CN111693423A - Goaf permeability coefficient inversion method based on genetic algorithm - Google Patents
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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 an initial population about the permeability coefficient K; step 2: setting an expected value and calculating a goaf speed field value V; and step 3: solving velocity field distribution value V of each individual in the populationij(ii) a And 4, step 4: calculating V and VijThe Euclidean distance between them; 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 Dl(ii) a And 7: will DlThe individuals in (1) are crossed and mutated by genetic algorithm to generate Dl'; 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
Technical Field
The invention relates to the technical field of mine ventilation, in particular to a goaf permeability coefficient inversion method based on a genetic algorithm.
Background
The physical structure of the mine goaf has complexity and variability. The deformation of a rock in a goaf caused by stress can cause the change of the permeability coefficient in the whole goaf. A great influence is exerted on the state of all gas flows in the goaf. If the permeability coefficient and the gas flow rule in the goaf cannot be mastered. Accidents such as gas and fire are easy to happen. The natural ignition position of the goaf can be judged by researching the permeability coefficient in the goaf, and a prediction theory is established. The permeability coefficient can be obtained by combining the method with a genetic algorithm for inversion, and the method has great significance for preventing accidental disasters and improving the overall safety coefficient of the mine goaf.
The existing permeability coefficient measuring method mainly comprises two categories of laboratory measurement and field measurement. However, when the method is used in the goaf, the seepage medium and the boundary condition are often complex, and it is particularly difficult to solve the permeability coefficient or permeability tensor by using an analytical formula. In addition, the existing test method has the problems of difficult practical application, high cost, discrete data, poor representativeness, time delay and the like in field test.
Disclosure of Invention
The invention aims to solve the technical problem of providing a goaf permeability coefficient inversion method based on a genetic algorithm aiming at the defects of the prior art.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the invention provides a goaf permeability coefficient inversion method based on a genetic algorithm, which comprises the following steps:
step 1: randomly generating a binary population about the permeability coefficient K, setting the population size to be m, namely m individuals in the population, initializing the population, and enabling binary individuals U in the populationiConversion to decimal number AiThen to AiLimiting the size range; the optimization range of the genetic algorithm is controlled by adjusting the length of each individual chromosome in the population to form an initial generation population D0＝{d1,d2…di…dmWherein i represents the number of individuals in the population, and i is more than or equal to 1 and less than or equal to m;
step 2: setting an expected value K0Solving out a goaf velocity field value V by a numerical calculation method of a two-dimensional stable seepage finite volume method;
and step 3: substituting the population into a numerical calculation method of a two-dimensional stable seepage finite volume method, and correspondingly solving a group of velocity field distribution numerical values V of each individual in the populationijWherein i represents the number of individuals in the population, and j represents the number of iterations;
and 4, step 4: calculating V and VijThe Euclidean distance OP between them;
in the formula x1qDenotes the q-th individual in V, x1qRepresents VijThe q individual in the population, N is the total number of individuals, and OP is the Euclidean distance between two groups; if the OP value is small, the similarity of the numerical values of the two matrixes is high;
and setting a fitness function, and substituting the calculated Euclidean distance into an expression:
fitness fiRepresents the fitness of the ith individual in the population; fitness fiIf the value is large, indicating that OP is small, the velocity field value V isijIs similar to V; otherwise, the individual fitness of the group is low;
and 5: according to the step 4, starting iteration to select the individual with the highest fitness; after each iterative calculation is finished, judging whether the termination conditions are met or not, if any one of the termination conditions is met, stopping the iteration to obtain the optimal individualKbAnd an optimum fitness fiObtaining an optimal solution; if the termination condition cannot be met, performing step 6;
the termination conditions were:
when the fitness value of an individual is larger than the artificially set fitness value through iteration, the individual is the optimal solution;
and secondly, when the iteration times of the population reach the maximum iteration step number set manually, taking the individual with the highest fitness value in the current population as an optimal solution.
Step 6: performing a selection operation of a genetic algorithm; selecting the individual with the highest fitness value from the population obtained after iterative computation in step 5 to preferentially copy as the population DlWherein l represents the population number, 1,2,3, …; then determining the fitness value of each individual according to the fitness function, determining the probability Pi of each individual being selected, and determining the probability P according to the probability PiSelecting individuals with larger fitness, selecting one individual at a time, and selecting m-1 times to obtain a population D containing m individualsl；
And 7: the population DlCarrying out cross and variation operations in a genetic algorithm on the individuals; adopting a single-point crossing method to interchange alleles in two chromosomes, setting a crossing probability pc, setting a variation rate pm, setting the variation rate as a small value, and generating a population Dl'; executing the step 8;
and 8: repeating the step 3 to the step 5, and if the termination condition is met, outputting the optimal individual and the optimal fitness; if the termination condition is not satisfied, executing step 6 to step 7 while adding 1 to l in step 6.
Probability P in said step 6iThe formula of (1) is as follows:
wherein sum (f)i) Is the sum of the fitness of all individuals in the population of this generation.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: according to the goaf permeability coefficient inversion method based on the genetic algorithm, the genetic algorithm is used for randomly generating a population related to the permeability coefficient K, and the population is set through a fitness function and approximates to a permeability coefficient expected value instead of the population, so that the goaf permeability coefficient is relatively accurate. The internal structure of the goaf is complex and changeable, and the change time of the permeability coefficient of the porous medium area influences the fluid flow state in the goaf. The method has the advantages that the inversion of the permeability coefficient in the goaf is researched, the gas flow rule is mastered, the method has important significance for preventing and controlling the spontaneous combustion of coal in the goaf, the method is a basis for judging the natural fire position of the goaf and establishing a prediction theory, and can provide guidance for the development of a fire prevention and control technology of the goaf; the inversion method provided by the invention solves the defects of high cost, poor data representativeness, long time consumption and the like exposed in the existing permeability coefficient measuring method to a certain extent. Modifying the initial model by using an iterative inversion thought principle and combining a genetic optimization method, and performing generation optimization; the method has the advantages of simplicity, less human intervention, short time consumption and the like. And has better accuracy on the result of the reverse performance.
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Fig. 1 is a flowchart of a goaf permeability coefficient inversion method according to an embodiment of the present invention;
fig. 2 is a diagram of a change of fitness with iteration times in an iterative inversion process according to an embodiment of the present invention;
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
According to the method, a numerical method based on CFD (computational fluid dynamics) is utilized to calculate the goaf velocity field to obtain the goaf velocity distribution numerical value, a fitness function is set, and a goaf permeability coefficient iterative inversion model based on genetic optimization is constructed. And carrying out inversion research on the permeability coefficient of the goaf. Theoretically, the mine goaf structure is a three-dimensional complex and variable condition, but unnecessary interference factors are eliminated in order to simplify calculation, so that only two-dimensional change in the goaf is considered in the embodiment;
as shown in fig. 1, the method of the present embodiment is as follows.
The invention provides a goaf permeability coefficient inversion method based on a genetic algorithm, which comprises the following steps:
step 1: randomly generating a binary population about the permeability coefficient K, setting the population size to be m, namely m individuals in the population, initializing the population, and enabling binary individuals U in the populationiConversion to decimal number AiThen to AiLimiting the size range; the optimization range of the genetic algorithm is controlled by adjusting the length of each individual chromosome in the population to form an initial generation population D0＝{d1,d2…di…dmWherein i represents the number of individuals in the population, and i is more than or equal to 1 and less than or equal to m;
firstly, binary individual U in populationiConversion to decimal number Ai(i ∈ (1,500)), and then pair A is expressed byiLimiting the value range to generate di；
Wherein MaxvalueRepresents diThe upper value limit of (2) needs to be set manually;
max is defined in the present embodimentvalue1, i.e. in [0, 1 ]]Performing optimization inversion on the expected value in the range of (1);
in the embodiment, m is 500;
step 2: setting an expected value K0Solving the speed field value V of each control unit of the goaf by a numerical calculation method of a two-dimensional stable seepage finite volume method; (because of the goaf boundary conditions in the goaf numerical solution, the velocity field solution result V is a 400 x 100 array, and the velocity field solution result in the following is consistent with the V form);
the numerical calculation method of the two-dimensional stable seepage finite volume method is a numerical method for calculating the goaf;
and step 3: substituting the population into a two-dimensional stable seepage finite volumeIn the method for calculating numerical values, each individual in the population correspondingly solves a group of velocity field distribution numerical values VijWherein i represents the number of individuals in the population, and j represents the number of iterations;
need to explain: when the goaf velocity field is resolved on the expected value and the population, the settings of other boundary conditions except the permeability coefficient are kept the same;
the velocity field resolving result obtained in the invention is an array consisting of velocity values of all points of the goaf, and the scale size is equal to the length and width boundary of the set goaf in value. That is, if the size of the goaf boundary is set to 400m × 100m, an array consisting of 400 × 100 velocity values of the velocity field solution result V is finally obtained.
And 4, step 4: calculating V and VijThe Euclidean distance OP between them; so as to judge the approximation degree between the velocity field distribution value and V in each generation of the genetic algorithm;
in the formula x1qDenotes the q-th individual in V, x1qRepresents VijThe q individual in the population, N is the total number of individuals, and OP is the Euclidean distance between two groups; the smaller the OP value is, the higher the numerical similarity of the two matrixes is;
and setting a fitness function, and substituting the calculated Euclidean distance into an expression:
fitness fiRepresents the fitness of the ith individual in the population; fitness fiThe larger the value, the smaller OP, the velocity field value VijThe more similar to V; otherwise, the lower the individual fitness of the group is;
and 5: according to the step 4, starting iteration to select the individual with the highest fitness; after each iterative calculation, judging whether the termination condition is met, if any one of the termination conditions is met, stopping the iteration,obtaining the optimal individual KbAnd an optimum fitness fiObtaining an optimal solution; if the termination condition cannot be met, performing step 6;
the termination conditions were as follows:
when the fitness value of an individual is larger than the artificially set fitness value through iteration, the individual is the optimal solution;
secondly, when the iteration times of the population reach the maximum iteration steps set by people, taking the individual with the highest fitness value in the current population as an optimal solution;
step 6: performing a selection operation of a genetic algorithm; preferentially copying the individual with the highest fitness value in the population obtained after iterative computation in the step 5 as a population DlWherein l represents the population number, 1,2,3, …; then, a fitness value of each individual is determined according to a fitness function, and a probability Pi of each individual being selected is determined as fi/sum (f)i) Wherein sum (f)i) Represents the sum of the fitness of all individuals in the population of the generation; according to the probability PiSelecting individuals with larger fitness, selecting one individual at a time, and selecting m-1 times to obtain a population D containing m individualsl；
And 7: the population DlCarrying out cross and variation operations in a genetic algorithm on the individuals; adopting a single-point crossing method to interchange alleles in two chromosomes, setting a crossing probability pc, setting a variation rate pm, setting the variation rate as a small value, and generating a population Dl'; executing the step 8;
and 8: repeating the step 3 to the step 5, and if the termination condition is met, outputting the optimal individual and the optimal fitness; if the termination condition is not satisfied, executing step 6 to step 7 while adding 1 to l in step 6.
In this embodiment, the goaf permeability coefficient distribution is taken as an example for detailed description, and for the purpose of exploring the feasibility of the method, the present invention is given as an example: except for the working surface, the permeability coefficient of each part of the goaf is constant and is equal to 0.01. Iterative iterations were performed using genetic algorithms to generate populations of 500 individuals per generation.
The invention adopts the termination condition of the maximum iteration times, sets the maximum iteration times as 150 generations, and outputs the optimal fitness and the optimal individual when the iteration times reach 150 generations. The method of single point crossing was used to interchange alleles in two chromosomes, and the crossing probability pc was set to 0.6. In addition, when setting the mutation rate, in order to ensure that the individual in the population maintains a condition of high fitness, it should be set to a very small number, and the mutation probability pm is set to 0.01.
After the iteration shown in fig. 2, when the maximum iteration number of 150 generations is finally reached, the fitness f is outputiValue fi＝0.94799。fiThe value is continuously approaching 1, and the expected trend of the invention is met. The final result K obtained by inversionb＝0.00977517。
Using a set desired value K0The relative error of the inversion method is calculated as 0.01, and σ is 0.023. I.e. the relative error is less than 3%. It can therefore be considered that the inversion of the permeability coefficient is achieved. The goaf permeability coefficient obtained by the method can guide production work, the goaf permeability coefficient is definite, and the method has great significance for mastering goaf fluid flow state, goaf gas concentration distribution and other goaf internal information. The method has guiding significance for predicting the fire occurrence position and preventing and controlling behaviors such as gas overrun in partial areas. Meanwhile, by means of the high efficiency and the rapidness of a computer program, the defects of long time consumption, high cost and the like in the existing permeability coefficient testing method are avoided. And the application of a computer method in the field of coefficient measurement is promoted.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (2)
1. A goaf permeability coefficient inversion method based on a genetic algorithm is characterized by comprising the following steps: the method comprises the following steps:
step 1: randomly generating a binary population about the permeability coefficient K, setting the population size to be m, namely m individuals in the population, initializing the population, and enabling binary individuals U in the populationiConversion to decimal number AiThen to AiLimiting the size range; the optimization range of the genetic algorithm is controlled by adjusting the length of each individual chromosome in the population to form an initial generation population D0＝{d1,d2…di…dmWherein i represents the number of individuals in the population, and i is more than or equal to 1 and less than or equal to m;
step 2: setting an expected value K0Solving out a goaf velocity field value V by a numerical calculation method of a two-dimensional stable seepage finite volume method;
and step 3: substituting the population into a numerical calculation method of a two-dimensional stable seepage finite volume method, and correspondingly solving a group of velocity field distribution numerical values V for each individual in the populationijWherein i represents the number of individuals in the population, and j represents the number of iterations;
and 4, step 4: calculating V and VijThe Euclidean distance OP between them;
in the formula x1qDenotes the q-th individual in V, x2qRepresents VijThe q individual in the population, N is the total number of individuals, and OP is the Euclidean distance between two groups; if the OP value is small, the similarity of the numerical values of the two matrixes is high;
and setting a fitness function, and substituting the calculated Euclidean distance into an expression:
fitness fiThe size of (a) represents the fitness of the ith individual in the population; fitness fiIf the value is large, it means that OP is small, thenValue of velocity field VijIs similar to V; otherwise, the individual fitness of the group is low;
and 5: according to the step 4, starting iteration to select the individual with the highest fitness; after each iterative calculation is finished, judging whether the termination conditions are met or not, if any one of the termination conditions is met, stopping the iteration to obtain the optimal individual KbAnd an optimum fitness fiObtaining an optimal solution; if the termination condition cannot be met, performing step 6;
the termination conditions were:
when the fitness value of an individual is larger than the artificially set fitness value through iteration, the individual is the optimal solution;
secondly, when the iteration times of the population reach the maximum iteration steps set by people, taking the individual with the highest fitness value in the current population as an optimal solution;
step 6: performing a selection operation of a genetic algorithm; selecting the individual with the highest fitness value from the population obtained after iterative computation in step 5 to preferentially copy as the population DlWherein l represents the population number, 1,2,3, …; then determining the fitness value of each individual according to the fitness function, determining the probability Pi of each individual being selected, and determining the probability P according to the probability PiSelecting individuals with larger fitness, selecting one individual at a time, and selecting m-1 times to obtain a population D containing m individualsl；
And 7: the population DlCarrying out cross and variation operations in a genetic algorithm on the individuals; adopting a single-point crossing method to exchange alleles in two chromosomes, simultaneously setting the variation rate, and setting the variation rate as a decimal value: generating a population Dl'; executing the step 8;
and 8: repeating the step 3 to the step 5, and if the termination condition is met, outputting the optimal individual and the optimal fitness; if the termination condition is not satisfied, executing step 6 to step 7 while adding 1 to l in step 6.
2. The goaf permeability coefficient inversion method based on genetic algorithm as claimed in claim 1, wherein the goaf permeability coefficient inversion method is characterized in thatThe method comprises the following steps: probability P in said step 6iThe formula of (1) is as follows:
wherein sum (f)i) Is the sum of the fitness of all individuals in the population of this generation.
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