Prediction of Uniaxial Strength of Rocks Using Relevance Vector Machine Improved with Dual Kernels and Metaheuristic Algorithms

The uniaxial compressive strength (UCS) is an essential parameter to study rock characteristics, determined by direct and indirect methods. However, the direct methods of determining rock UCS are lengthy and arduous, presenting a requirement of developing a robust indirect method. This investigation introduces an optimal computational model based on the artificial intelligence approach. For that aim, the relevance vector machine (RVM) and long short-term memory (LSTM) approaches have employed 24 computational models in estimating rock UCS and introducing an optimal computational model. The 514, 146, and 74 data points have trained, tested, and validated the 24 models compiled from the literature. The model comparison reveals that implementing a secondary kernel function in a single kernel-based RVM model enhances the performance. Moreover, the particle swarm (PSO) optimized dual kernel-based RVM model attains higher performance than genetic (GA) optimized RVM models. Conversely, the Adam-optimized LSTM model achieved higher performance than other LSTM models. The overall comparison introduces model MD21 (PSO-optimized RVM model implemented by dual kernels, i.e., Laplacian + polynomial) as an optimal performance model in predicting rock UCS with a correlation coefficient of 0.9979 (in the testing phase) and 0.9939 (in the validation phase). In addition, the multicollinearity analysis reveals that the database variables consist of weak multicollinearity. It is noted that the optimized RVM and LSTM models attain overfitting because of weak multicollinearity and optimization algorithms. The analysis of variance (ANOVA), Z, and Anderson–Darling tests accept the research hypothesis for the compiled database. In addition, the trend of simulated results illustrates the robustness and correctness of the employed model MD21.