CN115809608A - Parameter identification and optimization method for mining heavy-load solid tire - Google Patents
Parameter identification and optimization method for mining heavy-load solid tire Download PDFInfo
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Abstract
The invention discloses a parameter identification and optimization method for a mining heavy-load solid tire, which comprises the following steps: 1. carrying out test operation on the tire according to a mining heavy-load solid tire test to obtain test data, 2, carrying out primary optimization on a mining heavy-load solid MF tire model based on the test data to obtain a first objective function value and obtain the mining heavy-load MF solid tire model, 3, carrying out primary identification on parameters in the mining heavy-load MF solid tire model through a Gauss-Newton iteration method, 4, carrying out rapid optimization and deep optimization on the parameters obtained by primary identification through a hybrid optimization algorithm to obtain parameters with higher accuracy and precision. The method can efficiently and quickly identify the parameters in the mine heavy-load MF solid tire model, is easy to realize, has good adaptability and high identification precision, and is suitable for dynamics and stability research of typical pavement environment of mines and heavy-load transport vehicles.
Description
Technical Field
The invention belongs to the technical field of vehicles, and particularly relates to a parameter identification and optimization method for a mining heavy-duty solid tire.
Background
The rapid development of ground vehicle technology and computer information technology, no matter for traditional automobiles or new energy vehicles, the vehicle design tends to be more and more efficient, informationized and the like, the information technology, particularly the application of computer simulation technology in the automobile industry, is greatly convenient for the design and development of products, improves the quality of the products, and provides effective help for production enterprises and related scientific research institutions, wherein the vehicle simulation analysis technology can realize the early prediction and analysis of the performance and the manufacturability of the products, thereby shortening the product design and manufacturing period, reducing the product development cost and improving the capability of the research and development design system for responding to the market change at the speed.
Under the call of national energy conservation and emission reduction, the coal mine has objective requirements of reducing personnel and increasing efficiency, improving the safety of the coal mine and reducing the accident rate, and the development of clean, efficient and intelligent coal mining equipment is urgently needed to realize mechanized people reduction. With the rapid growth of the mining vehicle industry and the great improvement of the market reserve, the overall performance and parameters of the mining vehicle are difficult to achieve reasonable configuration after explosion-proof transformation, the underground driving road condition is complex and limited, and the ventilation condition is poor, so that compared with the ground vehicle with the same design capability, the underground driving road condition has obvious pain points of low efficiency, poor safety and poor working condition adaptability, and the ground vehicle technology and the computer information technology, particularly the vehicle simulation technology, are urgently used for reference to improve the power performance.
The heavy-load solid rubber tire of the mining vehicle is used as a part for the direct contact between the mining vehicle and the ground, the mechanical property of the heavy-load solid rubber tire directly influences the vehicle dynamics and the driving smoothness characteristics, compared with the conventional tire, the tire structure, the material characteristics and the rolling contact mechanism of the tire have certain differences with the conventional pneumatic tire model, and the heavy-load solid rubber tire has the characteristics of solid rubber, low damping, thick patterns, large flattening rate and the like. Therefore, when the pneumatic tire model and the empirical parameters in the traditional method are adopted to carry out dynamic modeling and simulation calculation on the mine vehicle, a larger model mismatch error is likely to be generated, the actual motion state of the mine heavy-duty vehicle cannot be accurately described, and the behavior of the mine heavy-duty vehicle is accurately regulated and controlled, so that the method becomes a key problem which restricts the dynamics and stability research of the mine vehicle for a long time and is not fundamentally solved all the time. Therefore, the important influence of the tire road contact mechanical characteristics on the regulation and control of the transverse stability performance of the vehicle is considered, the nonlinear rolling and sliding contact mechanical characteristics of the heavy-load traction solid rubber tire of the mine vehicle on the road cement road surface are researched, the model parameters of the heavy-load solid or filling tire are accurately identified according to tire materials, geometric structural characteristics and the like, and the establishment of the solving model suitable for the typical road surface environment of the mine and the tire force of the heavy-load transport vehicle is particularly important.
A reasonable tire dynamics model is established, and the influence of longitudinal force, lateral force, vertical load and aligning moment on the tire on the dynamic property, the operation stability, the braking stability, the riding adaptability and the driving safety of a vehicle is analyzed, so that the reasonable tire dynamics model is an important component of a vehicle simulation technology and plays a key role in product development and whole vehicle performance analysis, and the precision of the tire model directly influences the key technology research of vehicle products. At present, the research of the mining vehicle on the aspect of the technology mainly adopts a method of transplanting ground related technology, the ground vehicle dynamics generally adopts an empirical model formula obtained based on test data in the aspects of analyzing the cornering performance and the like of the tire, the formula is obtained by combining and fitting trigonometric functions, and the combined action working conditions of longitudinal force, aligning moment, overturning moment and resistance distance respectively and longitudinal force and lateral force borne by the tire can be completely expressed. However, the formula has the characteristics of more parameters and high nonlinearity, the identification of the parameters is difficult, and the adopted algorithm has low convergence speed and poor real-time performance. In addition, the structural particularity of the mining vehicle and the driving road conditions are complex and changeable, so that the parameter identification is difficult, and the level of the vehicle simulation technology in the aspect of researching and evaluating the identification precision of tire model parameters is urgently needed to be improved.
In summary, how to establish a parameter identification and optimization method for a mining tire is a technical problem to be solved urgently by those skilled in the art.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a parameter identification and optimization method for a mining heavy-load solid tire, so that parameters in a mining heavy-load MF solid tire model can be efficiently and quickly identified, and the effects of high calculation efficiency, strong global solving capability and high precision are achieved, and the power performance of a whole vehicle can be fundamentally improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to a parameter identification and optimization method for a mining heavy-load solid tire, which is characterized by comprising the following steps of:
step 1, performing test operation on a tire according to a mining heavy-load solid tire test to obtain test data, and constructing a mining heavy-load solid MF tire model by using the test data;
step 1.1, defining the current test frequency as s, and initializing s =1;
step 1.2, performing the test for the second time on the tire sample piece of the heavy-load rubber solid traction of the mining vehicle through a six-component force test experiment table to obtain n groups of test data under the test for the second time
Wherein,
represents any ith set of test data under the s-th test, an
Denotes the i-th set of test data x i And the ith characteristic quantity of (1), and the test data of the ith group
Characteristic quantity of
The fitting value of (D) is recorded as
The test values of (A) are recorded as
m represents the total number of feature quantities;
step 1.3, establishing an objective function Z of the semi-empirical tire model in the s-th test by using the formula (1) s ：
Step 1.4, after assigning s +1 to s, judging whether s > Smax is true, if so, executing step 2, otherwise, returning to step 1.2 for sequential execution, wherein Smax represents the maximum test times;
step 2, sequencing the objective function values in Smax tests in an ascending order to obtain a first ordered objective function value serving as an initial value of the semi-empirical tire model, so as to obtain a mining heavy-load MF solid tire model;
step 3, identifying parameters in the mining heavy load MF solid tire model by a Gauss-Newton iteration method:
step 3.1, performing Taylor series expansion on the mining heavy-load MF solid tire model, and deleting partial derivative terms of second order and above to obtain a nonlinear regression tire model;
step 3.2, defining the current iteration number as v, and initializing v =1;
3.3, estimating the nonlinear regression tire model by using a least squares method for the v time to obtain a correction factor estimated for the v time;
step 3.4, calculating residual square sum SSR of correction factor estimated at the v time v ；
Step 3.5, identifying a coefficient to be regressed:
for a given allowable error rate k, when
Stopping iteration, and substituting the correction factor obtained by estimating for the v time into the nonlinear regression tire model to obtain a corrected mining heavy-load MF solid tire model; otherwise, after v +1 is assigned to v, returning to the step 3.3 for sequential execution;
step 4, generating an initial population according to the parameter value to be identified in the corrected mining heavy-load MF solid tire model;
step 4.1, setting the population size as U, and defining the current algebra of the population as g; and initializing g =1;
taking all parameter values to be identified in the corrected mining heavy-load MF solid tire model as the u-th chromosome in the g-th generation population
Thereby obtaining the g generation population set
Step 4.2, calculating according to the formula (1) to obtain the g generation population A g Middle u chromosome
Fitness value of
And the u-th chromosome
Performing cross operation on the two genes with the highest medium fitness value to obtain the u-th chromosome
Two new genes of (2) for replacing the u-th chromosome
The two genes with the highest fitness value in the genome are obtained, and the updated u-th chromosome is obtained
Further obtaining the updated g generation population A' g ；
Step 4.3, the u-th chromosome
The two new genes are used as initial optimal solutions of simulated annealing operators and annealing operation is carried out:
step 4.3.1, defining the current cycle number of the annealing operation as k, and initializing k =0;
let the temperature T of the kth cycle k Randomly generating the state omega of the current k-th cycle k The optimal solution of the kth cycle is obtained;
step 4.3.2, temperature T of cycle k +1 k+1 ＝αT k (ii) a Wherein alpha represents a cooling factor, and alpha is more than 0 and less than 1;
step 4.3.3, after k +1 is assigned to k, according to T k Obtaining the state omega of the kth cycle k And as the optimal solution omega for the kth cycle k ；
Step 4.3.4, let the increment of the kth cycle be Δ Z k ＝Z(ω k )-Z(ω k-1 ) Wherein Z represents an objective function of the semi-empirical tire model; omega k-1 Represents the state of the k-1 th cycle;
if Δ Z k If not more than 0, the optimal solution omega of the kth cycle is k Replacement of the u-th chromosome
Two new genes and obtaining the g +1 generation population A g+1 U th chromosome of
Otherwise, executing step 4.3.5;
step 4.3.5, if
The optimal solution omega for the kth cycle is then calculated k Replacement of the u-th chromosome
Two new genes of (2) and obtaining the g +1 generation population A g+1 U th chromosome of
Otherwise, the optimal solution ω of the k-1 th cycle k-1 Replacement of the u-th chromosome
Two new genes and obtaining the g +1 generation population A g+1 U th chromosome of
Wherein ε represents a coefficient; r is k Represents a random number of the kth cycle, and r k ∈[0,1]；
Step 4.4, according to the variation probability P m For the g +1 generation population A g+1 Any j th chromosome of
Performing mutation operation to obtain new chromosome
If the j increment of the g +1 th generation
Then the new chromosome will be
Adding the g +1 generation population A g+1 And updated g +1 th generation population A 'is obtained' g+1 Otherwise, in [0,1]Generates the j (th) random number of the g +1 (th) generation
If it is
Then the new chromosome will be
Adding the g +1 generation population A g+1 And obtaining the updated g +1 th generation population A' g+1 Otherwise, the jth chromosome is divided into
Still remain in the g +1 th generation of population A g+1 Wherein, t j Representing a jth annealing function;
step 4.5, calculating the updated g +1 th generation of population A 'according to the formula (1)' g+1 Middle u chromosome
Fitness value of
Judging the u-th chromosome
And taking the two genes with high medium fitness value as initial optimal solutions of simulated annealing operators and carrying out annealing operation:
step 4.5.1, initializing the current cycle number k =0 of annealing operation;
let temperature T of cycle k k ', randomly generating the state ω of the current kth cycle k ' is the optimal solution for the kth cycle;
step 4.5.2, let temperature T of cycle k +1 k ′ +1 ＝αT k '; wherein alpha represents a cooling factor, and alpha is more than 0 and less than 1;
step 4.5.3, after k +1 is assigned to k, according to T k ' obtaining the state ω of the kth cycle k ', and as the optimal solution ω for the kth cycle k ′；
Step 4.5.4, let the increment of the kth cycle be Δ Z k ′＝Z(ω k ′)-Z(ω k ′ -1 ) Wherein, ω is k ′ -1 Represents the state of the k-1 th cycle;
if Δ Z k ' is less than or equal to 0, the optimal solution omega of the kth cycle is obtained k ' substitution of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation population A g+2 U th chromosome of
Otherwise, executing step 4.5.5;
step 4.5.5, if
The optimal solution omega for the kth cycle is then calculated k ' substitution of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation population A g+2 U th chromosome of
Otherwise, the optimal solution ω of the k-1 th cycle k ′ -1 Replacement of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation population A g +2 U th chromosome of
Wherein r is k ' denotes a random number of the kth cycle, and r k ′∈[0,1]；
And 4.6, assigning g +2 to g, judging whether g > gmax is established or not, if so, indicating that a gmax generation population is obtained, selecting a chromosome with the highest fitness as an optimal identification parameter value of the corrected mining heavy load MF solid tire model, and otherwise, returning to the step 4.2 for sequential execution.
The electronic device comprises a memory and a processor, wherein the memory is used for storing programs for supporting the processor to execute the parameter identification and optimization method, and the processor is configured to execute the programs stored in the memory.
The invention relates to a computer-readable storage medium, on which a computer program is stored, characterized in that the computer program executes the steps of the parameter identification and optimization method when being executed by a processor.
Compared with the prior art, the method is suitable for the typical road surface environment and the heavy-load transportation working condition of a mine, the tire is subjected to test operation and collection according to the heavy-load solid tire test for the mine to obtain test data, then an optimization model and an evaluation index are established based on a semi-empirical tire model, the identified parameters are brought into the tire model, and the corresponding solution is optimal if the square root of the difference value between the calculation result and the actual test value is minimum under the same condition, namely the solution corresponding to a smaller target function value is expected to have a high adaptability value. Firstly, performing Taylor expansion on a function to be identified by utilizing a Gauss-Newton method, neglecting partial derivative terms of second order and above, iterating to obtain a nonlinear regression tire model, estimating a coefficient to be regressed by the nonlinear regression tire model by using a least squares method, and obtaining a corrected mining heavy-load MF solid tire model; the initial identification parameters are deeply optimized through a genetic algorithm and a simulated annealing algorithm, the optimal solution in each generation of population is searched again through the simulated annealing algorithm, the searching capability of the algorithm is enhanced, the diversity of the population is kept through the simulated annealing algorithm, and the situation that the population converges in a certain local area is avoided. The method can realize the self-adaptive adjustment, final identification and optimization of parameters in the common tire empirical formula, and the obtained parameter identification value is used for calculating and analyzing the stress condition of the tire under the complex working condition to guide the design of the whole vehicle, thereby being an important component of the vehicle simulation analysis technology. The method has the advantages of strong purposiveness, very high convergence rate and high solving precision. The concrete advantages are that:
1. the invention provides an identification target function to establish an optimization model and evaluation indexes, a Gauss-Newton iteration method, a genetic algorithm and a self-adaptive simulated annealing algorithm are combined, firstly, the Gauss-Newton iteration method is used for carrying out primary identification on main parameters of test sampling data, then, the genetic algorithm is used for optimizing and identifying primary identification results, optimal solutions in each generation of population are searched again by the simulated annealing algorithm, the searching capability of the algorithm is enhanced, finally, local optimal solutions are jumped out by the self-adaptive simulated annealing algorithm, global optimal solutions are searched, the diversity of the population is kept, the searching capability is strong, the running time is short, the solving precision is high, the method is easy to realize, the method aims at the strong nonlinear characteristic caused by the large vertical load range of the mine vehicle tires, the fixed parameter setting and the optimization strategy are difficult to adapt to the situation, the related test data can be obtained by six-component testing equipment, the tire model parameters under the complex working condition are identified, further, the whole vehicle traction characteristic real vehicle experiment under the different load working conditions is carried out, the test result shows that the pain of the identification model is greatly improved compared with the pure genetic algorithm, the accuracy of the traction of the model, the solid vehicle traction, the multi-load tire model parameters under the high-load condition, the accuracy of the calculation is solved, and the calculation difficulty of the non-linear speed of the calculation is caused by the non-linear model under the high-linear speed under the high-load working condition, and the calculation is caused by the high-point. The optimal identification algorithm is provided for establishing a solving model suitable for the typical road surface environment of the mine and the tire force of the heavy-load transport vehicle.
2. The hybrid optimization algorithm adopted by the invention has the advantages that: in view of the important influence of the tire road contact mechanical characteristics on the regulation and control of the transverse stability of the vehicle, the algorithm aims at accurately identifying the model parameters of the heavy-load solid or filled tire according to tire materials, geometric structural characteristics and the like by researching the nonlinear rolling-sliding contact mechanical characteristics of the heavy-load traction solid rubber tire of the mine vehicle on the road cement road surface, and establishes a solving model suitable for the typical road surface environment of the mine and the tire force of the heavy-load transport vehicle. Under a certain working condition of a mining vehicle heavy load traction solid tire model, such as a pure longitudinal sliding mode, the longitudinal force parameter identification global optimization and rapid convergence capability is greatly improved compared with a genetic algorithm, the success rate of convergence to global optimum reaches 70%, the success rate is increased by more than 50% compared with the genetic algorithm, the average algebra convergence to global optimum is reduced by more than 35%, the total time of convergence to global optimum is increased by 6%, and the average time of convergence to global optimum is reduced by more than 30%; the evaluation indexes of the longitudinal force identification target function under the pure longitudinal and smooth working condition are respectively improved by more than 10% compared with a single genetic algorithm.
The method is based on a basic model of a PAC2002 magic formula, provides a hybrid optimization algorithm for parameter identification on the basis of correcting and providing a composite working condition mathematical model of the heavy-load traction solid tire of the mine vehicle, and verifies the result, which shows that the provided hybrid optimization algorithm has better identification stability and higher identification precision. The deviation between the tire longitudinal traction force obtained by calculation according to the identification parameters and the real vehicle experiment result is not more than 4%, the effectiveness of the identification model is verified, a foundation is laid for accurately describing the actual motion state of the mine heavy-load vehicle and accurately regulating and controlling the behavior of the mine heavy-load vehicle, and the key problem that the dynamics and stability of the mine vehicle are limited for a long time is solved.
Drawings
FIG. 1 is a flow chart of the hybrid optimization algorithm parameter identification of the present invention;
FIG. 2 is a graph illustrating the evolution of the hybrid optimization algorithm of the present invention.
Detailed Description
In this embodiment, as shown in fig. 1, a method for identifying and optimizing parameters of a heavy-duty solid tire for mining is performed according to the following steps:
step 1, performing test operation on a tire according to a mining heavy-load solid tire test to obtain test data, and constructing a mining heavy-load solid MF tire model by using the test data;
the method comprises the steps of carrying out stress mechanical characteristic tests on tires under different working conditions, detecting and acquiring various data in a tire model under each working condition through a sensor in the tests, wherein the data comprise independent variables and dependent variables such as lateral force, aligning moment or longitudinal force, and the slip angles or the longitudinal slip rates of the tires respectively corresponding to the different working conditions.
Step 1.1, defining the current test frequency as s, and initializing s =1;
step 1.2, performing the test for the second time on the tire sample piece of the heavy-load rubber solid traction of the mining vehicle through a six-component force test experiment table to obtain n groups of test data under the test for the second time
Wherein,
represents any ith set of test data under the s-th test, an
Denotes the i-th test data x i And the jth characteristic quantity in (b), and the ith group of test data
The j (th) characteristic quantity
The fitting value of (D) was recorded as
The test value of (D) is recorded as
m represents the total number of feature quantities;
step 1.3, establishing an objective function Z of the semi-empirical tire model in the s-th test by using the formula (1) s ：
And 1.4, assigning s +1 to s, judging whether s > Smax is true, if so, executing the step 2, otherwise, returning to the step 1.2 for sequential execution, wherein Smax represents the maximum test times.
And 2, sequencing the objective function values in Smax tests in an ascending order to obtain a first ordered objective function value serving as an initial value of the semi-empirical tire model, so as to obtain the mining heavy-load MF solid tire model.
Step 3, identifying parameters in the mining heavy-load MF solid tire model by a Gauss-Newton iteration method:
and (2) firstly identifying main parameters in the target function by adopting a Gauss-Newton iteration method, mainly performing nonlinear least square estimation and iterative correction on the data sampled in the step (1) to enable the regression coefficient to continuously approximate to the optimal regression coefficient of the nonlinear regression model, and finally enabling the sum of squares of the residual errors of the original model to be minimum, and obtaining the parameter values in the target function through primary identification.
The Gauss Newton iteration method identifies parameter values through five parts of selection of an initial value, taylor series expansion, estimation of a correction factor, accuracy inspection and repeated iteration, approximately replaces a nonlinear regression model by using the Taylor series expansion after the initial value of the iteration is selected or solved, then continuously approximates the regression coefficient to the optimal regression coefficient of the nonlinear regression model through repeated iteration and repeated correction of the regression coefficient, and finally minimizes the sum of squares of residual errors of an original model. The gauss-newton method is characterized in that the problem of large model errors generated by parameter estimation by linear approximation when the nonlinear strength of the model is high is solved, and the resolving precision is high; meanwhile, the method is similar to linear least square in principle, the formula is simple in structure, and the method has quick convergence capacity, so that the method is extremely convenient to apply and is still a widely applied nonlinear least square estimation method at present. The general procedure for gauss-newton method is:
step 3.1, performing Taylor series expansion on the mining heavy-load MF solid tire model, and deleting partial derivative terms of second order and above to obtain a nonlinear regression tire model;
(1) The initial value is selected by three methods, one is to select the initial value according to the past experience, and the other is to calculate the initial value by a segmentation method; and thirdly, obtaining an initial value of the nonlinear regression model which can be linearized through linear transformation and then a least square method.
(2) The Taylor series expansion is set as the nonlinear regression model:
in the formula (2), r is a coefficient to be regressed, x i As the parameter to be identified, the identification information is obtained,
error term ε for equation output value i ～N(0,σ 2 ) Is provided with
Is the coefficient r = (r) to be regressed 0 ,r 1 ,…,r p-1 ) T Is given as an initial value of (a) f (x) of the formula (2) i R) in g 0 And (3) performing Taylor expansion near the point, and omitting partial derivative terms of the second order and above of the second order of the nonlinear regression model to obtain:
substituting equation (3) into equation (2), then:
item shifting:
order to
Then:
the expression above is expressed in matrix form as follows:
Y (0) ≈D (0) b (0) +ε (4)
in formula (4):
step 3.2, defining the current iteration number as v, and initializing v =1;
step 3.3, carrying out the estimation correction factor for the v time on the nonlinear regression tire model of the formula (4) by using a least squares method, wherein the correction factor b of the v time iteration is (v) ：
b (v) ＝(D (v)T D (v) ) -1 D (v)T Y (v ) (5)
V +1 th iteration value: g (v+1) ＝g (v) +b (v) ；
In the formula (5), D (v) For the calculation factor of the v-th iteration under composite conditions, Y (v) Outputting a matrix for the equation;
step 3.4, calculating residual square sum SSR of correction factor estimated at the v time v ；
Step 3.5, identifying the coefficient to be regressed:
for a given allowable error rate k, when
When the iteration is stopped; substituting the correction factor estimated for the v time into a nonlinear regression tire model to obtain a corrected mining heavy-load MF solid tire model; otherwise, after v +1 is assigned to v, the step 3.3 is returned to execute in sequence.
Step 4, generating an initial population according to a parameter value obtained by the corrected initial suboptimal identification of the mine heavy-load MF solid tire model; calculating an initial value by adopting a genetic algorithm, optimizing the fitness value by using the parameter value primarily identified in the step 3, and finding out a scientific and reasonable formula parameter value which is close to an optimal solution in a global range according to continuous crossing, variation and optimization of the genetic operator by the genetic algorithm.
The global probability search algorithm based on the natural selection rule and the Mendel genetic law determines an objective function formula (1) according to the researched problem, then randomly initializes a population, individuals in the population represent a possible solution of the researched problem, a preferred mode of the individuals is to select the individuals with high fitness value, the fitness value is obtained by calculation according to the objective function formula (1), a plurality of selected excellent individuals form a new next generation population, the diversity of the new population is increased by crossing and mutation operations, and the process is continuously repeated, so that the population can be continuously evolved and generate a more excellent next generation population.
And selecting real number codes to encode parameter values to be identified, setting upper and lower limits of the parameters to be identified, and initializing the population. The population size Np =10 to 200 in the normal case, and in the present embodiment, the population size Np =200 when the longitudinal force and the yawing force are parameter-discriminated.
The method comprises the steps of eliminating individuals with poor fitness value through a mechanism of high-out and low-out, selecting stored individuals according to a certain rule according to the fitness, breeding the individuals to form a new group, wherein in general, the higher the fitness is, the better the solution is represented, and the lower the fitness is, the worse the quality of the solution is represented, and the selection operation uses a proportion selection method to select the good individuals.
And generating a next generation population through crossing and mutation operations. The crossing is to randomly select two individuals (parents) and to exchange genes at a certain point or multiple points to generate two new individuals, and the mutation is to generate mutation at a certain point or multiple points in the genes. If the cross probability Pc is too small, it is difficult to search forward, and if it is too large, it is easy to destroy some good individuals, usually Pc = 0.25-1.00, and herein, a single-point cross is selected, and the cross probability Pc =0.65. If the variation probability Pm is too small, a new gene structure is difficult to generate, and if it is too large, the genetic algorithm becomes a random search, where Pm =0.001 to 0.1 in general, and in this embodiment, the variation probability is selected to be Pm =0.07.
The offspring repeats the above operations to perform a new round of genetic evolution process, and based on the characteristic that the fitness function of the method is fast in calculation, in this embodiment, the maximum genetic algebra is set to 10000 generations. As shown in fig. 2;
judging whether the group meets the termination condition, if so, ending the algorithm to obtain an approximate optimal solution, then adopting a self-adaptive simulated annealing algorithm to improve the calculation efficiency, further performing local optimization, iteratively outputting the optimal solution through a random value, and judging whether the objective function meets the evaluation index requirement.
The simulated annealing algorithm is an extension of a local search algorithm and is mainly applied to tW in a combined optimization problem. The method is based on the metal annealing principle, metal is heated to a certain temperature and then is slowly cooled, the interior of metal particles gradually tends to be ordered during cooling, and when the temperature is reduced to a certain degree, the internal energy is reduced to the minimum. Based on the characteristic, the simulated annealing algorithm randomly searches a global optimal solution in a solution space from a certain higher temperature along with the continuous reduction of temperature parameters by combining probability map jumping characteristics, namely, the local optimal solution can be jumped probabilistically, and finally the global optimal local searching capability is stronger, and the running time is short.
An Adaptive Simulated Annealing (ASA) algorithm is improved in a quenching mode, a re-annealing mode and a fire reducing mode on the basis of a simulated annealing algorithm, and has better calculation efficiency and global solving capability compared with the simulated annealing algorithm.
The method comprises the following specific steps:
step 4.1, setting the population size as U, and defining the current algebra of the population as g; and initializing g =1;
taking all parameter values to be identified in the corrected mining heavy-load MF solid tire model as the u-th chromosome in the g-th generation population
Thereby obtaining the g generation population set
Step 4.2, calculating according to the formula (1) to obtain the g generation population A g Middle u chromosome
Fitness value of
And the u-th chromosome
Performing cross operation on the two genes with the highest medium fitness value to obtain the u-th chromosome
Two new genes of (2) for replacing the u-th chromosome
The two genes with the highest fitness value in the genome are obtained, and the updated u-th chromosome is obtained
Further obtaining the updated g generation population A' g 。
Step 4.3, the u th chromosome
The two new genes are used as initial optimal solutions of simulated annealing operators and annealing operation is carried out:
step 4.3.1, defining the current cycle number of the annealing operation as k, and initializing k =0;
let the temperature T of the kth cycle k Randomly generating the state omega of the current k-th cycle k Is the optimal solution of the kth cycle;
step 4.3.2 temperature T of cycle k +1 k+1 ＝αT k (ii) a Wherein alpha represents a cooling factor, and alpha is more than 0 and less than 1;
step 4.3.3, after k +1 is assigned to k, according to T k The state omega of the kth cycle is obtained k And as the optimal solution omega for the kth cycle k ；
Step 4.3.4, let the increment of the kth cycle be Δ Z k ＝Z(ω k )-Z(ω k-1 ) Wherein Z represents an objective function of the semi-empirical tire model; omega k-1 Represents the state of the k-1 cycle;
if Δ Z k If not more than 0, the optimal solution omega of the kth cycle is k Replacement of the u-th chromosome
Two new genes and obtaining the g +1 generation population A g+1 U th chromosome of
Otherwise, executing step 4.3.5;
step 4.3.5, if
The optimal solution omega for the kth cycle is then calculated k Replacement of the u-th chromosome
Two new genes and obtaining the g +1 generation population A g+1 U th chromosome of
Otherwise, the optimal solution ω of the k-1 th cycle k-1 Replacement of the u-th chromosome
Two new genes of (2) and obtaining the g +1 generation population A g+1 U th chromosome of
Wherein ε represents a coefficient; r is k Represents a random number of the kth cycle, and r k ∈[0,1]。
Step 4.4, according to the mutation probability P m Inserting the obtained new individual into a parent population to obtain a new population, inserting the obtained new individual into the parent population by a certain generation ditch (GAP = 0.95) to obtain a temporary population tempop instead of being used as a next generation population, judging whether the chromosome in the temporary population tempop can enter the next generation population by using a Metropolis sampling standard, and specifically, the following steps of:
for the g +1 generation population A g+1 Any of the j th chromosomes
Performing mutation operation to obtain new chromosome
If the j increment of the g +1 th generation
Then the new chromosome will be
Adding the g +1 generation population A g+1 And updated g +1 th generation population A 'is obtained' g+1 Otherwise, in [0,1]Generates the j random number of the g +1 generation
If it is
Then the new chromosome will be
Adding the g +1 generation population A g+1 And updated g +1 th generation population A 'is obtained' g+1 Otherwise, the jth chromosome is divided into
Still remain in the g +1 th generation of population A g+1 Wherein, t j Representing the annealing function.
Step 4.5, calculating the updated g +1 th generation population A 'according to the formula (1)' g+1 Middle u chromosome
Fitness value of
Judging the u-th chromosome
And taking the two genes with high medium fitness value as initial optimal solutions of simulated annealing operators and carrying out annealing operation:
step 4.5.1, initializing the current cycle number k =0 of the annealing operation;
let temperature T of cycle k k ', randomly generating the state ω of the current kth cycle k ' is the optimal solution for the kth cycle;
step 4.5.2, let temperature T of cycle k +1 k ′ +1 ＝αT k '; wherein alpha represents a cooling factor, and alpha is more than 0 and less than 1;
step 4.5.3, after k +1 is assigned to k, according to T k ' obtaining the state ω of the kth cycle k ', and as the optimal solution ω for the kth cycle k ′；
Step 4.5.4, let the increment of the kth cycle be Δ Z k ′＝Z(ω k ′)-Z(ω k ′ -1 ) Wherein, ω is k ′ -1 Represents the state of the k-1 cycle;
if Δ Z k ' is less than or equal to 0, the optimal solution omega of the kth cycle is obtained k ' replacement of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation populationA g+2 U th chromosome of
Otherwise, executing step 4.5.5;
step 4.5.5, if
The optimal solution omega for the kth cycle is then calculated k ' substitution of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation population A g+2 U th chromosome of
Otherwise, the optimal solution ω of the k-1 th cycle k ′ -1 Replacement of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation population A g +2 U th chromosome of
Entering the next generation population, wherein r k ' denotes a random number of the kth cycle, and r k ′∈[0,1]。
Step 4.6, calculating the chromosome fitness value in the new generation population, and finding out the maximum fitness value Z (i) max Judging whether a termination condition of the number of iterations GEN = MAXGEN =100 is satisfied, that is, judging Z (i) max 、Z(i-1) max 、…、Z(i-q) max If yes, the calculation is terminated, and the specific steps are as follows:
and assigning g +2 to g, judging whether g > gmax is true, if so, obtaining a gmax generation population, selecting a chromosome with the highest fitness as an optimal identification parameter value of the corrected mining heavy load MF solid tire model, and otherwise, returning to the step 4.2 for sequential execution.
In this embodiment, an electronic device includes a memory for storing a program that supports a processor to execute the parameter identification and optimization method, and a processor configured to execute the program stored in the memory.
In this embodiment, a computer-readable storage medium stores a computer program, and the computer program is executed by a processor to perform the steps of the parameter identification and optimization method.
Claims (3)
1. A parameter identification and optimization method for a mining heavy-load solid tire is characterized by comprising the following steps of:
step 1, performing test operation on a tire according to a mining heavy-load solid tire test to obtain test data, and constructing a mining heavy-load solid MF tire model by using the test data;
step 1.1, defining the current test frequency as s, and initializing s =1;
step 1.2, performing a test for the second time on the mining vehicle heavy-load rubber solid traction tire sample piece through a six-component test experiment table to obtain n groups of test data under the test for the second time
Wherein,
represents any ith set of test data under the s-th test, an
Denotes the i-th set of test data x i And the ith characteristic quantity of (1), and the test data of the ith group
The j (th) characteristic quantity
The fitting value of (D) was recorded as
The test values of (A) are recorded as
m represents the total number of feature quantities;
step 1.3, establishing an objective function Z of the semi-empirical tire model in the s-th test by using the formula (1) s ：
Step 1.4, after assigning s +1 to s, judging whether s > Smax is true, if so, executing step 2, otherwise, returning to step 1.2 for sequential execution, wherein Smax represents the maximum test times;
step 2, sequencing the objective function values in Smax tests in an ascending order to obtain a first ordered objective function value serving as an initial value of the semi-empirical tire model, so as to obtain a mining heavy-load MF solid tire model;
step 3, identifying parameters in the mining heavy-load MF solid tire model through a Gauss-Newton iteration method:
step 3.1, performing Taylor series expansion on the mining heavy-load MF solid tire model, and deleting partial derivative terms of second order and above to obtain a nonlinear regression tire model;
step 3.2, defining the current iteration number as v, and initializing v =1;
3.3, estimating the nonlinear regression tire model by using a least squares method for the v time to obtain a correction factor estimated for the v time;
step 3.4, calculating residual square sum SSR of correction factor estimated at the v time v ；
Step 3.5, identifying the coefficient to be regressed:
for a given allowable error rate k, when
Stopping iteration, and substituting the correction factor obtained by estimating for the v time into the nonlinear regression tire model to obtain a corrected mining heavy-load MF solid tire model; otherwise, after v +1 is assigned to v, returning to the step 3.3 for sequential execution;
step 4, generating an initial population according to the parameter value to be identified in the corrected mining heavy-load MF solid tire model;
step 4.1, setting the population size as U, and defining the current algebra of the population as g; and initializing g =1;
taking all parameter values to be identified in the corrected heavy load MF solid tire model for the mine as the u chromosome in the g generation population
Thereby obtaining the g generation population set
Step 4.2, calculating according to the formula (1) to obtain the g generation population A g Middle u chromosome
Fitness value of
And the u-th chromosome
Performing cross operation on the two genes with the highest medium fitness value to obtain the u-th chromosome
Two new genes of (2) for replacing the u-th chromosome
The two genes with the highest fitness value in the genome are obtained, and the updated u-th chromosome is obtained
Further, updated g generation population A 'is obtained' g ；
Step 4.3, the u-th chromosome
As initial optimal solution of simulated annealing operator and annealing operation are carried out:
step 4.3.1, defining the current cycle number of the annealing operation as k, and initializing k =0;
let the temperature T of the kth cycle k Randomly generating the state omega of the current k-th cycle k The optimal solution of the kth cycle is obtained;
step 4.3.2 temperature T of cycle k +1 k+1 ＝αT k (ii) a Wherein alpha represents a cooling factor, and alpha is more than 0 and less than 1;
step 4.3.3, after k +1 is assigned to k, according to T k Obtaining the state omega of the kth cycle k And as the optimal solution omega for the kth cycle k ；
Step 4.3.4, let the increment of the kth cycle be Δ Z k ＝Z(ω k )-Z(ω k-1 ) Wherein Z represents an objective function of the semi-empirical tire model; omega k-1 Represents the state of the k-1 th cycle;
if Δ Z k If the value is less than or equal to 0, the optimal solution omega of the kth cycle is obtained k Replacement of the u-th chromosome
Two new genes of (2) and obtaining the g +1 generation population A g+1 U th chromosome of
Otherwise, executing step 4.3.5;
step 4.3.5, if
The optimal solution omega for the kth cycle is then calculated k Replacement of the u-th chromosome
Two new genes of (2) and obtaining the g +1 generation population A g+1 U th chromosome of
Otherwise, the optimal solution ω of the k-1 th cycle k-1 Replacement of the u-th chromosome
Two new genes of (2) and obtaining the g +1 generation population A g+1 U th chromosome of
Wherein ε represents a coefficient; r is k Represents a random number of the kth cycle, and r k ∈[0,1]；
Step 4.4, according to the variation probability P m For the g +1 generation population A g+1 Any j th chromosome of
Performing mutation operation to obtain new chromosome
If the jth increment of the g +1 th generation
Then the new chromosome will be
Adding the g +1 generation population A g+1 And updated g +1 th generation population A 'is obtained' g+1 Otherwise, in [0,1]Generates the j (th) random number of the g +1 (th) generation
If it is
Then the new chromosome will be
Adding the g +1 generation population A g +1 And obtaining the updated g +1 th generation population A' g+1 Otherwise, the jth chromosome is divided into
Still remain in the g +1 th generation of population A g +1 Wherein, t j Representing a jth annealing function;
step 4.5, calculating the updated g +1 th generation population A 'according to the formula (1)' g+1 Middle u chromosome
Fitness value of
Judging the u-th chromosome
And taking the two genes with high medium fitness value as initial optimal solutions of simulated annealing operators and carrying out annealing operation:
step 4.5.1, initializing the current cycle number k =0 of the annealing operation;
let the temperature T of the kth cycle k ', randomly generating the state ω of the current kth cycle k ' is the optimal solution for the kth cycle;
step 4.5.2, let temperature T of cycle k +1 k ′ +1 ＝αT k '; wherein alpha represents a cooling factor, and alpha is more than 0 and less than 1;
step 4.5.3, after k +1 is assigned to k, according to T k ' obtaining the state ω of the kth cycle k ', and as the optimal solution omega for the k-th cycle k ′；
Step 4.5.4, let the increment of the kth cycle be Δ Z k ′＝Z(ω k ′)-Z(ω k ′ -1 ) Wherein, ω is k ′ -1 Represents the state of the k-1 th cycle;
if Δ Z k ' is less than or equal to 0, the optimal solution omega of the kth cycle is obtained k ' substitution of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation population A g+2 U th chromosome of
Otherwise, executing step 4.5.5;
step 4.5.5, if
The optimal solution omega for the kth cycle is then calculated k ' substitution of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation population A g+2 U th chromosome of
Otherwise, the optimal solution ω of the k-1 th cycle k ′ -1 Replacement of the u-th chromosome
Two genes with high medium fitness value and obtaining the g +2 generation population A g+2 U th chromosome of
Wherein r is k ' denotes a random number of the kth cycle, and r k ′∈[0,1]；
And 4.6, assigning g +2 to g, judging whether g > gmax is established or not, if so, indicating that a gmax generation population is obtained, selecting a chromosome with the highest fitness as an optimal identification parameter value of the corrected mining heavy load MF solid tire model, and otherwise, returning to the step 4.2 for sequential execution.
2. An electronic device comprising a memory and a processor, wherein the memory is used for storing a program that supports the processor to execute the parameter identification and optimization method of claim 1, and the processor is configured to execute the program stored in the memory.
3. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the parameter identification and optimization method according to claim 1.
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