An evolutionary-based polynomial regression modeling approach to predicting discharge flow rate under sheet piles

Abstract

The discharge flow rate beneath sheet plies is an essential parameter in designing these water retaining structures. This paper presents a unified framework for modeling and predicting discharge flow rate using an evolutionary-based polynomial regression technique. EPR (Evolutionary Polynomial Regression) is a data-driven method based on evolutionary computing to search for polynomial structures representing a system. The input parameters in the modeling procedure included the sheet pile height, upstream water head, and the hydraulic conductivity anisotropy ratio. Due to ever-increasing demand for water, a widely held view on predicting and controlling the available water behind reservoirs, dams, barrages, and weirs is of vital importance. To this end, the sheer novelty of the current study has been worn off through the development of a comprehensive model to predict the flow rate considering the most effective variables in the seepage issue. To the best of our knowledge, the research conducted in the literature has yet to cover the whole seepage problem using a comprehensive database extracted by numerical methods; thus, a comprehensive finite-element-based artificial database including 1000 data lines was created using the Scaled Boundary Finite Element Method (SBFEM) by simulating seepage beneath sheet plies covering a considerably wide range of seepage-related real-world values. The database was then employed to develop and validate the EPR flow rate prediction model. Data were divided into training (used for creating the models) and testing (for validating the developed models) data based on a statistical process. The procedure for preparing the data and developing and validating the models is presented in detail in this paper. The main advantage of the proposed models over a conventional and neural network and most GP (Genetic Programming)-based constitutive models is that they provide the optimum structure for the material constitutive model representation as well as its parameters, directly from raw experimental (or field) data. EPR can learn nonlinear and complex material behavior without any prior assumptions on the constitutive relationships. The proposed algorithm captures and transparently presents relationships between contributing parameters in polynomial expressions providing the user with a clear insight into the problem. EPR-based model predictions demonstrated an excellent agreement with the unseen simulated data used for validating the developed model. A parametric study on the presented models was conducted to investigate the effects of the contributing parameters on model predictions and the consistency of the parameter relationships with the database. Results of the parametric study showed that the effects of variations in the contributing parameters on EPR predictions are in line with the expected behavior. The merits and advantages of the proposed technique are discussed in the paper.