Identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm

The response of rocks to stress can be highly non-linear, so sometimes it is difficult to establish a suitable constitutive model using traditional mechanics methods. It is appropriate, therefore, to consider modeling methods developed in other fields in order to provide adequate models for rock behavior, and this particularly applies to the time-dependent behavior of rock. Accordingly, a new system identification method, based on a hybrid genetic programming with the improved particle swarm optimization (PSO) algorithm, for the simultaneous establishment of a visco-elastic rock material model structure and the related parameters is proposed. The method searches for the optimal model, not among several known models as in previous methods proposed in the literatures, but in the whole model space made up of elastic and viscous elementary components. Genetic programming is used for exploring the model's structure and the modified PSO is used to identify parameters (coefficients) in the provisional model. The evolution of the provisional models (individuals) is driven by the fitness based on the residual sum of squares of the behavior predicted by the model and the actual behavior of the rock given by a set of mechanical experiments. Using this proposed algorithm, visco-elastic models for the celadon argillaceous rock and fuchsia argillaceous rock in the Goupitan hydroelectric power station, China, are identified. The results show that the algorithm is feasible for rock mechanics use and has a useful ability in finding potential models. The algorithm enables the identification of models and parameters simultaneously and provides a new method for studying the mechanical characteristics of visco-elastic rocks.