CN111693423B - Goaf permeability coefficient inversion method based on genetic algorithm - Google Patents

Abstract

The invention provides a goaf permeability coefficient inversion method based on a genetic algorithm, and relates to the technical field of mine ventilation. The invention comprises the following steps: step 1: randomly generating a primary population about the permeability coefficient K; step 2: setting an expected value and calculating a goaf velocity field value V; and step 3: solving the velocity field distribution value V of each individual in the population _ij (ii) a And 4, step 4: calculating V and V _ij The Euclidean distance therebetween; and 5: starting iteration, judging whether a termination condition is met, and outputting an optimal solution if the termination condition is met; step 6 cannot be satisfied; step 6: performing a selection operation to obtain a population D _l (ii) a And 7: will D _l The individuals in (1) are crossed and mutated by genetic algorithm to generate D _l '; and 8: repeating the step 3 to the step 7, and outputting an optimal solution if a termination condition is met; if l in step 6 is not satisfied, adding 1. The method is simple and easy to implement, less in human intervention, short in time consumption, and good in accuracy of the reverse performance result.

Description

A method for inversion of gob permeability coefficient based on genetic algorithm

technical field

The invention relates to the technical field of mine ventilation, in particular to a method for inversion of goaf permeability coefficient based on genetic algorithm.

Background technique

The physical structure of mine goaf is complex and variable. The deformation caused by the stress of a certain rock in the goaf will lead to the change of the permeability coefficient in the whole goaf. It has a huge impact on the state of all gas flows in the goaf. If the permeability coefficient and gas flow law in the goaf cannot be mastered. It is easy to cause gas, fire and other accidents. Studying the permeability coefficient in the goaf can determine the natural ignition position of the goaf and establish a prediction theory. The above-mentioned permeability coefficients can be obtained by using this method combined with the genetic algorithm, which is of great significance for preventing accidental disasters and improving the overall safety factor of mine goafs.

At present, the measurement methods of permeability coefficient are mainly divided into two categories: "laboratory measurement" and "field field measurement". However, when this method is used in gobs, since the seepage medium and boundary conditions are often complex, it is very difficult to use analytical formulas to solve the permeability coefficient or permeability tensor. In addition, the current test method still has difficulties in practical application and high cost. At the same time, there are problems such as discrete data, weak representativeness, and timing delay in field testing.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for inversion of goaf permeability coefficient based on genetic algorithm, which is simple and easy to implement, with less human intervention and short time-consuming, and is suitable for inversion. The results of the show have better accuracy.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

The invention provides a goaf permeability coefficient inversion method based on a genetic algorithm, comprising the following steps:

Step 1: Randomly generate a binary population with respect to the permeability coefficient K, set the population size to m, that is, there are m individuals in the population, and perform population initialization, convert the binary individual U _i in the population into a decimal number A _i , and then set A _i limits the size range; by adjusting the chromosome length of each individual in the population to control the optimization range of the genetic algorithm to form the first generation population D ₀ ={d ₁ ,d ₂ …d _i …d _m }, where i means that the individual is in the population The number in , 1≤i≤m;

Step 2: Set the expected value K ₀ , and calculate the velocity field value V of the goaf through the finite volume method in the two-dimensional stable seepage numerical calculation method;

Step 3: Substituting the population into the finite volume method in the two-dimensional stable seepage numerical calculation method, and solving a set of velocity field distribution values V _ij for each individual in the population, where i represents the number of the individual in the population, and j represents iteration frequency;

Step 4: Calculate the Euclidean distance OP between V and V _ij ;

In the formula, x _1q represents the qth individual in V, x _1q represents the qth individual in V _ij , N is the total number of individuals, OP is the Euclidean distance between the two arrays; if the OP value is small, it means that the numerical similarity between the two matrices is high ;

The fitness function is set, and the calculated Euclidean distance is brought into the expression:

The size of the fitness f _i represents the fitness of the i-th individual in the population; a large value of the fitness f _i means that the OP is small, and the value of the velocity field V _ij is similar to V; otherwise, it means that the individual fitness of the population is low ;

Step 5: According to step 4, start to iterate and select the individual with the highest fitness; after each iteration is calculated, judge whether the termination condition is satisfied, if any one of the termination conditions is satisfied, the iteration can be stopped to obtain the optimal individual K _b and the optimal fitness f _i to obtain the optimal solution; if the termination condition cannot be met, proceed to step 6;

The termination condition is:

1. When the fitness value of an individual is iterated to be greater than the artificially set fitness value, the individual is the optimal solution;

2. When the number of population iterations reaches the artificially set maximum number of iteration steps, the individual with the highest fitness value in the current population is taken as the optimal solution.

Step 6: Execute the selection operation of the genetic algorithm; in the population obtained after iterative calculation in step 5, select the individual with the highest fitness value to be copied first, as the individual in the population Dl, where _l represents the population number, l=1, 2, 3, ...; then determine the fitness value of each individual according to the fitness function, determine the probability Pi of each individual being selected, select individuals with higher fitness according to the probability _Pi , select one individual at a time, and select m-1 times , to obtain a population D _l containing m individuals;

Step 7: Perform the crossover and mutation operations in the genetic algorithm on the individuals in the population _D1 ; use the single-point crossover method to exchange the alleles in the two chromosomes, set the crossover probability pc, and set the mutation rate pm at the same time, set The mutation rate is set to a small value to generate a population D _l '; perform step 8;

Step 8: Repeat steps 3 to 5. If the termination condition is met, then output the optimal individual and optimal fitness; if the termination condition is not met, add 1 to the population number l, update the population number l, and perform steps 6 to 1 7;

The formula of the probability P _i in the step 6 is as follows:

Where sum(f _i ) is the sum of fitness of all individuals in this generation population.

The beneficial effect produced by adopting the above-mentioned technical scheme is: a kind of goaf seepage coefficient inversion method based on genetic algorithm provided by the present invention, this method utilizes genetic algorithm to randomly generate the population about the seepage coefficient K, set by fitness function, The expected value of the permeability coefficient is approximated from generation to generation, so as to obtain a more accurate permeability coefficient of the goaf. The internal structure of the goaf is complex and changeable, and the change of the permeability coefficient in the porous medium area always affects the fluid flow state inside the goaf. It is of great significance to study the inversion of the permeability coefficient in the goaf and master the law of gas flow in the prevention and control of coal spontaneous combustion in the goaf. The development of technology provides guidance; the inversion method proposed by the invention solves the disadvantages of high cost, poor data representativeness and long time consumption exposed in the current permeability coefficient measurement method to a certain extent. Using the principle of iterative inversion, combined with the genetic optimization method to modify the initial model, and search for optimization from generation to generation; this embodies the advantages of the present invention, such as simple method for inverting permeability coefficient, less human intervention, and short time consumption. And it has better accuracy for the inversion result.

Description of drawings

Fig. 1 is the flowchart of the goaf permeability coefficient inversion method provided by the embodiment of the present invention;

FIG. 2 is a figure showing the variation of fitness with the number of iterations in the iterative inversion process provided by the embodiment of the present invention;

detailed description

The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

The present invention uses the numerical method based on CFD (computational fluid dynamics) to calculate the goaf velocity distribution value obtained by solving the goaf velocity field, sets the fitness function, and constructs the goaf permeability coefficient iteration based on genetic optimization inversion model. Inversion study on the permeability coefficient of the gob. Theoretically speaking, the mine goaf structure is a three-dimensional complex and changeable situation, but in order to simplify the calculation and eliminate unnecessary interference factors, only two-dimensional changes in the goaf are considered in this embodiment;

As shown in FIG. 1 , the method of this embodiment is as follows.

The invention provides a goaf permeability coefficient inversion method based on a genetic algorithm, comprising the following steps:

Step 1: Randomly generate a binary population with respect to the permeability coefficient K, set the population size to m, that is, there are m individuals in the population, and perform population initialization, convert the binary individual U _i in the population into a decimal number A _i , and then set A _i limits the size range; by adjusting the chromosome length of each individual in the population to control the optimization range of the genetic algorithm to form the first generation population D ₀ ={d ₁ ,d ₂ …d _i …d _m }, where i means that the individual is in the population The number in , 1≤i≤m;

First, the binary individual U _i in the population is converted into a decimal number A _i (i∈(1,500)), and then the value range of A _i is limited by the following expression to generate d _i ;

Among them, Max _value represents the upper limit of the value of d _i , which needs to be set artificially;

In this embodiment, Max _value = 1 is defined, that is, an optimal inversion is performed on the expected value within the range of [0, 1];

In the present embodiment, m=500;

Step 2: Set the expected value K ₀ , and calculate the velocity field value V of each control unit in the goaf through the finite volume method in the two-dimensional stable seepage numerical calculation method; Set, the velocity field solution result V is an array of 400*100, the velocity field solution result in the following is consistent with the form of V);

The finite volume method in the numerical calculation method of two-dimensional stable seepage is the numerical method for solving the goaf;

Step 3: Substituting the population into the finite volume method in the two-dimensional stable seepage numerical calculation method, each individual in the population correspondingly solves a set of velocity field distribution values V _ij , where i represents the number of the individual in the population, and j represents the number of iterations ;

Need to explain: When calculating the velocity field of the goaf for the expected value and population, the settings of other boundary conditions should be kept the same except for the permeability coefficient;

The velocity field calculation result obtained in the present invention is an array composed of the velocity values of each point in the goaf, and its scale is numerically equal to the set length and width boundaries of the goaf. That is, if the boundary size of the gob is set to 400m*100m, the velocity field calculation result V will be an array composed of 400*100 velocity values.

Step 4: Calculate the Euclidean distance OP between V and V _ij ; to judge the degree of approximation between the velocity field distribution value and V in each generation of the genetic algorithm;

In the formula, x _1q represents the qth individual in V, x _1q represents the qth individual in V _ij , N is the total number of individuals, OP is the Euclidean distance between the two arrays; the smaller the value of OP, the numerical similarity between the two matrices higher;

The fitness function is set, and the calculated Euclidean distance is brought into the expression:

The size of the fitness f _i represents the fitness of the i-th individual in the population; the larger the value of the fitness f _i , the smaller the OP, and the closer the velocity field value V _ij is to V; otherwise, it means that the population individual The lower the fitness;

Step 5: According to step 4, start to iterate and select the individual with the highest fitness; after each iteration is calculated, judge whether the termination condition is satisfied, if any one of the termination conditions is satisfied, the iteration can be stopped to obtain the optimal individual K _b and the optimal fitness f _i to obtain the optimal solution; if the termination condition cannot be met, proceed to step 6;

The termination conditions are as follows:

1. When the fitness value of an individual is iterated to be greater than the artificially set fitness value, the individual is the optimal solution;

2. When the number of population iterations reaches the artificially set maximum number of iteration steps, the individual with the highest fitness value in the current population is taken as the optimal solution;

Step 6: Execute the selection operation of the genetic algorithm; the individual with the highest fitness value in the population obtained after the iterative calculation in step 5 is preferentially copied as the individual in the population Dl, where _l represents the population number, l=1,2,3 , ...; then determine the fitness value of each individual according to the fitness function, and determine the probability that each individual is selected Pi=fi/sum(f _i ), where sum(f _i ) represents the fitness of all individuals in this generation population sum; according to the probability P _i , select individuals with greater fitness, select one individual at a time, and select m-1 times to obtain a population D _l containing m individuals;

Step 7: Perform the crossover and mutation operations in the genetic algorithm on the individuals in the population _D1 ; use the single-point crossover method to exchange the alleles in the two chromosomes, set the crossover probability pc, and set the mutation rate pm at the same time, set The mutation rate is set to a small value to generate a population D _l '; perform step 8;

Step 8: Repeat steps 3 to 5. If the termination condition is met, then output the optimal individual and optimal fitness; if the termination condition is not met, add 1 to the population number l, update the population number l, and perform steps 6 to 1 7.

In this embodiment, according to the distribution of the goaf permeability coefficient as an example, it will be described in detail. Because the feasibility of the method is intended to be explored, in the example given by the present invention: it is set that the permeability coefficients are constant everywhere in the goaf except the working face. It is K=0.01. A genetic algorithm is used to generate a population of 500 individuals per generation for iteration.

The present invention adopts the termination condition of the maximum number of iterations, sets the maximum number of iterations to 150 generations, and outputs the optimal fitness and the optimal individual when the number of iterations reaches 150 generations. It is assumed that the alleles in the two chromosomes are exchanged by a single-point crossover method, and the crossover probability pc=0.6 is set. In addition, when setting the mutation rate, in order to ensure that the individuals in the population maintain a high fitness condition, it should be set to a very small number, and the mutation probability pm=0.01.

After the iterations shown in Figure 2, when the maximum number of iterations reaches 150 generations, the fitness f _i value is output, f _i =0.94799. The f _i value is constantly approaching 1, which is in line with the expected trend of the present invention. The final result obtained by the inversion is K _b =0.00977517.

Using the set expected value K ₀ =0.01, the relative error of this inversion method is calculated, σ=(predicted value−true value)/real value, and σ=0.023 is obtained. That is, the relative error is less than 3%. Therefore, it can be considered that the inversion of the permeability coefficient has been realized. The permeability coefficient of the goaf obtained by this method can be used to guide the production work, clarify the permeability coefficient of the goaf, and play a role in mastering the internal information of the goaf such as the fluid flow state of the goaf and the gas concentration distribution of the goaf. Great significance. It has guiding significance for predicting the location of fire occurrence and preventing gas overrun in some areas. At the same time, with the help of the high efficiency and quickness of the computer program, the shortcomings of the existing permeability coefficient testing methods such as long time consumption and high cost are avoided. Promote the use of computer methods in the field of coefficient measurement.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still be Modifications are made to the technical solutions described in the foregoing embodiments, or equivalent replacements are made to some or all of the technical features; these modifications or replacements do not make the essence of the corresponding technical solutions depart from the scope defined by the claims of the present invention.

Claims (2)

1. A goaf permeability coefficient inversion method based on genetic algorithm, is characterized in that: comprise the steps: Step 1: Randomly generate a binary population with respect to the permeability coefficient K, set the population size to m, that is, there are m individuals in the population, and perform population initialization, convert the binary individual U _i in the population into a decimal number A _i , and then set A _i limits the size range; by adjusting the chromosome length of each individual in the population to control the optimization range of the genetic algorithm to form the first generation population D ₀ ={d ₁ ,d ₂ …d _i …d _m }, where i means that the individual is in the population The number in , 1≤i≤m; Step 2: Set the expected value K ₀ , and calculate the velocity field value V of the goaf through the finite volume method in the two-dimensional stable seepage numerical calculation method; Step 3: Substituting the population into the finite volume method in the two-dimensional stable seepage numerical calculation method, each individual in the population correspondingly solves a set of velocity field distribution values V _ij , where i represents the number of the individual in the population, and j represents the number of iterations ; Step 4: Calculate the Euclidean distance OP between V and V _ij ;

In the formula, x _1q represents the qth individual in V, x _2q represents the qth individual in V _ij , N is the total number of individuals, OP is the Euclidean distance between the two arrays; if the OP value is small, it means that the numerical similarity between the two matrices is high ; The fitness function is set, and the calculated Euclidean distance is brought into the expression:

The size of the fitness f _i represents the fitness of the i-th individual in the population; a large value of the fitness f _i means that the OP is small, and the value of the velocity field V _ij is similar to V; otherwise, it means that the fitness of the individual in the population is low; Step 5: According to step 4, start to iterate and select the individual with the highest fitness; after each iteration is calculated, judge whether the termination condition is satisfied, if any one of the termination conditions is satisfied, the iteration can be stopped to obtain the optimal individual K _b and the optimal fitness f _i to obtain the optimal solution; if the termination condition cannot be met, proceed to step 6; The termination condition is: 1. When the fitness value of an individual is iterated to be greater than the artificially set fitness value, the individual is the optimal solution; 2. When the number of population iterations reaches the artificially set maximum number of iteration steps, the individual with the highest fitness value in the current population is taken as the optimal solution; Step 6: Execute the selection operation of the genetic algorithm; in the population obtained after iterative calculation in step 5, select the individual with the highest fitness value to be copied first, as the individual in the population D _L , where L represents the population number, L=1,2, 3, ...; Then determine the fitness value of each individual according to the fitness function, determine the probability P _i of each individual being selected, select individuals with higher fitness according to the probability P _i , select one individual at a time, and select m-1 times, get the population D _L containing m individuals; Step 7: Perform the crossover and mutation operations in the genetic algorithm on the individuals in the population D _L ; use the single-point crossover method to exchange the alleles in the two chromosomes, and set the mutation rate at the same time, and set the mutation rate to a small value : generate population D _L ′; execute step 8; Step 8: Repeat steps 3 to 5. If the termination condition is met, output the optimal individual and optimal fitness; if the termination condition is not met, add 1 to the population number L, update the population number L, and perform steps 6 to 5 7. 2. a kind of goaf permeability coefficient inversion method based on genetic algorithm according to claim 1, is characterized in that: the formula of probability _Pi in the described step 6 is as follows:

Among them, sum(f _i ) is the sum of fitness of all individuals in this generation population.

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