## 6 Dynamic Regulation Evaluation Methodology for Strata Pressure Manifestations
is adopted as the corresponding threshold for high-speed operations. When thresholds are breached, the advance rate is reduced by two cutting cycles/d (equivalent to ~1.2 m/d) until energy stabilizes. To conduct a more precise analysis of microseismic energy variations under different mining advance rates, the relationship between daily total energy and event frequency was extracted from the dataset in Figures 20 and 21 for specific advancement velocities of 0 m/d, 2 m/d, 4 m/d, 6 m/d, 8 m/d, 10 m/d, and 12 m/d. The statistical compilation of these extracted correlations is systematically presented in Figure 24.  
The statistical regression model correlating mining advance rates with daily cumulative microseismic energy release, derived from scatter data analysis, is mathematically expressed as  
\[y_{1}=908.366v_{s}+24195.43 \tag{17}\]  
The scatter plot-derived empirical formula characterizing the correlation between mining advance rates and daily microseismic event frequency is mathematically defined as  
\[y_{2}=-0.04384v_{s}{}^{2}+0.65306v_{s}+2.40326 \tag{18}\]  
As evidenced by the analytical results presented in Figure 24, the mining advance rate demonstrates a linear correlation with daily cumulative microseismic energy release while exhibiting a nonlinear relationship with daily microseismic event frequency. Notably, when the working face advance rate exceeds 6 m/d, a distinct decline in microseismic event frequency is observed, accompanied by a stabilization of energy-frequency coupling dynamics. The daily single-event microseismic energy \(E_{w}\) is employed to assess the influence of the face advancing rate vs. on strata pressure manifestations, expressed as \(E_{w}=y_{1}/y_{2}\), where \(y_{1}\) represents the functional relationship between the daily total microseismic energy and advancing rate, and \(y_{2}\) denotes the correlation between the daily microseismic event frequency and advancing rate. This formulation thus establishes the mathematical relationship between the daily single-event microseismic energy \(E_{w}\) and face advancing rate \(v_{s}\):  
\[E_{w}=\frac{908.366v_{s}+24195.43}{-0.04384v_{s}^{2}+0.65306v+2.40326} \tag{19}\]  
Figure 24: Scatter plots of daily microseismic energy vs. frequency under different advance rates. Higher single-event microseismic energy values correlate with an increased likelihood of inducing strata pressure manifestations. This causal relationship is graphically represented in Figure 25, which illustrates the correlation curve between the face advancing rate and single-event microseismic energy. As illustrated in Figure 25, the daily single-event microseismic energy attains its minimum value at an advance rate of 6 m/d, corresponding to a reduced probability of high-energy events. When the advance rate falls below 6 m/d, the energy released per microseismic event exhibits a linear increasing trend. Conversely, at advance rates exceeding 6 m/d, the single-event energy demonstrates a nonlinear growth pattern. From the perspective of microseismic energy optimization, the most rational advance rate for the 12308 working face is determined to be 6 m/d. Based on the case conditions of this study, the optimal excavation rate of 6 m/d can serve as a preliminary recommended value. However, in practical applications, it should be dynamically adjusted according to the engineering context. For instance, if the roof strata exhibit high joint density or the mudstone contains elevated water content, the excavation rate should be reduced to prevent roof instability. The aforementioned regulation methodology has been implemented at the Hongqingliang Coal Mine. This approach not only effectively confines strata pressure manifestations within safe and rational thresholds but also ensures consistent production output. Furthermore, it provides actionable guidance for strata pressure control, achieving a 73% reduction in support yield incidents and maintaining shield resistance within 92-98% of the rated capacity (15,000 kN) during high-speed phases.