# A Comprehensive Review of Mechanisms, Predictive Techniques, and Control Strategies of Rockburst
## 5 Rockburst Prediction Methods
### Mathematical Model Approaches  
The factors influencing rockbursts are partly defined and measurable, while others are random, qualitative, and fuzzy [16]. This makes it difficult to establish a suitable mathematical model for rockburst prediction. Data-driven models based on empirical criteria and previous engineering examples can be reliable, but the accuracy of the prediction depends on the amount and quality of data. Rockburst is a complex system influenced by many factors, including some that are uncertain. Research has compared the predicted performance of various data-driven techniques, including uncertainty theory (UT) algorithms, unsupervised learning (UL) algorithms, and supervised learning (SL) algorithms. However, challenges in applying these techniques include insufficient data and the uncertain nature of the rockburst system. As a result, recent theories, such as fuzzy mathematics, rough set theory, and others, have emerged to evaluate rockbursts.  
Unsupervised learning algorithms aim to categorize data without predefined labels. They do this by finding similarities among data and grouping them into clusters. This family of machine learning approaches has been applied in the field of rockburst prediction, where accurate forecasting is crucial due to the catastrophic nature of rockbursts in deep subsurface engineering. Researchers such as [PERSON] [171] have used a fuzzy self-organization map approach in combination with a neural network-based geographical information system to assess rockburst tendency. [PERSON] [157] used hierarchical clustering analysis and the complete linkage method to classify rockburst intensity based on energy as an evaluation index. With the advancement of scientific computing tools, the field of rockburst prediction has seen the integration of modern nonlinear science and artificial intelligence methodologies. Over the years, researchers have explored different supervised learning techniques to predict rockbursts.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index** & **Formula** & **Method** & **The constitutive Model** & **Researchers (Year)** \\ \hline ESS & ESS \(=|\tau|-\sigma_{n}tan\varphi_{d}\) & FLAC & \begin{tabular}{c} Elastic model; CY joint \\ model and MC joint model \\ \end{tabular} & [PERSON], 1988 [49]; [PERSON], 2013 [94] \\ \hline FAI & \begin{tabular}{c} FAI = \(\omega(0<\omega<1)\) \\ or, FAI = \(1+\text{FD}\) \\ (\(\omega=1,\text{FD}\geq 0\)) \\ \end{tabular} & FLAC & \begin{tabular}{c} Elastic-Plastic, Elastic-brittle \\ plastic model \\ \end{tabular} & [PERSON] et al. (2011) [165] \\ \hline LERR & \begin{tabular}{c} LERR\({}_{i}=U_{max}-U_{imin}\) \\ \end{tabular} & FLAC & \begin{tabular}{c} Elastic-brittle plastic model \\ \end{tabular} & [PERSON] et al. (2010) [166] \\ \hline LERD & \begin{tabular}{c} LERD = \(\iint\sigma d\delta A/V\) \\ \end{tabular} & Map3D & Elastic & Wiles, 2005 [167] \\ \hline BPR & \begin{tabular}{c} BPR = \(|K_{p}/K_{e}|\) \\ \end{tabular} & SATURN & Nonlinear & Simon, 1999 [168] \\ \hline OBI & \begin{tabular}{c} OBI = \(F_{cb}/F_{res}\) \\ \end{tabular} & SATURN & Nonlinear & Simon, 1999 [168] \\ \hline BSR & \
\begin{tabular}{c} BSR = \((\sigma_{1}-\sigma_{3})/\sigma_{c}\) \\ \end{tabular} &
\begin{tabular}{c} Map3D FLAC3D, \\ 3 DEC, PFC \\ \end{tabular} & Elastic & Castro et al., 2012 [19] \\ \hline \hline \end{tabular}
\end{table}
Table 8: _Cont._