CN107330174B - Wheel hub motor optimization method based on genetic annealing algorithm - Google Patents
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Abstract
The invention discloses a hub motor optimization method based on a genetic annealing algorithm, which comprises the following steps of obtaining an optimization target and constraint conditions of a hub motor; carrying out inverse solution on the hub motor by adopting a genetic annealing algorithm, and solving to obtain a hub motor design variable parameter value; and generating stable and continuous torque of the hub motor according to the acquired variable parameter values. The genetic annealing algorithm is improved on the basis of the genetic algorithm, and the genetic algorithm and the simulated annealing algorithm are organically combined together, so that the efficiency of the algorithm is improved, the global control capability of the algorithm can be enhanced, and the genetic annealing algorithm has high accuracy, high convergence speed and high efficiency. The method is feasible when being applied to the optimized design of the hub motor of the electric vehicle, and has wide engineering application value.
Description
Technical Field
The invention belongs to the field of lightweight design of hub motor driven electric wheels, and particularly relates to a hub motor design optimization method.
Background
In recent years, with the support and attention of the aspects, new energy vehicles, especially pure electric vehicles, are rapidly developed, and electric vehicles will be important transportation means for people in the future. The hub motor is one of the most central components of the electric automobile, and has the greatest characteristic that devices such as driving, transmission and braking are integrated into a hub, and traditional transmission components such as a clutch, a transmission shaft, a differential mechanism and a transfer case are omitted. The development of the wheel hub motor technology will bring a revolution of the driving mode of the vehicle.
As a new energy automobile, the hub motor driven electric automobile is always the focus of research of scholars at home and abroad. There has been a significant problem in the research of in-wheel motor systems: the integration of the motor and the wheel leads to larger unsprung mass, the reduction of the isolation vibration performance and the influence on the smoothness and the safety of the vehicle under the driving condition, and the increase of the unsprung mass of the hub motor driven electric vehicle is one of the main reasons for the deterioration of the smoothness. Analysis shows that the total mass of the hub motor is reduced, and the smoothness of the vehicle can be effectively improved. Therefore, it is highly necessary to design the hub motor drive system to be lightweight.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide an optimal design method of a hub motor based on a genetic annealing algorithm.
The idea for solving the technical problems is as follows: obtaining an optimized target and constraint conditions of the hub motor; carrying out inverse solution on the hub motor by adopting a genetic annealing algorithm to obtain a design variable parameter value of the hub motor; and finding a group of values according to the obtained plurality of groups of variable parameter values to enable the performance index and the economic and technical index of the hub motor to meet the optimal condition, wherein the group of variable parameter values is the optimal solution.
The details are as follows:
a hub motor optimization method based on a genetic annealing algorithm comprises the following steps:
(1) determining variable parameters of the hub motor, including the outer diameter of the stator, the inner diameter of the stator, the length of an iron core, the length of an air gap, the thickness of a permanent magnet, the number of conductors in each slot, the diameter of a lead and the slot filling rate;
(2) determining the target and constraint conditions of the hub motor to be optimized: the optimized objective function of the hub motor is that the motor efficiency is highest on the basis of certain mass and material cost of effective materials used by the motor; the constraint conditions are restrictive constraint functions applied according to specific use environments and conditions of the in-wheel motor, all or part of variable parameters are contained in a mathematical expression of the constraint functions, and the constraint conditions of the in-wheel motor optimization design are respectively starting current g of the in-wheel motor1(X), starting Torque g2(X), air gap magnetic induction g3(X) rated speed g4(X) thermal load g5(X) stator teeth magnetic density g6(X) stator yoke magnetic density g7(X) rotor yoke magnetic density g8(X)；
(3) Generating an initial population P of a genetic simulated annealing algorithm according to variable parameters of a hub motor0(t) setting a genetic modelA fitness function of a pseudo-annealing algorithm;
(4) calculating the probability of each individual in the population to be selected, and randomly selecting the initial population according to the calculated probability of being selected;
(5) performing crossing and mutation operations on the randomly selected population to obtain a population P1(t)；
(6) Judging whether a preset stopping criterion is met, namely whether the maximum genetic iteration number and the annealing termination temperature are reached, if so, ending the genetic algorithm and outputting the optimal individual as the optimal design parameter matrix of the hub motor, otherwise, updating the individual in the population;
(7) updating iteration parameters and simulating genetic annealing algorithm temperature TtAnd (4) after the descent, the genetic algebra K is increased and the population array is updated, returning to the step (4) for iteration until the hub motor meets the target function of the hub motor according to the obtained variable parameter values.
Further, in step (3), the initial population P0(t) is comprised of initial individuals of the formula:
X＝[x0，x1，，Λ，xi，Λ，xn-1]T
in the formula, n represents the number of design variables of the hub motor, X represents a vector of a solution space, and elements in X are composed of variable parameters.
Further, in step (3), the fitness function is:
min F(X，γ)＝f(X)+P(X，γ) (1)
wherein f (X) is a predetermined objective function, P (X, gamma) is a penalty function, and is related to the constraint condition gi(X) a function of interest;
wherein the predetermined objective function is
In the formula, alphaiIs a weight coefficient, fi(x) Is a single objective function, and N is the number of the objective functions;
wherein the constraint function giThe expression (X) is:
in the formula IstFor optimized starting current, Ist0Is the starting current before optimization; t isstFor optimized starting torque, Tst0The starting torque before optimization; b isFor optimized air gap magnetic induction, B0The air gap magnetic induction intensity before optimization; n is a radical ofFor the optimized rated rotating speed, N0The rated rotating speed before optimization; h is the optimized thermal load, H0To optimize the thermal load before; b istFor optimized stator tooth magnetic density, Bt0The magnetic density of the stator tooth part before optimization; b isjFor optimized stator yoke magnetic density, Bj0The magnetic density of the stator yoke part before optimization; b isiFor optimized rotor yoke magnetic density, Bi0The magnetic density of the yoke part of the rotor before optimization;
the expression of the penalty function P (X, γ) is:
in the formula, gamma is a penalty factor; h isu(x) Is the equation part in the u-th constraint function; q. q.su(x) Is the inequality part in the u constraint function; u denotes the order of the constraint function, u ═ 1, 2, Λ M; m is the number of constraint functions.
Further, in step (4), the probability of being selected for each individual in the population is obtained by:
wherein f isminRepresents the minimum value of the fitness function values of the individuals in the population, f (i) represents the fitness function value of the ith individual, pi(Tt) Representing the current temperature T during the updating of the iteration parametertThe probability that the individual is selected is then determined.
Further, the step (5) comprises the following steps:
s51, selecting individuals in the population by adopting a proportion selection operator according to the cross rate and the variation rate;
s52, performing cross operation on the selected population;
and S53, performing mutation operation on the crossed population.
Wherein, the step S51 is divided into the following steps,
s511, according to the crossing rate PcAnd the rate of variation PvSearching in the population, calculating the adaptive value of each individual, and sequencing according to the sequence from large to small, wherein the cross rate PcAnd the rate of variation PvComprises the following steps:
in the formula, Pc1Representing a preset crossing rate, and taking a value in a (0, 1) interval; pv1Representing the preset variation rate, and taking the value of the (0, 1) interval; f. ofminRepresenting the minimum fitness of the individuals in the population; f. ofavgRepresenting the average fitness of individuals in the population; f' represents the relatively smaller individual fitness of two individuals which are mutually crossed;
s512, calculating the proportion P of the fitness value of each individual to the total fitness value according to the following formulak(Xi) Then, a roulette wheel is composed:
in the above formula, f (X)i) Representing the fitness value of the ith individual;
s513, randomly generating a random number between 0 and 1, and selecting a corresponding individual according to the group point of the random number on the roulette plate;
and S514, repeatedly executing the step S513 until the selected individual reaches the maximum value of the population capacity.
In step S52, the method includes the following steps,
s521, regarding the population P1(t) each individual XiCalculating the fitness function value f (X)i) Press f (X)i) Rearranging P from small to large1(t) and adding P1(t) in f (X)i) The smallest individual as the globally optimal individual XeStoring;
s522, fitness of an individual can be expressed as a function of its position i in the population, written as: (i +1)/(n +1), wherein i represents the position of the individual in the population i e [0, Λ, n-1]From the population P1(t) selecting r.n individuals according to the probability Random (0, 1) < f (i); r is the crossover rate and n is the population size, X for each individualiPerforming intersection according to the following formula;
in the above formula, Random (0, 1) represents a Random number between 0 and 1.
In step S53, specifically, the method includes:
slave population P1(t) m.n individuals are selected according to the probability Random (0, 1) > f (i), and X is taken as each cross-operated individuali' performing variation according to a variation function;
X″i＝X′i+(f(α)Scale-X′i)Rand(0，1)+fn(i)+ft(Tt) (10)
wherein Scale represents the radius of the variable parameter definition domain; xi' denotes individuals after crossover operation, Xi"represents an individual after mutation operation, Random (0, 1) represents a Random number between 0 and 1, and ft(Tt) Representing individual AdaptationThe relation function of the degree and the current temperature, wherein f (alpha) is a coefficient function;
fn(i) a function representing the fitness of an individual as a function of the position of the individual in the population, wherein i represents the position of the current individual:
fn(i)＝2πRand(0，1)f(α)f(i) (11)
wherein f (i) represents the individual fitness;
ft(Tt) And (3) representing the relation function of the individual fitness and the current temperature:
ft(Tt)＝2πRand(0，1)f(α)(Tstart-Tt)/Tstart (12)
in the above formula, TtIs the current temperature; t isstartF (alpha) is a coefficient function for the annealing initiation temperature;
wherein the coefficient function f (α) is:
Further, the step of determining whether the preset stop criterion is met in the step S6 specifically includes:
judging whether the maximum genetic algebra and the annealing termination temperature are reached or whether the following conditions are met:
f(X″i) > 500 or Tt＜Tend (13)
Wherein, f (X ″)i) Denotes the fitness value of the ith individual, X' denotes the new solution vector after the mutation operation, TendIndicating the annealing end temperature.
In addition to this, the present invention is,
s11, setting the initial temperature and the temperature reduction factor of the genetic annealing algorithm according to the optimized objective function of the hub motor, and setting the annealing operation function as follows:
Tt+1＝kTt (14)
in the formula: t istIndicating the current temperature, Tt+1Indicating quitThe temperature after warm operation, k, represents a temperature drop factor, the value of which is slightly less than 1.0.
S12, the number of iterations may be set to different values according to the size and structure of the hub motor, where the number of iterations is 500.
The invention has the beneficial effects that: the invention discloses a hub motor optimization design method based on a genetic annealing algorithm, which comprises the following steps: obtaining an optimized target and constraint conditions of the hub motor; carrying out inverse solution on the hub motor by adopting a genetic annealing algorithm, and solving to obtain a design variable parameter value of the hub motor; the hub motor generates stable and continuous torque according to the acquired variable parameter values. The single genetic algorithm is easy to generate premature phenomenon, poor local optimization capability and low operation efficiency, so that certain improvement on the genetic algorithm is needed. Therefore, the method carries out inverse solution on the hub motor through the genetic annealing algorithm, compensates the precision problem of the simulated annealing algorithm by using the search strategy of the genetic algorithm, and avoids the dilemma that the genetic algorithm is trapped in local optimum by using the global search capability of the simulated annealing algorithm. The genetic annealing algorithm organically combines the advantages of the two algorithms, so that the efficiency of the algorithm can be improved, and the global control capability of the algorithm can be enhanced. The optimization method of the hub motor executed based on the algorithm has the advantages of high accuracy, high convergence speed and high efficiency.
Drawings
The invention is further illustrated by the following figures and examples.
FIG. 1 is a flow chart of the hub motor optimization design method based on the genetic annealing algorithm.
Detailed Description
Firstly, obtaining an optimized target and constraint conditions of a hub motor; and then, encoding, selecting, crossing and mutating the variable parameters of the hub motor by adopting a genetic annealing algorithm to obtain the optimal values of the variable parameters, so that the performance indexes and the economic and technical indexes of the hub motor are optimized.
Referring to fig. 1, the invention provides a method for optimally designing a hub motor based on a genetic annealing algorithm, which comprises the following steps:
s1, setting initial temperature, temperature reduction factor, termination temperature and iteration number of the initialized genetic annealing algorithm;
s2, obtaining an optimized target and constraint conditions of the hub motor;
s3, encoding the variable parameters to generate an initial population P of the genetic annealing algorithm0(t)；
S4, calculating the probability of each individual in the population to be selected, and randomly selecting the population according to the calculated probability of being selected;
s5, performing crossing and mutation operations on the randomly selected population to obtain a population P1(t)；
S6, judging whether a preset stop criterion is met, namely judging whether a set maximum genetic algebra and an annealing termination temperature are reached, if so, ending the genetic algorithm and outputting an optimal individual as an optimal design parameter matrix of the hub motor, otherwise, updating the individuals in the population;
s7, updating iteration parameters and simulating the genetic annealing algorithm temperature TtAnd after the descent, the genetic algebra K is increased and the population array is updated, returning to the step S4 for iteration.
Further preferably, the step S1 includes:
s11, setting the initial temperature and the temperature reduction factor of the genetic annealing algorithm according to the optimized objective function of the hub motor, and setting the annealing operation function as follows:
Tt+1＝kTt (1)
in the formula: t istIndicating the current temperature, Tt+1The temperature after the annealing operation is shown, and k represents a temperature reduction factor, and the value of the temperature reduction factor is slightly less than 1.0.
And S12, setting the iteration times to be different values according to the size and the structure of the hub motor, wherein the iteration times are 500.
In connection with the problem to be solved by the present invention, in step S1, the settings of the initial temperature, the temperature drop factor, the termination temperature, and the number of iterations of the genetic annealing algorithm are initialized. The initial temperature represents the temperature of the variable parameter of the hub motor in an initial state; the temperature drop factor represents a temperature drop coefficient selected for simple calculation in the optimization process; the termination temperature represents a temperature set under the condition that the variable parameters of the hub motor meet the optimization objective function as much as possible; the iteration number represents a parameter set under the condition that the variable parameter of the hub motor meets the optimization objective function as much as possible.
Step S2, determining the target and constraint conditions to be optimized for the in-wheel motor: the objective function of the hub motor is: on the basis of certain quality and certain cost of effective materials (including permanent magnets, copper wires and silicon steel sheets), the motor efficiency is maximized; the constraint condition is a restrictive condition applied according to various specific problems, all or part of variable parameters are contained in a mathematical expression, and the constraint condition of the hub motor optimization design comprises g related to the starting current of the hub motor1(X), starting Torque-dependent g2(X), g related to air gap magnetic induction3(X), g in relation to the rated speed4(X) g relating to thermal load5(X) g relating to magnetic density of stator teeth6(X) g relating to flux density of stator yoke7(X) g relating to the magnetic density of the rotor yoke8(X)。
Step S3, generating an initial population of the genetic simulated annealing algorithm according to variable parameters of the in-wheel motor, where the variable parameters include stator outer diameter, stator inner diameter, core length, air gap length, permanent magnet thickness, number of conductors per slot, wire diameter, and slot fill factor, and the initial population is composed of initial individuals of the following formula:
X＝[Dout，Din，Liron，Lgas，Mt，Ns，Dc，Sf]T (2)
in the above formula, X represents a vector of a solution space, DoutIs the outer diameter of the stator, DinIs the stator inner diameter, LironIs the length of the core, LgasIs the length of the air gap, MtIs the thickness of the permanent magnet, NsNumber of conductors per slot, DcIs the diameter of the wire, SfIs the slot fill ratio.
Further preferably, the step S4 includes:
s41, setting a fitness function of the genetic simulated annealing algorithm;
s42, calculating the probability of being selected of each individual in the population according to the fitness function by adopting the following formula, and randomly selecting the population according to the calculated probability of being selected:
wherein f isminRepresents the minimum value of the fitness function values of the individuals in the population, f (i) represents the fitness function value of the ith individual, pi(Tt) Representing the current temperature T during the updating of the iteration parametertThe probability that the individual is selected is then determined.
Further preferably, the step S41 includes:
s411, setting a fitness function of the genetic annealing algorithm as follows:
min F(X，γ)＝f(X)+P(X，γ) (4)
where f (X) is a predetermined objective function, and P (X, γ) is a penalty function, which is a function of the constraint.
S412, presetting an objective function expression according to design requirements as follows:
in the above formula, αiIs a weight coefficient, fi(x) Is a single objective function, and N is the number of objective functions.
Wherein the constraint function expression is:
in the formula IstFor optimized starting current, Ist0Is the starting current before optimization; t isstFor optimized starting torque, Tst0The starting torque before optimization; b isFor optimized air gap magnetic induction, B0The air gap magnetic induction intensity before optimization; n is a radical ofFor the optimized rated rotating speed, N0The rated rotating speed before optimization; h is the optimized thermal load, H0To optimize the thermal load before; b istFor optimized stator tooth magnetic density, Bt0The magnetic density of the stator tooth part before optimization; b isjFor optimized stator yoke magnetic density, Bj0The magnetic density of the stator yoke part before optimization; b isiFor optimized rotor yoke magnetic density, Bi0The magnetic density of the rotor yoke part before optimization.
The expression of the penalty function is:
in the formula, gamma is a penalty factor; h isu(x) Is the equation part in the u-th constraint function; q. q.su(x) Is the inequality part in the u constraint function; u denotes the order of the constraint function, u ═ 1, 2, Λ M; m is the number of constraint functions.
Further preferably, the step S5 includes:
s51, selecting individuals in the population by adopting a proportion selection operator according to the set cross rate and the set variation rate;
s52, performing cross operation on the selected population;
and S53, performing mutation operation on the crossed population.
Actually performed in step S5 is a genetic manipulation which is a key part of the entire algorithm, and the genetic manipulation selects individuals of the previous generation, and the selected individuals generate individuals of the next generation by crossover and mutation. The process is full of randomness, but the ability to control the search direction is required in the global scope. The genetic manipulation includes three steps of selection, crossover and mutation, and corresponding steps S51-S53.
Further preferably, the step S51 includes:
s511, according to the crossing rate PcAnd the rate of variation PvSearching in the population, calculating the adaptive value of each individual, and sequencing according to the sequence from large to small, wherein the cross rate PcAnd the rate of variation PvComprises the following steps:
in the formula, Pc1Representing a preset crossing rate, and taking a value in a (0, 1) interval; pv1Representing the preset variation rate, and taking the value of the (0, 1) interval; f. ofminRepresenting the minimum fitness of the individuals in the population; f. ofavgRepresenting the average fitness of individuals in the population; f' represents the relatively small individual fitness among two individuals crossing each other.
Crossing rate PcIs an important parameter in the cross operation process, and influences the diversity of offspring and the search range of the algorithm. The main purpose of the crossover operation is to pass on the partial features of the optimal individual to the children so that the children can quickly reach the global optimal state. If the crossing rate PcIf the gain is too high, the good modes in the population are easy to damage, and the convergence of the algorithm is not facilitated; if the cross rate is too low, the diversity of individuals is reduced, the algorithm is trapped in local optimization, and the quality of the obtained solution is not high. Therefore, an appropriate crossover rate is selected.
S512, calculating the proportion P of the fitness value of each individual to the total fitness value according to the following formulak(Xi) Then, a roulette wheel is composed:
in the above formula, f (X)i) Representing the fitness value of the ith individual;
s513, randomly generating a random number between 0 and 1, and selecting a corresponding individual according to the group point of the random number on the roulette plate;
and S514, repeatedly executing the step S413 until the selected individuals reach the maximum value of the population capacity.
Further preferably, the step S52 includes:
s521, regarding the population P1(t) each individual XiCalculating the fitness function value f (X)i) Press f (X)i) Rearranging P from small to large1(t) and adding P1(t) in f (X)i) The smallest individual as the globally optimal individual XeAnd (5) storing.
S522, fitness of an individual can be expressed as a function of its position i in the population, and is written as: (i +1)/(n +1), wherein i represents the position of the individual in the population i e [0, Λ, n-1]From the population P1In (t), r.n (r is the crossover rate, and n is the population size) individuals are selected according to the probability Random (0, 1) < f (i). For each individual XiAnd performing intersection according to a formula.
In the above formula, Random (0, 1) represents a Random number between 0 and 1.
Further, as a preferred embodiment, in step S53, specifically, the method includes:
slave population P1In (t), m.n individuals are selected according to the probability Random (0, 1) > f (i). For each cross-operation individual Xi' mutation is performed according to a mutation function.
X″i＝X′i+(f(α)Scale-X′i)Rand(0，1)+fn(i)+ft(Tt) (12)
Wherein Scale represents the radius of the variable parameter definition domain; xi' denotes individuals after crossover operation, Xi"represents an individual after mutation operation, Random (0, 1) represents a Random number between 0 and 1, and fn(i) A function representing the fitness of an individual as a function of the position of the individual in the population, ft(Tt) And f (alpha) is a coefficient function.
fn(i) As a function of the fitness of the individual versus the position of the individual in the population, where i represents the position of the current individual:
fn(i)＝2πRand(0，1)f(α)f(i) (13)
wherein f (i) represents the individual fitness;
ft(Tt) As a function of the individual fitness and the current temperature:
ft(Tt)＝2πRand(0，1)f(α)(Tstart-Tt)/Tstart (14)
in the above formula, TtIs the current temperature; t isstartF (α) is a coefficient function for the annealing initiation temperature.
Wherein the coefficient function f (α) is:
it can be seen that in order to maintain a good diversity of population, the individual must maintain a large intensity of perturbation. The disturbance strength of the individuals in the group is gradually increased from front to back according to the positions of the individuals in the group, and is gradually increased along with the reduction of the temperature. Therefore, the individual jitter which is closer to the optimal solution is smaller when the temperature is higher, and the individual still can keep a certain intensity of disturbance when the temperature is lower, so that a more appropriate group diversity keeping strategy is provided for searching the global optimal solution.
Further as a preferred embodiment, the step of judging whether the preset stop criterion is met in step S6 specifically includes:
judging whether the maximum genetic algebra and the annealing termination temperature are reached or whether the following conditions are met:
f(X″i) > 500 or Tt＜Tend (16)
Wherein, f (X ″)i) Denotes the fitness value of the i-th individual, X' denotes the individual after the mutation operation, TendIndicating the annealing end temperature.
According to the invention, the hub motor is inversely solved through the genetic annealing algorithm, the precision problem of the simulated annealing algorithm is made up by using the search strategy of the genetic algorithm, and the dilemma that the genetic algorithm is trapped in local optimum is avoided by using the global search capability of the simulated annealing algorithm. The genetic annealing algorithm organically combines the advantages of the two algorithms, so that the efficiency of the algorithm can be improved, and the global control capability of the algorithm can be enhanced. The optimization method of the hub motor executed based on the algorithm has the advantages of high accuracy, high convergence speed and high efficiency.
Claims (8)
1. A hub motor optimization method based on a genetic annealing algorithm comprises the following steps:
(1) determining variable parameters of the hub motor, including the outer diameter of the stator, the inner diameter of the stator, the length of an iron core, the length of an air gap, the thickness of a permanent magnet, the number of conductors in each slot, the diameter of a lead and the slot filling rate;
(2) determining the target and constraint conditions of the hub motor to be optimized: the optimized objective function of the hub motor is that the motor efficiency is highest on the basis of certain mass and material cost of effective materials used by the motor; the constraint conditions are restrictive constraint functions applied according to specific use environments and conditions of the in-wheel motor, all or part of variable parameters are contained in a mathematical expression of the constraint functions, and the constraint conditions of the in-wheel motor optimization design are respectively starting current g of the in-wheel motor1(X), starting Torque g2(X), air gap magnetic induction g3(X) rated speed g4(X) thermal load g5(X) stator teeth magnetic density g6(X) stator yoke magnetic density g7(X) rotor yoke magnetic density g8(X)；
(3) According to the in-wheel motorVariable parameters, generating initial population P of genetic simulated annealing algorithm0(t) setting a fitness function of the genetic simulated annealing algorithm; the fitness function is:
min F(X，γ)＝f(X)+P(X，γ) (1)
wherein f (X) is a predetermined objective function, P (X, gamma) is a penalty function, and f (X) is a constraint function gi(X) a function of interest; gamma is a penalty factor;
the preset objective function is
In the formula, alphaiIs a weight coefficient, fi(x) Is a single objective function, and N is the number of the objective functions;
wherein the constraint function giThe expression (X) is:
in the formula IstFor optimized starting current, Ist0Is the starting current before optimization; t isstFor optimized starting torque, Tst0The starting torque before optimization; b isFor optimized air gap magnetic induction, B0The air gap magnetic induction intensity before optimization; n is a radical ofTFor the optimized rated rotating speed, NT0The rated rotating speed before optimization; h is the optimized thermal load, H0To optimize the thermal load before; b isiFor optimized stator tooth magnetic density, Bt0The magnetic density of the stator tooth part before optimization; b isjFor optimized stator yoke magnetic density, Bj0The magnetic density of the stator yoke part before optimization; b isiFor optimized rotor yoke magnetic density, Bi0The magnetic density of the yoke part of the rotor before optimization;
the expression of the penalty function P (X, γ) is:
in the formula, gamma is a penalty factor; h isu(x) Is the equation part in the u-th constraint function; q. q.su(x) Is the inequality part in the u constraint function; u denotes the sequence number of the constraint function, and u is 1, 2, … M; m is the number of constraint functions;
(4) calculating the probability of each individual in the population to be selected, and randomly selecting the initial population according to the calculated probability of being selected;
(5) performing crossing and mutation operations on the randomly selected population to obtain a population P1(t)；
(6) Judging whether a preset stopping criterion is met, namely whether the maximum genetic iteration number and the annealing termination temperature are reached, if so, ending the genetic algorithm and outputting the optimal individual as the optimal design parameter matrix of the hub motor, otherwise, updating the individual in the population;
(7) updating iteration parameters and simulating genetic annealing algorithm temperature TtAnd (4) after the descent, the genetic algebra K is increased and the population array is updated, returning to the step (4) for iteration until the hub motor meets the target function of the hub motor according to the obtained variable parameter values.
2. The genetic annealing algorithm-based in-wheel motor optimization method according to claim 1, characterized in that: in step (3), the initial population P0(t) is comprised of initial individuals of the formula:
X＝[x0，x1，，…，xi，…，xn-1]T
in the formula, n represents the number of design variables of the hub motor, X represents a vector of a solution space, and elements in X are composed of variable parameters.
3. The genetic annealing algorithm-based in-wheel motor optimization method according to claim 1, characterized in that: in step (4), the probability of each individual in the population being selected is obtained by the following formula:
wherein f isminRepresents the minimum value of the fitness function values of the individuals in the population, f (i) represents the fitness function value of the ith individual, pi(Tt) Representing the current temperature T during the updating of the iteration parametertThe probability that the individual is selected is then determined.
4. The genetic annealing algorithm-based hub motor optimization method according to claim 1, wherein the step (5) comprises the following steps:
s51, selecting individuals in the population by adopting a proportion selection operator according to the cross rate and the variation rate;
s52, performing cross operation on the selected population;
and S53, performing mutation operation on the crossed population.
5. The genetic annealing algorithm-based in-wheel motor optimization method according to claim 4, characterized in that: the step S51 is divided into the following steps,
s511, according to the crossing rate PcAnd the rate of variation PvSearching in the population, calculating the adaptive value of each individual, and sequencing according to the sequence from large to small, wherein the cross rate PcAnd the rate of variation PvComprises the following steps:
in the formula, Pc1Representing a preset crossing rate, and taking a value in a (0, 1) interval; pv1The variation rate is expressed in a preset variation rate,taking the value in the interval (0, 1); f. ofminRepresenting the minimum fitness of the individuals in the population; f. ofavgRepresenting the average fitness of individuals in the population; f' represents the relatively smaller individual fitness of two individuals which are mutually crossed;
s512, calculating the proportion P of the fitness value of each individual to the total fitness value according to the following formulak(Xi) Then, a roulette wheel is composed:
in the above formula, f (X)i) Representing the fitness value of the ith individual;
s513, randomly generating a random number between 0 and 1, and selecting a corresponding individual according to the group point of the random number on the roulette plate;
and S514, repeatedly executing the step S513 until the selected individual reaches the maximum value of the population capacity.
6. The genetic annealing algorithm-based in-wheel motor optimization method according to claim 5, characterized in that: in step S52, the following steps are included,
s521, regarding the population P1(t) each individual XiCalculating the fitness function value f (X)i) Press f (X)i) Rearranging P from small to large1(t) and adding P1(t) in f (X)i) The smallest individual as the globally optimal individual XeStoring;
s522, fitness of an individual can be expressed as a function of its position i in the population, written as: (i +1)/(n +1), wherein i represents the position i e [0, …, n-1 of the individual in the population]From the population P1(t) selecting r.n individuals according to the probability Random (0, 1) < f (i); r is the crossover rate and n is the population size, X for each individualiPerforming intersection according to the following formula;
in the above formula, Random (0, 1) represents a Random number between 0 and 1.
7. The genetic annealing algorithm-based in-wheel motor optimization method according to claim 6, characterized in that: step S53 specifically includes:
slave population P1(t) selecting m.n individuals according to the probability Random (0, 1) > f (i), wherein m is the crossing rate, n is the population scale, and each crossed individual Xi' performing variation according to a variation function;
X″i＝X′i+(f(α)Scale-X′i)Random(0，1)+fn(i)+ft(Tt) (10)
wherein Scale represents the radius of the variable parameter definition domain; xi' denotes individuals after crossover operation, Xi"represents an individual after a mutation operation, Random (0, 1) represents a Random number between 0 and 1, and f (alpha) is a coefficient function;
fn(i) a function representing the fitness of an individual as a function of the position of the individual in the population, wherein i represents the position of the current individual:
fn(i)＝2πRandom(0，1)f(α)f(i) (11)
wherein f (i) represents the individual fitness;
ft(Tt) And (3) representing the relation function of the individual fitness and the current temperature:
ft(Tt)＝2πRandom(0，1)f(α)(Tstart-Tt)/Tstart (12)
in the above formula, TtIs the current temperature; t isstartF (alpha) is a coefficient function for the annealing initiation temperature;
wherein the coefficient function f (α) is:
8. The genetic annealing algorithm-based in-wheel motor optimization method according to claim 1, characterized in that: the step of judging whether the preset stop criterion is met in the step (6) specifically includes:
judging whether the maximum genetic algebra and the annealing termination temperature are reached or whether the following conditions are met:
f(X″i) > 500 or Tt＜Tend (13)
Wherein, f (X ″)i) Denotes the fitness value, X, of the ith individuali"means the individual after mutation operation, and is also a new solution vector after mutation operation, TendRepresents an annealing end temperature;
in addition to this, the present invention is,
s11, setting the initial temperature and the temperature reduction factor of the genetic annealing algorithm according to the optimized objective function of the hub motor, and setting the annealing operation function as follows:
Tt+1＝kTt (14)
in the formula: t istIndicating the current temperature, Tt+1The temperature after the annealing operation is represented, k represents a temperature reduction factor, and the value of k is slightly less than 1.0;
s12, the number of iterations may be set to different values according to the size and structure of the hub motor, where the number of iterations is 500.
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