function, which proves to have high computational efficiency. The variable scale gradient method incessantly changes the spatial matrix scale to engender new search directions during the iterative processes, which makes the derived accumulative Bayesian detection of the displacement constants more efficient.
Highlights
Compute the gradient vector difference YkHkYk (Yk)T Hk (Yk )T HkYk ð30Þ where DHk is the incremental matrix of the variable scale matrix
With general Bayesian theory, the accumulative Bayesian objective function of displacement constants of a hybrid indeterminate box girder was found
The results indicate that, compared with the Powell direct optimal results,[18,19] the variable scale theory is more efficient because the computational times of the accumulative Bayesian objective function mainly resulting from the finite curvilinear strip element model are fewer
Summary
HkYk (Yk)T Hk (Yk )T HkYk ð30Þ where DHk is the incremental matrix of the variable scale matrix. Let k = k + 1 and return to step (3) to continue reiteration. The 1D search of step length l is necessary in step (4) of accumulative Bayesian detection steps of displacement constants of the hybrid indeterminate curvilinear box girder and it is a fairly complicate issue in constant detection. Compute the accumulative Bayesian objective function J (Ek + 1) and the gradient rJ (Ek + 1). The variable scale gradient iteration is convergent and the detection results of displacement constants E are E^ = Ek + 1. 6. If J (Ek + 1).J (Ek), let E0 = Ek + 1 and return to step (2) to reiterate.
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