基于最大熵原理的贝叶斯不确定性反分析方法

Bayesian uncertainty inverse analysis method based on pome

针对基于确定性数值模型的各种常规反分析方法未能综合考虑各种不确定性因素影响,因而难以有效模拟复杂工程系统的不确定性特性这一不足,对工程结构系统中的不确定性反分析方法问题进行了研究.从不确定性分析角度,把工程结构看作为不确定性系统,提出基于最大熵原理的贝叶斯不确定性反分析方法,将信息熵理论与贝叶斯法有机结合,使不确定性反分析的系统辨识问题转换为对贝叶斯准则函数的最优化求解问题,并通过适当的优化求解方法,实现对工程结构参数或荷载项源的反演分析.对坝体和坝基材料参数的实例计算结果表明,该方法反演结果正确,精度高于目前常用的确定性反分析方法.

The routine methods of inverse analysis based on deterministic models of numerical analysis can not synthetically take into account the influences of various uncertainty factors, and so are difficult to be utilized to simulate the uncertainty characteristics of complicated engineering system. Aimed at this shortage, an uncertainty inverse analysis method for engineering system was studied. From uncertainty analysis point of view, the engineering structure was considered as an uncertainty system, and a Bayesian uncertainty inverse analysis method based on the principle of maximum entropy （POME） was put forward, which organically combined information entropy theory and Bayesian method of inverse analysis, so that the system discriminance problem of uncertainty inverse analysis was transformed into an optimization evaluation problem for Bayesian rule function. Utilizing appropriate optimization method, uncertainty inverse analysis could be realized for evaluations of engineering structure parameters or fountainhead loads. As an engineering example, the method advanced was utilized to carry out inverse analyses of material parameters of dam concrete elastic modulus and bedrock deformation modulus. The calculation results show that the material parameters obtained are right and that the precision is higher than that of the conventional deterministic methods of inverse analysis which is widely used presently.