CN110008641A - A kind of multiple objectives structure optimization method of magnetic gear brshless DC motor - Google Patents

A kind of multiple objectives structure optimization method of magnetic gear brshless DC motor Download PDF

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CN110008641A
CN110008641A CN201910337534.6A CN201910337534A CN110008641A CN 110008641 A CN110008641 A CN 110008641A CN 201910337534 A CN201910337534 A CN 201910337534A CN 110008641 A CN110008641 A CN 110008641A
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CN110008641B (en
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杨益飞
汪红兵
黄海洋
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Suzhou Vocational University
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • G06F30/23Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00Road transport of goods or passengers
    • Y02T10/60Other road transportation technologies with climate change mitigation effect
    • Y02T10/64Electric machine technologies in electromobility

Abstract

The invention discloses a kind of multiple objectives structure optimization methods of magnetic gear brshless DC motor, using volume minimization and efficiency maximum as optimization aim, during analysis, consider the related restrictive condition such as electric current, slippage, magnetic flux density and power factor, select number of stator slots, rotor slot number, the outer diameter of rotor end ring, rotor end ring internal diameter be optimization object, so as to allow magnetic gear brushless DC motor system performance improve.This method mainly includes that Chaos Search backward learning calculus of finite differences has concentrated Chaos Search, backward learning to be dissolved into Differential evolution, the present invention can be with the search capability of improved differential evolution method outside, because need to only be specified there are two control parameter, therefore, Chaos Search backward learning calculus of finite differences has robustness, the framework has on-line tuning parameter capabilities, has preferable optimization structural capacity for magnetic gear brshless DC motor, and can effectively improve the dynamic characteristic of drive system.

Description

Multi-objective structure optimization method of magnetic gear brushless direct current motor
Technical Field
The invention relates to the technical field of electric transmission, in particular to a multi-target structure optimization method of a magnetic gear brushless direct current motor.
Background
Compared with a mechanical gear, the magnetic gear has the advantages of low noise, high efficiency, convenience in maintenance, high reliability, overload protection and the like. The magnetic gear has wide application in the field of electric transmission of high-force density driving devices and the like, and is particularly suitable for occasions without lubrication, noise, friction energy consumption, oil pollution and water and dust. The magnetic gear and the brushless direct current motor are integrated to form the magnetic gear brushless direct current motor, and the magnetic gear brushless direct current motor is applied to electric automobiles, has high power density, high torque density and wide speed range, and comprises a low-speed climbing region, a high-speed driving region, a high-efficiency region, a wide fixed power region, a fixed rotating speed region and high reliability. Therefore, how to improve the efficiency of the magnetic gear brushless dc motor becomes a very important issue, and in order to establish and improve the minimum efficiency of the induction motor, the invention provides a method for applying the chaos search reverse learning difference method to the magnetic gear brushless dc motor to optimize the structure and improve the performance thereof.
The chaotic search reverse learning difference method integrates chaotic search and a reverse learning method into a differential evolution method so as to overcome the defects of the differential evolution method on cross factors, proportional parameters and variable operand selection. Through retrieving related patents and documents at home and abroad, a multi-target structure optimization method of applying a chaos search reverse learning difference method to a magnetic gear brushless direct current motor is not available.
Disclosure of Invention
The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a method for optimizing a multi-objective structure of a magnetic gear brushless dc motor, wherein the method takes volume minimization and efficiency maximization as analysis targets, and in the analysis process, relevant limiting conditions such as current, slip, flux density and power factor are considered, and the number of stator slots, the number of rotor slots, the outer diameter of a rotor end ring and the inner diameter of the rotor end ring are selected as optimization targets, so that a magnetic gear brushless dc motor system is more suitable for electric vehicles and the like.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a multi-objective structure optimization method of a magnetic gear brushless direct current motor, which is characterized by comprising the following steps of:
step S1, initialization
Selecting the number of stator slots, the number of rotor slots, the outer diameter of a rotor end ring and the inner diameter of the rotor end ring in the structural parameters of the magnetic gear brushless direct current motor as structural parameters, and generating the initial 4 groups at the same time; selecting any one of the structure parameters as one of the populations, the initial population generation being started randomly in the search space, as performed by equation (1)
wherein ,is the initial population, σi∈(0,1]The random number of (1), in the initial population, is generated by all individuals; n is a radical ofpIs the size of the population, Xi,max and Xi,minRespectively representing the upper limit value and the lower limit value of the ith individual;
step S2, mutation operation
In the differential evolution method, the operation mode of the variant operand is performed in a vector difference mode, in the group of the G generation, any two individuals define the vector difference of the formula (2),
wherein ,DjkIn order to be the vector difference,respectively the j and k individuals in the G generation group;
by the above-mentioned vector difference concept, the next generation candidate individuals are generated by the individuals using the variation operand, as formula (3);
wherein ,is the estimated value of the ith individual in the G +1 generation group,is the p-th individual in the G generation group, F is a scale factor;
simultaneously, the cross operation of the following formula (4) is carried out,
n, wherein i is 1pAnd g is 1, m, g is a natural number of (0, m), m is a natural number, CrE (0,1) is selected,is the ith gene of the G individual in the G +1 generation group,is the ith gene of the G individuals in the G generation group,is an estimate of the ith gene of the G th individual in the G th generation population; the concept of the quantitative mechanism is introduced here to generate the next generation of offspring, and the variant operand is generated as shown in the following formula (5):
wherein u is belonged to (0,1)]And u is a random number,is the 1 st gene of the ith individual in the G generation group,is the 2 nd gene of the ith individual in the G generation group,is the ith individual in the G generation group;
step S3, judging and selecting
Aiming at the mutual competition between the individuals of the filial generations and the corresponding individuals of the parents, the generation mode is as follows:
wherein argmin is the minimum of two expressions of the following expression,is an individual in the G +1 th generation,is an individual in the G-th generation,is an estimation value function expression of an individual in the G +1 generation;
step S4, elimination method
The chaotic search inverse learning difference method introduces an elimination method, and the operation mode of the chaotic search inverse learning difference method is that a new individual is generated by the following method,
wherein α and δ are both randomly generated numbers between 0 and 1,andthe worst and best individuals in the G +1 generation respectively,is a new individual in the G +1 generation,is the 1 st gene of the ith individual in the G +1 generation,the 2 nd gene of the ith individual in the G +1 generation; if the new individual of formula (7) is better than the worst individual in the G-th generation, this individual will replace the worst individual in the G-th generation;
step S5, number shift operation
The number-shift operation is based on the current best population group individual to regenerate a new population group to maintain the diversity of the population group and enhance the small population group searching capability, the g gene generation method of the i individual is as follows:
wherein the parameter σiAnd δ is a random number, i ═ 1, …, NpAnd g is 1, …, m,is the g gene of the i individual, XgminIs the g gene minimum, XgmaxIs the g gene maximum;
step S6, acceleration calculation
When the generation of the individuals is generated, if no more optimal individuals than the previous best individuals are generated, the acceleration operation element is executed, the descent method is adopted as the acceleration operation element, and the expression (9) is as follows,
wherein ,representing the best individual of the G-th generation, ▽ f representing the gradient of the objective function, phi being the step size,is the best individual in the G +1 th generation,for the optimal individual function formula of the G +1 th generation,the current G generation optimal individual function formula is obtained;
step S7, repeating steps S2 to S4 for each group of 4 structural parameters, i.e., the number of stator slots, the number of rotor slots, the outer diameter of a rotor end ring, and the inner diameter of the rotor end ring, and repeating steps S2 to S4 to N times for each group, where N is a predetermined number of times, so that all structural parameters can be optimized.
▽ f is obtained by approximate calculation through a finite difference method and serves as a further optimization scheme of the multi-objective structure optimization method of the magnetic gear brushless direct current motor.
As a further optimization scheme of the multi-target structure optimization method of the magnetic gear brushless direct current motor, the initial value of phi is set to be 1.
The invention relates to a further optimization scheme of a multi-target structure optimization method of a magnetic gear brushless direct current motor, wherein a parameter sigma isiIs a random number between 0 and 1.
As a further optimization scheme of the multi-objective structure optimization method of the magnetic gear brushless direct current motor, the parameter delta is a random number between 0 and 1.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
(1) compared with chaotic search and inverse learning methods, the chaotic search and inverse learning difference method has the advantages of high online learning convergence speed, strong function simulation capability and memory capability, can obviously improve the magnetic gear brushless direct current motor structure optimization method, and can obviously improve the system performance;
(2) the chaos search reverse learning difference method overcomes the defect that the chaos search and the reverse learning methods need to set a larger population number so as to search a solution.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the embodiment 1 provides a multi-objective structure optimization method for a magnetic gear brushless direct current motor, which includes the following steps:
the chaos search inverse learning difference method can be briefly described as follows:
step S1, initialization
Selecting the number of stator slots, the number of rotor slots, the outer diameter of a rotor end ring and the inner diameter of the rotor end ring in the structural parameters of the magnetic gear brushless direct current motor as structural parameters, and generating the initial 4 groups at the same time; selecting any one of the structure parameters as one of the clusters, the initial cluster generation is started randomly in the search space by the following method
In the formula (1), the reaction mixture is,is the initial population, σi∈(0,1]The random number of (2) is generated by all individuals in the initial population in the same manner as in formula (1). N is a radical ofpIs the size of the population, Xi,max and Xi,minRespectively represent the ith individual upper limit value and the ith individual lower limit value.
Step S2, mutation operation
In the differential evolution method, the operation of the variant operands is performed as a vector difference, and in the G-th generation population, any two individuals can define a vector difference as shown in the following formula,
in the formula (2), DjkIn order to be the vector difference,the j and k individuals in the G generation group.
By the above-mentioned concept of vector difference, the next generation candidate individuals can be generated by using variant operands by individuals, as shown in formula (3).
In the formula (3), the reaction mixture is,is the estimated value of the ith individual in the G +1 generation group,is the p-th individual in the G generation group, and F in the above formula is a scale factor.
Meanwhile, in order to improve the characteristics of the population diversity, the differential evolution method performs the following cross-operations,
in formula (4), i ═ 1., NpAnd g is 1, m, g is a natural number of (0, m), m is a natural number, CrThe element belongs to the cross factor of (0,1), and is self-determined according to the situation;is the ith gene of the G individual in the G +1 generation group,is the ith gene of the G individuals in the G generation group,is an estimate of the ith gene of the G-th individual in the G-th generation population. The concept of the quantitative mechanism is incorporated herein to generate the next generation of offspring, and the variant operand is generated as follows:
in the formula (5), u ∈ (0,1)]And u is a random number,is the 1 st gene of the ith individual in the G generation group,is the 2 nd gene of the ith individual in the G generation group.
Step S3 judging and selecting
In this section, the individuals of the child compete with the individuals of the corresponding parent, and the generation mode is as follows:
in the formula (6), the reaction mixture is,for the ith individual in the G generation group, argmin is the minimum value of two expressions of the following expression;is an individual in the G +1 th generation,is an individual in the G-th generation,is a function expression of the estimated value of the individual in the G +1 generation.
Step S4 elimination method
The idea of the elimination method is to accelerate the convergence speed of the chaos search reverse learning difference method; the operation mode of introducing the elimination method by the chaos search inverse learning difference method is that a new individual is generated by utilizing the following procedures,
in formula (7), wherein α and δ are both randomly generated numbers between 0 and 1,andthe worst and best individuals in the G +1 th generation, respectively.Is a new individual in the G +1 generation,is the 1 st gene of the ith individual in the G +1 generation,is the 2 nd gene of the ith individual in the G +1 generation. If the new individual generated by formula (7) is better than the worst individual in the G-th generation, this individual will replace the worst individual in the G-th generation.
Step S5 number shift operation
The number-shift operation is based on the current best population group individual to regenerate a new population group to maintain the diversity of the population group and enhance the small population group searching capability, the g gene generation method of the i individual is as follows:
in the formula (8), the parameter σiAnd δ is a random number between 0 and 1, i ═ 1, …, NpAnd g is 1, …, m,is the g gene of the i individual, XgminIs the g gene minimum, XgmaxIs the g gene maximum.
Step S6 acceleration operation
When the generation of the individuals is generated, if no more optimal individuals than the previous best individuals are generated, the acceleration operation element is executed, wherein a descending method is adopted as the acceleration operation element, the expression formula is as follows,
representing the best individual of the G-th generation, ▽ f representing the gradient of the objective function, which can be approximated by finite difference method, phi being the step size, here set to 1,is the best individual in the G +1 th generation,for the optimal individual function formula of the G +1 th generation,is the current G-th generation optimal individual function formula.
Step S7
For the 4 structural parameters of the number of the stator slots, the number of the rotor slots, the outer diameter of the rotor end ring and the inner diameter of the rotor end ring, the steps S2 to S4 are repeated for each group, the steps S2 to S4 are repeated for each group for N times, where N is a preset number of times, and all the structural parameters can be optimized, and the process is as shown in fig. 1.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (5)

1. A multi-objective structure optimization method of a magnetic gear brushless direct current motor is characterized by comprising the following steps:
step S1, initialization
Selecting the number of stator slots, the number of rotor slots, the outer diameter of a rotor end ring and the inner diameter of the rotor end ring in the structural parameters of the magnetic gear brushless direct current motor as structural parameters, and generating the initial 4 groups at the same time; selecting any one of the structure parameters as one of the populations, the initial population generation being started randomly in the search space, as performed by equation (1)
wherein ,is the initial population, σi∈(0,1]The random number of (1), in the initial population, is generated by all individuals; n is a radical ofpIs the size of the population, Xi,max and Xi,minRespectively representing the upper limit value and the lower limit value of the ith individual;
step S2, mutation operation
In the differential evolution method, the operation mode of the variant operand is performed in a vector difference mode, in the group of the G generation, any two individuals define the vector difference of the formula (2),
wherein ,DjkIn order to be the vector difference,respectively the j and k individuals in the G generation group;
by the above-mentioned vector difference concept, the next generation candidate individuals are generated by the individuals using the variation operand, as formula (3);
wherein ,is the estimated value of the ith individual in the G +1 generation group,is the p-th individual in the G generation group, F is a scale factor;
simultaneously, the cross operation of the following formula (4) is carried out,
n, wherein i is 1pAnd g is 1, m, g is a natural number of (0, m), m is a natural number, CrE (0,1) is selected,is the ith gene of the G individual in the G +1 generation group,is the ith gene of the G individuals in the G generation group,is an estimate of the ith gene of the G th individual in the G th generation population; the concept of the quantitative mechanism is introduced here to generate the next generation of offspring, and the variant operand is generated as shown in the following formula (5):
wherein u is belonged to (0,1)]And u is a random number,is the 1 st gene of the ith individual in the G generation group,is the 2 nd gene of the ith individual in the G generation group,is the ith individual in the G generation group;
step S3, judging and selecting
Aiming at the mutual competition between the individuals of the filial generations and the corresponding individuals of the parents, the generation mode is as follows:
wherein argmin is the minimum of two expressions of the following expression,is an individual in the G +1 th generation,is an individual in the G-th generation,is an estimation value function expression of an individual in the G +1 generation;
step S4, elimination method
The chaotic search inverse learning difference method introduces an elimination method, and the operation mode of the chaotic search inverse learning difference method is that a new individual is generated by the following method,
wherein α and δ are both randomly generated numbers between 0 and 1,andthe worst and best individuals in the G +1 generation respectively,is a new individual in the G +1 generation,is the 1 st gene of the ith individual in the G +1 generation,the 2 nd gene of the ith individual in the G +1 generation; if the new individual of formula (7) is better than the worst individual in the G-th generation, this individual will replace the worst individual in the G-th generation;
step S5, number shift operation
The number-shift operation is based on the current best population group individual to regenerate a new population group to maintain the diversity of the population group and enhance the small population group searching capability, the g gene generation method of the i individual is as follows:
wherein the parameter σiAnd δ is a random number, i ═ 1, …, NpAnd g is 1, …, m,is the g gene of the i individual, XgminIs the g gene minimum, XgmaxIs the g gene maximum;
step S6, acceleration calculation
When the generation of the individuals is generated, if no more optimal individuals than the previous best individuals are generated, the acceleration operation element is executed, the descent method is adopted as the acceleration operation element, and the expression (9) is as follows,
wherein ,representing the best individual of the G-th generation, ▽ f representing the gradient of the objective function, phi being the step size,is the best individual in the G +1 th generation,for the optimal individual function formula of the G +1 th generation,the current G generation optimal individual function formula is obtained;
step S7, repeating steps S2 to S4 for each group of 4 structural parameters, i.e., the number of stator slots, the number of rotor slots, the outer diameter of a rotor end ring, and the inner diameter of the rotor end ring, and repeating steps S2 to S4 to N times for each group, where N is a predetermined number of times, so that all structural parameters can be optimized.
2. The method for optimizing the multi-objective structure of the magnetic gear brushless direct current motor as claimed in claim 1, wherein ▽ f is obtained by approximate calculation through a finite difference method.
3. The method of claim 1, wherein the initial value of φ is set to 1.
4. The method of claim 1, wherein the parameter σ is a multi-objective structural optimization method for a magnetic gear brushless DC motoriIs a random number between 0 and 1.
5. The method of claim 1, wherein the parameter δ is a random number between 0 and 1.
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