Bayesian Learning–Based Data Analysis of Uniaxial Compressive Strength of Rock: Relevance Feature Selection and Prediction Reliability Assessment

Abstract

Estimation on the uniaxial compressive strength (UCS) of rock is an important issue in geotechnical engineering. Empirical relation establishment for UCS estimation is particularly favorable since core sample measurement is expensive, time consuming, and even infeasible. In this paper, two-stage Bayesian learning–based data analysis of UCS of rock is proposed. In the first stage, the sparse Bayesian learning, through the use of the automatic relevance determination (ARD) prior, is adopted to automatically select the relevance features among a set of possible features for the optimal empirical model. In the second stage, the optimal model-based outlier analysis for prediction reliability assessment is performed. The probability of outlier (PO) is utilized as a probabilistic measure for outlierness of a test point. The Gauss–Hermite quadrature is developed for efficiently evaluating the integral for the PO. A binary classification (regular class or outlier class) in the feature space is conducted based on the spatial distribution of the detected regular points and outliers, and the prediction unreliable region is depicted based on the classification result. In the example, the proposed two-stage Bayesian learning is applied for analyzing the UCS of the granite from Macao. The results show that the proposed learning is capable of conducting relevance feature selection and prediction reliability assessment simultaneously.