Powell inversion mechanical model of foundation parameters with generalized Bayesian theory

Abstract

The inversion mechanical model of foundation parameters based on Powell optimizing theory was studied with generalized Bayesian theory. First, the generalized Bayesian objective function for foundation parameters was deduced with maximum likelihood theory. Then, the expectation expression and the covariance expression of the foundation parameters were obtained. After selecting the Winkler foundation as representative, the governing differential equations of the typical foundation were derived. With the orthogonal series transform method, the Fourier closed form solution of a moderately-thick plate on the Winkler foundation was achieved. After the optimal step length was determined with the quadratic parabolic interpolation method, the Powell inversion mechanical model of foundation parameters was resolved, and the corresponding inversion procedure was completed. Through particular example analysis, the highlight is that the Powell inversion mechanical model of foundation parameters with generalized Bayesian theory is correct and the derived Powell inversion model has universal significance, which can be applied in other kinds of foundation parameters. Besides, the Powell inversion iterative processes of foundation parameters have excellent numerical stability and convergence. The Powell optimizing theory is unconcerned with the partial derivatives of systematic responses to foundation parameters, which undoubtedly has a satisfying iterative efficiency compared with the available Kalman filtering or conjugate gradient inversion of the foundation parameters. The generalized Bayesian objective function can synchronously take the stochastic property of systematic parameters and systematic responses into account.