Development of Stability Formulas for Tetrapods and Rock Armors Using Multigene Genetic Programming

Abstract

Tetrapods and rock armors are widely used for armoring rubble mound breakwaters. Calculating the stability number of armor units is a necessary process to determine the optimal weight of armor units. Many stability formulas have been proposed to calculate the stability number of armor units since the Hudson formula in 1950s. Most of them are proposed by performing regression analysis for the parameters of the equation using the data obtained from the hydraulic model tests. In recent years, when there is a large amount of experimental data, machine learning methods have been introduced. For rock armors, an artificial neural network (ANN) model was proposed by Mast et al. (1995) and a combination of the ANN model with other models has also been proposed recently. The ANNs show good results, but it is complicated to calculate the output using the input data, so engineers have difficulty in using it in practice. To solve this problem, this study propose the definite functions to calculate the stability number of Tetrapods and rock armors through symbolic regression using multigene genetic programming (MGGP). This method, also known as multigene symbolic regression, has the advantage of obtaining both the parameters and the structure of the formula without assuming the structure of the formula. The proposed formulas are developed in terms of dimensionless variables and can be applied to both laboratory and field applications, and can be applied to any types of wave breaking. The final formulas are more accurate than the previous stability formulas and are simple to use by engineers.