An adaptive relaxation factor ventilation network solution method based on global air volume residual feedback

Abstract

The present application relates to a kind of based on global air volume residual feedback's adaptive relaxation factor ventilation network solution method, the method includes the following steps: step 1: ventilation network model establishment and parameter initialization;Step 2: calculate branch air volume and node air volume imbalance value;Step 3: calculate global air volume residual norm;Step 4: calculate adaptive relaxation factor;Step 5: revise node pressure;Step 6: convergence judgment and iteration;The convergence performance of the scheme is greatly improved, and the convergence success rate in complex ventilation network is improved to more than 98% from 58.8% of traditional method;Computational efficiency is obviously improved, and the average iteration number is reduced by about 45%, and the calculation time is shortened by more than 40%.

Description

Technical Field

[0001] This invention relates to a method, specifically an adaptive relaxation factor ventilation network solution method based on global airflow residual feedback, belonging to the field of mine ventilation engineering calculation technology. Background Technology

[0002] In the design and analysis of mine ventilation systems, ventilation network solution is a fundamental and crucial technical step. The commonly used Scott-Hinsley iterative algorithm has significant limitations in practical applications. With the expansion of mining scale and the increasing complexity of ventilation systems, traditional algorithms frequently encounter problems such as iterative oscillations, divergence, or excessively slow convergence when dealing with ventilation networks containing multiple levels of equipment stations, numerous air doors, and complex closed loops.

[0003] Existing improvement methods mostly focus on optimizing the algorithm's periphery or rely on empirical parameter adjustments, failing to fundamentally solve the convergence problem of the algorithm's core. This often necessitates multiple trials of different initial value settings in engineering practice, severely impacting the efficiency and reliability of ventilation design. Current technologies lack an adaptive relaxation factor adjustment mechanism based on global airflow residual feedback to address the convergence problem in ventilation network solutions; therefore, a new approach is urgently needed to solve this technical issue. Summary of the Invention

[0004] This invention addresses the technical problems existing in the prior art by providing an adaptive relaxation factor ventilation network solution method based on global airflow residual feedback. This invention solves the problems of poor convergence, insufficient stability, and sensitivity to initial values ​​in traditional ventilation network solution algorithms in complex networks.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: an adaptive relaxation factor ventilation network solution method based on global airflow residual feedback, the method comprising the following steps:

[0006] Step 1: Establishing the ventilation network model and initializing parameters

[0007] Input parameters such as the ventilation network topology, branch resistance, and fan characteristic curves. Set the initial pressure value P0 for all nodes, specify the convergence accuracy ε, and initialize the adaptive parameters (ω). max , ω min , γ). Where: ω max ω is the maximum relaxation factor, used to accelerate convergence in the early stages of iteration; it is typically set to 1.2-1.8. minγ is the minimum relaxation factor, used to ensure numerical stability in the later stages of iteration, and is usually taken as 0.3-0.7; γ is the decay coefficient, which is adaptive to the network size and is used to adjust the rate of change of the relaxation factor. It can be initially estimated according to γ ​​= 0.5 · log(N) + 0.5, where N is the number of network branches.

[0008] Step 2: Calculate the imbalance value between branch air volume and node air volume.

[0009] Based on the node pressure value P at the current iteration step k k The air volume Q of all branches is calculated based on the law of ventilation resistance. j k :

[0010] Q j k = sign(ΔP j ) · (|ΔP j | / R j ) 0.5

[0011] Where: ΔP j R represents the pressure difference between the beginning and end nodes of branch j. j Let be the wind resistance value of branch j.

[0012] Subsequently, based on the airflow balance condition, the airflow imbalance value ΔQ for each node i is calculated. i k .

[0013] Step 3: Calculate the global airflow residual norm

[0014] Solve for the global airflow residual norm ||ΔQ|| in this iteration. k ‖2, which represents the convergence state of the entire ventilation network in the current iteration step:

[0015] ||ΔQ k ||2 = (Σ(ΔQ)| ... i k )²) 0.5

[0016] Step 4: Calculate the adaptive relaxation factor

[0017] The relaxation factor for the current iteration step is dynamically calculated based on the global airflow residual norm.

[0018] ω k = ω min + (ω max - ω min ) · exp(-γ · (‖ΔQ k ||2 / ||ΔQ 0 ‖2))

[0019] In the formula: ||ΔQ 0 ||2 represents the norm of the initial air volume residual.

[0020] This exponential decay model ensures that the algorithm uses a larger step size to quickly approximate the solution in the early stages of iteration, and a smaller step size to achieve fine convergence in the later stages of iteration.

[0021] Step 5: Correct node pressure

[0022] Construct the wind resistance matrix A of the ventilation network, where:

[0023] diagonal element A mm =∑(1 / R j ), where j represents all branches connected to node m;

[0024] off-diagonal element A mn If there is a branch connecting node m and node n, then A mn =−1 / R mn If there is no directly connected branch A between node m and node n. mn =0.

[0025] Solve the linear system of equations A · ΔP corr k = -ΔQ k The pressure correction ΔP is obtained. corr k And an adaptive relaxation factor is used to correct the node pressure:

[0026] P k+1 = P k + ω k · ΔP corr k

[0027] Step 6: Convergence assessment and iteration

[0028] If the current global airflow residual norm satisfies ||ΔQ k If ||2 < ε, the algorithm is considered converged, and the solution results (including pressure at each node, airflow at each branch, etc.) are output; otherwise, the iteration step number k = k+1 is set, and the algorithm returns to step 2 to continue iterative calculation. A maximum number of iterations can be set to prevent infinite loops.

[0029] Compared with existing technologies, this invention has the following advantages: 1. The convergence performance is greatly improved, with the convergence success rate in complex ventilation networks increasing from 58.8% in traditional methods to over 98%; 2. The computational efficiency is significantly improved, with the average number of iterations reduced by about 45% and the computation time shortened by more than 40%; 3. The algorithm robustness is enhanced, with the sensitivity to initial values ​​reduced by more than 60%.

[0030] 4. It has a wide range of applications and can adapt to ventilation networks of different sizes through parameter self-adaptation mechanism. Attached Figure Description

[0031] Figure 1 Here is a flowchart of the ventilation network solution algorithm.

[0032] Figure 2 A comparison chart of convergence characteristics for ventilation network solutions. Detailed Implementation

[0033] To enhance understanding of the present invention, the embodiments will be described in detail below with reference to the accompanying drawings.

[0034] Example 1: See Figure 1 , Figure 2 An adaptive relaxation factor ventilation network solution method based on global airflow residual feedback is described below:

[0035] Step 1: Establishing the ventilation network model and initializing parameters

[0036] A ventilation system in a metal mine was selected as a test case. The network contains 285 nodes and 376 branches, with 3 main fans and 15 sets of regulating dampers. Input network topology data, including: node coordinates, branch connections (branch start and end node numbers), and branch resistance values ​​(range 0.15-2.6 N·s² / m). 8 ), main fan characteristic curve parameters. Set the initial pressure value P for all nodes. 0 = 0 Pa, convergence accuracy ε = 0.1 m³ / s, adaptive parameter value: ω max = 1.6, ω min = 0.5, γ = 0.5 × ln(376) + 0.5 ≈ 3.4.

[0037] Step 2: Calculate the imbalance value between branch air volume and node air volume.

[0038] Taking the k=0th iteration as an example, based on the initial pressure P 0 Calculate the air volume of each branch. For example, if branch j=25, connect nodes 12 and 38, ΔP 25 = 0 Pa, R 25= 0.82 N·s² / m 8 Then Q 25 0 = 0 m³ / s. Calculate the airflow imbalance value for all nodes. For example, at node i=57, the sum of the inflow to the branch is 12.5 m³ / s, and the sum of the outflow to the branch is 13.8 m³ / s. Then ΔQ 57 0 = -1.3 m³ / s.

[0039] Step 3: Calculate the global airflow residual norm

[0040] Calculate the initial global airflow residual norm ||ΔQ 0 2. Sum of squares of the airflow imbalance values ​​at 285 nodes:

[0041] Σ(ΔQᵢ 0 )² = 548.6 (m³ / s)², so ‖ΔQ 0 ||2 = (548.6) 0.5 ≈ 23.42 m³ / s.

[0042] Step 4: Calculate the adaptive relaxation factor

[0043] During the first iteration, the global airflow residual ||ΔQ 0 ||2 = 23.42 m³ / s, substituting into the formula: ω 0 = 0.5 + (1.6- 0.5) × exp(-3.4 × 23.42 / 23.42) = 0.5 + 1.1 × exp(-3.4) ≈ 0.5 + 1.1 ×0.033 ≈ 0.54

[0044] Step 5: Correct node pressure

[0045] Construct a 285×285 order wind resistance matrix A. For example, nodes 12 and 38 are connected through branch 25, R 25 =0.82, then:

[0046] A

[12]

[12] = 1 / 0.82 ≈ 1.22 A

[38]

[38] = 1 / 0.82 ≈ 1.22A

[12]

[38] = A

[38]

[12] =-1 / 0.82 ≈ -1.22

[0047] Solve the system of equations A·ΔP corr k =-ΔQ k This yields the pressure correction for each node. For example, the correction ΔP for node 57.corr k

[57] =8.3 Pa, then the new pressure P

[57] 1 = 0 + 0.54 × 8.3 ≈ 4.48 Pa.

[0048] Step 6: Convergence assessment and iteration

[0049] Repeat steps 2-5, recording the global airflow residual for each iteration. After 127 iterations, ||ΔQ¹² 7 Since ||2| = 0.098 m³ / s < ε = 0.1 m³ / s, the algorithm converges. Output the final solution, including pressure values ​​at each node and airflow values ​​at each branch.

[0050] Performance comparison results:

[0051] Table 1. Algorithm Performance Comparison (Simulation Statistical Results of Different Methods)

[0052]

[0053] Experimental results show that the method of the present invention can maintain stable convergence performance under various initial conditions, reduce the average number of iterations by 44.8%, and increase the convergence success rate to 100%, which significantly improves the efficiency and reliability of ventilation network solution.

[0054] The present invention can also combine at least one of the technical features described in embodiments 2, 3, and 4 with embodiment 1 to form a new implementation.

[0055] It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention. Equivalent transformations or substitutions made based on the above technical solutions all fall within the scope of protection of the claims of the present invention.

Claims

1. An adaptive relaxation factor ventilation network solution method based on global airflow residual feedback, characterized in that, The method includes the following steps: Step 1: Establishing the ventilation network model and initializing parameters; Step 2: Calculate the imbalance value between branch air volume and node air volume; Step 3: Calculate the global airflow residual norm; Step 4: Calculate the adaptive relaxation factor; Step 5: Adjust node pressure; Step 6: Convergence judgment and iteration.

2. The adaptive relaxation factor ventilation network solution method based on global airflow residual feedback according to claim 1, characterized in that, Step 1: Establishment of the ventilation network model and parameter initialization, as follows: Input parameters such as ventilation network topology, branch resistance, and fan characteristic curves; set the initial pressure value P0 for all nodes; specify the convergence accuracy ε; and initialize the adaptive parameters. , where: ω max ω is the maximum relaxation factor, used to accelerate convergence in the early stages of iteration, and its value ranges from 1.2 to 1.8; min γ is the minimum relaxation factor, used to ensure numerical stability in the later stages of iteration, and its value ranges from 0.3 to 0.7; γ is the decay coefficient, adaptive to the network size, used to adjust the rate of change of the relaxation factor, and can be determined according to... A preliminary estimate is made, where N represents the number of network branches.

3. The adaptive relaxation factor ventilation network solution method based on global airflow residual feedback as described in claim 2, step 2: calculate the imbalance value between branch airflow and node airflow. Based on the node pressure value P at the current iteration step k k The air volume Q of all branches is calculated based on the law of ventilation resistance. j k : Where: ΔP j R represents the pressure difference between the beginning and end nodes of branch j. j Let J be the wind resistance value of branch j. Subsequently, based on the airflow balance condition, the airflow imbalance value of each node i is calculated. .

4. The adaptive relaxation factor ventilation network solution method based on global airflow residual feedback according to claim 3, characterized in that, Step 3: Calculate the global airflow residual norm. Solve for the global airflow residual norm in this iteration. This characterizes the convergence state of the entire ventilation network at the current iteration step: 。 5. The adaptive relaxation factor ventilation network solution method based on global airflow residual feedback according to claim 2, characterized in that, Step 4: Calculate the adaptive relaxation factor. Dynamically calculate the relaxation factor for the current iteration step based on the global airflow residual norm. In the formula: Let the initial airflow residual norm be denoted as . This exponential decay model ensures that the algorithm uses a larger step size to quickly approximate the solution in the early stages of iteration, and a smaller step size to achieve fine convergence in the later stages of iteration.

6. The adaptive relaxation factor ventilation network solution method based on global airflow residual feedback according to claim 2, characterized in that, Step 5: Adjust the node pressure and construct the wind resistance matrix A of the ventilation network, where: diagonal elements j represents all branches connected to node m; off-diagonal element A mn If there is a branch connecting node m and node n, then A mn =−1 / R mn If there is no directly connected branch A between node m and node n. mn =0, Solve the system of linear equations The pressure correction ΔP is obtained. corr k And an adaptive relaxation factor is used to correct the node pressure: ； In the formula: This is the pressure correction amount. This represents the node pressure value at iteration step k+1.

7. The adaptive relaxation factor ventilation network solution method based on global airflow residual feedback according to claim 2, characterized in that, Step 6: Convergence assessment and iteration. If the current global airflow residual norm satisfies If the algorithm converges, the solution is output (including pressure at each node and airflow at each branch); otherwise, the iteration step number k = k+1 is set, and the algorithm returns to step 2 to continue iterative calculation. The maximum number of iterations can be set to prevent infinite loops.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the adaptive relaxation factor ventilation network solution method based on global airflow residual feedback as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the computer instruction is executed by the processor, it implements the adaptive relaxation factor ventilation network solution method based on global airflow residual feedback as described in any one of claims 1-7.

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