CN111125904A - Large-scale high-speed rotation equipment blade sorting method based on multi-target regulation - Google Patents
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Abstract
The invention discloses a method for sequencing blades of large-scale high-speed rotating equipment based on multi-target regulation. Step 1: setting an initial population; step 2: establishing a rotor mass, a mass moment and a frequency physical model, designing a fitness function according to the physical model and the fitness function requirement, and calculating the fitness of all chromosomes of the initial population; and step 3: selecting the initial population by adopting a roulette method; and 4, step 4: performing the following steps according to the probability generated by the cloud generator under the X condition as a necessary condition; and 5: performing cross operation by adopting a recombination cross operator; step 6: performing mutation operation by adopting a two-element optimization mutation operator; and 7: if the maximum iteration times are not reached, repeating the step 3-6; and if the maximum iteration times are reached, the iteration is finished, and the optimal chromosome is output. Aiming at the requirement of poor quality of the divided quadrants of the blades, the rotor blades of the large-scale high-speed rotation equipment are sequenced through a cloud self-adaptive genetic algorithm, and the mass moment of the large-scale high-speed rotation equipment is reduced.
Description
Technical Field
The invention belongs to the technical field of large-scale high-speed rotation equipment; in particular to a method for sequencing blades of large-scale high-speed rotating equipment based on multi-target regulation.
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 rotating equipment, improve the starting and stopping performance of the rotor and reduce the rotor vibration caused by blade resonance. Aiming at the problems, the invention provides a three-target optimization method for the mass, the frequency and the mass moment of the rotor blade.
The rotor mass characteristics relate to the inertia, start and stop and acceleration characteristics of large-scale high-speed rotation equipment. Therefore, the following requirements are made on the blade installation quality characteristics by the general rotating equipment: and (3) equally dividing the blades uniformly distributed on the circumference of the rotary equipment into n ≦ 10 quadrants, wherein the difference between the total mass of the blade in each quadrant and the total mass of the blade in the adjacent quadrant is not larger than a value.
The frequency of the blades of large high-speed rotating equipment affects the normal operation of the rotor blades. Two adjacent or similar rotor blades have the same frequency, which can cause resonance of the two blades with the same frequency, and the resonance can cause the blades not to work normally in the running process of the rotor, thereby reducing the efficiency. The following requirements are therefore made for the blade frequency: (1) the frequency difference of adjacent blades is not less than the value b; (2) the same frequency difference is not allowed for the consecutive three sets of blades.
The imbalance of the mass moment is a major part of the unbalance of the rotor. The rotor vibration generator can generate exciting force to cause rotor vibration, and the smaller the sum of the mass moments of the rotor is, the better the rotor vibration generator is.
The general blade sorting method has slow speed and long time consumption, such as an enumeration method and a search method; the neural network algorithm has a long learning process and is easy to fall into a local optimal condition; the particle swarm optimization is poor in discrete optimization problem processing, and a general genetic algorithm is high in randomness, easy to get early 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 sorting method of large-scale high-speed rotation equipment based on multi-target regulation comprises the following steps:
step 1: setting an initial population;
step 2: establishing a physical model of rotor mass, mass moment and frequency, designing a fitness function according to the physical model and the fitness function requirement, and calculating the fitness of all chromosomes of the initial population;
the rotor quality physical model establishing process specifically comprises the following steps: a blade disc has n blades, and is divided into k quadrants, and the number of the blades in each quadrant is equal
The adjacent quadrant mass difference Δ G 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 establishing 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 the minimum frequency difference requirement, the frequency difference between two adjacent blades is required to be not less than the value b, and p (i) means the frequency of the ith blade;
the process for establishing the physical model of the mass moment specifically comprises the following steps: for the blades distributed on the blade disc, the sum of mass moment vectors M and the total imbalance quantity Z of the rotor are as follows:
in the formula, MxMeaning the projection of the sum of the moment of mass vectors and M on the x-axis, MyMeaning the projection of the sum of the moment of mass vectors and M on the y-axis, MexMeaning the eccentric moment M of the blade disceProjection on the x-axis, MeyMeaning the eccentric moment M of the blade disceProjection on the y-axis, xi,yiIs the x, y coordinate of the ith blade centroid, mixi,miyiIs the component of the mass moment of the ith blade on the x, y coordinate axes, theta2The included angle between the installation position of the first blade and the mass moment of the blade disc;
and step 3: selecting the initial population by adopting a roulette method;
and 4, step 4: performing the following steps according to the probability generated by the cloud generator under the X condition as a necessary condition;
and 5: performing cross operation on the population after the selection operation by adopting a recombination cross operator;
step 6: performing mutation operation on the population subjected to the cross operation by adopting a two-element optimization mutation operator;
and 7: if the maximum iteration times are not reached, repeating the step 3-6; and if the maximum iteration times are reached, the iteration is finished, and the optimal chromosome is output.
Further, the setting of the initial population in step 1 specifically includes:
step 1.1: taking one leaf as a gene, and taking the sequence number of the whole leaf group of the first-stage leaf disc as a chromosome;
step 1.2: one chromosome, i.e. one individual, randomly generates an initial population with a population size of 2000, i.e. the population size contains 2000 chromosomes.
Further, the selection operator in step 3 adopts roulette method, specifically, for each individual, if its fitness value is f (x)i) Then its relative value of fitness is piPop is the size of the population, piWhen the selection probability of selecting the individual.
Further, the cross probability generated by the cloud generator under the condition of X in step 4 is specifically:
generating a random number [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 by:
He＝En/c2
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, fmaxThe maximum fitness of the population is obtained,
f' is the larger value of the fitness of the crossed two individuals for the average fitness.
Further, the step 5 of performing the intersection operation by using the recombination intersection operator specifically includes that an edge list is established for the leaves in the two parent individuals, the edge list represents the leaves connected with the leaves and the occurrence times, the two individuals are selected to perform the intersection, and if a certain edge appears twice in the parent, a "-" number is added to the top point of the edge in the list;
the edge recombination crossover operator starts to construct a descendant by selecting an initial point, and the principle of selecting individuals from a parent generation is to select the blade with the least number of blades in the adjacent blades, if the number of the blades is equal to the number of the blades connected with two phases, the blade with a minus number is selected first, and if the conditions of the two blades are the same, one of the blades is selected randomly.
Further, the variation probability generated by the cloud generator under the condition of X in step 4 is specifically:
a random number of [0-1] is generated, and the crossover operation is performed when the random number is less than the mutation probability. The conditional cloud generator gives the mutation probabilities as follows:
He＝En/c4
En′＝RANDN(En,He)
wherein f is the individual fitness of the variation, k1～k4∈[0～1]In this text, take k1＝k3＝1.0，k2＝k40.5, c1-c4 as control parameters, c1＝2.9，c3＝3.0，c2＝c4＝10。
Further, the mutation operation performed by using the two-element optimization mutation operator in step 6 specifically includes selecting individuals according to the mutation probability, randomly selecting leaf exchange at two positions of the individuals to obtain new leaf sequences, and performing the above mutation operation on all the individuals in the parent according to the mutation probability until a next generation group is generated.
Further, the fitness function designed in step 2 is specifically that, for the quality requirement, the number of blades in each quadrant is
Then there is
And (3) a classification method, namely obtaining the minimum quadrant quality difference, designing an evaluation coefficient:
suppose ng(i) Representing the quality difference substandard edge number under the ith classification, and if the total substandard edge number is N, then the constraint condition penalty function is as follows:
for the frequency requirement, the design evaluation coefficient:
for the blade group number N with unqualified frequencypIts constraint penalty function:
for the mass moment requirement, the evaluation coefficient is designed:
the fitness function is therefore as follows:
f＝rpfp·rgfg·fz。
the invention has the beneficial effects that:
according to the method, a dual-target optimization model of quality and quality moment is established, and under the condition of considering the integral unbalance of the rotor, the blade group individuals are subjected to crossover and mutation operator design by using a cloud self-adaptive genetic algorithm, so that the blade sequencing under the condition of dual-target optimization of the rotor quality and the quality moment is realized.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A blade sorting method of large-scale high-speed rotation equipment based on multi-target regulation comprises the following steps:
step 1: setting an initial population;
step 2: establishing a physical model of rotor mass, mass moment and frequency, designing a fitness function according to the physical model and the fitness function requirement, and calculating the fitness of all chromosomes of the initial population;
the rotor quality physical model establishing process specifically comprises the following steps: a blade disc has n blades, and is divided into k quadrants, and the number of the blades in each quadrant is equal
The adjacent quadrant mass difference Δ G 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 establishing 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 the minimum frequency difference requirement, the frequency difference between two adjacent blades is required to be not less than the value b, and p (i) means the frequency of the ith blade;
the process for establishing the physical model of the mass moment specifically comprises the following steps: for the blades distributed on the blade disc, the sum of mass moment vectors M and the total imbalance quantity Z of the rotor are as follows:
in the formula, MxMeaning the projection of the sum of the moment of mass vectors and M on the x-axis, MyMeaning the projection of the sum of the moment of mass vectors and M on the y-axis, xi,yiIs the x, y coordinate of the ith blade centroid, mixi,miyiIs the component of the mass moment of the ith blade on the x, y coordinate axes, theta2The included angle between the installation position of the first blade and the mass moment of the blade disc;
and step 3: selecting the initial population by adopting a roulette method;
and 4, step 4: performing the following steps according to the probability generated by the cloud generator under the X condition as a necessary condition;
and 5: performing cross operation on the population after the selection operation by adopting a recombination cross operator;
step 6: performing mutation operation on the population subjected to the cross operation by adopting a two-element optimization mutation operator;
and 7: if the maximum iteration times are not reached, repeating the step 3-6; and if the maximum iteration times are reached, the iteration is finished, and the optimal chromosome is output.
Further, the setting of the initial population in step 1 specifically includes:
step 1.1: taking one leaf as a gene, and taking the sequence number of the whole leaf group of the first-stage leaf disc as a chromosome;
step 1.2: one chromosome, i.e. one individual, randomly generates an initial population with a population size of 2000, i.e. the population size contains 2000 chromosomes.
Further, the selection operator in step 3 adopts roulette method, specifically, for each individual, if its fitness value is f (x)i) Then its relative value of fitness is piPop is the size of the population, piWhen the selection probability of selecting the individual.
Further, the cross probability generated by the cloud generator under the condition of X in step 4 is specifically:
generating a random number [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 by:
He＝En/c2
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, fmaxThe maximum fitness of the population is obtained,
f' is the larger value of the fitness of the crossed two individuals for the average fitness.
Further, the step 5 of performing the intersection operation by using the recombination intersection operator specifically includes that an edge list is established for the leaves in the two parent individuals, the edge list represents the leaves connected with the leaves and the occurrence times, the two individuals are selected to perform the intersection, and if a certain edge appears twice in the parent, a "-" number is added to the top point of the edge in the list;
the edge recombination crossover operator starts to construct a descendant by selecting an initial point, and the principle of selecting individuals from a parent generation is to select the blade with the least number of blades in the adjacent blades, if the number of the blades is equal to the number of the blades connected with two phases, the blade with a minus number is selected first, and if the conditions of the two blades are the same, one of the blades is selected randomly.
Further, the variation probability generated by the cloud generator under the condition of X in step 4 is specifically:
a random number of [0-1] is generated, and the crossover operation is performed when the random number is less than the mutation probability. The conditional cloud generator gives the mutation probabilities as follows:
He＝En/c4
En′＝RANDN(En,He)
wherein f is the individual fitness of the variation, k1～k4∈[0～1]In this text, take k1＝k3＝1.0，k2＝k40.5, c1-c4 as control parameters, c1＝2.9，c3＝3.0，c2＝c4＝10。
Further, the mutation operation performed by using the two-element optimization mutation operator in step 6 specifically includes selecting individuals according to the mutation probability, randomly selecting leaf exchange at two positions of the individuals to obtain new leaf sequences, and performing the above mutation operation on all the individuals in the parent according to the mutation probability until a next generation group is generated.
Further, the fitness function designed in step 2 is specifically that, for the quality requirement, the number of blades in each quadrant is
Then there is
And (3) a classification method, namely obtaining the minimum quadrant quality difference, designing an evaluation coefficient:
suppose ng(i) Representing the quality difference substandard edge number under the ith classification, and if the total substandard edge number is N, then the constraint condition penalty function is as follows:
for the frequency requirement, the design evaluation coefficient:
for the number of blade groups with unqualified frequencyNpIts constraint penalty function:
for the mass moment requirement, the evaluation coefficient is designed:
the fitness function is therefore as follows:
f＝rpfp·rgfg·fz。
Claims (8)
1. a method for sequencing blades of large-scale high-speed rotating equipment based on multi-target regulation is characterized by comprising the following steps:
step 1: setting an initial population;
step 2: establishing a physical model of rotor mass, mass moment and frequency, designing a fitness function according to the physical model and the fitness function requirement, and calculating the fitness of all chromosomes of the initial population;
the rotor quality physical model establishing process specifically comprises the following steps: a blade disc has n blades, and is divided into k quadrants, and the number of the blades in each quadrant is equal
The adjacent quadrant mass difference Δ G 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 establishing 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 the minimum frequency difference requirement, the frequency difference between two adjacent blades is required to be not less than the value b, and p (i) means the frequency of the ith blade;
the process for establishing the physical model of the mass moment specifically comprises the following steps: for the blades distributed on the blade disc, the sum of mass moment vectors M and the total imbalance quantity Z of the rotor are as follows:
in the formula, MxMeaning the projection of the sum of the moment of mass vectors and M on the x-axis, MyMeaning the projection of the sum of the moment of mass vectors and M on the y-axis, MexMeaning the eccentric moment M of the blade disceProjection on the x-axis, MeyMeaning the eccentric moment M of the blade disceProjection on the y-axis, xi,yiIs the x, y coordinate of the ith blade centroid, mixi,miyiIs the component of the mass moment of the ith blade on the x, y coordinate axes, theta2The included angle between the installation position of the first blade and the mass moment of the blade disc;
and step 3: selecting the initial population by adopting a roulette method;
and 4, step 4: performing the following steps according to the probability generated by the cloud generator under the X condition as a necessary condition;
and 5: performing cross operation on the population after the selection operation by adopting a recombination cross operator;
step 6: performing mutation operation on the population subjected to the cross operation by adopting a two-element optimization mutation operator;
and 7: if the maximum iteration times are not reached, repeating the step 3-6; and if the maximum iteration times are reached, the iteration is finished, and the optimal chromosome is output.
2. The leaf sorting method according to claim 1, wherein the setting of the initial population in step 1 specifically comprises:
step 1.1: taking one leaf as a gene, and taking the sequence number of the whole leaf group of the first-stage leaf disc as a chromosome;
step 1.2: one chromosome, i.e. one individual, randomly generates an initial population with a population size of 2000, i.e. the population size contains 2000 chromosomes.
3. The leaf sorting method according to claim 1, wherein the selection operator in step 3 employs roulette, in particular, if for each individual it has a fitness value of f (x)i) Then its relative value of fitness is piPop is the size of the population, piWhen the selection probability of selecting the individual.
4. The blade sorting method according to claim 4, wherein the cross probability generated by the cloud generator under the X condition in the step 4 is specifically:
generating a random number [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 by:
He＝En/c2
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, fmaxThe maximum fitness of the population is obtained,
f' is the larger value of the fitness of the crossed two individuals for the average fitness.
5. The leaf sorting method according to claim 1, wherein the step 5 of performing the intersection operation by using the recombination intersection operator specifically includes firstly establishing an edge list for the leaves in the two parent individuals, indicating the leaves connected to the leaf and the occurrence number, selecting two individuals to perform the intersection, and if an edge appears twice in the parent, adding a "-" number to the vertex of the edge in the list;
the edge recombination crossover operator starts to construct a descendant by selecting an initial point, and the principle of selecting individuals from a parent generation is to select the blade with the least number of blades in the adjacent blades, if the number of the blades is equal to the number of the blades connected with two phases, the blade with a minus number is selected first, and if the conditions of the two blades are the same, one of the blades is selected randomly.
6. The method for blade sorting according to claim 1, wherein the probability of variation generated by the cloud generator under the condition X in the step 4 is specifically:
a random number of [0-1] is generated, and the crossover operation is performed when the random number is less than the mutation probability. The conditional cloud generator gives the mutation probabilities as follows:
He＝En/c4
En′＝RANDN(En,He)
wherein f is the individual fitness of the variation, k1～k4∈[0～1]In this text, take k1＝k3＝1.0，k2＝k40.5, c1-c4 as control parameters, c1＝2.9，c3＝3.0，c2＝c4＝10。
7. The leaf sorting method according to claim 1, wherein the mutation operation performed in step 6 by using a two-element optimization mutation operator is specifically that individuals selected according to mutation probabilities are randomly selected to perform leaf exchange at two positions of the individuals to obtain new leaf sorting, and all individuals in the parents are subjected to the above mutation operation according to the mutation probabilities until a next generation group is generated.
8. The method for blade sequencing according to claim 1, wherein the fitness function is designed in step 2, specifically, for the quality requirement, the number of blades in each quadrant is
Then there is
And (3) a classification method, namely obtaining the minimum quadrant quality difference, designing an evaluation coefficient:
suppose ng(i) The number of the unqualified sides with poor quality under the ith classification is shown, and the total unqualified sides areN, then its constraint penalty function:
for the frequency requirement, the design evaluation coefficient:
for the blade group number N with unqualified frequencypIts constraint penalty function:
for the mass moment requirement, the evaluation coefficient is designed:
the fitness function is therefore as follows:
f＝rpfp·rgfg·fz。
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| CN113312705A (en) * | 2021-06-14 | 2021-08-27 | 西北工业大学 | Method for sequencing rotor blades of low-pressure fan of aircraft engine |
| CN116056158A (en) * | 2023-03-24 | 2023-05-02 | 新华三技术有限公司 | Frequency allocation method and device, electronic equipment and storage medium |
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