Prediction of time-dependent bearing capacity of concrete pile in cohesive soil using optimized relevance vector machine and long short-term memory models

The present investigation employs relevance vector machine (RVM) and long short-term memory (LSTM) models to predict the time-dependent bearing capacity of concrete piles. Each RVM model (SRVM) is configured by each linear, polynomial, gaussian, sigmoid, laplacian, and exponential kernel function. Each SRVM model has been optimized by each genetic (GA_SRVM) and particle swarm optimization (PSO_RVM) algorithm. Moreover, the double kernel-based RVM models (DRVM) have been employed and optimized by each GA (GA_DRVM) and PSO (PSO_DRVM) algorithm. Thus, an extensive comparison among 33 RVM (6SRVM + 6GA_RVM + 6PSO_RVM + 5DRVM + 5GA_DRVM + 5PSO_DRVM) has been carried out. Conversely, the Adam, root mean squared propagation and stochastic gradient descent with momentum algorithms have optimized the LSTM model. Each optimized RVM and LSTM model has been trained and tested by 100 and 26 datasets. In addition, the effect of structural and database multicollinearities has been analyzed on models' prediction capabilities. The performance index (PI), the variance accounted for (VAF), performance (R), mean absolute error (MAE), normalized mean bias error (NMBE), and root mean square error (RMSE) matrices have analyzed the prediction capabilities of each model. The comparison of 33 RVM and 3 LSTM models reveals that the genetic algorithm-optimized Gaussian kernel function-based SRVM model, i.e., UBC7, has been recognized as the optimal performance model with the RMSE = 146.3962 kPa, PI = 1.85, VAF = 94.60, NMBE = 30.1379 kPa, MAE = 105.7009 kPa, and R = 0.9727, close to the ideal values. Furthermore, the score (= 56), Wilcoxon (= 94.95% confidence), uncertainty (= 1^st rank), generalizability (= close to ideal values), and Anderson Darling (= 9.435 ≈ 9.336) tests confirm the superiority of model UBC7. Still, structural and database multicollinearity has drastically impacted dual kernel-based RVM and stochastic gradient descent optimized LSTM models.