CN109977559B - Pulverized coal furnace hearth radiation inverse problem solving method based on improved genetic algorithm - Google Patents
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Abstract
The invention relates to a pulverized coal furnace hearth radiation inverse problem solving method based on an improved genetic algorithm, which comprises the following steps of: establishing a model of convective radiation heat exchange quantity in the heat transfer process of a water wall pipe in a hearth of the pulverized coal furnace, and setting related parameters; according to a built model and related parameters of convective radiation heat exchange quantity in the heat transfer process of a water wall tube in a hearth of the pulverized coal furnace, solving the heat exchange quantity and estimating the heat exchange quantity by forward direction to set a target function, and determining a constraint condition; carrying out real number coding on the target function and the constraint condition to determine a relevant variable; an improved genetic algorithm is adopted to carry out inversion on the heat exchange quantity in the convection radiation heat transfer process of a water wall tube in a hearth of the pulverized coal furnace; the optimal value found by the improved genetic algorithm is the solution of the radiation inverse problem. The invention improves the defect of losing better solution in the original algorithm, improves the global searching capability and convergence rate, and has wide practical significance in solving the inverse problem of the convective radiation heat transfer process of the water wall tube in the hearth of the pulverized coal furnace.
Description
Technical Field
The invention relates to a radiation inverse problem solving method based on an improved genetic algorithm.
Background
The basic idea of genetic algorithms is to maintain a population representing potential solutions to the problem, which population will evolve by running selection, crossover, mutation operators. In genetic algorithms, each valid solution to the problem to be solved is called a "chromosome", which is embodied in the form of a code string generated using a particular coding scheme. Each coding unit in the coding string is referred to as a "gene". Modern genetics based on the mendelian theory proposes a recombination pattern of genetic information. In the genetic process of an organism, a chromosome is a carrier of genetic information-genes, and the genes are combined on the chromosome according to a certain order. Derived from these two important theories of bioscience, provides a valuable source of thought for Holland to seek methods to effectively study artificial adaptive systems. On the basis that thousands of people use computers to carry out biological simulation, holland discovers the similarity between a biological genetic evolution system in nature and an artificial adaptive system, successfully establishes a genetic algorithm model, and theoretically proves the effectiveness of genetic algorithm search. The genetic algorithm searches for an optimal solution in a D-dimensional problem space by utilizing a group consisting of N chromosomes, the algorithm can carry out iterative loop in the optimization searching process, the initial value influence of each iteration is large, better solutions are lost, local optimization can be easily caused in the optimization searching process, the searching capability is poor, the convergence speed is low, and the optimization searching precision and speed are influenced.
For the radiation reflection problem, in early research, the traditional optimization methods such as a gauss-newton method and a conjugate gradient method are mainly used for solving, but the result obtained by the algorithm is greatly interfered by an initial value and easily falls into local optimum, and a large amount of gradient-based information is needed in the calculation process. In recent years, more and more scholars have been trying to apply intelligent algorithms to the research of solving the radiation inverse problem. The intelligent optimization algorithm is a general term for designing various optimization algorithms by simulating the swarm intelligence principle in nature, and mainly comprises a genetic algorithm, an ant colony algorithm, a simulated annealing algorithm, a particle swarm algorithm and the like. The method has the advantages of simple concept, easy realization, no need of gradient information, relatively simple calculation and the like.
The pulverized coal furnace is a boiler device taking pulverized coal as fuel. It has the advantages of rapid and complete combustion, large capacity, high efficiency, wide coal adaptation range, convenient control and regulation, etc. The combustion characteristic of the pulverized coal furnace is that fuel enters a combustion chamber together with air and is combusted in a suspension state.
According to the known working conditions of the size parameter of the model of the convective radiation heat transfer of the water wall tube in the hearth of the pulverized coal furnace, the heat flux density of the system and the like, unknown parameters of the physical parameters, the temperature distribution, the boundary conditions and the like of each part of the model of the convective radiation heat transfer of the water wall tube in the hearth of the pulverized coal furnace are inverted. The method has strong practical significance for engineering construction problems. At present, the inversion is carried out by adopting a classical algorithm based on the gradient information of the target function, and the problems of difficult calculation, problem misinterpretation, infeasible solution acquisition and the like can be encountered; although some intelligent algorithms are adopted, gradient information is not needed, calculation is relatively simple, but the problems of local optimum, low convergence speed, low precision and the like can be encountered, and an accurate inversion solution cannot be achieved.
Disclosure of Invention
Aiming at the defects that the influence of an initial value of a genetic algorithm is large, the coal powder furnace hearth radiation inverse problem is easy to fall into local optimum and the like when the coal powder furnace hearth radiation inverse problem is solved in the prior art, the invention provides the coal powder furnace hearth radiation inverse problem solving method based on the improved genetic algorithm, which can improve the global searching capability and the convergence speed and improve the defect that better solution is lost in the original algorithm.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
the invention relates to a pulverized coal furnace hearth radiation inverse problem solving method based on an improved genetic algorithm, which comprises the following steps of:
1) Establishing a model of convective radiation heat exchange quantity in the heat transfer process of a water wall pipe in a hearth of the pulverized coal furnace, and setting related parameters;
2) According to a built model and related parameters of convective radiation heat exchange quantity in the heat transfer process of a water wall tube in a hearth of the pulverized coal furnace, solving the heat exchange quantity and estimating the heat exchange quantity by using a forward direction to set a target function, and determining a constraint condition;
3) Carrying out real number coding on the target function and the constraint condition to determine a relevant variable;
4) Carrying out inversion on the heat exchange quantity in the convective radiation heat transfer process of a water wall tube in a hearth of the pulverized coal furnace by adopting an improved genetic algorithm; the optimal value found by the improved genetic algorithm is the solution of the radiation inverse problem.
In the step 1), the model has two conditions of no slag bonding outside the pipe and slag bonding outside the pipe, and the two conditions are respectively subjected to inversion solving.
In the step 2), the heat exchange quantity of the convection radiation on the unit water wall obtained in the process of solving the problem in the forward direction is calculated through inversionVarious relevant parameters to the model, including the convective heat transfer coefficient h, the emissivity epsilon of the water wall tube, and the temperature T of the water in the tube 1 And flue gas temperature T 2 Setting target function by solving heat exchange quantity and estimating heat exchange quantity in forward direction
Φ * i,measured For solving the value, phi, in the forward direction * i,eatimated Is an algorithm estimate.
In the step 4), the improved genetic algorithm is improved on the basis of the standard genetic algorithm, and the specific steps are as follows:
401 Initializing a population;
402 Respectively calculating fitness values of each chromosome according to the evaluation function;
403 Selecting chromosomes of the population by adopting a roulette selection algorithm according to the fitness value of the chromosomes;
404 According to the cross probability P) c Selecting two parent chromosomes from the population, carrying out cross operation by adopting an improved cross operator, and replacing the parent chromosomes with the generated offspring chromosomes to enter a new population; according to the mutation probability P m Selecting chromosomes and carrying out mutation operation on the population;
405 After mutation operation, recalculating fitness values of the individual chromosomes in the population;
406 Evaluating whether a termination condition is met, if the termination condition is met, ending the algorithm; otherwise, returning to step 402)
In step 404), the specific contents of the improved crossover operator are as follows:
according to the cross probability P c Selection of two chromosomes from the t-generation
Performing a crossover operation, wherein (1 ≦ c2 ≦ N), d is the chromosome length, and the two chromosomal genes undergoing crossover are
(1. Ltoreq. I. Ltoreq. D), the corresponding gene generated after crossing is
(1≤i≤d)；
Novel chromosome X c1' Middle gene
Derived from the following three chromosomes (1. Ltoreq. I. Ltoreq. D):
i.e., the offspring chromosome
Wherein rand is [0,1 ]]Random numbers uniformly distributed among them;
is a chromosome;
the gene of the gene (ii) in (c),
is a chromosome
The ith gene;
newly generated offspring chromosomes
Randomly selecting genes from the three intermediate chromosomes, and similarly, selecting the offspring chromosome X c2' Gene (a) of (a)
Also obtained from the three intermediate chromosomes produced by the above method.
The invention has the following beneficial effects and advantages:
1. the radiation inverse problem solving method based on the improved genetic algorithm overcomes the defects that the initial value of the traditional classical algorithm is greatly influenced and is easy to fall into local optimum and the like, improves the defect that the original algorithm loses better solutions by comparing with other algorithms, improves the global searching capacity and the convergence speed, and has wide practical significance in solving the inverse problem of the convective radiation heat transfer process of the water wall tube in the hearth of the pulverized coal furnace.
2. The improved genetic algorithm applied by the method has a cross operator with a memory function, takes two parent chromosomes as the basis, and fully utilizes the global optimal individual and the individual optimal individual in the cross operation process, so that the chromosomes in a population are directionally close to the optimal solution of the objective function.
3. The invention is an algorithm based on real number coding, the variation of chromosome acts on the gene, in the improved algorithm, according to variation probability P m Judging whether each gene of the chromosome in the new population is mutated or not after crossing, and then testing and verifying by using a test function, so that the improved algorithm has certain advantages compared with other algorithms.
4. The improved genetic algorithm provided by the invention provides a new cross operator, improves the defect that a better solution is lost in the original algorithm, improves the global search capability and the convergence speed, and has wide practical significance in solving the inverse problem of the convection radiation heat transfer process of the water wall tube in the pulverized coal furnace hearth and the engineering construction problem by inverting unknown parameters such as physical parameters, temperature distribution, boundary conditions and the like of each part of the model of the convection radiation heat transfer of the water wall tube in the pulverized coal furnace hearth according to the known working conditions such as the model size parameter of the convection radiation heat transfer of the water wall tube in the pulverized coal furnace hearth, the system heat flux density and the like.
Drawings
FIG. 1A is a general flowchart of a solution method for solving the radiation inverse problem based on an improved genetic algorithm according to the present invention;
FIG. 1B is a detailed flow chart of the method of the present invention;
FIG. 2 is a clean ash free waterwall tube;
FIG. 3 water wall tubes with uniform ash buildup;
FIG. 4 is a curve of fitness value changes of a Sphere function in different algorithms;
fig. 5 is a adaptability value change curve of Schwefel Problem function in different algorithms.
Detailed Description
The invention is further elucidated with reference to the accompanying drawings.
As shown in fig. 1A, the present invention relates to a method for solving the inverse problem of radiation based on the improved genetic algorithm,
the method comprises the following steps:
1) Establishing a model of convective radiation heat exchange quantity in the heat transfer process of a water wall pipe in a hearth of the pulverized coal furnace, and setting related parameters;
2) According to a built model and related parameters of convective radiation heat exchange quantity in the heat transfer process of a water wall tube in a hearth of the pulverized coal furnace, solving the heat exchange quantity and estimating the heat exchange quantity by using a forward direction to set a target function, and determining a constraint condition;
3) Carrying out real number coding on the target function and the constraint condition to determine a relevant variable;
4) An improved genetic algorithm is adopted to carry out inversion on the heat exchange quantity in the convection radiation heat transfer process of a water wall tube in a hearth of the pulverized coal furnace; the optimal value found by the improved genetic algorithm is the solution of the radiation inverse problem.
In step 1), the model has two situations: no slag is formed outside the pipe and slag is formed outside the pipe. Modeling is respectively carried out on two conditions, specifically:
when the pipe is clean and has no ash, as shown in fig. 2, the model is established as follows:
heat transfer capacity phi per unit length of tube l Comprises the following steps:
Φ l ＝Φ lcon +Φ lrad
convective heat transfer phi lcon ：
Φ lcon ＝A l ×h×(T 2 -T 1 )
Radiation heat exchange quantity phi lrad ：
Φ lrad ＝A l ×σ 0 ×ε×(T 2 4 -T 1 4 )
When a layer of uniform ash exists outside the pipe, as shown in figure 3, the model is established as follows:
thermal resistance R of ash scale layer when slag is formed on surface of water wall tube A Comprises the following steps:
the total thermal resistance sigma R of convective heat transfer and radiant heat transfer is:
wherein h is rad ＝εσ 0 (T 2 3 +T 2 2 T d +T 2 T d 2 +T d 3 )
After slagging of the water wall tube, the surface temperature T of the ash scale d Satisfies the following formula
Radiation heat exchange quantity phi lcon,rad ：
Φ lcon,rad ＝A l (h+h rad )(T 2 -T d )
Wherein phi is 1 Is a unit length pipeAmount of heat exchange of 1con For convective heat transfer, phi 1rad For radiant heat exchange, A 1 Is the heat exchange area, h is the convective heat transfer coefficient, h con Is a convective heat transfer coefficient, h rad For radiative heat transfer coefficient, T 1 The temperature of water in the tube, T 2 Is the temperature of the flue gas, T d Surface temperature of the ash scale, epsilon emissivity, lambda thermal conductivity, sigma 0 Is a constant number d d And d 0 Respectively the inner and outer diameters R of the water-cooled tube A Is the thermal resistance of the ash scale layer.
In step 2), according to the convection radiation heat exchange quantity on the unit water wall obtained in the process of solving the problem in the forward direction, various parameters of the system, such as the convection heat transfer coefficient h, the emissivity epsilon of the water wall pipe and the water temperature T in the pipe, can be obtained through inverse calculation 1 And the temperature T of the flue gas 2 Setting target function by solving heat exchange quantity and estimating heat exchange quantity in forward direction
Φ * i,measured For solving the value, phi, in the forward direction * i,eatimated Is an algorithm estimate.
In step 3), the improved genetic algorithm is improved based on the standard genetic algorithm, and the specific steps are shown in fig. 1B and specifically include:
401 Initializing a population;
402 Respectively calculating fitness values of each chromosome according to the evaluation function;
403 Selecting the chromosomes of the population by adopting a roulette selection algorithm according to the fitness value of the chromosomes;
404 According to the cross probability P) c Two parent chromosomes are selected from the population, an improved crossover operator is adopted for crossover operation, and the generated offspring chromosomes replace the parent chromosomes to enter a new population. According to the mutation probability P m Selecting chromosomes and carrying out mutation operation on the population;
405 After mutation operation, recalculating fitness values of the individual chromosomes in the population;
406 Evaluating whether a termination condition is met, if the termination condition is met, ending the algorithm; otherwise return to step 402).
404 In the improved genetic algorithm, the specific contents of the crossover operator are as follows:
crossover probability two chromosomes were selected from the t-th generation
Performing a crossover operation, wherein (1. Ltoreq. C2. Ltoreq. N), d is the chromosome length, and two chromosome genes to be crossed are,
(1. Ltoreq. I. Ltoreq. D), the corresponding gene generated after crossing is
(1≤i≤d)。
Novel chromosome X c1' Middle gene
Derived from the following three chromosomes (1. Ltoreq. I. Ltoreq. D):
i.e., the offspring chromosomes
Wherein rand is [0,1 ]]Random numbers uniformly distributed among them;
is a chromosome
The gene of the gene (ii) in (c),
is a chromosome
The ith gene in (c).
Newly generated offspring chromosomes
Randomly selecting genes from the three intermediate chromosomes (1), (2) and (3), wherein the offspring chromosomes generated by the crossover operator can keep partial genes of the parent chromosomes and can intentionally approach to the current generation optimal individuals, so that the situation that the offspring chromosomes are locally optimal prematurely is avoided. In a similar manner, the offspring chromosome X c2' Of (2) gene
Also obtained from the three intermediate chromosomes produced by the above method.
And 4) performing inversion on the heat exchange quantity in the convection radiation heat transfer process of the water wall tube in the hearth of the pulverized coal furnace by using an improved genetic algorithm, and assuming that the saturated water temperature T1 of the model =600K. The outside of the pipe is subjected to the convection heat transfer of flue gas with T2=1500K, and the convection heat transfer coefficient h = 100W/(m) 2 K). When the pipe is clean and has no slag, the emissivity e of the water wall pipe is =0.8, and when the pipe is slag, the emissivity e of the slag surface is =0.9. The optimal value found by the improved genetic algorithm is the solution of the radiation inverse problem.
When the improved genetic algorithm and other eight algorithms are tested, fig. 4 is a fitness value change curve of a Sphere function in different algorithms, and fig. 5 is a fitness value change curve of a Schwefel Problem function in different algorithmsThe line, the optimizing speed and the optimizing precision are all higher than those of other algorithms, and the line, the optimizing speed and the optimizing precision are closer to an optimal value and higher in the iteration process, so that a better optimizing effect is obtained. The radiation inverse problem solving method based on the improved genetic algorithm is compared with the inversion results of other two algorithms, if the water wall pipe is subjected to inversion calculation when no slag is formed in the table 1, the estimation value of each parameter is obtained, and the data in the table shows that the actual value given in the comparison table is h = 100W/(m) m 2 ·K)，e＝0.8，T 1 * ＝0.4，T 2 =1500K, the result obtained by introducing the method (GA Memory) of the present invention is very close to the actual value, the emissivity e =0.8001 of the water wall tube obtained by inversion has a relative error of 0.01% with the actual value, and the average error of the results of the four parameters is only 0.4%, so that the accuracy is far better than that of the other two algorithms. As shown in the table 2, the estimated values of all the parameters are obtained by inversion calculation when the water wall tubes are slagging, although the accuracy is not much different from that of other two algorithms, the solving accuracy of the method is high, the relative error of the convective heat transfer coefficient is 0.7%, the relative errors of the estimated values and the actual values of other three parameters are all below 0.1%, and the average relative error of the four parameters is only 0.22%.
TABLE 1
TABLE 2
In conclusion, the method has better guiding significance for solving and practical application of other radiation inverse problems.
The improved genetic algorithm is used for inverting unknown parameters such as physical property parameters, temperature distribution, boundary conditions and the like of each part of the model for the convective radiation heat transfer of the water wall tubes in the pulverized coal furnace hearth according to the known working conditions such as the model size parameters, the system heat flow density and the like of the convective radiation heat transfer of the water wall tubes in the pulverized coal furnace hearth, the calculation is fast, the precision is high, and the method has strong guiding significance for solving and practical application of other radiation inverse problems.
Claims (3)
1. A pulverized coal furnace hearth radiation inverse problem solving method based on an improved genetic algorithm is characterized by comprising the following steps:
1) Establishing a model of convective radiation heat exchange quantity in the heat transfer process of a water wall pipe in a hearth of the pulverized coal furnace, and setting related parameters;
2) According to a built model and related parameters of convective radiation heat exchange quantity in the heat transfer process of a water wall tube in a hearth of the pulverized coal furnace, solving the heat exchange quantity and estimating the heat exchange quantity by using a forward direction to set a target function, and determining a constraint condition;
3) Real number coding is carried out on the target function and the constraint condition, and relevant variables are determined;
4) An improved genetic algorithm is adopted to carry out inversion on the heat exchange quantity in the convection radiation heat transfer process of a water wall tube in a hearth of the pulverized coal furnace; the optimal value found by the improved genetic algorithm is the solution of the radiation inverse problem;
in the step 4), the improved genetic algorithm is improved on the basis of a standard genetic algorithm, and the specific steps are as follows:
401 Initializing a population;
402 Respectively calculating fitness value of each chromosome according to the evaluation function;
403 Selecting chromosomes of the population by adopting a roulette selection algorithm according to the fitness value of the chromosomes;
404 According to the cross probability P) c Selecting two parent chromosomes from the population, carrying out cross operation by adopting an improved cross operator, and replacing the parent chromosomes with the generated offspring chromosomes to enter a new population; according to the mutation probability P m Selecting chromosomes and carrying out mutation operation on the population;
405 After mutation operation, recalculating fitness values of the individual chromosomes in the population;
406 Evaluating whether a termination condition is met, if the termination condition is met, ending the algorithm; otherwise, returning to the step 402);
in step 404), the specific content of the improved crossover operator is as follows:
according to the cross probability P c Selection of two chromosomes from the t-th generation
Performing crossover operation, wherein (1 ≦ c2 ≦ N), d is chromosome length, and two chromosome genes undergoing crossover are
The corresponding gene generated after crossing
Novel chromosome X c1' Middle gene
Derived from the following three chromosomes (1. Ltoreq. I. Ltoreq. D):
i.e., the offspring chromosome
Wherein rand is [0,1 ]]Random numbers uniformly distributed among them;
is a chromosome;
the gene of (i) th gene(s),
is a chromosome
The ith gene;
newly generated offspring chromosomes
Randomly selecting genes from the three intermediate chromosomes, and similarly, selecting the offspring chromosome X c2' Gene (a) of (a)
Also obtained from the three intermediate chromosomes produced by the above method.
2. The pulverized coal furnace hearth radiation inverse problem solving method based on the improved genetic algorithm as claimed in claim 1, wherein: in the step 1), the model has two conditions of no slag bonding outside the pipe and slag bonding outside the pipe, and the two conditions are respectively subjected to inversion solving.
3. The pulverized coal furnace hearth radiation inverse problem solving method based on the improved genetic algorithm as claimed in claim 1, characterized in that: in step 2), according to the convection radiation heat exchange quantity on the unit water wall obtained in the process of solving the problem in the forward direction, various relevant parameters of the model are obtained through inversion calculation, wherein the relevant parameters comprise the convection heat transfer coefficient h, the emissivity epsilon of the water wall pipe and the water temperature T in the pipe 1 And the temperature T of the flue gas 2 Setting target function by solving heat exchange quantity and estimating heat exchange quantity in forward direction
Φ * i,measured For solving the value, phi, in the forward direction * i,eatimated Is an algorithm estimate.
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