CN111125904B - Large-scale high-speed rotation equipment blade sequencing method based on multi-target regulation and control - Google Patents
Large-scale high-speed rotation equipment blade sequencing method based on multi-target regulation and control Download PDFInfo
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Abstract
The invention discloses a blade ordering method of a large-scale high-speed rotary device based on multi-target regulation and control. Step 1: setting an initial population; step 2: establishing a rotor mass, a mass moment and a frequency physical model, designing an fitness function according to the physical model and the fitness function requirement, and carrying out fitness calculation on all chromosomes of an initial population; step 3: selecting an initial population by adopting a roulette method; step 4: the following steps are carried out according to the probability generated by the cloud generator under the X condition as a necessary condition; step 5: performing cross operation by adopting a recombination cross operator; step 6: performing mutation operation by adopting a two-element optimization mutation operator; step 7: if the maximum iteration times are not reached, repeating the steps 3-6; and if the maximum number of the iterations is reached, outputting the optimal chromosome after the iteration is ended. Aiming at the requirements of poor quality of the divided quadrants of the blades, the rotor blades of the large-sized high-speed rotating equipment are ordered through a cloud self-adaptive genetic algorithm, and the rotor blades are used for reducing the mass moment of the large-sized high-speed rotating equipment.
Description
Technical Field
The invention belongs to the technical field of large-scale high-speed rotation equipment; in particular to a blade ordering method of a large-scale high-speed rotary device based on multi-target regulation and control.
Background
The unbalance optimization method of the large-scale high-speed rotation equipment is an important content in engineering. Reasonable blade sequencing can reduce the mass moment of the rotary equipment, improve the start-stop performance of the rotor and reduce the rotor vibration caused by blade resonance. Aiming at the problems, the invention provides a three-objective optimization method for rotor blade quality, frequency and mass moment.
The rotor mass characteristics relate to the inertia, start-stop and acceleration characteristics of large high-speed rotary equipment. Therefore, general turning equipment makes the following demands on blade mounting quality characteristics: for blades uniformly distributed on the circumference of the rotary equipment, equally dividing the blades into n < 10 quadrants, and requiring that the total mass difference between the blades in each quadrant and the adjacent quadrants is not greater than the value a.
The frequency of the large high-speed turning equipment blades affects the normal operation of the rotor blades. Two adjacent or similar rotor blades have the same frequency, so that resonance of the two blades with the same frequency is induced, and the resonance causes the blades to not work normally in the running process of the rotor, thereby reducing efficiency. The following requirements are therefore made on the blade frequency: (1) adjacent blade frequency differences are not less than the b value; (2) not allowing the same frequency difference for the three consecutive sets of blades.
The imbalance of the mass moment is a major part of the unbalance of the rotor. The vibration-induced vibration device can generate exciting force to induce rotor vibration, and the smaller the total required rotor mass moment is, the better the total required rotor mass moment is in the installation process.
The general blade sorting method has low speed and long time consumption, such as an enumeration method and a search method; the neural network algorithm has long learning process and is easy to fall into the local optimal condition; the particle swarm algorithm is poor in treatment of discrete optimization problems, and the general genetic algorithm is strong in randomness, easy to early ripen and easy to fall into a local optimal condition.
Disclosure of Invention
Aiming at the problems of the optimization method, the invention provides a mass and mass moment combination optimization method based on a cloud self-adaptive genetic algorithm.
The invention is realized by the following technical scheme:
a blade ordering method of large-scale high-speed rotary equipment based on multi-target regulation and control comprises the following steps:
step 1: setting an initial population;
step 2: establishing a physical model of rotor quality, mass moment and frequency, designing an fitness function according to the physical model and the fitness function requirement, and carrying out fitness calculation on all chromosomes of an initial population;
the rotor quality physical model building process specifically comprises the following steps: a bladed disk has n blades, which are divided into k quadrants, each quadrant having the number of bladesThe adjacent quadrant quality difference deltag is:
ΔG＝|G(j-1)-G(j)|
wherein G (j) means the sum of all blade masses G (i) in a quadrant;
the frequency model physical model building process specifically comprises the following steps:
Δp(i)＝|p(i-1)-p(i)|≥b i＝1,2,…,n
Δp(i)≠Δp(i+1)≠Δp(i+2)
wherein, b means minimum frequency difference requirement, the frequency difference of two adjacent blades is not less than b value, and p (i) means the frequency of the ith blade;
the mass moment physical model building process specifically comprises the following steps: for a blade distributed on the impeller, the mass moment vector sum M and the total unbalance Z of the rotor are as follows:
wherein M is x Meaning the projection of the mass moment vector and M on the x-axis, M y Meaning the projection of the mass moment vector and M on the y-axis, M ex Meaning the eccentric moment M of the impeller e Projection on the x-axis, M ey Meaning the eccentric moment M of the impeller e Projection on y-axis, x i ,y i Is the x, y coordinates, m of the i th blade centroid i x i ,m i y i For the component of the mass moment of the ith blade in the x, y coordinate axis, θ 2 The included angle between the installation position of the first blade and the mass moment of the blade disc;
step 3: selecting an initial population by adopting a roulette method;
step 4: the following steps are carried out according to the probability generated by the cloud generator under the X condition as a necessary condition;
step 5: performing cross operation on the selected population by adopting a recombination cross operator;
step 6: performing mutation operation on the cross-operated population by adopting a two-element optimization mutation operator;
step 7: if the maximum iteration times are not reached, repeating the steps 3-6; and if the maximum number of the iterations is reached, outputting the optimal chromosome after the iteration is ended.
Further, the initial population setting in the step 1 specifically includes:
step 1.1: taking a leaf as a gene, wherein the serial number of the whole leaf group of the primary leaf disk is a chromosome;
step 1.2: one chromosome, i.e., one individual, randomly generates an initial population of population size 2000, i.e., the population size comprises 2000 chromosomes.
Further, the selecting operator in the step 3 adopts a roulette method, specifically, if the fitness value of each individual is f (x i ) Then its fitness relative value is p i Pop is the population size, p i As the probability of selection of this individual.
Further, the cross probability generated by the cloud generator under the X condition in the step 4 is specifically:
generating a random number of [0-1], performing a crossover operation when the random number is less than a crossover probability, the crossover probability being generated by a conditional cloud generator, the conditional cloud generator generating the crossover probability as follows:
He＝En/c 2
En′＝RANDN(En,He)
wherein: RANDN (En, he) generates a normal random number with an expected value of En and a standard deviation of He, f max For the maximum fitness of the population,for average fitness, f' is the larger value of fitness across the two volumes.
Further, in the step 5, the crossover operation is performed by adopting a recombination crossover operator, specifically, an edge list is firstly established for the blade in two parent individuals, the blade connected with the blade and the occurrence frequency are represented, two individuals are selected for crossover, and if one edge appears twice in the parent, a "-" number is added on the vertex of the edge in the list;
the edge recombination crossover operator starts to construct offspring by selecting an initial point, and the principle of selecting an individual from the father is that the blade with the least number of blades in the adjacent blades is selected, if the number of the adjacent blades is equal to that of a certain two-phase connected blade, the blade with a "-" sign is selected, and if the two blades are the same, one of the blades is selected randomly.
Further, the variation probability generated by the cloud generator under the X condition in the step 4 is specifically:
generating a random number of [0-1], and executing the crossover operation when the random number is smaller than the variation probability. The probability of variation given by the conditional cloud generator is as follows:
He＝En/c 4
En′＝RANDN(En,He)
where f is the fitness of the variant, k 1 ～k 4 ∈[0～1]Herein take k 1 ＝k 3 ＝1.0，k 2 ＝k 4 =0.5, c1-c4 are control parameters, c 1 ＝2.9，c 3 ＝3.0，c 2 ＝c 4 ＝10。
Further, in the step 6, the mutation operation is performed by using a two-element optimization mutation operator, specifically, an individual selected according to the mutation probability is randomly selected, and the leaf exchange is performed at two positions of the individual, so that a new leaf ordering is obtained, and the mutation operation is performed on all the individuals of the father until the next generation of population is generated according to the mutation probability.
Further, the fitness function designed in the step 2 is specifically that for the quality requirement, the number of blades in each quadrant isThere is->In the classification method, the minimum quadrant quality difference is obtained, and an evaluation coefficient is designed:
let n be g (i) Representing the number of inferior quality substandard edges under the ith classification, wherein the total substandard edges are N, and the constraint condition penalty function is that:
for frequency requirements, the evaluation coefficients are designed:
for the number N of the blade groups with frequency not reaching the standard p Constraint penalty function:
for the mass moment requirement, the evaluation coefficient is designed:
the fitness function is therefore as follows:
f＝r p f p ·r g f g ·f z 。
the beneficial effects of the invention are as follows:
according to the method, a double-target optimization model of the mass and the mass moment is established, under the condition that the overall unbalance of the rotor is considered, a cloud self-adaptive genetic algorithm is used for carrying out cross and mutation operator design on the individual blade groups, and therefore blade sequencing under the condition of double-target optimization of the mass and the mass moment of the rotor is achieved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
A blade ordering method of large-scale high-speed rotary equipment based on multi-target regulation and control comprises the following steps:
step 1: setting an initial population;
step 2: establishing a physical model of rotor quality, mass moment and frequency, designing an fitness function according to the physical model and the fitness function requirement, and carrying out fitness calculation on all chromosomes of an initial population;
the rotor quality physical model building process specifically comprises the following steps: a bladed disk has n blades, which are divided into k quadrants, each quadrant having the number of bladesThe adjacent quadrant quality difference deltag is:
ΔG＝|G(j-1)-G(j)|
wherein G (j) means the sum of all blade masses G (i) in a quadrant;
the frequency model physical model building process specifically comprises the following steps:
Δp(i)＝|p(i-1)-p(i)|≥b i＝1,2,…,n
Δp(i)≠Δp(i+1)≠Δp(i+2)
wherein, b means minimum frequency difference requirement, the frequency difference of two adjacent blades is not less than b value, and p (i) means the frequency of the ith blade;
the mass moment physical model building process specifically comprises the following steps: for a blade distributed on the impeller, the mass moment vector sum M and the total unbalance Z of the rotor are as follows:
wherein M is x Meaning the projection of the mass moment vector and M on the x-axis, M y Meaning the projection of the mass moment vector and M on the y-axis, x i ,y i Is the x, y coordinates, m of the i th blade centroid i x i ,m i y i For the component of the mass moment of the ith blade in the x, y coordinate axis, θ 2 The included angle between the installation position of the first blade and the mass moment of the blade disc;
step 3: selecting an initial population by adopting a roulette method;
step 4: the following steps are carried out according to the probability generated by the cloud generator under the X condition as a necessary condition;
step 5: performing cross operation on the selected population by adopting a recombination cross operator;
step 6: performing mutation operation on the cross-operated population by adopting a two-element optimization mutation operator;
step 7: if the maximum iteration times are not reached, repeating the steps 3-6; and if the maximum number of the iterations is reached, outputting the optimal chromosome after the iteration is ended.
Further, the initial population setting in the step 1 specifically includes:
step 1.1: taking a leaf as a gene, wherein the serial number of the whole leaf group of the primary leaf disk is a chromosome;
step 1.2: one chromosome, i.e., one individual, randomly generates an initial population of population size 2000, i.e., the population size comprises 2000 chromosomes.
Further, the selecting operator in the step 3 adopts a roulette method, specifically, if the fitness value of each individual is f (x i ) Then its fitness relative value is p i Pop is the population size, p i As the probability of selection of this individual.
Further, the cross probability generated by the cloud generator under the X condition in the step 4 is specifically:
generating a random number of [0-1], performing a crossover operation when the random number is less than a crossover probability, the crossover probability being generated by a conditional cloud generator, the conditional cloud generator generating the crossover probability as follows:
He＝En/c 2
En′＝RANDN(En,He)
wherein: RANDN (En, he) generates a normal random number with an expected value of En and a standard deviation of He, f max For the maximum fitness of the population,for average fitness, f' is the larger value of fitness across the two volumes.
Further, in the step 5, the crossover operation is performed by adopting a recombination crossover operator, specifically, an edge list is firstly established for the blade in two parent individuals, the blade connected with the blade and the occurrence frequency are represented, two individuals are selected for crossover, and if one edge appears twice in the parent, a "-" number is added on the vertex of the edge in the list;
the edge recombination crossover operator starts to construct offspring by selecting an initial point, and the principle of selecting an individual from the father is that the blade with the least number of blades in the adjacent blades is selected, if the number of the adjacent blades is equal to that of a certain two-phase connected blade, the blade with a "-" sign is selected, and if the two blades are the same, one of the blades is selected randomly.
Further, the variation probability generated by the cloud generator under the X condition in the step 4 is specifically:
generating a random number of [0-1], and executing the crossover operation when the random number is smaller than the variation probability. The probability of variation given by the conditional cloud generator is as follows:
He＝En/c 4
En′＝RANDN(En,He)
where f is the fitness of the variant, k 1 ～k 4 ∈[0～1]Herein take k 1 ＝k 3 ＝1.0，k 2 ＝k 4 =0.5, c1-c4 are control parameters, c 1 ＝2.9，c 3 ＝3.0，c 2 ＝c 4 ＝10。
Further, in the step 6, the mutation operation is performed by using a two-element optimization mutation operator, specifically, an individual selected according to the mutation probability is randomly selected, and the leaf exchange is performed at two positions of the individual, so that a new leaf ordering is obtained, and the mutation operation is performed on all the individuals of the father until the next generation of population is generated according to the mutation probability.
Further, the fitness function designed in the step 2 is specifically that for the quality requirement, the number of blades in each quadrant isThere is->In the classification method, the minimum quadrant quality difference is obtained, and an evaluation coefficient is designed:
let n be g (i) Representing the number of inferior quality substandard edges under the ith classification, wherein the total substandard edges are N, and the constraint condition penalty function is that:
for frequency requirements, the evaluation coefficients are designed:
for the number N of the blade groups with frequency not reaching the standard p Constraint penalty function:
for the mass moment requirement, the evaluation coefficient is designed:
the fitness function is therefore as follows:
f＝r p f p ·r g f g ·f z 。
Claims (4)
1. the blade sorting method for the large-scale high-speed rotary equipment based on multi-target regulation and control is characterized by comprising the following steps of:
step 1: setting an initial population;
step 2: establishing a physical model of rotor quality, mass moment and frequency, designing an fitness function according to the physical model and the fitness function requirement, and carrying out fitness calculation on all chromosomes of an initial population;
the rotor quality physical model building process specifically comprises the following steps: a bladed disk has n blades, which are divided into k quadrants, each quadrant having the number of bladesThe adjacent quadrant quality difference deltag is:
ΔG＝|G(j-1)-G(j)|
wherein G (j) means the sum of all blade masses G (i) in a quadrant;
the frequency model physical model building process specifically comprises the following steps:
Δp(i)＝|p(i-1)-p(i)|≥b i＝1,2,…,n
Δp(i)≠Δp(i+1)≠Δp(i+2)
wherein, b means minimum frequency difference requirement, the frequency difference of two adjacent blades is not less than b value, and p (i) means the frequency of the ith blade;
the mass moment physical model building process specifically comprises the following steps: for a blade distributed on the impeller, the mass moment vector sum M and the total unbalance Z of the rotor are as follows:
wherein M is x Meaning the projection of the mass moment vector and M on the x-axis, M y Meaning the projection of the mass moment vector and M on the y-axis, M ex Meaning the eccentric moment M of the impeller e Projection on the x-axis, M ey Meaning the eccentric moment M of the impeller e Projection on y-axis, x i ,y i Is the x, y coordinates, m of the i th blade centroid i x i ,m i y i For the component of the mass moment of the ith blade in the x, y coordinate axis, θ 2 The included angle between the installation position of the first blade and the mass moment of the blade disc;
for the quality requirement, the number of blades in each quadrant isThere is->The classification method is to obtain the minimum quadrant quality difference and design the evaluation coefficient f g ：
Let n be g (i) Representing the number of inferior quality substandard edges under the ith classification, wherein the total substandard edges are N, and the constraint condition penalty function is that:
for frequency requirements, the evaluation coefficients are designed:
for the number N of the blade groups with frequency not reaching the standard p Constraint penalty function:
for the mass moment requirement, the evaluation coefficient is designed:
the fitness function is therefore as follows:
f＝r p f p ·r g f g ·f z；
step 3: selecting an initial population by adopting a roulette method;
step 4: performing cross probability calculation and variation probability calculation according to the probability generated by the cloud generator under the X condition as a necessary condition;
the cross probability generated by the cloud generator under the X condition is specifically as follows:
generating a random number of [0-1], performing a crossover operation when the random number is less than a crossover probability, the crossover probability being generated by a conditional cloud generator, the conditional cloud generator generating the crossover probability as follows:
He＝En/c 2
En′＝RANDN(En,He)
wherein, RANDN (En, he) generates a normal random number with an expected value of En and a standard deviation of He, f max For the maximum fitness of the population,for average fitness, f' is the larger value of fitness of the intersecting two volumes, c 1 And c 2 For controlling parameters, where c 1 ＝2.9，c 2 ＝10，k 1 ～k 4 ∈[0～1]Taking k 1 ＝k 3 ＝1.0；
The variation probability generated by the cloud generator under the condition X in the step 4 is specifically:
generating a random number of [0-1], and executing cross operation when the random number is smaller than variation probability; the probability of variation given by the conditional cloud generator is as follows:
He＝En/c 4
En′＝RANDN(En,He)
wherein f is the fitness of the variant, k 1 ～k 4 ∈[0～1]Taking k 2 ＝k 4 ＝0.5，c 3 And c 4 To control parameters c 3 ＝3.0，c 4 ＝10；
Step 5: performing cross operation on the selected population by adopting a recombination cross operator;
the crossover operation by adopting a recombination crossover operator is specifically that firstly, an edge list is established for the blade in two father individuals to represent the blade connected with the blade and the occurrence frequency, two individuals are selected for crossover, and if one edge appears twice in the father, a "-" number is added on the vertex of the edge in the list;
the edge recombination crossover operator starts to construct offspring by selecting an initial point, and the principle of selecting an individual from the father is that the blade with the least number of blades in the adjacent blades is selected, if the number of the adjacent blades is equal to that of a certain two-phase connected blade, the blade with a '-' sign is selected, and if the two blades are the same, one of the blades is selected randomly;
step 6: performing mutation operation on the cross-operated population by adopting a two-element optimization mutation operator;
step 7: if the maximum iteration times are not reached, repeating the steps 3-6; and if the maximum number of the iterations is reached, outputting the optimal chromosome after the iteration is ended.
2. The blade sorting method according to claim 1, wherein the initial population setting in step 1 is specifically:
step 1.1: taking a leaf as a gene, wherein the serial number of the whole leaf group of the primary leaf disk is a chromosome;
step 1.2: one chromosome, i.e., one individual, randomly generates an initial population of population size 2000, i.e., the population size comprises 2000 chromosomes.
3. The blade ordering method according to claim 1, wherein the selecting operator in step 3 uses roulette, specifically, if the fitness value of each individual is f (x i ) Then its fitness relative value is p i Pop is the population size, p i As the probability of selection of this individual.
4. The method for sorting the leaves according to claim 1, wherein the step 6 is characterized in that the mutation operation is performed by using a two-element optimized mutation operator, specifically, an individual selected according to the mutation probability is randomly selected, and the leaves at certain two positions of the individual are exchanged to obtain a new leaf sorting, and the mutation operation is performed on all the individuals of the father according to the mutation probability until the next generation population is generated.
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| CN106202755A (en) * | 2016-07-15 | 2016-12-07 | 西安交通大学 | Electric main shaft structure Optimization Design based on kinetic model and genetic algorithm |
| CN106919041A (en) * | 2017-01-23 | 2017-07-04 | 长春工业大学 | A kind of fan-shaped grinding sort method based on improved quantum genetic algorithm |
| CN109522665A (en) * | 2018-11-27 | 2019-03-26 | 北京石油化工学院 | A kind of Multipurpose Optimal Method of single flow gas-liquid cyclone separator guide vane |
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