Full-wind-network wind volume deduction method based on limited actually-measured wind volume and topological structure

Abstract

The invention discloses a whole wind network wind volume deduction method based on limited actual measurement wind volume and a topological structure, and relates to the technical field of wind volume deduction. The relation between the spanning tree air volume and the residual tree string air volume is obtained; the ratio of the number of independent loops to the number of total branches in the mine ventilation network is 1 / 3; establishing a maximum air volume residual tree string model and a minimum air volume residual tree string model; a corresponding minimum air volume spanning tree and a corresponding maximum air volume spanning tree are obtained; respectively putting known air volumes into the maximum remainder tree string, the minimum remainder tree string or the maximum spanning tree and the minimum spanning tree to construct four air volume deduction models; and solving the deduction model by adopting an FLA optimization algorithm, and outputting the air volume of each branch of the whole wind network. According to the method, through air volume adjustment and global optimization deduction, the air volume of the whole mine ventilation network is deduced rapidly and accurately, the air volume monitoring defect in the prior art can be effectively overcome, and more accurate and timely mine air volume state sensing is provided.

Description

Technical Field

[0001] This invention relates to the field of wind volume extrapolation technology, and in particular to a method for extrapolating wind volume across a whole wind network based on finite measured wind volume and topology. Background Technology

[0002] Intelligent mining technology has become a core approach to ensuring safe production in mines. In the construction of intelligent mining systems, intelligent sensing technologies, with air volume and velocity as the core, are particularly crucial. As mines expand, the structure of their ventilation networks becomes increasingly complex, especially in large mines with long operating histories, where monitoring points often only cover 10% to 20% of the total number of shafts and tunnels. This scarcity of monitoring points means that accurate monitoring of air volume in all branches of the mine is not yet possible, significantly impacting the efficiency of real-time ventilation network calculations and further affecting the safety management and optimization of the mine ventilation system. The lack of air volume sensing data not only threatens safe production and personnel safety but may also cause significant economic losses.

[0003] Existing technologies primarily focus on network calculation methods based on known wind resistance. These methods use estimated airflow to approximate measured airflow values ​​and further fit and monitor the parameters of the entire ventilation network. These techniques typically rely on obtaining wind resistance data and extrapolating airflow through precise wind resistance calculations. However, wind resistance calculations are relatively complex and are affected by various factors such as temperature, humidity, roadway deformation, and the movement of personnel and vehicles. Furthermore, wind resistance models are usually static and cannot reflect the dynamic changes of the mine ventilation system in real time, leading to errors in the calculated airflow, and these errors accumulate over time.

[0004] Currently, scholars both domestically and internationally primarily use network-based calculation methods to extrapolate the airflow of mine ventilation systems. These methods often employ loop, node, or cut-set methods to calculate airflow, reflecting the approximate airflow information of the entire ventilation network while fitting measured airflow data from a finite area. For example, Zhang Lang, Lu Xinming, and others proposed a real-time calculation method based on mine fan pressure data, roadway branch velocity and volume data, and fundamental mine resistance parameters. This method relies on accurate resistance parameters, and resistance measurement methods include wall roughness calculation, machine vision algorithms, and initial resistance calibration. While these techniques can obtain resistance data with a certain degree of accuracy, the complexity of acquiring resistance and the limitations of their static models result in insufficient accuracy in complex dynamic environments.

[0005] To address the limitations of traditional wind resistance models, some researchers have proposed iterative methods for wind volume calculation based on the coupling of dynamic air state parameters and air volume, such as the iterative calculation method based on the coupling of air state parameters and air volume proposed by Chen Kaiyan et al. This method improves upon the shortcomings of traditional static models by modeling the dynamic changes of the ventilation network. However, this method still relies on the accurate acquisition of initial wind resistance and does not solve the problem of accurately capturing the interaction between air volume and wind resistance during dynamic changes. In terms of wind resistance measurement, some studies have introduced fractal dimension models and machine learning techniques. Wu Bing et al. proposed a frictional wind resistance calculation method based on fractal dimension and combined it with a three-dimensional roughness model to improve the accuracy of wind resistance calculation. In addition, wind resistance calibration methods based on optimization theory, such as the quadratic programming model combining the loop wind pressure balance equation and wind resistance limit constraints proposed by Wu Fengliang et al., also help to accurately calibrate wind resistance parameters. Although these methods can provide optimized estimates of wind resistance, in practical applications, the accumulation of wind resistance errors is still difficult to avoid, affecting the real-time performance and accuracy of air volume calculation.

[0006] Existing technologies have made some progress in monitoring and extrapolating ventilation volume in mines, but still have the following significant drawbacks: (1) Obtaining air resistance is complex and affected by a variety of factors. Obtaining air resistance is more complex than obtaining air volume, and is affected by a variety of factors, including temperature, humidity, roadway deformation, and personnel and vehicle movement. Especially in the mine environment, the changes of these factors are highly dynamic, making it difficult to obtain accurate and stable results in air resistance calculation. Current air resistance measurement methods mainly rely on static models or calculations based on ideal conditions, which greatly reduces the real-time performance and accuracy of air resistance, and thus affects the accuracy of extrapolating the air volume of the entire mine ventilation network. (2) The calibration model lacks dynamic updates, leading to the accumulation of solution errors. Existing air resistance calibration models are usually based on static assumptions. Although they can provide a certain accuracy of the initial air resistance value, in the mine environment, air resistance is affected by the dynamic changes of a variety of factors. The calibrated air resistance model can only represent the static solution and cannot reflect the dynamic changes of the mine ventilation system in real time. As time goes by, errors accumulate, making the air volume calculations performed by the model inaccurate and unable to capture the true state of the mine ventilation system in a timely manner, thus affecting the safety and optimization of the ventilation system. (3) Data scarcity and limitations of the extrapolation results. Current air volume extrapolation methods usually rely on limited monitoring point data, especially when the mine is large in scale and there are few air volume and wind speed monitoring points, making real-time perception and accurate extrapolation of the air volume of the entire ventilation network particularly difficult. Although some studies have attempted to extrapolate the entire network through loop, node and other methods, these methods cannot effectively handle the scarcity and uncertainty of monitoring data when facing practical applications. Therefore, when extrapolating the air volume of the mine ventilation system in real time, the existing technology often fails to accurately reflect the air volume distribution and changing trend, thus affecting the real-time performance and accuracy of the ventilation network calculation. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology.

[0008] The technical solution adopted to solve the above technical problems is: a method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology, including the following steps: S1, Construct a topology model of the mine ventilation network; S2, combining the airflow balance law and singular value decomposition method, yields the spanning tree airflow. And Yu Shuxian wind volume The relationship between them; S3, the ratio of the number of independent loops to the total number of branches in the mine ventilation network is 1 / 3; S4. Based on finite measured air volume, establish the maximum air volume co-tree chord model and the minimum air volume co-tree chord model; S5. Based on the Kruskal algorithm, solve the maximum air volume cotree chord model and the minimum air volume cotree chord model to obtain the corresponding minimum air volume spanning tree and maximum air volume spanning tree. S6. The known air volume is placed into the maximum cotree chord, minimum cotree chord or maximum spanning tree and minimum spanning tree respectively to construct four air volume extrapolation models. S7 uses the FLA optimization algorithm to solve the deduction model and outputs the air volume of each branch of the whole wind network.

[0009] Furthermore, the tree generation airflow in S2 And Yu Shuxian wind volume The relationship between them is: , In the above formula, Indicates branch airflow outflow node , -1 indicates a branch. airflow into the node , Indicates branch airflow volumetric flow rate For the number of nodes, Indicates the number of branches; Branch air volume With the basic association matrix Arranging and dividing the data into blocks with cosine first and spanning tree last, we can obtain the matrix form of the law of conservation of air volume as follows: , Expanding, we get: , In the above formula, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. express * 3D matrix express The square formation, Representation matrix The reverse; For a given rank of The matrix, whose singular value decomposition form is: , In the above formula, ( )as well as ( Represents a unitary matrix. Represents a diagonal matrix. Representation matrix singular values, Representation matrix The transpose of the matrix; Assumption Moore-Penrose inverse ,but: , , In the above formula, Represents a diagonal matrix The inverse matrix, , Representation matrix The inverse matrix.

[0010] Furthermore, the method for inferring that the ratio of independent loops to total branches in the mine ventilation network in S3 is 1 / 3 is as follows: In a mine ventilation network, the airflow is directional; therefore, the ventilation network is a directed connected graph with a number of nodes. The number of branches is ventilation network middle, Represents a set of nodes. Represents a set of branches. The complete graph of order 1 has the most branches, containing a total of If there are branches, then the maximum number of independent loops is... Represented as: , The ratio of the maximum possible independent loops to the maximum possible branch number for: , As the number of nodes in the network increases, the ratio of the maximum possible number of independent loops to the number of branches in the ventilation network approaches 1, and each node is connected to other nodes through branches. ; Number of nodes With the number of branches The following linear relationship exists: , Each node corresponds to 3 / 2 branches. , According to the above formula, the ratio of the number of independent loops to the total number of branches in the ventilation network is 1 / 3.

[0011] Furthermore, the method for establishing the maximum air volume cotree chord model and the minimum air volume cotree chord model based on finite measured air volume in S4 is as follows: With the number of nodes The number of branches is ventilation network middle, Represents a set of nodes. Represents a set of branches, which contains The air volume of each branch is known. Let the set of branch numbers with known air volume be denoted as . The corresponding air volume set is ,in The corresponding set of nodes is When the known wind volume is set Based on the selection of a set of air volume residual tree string At that time, what was being searched for There exists a total inclusion. and some of the included Two situations; contain The types of spanning trees contained in the ventilation network of each node. The types can be calculated using the following formula, and their growth is non-linear with the increase of the number of network nodes: , In the formula, Indicates the type of spanning tree. Represents the basic correlation matrix. Represents the transpose of the basic incidence matrix. This indicates solving for the value of the determinant; Solving for the maximum air volume covariance tree chord Mathematical model Represented as: , In the above formula, the model consists of two objective functions and constraints on the spanning tree. express Contains the number of branches with known air volume. Indicates that the node is and Branches, Represents a spanning tree, express Weight, This represents the sum of the degrees of the nodes as a constraint. Represents a spanning tree Total of Branches, Represents a spanning tree It does not contain any loops. Represents a set of nodes. Indicates branch The weight of the branch If the air volume is known, then If branches If the air volume is unknown, the minimum permissible air volume for that branch needs to be provided according to the regulations. ; In the objective function Function change Function to solve for minimum airflow cotree chord .

[0012] Furthermore, the method in S5 for solving the maximum airflow cotree chord model and the minimum airflow cotree chord model based on the Kruskal algorithm to obtain the corresponding minimum airflow spanning tree and maximum airflow spanning tree is as follows: The steps to solve the maximum airflow cotree chord model by constructing a sequential model are as follows: S501, maximizing cotree chords Include The number of branches in the middle, such that maximum; S502, the solution set obtained is: Then at this time based on Make maximum; Input the basic correlation matrix of the ventilation network and for the known wind volume branch set The algorithm assigns extremely high weights to ensure priority selection into the cotree chord, while unknown wind volume branches are weighted according to the minimum wind volume. Then, it enters an iterative loop, where the algorithm continuously selects the edge with the smallest weight from the remaining edge set and checks its inclusion in the spanning tree candidate set through a loop avoidance mechanism. Will a loop be formed? If not, then add... And update the collection; the loop continues until... The number of edges reached (Spanning tree requirements), set Construct a minimum air volume spanning tree The unselected sides naturally form the maximum wind volume surplus tree string. This will provide a foundation for subsequent wind volume projections. and In Function transformed into The function can be used to solve for the minimum airflow cotree chord. and the maximum air volume generation tree .

[0013] Furthermore, the four airflow extrapolation models in S6 include airflow extrapolation models. Air volume projection model Air volume projection model Air volume projection model .

[0014] Furthermore, the aforementioned air volume projection model For: will Insert the maximum airflow into the tree string. In the middle, by analyzing the maximum wind volume of the remaining tree string Unknown air volume Optimize the model to minimize the number of airflow violations in the predicted airflow model. ,Right now: , In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints Indicates branch air volume, , These represent branches in the spanning tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. Represents the minimum airflow spanning tree. Represents the set of measured air volumes. express * 3D matrix express The square formation, Representation matrix The reverse, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This indicates the maximum wind volume of the tree string. This represents the minimum airflow spanning tree.

[0015] Furthermore, the aforementioned air volume projection model For: will Place in the maximum airflow generation tree Inside, by adjusting the minimum airflow of the tree string... Unknown air volume Optimization was performed to minimize the error between the estimated and measured air volume, and to minimize the number of constraints violated with other unknown air volumes. The multiplier method was used to establish the air volume estimation model. : , In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints Indicates branch air volume, , These represent branches in the spanning tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. This represents the maximum airflow spanning tree. Represents the set of measured air volumes. express * 3D matrix express The square formation, Representation matrix The reverse, This indicates that the penalty factor is a very large positive number. Indicates the branch number. Indicates branch The measured air volume express The air volume is extrapolated in the middle. This represents the measured-to-calculated error term. This indicates the number of violations of airflow constraints in the calculated airflow. Indicates a penalty item. Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This represents the minimum airflow rate of the tree chord. This represents the maximum airflow spanning tree. This represents the minimum airflow spanning tree.

[0016] Furthermore, the aforementioned air volume projection model For: will Insert the maximum airflow into the tree string. In the middle, by using the minimum air volume generating tree Unknown air volume The air volume is optimized and the estimated air volume is obtained, minimizing the error between the estimated and measured air volume and the number of constraints violated with other unknown air volumes. The multiplier method is also used to establish the air volume estimation model. : , In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints , They represent the branches in the chord of the tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. This also indicates that the penalty factor is a very large positive number. express The air volume is extrapolated in the middle. This represents the measured-to-calculated error term. Indicates a penalty item. Representation matrix Moore-Penrose inverse matrix, Represents the set of measured air volumes. express * 3D matrix Representation matrix Moore-Penrose inverse matrix, express The square formation, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This indicates the maximum wind volume of the tree string. This represents the minimum airflow rate of the tree chord. This represents the minimum airflow spanning tree.

[0017] Furthermore, the aforementioned air volume projection model For: will Place in the maximum airflow generation tree In the middle, by generating the maximum air volume tree Unknown air volume Optimize the model to minimize the number of constraints violated in the predicted airflow and establish an airflow prediction model. ,Right now: , In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints , They represent the branches in the chord of the tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. Represents the set of measured air volumes. express * 3D matrix Representation matrix Moore-Penrose inverse matrix, express The square formation, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This represents the minimum airflow rate of the tree chord. This represents the maximum airflow generation tree.

[0018] The beneficial effects of the present invention are as follows: (1) The present invention realizes rapid and accurate simulation of the air volume of the entire mine ventilation network under the conditions of incomplete wind resistance data and scarce monitoring points through air volume adjustment and global optimization simulation. It can effectively solve the defects of air volume monitoring in the existing technology, provide more accurate and timely mine air volume status perception, and provide important technical support for mine safety production and ventilation system optimization.

[0019] (2) By analyzing the structural characteristics of the ventilation network, this invention derives the linear relationship between the number of independent loops and the number of branches in the network based on Euler's theorem and the law of air volume balance. Combined with parameters such as average node degree, it proves that in a large mine ventilation network, installing wind speed sensors on 1 / 3 of the branches can achieve accurate monitoring of the air volume of the entire ventilation network. This can not only greatly improve the monitoring capability of the ventilation network, but also ensure the efficient operation of the mine ventilation system without increasing too much cost.

[0020] (3) This invention uses an improved priority queue-based sequential model and the Kruskal algorithm to effectively solve the maximum air volume spanning tree and the maximum air volume cosine, avoiding the cumbersome Pareto optimal solution calculation process, providing a reliable benchmark for air volume extrapolation, simplifying the calculation process, significantly improving the accuracy of the air volume extrapolation model, and providing a more efficient optimization method for mine ventilation systems.

[0021] (4) This invention establishes four airflow extrapolation models, verifying the feasibility of extrapolating the airflow of the entire ventilation network under limited measured airflow data, mine topology, and procedural airflow constraints. Especially in cases of data scarcity, the model can effectively compensate for the lack of airflow monitoring data and provide accurate extrapolation results. In hundreds of tests, model G_1 showed excellent extrapolation performance, with an R² of 0.96 and an RMSE of 2.23. The R² of the other extrapolation models were all greater than 0.88, and the RMSE was all less than 10, indicating that the extrapolation results have high accuracy and reliability. The various airflow extrapolation schemes provided by this invention can provide flexible, accurate, and reliable solutions for airflow perception in different mines, promoting the further development of intelligent ventilation systems in mines. Attached Figure Description

[0022] Figure 1 This is a flowchart of the Kruskal algorithm of this invention.

[0023] Figure 2 This is the flowchart of the FLA algorithm.

[0024] Figure 3 This is a comparison chart of the iterative convergence of different optimization algorithms.

[0025] Figure 4 This is a schematic diagram of the maximum airflow residual tree chord.

[0026] Figure 5 This is a schematic diagram of the maximum airflow generation tree.

[0027] Figure 6 It is an FLA air volume calculation model. , Convergence plot.

[0028] Figure 7It is an FLA air volume calculation model. , Convergence plot.

[0029] Figure 8 It is a measured model Comparison chart of simulated air volume.

[0030] Figure 9 It is a measured model Comparison chart of simulated air volume.

[0031] Figure 10 It is a measured model Comparison chart of simulated air volume.

[0032] Figure 11 It is a measured model Comparison chart of simulated air volume.

[0033] Figure 12 This is a diagram showing the error analysis of the projected air volume.

[0034] Figure 13 This is a performance comparison chart of the simulation models. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0036] This embodiment presents a method for extrapolating the airflow of a full-network airflow based on finite measured airflow and network topology, comprising the following steps: S1, Construct a topology model of the mine ventilation network.

[0037] S2, combining the airflow balance law and singular value decomposition method, yields the spanning tree airflow. And Yu Shuxian wind volume The relationship between them.

[0038] , In the above formula, Indicates branch airflow outflow node , -1 indicates a branch. airflow into the node , Indicates branch airflow volumetric flow rate For the number of nodes, Indicates the number of branches; Branch air volume With the basic association matrix Arranging and dividing the data into blocks with cosine first and spanning tree last, we can obtain the matrix form of the law of conservation of air volume as follows: , Expanding, we get: , In the above formula, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. express * 3D matrix express The square formation, Representation matrix The reverse; For a given rank of The matrix, whose singular value decomposition form is: , In the above formula, ( )as well as ( Represents a unitary matrix. Represents a diagonal matrix. Representation matrix singular values, Representation matrix The transpose of the matrix; Assumption Moore-Penrose inverse ,but: , , In the above formula, Represents a diagonal matrix The inverse matrix, , Representation matrix The inverse matrix.

[0039] S3, the ratio of the number of independent loops to the total number of branches in the mine ventilation network is 1 / 3.

[0040] The application of Euler's theorem to mine ventilation networks reveals a fundamental law of network structure: for a connected network... If we consider the outer region of the graph as a special "mesh", then the number of cycles in the connected planar graph is... Follow the formula For coal mine ventilation networks, if we disregard virtual atmospheric nodes and the loops they form, then the number of internal loops in the connected planar diagram is... This matches the number of cochord branches in the spanning tree corresponding to the ventilation network.

[0041] In a mine ventilation network, the airflow is directional; therefore, the ventilation network is a directed connected graph with a number of nodes. The number of branches is ventilation network middle, Represents a set of nodes. Represents a set of branches. The complete graph of order 1 has the most branches, containing a total of If there are branches, then the maximum number of independent loops is... Represented as: , This indicates that in a ventilation network, the maximum possible number of loops increases superlinearly with the number of nodes, and the ratio of the maximum possible independent loops to the maximum possible branch number is... for: , As the number of nodes in the network increases, the ratio of the maximum possible number of independent loops to the number of branches in the ventilation network approaches 1, and each node is connected to other nodes through branches. ; However, in the design of mine ventilation networks, to improve ventilation efficiency and management flexibility, and to avoid the occurrence of recirculating air, only one unidirectional airflow path exists between two nodes. Number of nodes With the number of branches The following linear relationship exists: , Therefore, when analyzing and calculating actual ventilation networks, it can be assumed that... Each node corresponds to 3 / 2 branches. , The formula above shows that the ratio of the number of independent loops to the total number of branches in the ventilation network is 1 / 3. Therefore, increasing the number of airflow sensors to approximately 1 / 3 of the total number of branches is sufficient to achieve real-time airflow monitoring for the entire mine.

[0042] S4. Based on finite measured air volume, establish the maximum air volume cotree chord model and the minimum air volume cotree chord model.

[0043] With the number of nodes The number of branches is ventilation network middle, Represents a set of nodes. Represents a set of branches, which contains The air volume of each branch is known. Let the set of branch numbers with known air volume be denoted as . The corresponding air volume set is ,in The corresponding set of nodes is When the known wind volume is set Based on the selection of a set of air volume residual tree string At that time, what was being searched for There exists a total inclusion. and some of the included There are two scenarios.

[0044] contain The types of spanning trees contained in the ventilation network of each node. The types can be calculated using the following formula, and their growth is non-linear with the increase of the number of network nodes: , In the formula, Indicates the type of spanning tree. Represents the basic correlation matrix. Represents the transpose of the basic incidence matrix. This indicates the solution to the determinant.

[0045] The selection mainly considers two principles. The first principle is the selection... Include Number of branches The more reference points there are, the more comprehensive the airflow analysis will have, and the more points can be used for the corresponding analysis. The better the calculation of unknown air volume, the better. Ideally, the selected... Includes all known airflow branches, i.e., airflow cochords. Include All branches in can be represented as There is no residual wind volume. Contains only In the case of a single branch, that is The second principle is selection. It should include branches with a known large air volume, i.e. air volume weights and The greater the wind speed and volume within the tunnel, the more accurate the data measured by sensors and other devices, and the smaller the error in the extrapolation process. Meeting these two principles... Essentially a minimum airflow tree Corresponding maximum air volume Yu Shuxian .

[0046] Solving for the maximum air volume covariance tree chord Mathematical model Represented as: , In the above formula, the model consists of two objective functions and constraints on the spanning tree. express Contains the number of branches with known air volume. Indicates that the node is and Branches, Represents a spanning tree, express Weight, This represents the sum of the degrees of the nodes as a constraint. Represents a spanning tree Total of Branches, Represents a spanning tree It does not contain any loops. Represents a set of nodes. Indicates branch The weight of the branch If the air volume is known, then If branches If the air volume is unknown, the minimum permissible air volume for that branch needs to be provided according to the regulations. .

[0047] In the objective function Function change Function to solve for minimum airflow cotree chord .

[0048] S5 uses the Kruskal algorithm to solve the cotree chord model of maximum air volume and the cotree chord model of minimum air volume, and obtains the corresponding minimum air volume spanning tree and maximum air volume spanning tree.

[0049] In solving , During the process, vector Corresponding to a type of spanning tree, vector This corresponds to a type of parallax string. The corresponding nonlinear space is exactly The set For the optimal solution It needs to include Number of branches and The sum of the weights of the inner branches is the largest.

[0050] Assuming that it is now incomplete When choosing a branch or branch When performing the edge addition operation, if Adding branches When a remainder sine cannot be formed, it will cause... and Contradictory, therefore choose The problem actually falls under the category of multi-objective programming.

[0051] To address the problem that the Pareto optimal solution set obtained from solving multi-objective programming problems cannot determine a set of optimal solutions, this section adopts a sequential optimization approach to solve the problem. Assuming that the solution for cochords is more biased towards the objective function. That is, first make a feasible solution Include Make as many branches as possible, and then base it on the objective function. Add to Other branches. The sequential model is constructed in two steps to solve the maximum airflow cotree chord model, as follows: S501, maximizing cotree chords Include The number of branches in the middle, such that maximum: , S502, the solution set obtained is: Then at this time based on Make maximum: , The optimal solution obtained through the above two steps is... This section uses Kruskal's algorithm to solve this sequential model, first assigning a very large weight to the known airflow branch. , making As many branches as possible appear on the wind-flow excess tree chord Then, based on the weights, other branches are added one by one, ultimately forming... and the corresponding minimum air volume spanning tree The algorithm flowchart is as follows: like Figure 1 As shown, the basic correlation matrix of the input ventilation network and for the known wind volume branch set The algorithm assigns extremely high weights to ensure priority selection into the cotree chord, while unknown wind volume branches are weighted according to the minimum wind volume. Then, it enters an iterative loop, where the algorithm continuously selects the edge with the smallest weight from the remaining edge set and checks its inclusion in the spanning tree candidate set through a loop avoidance mechanism. Will a loop be formed? If not, then add... And update the collection; the loop continues until... The number of edges reached (Spanning tree requirements), set Construct a minimum air volume spanning tree The unselected sides naturally form the maximum wind volume surplus tree string. This will provide a foundation for subsequent wind volume projections. and In Function transformed into The function can be used to solve for the minimum airflow cotree chord. and the maximum air volume generation tree .

[0052] S6. The known air volume is placed into the maximum cochord, minimum cochord, or maximum spanning tree, minimum spanning tree, respectively, to construct four air volume extrapolation models. These four models include the air volume extrapolation model... Air volume projection model Air volume projection model Air volume projection model .

[0053] Air volume projection model For: will Insert the maximum airflow into the tree string. In the middle, by analyzing the maximum wind volume of the remaining tree string Unknown air volume Optimize the model to minimize the number of airflow violations in the predicted airflow model. ,Right now: , In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints Indicates branch air volume, , These represent branches in the spanning tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. Represents the minimum airflow spanning tree. Represents the set of measured air volumes. express * 3D matrix express The square formation, Representation matrix The reverse, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This indicates the maximum wind volume of the tree string. This represents the minimum airflow spanning tree.

[0054] Air volume projection model For: will Place in the maximum airflow generation tree Inside, by adjusting the minimum airflow of the tree string... Unknown air volume Optimization was performed to minimize the error between the estimated and measured air volume, and to minimize the number of constraints violated with other unknown air volumes. The multiplier method was used to establish the air volume estimation model. : , In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints Indicates branch air volume, , These represent branches in the spanning tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. This represents the maximum airflow spanning tree. Represents the set of measured air volumes. express * 3D matrix express The square formation, Representation matrix The reverse, This indicates that the penalty factor is a very large positive number. Indicates the branch number. Indicates branch The measured air volume express The air volume is extrapolated in the middle. This represents the measured-to-calculated error term. This indicates the number of violations of airflow constraints in the calculated airflow. Indicates a penalty item. Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This represents the minimum airflow rate of the tree chord. This represents the maximum airflow spanning tree. This represents the minimum airflow spanning tree.

[0055] Air volume projection model For: will Insert the maximum airflow into the tree string. In the middle, by using the minimum air volume generating tree Unknown air volume The air volume is optimized and the estimated air volume is obtained, minimizing the error between the estimated and measured air volume and the number of constraints violated with other unknown air volumes. The multiplier method is also used to establish the air volume estimation model. : , In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints , They represent the branches in the chord of the tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. This also indicates that the penalty factor is a very large positive number. express The air volume is extrapolated in the middle. This represents the measured-to-calculated error term. Indicates a penalty item. Representation matrix Moore-Penrose inverse matrix, Represents the set of measured air volumes. express * 3D matrix Representation matrix Moore-Penrose inverse matrix, express The square formation, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This indicates the maximum wind volume of the tree string. This represents the minimum airflow rate of the tree chord. This represents the minimum airflow spanning tree.

[0056] Air volume projection model For: will Place in the maximum airflow generation tree In the middle, by generating the maximum air volume tree Unknown air volume Optimize the model to minimize the number of constraints violated in the predicted airflow and establish an airflow prediction model. ,Right now: , In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints , They represent the branches in the chord of the tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. Represents the set of measured air volumes. express * 3D matrix Representation matrix Moore-Penrose inverse matrix, express The square formation, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This represents the minimum airflow rate of the tree chord. This represents the maximum airflow generation tree.

[0057] When based on Solve and its corresponding At that time, I recorded Number of measured air volumes , ,but The number of measured air volumes is When based on Solve and its corresponding At that time, I recorded Number of measured air volumes , ,but The number of measured air volumes is , indicating a comparison of the parameters of the four models.

[0058] S7 uses the FLA optimization algorithm to solve the deduction model and outputs the air volume of each branch of the whole wind network.

[0059] Flood Algorithm (FLA) is a metaheuristic optimization algorithm inspired by natural flood phenomena, proposed by researchers such as M. Ghasemi. This algorithm simulates the movement patterns of water bodies during floods, such as slope flow, flow rate changes, soil infiltration effects, and water level fluctuations, transforming these phenomena into optimization search strategies through digital modeling. FLA aims to balance global exploration and local exploitation, effectively avoiding local optima, and is applicable to various engineering optimization problems. The algorithm improves performance by dynamically adjusting the search intensity. Its process is described in detail below, with key formulas listed separately. The algorithm begins with population initialization, randomly generating a set of potential solutions as the initial population. The population size is typically set to 90, which is the optimal value verified by numerous experiments, achieving a good balance on most test functions. Each member represents a solution, and its fitness value is calculated to identify the current best solution. Subsequently, the algorithm enters the main loop for iteration until the maximum number of iterations or the convergence condition is reached.

[0060] In the main loop, the FLA operation is divided into two core phases: the regular movement phase and the flood phase. The regular movement phase simulates the natural flow of water along a slope, emphasizing local development. Member positions are updated by moving towards the current optimal solution, introducing random perturbations to slightly adjust positions. This phase promotes population convergence to the optimal region, improving solution accuracy. Position updates during the regular movement phase... The formula is: , In the above formula, This is the current member's position. It is the best position globally. It is a random number in the range [0, 1].

[0061] The flood phase introduces random perturbations to enhance global exploration, simulating turbulence and diffusion during flood events. This phase's excitation is based on the water depletion coefficient. Its value decreases linearly with the number of iterations, leading to a lower probability of flooding and a greater focus on local development in later stages. Location updates incorporate normally distributed random numbers, subjecting less fit members to greater perturbations, thus encouraging them to explore new areas. Water depletion coefficient. The calculation formula is: , In the above formula, It is the current iteration number. It represents the maximum number of iterations.

[0062] The location update formula for the flood stage is: , In the above formula, It is a standard normally distributed random number (mean 0, variance 1). and It is the boundary of the search space. It is the water depletion coefficient.

[0063] Infiltration and diffusion effects Reflects the individual population of water mass The influence of fitness on search behavior: the lower the fitness value, the more severe the penetration and diffusion. The calculation formula is as follows: , In the above formula, Member fitness value, and These are the best and worst fitness values ​​in the current population, respectively.

[0064] The elimination probability Pt determines the likelihood of a member being replaced during population renewal, and is used to simulate the cycle of water volume increase and decrease. Its calculation formula is based on a sine function of random numbers and the number of iterations: , In the above formula, rand is a random number in the range [0, 1], and Iter is the current iteration number. Fitness evaluation and selection are performed immediately after each position update. The fitness value of the new position is compared with the old value; if it is better, the old position is replaced, and the global optimal solution is updated. The population update mechanism simulates the increase or decrease of water volume, periodically introducing new members to replace the worst members and eliminating weak members to maintain diversity. This process is based on the number of iterations and fitness values, ensuring that the algorithm continues to evolve. Based on probability... Update Individual : , Algorithm flowchart as follows Figure 2 As shown, the FLA algorithm begins with population initialization, followed by an iterative process. Each iteration first calculates the water depletion coefficient and the permeability-diffusion coefficient of each water mass individual. Then, based on the results of random number generation, different movement strategies are selected to update the water mass positions. After the update, the population fitness is reassessed, and some inferior individuals are eliminated, while new individuals are generated to replenish the population. This process repeats until the maximum number of iterations is reached, ultimately outputting the optimal solution. The entire process achieves a balance between global exploration and local exploitation by simulating the flow, permeation, and renewal mechanisms of water bodies.

[0065] The study also compared and evaluated the performance of various optimization algorithms using the standard test case CEC 2016 published by IEEE CEC, such as... Figure 3 As shown, for single-peak and multi-peak shift rotation functions " Compared to more widely used algorithms such as GWO, WOA, and PSO, FLA demonstrates superior iteration speed and optimization capabilities. Therefore, this invention selects the FLA algorithm to verify the extrapolation performance of four models.

[0066] The experiment in this embodiment is as follows: I. Case Overview The mine ventilation network, consisting of four intakes and two exhausts, comprises 35 branches and 22 nodes, with 14 independent loops. Fans are located on branches 34 and 35, with fixed airflow rates of 93.6 and 92.33 m³ / s, respectively; branches 20 and 25 are sealed; 11 branches have measured airflow rates: {1, 5, 6, 12, 14, 17, 23, 26, 30, 34, 35}. This application determines the velocity and airflow constraints for each roadway according to regulations and roadway types; the relevant parameters are shown in Table 1. Table 1 Initial parameters of the wind network ,

[0067] II. Analysis of Deduction Results like Figures 4 to 5 As shown, when the air volume of branches 1, 5, 6, 12, 14, 17, 23, 26, 30, 34, and 35 is known, the model is solved based on the Kruskal algorithm. The maximum airflow cochord containing the known airflow branches can be obtained. ={1, 2, 5, 6, 9, 12, 14, 17, 18, 26, 30, 31, 34, 35}, which corresponds to the minimum airflow spanning tree. {20, 25, 29, 32, 28, 16, 15, 33, 19, 24, 13, 3, 10, 21, 22, 4, 8, 11, 7, 27, 23}, where the air volume of branch 23 is known but does not belong to .

[0068] Maximum airflow spanning tree containing known airflow branches ={23, 14, 26, 6, 5, 30, 1, 17, 12, 35, 34, 20, 25, 29, 32, 28, 16, 33, 24, 13, 10}, then the minimum airflow cosine ={2, 3, 4, 7, 8, 9, 11, 15, 18, 19, 21, 22, 27, 31}. When using the model... When performing airflow extrapolation, the optimized airflow branches are {2, 9, 18, 31}, with a total of 4 optimization variables. The extrapolated airflow is 21, but the airflow of branch 23 is known; therefore, the actual extrapolated airflow is 20. (Model) The range of the fitness function is .

[0069] When using the model When performing airflow extrapolation, the optimized airflow branches are {2, 3, 4, 7, 8, 9, 11, 15, 18, 19, 21, 22, 27, 31}, totaling 14 optimization variables. There are 21 extrapolated airflows, of which 11 are known. The number of non-compliant constraints for the remaining 10 extrapolated airflows can be calculated. A fitness function is established using the generalized multiplier method, and the model... The upper limit of the fitness function range is .

[0070] When using the model When performing airflow extrapolation, the optimization component branches are {20, 25, 29, 32, 28, 16, 15, 33, 19, 24, 13, 3, 10, 21, 22, 4, 8, 11, 7, 27, 23}, of which the airflow of branch 23 is known. Therefore, there are a total of 20 optimization variables, and 14 extrapolated airflows. Among these, the airflows of 10 branches are known. Based on these known airflows, a measured-extrapolated airflow error function is established. The number of non-compliance issues for the other 4 extrapolated airflows is calculated, and a fitness function is established using the generalized multiplier method. The model... The upper limit of the fitness function range is .

[0071] When using the model When performing airflow extrapolation, the optimization component branches are {20, 25, 29, 32, 28, 16, 33, 24, 13, 10}, totaling 10 optimization variables. The extrapolated airflow has 14 components, therefore the model... The range of the fitness function is .

[0072] Model and The fitness function value is based on the number of non-compliant branches of the extrapolated air volume, indicating that the fitness value will not exceed the number of extrapolated air volume branches, and its fitness function range belongs to the same order of magnitude; while the model and This is based on the generalized multiplier method, which combines the measured-to-estimated air volume error and the number of non-compliance constraints in the estimated air volume. Its fitness function range is influenced by the weighting factor. and Due to the influence of [the factor], the range of its fitness function is within one order of magnitude. For example... Figures 6 to 7As shown, the FLA algorithm can solve for the optimal value using all four models. and The calculated air volume meets the constraints, while the model... and The calculated air volume not only minimizes the error between the measured and calculated air volume, but also ensures that other calculated air volumes meet the constraints. The calculation results are shown in Table 2.

[0073] Table 2. Airflow projection results for different models ,

[0074] like Figures 8 to 11 As shown, the relationship between the projected air volume, the measured air volume, and the upper and lower limits of air volume obtained from the four projection models is illustrated. By using air volume constraints and topology projection rules to project air volume, it is possible not only to ensure that the projected air volume is within the constraints, but also to obtain a more accurate air volume value.

Claims

1. A method for extrapolating the airflow of a whole wind network based on finite measured airflow and topology, characterized in that, Includes the following steps: S1, Construct a topology model of the mine ventilation network; S2, combining the airflow balance law and singular value decomposition method, yields the spanning tree airflow. And Yu Shuxian wind volume The relationship between them; S3, the ratio of the number of independent loops to the total number of branches in the mine ventilation network is 1 / 3; S4. Based on finite measured air volume, establish the maximum air volume co-tree chord model and the minimum air volume co-tree chord model; S5. Based on the Kruskal algorithm, solve the maximum air volume cotree chord model and the minimum air volume cotree chord model to obtain the corresponding minimum air volume spanning tree and maximum air volume spanning tree. S6. The known air volume is placed into the maximum cotree chord, minimum cotree chord or maximum spanning tree and minimum spanning tree respectively to construct four air volume extrapolation models. S7 uses the FLA optimization algorithm to solve the deduction model and outputs the air volume of each branch of the whole wind network.

2. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 1, is characterized in that, The tree generation airflow in S2 And Yu Shuxian wind volume The relationship between them is: ， In the above formula, Indicates branch airflow outflow node , -1 indicates a branch. airflow into the node , Indicates branch airflow volumetric flow rate For the number of nodes, Indicates the number of branches; Branch air volume With the basic association matrix Arranging and dividing the data into blocks with cosine first and spanning tree last, we can obtain the matrix form of the law of conservation of air volume as follows: ， Expanding, we get: ， In the above formula, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. express * 3D matrix express The square formation, Representation matrix The reverse; For a given rank of The matrix, whose singular value decomposition form is: ， In the above formula, ( )as well as ( Represents a unitary matrix. Represents a diagonal matrix. Representation matrix singular values, Representation matrix The transpose of the matrix; Assumption Moore-Penrose inverse ,but: ， ， In the above formula, Represents a diagonal matrix The inverse matrix, , Representation matrix The inverse matrix.

3. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 1, characterized in that, The method for inferring that the ratio of independent loops to total branches in the mine ventilation network in S3 is 1 / 3 is as follows: In a mine ventilation network, the airflow is directional; therefore, the ventilation network is a directed connected graph with a number of nodes. The number of branches is ventilation network middle, Represents a set of nodes. Represents a set of branches. The complete graph of order 1 has the most branches, containing a total of If there are branches, then the maximum number of independent loops is... Represented as: ， The ratio of the maximum possible independent loops to the maximum possible branch number for: ， As the number of nodes in the network increases, the ratio of the maximum possible number of independent loops to the number of branches in the ventilation network approaches 1, and each node is connected to other nodes through branches. ; Number of nodes With the number of branches The following linear relationship exists: ， Each node corresponds to 3 / 2 branches. ， According to the above formula, the ratio of the number of independent loops to the total number of branches in the ventilation network is 1 / 3.

4. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 1, characterized in that, The method for establishing the maximum air volume cotree chord model and the minimum air volume cotree chord model based on finite measured air volume in S4 is as follows: With the number of nodes The number of branches is ventilation network middle, Represents a set of nodes. Represents a set of branches, which contains The air volume of each branch is known. Let the set of branch numbers with known air volume be denoted as . The corresponding air volume set is ,in The corresponding set of nodes is When the known wind volume is set Based on the selection of a set of air volume residual tree string At that time, what was being searched for There exists a total inclusion. and some of the included Two situations; contain The types of spanning trees contained in the ventilation network of each node. The types can be calculated using the following formula, and their growth is non-linear with the increase of the number of network nodes: ， In the formula, Indicates the type of spanning tree. Represents the basic correlation matrix. Represents the transpose of the basic incidence matrix. This indicates solving for the value of the determinant; Solving for the maximum air volume covariance tree chord Mathematical model Represented as: ， In the above formula, the model consists of two objective functions and constraints on the spanning tree. express Contains the number of branches with known air volume. Indicates that the node is and Branches, Represents a spanning tree, express Weight, This represents the sum of the degrees of the nodes as a constraint. Represents a spanning tree Total of Branches, Represents a spanning tree It does not contain any loops. Represents a set of nodes. Indicates branch The weight of the branch If the air volume is known, then If branches If the air volume is unknown, the minimum permissible air volume for that branch needs to be provided according to the regulations. ; In the objective function Function change Function to solve for minimum airflow cotree chord .

5. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 1, characterized in that, The method described in S5 for solving the maximum airflow cotree chord model and the minimum airflow cotree chord model based on the Kruskal algorithm to obtain the corresponding minimum airflow spanning tree and maximum airflow spanning tree is as follows: The steps to solve the maximum airflow cotree chord model by constructing a sequential model are as follows: S501, maximizing cotree chords Include The number of branches in the middle, such that maximum; S502, the solution set obtained is: Then at this time based on Make maximum; Input the basic correlation matrix of the ventilation network and for the known wind volume branch set The algorithm assigns extremely high weights to ensure priority selection into the cotree chord, while unknown wind volume branches are weighted according to the minimum wind volume. Then, it enters an iterative loop, where the algorithm continuously selects the edge with the smallest weight from the remaining edge set and checks its inclusion in the spanning tree candidate set through a loop avoidance mechanism. Will a loop be formed? If not, then add... And update the collection; the loop continues until... The number of edges reached (Spanning tree requirements), set Construct a minimum air volume spanning tree The unselected sides naturally form the maximum wind volume surplus tree string. This will provide a foundation for subsequent wind volume projections. and In Function transformed into The function can be used to solve for the minimum airflow cotree chord. and the maximum air volume generation tree .

6. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 1, characterized in that, The four air volume extrapolation models in S6 include air volume extrapolation models. Air volume projection model Air volume projection model Air volume projection model .

7. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 6, is characterized in that, The aforementioned air volume extrapolation model For: will Insert the maximum airflow into the tree string. In the middle, by analyzing the maximum wind volume of the remaining tree string Unknown air volume Optimize the model to minimize the number of airflow violations in the predicted airflow model. ,Right now: ， In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints Indicates branch air volume, , These represent branches in the spanning tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. Represents the minimum airflow spanning tree. Represents the set of measured air volumes. express * 3D matrix express The square formation, Representation matrix The reverse, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This indicates the maximum wind volume of the tree string. This represents the minimum airflow spanning tree.

8. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 6, is characterized in that, The aforementioned air volume extrapolation model For: will Place in the maximum airflow generation tree Inside, by adjusting the minimum airflow of the tree string... Unknown air volume Optimization was performed to minimize the error between the estimated and measured air volume, and to minimize the number of constraints violated with other unknown air volumes. The multiplier method was used to establish the air volume estimation model. : ， In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints Indicates branch air volume, , These represent branches in the spanning tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. This represents the maximum airflow spanning tree. Represents the set of measured air volumes. express * 3D matrix express The square formation, Representation matrix The reverse, This indicates that the penalty factor is a very large positive number. Indicates the branch number. Indicates branch The measured air volume express The air volume is extrapolated in the middle. This represents the measured-to-calculated error term. This indicates the number of violations of airflow constraints in the calculated airflow. Indicates a penalty item. Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This represents the minimum airflow rate of the tree chord. This represents the maximum airflow spanning tree. This represents the minimum airflow spanning tree.

9. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 6, is characterized in that, The aforementioned air volume extrapolation model For: will Insert the maximum airflow into the tree string. In the middle, by using the minimum air volume generating tree Unknown air volume The air volume is optimized and the estimated air volume is obtained, minimizing the error between the estimated and measured air volume and the number of constraints violated with other unknown air volumes. The multiplier method is also used to establish the air volume estimation model. : ， In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints , They represent the branches in the chord of the tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. This also indicates that the penalty factor is a very large positive number. express The air volume is extrapolated in the middle. This represents the measured-to-calculated error term. Indicates a penalty item. Representation matrix Moore-Penrose inverse matrix, Represents the set of measured air volumes. express * 3D matrix Representation matrix Moore-Penrose inverse matrix, express The square formation, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This indicates the maximum wind volume of the tree string. This represents the minimum airflow rate of the tree chord. This represents the minimum airflow spanning tree.

10. The method for extrapolating the air volume of the entire wind network based on finite measured air volume and topology as described in claim 6, characterized in that, The aforementioned air volume extrapolation model For: will Place in the maximum airflow generation tree In the middle, by generating the maximum air volume tree Unknown air volume Optimize the model to minimize the number of constraints violated in the predicted airflow and establish an airflow prediction model. ,Right now: ， In the above formula, express The unknown air volume in the middle, Indicates branch air volume, , Representing branches Minimum airflow constraints and maximum airflow constraints , They represent the branches in the chord of the tree. Minimum airflow constraints and maximum airflow constraints Indicates branch The calculated air volume conforms to the air volume constraint. This indicates a violation of the constraints. Represents the set of measured air volumes. express * 3D matrix Representation matrix Moore-Penrose inverse matrix, express The square formation, Indicates the wind volume of the remaining tree string. Indicates the spanning tree airflow. This represents the minimum airflow rate of the tree chord. This represents the maximum airflow generation tree.

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