Evaluation of gene expression programming and artificial neural networks in PyTorch for the prediction of local scour depth around a bridge pier

Abstract

Local scouring around the piers of bridges has been identified as one of the main problems contributing to bridge failure globally. As such, the accurate prediction of safe scouring depths is crucial to assure safety and to develop effective maintenance routines. This study was thus intended to develop a new empirical equation and models to expect the depth of scour occurring around the pier of a bridge by utilising and assessing a variety of modelling proposals to develop the best possible performance. Three methods were used for this purpose: artificial neural networks (ANN), gene expression programming (GEP), and statistical non-linear regression (NLR). The ANN model used in this study was coded in Python, a major modern coding language, being based on the PyTorch interface. The empirical equations and models derived to predict local scour depth were all amended to incorporate the shape of the pier, flow depth, flow intensity, pier width and the attack angle based on data computed within a numerical simulation model in Flow-3D software. The performance of the functional relationship derived from the GEP approach was then compared to the results computed from both the ANN model and NLR empirical equation, with three statistical indices: root mean squared error (RMSE), mean absolute error (MAE) and coefficient of determination (R2), as well as appropriate scatter plots used to identify the most efficient of the three models. Based on this comparison, the ANN model performed more accurately than the other two empirical equations derived from the NLR and GEP models based on its smaller values for MAE (0.012) and RMSE (0.029), and its greater R2 value (0.969). Sensitivity analysis results from the model also suggest that flow depth has the most significant impact on depth of scour predictions for compared to different input variables in this model. Based on the results, it can be concluded that the performance of the equation obtained from the ANN-based PyTorch technique is more accurate in predicting the scour depth than GEP and NLR.