Genetic algorithm is an adaptive procedure that finds solutions to the inverse problem by an evolutionary process based on the natural selection. The application of genetic algorithm for solving the non-linear inversion of the initial stress fields is discussed. The inversion algorithm was built to identify the initial stress fields according to the observing data of deformation convergence during the tunnel excavation. The numerical calculations testify that the genetic algorithm for solving the inverse problem is robust, global and generally simpler to apply.
The values of the initial stress fields in the rock masses directly affect the strength and deformation of the structures under the ground and stability of surrounding rock masses. The most difficult aspects in analyzing the deformation and stress of a tunnel are the estimation of the initial stress fields and material constant. There is no doubt that the laboratory investigation and in-situ testing are the important measures, but have their limitations. In order to compensate for such deficiency, the revision of the initial stress fields is very important according to the observation of deformation during the construction process, so that the deformation of tunnel may be better predicted and agree with the observed ones. The initial stress fields of rock masses can be identified according to measured deformations of tunnel during excavation by means of back analysis. This method supplies other way of determining the values of initial stress fields in the rock masses. With the development of back analysis theory, the parameter identification algorithm has been successfully applied to various rocks engineering (Cividini 1983;Okabe 1998; Sakurai 1983; Giada1987). The traditional Linear inversion algorithms are to combined finite element methods with optimization methods and to solve the minimization of residual square sum. These optimization methods include Levenberg-Marquardt algorithm, Tihonov's regularizing procedure, Gauss-Newton method and modified Gauss-Newton method. The shortcomings of above linear inversion algorithms lie in converging a local optimum. Due to the presence of noise in the observations, the inverse problem is usually non-convex, and hence only a local optimum can be assured in the minimization (William 1986). Compared with traditional linear inversion algorithms, the genetic algorithm is robust, global and generally simpler to apply (Nath 1999). The genetic algorithm draws inspiration from the natural search and selection processes leading to the survival of the fittest individuals. They use a probabilistic search mechanism directed towards decreasing objective function and have a high probability of locating the global solution. The goal of the paper is to build the parameter identification procedure to estimate the initial stress field in the rock masses according to the observing data of deformation convergence during the tunnel excavation.
Genetic algorithm (G.A) is such a class of probabilistic algorithm that starts with a population of randomly generated candidates. The simulation of genetic evolution here is contrived by that the population size is forced to remain unchanged during the evolution process.