岩土工程反分析方法的信息论研究

本文以信息论为基础，针对岩土工程中的逆问题。在数学上建立了逆问题一般信息理论的基本框架．这个框架以本文提出并论证的三个基本定理为核心。揭示了逆问题的信息本质．其中心思想是：对被反演参数的观测信息，理论预测信息和经验性信息的综合，将给出关于这个参数的更高信息含量的信息表达．这种表达自然地在逆问题的求解过程即反分析中，综合考虑观测过程、理论分析及经验判断三者的不确定性，在一些限定条件下，这种表达退化为当前岩土工程中的几种反分析方法，这不仅为逆问题的求解提供了一条通用，有效的途径，而且为反分析方法的理论研究探索了新的途径．

STUDY OF BACK ANALYSIS METHODS IN ROCK AND SOIL ENGINEERING BY THE INFORMATION THEORY

Based on the information theory and aimed at the inverse problems in rock and soil engineering, this paper established a basic mathematical framework of general information theory for inverse problems. With the three basic theorems proposed and proved in this paper as the kernel, the above-mentioned framework has disclosed the information nature of inverse problems. The central idea of the framework is that a synthesis of the observational information, theoretically predicted information and empirical information for the parameter to be inverscd will give an informational representation for that parameter which is of higher information contents. Such a representation can automatically and comprehensively consider the uncertainties included in observational process, theoretical analysis and empirical judgement during the solution process of inverse problems, i.e., back analysis. Under some restraining conditions, this representation decays into some of the back analysis methods currently used in rock and soil engineering. The work presented here has provided not only a universal and effective way for solving inverse problems but also a new way for the theoretical study of back analysis methods.