Ventilation network resolving method

Abstract

The invention discloses a ventilation network resolving method. The method comprises the following steps: listing an air volume balance equation according to three constraint conditions of mine ventilation; any branch air volume of the air network is substituted into a Lagrange function of the obtained nonlinear programming model; an NCP-function and a smoothing parameter are introduced to construct a new function, so that the new function is smooth; the obtained NCP-smooth function algorithm inherits the fast convergence of the Newton algorithm, the initial point can be selected at will, the middle iteration point is not required to be an inner point, and the limitation of the inner point algorithm is broken. According to the method, the smooth Newton function is combined with the mine ventilation system theory, the NCP-function is smoothed, the NCP-function overcomes the non-differentiability of the NCP-function, the obtained NCP-smooth function algorithm inherits the rapid convergence of the Newton algorithm, the method can be used for solving the ventilation network optimization problem constrained by the air regulation site, the execution efficiency is high, and the method is suitable for large-scale popularization and application. The problem of large-scale ventilation network optimization can be solved.

Description

Technical Field

[0001] The invention belongs to the technical field of mine ventilation and safety, and in particular relates to a ventilation network solution method. Background Art

[0002] The task of the mine ventilation system is to use ventilation power to provide high-quality and sufficient fresh air to various wind-using locations underground in the most economical way to ensure the survival, safety and good working environment of underground workers. Aiming at the theoretical and technical problems faced by the optimization of mine ventilation networks in actual production, based on mine ventilation theory, optimization theory and graph theory, the ventilation network optimization analysis model is summarized and generalized, the advantages and disadvantages of the model solution algorithm are analyzed and summarized, and the data structure and graph theory related algorithm technology are used to automatically establish the mine ventilation system optimization model, and study the new algorithm for solving large-scale non-convex nonlinear programming models. The present invention adopts a ventilation network solution method to optimize the mine ventilation system.

[0003] The mine ventilation network optimization problem and the network multi-objective optimization problem have posed challenges to the optimization theory and methods, but at the same time they have also provided a promising research opportunity and a broad application field. The research on the mine ventilation network optimization theory and methods can improve the nonlinear optimization theory and multi-objective optimization theory, expand the solution methods and application fields of nonlinear optimization problems and multi-objective problems, and enhance the applicability of related optimization algorithms. Research on efficient, reliable and feasible mine ventilation network optimization algorithms can improve the accuracy of mine ventilation network optimization models and provide strong technical support for production mine ventilation network optimization and control, mine disaster prevention and safety. Summary of the invention

[0004] In view of the deficiencies in the prior art, the technical problem to be solved by the present invention is to provide a ventilation network solution method, which combines the smooth Newton function with the mine ventilation system theory, smoothes the NCP-function, and enables the NCP-function to overcome its non-differentiability. The obtained NCP-smooth function algorithm not only inherits the rapid convergence of the Newton algorithm, but also the initial point can be selected arbitrarily, and the intermediate iteration point is not required to be an interior point, breaking the limitations of the interior point algorithm.

[0005] In order to realize the above technical solution, a ventilation network solution method is proposed, which includes the following steps:

[0006] S1. List the air volume balance equation according to the three constraints of mine ventilation;

[0007] S2, bring the air volume of any branch of the wind network into the Lagrange function of the nonlinear programming model;

[0008] S3, introduce NCP-function and smooth parameter to construct a new function, so that the new function is smooth;

[0009] S4. The obtained NCP-smooth function algorithm inherits the fast convergence of Newton's algorithm, and the initial point can be selected arbitrarily, and the intermediate iteration points are not required to be interior points, breaking the limitations of the interior point algorithm.

[0010] Preferably, step S2 comprises the following steps:

[0011] Firstly, a mathematical model will be established according to the wind pressure balance law, wind volume balance law and wind resistance law, and then the actual air volume adjustment of the mine ventilation network will be combined. Finally, the air volume of any branch will be brought into the mathematical model and converted into the Lagrange function of the nonlinear programming model.

[0012] Further, the ventilation network optimization model solution method steps:

[0013] Step 1: Select y 0 ∈R n ,ρ>0,K>2,σ∈(0,0.5),η0≥0Let k=0;

[0014] Step 2: If || S(y k )||=0, terminate;

[0015] Step 3: Select Solving for (Δy) k : in, The following conditions must be met: If the above is not solvable or the following conditions do not hold: <(V k ) T S(y k ),(Δy) k >≤-ρ||(Δy) k || K , let (Δy) k =-(V k ) T S(y k );

[0016] Step 4: Let m k The smallest non-negative integer m that satisfies the following equation:

[0017] ψ(y k +2 -m (Δy) k )≤ψ(y k )+σ2 -m <(V k ) T S(y k ),(Δy)k >;

[0018] Step 5: Let y k+1 :=y k +2 -mk (Δy) k , select η k ≥0,k:=k+1, go to step 2.

[0019] From the above, the beneficial effects of the ventilation network solution method of the present invention are:

[0020] 1. The hybrid ventilation network optimization problem is transformed into two problems: ventilation network air volume distribution optimization and ventilation network control optimization, which greatly reduces the number of variables in the optimization model and improves the efficiency of the algorithm;

[0021] 2. The method of the present invention organically combines the smooth Newton algorithm and the NCP-function, giving full play to their respective advantages and making up for their respective shortcomings;

[0022] 3. The method of the present invention can conveniently solve the ventilation network optimization problem constrained by the air adjustment location;

[0023] 4. Through the testing and correctness verification of multiple schemes of simple ventilation network optimization and multi-fan ventilation network optimization examples, it is shown that the algorithm can optimize the ventilation network according to production needs and has certain effectiveness, feasibility and practicality;

[0024] 5. As long as the optimization model of the ventilation network has a theoretical solution, the present invention can be used to optimize the ventilation network.

[0025] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the following is a detailed description in combination with the preferred embodiments and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solution of the embodiment of the present invention, the drawings of the embodiment are briefly introduced below.

[0027] Figure 1 is a flow chart of the ventilation network solution method of the present invention;

[0028] Figure 2 This is a schematic diagram of a single fan + angle connection;

[0029] Figure 3 This is a schematic diagram of fixed air volume + angle connection;

[0030] Figure 4 This is a schematic diagram of two fans + natural wind pressure + corner connection. DETAILED DESCRIPTION

[0031] The following is a detailed description of the specific implementation of the present invention in conjunction with the accompanying drawings, which is a part of this specification and illustrates the principles of the present invention through examples. Other aspects, features and advantages of the present invention will become clear from the detailed description. In the drawings referred to, the same or similar parts in different figures are represented by the same reference numerals.

[0032] like Figures 1 to 4 As shown in the figure, in order to solve the non-convex programming model of the ventilation system, the nonlinear programming method is used to solve the problem of optimizing the mine ventilation network, namely, the defects of function derivation, matrix inversion, initial value sensitivity and low algorithm efficiency. The smooth Newton function is combined with the mine ventilation system theory, and the NCP function is smoothed to overcome its non-differentiability.

[0033] The ventilation network solution method of the present invention comprises the following steps:

[0034] Firstly, the air volume balance equation is listed according to the three constraints of mine ventilation, and then the air volume of any branch of the wind network is substituted into the Lagrange function of the nonlinear programming model, and the NCP-function and smooth parameter are introduced to construct a new function, so that the new function is smooth. The NCP-smooth function algorithm obtained in this way not only inherits the fast convergence of the Newton algorithm, but also the initial point can be selected arbitrarily, and the intermediate iteration point is not required to be an interior point, breaking the limitation of the interior point algorithm. The smooth Newton algorithm only needs to solve one linear equation group in each iteration. The present invention can be used to solve the ventilation network optimization problem with air adjustment location constraints, has high execution efficiency, and can solve large-scale ventilation network optimization problems.

[0035] First, a mathematical model is established based on the wind pressure balance law, wind volume balance law and wind resistance law. Then, the actual air volume adjustment of the mine ventilation network is combined. Finally, the air volume of any branch is brought into the mathematical model and converted into the Lagrange function of the nonlinear programming model. A ventilation network solution method can be written as follows:

[0036]

[0037] In the above constraint process, the first equality constraint equation is the wind volume balance equation. From this equation, the branch wind volume can be linearly expressed by the residual branch wind volume vector. The residual branch wind volume vector of the wind network is:

[0038] Q r =(q r1 ,q r2 ,…q rb ) T

[0039] The air volume q of any branch of the wind network is j It can be expressed as:

[0040]

[0041] Substituting equation (1) into the second set of equality constraints, we can obtain:

[0042]

[0043] The Lagrange function of the above nonlinear programming model is:

[0044]

[0045] Among them, λ1,λ2,η1,η2,ξ1,ξ2 are the corresponding Lagrange multiplier vectors. According to the optimization theory, the first-order necessary conditions (i.e., KKT conditions) of the above nonlinear programming model show that if (q * ,Δh * ) is the optimal solution of the above optimization model, then there exists a Lagrange multiplier vector λ1,λ2,η1,η2,ξ1,ξ2 such that is the solution of the following system of equations:

[0046]

[0047] in, It is not difficult to find through observation that the first and second to last equations of the above equation system are a standard problem, called complementarity problem.

[0048] Based on the smoothing of Fischer-Burmeister (FB) NCP-function, considering the nonlinear semidefinite cone complementarity problem, in order to find the solution: The matrix pair (X,Y)∈S n ×S n , where F:S n →S n For a continuously differentiable matrix-valued mapping, define the matrix-valued Fischer-Burmeister (FB) function Φ FB :S n ×S n →S n :Right now

[0049]

[0050] It can be transformed into:

[0051]

[0052] Here, “X⊥Y” means <X,Y>=0.

[0053] Obviously, Φ FB The matrix-valued FB-function can be used to transform the nonlinear semidefinite cone function problem into a nonsmooth system of equations. The matrix-valued FB-function is the Fischer-Burmeister function (FB-function) φ in the real number space. FB : Generalization of R×R→R:

[0054]

[0055] Known

[0056]

[0057] Therefore, the equivalent equation of the ventilation network model, the nonlinear complementarity problem (NCP), can be converted into a nonsmooth system of equations or an unconstrained minimization problem for solution using the FB-function: Find the vector x∈R n satisfy

[0058] x≥0,f(x)≥0,x T f(x)=0

[0059] Where, f:R n →R n is a continuously differentiable function.

[0060] Therefore, based on the Fischer-Burmeister (FB) NCP-function, the above equation system is equivalently transformed into the following equation system:

[0061]

[0062] Among them, F(z * ) contains 4 nonlinear complementarity constraints and 4 equality constraints. Because the Fischer-Burmeister (FB) NCP-function φ FB It is not differentiable at point (0,0), so the function F is not differentiable. In this way, some classical iterative algorithms (for example, Newton-type algorithms) cannot be used to solve this non-smooth system of equations. It is continuously differentiable at any point. F(z) = 0 has good mathematical properties. Let

[0063]

[0064] Then the solution of F(z)=0 can be transformed into the global optimal solution of the following optimization model with the help of mapping Ξ(z), that is,

[0065]

[0066] And the optimal value of the optimization model is zero. In general, the function It is called the value function or utility function.

[0067] But for most NCP functions, they are not differentiable. In order to overcome the non-differentiability of NCP-functions, they need to be smoothed. The way to smoothen is to introduce a smooth parameter and then construct a new function so that the new function is smooth. This new function is called NCP-smooth function. C. Kanzow FB This gives a smooth function:

[0068]

[0069] The μ in the formula is called the smooth parameter, and the smooth function is the NCP-function φ FB A smooth approximation of . The following theorem gives some properties of smooth functions.

[0070] Theorem 1: Smooth Function According to the above definition,

[0071] (i) For any If μ≠0, then the function Continuously differentiable.

[0072] (ii)

[0073] For any y: = (μ, q, Δh, λ1, λ2, η1, η2, ξ1, ξ2)∈R 7n+1 ,remember

[0074]

[0075] Thus, according to Theorem 1(ii), it is not difficult to see that And z is a solution to (2).

[0076] According to Theorem 1(i), the function S is continuously differentiable. Therefore, solving the non-smooth system of equations (2) can be transformed into solving the smooth system of equations S(y) = 0. With the help of the smooth function When μ↓0, the solution of S(y)=0 smoothly approaches the non-smooth equation system F(z)=0, and then approaches the solution of the KKT system. In this way, based on the continuous differentiability of the function S, a Newton-type algorithm with a very high convergence speed is designed to solve the smooth equation system S(y)=0, so as to obtain an approximate solution to the KKT system. The Jacobian matrix is:

[0077]

[0078] in,

[0079] and

[0080] and

[0081] and

[0082] and

[0083] and

[0084] and

[0085] and

[0086]

[0087] and

[0088]

[0089] and

[0090]

[0091] and

[0092]

[0093] and

[0094]

[0095] and

[0096]

[0097] The algorithm design of the ventilation network optimization model solution method of the present invention is a very effective Newton-type algorithm for solving S(y)=0, which is called the smooth Newton algorithm. This algorithm is similar to the interior point algorithm, both of which belong to the Newton-type algorithm. The smooth Newton algorithm not only inherits the fast convergence of the Newton algorithm, but also the initial point can be arbitrarily selected, and does not require the intermediate iteration point to be an interior point, breaking the limitations of the interior point algorithm. The smooth Newton algorithm only needs to solve one linear equation system in each iteration.

[0098] For any y: = (μ, q, Δh, λ1, λ2, η1, η2, ξ1, ξ2)∈R 7n+1 , define the function:

[0099]

[0100] The ventilation network optimization model solving method of the present invention comprises the following steps:

[0101] Step 1: Select y 0 ∈R n ,ρ>0,K>2,σ∈(0,0.5),η0≥0Let k=0;

[0102] Step 2: If || S(y k )||=0, terminate;

[0103] Step 3: Select Solving for (Δy) k :

[0104] in, The following conditions must be met: If the above is not solvable or the following conditions do not hold: <(V k ) T S(y k ),(Δy) k >≤-ρ||(Δy) k || K , let (Δy) k =-(V k ) T S(y k ).

[0105] Step 4: Let m k The smallest non-negative integer m that satisfies the following equation:

[0106] ψ(y k +2 -m (Δy) k )≤ψ(y k )+σ2 -m <(V k ) T S(yk ),(Δy) k >.

[0107] Step 5: Select η k ≥0,k:=k+1, go to step 2.

[0108] Computation of smooth Newton's equations: in,

[0109]

[0110] From the smooth Newton equation we get:

[0111] Δμ=-μ+β||S(y)||min{1,||S(y)|| γ};

[0112]

[0113] From the above formula, the smooth Newton equation is simplified to:

[0114]

[0115] in,

[0116]

[0117] Single fan + angle connection

[0118] Number of branches: 10, number of fans: 1, number of iterations: 6000, natural wind pressure: 1, fixed air volume: 0, iteration accuracy: 0.0001, the detailed data of the ventilation network are shown in Table 1, Table 2, and Table 3:

[0119] Table 1 Natural wind pressure

[0120]

[0121] Table 2 Wind network data

[0122]

[0123]

[0124] Table 3 Fan data

[0125]

[0126] The algorithm solution data is shown in Table 4, Table 5, and Table 6 below:

[0127] Table 4 Fan curve fitting coefficients

[0128]

[0129] Number of nodes = 7, number of loops = 4, cumulative number of loop branches = 17, number of loop reselections = 0, number of iterations = 12, iteration accuracy = 0.000100, loop closure error = 0.00013.

[0130] Table 5 Wind network solution data

[0131]

[0132]

[0133] Table 6 Fan calculation data

[0134]

[0135] Equal area hole A(1) = 2.0824m 2 .

[0136] Fixed air volume + angle connection

[0137] Number of branches: 7, number of fans: 0, number of iterations: 6000, natural wind pressure: 0, fixed air volume: 1, iteration accuracy: 0.0001, the detailed data of the ventilation network are shown in Table 7 and Table 8:

[0138] Table 7 Wind network data

[0139]

[0140] Table 8 Fixed air volume branches

[0141]

[0142]

[0143] Number of nodes = 5, number of loops = 3, cumulative number of loop branches = 11, number of reselected loops = 0, number of iterations = 3, iteration accuracy = 0.000100, loop closure error = 0.00002, the algorithm solution data are shown in Table 9 and Table 10 below:

[0144] Table 9 Wind network solution data

[0145]

[0146] Table 10 Fixed air volume calculation data

[0147]

[0148] Two fans + natural wind pressure + angle connection

[0149] Number of branches: 9, number of fans: 2, number of iterations: 6000, natural wind pressure: 1, fixed air volume: 0, iteration accuracy: 0.0001, the detailed data of the ventilation network are shown in Table 11, Table 12, and Table 13:

[0150] Table 11 Natural wind pressure

[0151]

[0152]

[0153] Table 12 Wind network data

[0154]

[0155] Table 13.1 Fan 1 data

[0156]

[0157] Table 13.2 Fan 2 data

[0158]

[0159] The algorithm solution data are shown in Table 14, Table 15, and Table 16 below:

[0160] Table 14.1 Fan 1 curve fitting coefficients

[0161]

[0162]

[0163] Table 14.2 Curve fitting coefficients for fan 2

[0164]

[0165] Number of nodes = 7, number of loops = 3, cumulative number of loop branches = 14, number of loop reselections = 0, number of iterations = 7, iteration accuracy = 0.000100, loop closure error = 0.00006.

[0166] Table 15 Wind network calculation data

[0167]

[0168] Table 16 Fan calculation data

[0169]

[0170] Equal area hole A(1) = 0.8631m 2 , equal area hole A(2) = 0.8026m 2 .

[0171] From the analysis of the experimental results, we can get:

[0172] (1) The algorithm can meet the specific requirements of hybrid ventilation network optimization in actual production;

[0173] (2) In a specific ventilation network, scientifically and rationally increasing the number of auxiliary fans will reduce energy consumption, but it will increase the complexity of daily fan management in the ventilation network. During the mine disaster period, the difficulty of ventilation network regulation will increase;

[0174] (3) Adding additional constraints for air conditioning comes at the cost of additional energy consumption in the ventilation network.

[0175] The above is only a preferred embodiment of the present invention, which certainly cannot be used to limit the scope of rights of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and changes can be made without departing from the principle of the present invention, and these improvements and changes are also regarded as the protection scope of the present invention.

Claims

1. A ventilation network solution method, characterized in that: The following steps are involved: S1. List the air volume balance equation according to the three constraints of mine ventilation; S2, bring the air volume of any branch of the wind network into the Lagrange function of the nonlinear programming model; S3, introduce NCP-function and smooth parameter to construct a new function, so that the new function is smooth; S4. The obtained NCP-smooth function algorithm inherits the fast convergence of Newton's algorithm, and the initial point can be selected arbitrarily, and the intermediate iteration points are not required to be interior points, breaking the limitations of the interior point algorithm.

2. The ventilation network solution method according to claim 1, characterized in that: Step S2 includes the following steps: Firstly, a mathematical model will be established according to the wind pressure balance law, wind volume balance law and wind resistance law, and then the actual air volume adjustment of the mine ventilation network will be combined. Finally, the air volume of any branch will be brought into the mathematical model and converted into the Lagrange function of the nonlinear programming model.

3. The ventilation network solution method according to claim 1, characterized in that: Ventilation network optimization model solution method steps: Step 1. Select y 0 ∈R n ,ρ>0,K>2,σ∈(0,0.5),η0≥0Let k=0; Step 2: If || S(y k )||=0, terminate; Step 3: Select Solved in, The following conditions must be met: If the above is not solvable or the following conditions do not hold: <(V k ) T S(y k ),(Δy) k >≤-ρ||(Δy) k || K , let (Δy) k =-(V k ) T S(y k ); Step 4: Let m k is the smallest non-negative integer m that satisfies the following equation: ψ(y k +2 -m (Dy) k )≤ψ(y k )+σ2 -m <(V k ) T S(y k ),(Δy) k >; Step 5: Let y k+1 :=y k +2 -mk (Δy) k , select η k ≥0,k:=k+1, go to step 2.

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