A method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function

Abstract

This invention discloses a method for locating air leakage sources in goaf areas driven by the second-order curvature of the energy potential function, relating to the field of ventilation safety monitoring technology in coal mine roadways. The method includes: real-time acquisition of dynamic parameters of roadways surrounding the goaf through distributed monitoring units; construction of a spatiotemporal coupling function for the actual energy potential; derivation of a spatiotemporal coupled first-order derivative model of the energy potential slope to obtain the first derivative result; construction of a multi-parameter coupled second-order derivative model of the second-order curvature of the energy potential to obtain the second derivative result; calculation of each energy loss component; based on the calculation results, sequentially solving the first and second derivative results; using a modified Canny edge detection algorithm to extract peak features, calculating the contribution ratio of the second-order partial derivatives of each loss component; and outputting the location of air leakage sources around the goaf based on the spatiotemporal coordinates corresponding to the peak features. This invention achieves precise location of air leakage sources by constructing a spatiotemporally coupled energy potential function system and a second-order derivative model.

Description

Technical Field

[0001] This invention relates to the field of safety monitoring technology for ventilation in coal mine tunnels, and more specifically to a method for locating air leakage sources in goaf areas driven by the second-order curvature of the energy number function. Background Technology

[0002] As a core infrastructure ensuring underground operational safety, coal mine ventilation systems face complex challenges in goaf-side roadways. These challenges include the dynamic development of surrounding rock fissures caused by mining, non-uniform deformation of roadway cross-sections, the evolution of collapsed rock fragmentation and compaction in the goaf, and uneven distribution of residual coal. These factors combine to create multi-path, dynamically evolving, and non-linear leakage channels, leading to frequent and extremely difficult-to-control air leaks. Air leaks not only disrupt the main airflow and significantly reduce ventilation efficiency, but also exacerbate the oxidation rate of residual coal in the goaf through oxygen supply channels, inducing major safety hazards such as gas accumulation and spontaneous combustion. These leaks seriously threaten the lives of underground personnel, disrupt mine production, and cause resource waste and environmental damage.

[0003] Existing technologies for locating air leakage sources around goaf areas mainly include analysis methods based on the first derivative (rate of change) of energy potential, smoke / gas tracer methods, pressure difference monitoring methods, and numerical simulation inversion methods. All of these methods suffer from insurmountable technical bottlenecks, specifically: First, the location accuracy is limited to the section level. Traditional first derivative techniques for energy potential can only quantify the spatial rate of change and identify only "areas of abnormal energy potential change" (typically 10-20 meter-level roadway sections). They cannot capture the local characteristics caused by sudden changes in energy loss when air leakage occurs, making it difficult to accurately pinpoint the critical point of air leakage. The spatiotemporal coordinates are insufficient to meet the core requirement of meter-level positioning for refined prevention and control in high-risk areas surrounding goaf areas; secondly, dynamic adaptability is severely lacking. Existing technologies mostly use static parameters to construct models (such as constant frictional resistance coefficient, fixed local resistance coefficient, initial porosity, etc.), without considering the synergistic effect of wall wear and airflow erosion throughout the entire life cycle of the roadway, the material fatigue attenuation effect of local structures (supports, air doors), the time-varying feedback of the oxidative heat accumulation of residual coal in the goaf area, and the spatial gradient distribution of porosity evolution. This results in significant deviations between the model and actual complex dynamic working conditions. First, the positioning error continues to increase with the extension of service time; second, the anti-interference capability is weak, and it is impossible to effectively decouple the abnormal air leakage from the interference factors. For non-air leakage factors such as the gradual change in resistance caused by roadway deformation, sensor noise generated by equipment operation, and airflow disturbance caused by gas outburst, it is easy to make misjudgments and omissions by judging only a single threshold, which seriously affects the reliability of the positioning results; third, the multi-field coupling effect is not considered. The cross-coupling mechanism of ventilation energy potential field, porosity evolution field of goaf, stress-strain field of surrounding rock, and oxidation heat field of residual coal is not fully integrated, and the stress-strain field of residual coal is ignored. The effects of compression on the roadway cross-section, the disturbance of airflow state by oxidative heat, and the regulatory effect of porosity evolution on the permeability of leakage channels make it difficult to accurately characterize the dynamic propagation law and spatiotemporal evolution characteristics of air leakage in the complex environment surrounding the goaf; fifth, the spatiotemporal characteristics are coarsely characterized, relying only on the single-dimensional rate of change analysis of the first derivative of the energy potential, which cannot quantify the "acceleration of energy potential slope change" caused by sudden changes in air leakage, and it is difficult to capture the nonlinear characteristics of sudden changes in energy consumption, resulting in insufficient timeliness and accuracy in locating air leakage sources, and failing to provide timely and effective technical support for disaster prevention and control.

[0004] To address the technical requirement of "high-precision positioning of air leakage sources around goaf driven by the second-order curvature of the energy number function," it is urgent to overcome the core bottlenecks of existing technologies in terms of positioning accuracy, dynamic adaptability, anti-interference capability, multi-field coupling fusion, and spatiotemporal feature characterization. The goal is to construct a high-precision positioning technology capable of accurately capturing abrupt changes in air leakage characteristics, adapting to complex dynamic working conditions, and effectively distinguishing interference factors. This will provide reliable technical support for ventilation safety control around goaf areas, accurate early warning of air leakage disasters, and prevention of spontaneous combustion of residual coal.

[0005] Therefore, proposing a second-order curvature-driven method for locating air leakage sources in goaf areas to address the difficulties in existing technologies is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function. By constructing a spatiotemporally coupled energy number function system and a second derivative model, the method achieves accurate location of the air leakage source.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for locating air leakage sources in goaf areas driven by the second-order curvature of the energy number function includes the following steps: S1. Real-time collection of dynamic parameters of roadways surrounding the goaf through distributed monitoring units; S2, Constructing a system containing theoretical energy numbers Total energy consumption Disturbance correction item Coupled with goaf area The actual energy number spacetime coupling function is expressed as:

[0008] in, The theoretical energy number is defined by the global constraints of the embedded ventilation network and the discrete effects of local resistance points; α is the real-time frictional resistance coefficient, L is the tunnel section length, and U is the tunnel perimeter. For the Dirac function, For the real-time resistance loss of the k-th local structure, This indicates the location of the local resistance point; Total energy consumption Covering friction loss along the way Local resistance loss air leakage loss and coupling loss in goaf Four types of losses, each loss component is embedded in a dynamic time-varying model:

[0009] Where λ0 is the initial friction coefficient, k1 is the time wear coefficient, and k2 is the air volume correlation coefficient;

[0010] in, The attenuation coefficient is... Let ρ be the wetted perimeter of the tunnel, and ρ be the air density. The initial local drag coefficient, For airflow velocity;

[0011] Where S0 is the cross-sectional area of ​​the entrance, and Q0(t) is the real-time flow rate at the entrance of the tunnel. Here, a and b are the resistance coefficients of the air leakage channel, and a and b are the fitting coefficients. This refers to the real-time air leakage rate.

[0012] Where c is the heat dissipation coefficient. K is the initial temperature, and k4 is the oxidation heat correlation coefficient;

[0013] in, This is the energy level prediction value from the previous moment. To monitor the moving standard deviation of the data, These are the initial weights; S3. Based on the constructed actual potential energy level spatiotemporal coupling function, considering the wind propagation time delay effect, derive the spatiotemporal coupling first derivative model of the potential slope and obtain the first derivative result; The first derivative model expression is: ; S4. Construct a multi-parameter coupled quadratic derivative model of the second-order curvature of the potential, and perform coupled calculations of spatial and temporal partial derivatives on the first derivative result to obtain the quadratic derivative result. The expression for the second derivative model is: ; S5. Input the collected dynamic parameters of the surrounding roadways of the goaf into the constructed spatiotemporal coupling function of the actual energy number, and calculate the result. and each energy loss component; S6. Based on the calculation results of S5, solve for the first derivative of S3 sequentially. The second derivative of S4 ; S7. Extracting edge detection using an improved Canny edge detection algorithm. The peak characteristics are used to calculate the contribution ratio of the second-order partial derivatives of each loss component. S8. Based on the spatiotemporal coordinates corresponding to the peak characteristics Output the location of air leakage sources around the goaf.

[0014] Optionally, the distributed monitoring unit in S1 includes an air volume sensor, a pressure sensor, a temperature sensor, a micro-vibration sensor, and a cross-sectional monitoring device.

[0015] Optional, theoretical energy number in S2 During the calculation process, the location of the local resistance point Local resistance loss is pre-calibrated using 3D tunnel scanning technology. Dynamic correction equations were obtained through experimental fitting based on local structural types, including supports, dampers, and bends.

[0016] Optional, air leakage in the goaf area of ​​S2 The correlation model between the permeability coefficient and potential difference of the goaf is used for auxiliary calculation, and the expression is as follows:

[0017] in, The permeability coefficient of the goaf is obtained through field drilling tests and numerical simulation fitting.

[0018] Optionally, coupling loss in the goaf area of ​​S2 A three-dimensional porosity distribution model of the goaf and its coupling mechanism with oxidation kinetics are introduced, along with the porosity of the goaf. A dynamic evolution equation is constructed based on the rock fragmentation coefficient, compaction degree, and time decay effect:

[0019] in, The initial porosity of the goaf. The porosity attenuation coefficient is... Vertical depth The x-coordinate of the central axis of the goaf; The oxidation kinetic coupling mechanism modifies the time-varying equation for oxidation temperature by introducing the Arrhenius equation. The modified expression is as follows:

[0020] Where kArr is the oxidation kinetic coefficient, The activation energy is given by R, and R is the universal gas constant. Meanwhile, the air leakage in the goaf Solving using the three-dimensional seepage equation:

[0021] in, To ensure that the permeability and porosity of the goaf meet the requirements , Initial penetration rate, The source and sink factors of the goaf are calibrated by coupling field measured data with numerical simulation.

[0022] Optionally, the multi-parameter coupled second-order derivative model of the potential second-order curvature in S4 is further embedded with a correction term for the stress-strain coupling effect of the surrounding rock in the roadway, and the surrounding rock stress Dynamic equations are constructed based on elastoplastic mechanics theory:

[0023] in, The initial surrounding rock stress, The stress evolution coefficient; Stress-strain coupling effect through correction of roadway cross-sectional area To achieve this, the corrected equation is:

[0024] in, The elastic strain coefficient of the surrounding rock. The elastic modulus of the surrounding rock; Meanwhile, an incremental term for the local drag coefficient due to stress is introduced into the second-order curvature calculation:

[0025] Corrected local drag coefficient

[0026] Furthermore, by constructing a modified model of wind and turbulence effects, based on the Reynolds number... , To determine the air kinematic viscosity, a turbulence correction is applied to the second-order curvature of the energy potential, with the correction factor being: , The critical Reynolds number; The final corrected expression for the second-order curvature is: .

[0027] Optionally, S7 employs an improved Canny edge detection algorithm with an adaptive threshold adjustment mechanism to optimize spike recognition performance. The threshold calculation is based on the sliding window... The mean and standard deviation are expressed as: ,in, Within the sliding window The mean, Within the sliding window The standard deviation is calculated, and the sliding window size is set to 5-10 sampling points.

[0028] Optionally, the contribution percentage of the second-order partial derivatives of each loss component in S7 is obtained through normalization calculation, and the contribution percentage of a certain loss component is...

[0029] Where j = along the process, local, air leakage, goaf, when the contribution ratio of the air leakage loss component. If the leakage is abnormal, it is determined to be an air leak; otherwise, it is determined to be another interfering factor.

[0030] As can be seen from the above technical solution, compared with the prior art, the present invention provides a method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function, which has the following beneficial effects: (1) The positioning accuracy is significantly improved, upgrading the traditional segment-level positioning to meter-level positioning, which can accurately lock the critical point of air leakage; (2) It has strong anti-interference ability and can distinguish between air leakage anomaly (abrupt peak) and resistance anomaly (gradual fluctuation) by the peak characteristics of the second derivative, thus reducing misjudgment; (3) It has good dynamic adaptability and can be embedded with a multi-parameter time-varying model to respond in real time to dynamic changes such as roadway wall wear, structural fatigue, and goaf oxidation. (4) It has a wide range of applications and can be adapted to coal mine tunnels of different cross-section types and lengths. It is especially suitable for monitoring high-risk air leakage areas around goaf areas. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0032] Figure 1 A flowchart of a method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function provided by the present invention; Figure 2 The 31110 working surface energy potential diagram provided by the present invention; Figure 3 This is a schematic diagram of the planar arrangement of measuring points on the 31110 working surface provided by the present invention; Figure 4 The energy level diagram of the main transport roadway of the 31110 working face provided by the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] See Figure 1 As shown, this invention discloses a method for locating air leakage sources in goaf areas driven by the second-order curvature of the energy number function, comprising the following steps: S1. Real-time collection of dynamic parameters of roadways surrounding the goaf through distributed monitoring units; S2, Constructing a system containing theoretical energy numbers Total energy consumption Disturbance correction item Coupled with goaf area The actual energy number spacetime coupling function is expressed as:

[0035] in, The theoretical energy number is defined by the global constraints of the embedded ventilation network and the discrete effects of local resistance points; α is the real-time frictional resistance coefficient, L is the tunnel section length, and U is the tunnel perimeter. For the Dirac function, For the real-time resistance loss of the k-th local structure, This indicates the location of the local resistance point; Total energy consumption Covering friction loss along the way Local resistance loss air leakage loss and coupling loss in goaf Four types of losses, each loss component is embedded in a dynamic time-varying model:

[0036] Where λ0 is the initial friction coefficient, k1 is the time wear coefficient, and k2 is the air volume correlation coefficient;

[0037] in, The attenuation coefficient is... Let ρ be the wetted perimeter of the tunnel, and ρ be the air density. The initial local drag coefficient, For airflow velocity;

[0038] Where S0 is the cross-sectional area of ​​the entrance, and Q0(t) is the real-time flow rate at the entrance of the tunnel. Here, a and b are the resistance coefficients of the air leakage channel, and a and b are the fitting coefficients. This refers to the real-time air leakage rate.

[0039] Where c is the heat dissipation coefficient. K is the initial temperature, and k4 is the oxidation heat correlation coefficient;

[0040] in, This is the energy level prediction value from the previous moment. To monitor the moving standard deviation of the data, These are the initial weights; S3. Based on the constructed actual potential energy level spatiotemporal coupling function, considering the wind propagation time delay effect, derive the spatiotemporal coupling first derivative model of the potential slope and obtain the first derivative result; The first derivative model expression is: ; S4. Construct a multi-parameter coupled quadratic derivative model of the second-order curvature of the potential, and perform coupled calculations of spatial and temporal partial derivatives on the first derivative result to obtain the quadratic derivative result. The expression for the second derivative model is: ; S5. Input the collected dynamic parameters of the surrounding roadways of the goaf into the constructed spatiotemporal coupling function of the actual energy number, and calculate the result. and each energy loss component; S6. Based on the calculation results of S5, solve for the first derivative of S3 sequentially. The second derivative of S4 ; S7. Edge detection extracted using an improved Canny edge detection algorithm. Peak characteristics, calculate the contribution ratio of the second-order partial derivatives of each loss component; S8. Based on the spatiotemporal coordinates corresponding to the peak characteristics Output the location of air leakage sources around the goaf.

[0041] Specifically, the expression for the first derivative of the S3 model is: ; When expanded, it appears as follows: = / x-[ / x+ / x+ / x+ / x]+ / x+(1 / v(x,t))·[ / - / t+ / t] The expression for the S4 quadratic derivative model is: ; Expand and substitute The expression yields: ² / x²-[ ² / x²+ ² / x²+ ² / x²+ ² / x²]+ ² / x²+(1 / v(x,t))·[ ² / ( x t)- ² / ( x t)+ ² / ( x t)]-( v(x,t) / x)·(1 / v²(x,t))·[ / t- / t+ / t]+(1 / v(x,t))·[ ² / t²·(1 / v(x,t))- ² / t²·(1 / v(x,t))+ ² / t²·(1 / v(x,t))].

[0042] Furthermore, the distributed monitoring unit in S1 includes an air volume sensor, a pressure sensor, a temperature sensor, a micro-vibration sensor, and a cross-sectional monitoring device.

[0043] Specifically, the measurement accuracies of each sensor are as follows: air volume sensor ±0.1 m³ / s, pressure sensor ±1 Pa, temperature sensor ±0.1 ℃, and cross-sectional monitoring device ±0.01 m².

[0044] Microseismic sensors are used to collect rock fracture propagation signals in real time. When the energy of a microseismic event exceeds 10³J, the monitoring unit density in that area is automatically increased to twice the original density.

[0045] Furthermore, the theoretical energy number in S2 During the calculation process, the location of the local resistance point Local resistance loss is pre-calibrated using 3D tunnel scanning technology. Dynamic correction equations were obtained through experimental fitting based on local structural types, including supports, dampers, and bends.

[0046] Furthermore, the air leakage in the goaf of S2 The correlation model between the permeability coefficient and potential difference of the goaf is used for auxiliary calculation, and the expression is as follows:

[0047] in, The permeability coefficient of the goaf is obtained through field drilling tests and numerical simulation fitting.

[0048] Furthermore, the coupling loss in the goaf area of ​​S2 A three-dimensional porosity distribution model of the goaf and its coupling mechanism with oxidation kinetics are introduced, along with the porosity of the goaf. A dynamic evolution equation is constructed based on the expansion coefficient, compaction degree, and time decay effect of collapsed rock:

[0049] in, The initial porosity of the goaf. The porosity attenuation coefficient is... Vertical depth The x-coordinate of the central axis of the goaf; The oxidation kinetic coupling mechanism modifies the time-varying equation for oxidation temperature by introducing the Arrhenius equation. The modified expression is as follows:

[0050] Where kArr is the oxidation kinetic coefficient, The activation energy is given by R, and R is the universal gas constant. Meanwhile, the air leakage in the goaf Solving using the three-dimensional seepage equation:

[0051] in, To ensure that the permeability and porosity of the goaf meet the requirements , Initial penetration rate, The source and sink factors of the goaf are calibrated by coupling field measured data with numerical simulation.

[0052] Furthermore, the multi-parameter coupled second-order derivative model of the second-order curvature of the potential in S4 is further embedded with a correction term for the stress-strain coupling effect of the surrounding rock in the tunnel, and the surrounding rock stress... Dynamic equations are constructed based on elastoplastic mechanics theory:

[0053] in, The initial surrounding rock stress, The stress evolution coefficient; Stress-strain coupling effect through correction of roadway cross-sectional area To achieve this, the corrected equation is:

[0054] in, The elastic strain coefficient of the surrounding rock. The elastic modulus of the surrounding rock; Meanwhile, an incremental term for the local drag coefficient due to stress is introduced into the second-order curvature calculation:

[0055] Corrected local drag coefficient

[0056] Furthermore, by constructing a modified model of wind and turbulence effects, based on the Reynolds number... , To determine the air kinematic viscosity, a turbulence correction is applied to the second-order curvature of the energy potential, with the correction factor being: , The critical Reynolds number; The final corrected expression for the second-order curvature is: .

[0057] Specifically, in the calculation process of the second-order curvature model of potential in S4, the finite difference method is used to solve the partial derivatives, with the spatial step size set to 0.1-0.5 meters and the time step size set to 0.1-1 seconds to ensure the accuracy and real-time performance of the derivative calculation.

[0058] Furthermore, S7 employs an improved Canny edge detection algorithm that optimizes spike recognition performance through an adaptive threshold adjustment mechanism. The threshold calculation is based on the sliding window... The mean and standard deviation are expressed as: ,in, Within the sliding window The mean, Within the sliding window The standard deviation is calculated, and the sliding window size is set to 5-10 sampling points.

[0059] Furthermore, the contribution percentage of the second-order partial derivatives of each loss component in S7 is obtained through normalization calculation, and the contribution percentage of a certain loss component is...

[0060] Where j = along the process, local, air leakage, goaf, when the contribution ratio of the air leakage loss component. If the leakage is abnormal, it is determined to be an air leak; otherwise, it is determined to be another interfering factor.

[0061] Specifically, the method of the present invention is applicable to coal mine roadways with different cross-sectional types such as rectangular, trapezoidal, and circular, and can be adapted to ventilation systems around goaf areas with roadway lengths of 100-5000 meters and cross-sectional areas of 4-20 m².

[0062] Specifically, in S8, the spatiotemporal coordinates corresponding to the peak features are... The specific steps for locating the air leakage sources around the goaf are as follows: Data acquisition involves real-time collection of the cross-sectional area corresponding to the axial distance x and time t of the roadway via a distributed monitoring unit. Air volume Friction resistance coefficient Dynamic parameters, sampling frequency not less than 10Hz; Basic calculations are performed by substituting the collected parameters into the actual energy number spatiotemporal coupling function to obtain the results. and each energy loss component; Solving for the derivative involves calculating the derivative once for each iteration. and the result of the second derivative ; Feature recognition is performed using an improved Canny edge detection algorithm. The peak characteristics, combined with the contribution ratio of the second-order partial derivatives of each loss component, eliminate the interference of abnormal resistance. Location output, based on the spatiotemporal coordinates corresponding to the peak features. It outputs the location of the air leakage source with a positioning accuracy of ±0.5 meters.

[0063] Example 1: High-precision positioning of air leakage sources around goaf areas driven by the second-order curvature of the energy number function of the present invention

[0064] 1.1 Implementation Scenarios

[0065] This embodiment is applied to the roadway surrounding the goaf of the 31110 main haulage roadway in a coal mine (see the schematic diagram of the measuring point layout for the 31110 working face). Figure 3 As shown, the roadway is 1500m long, with a trapezoidal cross-section and a designed cross-sectional area of ​​8m². The entrance cross-sectional area is S0=8m², and the roadway section length is L=50m. The wetted perimeter of the roadway, P(x,t), changes dynamically with the axial distance x (range 8-12m). The distance between the goaf and the roadway sidewall is 5-15m. The test range of the working face includes measuring points 1-23, involving airflow convergence points and sealed wall areas. There are complex working conditions such as the development of surrounding rock fissures and the accumulation of oxidative heat from residual coal. It is necessary to accurately locate the air leakage source to prevent the risk of spontaneous combustion.

[0066] 1.2 Monitoring Equipment Configuration

[0067] A distributed multi-parameter synchronous monitoring system was adopted, and equipment was deployed in the 31110 main haulage roadway and related roadways (corresponding to test routes 1→2→3→4→5→6): Air volume sensor: Measurement range 0-20 m³ / s, accuracy ±0.1 m³ / s, sampling frequency 10 Hz, deployed at measuring points 1, 3, and 6; Pressure sensor: Measurement range 0-5000 Pa, accuracy ±1 Pa, sampling frequency 10 Hz, deployed at measuring points 2, 4, and 5; Temperature sensor: Measurement range 0-100℃, accuracy ±0.1℃, sampling frequency 10 Hz, deployed at measuring points 3 and 5 near the goaf; Cross-section monitoring equipment: Measurement range 4-20 m², accuracy ±0.01 m², sampling frequency 5 Hz, deployed throughout the main haulage roadway; Data acquisition terminal: Supports synchronous storage and transmission of multi-sensor data, delay ≤0.1 s, deployed in the working face control chamber.

[0068] 1.3 Known parameter settings are shown in Table 1.

[0069] Table 1 Parameter Settings

[0070] 1.4 Location Execution Process

[0071] Step 1: Data Collection

[0072] Along the test route of the 31110 main transport roadway (1→2→3→4→5→6), dynamic parameters were collected at x=1000m (corresponding to measuring point 5) and t=300s: The cross-sectional area of ​​the tunnel is S(1000,300) = 7.5 m²; Real-time air volume Q(1000,300) = 8.2 m³ / s; The wetted perimeter of the tunnel is P(1000,300) = 10m; The airflow velocity v(1000,300) = Q(1000,300) / S(1000,300) = 1.093 m / s; Real-time temperature of the goaf θ(1000,300) = 25 + 0.02 × 0³ 00 Q is mined out (1000, )d =34℃.

[0073] Step 2: Calculation of actual potential energy (energy potential diagram of the 31110 working face as shown in the figure) Figure 2 (As shown)

[0074] 1. Theoretical energy number :

[0075] =1400+0.5×300- 0¹ 000 [0.02×50×10×8.2² / 7.5³]d -2×50× (0.0001×300)

[0076] =1550-1000×0.254-103.05

[0077] =1280 Pa

[0078] 2. Total energy consumption : Friction loss along the way : λ(1000,300)=λ0+k1t+k2 0 t Q(1000, )d

[0079] = 0.02 + 5×10-5 ×300 + 2×10 -6 ×8.2×300

[0080] = 0.03992 λ(1000,300)·[4S(1000,300) / P(1000,300)]·[ρQ²(1000,300) / (2S²(1000,300))] = 0.03992×(4×7.5 / 10)×(1.2×8.2² / (2×7.5²)) = 32.5 Pa Local resistance loss : (1000, 300) = 0· (k3t)=0.8× (1×10 -4 (×300)=0.8244 ΔE local(1000,300)= (1000,300)·[ρv²(1000,300) / 2] =0.8244×(1.2×1.093² / 2)=0.62 Pa air leakage loss : (1000,300)=Q(1000,300)-Q0(300)·[S(1000,300) / S0] = 8.2 - 10 × (7.5 / 8) = -1.175 m³ / s (absolute value is taken as 1.175) (1000)=a+b×1000=50+0.1×1000 = 150 Pa·s² / m 6 (1000, 300) = ρ·[ ²(1000,300) / (2S²(1000,300))]+ (1000)· ²(1000,300) =1.2×(1.175² / (2×7.5²))+150×1.175² =0.014 + 18.29 = 18.3 Pa Coupling loss in goaf (1000, 300): (1000,300)=c·θ(1000,300)· (1000, 300) = 1.2×34×(0.5+0.005×1000)=22.7Pa Total energy consumption: (1000,300)=32.5+0.62+18.3+22.7=74.12 Pa 3. Disturbance Correction Term (1000, 300): α(1000,300)=α(1000,299)·[| (1000,299)- (1000,299)| / σ(1000,300)]≈0.125 (1000,300)=α(1000,300)·σ(1000,300)=0.125×1.2=0.15 Pa 4. Actual number of energy points: (1000,300)=1280-74.12+0.15=1206.03 Pa Step 3: Solving for the derivative (the theoretical potential slope and the actual potential slope of the 31110 working surface are as follows) Figure 4 (As shown) 1. First derivative (potential slope) ): (1000,300) / x=-[αLUQ²(1000,300) / S³(1000,300)]=-0.254 Pa / m (1000,300) / x=k2Q(1000,300)·[4S(1000,300) / P(1000,300)]·[ρQ²(1000,300) / (2S²(1000,300))]=0.003 Pa / m (1000,300) / x=b· ²(1000,300)=0.1×1.175²=0.08 Pa / m (1000,300) / x = 0.01 Pa / m (based on sensor spatial gradient calibration) (1000,300) / t=0.5 Pa / s Δ (1000,300) / t=0.002 Pa / s (1000, 300) = -0.254 - (0.003 + 0.08 + 0.01) + 0.01 + [1 / 1.093] × (0.5 - 0.002) =-0.246+0.457=0.211 Pa / m 2. Second derivative (energy potential curvature) ): ² (1000,300) / x²=0 ² (1000,300) / x² = 0.1 × 2 × | (1000,300)|×(-Q0(300) / S0) = -0.03Pa / m² v(1000,300) / x= / x[Q(1000,300) / S(1000,300)] = 0.0009 m / (s·m) ² (1000,300) / ( x t)=0 ²Δ (1000,300) / ( x t) = 0.0001 Pa / (m·s) K''(1000,300)=0-(-0.03)+[1 / 1.093]×(0-0.0001)-0.0009×(1 / 1.093²)×(0.5-0.002)=0.03-0.00009-0.00037=0.0295 Pa / m² Step 4: Feature Recognition and Interference Elimination An improved Canny edge detection algorithm was adopted, with a sliding window size of 8 sampling points, and the threshold T = 0.011 Pa / m² was calculated. K''(1000,300)=0.0295 Pa / m²>T, triggering peak feature recognition; Calculate the contribution percentage of the second-order partial derivatives of each loss component: =| ² / x²| / Σ| ²ΔE_j / x²|=0.03 / (0.03+0.001+0.0005)=95.2%>85% The problem was determined to be an air leakage anomaly, and abnormal resistance and equipment noise interference were ruled out.

[0081] Step 5: Positioning Output

[0082] Based on the spatiotemporal coordinates corresponding to the peak feature (x=1000m (measuring point 5 of the 31110 main transport roadway), t=300s), the location of the air leakage source is output with a positioning accuracy of ±0.5m, which is consistent with the on-site drilling verification results (the actual air leakage point is located at x=1000.3m next to measuring point 5).

[0083] Comparative Example 1: Traditional method for locating leakage sources by first derivative of energy number (based on the No. 31 coal face)

[0084] 1.1 Comparative Technical Solution

[0085] Using existing technology, based on the data from measuring points 1-23 of the 31110 main haulage roadway working face of coal seam 31, the core logic is as follows: 1. Construct a static energy number model using fixed parameters (λ=0.02, ξ=0.8); 2. Calculate only the potential slope (first derivative), and set a threshold K. th =0.2Pa / m; 3. Collect data along the test route 23→22→20→19→22→11→12→13, without introducing disturbance correction and goaf coupling terms; 4. The location results output "Air Leakage Area" (50m segment level).

[0086] 1.2 Implementation process of the comparative model

[0087] Step 1: Data Collection

[0088] Along the test route 23→22→20→19→22→11→12→13, obtain the potential data for x=950-1050m (corresponding to the interval of measuring points 11-22).

[0089] Step 2: Calculation of the number of energy points and first derivative

[0090] Static energy number model: (x,t)= (t)- 0 x (λLUQ² / S³)dξ-ΣΔ ,k; x = 950m (measuring point 11): =1320Pa, =-0.24Pa / m; x = 1000m (measuring point 22): =1290Pa, =-0.26Pa / m; x=1050m (measuring point 13): =1260Pa, = -0.28Pa / m.

[0091] Step 3: Leakage detection and location output

[0092] Theoretical potential slope =-0.254Pa / m; Within the interval x=950-1050m | - The threshold value indicates that the 50m section is an air leakage area, but no specific air leakage point is output (corresponding to the measurement point interval of 11-22).

[0093] 1.3 Performance comparison between Example 1 and Comparative Example 1 is shown in Table 2.

[0094] Table 2 Performance Comparison of Example 1 and Comparative Example 1

[0095] 1.4 Comparative Conclusions

[0096] Through actual measurement comparisons at the 31110 main haulage roadway working face of Coal Mine No. 31, it can be seen that the present invention achieves meter-level precise positioning of air leakage sources around the goaf of the working face, solving the defect of traditional technology that can only identify section-level areas, and providing reliable support for ventilation safety control of the working face.

[0097] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0098] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for locating air leakage sources in goaf areas driven by the second-order curvature of the energy number function, characterized in that, Includes the following steps: S1. Real-time collection of dynamic parameters of roadways surrounding the goaf through distributed monitoring units; S2, Constructing a system containing theoretical energy numbers Total energy consumption Disturbance correction item Coupled with goaf area The actual energy number spacetime coupling function is expressed as: in, The theoretical energy number is defined by the global constraints of the embedded ventilation network and the discrete effects of local resistance points; α is the real-time frictional resistance coefficient, L is the tunnel section length, and U is the tunnel perimeter. For the Dirac function, For the real-time resistance loss of the k-th local structure, This indicates the location of the local resistance point; Total energy consumption Covering friction loss along the way Local resistance loss air leakage loss and coupling loss in goaf Four types of losses, each loss component is embedded in a dynamic time-varying model: Where λ0 is the initial friction coefficient, k1 is the time wear coefficient, and k2 is the air volume correlation coefficient; in, The attenuation coefficient is... Let ρ be the wetted perimeter of the tunnel, and ρ be the air density. The initial local drag coefficient, For airflow velocity; Where S0 is the cross-sectional area of ​​the entrance, and Q0(t) is the real-time flow rate at the entrance of the tunnel. Here, a and b are the resistance coefficients of the air leakage channel, and a and b are the fitting coefficients. This refers to the real-time air leakage rate. Where c is the heat dissipation coefficient. K is the initial temperature, and k4 is the oxidation heat correlation coefficient; in, This is the energy level prediction value from the previous moment. To monitor the moving standard deviation of the data, These are the initial weights; S3. Based on the constructed actual potential energy level spatiotemporal coupling function, considering the wind propagation time delay effect, derive the spatiotemporal coupling first derivative model of the potential slope and obtain the first derivative result; The first derivative model expression is: ； S4. Construct a multi-parameter coupled quadratic derivative model of the second-order curvature of the potential, and perform coupled calculations of spatial and temporal partial derivatives on the first derivative result to obtain the quadratic derivative result. The expression for the second derivative model is: ； S5. Input the collected dynamic parameters of the surrounding roadways of the goaf into the constructed spatiotemporal coupling function of the actual energy number, and calculate the result. and each energy loss component; S6. Based on the calculation results of S5, solve for the first derivative of S3 sequentially. The second derivative of S4 ; S7. Extracting edge detection using an improved Canny edge detection algorithm. The peak characteristics are used to calculate the contribution ratio of the second-order partial derivatives of each loss component. S8. Based on the spatiotemporal coordinates corresponding to the peak characteristics Output the location of air leakage sources around the goaf.

2. The method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function according to claim 1, characterized in that, The distributed monitoring unit in S1 includes air volume sensors, pressure sensors, temperature sensors, micro-vibration sensors, and cross-section monitoring equipment.

3. The method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function according to claim 1, characterized in that, Theoretical energy number in S2 During the calculation process, the location of the local resistance point Local resistance loss is pre-calibrated using 3D tunnel scanning technology. Dynamic correction equations were obtained through experimental fitting based on local structural types, including supports, dampers, and bends.

4. The method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function according to claim 1, characterized in that, S2 goaf air leakage The correlation model between the permeability coefficient and potential difference of the goaf is used for auxiliary calculation, and the expression is as follows: in, The permeability coefficient of the goaf is obtained through field drilling tests and numerical simulation fitting.

5. The method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function according to claim 1, characterized in that, Coupling loss in the goaf area of ​​S2 A three-dimensional porosity distribution model of the goaf and its coupling mechanism with oxidation kinetics are introduced, along with the porosity of the goaf. A dynamic evolution equation is constructed based on the rock fragmentation coefficient, compaction degree, and time decay effect: in, The initial porosity of the goaf. The porosity attenuation coefficient is... Vertical depth The x-coordinate of the central axis of the goaf; The oxidation kinetic coupling mechanism modifies the time-varying equation for oxidation temperature by introducing the Arrhenius equation. The modified expression is as follows: Where kArr is the oxidation kinetic coefficient, The activation energy is R, and the universal gas constant is R. Meanwhile, the air leakage in the goaf Solving using the three-dimensional seepage equation: in, To ensure that the permeability and porosity of the goaf meet the requirements , Initial penetration rate, The source and sink factors of the goaf are calibrated by coupling field measured data with numerical simulation.

6. The method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function according to claim 1, characterized in that, The S4 model, with its multi-parameter coupled second-order derivative and potential second-order curvature, further incorporates a correction term for the stress-strain coupling effect of the surrounding rock in the tunnel. Dynamic equations are constructed based on elastoplastic mechanics theory: in, The initial surrounding rock stress, The stress evolution coefficient; Stress-strain coupling effect through correction of roadway cross-sectional area To achieve this, the corrected equation is: in, The elastic strain coefficient of the surrounding rock. The elastic modulus of the surrounding rock; Meanwhile, an incremental term for the local drag coefficient due to stress is introduced into the second-order curvature calculation: Corrected local drag coefficient Furthermore, by constructing a modified model of wind and turbulence effects, based on the Reynolds number... , To determine the air kinematic viscosity, a turbulence correction is applied to the second-order curvature of the energy potential, with the correction factor being: , The critical Reynolds number; The final corrected expression for the second-order curvature is: .

7. The method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function according to claim 1, characterized in that, S7 employs an improved Canny edge detection algorithm with an adaptive threshold adjustment mechanism to optimize spike recognition performance. Threshold calculation is based on the sliding window... The mean and standard deviation are expressed as: ,in, Within the sliding window The mean, Within the sliding window The standard deviation is calculated, and the sliding window size is set to 5-10 sampling points.

8. The method for locating air leakage sources in goaf driven by the second-order curvature of the energy number function according to claim 1, characterized in that, The contribution percentage of the second-order partial derivatives of each loss component in S7 is obtained through normalization calculation; the contribution percentage of a certain loss component... Where j = along the process, local, air leakage, goaf, when the contribution ratio of the air leakage loss component. If the leakage is abnormal, it is determined to be an air leak; otherwise, it is determined to be another interfering factor.

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