# GNSS-Based Monitoring Methods for Mining Headframes
## 4 Correlation Analysis and Risk Assessment
### Correlation Analysis of Deformation Factors  
In this study, the Pearson correlation coefficient (PCC) method [33] integrated within SPSS software is employed to evaluate interdependencies among deformation factors. The PCC quantifies the linear association between two continuous variables, with its value  
Figure 6: Base state with amendments model of some monitoring stations. falling within the interval \([-1,1]\). A value approaching \(+1\) indicates a strong positive linear relationship between variables, while a value nearing \(-1\) reflects a pronounced negative linear correlation. Coefficients close to zero suggest the absence of a statistically significant linear relationship. The computational formula governing this metric is presented below:  
\[r=\frac{l_{xy}}{\sqrt{l_{xx}l_{yy}}}=\frac{\sum\limits_{i=1}^{n}{{{(x-\widetilde {x})}(y-\widetilde{y})}/{{(n-1)}}}}{\sqrt{\sum\limits_{i=1}^{n}{{{(x-\widetilde {x})}^{2}}/{{(n-1)}}}}\cdot\sqrt{\sum\limits_{i=1}^{n}{{{(y-\widetilde{y})}^{2 }}/{{(n-1)}}}}} \tag{7}\]  
where are the corresponding random variables, \(n\) is the sample size, the numerator part is the covariance, and the denominator part is the product of their respective standard deviations. On the basis of deformation characteristics, the vertical distance of the monitoring station from the ground (hereinafter referred to as \"height\") and the distance of the monitoring station from the sheave wheel axis (hereinafter referred to as \"sheave wheel distance\") are set as the inducing factors for headframe deformation. When the effect of height on headframe deformation is explored, with sheave wheel distance held constant, the monitoring stations XTL-L and STL-L are used as height groups for comparative analysis of correlation based on different heights. When the effect of sheave wheel distance on headframe deformation is evaluated, with height held constant, the monitoring station XTL-L, which is closer to the sheave wheel, and the monitoring station JC02, which is farther away, are employed as sheave wheel distance groups for comparative analysis of correlation. The Pearson correlation coefficients of each factor on headframe deformation are calculated using SPSS software, and an assessment of correlation is performed. The correlations between height and deformation and between sheave wheel distance and deformation are shown in Tables 1 and 2, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \(\Delta\)**X/mm** & \(\Delta\)**Y/mm** & \(\Delta\)**H/mm** & **Height** \\ \hline \(\Delta\)X/mm & Pearson Correlation & \(1\) & \(-0.10\) & \(0.16\) & \(0.03\) \\  & Number of Cases & \(448\) & \(448\) & \(448\) & \(448\) \\ \hline \(\Delta\)Y/mm & Pearson Correlation & \(-0.10\) & \(1\) & \(-0.14\) & \(0.11\) \\  & Number of Cases & \(448\) & \(448\) & \(448\) & \(448\) \\ \hline \(\Delta\)H/mm & Pearson Correlation & \(0.16\) & \(-0.14\) & \(1\) & \(0.43\) \\  & Number of Cases & \(448\) & \(448\) & \(448\) & \(448\) \\ \hline Height & Pearson Correlation & \(0.03\) & \(0.11\) & \(0.43\) & \(1\) \\  & Number of Cases & \(448\) & \(448\) & \(448\) & \(448\) \\ \hline \end{tabular}
\end{table} 
Table 1: Correlation between height and deformation. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \(\Delta\)**X/mm** & \(\Delta\)**Y/mm** & \(\Delta\)**H/mm** & **Sheave Wheel Distance** \\ \hline \(\Delta\)X/mm & Pearson Correlation & \(1\) & \(-0.09\) & \(0.22\) & \(0.70\) \\  & Number of Cases & \(448\) & \(448\) & \(448\) & \(448\) \\ \hline \(\Delta\)Y/mm & Pearson Correlation & \(-0.09\) & \(1\) & \(-0.12\) & \(0.67\) \\  & Number of Cases & \(448\) & \(448\) & \(448\) & \(448\) \\ \hline \(\Delta\)H/mm & Pearson Correlation & \(0.22\) & \(-0.12\) & \(1\) & \(0.09\) \\  & Number of Cases & \(448\) & \(448\) & \(448\) & \(448\) \\ \hlineFrom the results in Tables 1 and 2, the Pearson correlation coefficients for the height factor with \(\Delta\)X, \(\Delta\)Y, and \(\Delta\)H are all below 0.42.