Elastic modulus prediction for high-temperature treated rock using multi-step hybrid ensemble model combined with coronavirus herd immunity optimizer

Abstract

Elastic modulus is a crucial mechanical parameter that measures the stiffness property of rock materials. In underground rock engineering, such as deep energy development and geological disposal of high-level nuclear waste, accurately determining the elastic modulus of engineering rock masses in high-temperature environments plays a vital role in understanding the instability-triggering conditions of hard and brittle rock masses in deep underground engineering and maintaining the safety and stability of deep underground engineering. Traditionally, conducting indoor experimental tests is time-consuming, labor-intensive, and costly. Therefore, developing a convenient and accurate rock elastic modulus prediction model based on machine learning technology holds significant importance. To this end, this study proposed a multi-step hybrid ensemble model (MHEM) for predicting high-temperature treated rock elastic modulus. The input parameters of the model include diameter, height, density, temperature, confining pressure, crack damage stress, and strength, while the output parameter is the elastic modulus. Subsequently, a coronavirus herd immunity optimizer (CHIO) intelligent optimization algorithm was employed to optimize the MHEM, and the CHIO-MHEM was established. Then, the performance of the developed models was compared and evaluated with eight other different prediction models. Finally, SHAP method and tree model feature analysis were used to quantify the feature importance of the prediction model. The research results indicate that, compared with other prediction models, the CHIO-MHEM exhibits superior performance, achieving accurate prediction of the elastic modulus of rocks treated at different high temperatures. Additionally, among all input parameters, rock density and temperature have the most significant influence on the rock elastic modulus.