CN110008641B - Multi-objective structure optimization method for magnetic gear brushless direct current motor - Google Patents
Multi-objective structure optimization method for magnetic gear brushless direct current motor Download PDFInfo
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Abstract
The invention discloses a multi-objective structure optimization method of a magnetic gear brushless direct current motor, which takes volume minimization and efficiency maximization as optimization targets, and in the analysis process, relevant limiting conditions such as current, slip, magnetic flux density, power factor and the like are considered, and stator slot number, rotor slot number, outer diameter of a rotor end ring and inner diameter of the rotor end ring are selected as optimization targets, so that the performance of the magnetic gear brushless direct current motor system is improved. The method mainly comprises the steps that the chaotic search reverse learning difference method integrates the chaotic search and the reverse learning method into the differential evolution method, and besides the searching capability of the differential evolution method can be improved, only two control parameters need to be specified, so that the chaotic search reverse learning difference method has robustness, the framework has the capability of on-line parameter adjustment, has better structural optimization capability for the magnetic gear brushless direct current motor, and can effectively improve the dynamic characteristics of a driving system.
Description
Technical Field
The invention relates to the technical field of electric transmission, in particular to a multi-objective structure optimization method of a magnetic gear brushless direct current motor.
Background
Compared with mechanical gears, 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, 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 an electric automobile, has high power density, high torque density and wide speed range, and comprises low-speed climbing and high-speed running, high efficiency, wide fixed power area, fixed rotating speed area and high reliability. Therefore, how to improve the efficiency of the magnetic gear brushless direct current motor becomes a very important subject, and in order to formulate and improve the lowest efficiency of the induction motor, the invention provides a method for applying the chaotic search reverse learning difference method to the magnetic gear brushless direct current motor so as to optimize the structure and improve the performance of the magnetic gear brushless direct current motor.
The chaotic search reverse learning difference method integrates the chaotic search and the reverse learning method into the differential evolution method so as to overcome the defects of the differential evolution method on the selection of crossing factors, proportion parameters and variation operation elements, and besides the search capability of the differential evolution method can be improved, only two control parameters need to be specified, so that the chaotic search reverse learning difference method has robustness. Through searching related patents and documents at home and abroad, a multi-objective structure optimization method for applying the chaotic search reverse learning difference method to the magnetic gear brushless direct current motor is not available.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art and provide a multi-objective structure optimization method of a magnetic gear brushless direct current motor, which takes volume minimization and efficiency maximization as analysis targets, and in the analysis process, relevant limiting conditions such as current, slip, magnetic flux density, power factor and the like are considered, and the number of stator grooves, the number of rotor grooves, the outer diameter of a rotor end ring and the inner diameter of the rotor end ring are selected as optimization targets, so that the magnetic gear brushless direct current motor system is more in line with an electric vehicle and the like.
The invention adopts the following technical scheme for solving the technical problems:
the multi-objective structure optimization method of the magnetic gear brushless direct current motor provided by the invention is characterized by comprising the following steps of:
step S1, initializing
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 initial 4 groups simultaneously; selecting any one of the structural parameters as one of the groups, wherein the initial group generation is randomly started in the search space, and the implementation is as shown in formula (1)
wherein ,sigma, the initial population i ∈(0,1]In the initial population, all individuals produce the random numbers in the manner shown in formula (1); n (N) p Is the size of the group, X i,max and Xi,min Respectively 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 variation operand is carried out in a vector difference mode, and in the group of the G generation, any two individuals define the vector difference of the formula (2),
wherein ,Djk In the form of a vector difference,the j and k individuals in the G generation population, respectively;
by the vector difference concept, the next generation candidate individuals are generated by individuals by using a variation operand, as shown in formula (3);
wherein ,is the i-th individual estimate in the G+1 generation population, < >>Is the p-th individual in the G generation population, F is the scale factor;
simultaneously performs the crossover operation of the following formula (4),
wherein i=1 p And g=1..m, g e (0, m) natural number, m is natural number, C r The cross factor of e (0, 1),the ith gene of the G-th individual in the G+1 generation group,>the ith gene of the G-th individual in the G-th generation group,/-th individual in the G-th generation group>An estimate of the ith gene for the G-th individual in the G-th generation population; the concept of quantitative mechanism is cited here to generate the next generation of offspring, and the variant operand is generated in the following formula (5):
wherein u is E (0, 1)]U is a random number, and u is a random number,1 st gene of the ith individual in the G generation group,/I>2 nd gene of the i-th individual in the G generation group,/I>I individuals in the G generation population;
step S3, judging and selecting
The individuals aiming at the offspring compete with the individuals aiming at the corresponding father, and the generation mode is as follows:
wherein argmin is the minimum of the two expressions taking this latter expression,is the individual in the G+1 generation, +.>For individuals in the G generation,/->An estimated value function expression for individuals in generation G+1;
step S4, elimination method
The chaotic search reverse learning difference method introduces the elimination method, and the operation mode is that a new individual is generated by the following method,
wherein, alpha and delta are numbers randomly generated between 0 and 1, and />The worst and best individuals in the g+1 generation, respectively,/-on>Is a new individual in the generation G+1, < >>1 st gene of the ith individual in the G+1 generation,/o>The ith individual in the G+1 generation2 genes; if the new individual generated by formula (7) is better than the worst individual in the G generation, this individual will replace the worst individual in the G generation;
step S5, number shifting operation
The shift operation is based on the current best population, and regenerates new population to maintain the diversity of the population, enhance the searching ability of the minor population, and generate the g gene of the i-th individual as follows:
wherein the parameter sigma i And δ is a random number, i=1, …, N p And g=1, …, m,the g gene, X, of the i-th individual gmin Minimum value of g gene, X gmax Is the maximum value of the g gene;
step S6, accelerating operation
When the generation of the individual is not more preferable than the previous optimal individual, the acceleration operand is executed, and the descent method is adopted as the acceleration operand, wherein the expression (9) is as follows,
wherein ,represents the G generation optimal individual, f represents the objective function gradient, phi is the step size,/>For the best individual of the G+1st generation, < >>Formula for optimal individual function of generation G+1, < ->The optimal individual function formula of the current G generation;
step S7, repeating the steps S2 to S4 for 4 structural parameters of the stator slot number, the rotor end ring outer diameter and the rotor end ring inner diameter, wherein each group repeats the steps S2 to S4 to N times, N is a preset number of times, and all the structural parameters can be optimized.
As a further optimization scheme of the multi-objective structure optimization method of the magnetic gear brushless direct current motor, v f is obtained through approximate calculation by a finite difference method.
As a further optimization scheme of the multi-objective structure optimization method of the magnetic gear brushless direct current motor, the initial value of phi is set to be 1.
As the multi-objective structure optimization method of the magnetic gear brushless direct current motor, the parameter sigma is further optimized i Is 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 technical scheme provided by the invention has the following technical effects:
(1) Compared with the chaotic search and reverse learning method, the chaotic search and reverse learning difference method has the advantages of high online learning convergence speed, strong function imitation capability and memory capability, and can obviously improve the structural optimization method of the magnetic gear brushless direct current motor and obviously improve the system performance;
(2) The chaotic search reverse learning difference method overcomes the defect that the chaotic search and the reverse learning method all need to set a larger population number so as to be capable of searching solutions.
Drawings
Fig. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings:
the embodiment 1 provides a multi-objective structure optimization method of a magnetic gear brushless direct current motor, which comprises the following steps:
the chaotic search reverse learning differencing method steps can be briefly described as follows:
step S1, initializing
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 initial 4 groups simultaneously; selecting any one of the structural parameters as one of the groups, the initial group generation is performed by randomly starting in the search space, and the method is as follows
In the formula (1), the components are as follows,sigma, the initial population i ∈(0,1]In the initial population, all individuals generate the random numbers in the manner shown in formula (1). N (N) p Is the size of the group, X i,max and Xi,min Representing the i-th individual upper limit and lower limit, respectively.
Step S2, mutation operation
In the differential evolution method, the operation mode of the variation operand is carried out in a vector difference mode, and any two individuals in the group of the G generation can define the vector difference of the following formula,
in the formula (2), D jk In the form of a vector difference,the j and k individuals in the G generation population, respectively.
By the vector difference concept, the next generation candidate individual can be generated by using the variant operand as in formula (3).
In the formula (3), the amino acid sequence of the compound,is the i-th individual estimate in the G+1 generation population, < >>Is the p-th individual in the G generation group, where F is a scale factor.
Meanwhile, in order to enhance the characteristics of the population variability, the differential evolution method performs a crossover operation of the following formula,
in the formula (4), the amino acid sequence of the compound, i=1 and, N p And g=1..m, g e (0, m) natural number, m is natural number, C r The crossing factor of E (0, 1) is self-determined according to the situation;the ith gene of the G-th individual in the G+1 generation group,>the ith gene of the G-th individual in the G-th generation group,/-th individual in the G-th generation group>An estimate of the ith gene of the G-th individual in the G-th generation population. The concept of quantitative mechanism is cited here to generate the next generation of offspring, the variant operand is generated as follows:
in the formula (5), u is E (0, 1)]U is a random number, and u is a random number,is the 1 st gene of the i-th individual in the G generation group,/I>The 2 nd gene of the i-th individual in the G-generation group.
Step S3 judgment and selection
In this part, the offspring are mutually competing with the parent corresponding to the offspring, and the generation mode is as follows:
in the formula (6), the amino acid sequence of the compound,for the ith individual in the G generation population, argmin is the minimum of the two expressions of this latter formula; />Is the individual in the G+1 generation, +.>For individuals in the G generation,/->Is an estimated value function expression of individuals in the generation G+1.
Step S4 elimination method
The idea of the elimination method is to accelerate the convergence speed of the chaotic search reverse learning difference method; the chaotic search reverse learning difference method is introduced into the elimination method by firstly utilizing the following procedures to generate a new individual,
in formula (7), wherein alpha and delta are each a number randomly generated between 0 and 1, and />The worst and best individuals in the g+1 generation, respectively. />Is a new individual in the generation G+1, < >>1 st gene of the ith individual in the G+1 generation,/o>Is the 2 nd gene of the i-th individual in the generation G+1. If the new individual generated by formula (7) is better than the worst individual in the G generation, this individual will replace the worst individual in the G generation.
Step S5 of the number-shift operation
The shift operation is based on the current best population, and regenerates new population to maintain the diversity of the population, enhance the searching ability of the minor population, and generate the g gene of the i-th individual as follows:
in the formula (8), the parameter sigma i And δ is a random number between 0 and 1, i=1, …, N p And g=1, …, m,the g gene, X, of the i-th individual gmin Minimum value of g gene, X gmax Is the maximum value of the g gene.
Step S6 of accelerating operation
When the generation of the individual is not more preferable than the previous optimal individual, the acceleration operand is executed, and the descent method is adopted as the acceleration operand,
represents the G generation optimal individual, and f represents the objective function gradient, wherein the gradient can be obtained by approximate calculation through a finite difference method, phi is the step size, and is set as 1 +.>For the best individual of the G+1st generation, < >>Formula for optimal individual function of generation G+1, < ->And the optimal individual function formula for the current generation G.
Step S7
For the 4 structural parameters of the stator slot number, the rotor end ring outer diameter and the rotor end ring inner diameter, each group repeats steps S2 to S4 to N times, N is a preset number of times, and all the structural parameters can be optimized, and the process is shown in fig. 1.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention.
Claims (5)
1. The multi-target structure optimization method of the magnetic gear brushless direct current motor is characterized by comprising the following steps of:
step S1, initializing
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 initial 4 groups simultaneously; selecting any one of the structural parameters as one of the groups, wherein the initial group generation is randomly started in the search space, and the implementation is as shown in formula (1)
wherein ,sigma, the initial population i ∈(0,1]In the initial population, all individuals produce the random numbers in the manner shown in formula (1); n (N) p Is the size of the group, X i,max and Xi,min Respectively 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 variation operand is carried out in a vector difference mode, and in the group of the G generation, any two individuals define the vector difference of the formula (2),
wherein ,Djk In the form of a vector difference,the j and k individuals in the G generation population, respectively;
by the vector difference D jk A next generation candidate individual generated by the individual using a variant operand, as in formula (3);
wherein ,is the i-th individual estimate in the G+1 generation population, < >>Is the p-th individual in the G generation population, F is the scale factor;
simultaneously performs the crossover operation of the following formula (4),
wherein i=1 p And g=1..m, g e (0, m) natural number, m is natural number, C r The cross factor of e (0, 1),the ith gene of the G-th individual in the G+1 generation group,>the ith gene of the G-th individual in the G-th generation group,/-th individual in the G-th generation group>An estimate of the ith gene for the G-th individual in the G-th generation population; the concept of quantitative mechanism is cited here to generate the next generation of offspring, and the variant operand is generated in the following formula (5):
wherein u is E (0, 1)]U isA random number is used to determine the random number,1 st gene of the ith individual in the G generation group,/I>2 nd gene of the i-th individual in the G generation group,/I>I individuals in the G generation population;
step S3, judging and selecting
The individuals aiming at the offspring compete with the individuals aiming at the corresponding father, and the generation mode is as follows:
wherein argmin is the minimum of the two expressions taking this latter expression,is an individual in the generation G+1,is a functional expression of individuals in the G generation, < >>An estimated value function expression for individuals in generation G+1;
step S4, elimination method
The chaotic search reverse learning difference method introduces the elimination method, and the operation mode is that a new individual is generated by the following method,
wherein, alpha and delta are numbers randomly generated between 0 and 1, and />The worst and best individuals in the g+1 generation, respectively,/-on>Is a new individual in the generation G+1, < >>1 st gene of the ith individual in the G+1 generation,/o>The 2 nd gene of the i-th individual in the G+1 generation; if the new individual generated by formula (7) is better than the worst individual in the G generation, this individual will replace the worst individual in the G generation;
step S5, number shifting operation
The shift operation is based on the current best population, and regenerates new population to maintain the diversity of the population, enhance the searching ability of the minor population, and generate the g gene of the i-th individual as follows:
wherein the parameter sigma i And δ is a random number, i=1, …, N p And g=1, …, m,the g gene, X, of the i-th individual gmin Minimum value of g gene, X gmax Is the maximum value of the g gene;
step S6, accelerating operation
When the generation of the individual is not more preferable than the previous optimal individual, the acceleration operand is executed, and the descent method is adopted as the acceleration operand, wherein the expression (9) is as follows,
wherein ,represents the best individual of the G generation,>represents the gradient of the objective function, phi is the step size,/-, and>for the best individual of the G+1st generation, < >>Formula for optimal individual function of generation G+1, < ->The optimal individual function formula of the current G generation;
step S7, repeating the steps S2 to S4 for 4 structural parameters of the stator slot number, the rotor end ring outer diameter and the rotor end ring inner diameter, wherein each group repeats the steps S2 to S4 to N times, N is a preset number of times, and all the structural parameters can be optimized.
2. The method for optimizing the multi-objective structure of a magnetic gear brushless DC motor of claim 1, wherein,and the method is obtained by approximate calculation through a finite difference method.
3. The method of optimizing a multi-objective structure of a magnetic gear brushless dc motor of claim 1, wherein the initial value of Φ is set to 1.
4. The method for optimizing the multi-objective structure of a magnetic gear brushless direct current motor according to claim 1, wherein the parameter σ is i Is 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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