CN116796597A - Multi-objective optimization method suitable for multi-parameter coupling permanent magnet vernier rim propulsion motor - Google Patents
Multi-objective optimization method suitable for multi-parameter coupling permanent magnet vernier rim propulsion motor Download PDFInfo
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Abstract
The application discloses a multi-objective optimization method suitable for a multi-parameter coupling permanent magnet vernier rim propulsion motor, which comprises the following steps: s1: establishing a motor no-load model; s2: the average torque and torque pulsation of a permanent magnet vernier rim propulsion motor when the motor is loaded are used as optimization targets; s3: on the basis of completing the design of no-load working conditions, determining a value range of related structural parameters affecting the average torque and torque pulsation; s4: returning the value range of the structural parameter to the no-load model of the motor, and checking whether the value range meets the design requirement under the no-load working condition of the motor; s5: constructing a sample library by adopting a Lat Ding Chao cube test, and supplementing certain sample data by adopting an optimized Latin hypercube method in a sampling range of sparse samples by referring to the distribution condition of the sample library data; s6: carrying out sensitivity sequencing and layering treatment on motor structure parameters according to a parameter sensitivity analysis mode; s7: searching a global optimal solution, and adopting structural parameters with weak sensitivity to adjust so as to complete optimization.
Description
Technical Field
The application relates to the field of motor optimization design, in particular to multi-objective optimization of a multi-parameter coupling permanent magnet vernier rim propulsion motor.
Background
Sea trade communication among countries is increasingly frequent, and higher requirements are put on the transportation capacity and propulsion capacity of ships. The traditional ship propulsion device adopts a combination of a propulsion shafting and a propeller, occupies a large amount of space, and reduces the propulsion efficiency and the reliability. In recent years, a highly integrated electric propulsion device, a shaftless rim propulsion, has emerged. The propeller has the advantages that a propulsion shafting is omitted, a motor rotor and a propeller blade are directly integrated into a whole, current is adopted to directly drive, and the motor rotor and the propeller blade are welded, so that the propulsion motor can directly drive the propeller blade to do work, and the hydrodynamic performance of the propeller is improved. Compared with the traditional propulsion shafting, the shaftless rim propeller has the characteristics of small occupied space, less noise, low vibration, high efficiency and the like.
The permanent magnet vernier motor has the advantages of low-speed large torque output, less slot number, high stator core utilization rate at low speed and small torque pulsation, and can be combined with a rim propeller to form the permanent magnet vernier rim propulsion motor, so that the functions of low-speed large torque output and direct drive are realized, and the performance of a ship propulsion system is further improved.
However, the permanent magnet vernier motor belongs to a magnetic field modulation type motor, and because of the modulation behavior, the air gap magnetic field is complex, various higher harmonics are modulated by the fundamental wave component with larger amplitude, and the parameters of the permanent magnet vernier motor are more and the coupling degree is more serious. The traditional univariate optimization method has small calculated amount and solves the speed block, but the optimizing result obtained aiming at a single parameter can not reflect the overall optimization. The conventional multi-objective optimization method mostly adopts a response surface and multi-objective optimization algorithm, so that the calculation accuracy is high, the calculation amount is large, the solving time is long, and once the optimization parameters are more than three, the calculation difficulty is exponentially increased. At present, the multi-objective optimization method still has the problems of long time consumption in the optimization process, low optimization efficiency, non-ideal optimization effect and the like. Therefore, how to quickly and accurately find out the optimal structural parameters of the motor is also a problem to be solved.
Disclosure of Invention
According to the problems existing in the prior art, the application discloses a multi-objective optimization method suitable for a multi-parameter coupling permanent magnet vernier rim propulsion motor, and the optimization purpose of maximizing average torque and minimizing torque pulsation is realized by carrying out multi-objective optimization on the permanent magnet vernier rim propulsion motor.
In order to achieve the above purpose, the application adopts the following technical scheme:
s1, building a two-dimensional finite element model on Maxwelll software, setting material characteristics of a stator, a rotor and a permanent magnet of a motor, selecting winding arrangement of fractional concentrated winding teeth winding, and applying zero current excitation to perform no-load experiments. The method mainly refers to no-load back electromotive force and waveform distortion rate of a motor in the early design stage, and proper slot pole matching, stator and rotor dimensions are selected;
s2, after the early design is determined, applying proper current excitation to carry out a load experiment according to the target rated power of the designed motor, mainly taking the average torque and torque pulsation of the permanent magnet vernier rim propulsion motor as optimization targets, and analyzing and screening structural parameters which can obviously influence the average torque and torque pulsation by combining a parameterized modeling method;
s3, determining a value range of related structural parameters affecting the average torque and torque pulsation on the basis of preliminarily completing motor design simulation, and reducing the follow-up optimization workload. The selection standard of the value range is as follows: changing a certain structural parameter on the premise of keeping other structural parameters unchanged by taking the maximum average torque and the minimum torque pulsation which can be achieved in the step S2 as standards, wherein the response is higher than the maximum average torque by 0.9 or the torque pulsation is not more than 1.1 of the minimum torque pulsation;
s4, taking the logic before and after design into consideration, carrying the structural parameters determined in the step S3 back to electricity; and (5) in an idle model. If the value range determined in the step S3 is in the value range, the value space of the segment which is required to be removed and is used for obviously reducing the empty counter electromotive force or obviously increasing the waveform distortion rate exists, so that the subsequent optimization range is further reduced;
s5, constructing a sample library through Latin hypercube test design, and simultaneously referring to the distribution of sample library data, supplementing a certain number of samples in a sample sparse range by adopting an optimized Latin hypercube method, ensuring that sample points are distributed in a value space as uniformly as possible, and conveniently constructing a smoother response surface;
s6: and (3) reducing the high-dimensional multi-objective optimization problem into a plurality of two-dimensional multi-objective optimization problems for the motor structural parameters by pairwise permutation and combination, and respectively establishing a Kriging response surface model. According to the parameter sensitivity analysis, sensitivity sequencing and layering processing are carried out on the motor structure parameters;
s7: based on a multi-objective whale optimization algorithm, carrying out multi-objective optimization on structural parameters with strong sensitivity, searching a global optimal solution, and then adjusting by using structural parameters with weak sensitivity to finish optimization.
Further, the step S1 affects the no-load back electromotive force and waveform distortion rate of the motor, and is mainly the selection of slot pole schemes. The permanent magnet vernier rim propulsion motor operates based on a magnetic field modulation principle, the stator modulation pole number Zs, the permanent magnet pole pair number Pr and the armature winding pole pair number Pw meet the following relation:
Z s ＝P r +P w
the structural parameter packet block affecting the average torque and torque ripple of the motor in the step S2: permanent magnet thickness h g Polar arc coefficient alpha, modulation tooth width f h Modulating tooth height h, isolating tooth width f s Modular air gap thickness h g 。
In the step S3, the thickness h of the permanent magnet is respectively equal to g Polar arc coefficient alpha, modulation tooth width f h Modulating tooth height h, isolating tooth width f s Modular air gap thickness h g Single parameter simulation is carried out, and each structural parameter is given out according to the average torque and the torque pulsation performance of the motor and combining with the design targetA range of numbers.
And S4, the parameters are reversely brought back to the no-load model, and partial unsuitable parameters can be eliminated according to no-load back electromotive force and waveform distortion rate, so that the optimization selection range is further reduced.
In the step S5, sample points are set in each structural parameter optimization range through latin hypercube experiments, and the principle is a hierarchical sampling, namely, sampling is approximately completed from multivariate parameter distribution, and the principle mathematical formula is expressed as follows:
the formula describes the extraction of n sample points from q design variables, where a ik Is matrix a= (a) ik ) Is a matrix of n x q, a ik The value of the kth variable representing the ith sample point, each column in matrix A representing a random arrangement of 1 to n, sharing n ≡! An arrangement mode. U is also a matrix of n x q, U ik Obeying a uniform distribution of 0-1.
However, the general latin hypercube sampling has the phenomenon of uneven local distribution, and certain sample points need to be added in the sparse space of the sample points in order to make the sample points discrete and full of the whole space as much as possible. Latin hypercube sampling optimized based on maximum and minimum methods can ensure that complementary sample points can be discrete to fill sparse value space, and the principle formula is as follows:
D i ＝min(d i1 ,d i2 ...d in )
d in ij Represents the distance, D, between sample point i and sample point j i The characteristic value of the sample point i is recorded and represents the minimum distance from other sample points. Through repeated iterative inspection, the supplementary sample points can be ensured to fill the sparse value space only by ensuring that the characteristic value of each sample point is as large as possible.
In the step S6, the kriging model predicts a random process by using a covariance function, so that unbiased estimation can be achieved, the kriging model estimates a predicted point through a known sample point, and the relationship between the sample point and the predicted point is as follows:
wherein is Z * (x) Prediction point, Z (x) i ) For known sample points, N is the number of sample points, lambda i Is the association coefficient. The value of the unknown predicted point and the associated coefficients can be expressed as:
wherein θ is p To characterize the covariance coefficient of Gao Sixie variance function influence, the optimum θ p Typically obtained by maximum likelihood estimation.
In the step S6, according to the sensitivity analysis result in Optislang, the six structural parameters in S2 are ranked in sensitivity, and are divided into a high sensitivity parameter and a low sensitivity parameter.
In the step S7, according to the order of strong first and weak second, based on the multi-objective whale optimization algorithm, multi-objective optimization is performed on the structural parameters with strong sensitivity, a global optimal solution is found, and then the structural parameters with weak sensitivity are used for adjustment, so that optimization is completed. The multi-objective whale optimization algorithm simulates the behavior of the natural white whale and comprises the following steps: swimming (search), foraging (optimizing) and whale falling (screening).
The specific flow of the multi-target whale optimization algorithm is as follows: firstly, initializing the number n of white whale populations, the current iteration time T=1 and the maximum iteration time T max And randomly generating the initial position of the population and calculating the population fitness according to the objective function. According to balance factor B of each whale f Determining that the swimming or foraging state is carried out, wherein the balance factor is calculated according to the following formula, wherein B 0 Is a random number between (0, 1):
B f ＝B 0 (1-T/2T max )
when B is f When more than 0.5, whale is in a swimming stage, the global searching capability of an algorithm is ensured by continuously updating the position information of whale individuals, and a mathematical model of the position update of the whale in the swimming process is as follows:
d represents the dimension of the variable and,representing the new position of the i (i=1, 2 … n) th whale in the j (j=1, 2..d) dimension,/-for>And->Respectively represent the current position, p, of the ith whale and the r whale j Is a random number of 1 to d, r is a random number of 1 to n, r 1 And r 2 Are random numbers between (0, 1) for increasing the randomness of the global search, the selection of the parity dimension reflecting the synchronisation behaviour between the beluga when swimming.
When B is f When less than or equal to 0.5, whales are in a foraging stage, the white whales are used for hunting cooperatively by sharing position information, and meanwhile, a flight function is introduced to enhance convergence, and a position updating mathematical model is as follows:
and->Respectively representing the current position of the ith and r whales,/->Representing the new position of the ith whale, < ->Representing the optimal hunting position, r, in a white whale population 3 And r 4 Is a random number between (0, 1), C 1 ＝2r 4 (1-T/T max ) Flight function L F The calculation formula is as follows:
u, v are random numbers satisfying normal distribution, Γ (x) is a gamma function. Regardless of whether whale is in swimming or foraging, the population fitness is recalculated and ranked when a location update occurs.
Because swimming and foraging processes may be accompanied by dangers, the population whale needs to be updated every time the position changes, the simulated white whales are naturally competitive and screened out under various threat factors, the natural adaptation force of the white whale population is improved, and the process position updating mathematical model is as follows:
X step ＝(a-b)exp(-C 2 T/T max )
C 2 ＝2W f ×n
W f ＝0.1-0.05T/T max
r 5 、r 6 、r 7 is a random number between (0, 1), X step Is of short length and C 2 Represents step factor, W f Is whale probability, and the upper and lower bounds of variables are from a and b. Every time whale data is updated, the iteration number is increased by one, the population fitness is recalculated, and the current optimal solution is found out. Repeating the iteration according to the steps until the current iteration timesAnd if the number of the iterations is larger than the maximum number of iterations, terminating the loop, and obtaining the current position as the optimal solution.
In general, the above technical solutions conceived by the present application, compared with the prior art, enable the following beneficial effects to be obtained:
two working conditions of motor operation, namely no-load and load, are fully considered, and targeted optimization design is carried out. Meanwhile, after the tape loading design is completed, tape parameters are returned, so that the compatibility of the front and rear designs can be ensured, an unreasonable value range can be eliminated, the workload is reduced for subsequent optimization, and calculation is not performed by virtue of finite element software and equipment.
On the basis of determining sample points by sampling the ordinary Latin Ding Chao cube, the method combines Latin hypercube based on the maximum and minimum method to perform point filling operation, so that sample points are distributed more uniformly, a response surface is constructed more smoothly, and the accuracy of a motor equivalent model is improved.
The conventional multi-objective solving method is used for processing structural optimization with more than three parameters, and has the advantages of huge calculated amount and long solving speed. And the parameters are arranged and combined pairwise to construct a response surface, and the response surface is sequenced according to the sensitivity analysis result, and is optimized step by step according to the sequence of strong first and weak second, so that the influence of each structural parameter is fully considered, and the optimization accuracy is ensured. Meanwhile, the higher-order multi-objective solution is degraded intoThe number of second-order multi-objective solutions greatly reduces the operand and shortens the solving time.
The multi-objective whale optimization algorithm is simple to operate and easy to implement, does not depend on a large amount of computing resources, can solve large-scale complex problems, is suitable for searching a global optimal solution in a multi-dimensional space, and has an optimization effect independent of the selection of an initial population.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings may be obtained according to the drawings without inventive effort to those skilled in the art.
FIG. 1 is a schematic diagram of a permanent magnet fault-tolerant vernier rim propulsion motor according to the present application
FIG. 2 is a schematic diagram of an overall optimization flow provided by the present application
FIG. 3 is a graph showing the comparison of motor parameters before and after optimization according to the present application
FIG. 4 is a graph showing torque contrast before and after optimization according to the present application
FIG. 5 is a graph showing torque data before and after optimization according to the present application
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
In the drawings of the specific embodiments of the present application, in order to better and more clearly describe the working principle of each element in the system, the connection relationship of each part in the device is represented, but only the relative positional relationship between each element is clearly distinguished, and the limitations on the signal transmission direction, connection sequence and the structure size, dimension and shape of each part in the element or structure cannot be constructed.
A permanent magnet fault-tolerant vernier rim propulsion motor shown in figure 1 consists of a stator 1, a rotor 2 and a propeller blade 3. The stator comprises a stator core 4, a modulation tooth 5, a fault-tolerant tooth 6, 24 stator slots 7 and a single-layer concentrated winding 8; the rotor comprises a rotor core 9, core poles 10 in alternating poles, radially magnetized permanent magnet poles 11, tangentially magnetized permanent magnets 12 magnetized 45 degrees to the right and tangentially magnetized permanent magnets 13 magnetized 45 degrees to the left.
The stator core 4 is provided with 24 uniform winding grooves 7, and a single-layer concentrated winding 8 is embedded in the stator core; the rotor 2 is of a short-axis flat structure, the outer side of the rotor core is provided with iron core poles 10 and permanent magnet poles 11, 12 and 13 which are alternately arranged, and the equivalent is 26 pairs of pole permanent magnets. Wherein the permanent magnets adopt Halbach arrays, the middle permanent magnet 11 adopts radial magnetization, and the permanent magnets 12 and 13 on two sides adopt tangential 45-degree magnetization; the inner side of the rotor core 9 is directly welded with the non-magnetic propeller blade 3.
The flow chart of the multi-objective optimization design method suitable for the multi-parameter coupling permanent magnet vernier rim propulsion motor is shown in the attached figure 2, and the specific steps are as follows:
s1, building a two-dimensional finite element model on Maxwelll software, setting material characteristics of a stator, a rotor and a permanent magnet of a motor, selecting winding arrangement of fractional slot concentrated winding teeth winding, and applying zero current excitation to perform no-load experiments. According to the related theory of the magnetic field modulation motor, the influence on the no-load back electromotive force and the waveform distortion rate of the motor is mainly the selection of a slot pole scheme. The permanent magnet vernier rim propulsion motor operates based on a magnetic field modulation principle, the stator modulation pole number Zs, the permanent magnet pole pair number Pr and the armature winding pole pair number Pw meet the following relation:
Z s ＝P r +P w
on the basis, a theoretically proper slot pole matching scheme is selected, simulation verification is carried out by building a model, and proper slot pole matching and main sizes of stator and rotor are selected;
s2, after the early design is determined, applying proper current excitation to carry out a load experiment according to the target rated power of the designed motor, wherein the average torque and torque pulsation of the permanent magnet vernier rim propulsion motor are mainly used as optimization targets. Among a plurality of design parameters of the motor, a structural parameter which can obviously influence the average torque and torque pulsation of the motor is found out by combining a parameterized modeling method, and finally, the following six motor structural parameters are determined and optimized through multiple analysis and screening: permanent magnet thickness h g Polar arc coefficient alpha, modulation tooth width f h Modulating tooth height h, isolating tooth width f s Modular air gap thickness h g ；
S3, on the basis of preliminarily completing motor design simulation, the thickness of the permanent magnet is respectively calculatedh g Polar arc coefficient alpha, modulation tooth width f h Modulating tooth height h, isolating tooth width f s Modular air gap thickness h g And single-parameter simulation is carried out, and the value range of the structural parameters related to the average torque and the torque pulsation is determined according to the average torque and the torque pulsation performance of the motor, so that the subsequent optimization workload is reduced. The selection standard of the value range is as follows: changing a certain structural parameter on the premise of keeping other structural parameters unchanged by taking the maximum average torque and the minimum torque pulsation which can be achieved in the step S2 as standards, wherein the response is higher than the maximum average torque by 0.9 or the torque pulsation is not more than 1.1 of the minimum torque pulsation;
s4, taking the logic before and after design into consideration, carrying the structural parameters determined in the step S3 back to electricity; in the machine no-load model, partial unsuitable parameters are eliminated according to no-load back electromotive force and waveform distortion rate. If the value range determined in the step S3 is in the value range, the value space of the segment which is required to be removed and is used for obviously reducing the empty counter electromotive force or obviously increasing the waveform distortion rate exists, so that the subsequent optimization range is further reduced;
s5, constructing a sample library through Latin hypercube test design, simultaneously referring to the distribution of sample library data, supplementing a certain number of samples by adopting an optimized Latin hypercube method in a sparse range of the samples, ensuring that sample points are distributed in a value space as uniformly as possible, and conveniently constructing a smoother response surface. The Latin hypercube experiment sets sample points in the optimization range of each structural parameter, and the principle is a hierarchical sampling, namely, sampling is approximately completed from the distribution of multiple parameters. The principle mathematical formula is expressed as follows:
the formula describes the extraction of n sample points from q design variables, where a ik Is matrix a= (a) ik ) Is a matrix of n x q, a ik The value of the kth variable representing the ith sample point, each column in matrix A representing a random arrangement of 1 to n, sharing n ≡! An arrangement mode. U is also a matrix of n x q, U ik Obeying a uniform distribution of 0-1.
However, the general latin hypercube sampling has the phenomenon of uneven local distribution, and certain sample points need to be added in the sparse space of the sample points in order to make the sample points discrete and full of the whole space as much as possible. Latin hypercube sampling optimized based on maximum and minimum methods can ensure that complementary sample points can be discrete to fill sparse value space, and the principle formula is as follows:
D i ＝min(d i1 ,d i2 ...d in )
d in ij Represents the distance, D, between sample point i and sample point j i The characteristic value of the sample point i is recorded and represents the minimum distance from other sample points. Through repeated iterative inspection, the supplementary sample points can be ensured to fill a sparse value space only by ensuring that the characteristic value of each sample point is as large as possible;
s6, arranging and combining motor structural parameters in pairs, respectively establishing Kriging response surfaces, and carrying out sensitivity sequencing on six structural parameters in S2 according to sensitivity analysis results in Optislang. The Kerling model is used for predicting a random process by using a covariance function, unbiased estimation can be realized, the Kerling model estimates a predicted point through known sample points, and the relation between the sample points and the predicted point is as follows:
wherein is Z * (x) Prediction point, Z (x) i ) For known sample points, N is the number of sample points, lambda i Is the association coefficient. The value of the unknown predicted point and the associated coefficients can be expressed as:
wherein θ is p To characterize the covariance coefficient of Gao Sixie variance function influence, the optimum θ p Typically obtained by maximum likelihood estimation; and according to the sensitivity analysis result in the Optislang, the six structural parameters in the S2 are subjected to sensitivity sorting and are divided into high-sensitivity parameters and low-sensitivity parameters.
S7, performing multi-objective optimization on structural parameters with strong sensitivity based on a multi-objective whale optimization algorithm, searching a global optimal solution, and then adjusting by using structural parameters with weak sensitivity to complete optimization. Motor parameters were compared before and after optimization as shown in fig. 3. The multi-objective whale optimization algorithm simulates the behavior of the natural white whale and comprises the following steps: swimming (search), foraging (optimizing) and whale falling (screening).
The specific flow of the multi-target whale optimization algorithm is as follows: firstly, initializing the number n of white whale populations, the current iteration time T=1 and the maximum iteration time T max And randomly generating the initial position of the population and calculating the population fitness according to the objective function. According to balance factor B of each whale f Determining that the swimming or foraging state is carried out, wherein the balance factor is calculated according to the following formula, wherein B 0 Is a random number between (0, 1):
B f ＝B 0 (1-T/2T max )
when B is f When more than 0.5, whale is in a swimming stage, the global searching capability of an algorithm is ensured by continuously updating the position information of whale individuals, and a mathematical model of the position update of the whale in the swimming process is as follows:
d represents the dimension of the variable and,representing the new position of the i (i=1, 2 … n) th whale in the j (j=1, 2..d) dimension,/-for>And->Respectively represent the current position, p, of the ith whale and the r whale j Is a random number of 1 to d, r is a random number of 1 to n, r 1 And r 2 Are random numbers between (0, 1) for increasing the randomness of the global search, the selection of the parity dimension reflecting the synchronisation behaviour between the beluga when swimming.
When B is f When less than or equal to 0.5, whales are in a foraging stage, the white whales are used for hunting cooperatively by sharing position information, and meanwhile, a flight function is introduced to enhance convergence, and a position updating mathematical model is as follows:
and->Respectively representing the current position of the ith and r whales,/->Representing the new position of the ith whale, < ->Representing the optimal hunting position, r, in a white whale population 3 And r 4 Is a random number between (0, 1), C 1 ＝2r 4 (1-T/T max ) Flight function L F The calculation formula is as follows:
u, v are random numbers satisfying normal distribution, Γ (x) is a gamma function. Regardless of whether whale is in swimming or foraging, the population fitness is recalculated and ranked when a location update occurs.
Because swimming and foraging processes may be accompanied by dangers, the population whale needs to be updated every time the position changes, the simulated white whales are naturally competitive and screened out under various threat factors, the natural adaptation force of the white whale population is improved, and the process position updating mathematical model is as follows:
X step ＝(a-b)exp(-C 2 T/T max )
C 2 ＝2W f ×n
W f ＝0.1-0.05T/T max
r 5 、r 6 、r 7 is a random number between (0, 1), X step Is of short length and C 2 Represents step factor, W f Is whale probability, and the upper and lower bounds of variables are from a and b. Every time whale data is updated, the iteration number is increased by one, the population fitness is recalculated, and the current optimal solution is found out. And repeating iteration according to the steps until the current iteration times are greater than the maximum iteration times, terminating the loop, and obtaining the optimal solution at the current position. Before and after optimization, motor torque waveform pairs such as shown in fig. 4, and specific value pairs of average torque and torque ripple such as shown in fig. 5.
In the above embodiments, it may be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. The computer may be a general purpose computer, a special purpose computer, a computer network, or other programmable apparatus. The computer instructions may be stored in or transmitted across a computer-readable storage medium. The computer readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that contains an integration of one or more available media. The usable medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a magnetic tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a Solid State Disk (SSD)), or the like.
While the application has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the application. Therefore, the protection scope of the application is subject to the protection scope of the claims.
Claims (9)
1. A multi-objective optimization method suitable for a multi-parameter coupling permanent magnet vernier rim propulsion motor is characterized in that: the method comprises the following steps:
s1: based on the no-load back electromotive force and waveform distortion rate of the motor, optimally designing the permanent magnet vernier rim propulsion motor under no-load working conditions, and establishing a no-load motor model;
s2: taking the average torque and torque pulsation of the permanent magnet vernier rim propulsion motor when in load as optimization targets, and analyzing and screening motor structural parameters which can obviously influence the average torque and torque pulsation by combining a parameterized modeling method;
s3: on the basis of completing the design of no-load working conditions, determining a value range of related structural parameters affecting the average torque and torque pulsation;
s4: returning the value range of the structural parameter to the no-load model of the motor, and checking whether the value range meets the design requirement under the no-load working condition of the motor;
s5: constructing a sample library by adopting a Lat Ding Chao cube test, and supplementing certain sample data by adopting an optimized Latin hypercube method in a sampling range of sparse samples by referring to the distribution condition of the sample library data;
s6: the method comprises the steps of arranging and combining motor structural parameters pairwise, reducing a high-dimensional multi-objective optimization problem into a plurality of two-dimensional multi-objective optimization problems, respectively establishing a Kriging model, and carrying out sensitivity sequencing and layering treatment on the motor structural parameters according to a parameter sensitivity analysis mode;
s7: and carrying out multi-objective optimization on the structural parameters with strong sensitivity based on a multi-objective whale optimization algorithm, searching a global optimal solution, and adopting the structural parameters with weak sensitivity to adjust so as to complete the optimization.
2. The multi-objective optimization method applicable to the multi-parameter coupling permanent magnet vernier rim propulsion motor according to claim 1, wherein the method comprises the following steps: the permanent magnet vernier rim propulsion motor operates based on a magnetic field modulation principle, wherein the stator modulation pole number Zs, the permanent magnet pole pair number Pr and the armature winding pole pair number Pw meet the following relation:
Z s ＝P r +P w 。
3. the multi-objective optimization method applicable to the multi-parameter coupling permanent magnet vernier rim propulsion motor according to claim 1, wherein the method comprises the following steps: structural parameters affecting the average torque and torque ripple of the motor include: permanent magnet thickness h g Polar arc coefficient alpha, modulation tooth width f h Modulating tooth height h, isolating tooth width f s And modular air gap thickness h g 。
4. A multi-objective optimization method for a multi-parameter coupled permanent magnet vernier rim propulsion motor as defined in claim 3, wherein: respectively to the thickness h of the permanent magnet g Polar arc coefficient alpha, modulation tooth width f h Modulating tooth height h, isolating tooth width f s Modular air gap thickness h g And (3) carrying out single-parameter simulation, and outputting each structural parameter range according to the average torque and torque pulsation performance of the motor and the design target.
5. The multi-objective optimization method applicable to the multi-parameter coupling permanent magnet vernier rim propulsion motor according to claim 1, wherein the method comprises the following steps: and when the structural parameter value range is returned to the motor no-load model, removing partial unsuitable parameters according to no-load back electromotive force and waveform distortion rate so as to reduce the optimization selection range.
6. The multi-objective optimization method applicable to the multi-parameter coupling permanent magnet vernier rim propulsion motor according to claim 1, wherein the method comprises the following steps: sample points are set in the optimization range of each structural parameter through Latin hypercube experiment, sampling is approximately completed from the multielement parameter distribution, and a specific formula is expressed as follows:
the formula is to extract n sample points from q design variables, where a ik Is matrix a= (a) ik ) Is a matrix of n x q, a ik The value of the kth variable representing the ith sample point, each column in matrix A represents a random arrangement of 1 to n, sharing n ≡! The arrangement of the species, U is a matrix of n x q, U ik Obeying a uniform distribution of 0-1;
adding a certain sample point in the sparse space of the sample point, optimizing Latin hypercube sampling based on a maximum and minimum method, and ensuring that the supplemented sample point is discrete to fill the sparse value space, wherein the principle formula is as follows:
and i not equal to j
D i ＝min(d i1 ,d i2 ...d in )
D in ij Represents the distance, D, between sample point i and sample point j i And (3) marking the characteristic value of the sample point i, representing the minimum distance between the characteristic value and other sample points, and ensuring that the supplemented sample point can fill a sparse value space through repeated iterative inspection.
7. The multi-objective optimization method applicable to the multi-parameter coupling permanent magnet vernier rim propulsion motor according to claim 1, wherein the method comprises the following steps: the Kerling model is used for carrying out random process prediction by utilizing a covariance function to realize unbiased estimation, the Kerling model estimates a predicted point through known sample points, and the relation between the sample points and the predicted point is as follows:
wherein is Z * (x) Prediction point, Z (x) i ) For known sample points, N is the number of sample points, lambda i As the correlation coefficient, the value of the unknown predicted point and the correlation coefficient can be expressed as:
wherein θ is p To characterize the covariance coefficient of Gao Sixie variance function influence, the optimum θ p Obtained by maximum likelihood estimation.
8. The multi-objective optimization method applicable to the multi-parameter coupling permanent magnet vernier rim propulsion motor according to claim 1, wherein the method comprises the following steps: and carrying out sensitivity sequencing on the six structural parameters according to the sensitivity analysis result in the Optislang, and dividing the six structural parameters into high sensitivity parameters and low sensitivity parameters.
9. The multi-objective optimization method applicable to the multi-parameter coupling permanent magnet vernier rim propulsion motor according to claim 1, wherein the method comprises the following steps:
the multi-objective whale optimization algorithm specifically comprises the following steps: firstly, initializing the number n of white whale populations, the current iteration time T=1 and the maximum iteration time T max Randomly generating initial positions of the population, calculating population fitness according to an objective function, and calculating balance factor B of each whale f Determining that the swimming or foraging state is carried out, wherein the balance factor is calculated according to the following formula, wherein B 0 Is a random number between (0, 1):
B f ＝B 0 (1-T/2T max )
when B is f At > 0.5, whale is in swimming stage by continuouslyUpdating the position information of whale individuals to ensure the global searching capability of an algorithm, wherein a mathematical model for updating the position of the whales in the swimming process is as follows:
d represents the dimension of the variable and,representing the new position of the i (i=1, 2 … n) th whale in the j (j=1, 2..d) dimension,/-for>And->Respectively represent the current position, p, of the ith whale and the r whale j Is a random number of 1 to d, r is a random number of 1 to n, r 1 And r 2 Are random numbers between (0, 1) for increasing the randomness of the global search, and the selection of the parity dimension reflects the synchronous behavior of the white whales during swimming;
when B is f When less than or equal to 0.5, whales are in a foraging stage, the white whales are used for hunting cooperatively by sharing position information, and meanwhile, a flight function is introduced to enhance convergence, and a position updating mathematical model is as follows:
and->Respectively representing the current position of the ith and r whales,/->Representing the new position of the ith whale, < ->Representing the optimal hunting position, r, in a white whale population 3 And r 4 Is a random number between (0, 1), C 1 ＝2r 4 (1-T/T max ) Flight function L F The calculation formula is as follows:
u and v are random numbers meeting normal distribution, Γ (x) is a gamma function, whales are in a swimming state or a foraging state, and when position updating occurs, population fitness is recalculated and ordered;
because swimming and foraging processes may be accompanied by dangers, the population whale needs to be updated every time the position changes, the simulated white whales are naturally competitive and screened out under various threat factors, the natural adaptation force of the white whale population is improved, and the process position updating mathematical model is as follows:
X step ＝(a-b)exp(-C 2 T/T max )
C 2 ＝2W f ×n
W f ＝0.1-0.05T/T max
r 5 、r 6 、r 7 is a random number between (0, 1), X step Is of short length and C 2 Represents step factor, W f Is whale probability, a and b are upper and lower bounds of variables, each time whale data is updated, iteration times are increased by one, population fitness is recalculated and ordered, a current optimal solution is found,and repeating iteration according to the steps until the current iteration times are greater than the maximum iteration times, terminating the loop, and obtaining the optimal position solution at the current position.
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