CN115809608A - A parameter identification and optimization method for mining heavy-duty solid tires - Google Patents
A parameter identification and optimization method for mining heavy-duty solid tires Download PDFInfo
- Publication number
- CN115809608A CN115809608A CN202211704447.8A CN202211704447A CN115809608A CN 115809608 A CN115809608 A CN 115809608A CN 202211704447 A CN202211704447 A CN 202211704447A CN 115809608 A CN115809608 A CN 115809608A
- Authority
- CN
- China
- Prior art keywords
- chromosome
- cycle
- duty
- population
- tire model
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 239000007787 solid Substances 0.000 title claims abstract description 54
- 238000000034 method Methods 0.000 title claims abstract description 45
- 238000005065 mining Methods 0.000 title claims abstract description 30
- 238000005457 optimization Methods 0.000 title claims abstract description 29
- 238000012360 testing method Methods 0.000 claims abstract description 58
- 210000000349 chromosome Anatomy 0.000 claims description 83
- 108090000623 proteins and genes Proteins 0.000 claims description 27
- 230000006870 function Effects 0.000 claims description 26
- 238000002922 simulated annealing Methods 0.000 claims description 18
- 238000012937 correction Methods 0.000 claims description 13
- 230000035772 mutation Effects 0.000 claims description 13
- 238000001816 cooling Methods 0.000 claims description 11
- 238000000137 annealing Methods 0.000 claims description 8
- 238000004590 computer program Methods 0.000 claims description 8
- 238000003860 storage Methods 0.000 claims description 6
- 230000001174 ascending effect Effects 0.000 claims description 3
- 238000004422 calculation algorithm Methods 0.000 abstract description 37
- 238000011160 research Methods 0.000 abstract description 7
- 238000005516 engineering process Methods 0.000 description 13
- 230000002068 genetic effect Effects 0.000 description 13
- 238000004364 calculation method Methods 0.000 description 10
- 238000013461 design Methods 0.000 description 6
- 230000003044 adaptive effect Effects 0.000 description 5
- 238000004088 simulation Methods 0.000 description 5
- 238000004458 analytical method Methods 0.000 description 4
- 238000011156 evaluation Methods 0.000 description 4
- 239000003245 coal Substances 0.000 description 3
- 238000012356 Product development Methods 0.000 description 2
- 230000006399 behavior Effects 0.000 description 2
- 230000008901 benefit Effects 0.000 description 2
- 239000004568 cement Substances 0.000 description 2
- 150000001875 compounds Chemical class 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 239000011159 matrix material Substances 0.000 description 2
- 239000002184 metal Substances 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- 238000010845 search algorithm Methods 0.000 description 2
- 230000009466 transformation Effects 0.000 description 2
- 206010064571 Gene mutation Diseases 0.000 description 1
- 238000010367 cloning Methods 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 238000013016 damping Methods 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000004134 energy conservation Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000009916 joint effect Effects 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 239000002923 metal particle Substances 0.000 description 1
- 238000010791 quenching Methods 0.000 description 1
- 230000000171 quenching effect Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000010187 selection method Methods 0.000 description 1
- 238000004904 shortening Methods 0.000 description 1
- 230000004083 survival effect Effects 0.000 description 1
- 230000007704 transition Effects 0.000 description 1
- 238000009423 ventilation Methods 0.000 description 1
Images
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T10/00—Road transport of goods or passengers
- Y02T10/10—Internal combustion engine [ICE] based vehicles
- Y02T10/40—Engine management systems
Landscapes
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
本发明公开了一种用于矿用重载实心轮胎的参数辨识及优化方法,包括:1.按照矿用重载实心轮胎试验对轮胎进行试验操作,得到试验数据,2.基于试验数据,对矿用重载实心MF轮胎模型进行初次优化,得到第一目标函数值,并得到矿用重载MF实心轮胎模型,3.通过高斯牛顿迭代法初次辨识矿用重载MF实心轮胎模型中的参数,4.通过混合寻优算法对初次辨识得到的参数进行快速寻优、深度优化,得到准确度、精确度更高的参数。本发明能高效快速地辨识出矿用重载MF实心轮胎模型中的参数,易于实现,适应性好,识别精度高,适用于矿山典型路面环境和重载运输车辆的动力学和稳定性研究。
The invention discloses a parameter identification and optimization method for mining heavy-duty solid tires, including: 1. performing test operations on the tires according to the test of mine-used heavy-duty solid tires to obtain test data; 2. based on the test data, The mine heavy-duty solid MF tire model is optimized for the first time, and the first objective function value is obtained, and the mining heavy-duty MF solid tire model is obtained. 3. The parameters in the mining heavy-duty MF solid tire model are initially identified by Gauss-Newton iteration method , 4. Through the hybrid optimization algorithm, the parameters obtained by the initial identification are quickly optimized and deeply optimized to obtain parameters with higher accuracy and precision. The invention can efficiently and quickly identify the parameters in the mine heavy-duty MF solid tire model, is easy to implement, has good adaptability and high identification accuracy, and is suitable for the typical mine road environment and the dynamics and stability research of heavy-duty transport vehicles.
Description
技术领域technical field
本发明属于车辆技术领域,具体的说是一种用于矿用重载实心轮胎的参数辨识及优化方法。The invention belongs to the technical field of vehicles, in particular to a parameter identification and optimization method for mining heavy-duty solid tires.
背景技术Background technique
地面车辆技术和计算机信息技术的快速发展,无论是对传统汽车还是新能源车辆,车辆设计越来越趋向于高效化、信息化等,信息技术特别是计算机仿真技术在汽车工业中的应用,极大方便了产品的设计研发,提高了产品的质量,给生产企业以及相关科研机构提供了有效的帮助,其中车辆仿真分析技术可实现产品的性能及其可制造性的前期预测和分析,从而缩短产品设计与制造周期,降低产品开发成本,提高研发设计系统决速响应市场变化的能力。With the rapid development of ground vehicle technology and computer information technology, whether it is for traditional vehicles or new energy vehicles, vehicle design tends to be more efficient and informatized, and the application of information technology, especially computer simulation technology, in the automotive industry is extremely important. It greatly facilitates the design and development of products, improves the quality of products, and provides effective help to manufacturers and related scientific research institutions. Among them, vehicle simulation analysis technology can realize the early prediction and analysis of product performance and manufacturability, thereby shortening the production time. Product design and manufacturing cycles reduce product development costs and improve the ability of the R&D design system to quickly respond to market changes.
在国家节能减排的号召下,煤矿存在减员增效、提高煤矿安全和降低事故发生率的客观要求,迫切需要发展清洁、高效、智能化的煤机装备,实现机械化减人。随着矿用车辆产业的迅速壮大以及市场保有量的大幅提高,矿用车辆由于防爆改造后整体性能及参数难以达到合理配置,而井下行驶路况复杂速度受限,加之通风条件较差,与同等设计能力的地面车辆相比存在明显的效率低下、安全性差、工况适应性较差的痛点,急需借鉴地面车辆技术和计算机信息技术,特别是车辆仿真技术,提升动力性能。Under the call of the state for energy conservation and emission reduction, coal mines have the objective requirements of reducing staff and increasing efficiency, improving coal mine safety and reducing the incidence of accidents. There is an urgent need to develop clean, efficient and intelligent coal machinery equipment to achieve mechanization and reduce manpower. With the rapid expansion of the mining vehicle industry and the substantial increase in market inventory, it is difficult to achieve a reasonable configuration of the overall performance and parameters of mining vehicles due to explosion-proof transformation, and the speed of underground driving is complicated due to complex road conditions, coupled with poor ventilation conditions. Compared with ground vehicles with design capabilities, there are obvious pain points of low efficiency, poor safety, and poor adaptability to working conditions. It is urgent to learn from ground vehicle technology and computer information technology, especially vehicle simulation technology, to improve power performance.
矿山车辆重载实心橡胶轮胎作为矿山车辆与地面直接接触的部件,其力学性能直接影响车辆动力学和行驶平顺特性,与常规轮胎相比,轮胎结构、材料特性以及胎路滚滑接触机理方面与常规充气轮胎模型均有一定的差别,具有橡胶实心、阻尼低、花纹粗大、扁平率大等特点。因而,采用传统方法中的充气轮胎模型及经验参数对矿山车辆进行动力学建模及仿真计算时,很可能产生较大的模型失配误差,也就无法准确描述矿山重载车辆的实际运动状态,并对其行为进行精准调控,成为长期制约矿山车辆动力学和稳定性研究的关键难题,始终未得到根本解决。因此,考虑到胎路接触力学特性对车辆横向稳定性能调控的重要影响,研究矿山车辆重载牵引实心橡胶轮胎在道水泥路面上的非线性滚滑接触力学特性,针对性地根据轮胎材料、几何结构特征等对重载实心或填充胎的模型参数进行准确辨识,建立适用于矿山典型路面环境和重载运输车辆轮胎力的求解模型显得尤为重要。Heavy-duty solid rubber tires for mining vehicles are components that directly contact the ground, and their mechanical properties directly affect vehicle dynamics and ride comfort characteristics. Conventional pneumatic tire models have certain differences, and have the characteristics of solid rubber, low damping, thick patterns, and large flattening ratio. Therefore, when using the pneumatic tire model and empirical parameters in the traditional method for dynamic modeling and simulation calculation of mining vehicles, it is likely to produce large model mismatch errors, and it is impossible to accurately describe the actual motion state of mining heavy-duty vehicles , and the precise control of its behavior has become a key problem that has long restricted the research on the dynamics and stability of mining vehicles, and has not been fundamentally resolved. Therefore, considering the important influence of tire-road contact mechanical properties on vehicle lateral stability regulation, the non-linear rolling-sliding contact mechanical properties of heavy-duty traction solid rubber tires of mining vehicles on road cement pavement are studied, and the tire material, geometric It is particularly important to accurately identify the model parameters of heavy-duty solid or filled tires based on structural characteristics, and to establish a solution model suitable for the typical mine road environment and heavy-duty transport vehicle tire forces.
建立合理的轮胎动力学模型,分析轮胎所受到的纵向力、侧向力、垂直载荷以及回正力矩对车辆的动力性、操纵稳定性、制动稳定性、乘坐适性以及行驶安全性的影响是车辆仿真技术的重要组成部分,对产品开发和整车性能分析起到关键作用,所以轮胎模型的精度直接影响车辆产品关键技术研究。目前矿用车辆在该技术方面的研究主要采用移植地面相关技术的方法,地面车辆动力学在分析轮胎的侧偏性能等方面一般采用基于试验数据得到的经验型模型公式,该公式由三角函数的组合拟合得到,可完整地表达轮胎所受到的纵向力、回正力矩、翻转力矩以及阻力距分别和纵向力、侧向力的联合作用工况。但该公式本身便具有参数多、高度非线性化的特点,对其中参数的辨识较为困难,采用的算法收敛速度慢、实时性欠佳。加之矿用车辆本身的结构特殊性和行驶路况条件复杂多变,使得参数辨识难上加难,急需提升车辆仿真技术在研究和评价轮胎模型参数的辨识精度方面的水平。Establish a reasonable tire dynamics model to analyze the impact of the longitudinal force, lateral force, vertical load and aligning moment on the vehicle's dynamic performance, handling stability, braking stability, ride comfort and driving safety It is an important part of vehicle simulation technology and plays a key role in product development and vehicle performance analysis, so the accuracy of the tire model directly affects the key technology research of vehicle products. At present, the research on this technology of mining vehicles mainly adopts the method of transplanting related technologies on the ground. The dynamics of ground vehicles generally adopts the empirical model formula obtained based on test data in the aspect of analyzing tire cornering performance, which is composed of trigonometric functions. Combination fitting is obtained, which can completely express the joint action conditions of longitudinal force, righting moment, overturning moment and drag distance respectively and longitudinal force and lateral force on the tire. However, the formula itself has the characteristics of many parameters and high nonlinearity, and it is difficult to identify the parameters. The algorithm adopted has a slow convergence speed and poor real-time performance. In addition, the structural particularity of the mining vehicle itself and the complex and changeable driving conditions make parameter identification even more difficult. It is urgent to improve the level of vehicle simulation technology in researching and evaluating the identification accuracy of tire model parameters.
综上所述,如何建立矿用轮胎的参数辨识及优化方法,是本领域技术人员亟待解决的技术问题。To sum up, how to establish a parameter identification and optimization method for mining tires is a technical problem to be solved urgently by those skilled in the art.
发明内容Contents of the invention
本发明是为了解决上述现有技术存在的不足之处,提出一种用于矿用重载实心轮胎的参数辨识及优化方法,以期能高效快速地辨识出矿用重载MF实心轮胎模型中的参数,并达到计算效率高、全局求解能力强、精度高的效果,从而能从根本上提高整车的动力性能。The present invention aims to solve the shortcomings of the above-mentioned prior art, and proposes a parameter identification and optimization method for mining heavy-duty solid tires, in order to efficiently and quickly identify the parameters in the mining heavy-duty MF solid tire model. parameters, and achieve the effects of high calculation efficiency, strong global solution ability, and high precision, which can fundamentally improve the dynamic performance of the vehicle.
本发明为达到上述发明目的,采用如下技术方案:The present invention adopts following technical scheme in order to achieve the above-mentioned purpose of the invention:
本发明一种用于矿用重载实心轮胎的参数辨识及优化方法的特点在于,是按以下步骤进行:A kind of parameter identification and optimization method for mining heavy-duty solid tires of the present invention is characterized in that it is carried out according to the following steps:
步骤1、按照矿用重载实心轮胎试验对轮胎进行试验操作,得到试验数据,并利用试验数据构建矿用重载实心MF轮胎模型;Step 1. Carry out the test operation on the tire according to the mine heavy-duty solid tire test, obtain the test data, and use the test data to construct the mine heavy-duty solid MF tire model;
步骤1.1、定义当前测试次数为s,并初始化s=1;Step 1.1, define the current number of tests as s, and initialize s=1;
步骤1.2、将矿山车辆重载橡胶实心牵引的轮胎样件通过六分力测试实验台进行第s次测试,获取第s次测试下的n组试验数据其中,表示第s次测试下的任意第i组试验数据,且 表示第i组试验数据xi中的第j个特征量,并将第i组试验数据中第j个特征量的拟合值记作 的试验值记作m表示特征量的总数;Step 1.2, carry out the s-th test on the tire sample of the heavy-duty rubber solid traction of the mining vehicle through the six-component force test bench, and obtain the n-group test data under the s-th test in, represents any i-th test data under the s-th test, and Indicates the jth feature quantity in the i-th group of experimental data x i , and the i-th group of experimental data The jth feature quantity in The fitting value of is denoted as The test value of m represents the total number of feature quantities;
步骤1.3、利用式(1)建立半经验轮胎模型在第s次测试时的目标函数Zs:Step 1.3, using formula (1) to establish the objective function Z s of the semi-empirical tire model during the s-th test:
步骤1.4、将s+1赋值给s后,判断s>Smax是否成立,若成立,则执行步骤2,否则,返回步骤1.2顺序执行,其中,Smax表示最大试验次数;Step 1.4, after assigning s+1 to s, judge whether s>Smax is true, if true, execute step 2, otherwise, return to step 1.2 and execute sequentially, where Smax represents the maximum number of trials;
步骤2、将Smax次测试时的目标函数值进行升序排序,得到排序后的第一目标函数值作为半经验轮胎模型的初值,从而得到矿用重载MF实心轮胎模型;Step 2, sort the objective function values during the Smax times of testing in ascending order, and obtain the sorted first objective function value as the initial value of the semi-empirical tire model, thereby obtaining the mine heavy-duty MF solid tire model;
步骤3、将通过高斯牛顿迭代法辨识所述矿用重载MF实心轮胎模型中的参数:Step 3, will identify the parameters in the mine heavy-duty MF solid tire model by Gauss-Newton iteration method:
步骤3.1、对矿用重载MF实心轮胎模型进行泰勒级数展开,并删除二阶及二阶以上的偏导数项,得到非线性回归轮胎模型;Step 3.1, carrying out Taylor series expansion on the mine heavy-duty MF solid tire model, and deleting the second-order and above partial derivative items to obtain a nonlinear regression tire model;
步骤3.2、定义当前迭代次数为v,并初始化v=1;Step 3.2, define the current number of iterations as v, and initialize v=1;
步骤3.3、用最小平方法第v次对所述非线性回归轮胎模型进行估计,得到第v次估计的修正因子;Step 3.3, using the least squares method to estimate the nonlinear regression tire model for the vth time, and obtain the correction factor for the vth estimation;
步骤3.4、计算第v次估计的修正因子的残差平方和SSRv;Step 3.4, calculate the residual sum of squares SSR v of the correction factor estimated for the vth time;
步骤3.5、辨识待回归系数:Step 3.5, identify the coefficients to be regressed:
对于给定的允许误差率k,当时,停止迭代,并将得到第v次估计的修正因子代入所述非线性回归轮胎模型中,得到修正后的矿用重载MF实心轮胎模型;否则,将v+1赋值给v后,返回步骤3.3顺序执行;For a given allowable error rate k, when , stop the iteration, and substitute the correction factor estimated for the vth time into the nonlinear regression tire model to obtain the revised mine heavy-duty MF solid tire model; otherwise, after assigning v+1 to v, return Step 3.3 is executed sequentially;
步骤4、根据修正后的矿用重载MF实心轮胎模型中待辨识的参数值,产生初始种群;Step 4. Generate an initial population according to the parameter values to be identified in the revised mine heavy-duty MF solid tire model;
步骤4.1、设定种群规模为U,定义种群的当前代数为g;并初始化g=1;Step 4.1, set the population size as U, define the current generation of the population as g; and initialize g=1;
将修正后的矿用重载MF实心轮胎模型中的所有待辨识参数值作为第g代种群中第u个染色体从而得到第g代种群集合记为 All the parameter values to be identified in the revised mine heavy-duty MF solid tire model are taken as the u-th chromosome in the g-th generation population Thus, the population set of the gth generation is obtained and denoted as
步骤4.2、根据式(1)计算得到第g代种群Ag中第u个染色体的适应度值并将第u个染色体中适应度值最高的两个基因进行交叉操作后,得到第u个染色体的两个新基因,用于替换第u个染色体中适应度值最高的两个基因,从而得到更新后的第u个染色体进而得到更新后的第g代种群A′g;Step 4.2, calculate according to formula (1) to obtain the uth chromosome in the gth generation population A g fitness value and put the uth chromosome After the two genes with the highest fitness value are crossed over, the uth chromosome is obtained Two new genes of , used to replace the u-th chromosome The two genes with the highest fitness values in , so as to get the updated uth chromosome And then get the updated g generation population A′ g ;
步骤4.3、将第u个染色体的两个新基因作为模拟退火算子的初始最优解并进行退火操作:Step 4.3, the u-th chromosome The two new genes of are used as the initial optimal solution of the simulated annealing operator and are annealed:
步骤4.3.1、定义退火操作的当前循环次数为k,并初始化k=0;Step 4.3.1, define the current number of cycles of the annealing operation as k, and initialize k=0;
令第k次循环的温度Tk,随机产生当前第k次循环的状态ωk为第k次循环的最优解;Let the temperature T k of the k-th cycle randomly generate the state ω k of the current k-th cycle as the optimal solution of the k-th cycle;
步骤4.3.2、令第k+1次循环的温度Tk+1=αTk;其中,α表示退温因子,0<α<1;Step 4.3.2, set the temperature T k+1 of the k+1th cycle = αT k ; where α represents the cooling factor, 0<α<1;
步骤4.3.3、将k+1赋值给k后,根据Tk得到第k次循环的状态ωk,并作为第k次循环的最优解ωk;Step 4.3.3. After assigning k+1 to k, obtain the state ω k of the k-th cycle according to T k , and use it as the optimal solution ω k of the k-th cycle;
步骤4.3.4、令第k次循环的增量为ΔZk=Z(ωk)-Z(ωk-1),其中,Z表示半经验轮胎模型的目标函数;ωk-1表示第k-1次循环的状态;Step 4.3.4. Let the increment of the k-th cycle be ΔZ k =Z(ω k )-Z(ω k-1 ), where Z represents the objective function of the semi-empirical tire model; ω k-1 represents the k-th -1 cycle status;
若ΔZk≤0,则将第k次循环的最优解ωk替换第u个染色体的两个新基因并得到第g+1代种群Ag+1的第u个染色体否则,执行步骤4.3.5;If ΔZ k ≤ 0, replace the u-th chromosome with the optimal solution ω k of the k-th cycle and get the uth chromosome of population A g+1 of g+ 1th generation Otherwise, perform step 4.3.5;
步骤4.3.5、若则将第k次循环的最优解ωk替换第u个染色体的两个新基因并得到第g+1代种群Ag+1的第u个染色体否则,第k-1次循环的最优解ωk-1替换第u个染色体的两个新基因并得到第g+1代种群Ag+1的第u个染色体其中,ε表示系数;rk表示第k次循环的随机数,且rk∈[0,1];Step 4.3.5, if Then replace the u-th chromosome with the optimal solution ω k of the k-th cycle and get the uth chromosome of population A g+1 of g+ 1th generation Otherwise, the optimal solution ω k-1 of the k-1th cycle replaces the u-th chromosome and get the uth chromosome of population A g+1 of g+ 1th generation Among them, ε represents the coefficient; r k represents the random number of the kth cycle, and r k ∈ [0,1];
步骤4.4、按照变异概率Pm对第g+1代种群Ag+1中任意第j条染色体进行变异操作,得到新的染色体若第g+1代的第j个增量则将新的染色体加入第g+1代种群Ag+1,并得到更新后的第g+1代种群A′g+1,否则,在[0,1]之间产生第g+1代的第j个随机数若则将新的染色体加入第g+1代种群Ag+1,并得到更新后的第g+1代种群A′g+1,否则,将第j条染色体仍然保持在第g+1代种群Ag+1中,其中,tj表示第j个退温函数;Step 4.4, according to the mutation probability P m, any jth chromosome in the g+1th generation population A g+1 Perform mutation operations to obtain new chromosomes If the jth increment of the g+1th generation the new chromosome Join the g+1th generation population A g+1 , and get the updated g+1th generation population A′ g+1 , otherwise, generate the jth random number like the new chromosome Join the g+1th generation population A g+1 , and get the updated g+1th generation population A′ g+1 , otherwise, the jth chromosome Still remain in the g+1th generation population A g+1 , where t j represents the jth cooling function;
步骤4.5、根据式(1)计算更新后的第g+1代种群A′g+1中第u个染色体的适应度值判第u个染色体中适应度值高的两个基因作为模拟退火算子的初始最优解并进行退火操作:Step 4.5. Calculate the uth chromosome in the updated g+1th generation population A' g+1 according to formula (1) fitness value judge the uth chromosome The two genes with high fitness values are used as the initial optimal solution of the simulated annealing operator and annealed:
步骤4.5.1、初始化退火操作的当前循环次数k=0;Step 4.5.1, initializing the current number of cycles of the annealing operation k=0;
令第k次循环的温度Tk′,随机产生当前第k次循环的状态ωk′为第k次循环的最优解;Let the temperature T k ′ of the k-th cycle randomly generate the state ω k ′ of the current k-th cycle as the optimal solution of the k-th cycle;
步骤4.5.2、令第k+1次循环的温度Tk′+1=αTk′;其中,α表示退温因子,0<α<1;Step 4.5.2, let the temperature T k ′ + 1 of the k+1th cycle = αT k ′; where α represents the cooling factor, 0<α<1;
步骤4.5.3、将k+1赋值给k后,根据Tk′得到第k次循环的状态ωk′,并作为第k次循环的最优解ωk′;Step 4.5.3, after assigning k+1 to k, obtain the state ω k ′ of the k-th cycle according to T k ′, and use it as the optimal solution ω k ′ of the k-th cycle;
步骤4.5.4、令第k次循环的增量为ΔZk′=Z(ωk′)-Z(ωk′-1),其中,ωk′-1表示第k-1次循环的状态;Step 4.5.4. Let the increment of the kth cycle be ΔZ k ′=Z(ω k ′)-Z(ω k ′ -1 ), where ω k ′ -1 represents the state of the k-1th cycle ;
若ΔZk′≤0,则将第k次循环的最优解ωk′替换第u个染色体中适应度值高的两个基因并得到第g+2代种群Ag+2的第u个染色体否则,执行步骤4.5.5;If ΔZ k ′≤0, replace the uth chromosome with the optimal solution ω k ′ of the kth cycle Two genes with high fitness value and get the uth chromosome of the g+2th generation population A g+2 Otherwise, go to step 4.5.5;
步骤4.5.5、若则将第k次循环的最优解ωk′替换第u个染色体中适应度值高的两个基因并得到第g+2代种群Ag+2的第u个染色体否则,第k-1次循环的最优解ωk′-1替换第u个染色体中适应度值高的两个基因并得到第g+2代种群Ag +2的第u个染色体其中,rk′表示第k次循环的随机数,且rk′∈[0,1];Step 4.5.5, if Then replace the u-th chromosome with the optimal solution ω k ′ of the k-th cycle Two genes with high fitness value and get the uth chromosome of the g+2th generation population A g+2 Otherwise, the optimal solution ω k ′ -1 of the k-1th cycle replaces the uth chromosome Two genes with high fitness value and get the uth chromosome of the g+2 generation population A g +2 Among them, r k ′ represents the random number of the kth cycle, and r k ′∈[0,1];
步骤4.6、将g+2赋值给g后,判断g>gmax是否成立,若成立,则表示得到第gmax代种群,并选择适应度最高的染色体作为修正后的矿用重载MF实心轮胎模型的最优辨识参数值,否则,返回步骤4.2顺序执行。Step 4.6. After assigning g+2 to g, judge whether g>gmax is established. If it is established, it means that the gmax generation population is obtained, and the chromosome with the highest fitness is selected as the corrected mine heavy-duty MF solid tire model. The optimal identification parameter value, otherwise, return to step 4.2 and execute sequentially.
本发明一种电子设备,包括存储器以及处理器的特点在于,所述存储器用于存储支持处理器执行所述参数辨识及优化方法的程序,所述处理器被配置为用于执行所述存储器中存储的程序。An electronic device according to the present invention, comprising a memory and a processor, is characterized in that the memory is used to store a program that supports the processor to execute the parameter identification and optimization method, and the processor is configured to execute the program in the memory stored program.
本发明一种计算机可读存储介质,计算机可读存储介质上存储有计算机程序的特点在于,所述计算机程序被处理器运行时执行所述参数辨识及优化方法的步骤。The present invention is a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the parameter identification and optimization method when the computer program is run by a processor.
与现有技术相比,本发明的方法在适用于矿山典型路面环境和重载运输工况基础上,按照矿用重载实心轮胎试验对轮胎进行试验操作采集得到试验数据,然后基于半经验型轮胎模型建立优化模型及评价指标,将识别得到的参数带入到轮胎模型中,相同条件下计算结果与实际测试数值差值的平方根最小则对应的解最优,即希望较小目标函数值对应解的适应度值高。首先利用高斯牛顿法算将待辨识函数泰勒展开,忽略二阶及二阶以上的偏导数项,迭代得到非线性回归轮胎模型,用最小平方法估计非线性回归轮胎模型辨识待回归系数,得到修正后的矿用重载MF实心轮胎模型;通过遗传算法和模拟退火算法对初次辨识参数进行深度寻优,每代种群中最优解用模拟退火算法进行再次搜索,增强算法的搜索能力,并通过模拟退火算法保持种群的多样性,避免了种群收敛于某一局部区域。该方法能够实现对常用轮胎经验公式中的参数自适应调整、最终辨识及优化,获得的参数辨识值用于计算和分析轮胎在复杂工况下的受力情况,指导整车设计,是车辆仿真分析技术的重要组成部分。该方法目的性强,收敛速度非常快,并且求解精度高。具体优点为:Compared with the prior art, the method of the present invention is applicable to the typical mine road surface environment and heavy-duty transportation conditions, according to the mine-used heavy-duty solid tire test, the tires are tested and collected to obtain test data, and then based on semi-empirical The tire model establishes an optimization model and evaluation index, and brings the identified parameters into the tire model. Under the same conditions, the square root of the difference between the calculation result and the actual test value is the smallest, and the corresponding solution is optimal, that is, it is hoped that the smaller objective function value corresponds to The fitness value of the solution is high. First, the Gauss-Newton method is used to expand the function to be identified by Taylor, ignoring the second-order and above-order partial derivatives, and iteratively obtains the nonlinear regression tire model, and the least square method is used to estimate the nonlinear regression tire model to identify the coefficients to be regressed, and the correction is obtained The final heavy-duty MF solid tire model for mines; through the genetic algorithm and simulated annealing algorithm, the initial identification parameters are deeply optimized, and the optimal solution in each generation population is searched again with the simulated annealing algorithm to enhance the search ability of the algorithm, and through The simulated annealing algorithm maintains the diversity of the population and prevents the population from converging on a certain local area. This method can realize the adaptive adjustment, final identification and optimization of the parameters in the common tire empirical formula. The obtained parameter identification value is used to calculate and analyze the force of the tire under complex working conditions, and guide the design of the whole vehicle. An important part of analytical techniques. This method has strong purpose, very fast convergence speed, and high solution accuracy. The specific advantages are:
1.本发明提出辨识目标函数建立优化模型及评价指标,将高斯牛顿迭代法、遗传算法与自适应模拟退火算法相结合,首先选用高斯牛顿迭代法对试验采样数据进行初次辨识主要参数,再用遗传算法对初次辨识结果进行优化再辨识,每代种群中最优解用模拟退火算法进行再次搜索,增强算法的搜索能力,最后用自适应模拟退火算法跳出局部最优解,寻找全局最优解,保持种群的多样性,搜索能力强、运行时间短且求解精度高,容易实现,针对矿山车辆轮胎垂向载荷范围大所导致的强非线性特点,传统算法固定的参数设置与寻优策略难以适应的状况,本发明的方法能够通过六分力测试设备获取相关试验数据,对复杂工况下的轮胎模型参数进行辨识,进一步通过进行不同载荷工况下整车牵引特性实车实验,试验结果表明,与单纯的遗传算法在算法性能上相比,辨识模型的准确性大大提升,解决了矿山车辆重载牵引实心轮胎模型参数多、高度非线性导致准确建模难度大的痛点,计算效率和计算速度高。为建立适用于矿山典型路面环境和重载运输车辆轮胎力的求解模型提供了最佳的辨识算法。1. The present invention proposes to identify the objective function to establish an optimization model and an evaluation index, combine the Gauss-Newton iterative method, the genetic algorithm and the adaptive simulated annealing algorithm, first select the Gauss-Newton iterative method to first identify the main parameters of the test sampling data, and then The genetic algorithm optimizes and re-identifies the initial identification results, and the optimal solution in each generation population is searched again with the simulated annealing algorithm to enhance the search ability of the algorithm. Finally, the adaptive simulated annealing algorithm is used to jump out of the local optimal solution and find the global optimal solution , maintain the diversity of the population, have strong search ability, short running time and high solution accuracy, and are easy to implement. In view of the strong nonlinear characteristics caused by the large vertical load range of mining vehicle tires, the fixed parameter settings and optimization strategies of traditional algorithms are difficult to solve. To adapt to the situation, the method of the present invention can obtain relevant test data through the six-component force testing equipment, identify the tire model parameters under complex working conditions, and further conduct real vehicle experiments on the traction characteristics of the whole vehicle under different load conditions, and the test results It shows that compared with the pure genetic algorithm in terms of algorithm performance, the accuracy of the identification model is greatly improved, and it solves the pain points of the heavy-duty traction solid tire model of mining vehicles, which has many parameters and is highly nonlinear, which makes accurate modeling difficult. The calculation efficiency and High calculation speed. It provides the best identification algorithm for establishing a solution model suitable for the typical mine road environment and the tire force of heavy-duty transport vehicles.
2.本发明采用的混合寻优算法的优点为:鉴于胎路接触力学特性对车辆横向稳定性能调控的重要影响,该算法通过研究矿山车辆重载牵引实心橡胶轮胎在道水泥路面上的非线性滚滑接触力学特性,针对性地根据轮胎材料、几何结构特征等对重载实心或填充胎的模型参数进行准确辨识,建立适用于矿山典型路面环境和重载运输车辆轮胎力的求解模型。该算法在矿山车辆重载牵引实心轮胎模型某一工况下,如纯纵滑模式下纵向力参数辨识全局寻优及快速收敛能力上较遗传算法有较大的提高,收敛至全局最优的成功率达到70%,较遗传算法增加50%以上,收敛至全局最优的平均代数上减小35%以上,收敛至全局最优的总时间增加了6%,收敛至全局最优的平均时间减小30%以上;纯纵滑工况下纵向力辨识目标函数评价指标较单一遗传算法分别提升了10%以上。2. The advantage of the mixed optimization algorithm adopted in the present invention is: in view of the important impact of tire road contact mechanical characteristics on the regulation and control of vehicle lateral stability, this algorithm is by studying the nonlinearity of the heavy-duty traction solid rubber tire of the mine vehicle on the road cement road surface. Rolling-sliding contact mechanical properties, accurately identify the model parameters of heavy-duty solid or filled tires based on tire materials and geometric structure characteristics, and establish a solution model suitable for typical mine road environments and heavy-duty transport vehicle tire forces. Compared with the genetic algorithm, the algorithm has a greater improvement in the global optimization and rapid convergence ability of the longitudinal force parameter identification in the pure longitudinal sliding mode under a certain working condition of the solid tire model of the heavy-duty traction of the mining vehicle, and converges to the global optimal The success rate reaches 70%, an increase of more than 50% compared with the genetic algorithm, the average algebra of convergence to the global optimum is reduced by more than 35%, the total time of convergence to the global optimum has increased by 6%, and the average time of convergence to the global optimum It is reduced by more than 30%; the evaluation index of the objective function of longitudinal force identification under the pure longitudinal sliding condition is increased by more than 10% compared with the single genetic algorithm.
本发明方法基于PAC2002魔术公式基础模型,在修正提出矿山车辆重载牵引实心轮胎复合工况数学模型基础上提出混合寻优算法进行参数辨识,并对结果加以验证,其表明提出的混合寻优算法辨识稳定性更好,识别精度也更高。依据辨识参数计算得到的轮胎纵向牵引力与实车实验结果之间的偏差不超过4%,验证了辨识模型的有效性,为准确描述矿山重载车辆的实际运动状态,并对其行为进行精准调控奠定了基础,攻克了长期制约矿山车辆动力学和稳定性研究的关键难题。The method of the present invention is based on the PAC2002 magic formula basic model, on the basis of correcting and proposing the mathematical model of the compound working condition of heavy-duty traction solid tires of mine vehicles, a hybrid optimization algorithm is proposed for parameter identification, and the results are verified, which shows that the proposed hybrid optimization algorithm The recognition stability is better, and the recognition accuracy is also higher. The deviation between the tire longitudinal traction calculated according to the identification parameters and the real vehicle test results is no more than 4%, which verifies the validity of the identification model. In order to accurately describe the actual state of motion of heavy-duty mine vehicles and precisely control their behavior The foundation has been laid and the key problems that have long restricted the study of mine vehicle dynamics and stability have been overcome.
附图说明Description of drawings
图1为本发明混合寻优算法参数辨识流程图;Fig. 1 is the flowchart of parameter identification of hybrid optimization algorithm of the present invention;
图2为本发明混合寻优算法进化曲线图。Fig. 2 is an evolution curve diagram of the hybrid optimization algorithm of the present invention.
具体实施方式Detailed ways
本实施例中,如图1所示,一种用于矿用重载实心轮胎的参数辨识及优化方法,是按以下步骤进行:In this embodiment, as shown in Figure 1, a parameter identification and optimization method for mining heavy-duty solid tires is carried out in the following steps:
步骤1、按照矿用重载实心轮胎试验对轮胎进行试验操作,得到试验数据,并利用试验数据构建矿用重载实心MF轮胎模型;Step 1. Carry out the test operation on the tire according to the mine heavy-duty solid tire test, obtain the test data, and use the test data to construct the mine heavy-duty solid MF tire model;
对轮胎进行不同工况下相应力学特性的试验,通过试验中传感器检测并采集得各工况下轮胎模型中的各项数据,包括自变量与因变量,如侧向力、回正力矩或纵向力,以及不同工况下分别对应的轮胎的侧偏角或纵向滑移率等。Carry out tests on the corresponding mechanical properties of tires under different working conditions, and collect various data in the tire model under each working condition through the detection and collection of sensors in the test, including independent variables and dependent variables, such as lateral force, righting moment or longitudinal force, and the side slip angle or longitudinal slip rate of the tire corresponding to different working conditions.
步骤1.1、定义当前测试次数为s,并初始化s=1;Step 1.1, define the current number of tests as s, and initialize s=1;
步骤1.2、将矿山车辆重载橡胶实心牵引的轮胎样件通过六分力测试实验台进行第s次测试,获取第s次测试下的n组试验数据其中,表示第s次测试下的任意第i组试验数据,且 表示第i组试验数据xi中的第j个特征量,并将第i组试验数据中第j个特征量的拟合值记作 的试验值记作m表示特征量的总数;Step 1.2, carry out the s-th test on the tire sample of the heavy-duty rubber solid traction of the mining vehicle through the six-component force test bench, and obtain the n-group test data under the s-th test in, represents any i-th test data under the s-th test, and Indicates the jth feature quantity in the i-th group of experimental data x i , and the i-th group of experimental data The jth feature quantity in The fitting value of is denoted as The test value of m represents the total number of feature quantities;
步骤1.3、利用式(1)建立半经验轮胎模型在第s次测试时的目标函数Zs:Step 1.3, using formula (1) to establish the objective function Z s of the semi-empirical tire model during the s-th test:
步骤1.4、将s+1赋值给s后,判断s>Smax是否成立,若成立,则执行步骤2,否则,返回步骤1.2顺序执行,其中,Smax表示最大试验次数。Step 1.4: After assigning s+1 to s, judge whether s>Smax is true, if true, execute step 2, otherwise, return to step 1.2 and execute sequentially, where Smax represents the maximum number of trials.
步骤2、将Smax次测试时的目标函数值进行升序排序,得到排序后的第一目标函数值作为半经验轮胎模型的初值,从而得到矿用重载MF实心轮胎模型。Step 2. Sorting the objective function values in ascending order for the Smax times of testing, and obtaining the first objective function value after sorting as the initial value of the semi-empirical tire model, thereby obtaining the heavy-duty MF solid tire model for mine use.
步骤3、将通过高斯牛顿迭代法辨识矿用重载MF实心轮胎模型中的参数:Step 3. The parameters in the mining heavy-duty MF solid tire model will be identified by the Gauss-Newton iterative method:
采用高斯牛顿迭代法先初次辨识目标函数中的主要参数,主要是对步骤1中采样到的数据进行非线性最小二乘估计、迭代修正,使回归系数不断逼近非线性回归模型的最佳回归系数,最后使原模型的残差平方和达到最小,初次辨识得到目标函数中的参数值。The Gauss-Newton iterative method is used to first identify the main parameters in the objective function, mainly to perform nonlinear least squares estimation and iterative correction on the data sampled in step 1, so that the regression coefficient is continuously approaching the best regression coefficient of the nonlinear regression model , and finally the residual sum of squares of the original model is minimized, and the parameter values in the objective function are obtained from the initial identification.
高斯牛顿迭代法通过初始值的选择、泰勒级数展开式、估计修正因子、精确度的检验及重复迭代五部分进行辨识参数值,在选定或求出迭代初始值后,通过使用泰勒级数展开式去近似地代替非线性回归模型,然后通过多次迭代,多次修正回归系数,使回归系数不断逼近非线性回归模型的最佳回归系数,最后使原模型的残差平方和达到最小。高斯牛顿法最大的特点在于它克服了当模型非线性强度较高时,用线性近似进行参数估计所产生的较大模型误差问题,解算精度高;同时,它在原理上与线性最小二乘近似,公式构造简单,具有快速收敛能力,因此应用起来极为方便,目前仍是广泛应用的非线性最小二乘估计方法。高斯牛顿法的一般步骤为:The Gauss-Newton iterative method identifies parameter values through five parts: initial value selection, Taylor series expansion, estimated correction factor, accuracy test, and repeated iterations. After selecting or calculating the iterative initial value, the Taylor series is used to The expansion formula approximately replaces the nonlinear regression model, and then through multiple iterations, the regression coefficient is revised multiple times, so that the regression coefficient is continuously approaching the optimal regression coefficient of the nonlinear regression model, and finally the residual sum of squares of the original model is minimized. The biggest feature of the Gauss-Newton method is that it overcomes the large model error problem caused by linear approximation for parameter estimation when the nonlinear strength of the model is high, and the solution accuracy is high; at the same time, it is in principle the same as the linear least squares Approximation, the formula is simple in structure and has fast convergence ability, so it is very convenient to apply, and it is still a widely used nonlinear least squares estimation method. The general steps of the Gauss-Newton method are:
步骤3.1、对矿用重载MF实心轮胎模型进行泰勒级数展开,并删除二阶及二阶以上的偏导数项,得到非线性回归轮胎模型;Step 3.1, carrying out Taylor series expansion on the mine heavy-duty MF solid tire model, and deleting the second-order and above partial derivative items to obtain a nonlinear regression tire model;
(1)初始值的选择,其方法有三种,一是根据以往的经验选定初始值,二是用分段法求出初始值;三是对于可线性化的非线性回归模型,通过线性变换,然后施行最小平方法求出初始值。(1) There are three ways to select the initial value, one is to select the initial value based on previous experience, the other is to use the segment method to obtain the initial value; the third is to use linear transformation for the nonlinear regression model that can be linearized , and then implement the least square method to find the initial value.
(2)泰勒级数展开式,设非线性回归模型为:(2) Taylor series expansion, let the nonlinear regression model be:
式(2)中,r为待回归系数,xi为待辨识参数,为方程输出值,误差项εi~N(0,σ2),设为待回归系数r=(r0,r1,…,rp-1)T的初始值,将公式(2)的f(xi,r)在g0点附近作泰勒展开,并略去非线性回归模型的二阶及二阶以上的偏导数项,得:In formula (2), r is the coefficient to be regressed, x i is the parameter to be identified, is the output value of the equation, the error term ε i ~N(0,σ 2 ), let To be the initial value of regression coefficient r=(r 0 ,r 1 ,…,r p-1 ) T , make Taylor expansion of f( xi ,r) in formula (2) around point g 0 , and omit The partial derivative terms of the second order and above the second order of the nonlinear regression model, get:
将式(3)代入式(2),则:Substituting formula (3) into formula (2), then:
移项:Transition:
令 make
则: but:
用矩阵的形式表示上式则为:Expressing the above formula in matrix form is:
Y(0)≈D(0)b(0)+ε (4)Y (0) ≈ D (0) b (0) +ε (4)
式(4)中: In formula (4):
步骤3.2、定义当前迭代次数为v,并初始化v=1;Step 3.2, define the current number of iterations as v, and initialize v=1;
步骤3.3、用最小平方法对式(4)的非线性回归轮胎模型进行第v次估计修正因子,则第v次迭代的修正因子b(v):Step 3.3, use the least squares method to estimate the correction factor for the vth nonlinear regression tire model of formula (4), then the correction factor b (v) of the vth iteration:
b(v)=(D(v)TD(v))-1D(v)TY(v) (5)b (v) = (D (v)T D (v) ) -1 D (v)T Y (v ) (5)
第v+1次迭代值:g(v+1)=g(v)+b(v);v+1 iteration value: g (v+1) = g (v) + b (v) ;
式(5)中,D(v)为复合工况下第v次迭代的计算因子,Y(v)为方程输出矩阵;In formula (5), D (v) is the calculation factor of the vth iteration under compound working conditions, and Y (v) is the output matrix of the equation;
步骤3.4、计算第v次估计的修正因子的残差平方和SSRv;Step 3.4, calculate the residual sum of squares SSR v of the correction factor estimated for the vth time;
步骤3.5、辨识待回归系数:Step 3.5, identify the coefficients to be regressed:
对于给定的允许误差率k,当时,停止迭代;并将得到第v次估计的修正因子代入非线性回归轮胎模型中,得到修正后的矿用重载MF实心轮胎模型;否则,将v+1赋值给v后,返回步骤3.3顺序执行。For a given allowable error rate k, when When , stop the iteration; and substitute the estimated correction factor of the vth time into the nonlinear regression tire model to obtain the revised mining heavy-duty MF solid tire model; otherwise, after assigning v+1 to v, return to step 3.3 Execute sequentially.
步骤4、根据修正后的矿用重载MF实心轮胎模型初次优化辨识得到的参数值产生初始种群;采用遗传算法计算初值,通过步骤3初次辨识的参数值进行适应度值优化,按照遗传算法对遗传算子的经过不断的交叉、变异、优化,在全局范围内找到逼近最优解即科学合理的公式参数值。Step 4. Generate an initial population based on the parameter values obtained from the initial optimization identification of the revised mining heavy-duty MF solid tire model; use the genetic algorithm to calculate the initial value, and optimize the fitness value through the initial parameter values identified in step 3. According to the genetic algorithm After continuous crossover, mutation, and optimization of genetic operators, a scientific and reasonable formula parameter value close to the optimal solution is found in the global scope.
基于自然选择规律以及孟德尔遗传定律的全局概率搜索算法,根据所研究的问题,确定目标函数式(1),然后随机初始化种群,种群中的个体代表所研究问题的一个可能解,对个体进行优选的方式是选出适应度值高的个体,适应度值是根据目标函数式(1)计算得到的,多个所选出的优秀个体就构成了新的下一代种群,再通过交叉和变异操作来增加这一新种群的多样性,不断重复这一过程,可以使得种群不断的进化并产生更优秀的下一代种群。Based on the global probability search algorithm of natural selection and Mendelian law of inheritance, according to the research problem, determine the objective function formula (1), and then initialize the population randomly, the individual in the population represents a possible solution of the research problem, and the individual is carried out The preferred way is to select individuals with high fitness values. The fitness value is calculated according to the objective function formula (1). Multiple selected excellent individuals constitute a new next-generation population, and then through crossover and mutation Operation to increase the diversity of this new population, and repeating this process, can make the population continuously evolve and produce a better next-generation population.
选定实数编码对待辨识参数值进行编码,并设定待辨识参数的上下限,对种群初始化。通常情况下群体规模Np=10~200,本实施例中,在对纵向力和侧偏力进行参数辨识时,群体规模Np=200。Select the real code to encode the value of the parameter to be identified, set the upper and lower limits of the parameter to be identified, and initialize the population. Usually, the group size Np=10-200. In this embodiment, the group size Np=200 when performing parameter identification on the longitudinal force and cornering force.
通过优胜劣汰的机制,将适应度值度差的个体进行淘汰,对存下来的个体按照适应度的高低,按一定的规则进行选择,进行繁殖,进而新成新的群体,通常情况下适应度越高代表解越优良,适应度越低代表解的质量越差,本发明选择运算使用比例选择方法来选取优良个体。Through the mechanism of survival of the fittest, the individuals with poor fitness value are eliminated, and the surviving individuals are selected according to the level of fitness and according to certain rules, and reproduced to form new groups. The higher the fitness, the better the solution, and the lower the fitness, the worse the quality of the solution. The selection operation of the present invention uses a proportional selection method to select excellent individuals.
通过交叉、变异的操作,产生下一代种群。交叉是随机选择两个个体(双亲),将某一个点或多点的基因互换而产生两个新个体,变异是基因中某一点或多点发生突变。交叉概率Pc太小时难以向前搜索,太大则容易破坏一些优良个体,通常情况下Pc=0.25~1.00,本文选择单点交叉,交叉概率Pc=0.65。变异概率Pm太小难以产生新的基因结构,太大则使得遗传算法变为随机搜索,通常情况下Pm=0.001~0.1,本实施例中,变异概率选定为Pm=0.07。Through crossover and mutation operations, the next generation population is generated. Crossover is to randomly select two individuals (parents), and exchange genes at one or more points to generate two new individuals. Mutation is a mutation at one or more points in a gene. If the crossover probability Pc is too small, it is difficult to search forward, and if it is too large, it will easily destroy some excellent individuals. Usually, Pc=0.25~1.00. In this paper, single-point crossover is selected, and the crossover probability Pc=0.65. If the mutation probability Pm is too small, it is difficult to generate a new gene structure, and if it is too large, the genetic algorithm will become a random search. Usually, Pm=0.001-0.1. In this embodiment, the mutation probability is selected as Pm=0.07.
子代重复上述操作,进行新一轮遗传进化过程,基于本方法适应度函数计算速度较快的特点,本实施例中,设定最大遗传代数为10000代。如图2所示;The offspring repeat the above operations to carry out a new round of genetic evolution process. Based on the characteristics of the fast calculation speed of the fitness function of this method, in this embodiment, the maximum number of genetic generations is set to 10,000 generations. as shown in picture 2;
判断群体是否满足终止条件,若满足则算法结束,得到近似最优解,接下来采用自适应模拟退火算法提高计算效率,进一步局部寻优,通过随机值迭代输出最优解,判断目标函数是否达到评价指标要求。Judging whether the population meets the termination condition, if so, the algorithm ends, and an approximate optimal solution is obtained. Next, the adaptive simulated annealing algorithm is used to improve the calculation efficiency, and further local optimization is performed. The optimal solution is output through random value iteration, and it is judged whether the objective function reaches Evaluation index requirements.
模拟退火算法是一种局部捜索算法的扩展,主要应用于组合优化问题中tW。它是源于金属退火原理,将金属加温至一定温度再让其慢慢冷却,冷却时金属粒子内部逐渐趋于有序,当温度降到一定程度时,内能减为最小。基于这一特性,模拟退火算法是从某一较高温度出发,随着温度参数的不断下降,结合概率图跳特性在解空间中随机寻找全局最优解,即能概率性地跳出局部最优解最终趋于全局最优局部搜索能力较强,运行时间短。The simulated annealing algorithm is an extension of the local search algorithm, which is mainly used in combinatorial optimization problems. It is derived from the principle of metal annealing. The metal is heated to a certain temperature and then allowed to cool slowly. When cooling, the interior of the metal particles gradually tends to be orderly. When the temperature drops to a certain level, the internal energy is minimized. Based on this characteristic, the simulated annealing algorithm starts from a certain higher temperature, and with the continuous decrease of the temperature parameter, combines the probability map jump feature to randomly search for the global optimal solution in the solution space, that is, it can jump out of the local optimal solution probabilistically. The solution eventually tends to the global optimum, and the local search ability is strong, and the running time is short.
自适应模拟退火算法(Adaptive SimulatedAnnealing,ASA)在模拟退火算法的基础上,分别在淬火方式、重退火方面和降火方式方面进行了改进,相比较模拟退火算法,有着更好的计算效率和全局求解能力。Based on the simulated annealing algorithm, the adaptive simulated annealing algorithm (ASA) has been improved in the quenching method, re-annealing method and cooling method. Compared with the simulated annealing algorithm, it has better calculation efficiency and overall Solving ability.
具体步骤如下:Specific steps are as follows:
步骤4.1、设定种群规模为U,定义种群的当前代数为g;并初始化g=1;Step 4.1, set the population size as U, define the current generation of the population as g; and initialize g=1;
将修正后的矿用重载MF实心轮胎模型中的所有待辨识参数值作为第g代种群中第u个染色体从而得到第g代种群集合记为 All the parameter values to be identified in the revised mine heavy-duty MF solid tire model are taken as the u-th chromosome in the g-th generation population Thus, the population set of the gth generation is obtained and denoted as
步骤4.2、根据式(1)计算得到第g代种群Ag中第u个染色体的适应度值并将第u个染色体中适应度值最高的两个基因进行交叉操作后,得到第u个染色体的两个新基因,用于替换第u个染色体中适应度值最高的两个基因,从而得到更新后的第u个染色体进而得到更新后的第g代种群A′g。Step 4.2, calculate according to formula (1) to obtain the uth chromosome in the gth generation population A g fitness value and put the uth chromosome After the two genes with the highest fitness value are crossed over, the uth chromosome is obtained Two new genes of , used to replace the u-th chromosome The two genes with the highest fitness values in , so as to get the updated u-th chromosome Then the updated g-th generation population A' g is obtained.
步骤4.3、将第u个染色体的两个新基因作为模拟退火算子的初始最优解并进行退火操作:Step 4.3, the u-th chromosome The two new genes of are used as the initial optimal solution of the simulated annealing operator and are annealed:
步骤4.3.1、定义退火操作的当前循环次数为k,并初始化k=0;Step 4.3.1, define the current number of cycles of the annealing operation as k, and initialize k=0;
令第k次循环的温度Tk,随机产生当前第k次循环的状态ωk为第k次循环的最优解;Let the temperature T k of the k-th cycle randomly generate the state ω k of the current k-th cycle as the optimal solution of the k-th cycle;
步骤4.3.2、令第k+1次循环的温度Tk+1=αTk;其中,α表示退温因子,0<α<1;Step 4.3.2, set the temperature T k+1 of the k+1th cycle = αT k ; where α represents the cooling factor, 0<α<1;
步骤4.3.3、将k+1赋值给k后,根据Tk得到第k次循环的状态ωk,并作为第k次循环的最优解ωk;Step 4.3.3. After assigning k+1 to k, obtain the state ω k of the k-th cycle according to T k , and use it as the optimal solution ω k of the k-th cycle;
步骤4.3.4、令第k次循环的增量为ΔZk=Z(ωk)-Z(ωk-1),其中,Z表示半经验轮胎模型的目标函数;ωk-1表示第k-1次循环的状态;Step 4.3.4. Let the increment of the k-th cycle be ΔZ k =Z(ω k )-Z(ω k-1 ), where Z represents the objective function of the semi-empirical tire model; ω k-1 represents the k-th -1 cycle status;
若ΔZk≤0,则将第k次循环的最优解ωk替换第u个染色体的两个新基因并得到第g+1代种群Ag+1的第u个染色体否则,执行步骤4.3.5;If ΔZ k ≤ 0, replace the u-th chromosome with the optimal solution ω k of the k-th cycle and get the uth chromosome of population A g+1 of g+ 1th generation Otherwise, perform step 4.3.5;
步骤4.3.5、若则将第k次循环的最优解ωk替换第u个染色体的两个新基因并得到第g+1代种群Ag+1的第u个染色体否则,第k-1次循环的最优解ωk-1替换第u个染色体的两个新基因并得到第g+1代种群Ag+1的第u个染色体其中,ε表示系数;rk表示第k次循环的随机数,且rk∈[0,1]。Step 4.3.5, if Then replace the u-th chromosome with the optimal solution ω k of the k-th cycle and get the uth chromosome of population A g+1 of g+ 1th generation Otherwise, the optimal solution ω k-1 of the k-1th cycle replaces the u-th chromosome and get the uth chromosome of population A g+1 of g+ 1th generation Among them, ε represents the coefficient; r k represents the random number of the kth cycle, and r k ∈ [0,1].
步骤4.4、按照变异概率Pm将得到新的个体插入到父代种群中得到新种群,经过克隆基因变异操作后产生的新种群并不作为下一代群体,而是要将得到新的个体以一定的代沟(GAP=0.95)插入到父代种群中得到临时种群tempop,运用MetropoliS抽样准对临时群体tempop中的染色体进行判别,决定其是否能进入下一代群体,具体操作如下:Step 4.4. According to the mutation probability P m , insert the new individual into the parent population to obtain a new population. The new population generated after the cloning gene mutation operation is not used as the next generation population, but the new individual should be obtained with a certain Insert the generation gap (GAP=0.95) into the parent population to obtain the temporary population tempop, use the MetropoliS sampling standard to discriminate the chromosomes in the temporary population tempop, and determine whether it can enter the next generation population, the specific operation is as follows:
对第g+1代种群Ag+1中任意第j条染色体进行变异操作,得到新的染色体若第g+1代的第j个增量则将新的染色体加入第g+1代种群Ag+1,并得到更新后的第g+1代种群A′g+1,否则,在[0,1]之间产生第g+1代的第j个随机数若则将新的染色体加入第g+1代种群Ag+1,并得到更新后的第g+1代种群A′g+1,否则,将第j条染色体仍然保持在第g+1代种群Ag+1中,其中,tj表示退温函数。For any jth chromosome in the g+1th generation population A g+1 Perform mutation operations to obtain new chromosomes If the jth increment of the g+1th generation the new chromosome Join the g+1th generation population A g+1 , and get the updated g+1th generation population A′ g+1 , otherwise, generate the jth random number like the new chromosome Join the g+1th generation population A g+1 , and get the updated g+1th generation population A′ g+1 , otherwise, the jth chromosome Still remain in the g+1th generation population A g+1 , where t j represents the cooling function.
步骤4.5、根据式(1)计算更新后的第g+1代种群A′g+1中第u个染色体的适应度值判第u个染色体中适应度值高的两个基因作为模拟退火算子的初始最优解并进行退火操作:Step 4.5. Calculate the uth chromosome in the updated g+1th generation population A' g+1 according to formula (1) fitness value judge the uth chromosome The two genes with high fitness values are used as the initial optimal solution of the simulated annealing operator and annealed:
步骤4.5.1、初始化退火操作的当前循环次数k=0;Step 4.5.1, initializing the current number of cycles of the annealing operation k=0;
令第k次循环的温度Tk′,随机产生当前第k次循环的状态ωk′为第k次循环的最优解;Let the temperature T k ′ of the k-th cycle randomly generate the state ω k ′ of the current k-th cycle as the optimal solution of the k-th cycle;
步骤4.5.2、令第k+1次循环的温度Tk′+1=αTk′;其中,α表示退温因子,0<α<1;Step 4.5.2, let the temperature T k ′ + 1 of the k+1th cycle = αT k ′; where α represents the cooling factor, 0<α<1;
步骤4.5.3、将k+1赋值给k后,根据Tk′得到第k次循环的状态ωk′,并作为第k次循环的最优解ωk′;Step 4.5.3, after assigning k+1 to k, obtain the state ω k ′ of the k-th cycle according to T k ′, and use it as the optimal solution ω k ′ of the k-th cycle;
步骤4.5.4、令第k次循环的增量为ΔZk′=Z(ωk′)-Z(ωk′-1),其中,ωk′-1表示第k-1次循环的状态;Step 4.5.4. Let the increment of the kth cycle be ΔZ k ′=Z(ω k ′)-Z(ω k ′ -1 ), where ω k ′ -1 represents the state of the k-1th cycle ;
若ΔZk′≤0,则将第k次循环的最优解ωk′替换第u个染色体中适应度值高的两个基因并得到第g+2代种群Ag+2的第u个染色体否则,执行步骤4.5.5;If ΔZ k ′≤0, replace the uth chromosome with the optimal solution ω k ′ of the kth cycle Two genes with high fitness value and get the uth chromosome of the g+2th generation population A g+2 Otherwise, go to step 4.5.5;
步骤4.5.5、若则将第k次循环的最优解ωk′替换第u个染色体中适应度值高的两个基因并得到第g+2代种群Ag+2的第u个染色体否则,第k-1次循环的最优解ωk′-1替换第u个染色体中适应度值高的两个基因并得到第g+2代种群Ag +2的第u个染色体进入下一代种群,其中,rk′表示第k次循环的随机数,且rk′∈[0,1]。Step 4.5.5, if Then replace the u-th chromosome with the optimal solution ω k ′ of the k-th cycle Two genes with high fitness value and get the uth chromosome of the g+2th generation population A g+2 Otherwise, the optimal solution ω k ′ -1 of the k-1th cycle replaces the uth chromosome Two genes with high fitness value and get the uth chromosome of the g+2 generation population A g +2 Enter the next generation population, where r k ′ represents the random number of the kth cycle, and r k ′∈[0,1].
步骤4.6、计算新一代群体中的染色体适应值,找出最大适应值Z(i)max,判断是否满足迭代次数GEN=MAXGEN=100的终止条件,即判断Z(i)max、Z(i-1)max、…、Z(i-q)max是否相同,是的话则终止计算,具体步骤如下:Step 4.6. Calculate the chromosome fitness value in the new generation population, find out the maximum fitness value Z(i) max , and judge whether the termination condition of the number of iterations GEN=MAXGEN=100 is satisfied, that is, judge Z(i) max , Z(i- 1) Whether max , ..., Z(iq) max are the same, if yes, the calculation will be terminated, the specific steps are as follows:
将g+2赋值给g后,判断g>gmax是否成立,若成立,则表示得到第gmax代种群,并选择适应度最高的染色体作为修正后的矿用重载MF实心轮胎模型的最优辨识参数值,否则,返回步骤4.2顺序执行。After assigning g+2 to g, judge whether g>gmax is established. If it is established, it means that the gmax generation population is obtained, and the chromosome with the highest fitness is selected as the optimal identification of the revised mining heavy-duty MF solid tire model parameter value, otherwise, return to step 4.2 and execute sequentially.
本实施例中,一种电子设备,包括存储器以及处理器,该存储器用于存储支持处理器执行上述参数辨识及优化方法的程序,所述处理器被配置为用于执行所述存储器中存储的程序。In this embodiment, an electronic device includes a memory and a processor, the memory is used to store a program that supports the processor to execute the above parameter identification and optimization method, and the processor is configured to execute the program stored in the memory program.
本实施例中,一种计算机可读存储介质,是在计算机可读存储介质上存储有计算机程序,该计算机程序被处理器运行时执行上述参数辨识及优化方法的步骤。In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and when the computer program is run by a processor, the steps of the above parameter identification and optimization method are executed.
Claims (3)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202211704447.8A CN115809608A (en) | 2022-12-29 | 2022-12-29 | A parameter identification and optimization method for mining heavy-duty solid tires |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202211704447.8A CN115809608A (en) | 2022-12-29 | 2022-12-29 | A parameter identification and optimization method for mining heavy-duty solid tires |
Publications (1)
Publication Number | Publication Date |
---|---|
CN115809608A true CN115809608A (en) | 2023-03-17 |
Family
ID=85487022
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202211704447.8A Pending CN115809608A (en) | 2022-12-29 | 2022-12-29 | A parameter identification and optimization method for mining heavy-duty solid tires |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN115809608A (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN117192371A (en) * | 2023-11-03 | 2023-12-08 | 南通清浪智能科技有限公司 | Test method and system for motor driver of new energy automobile |
-
2022
- 2022-12-29 CN CN202211704447.8A patent/CN115809608A/en active Pending
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN117192371A (en) * | 2023-11-03 | 2023-12-08 | 南通清浪智能科技有限公司 | Test method and system for motor driver of new energy automobile |
CN117192371B (en) * | 2023-11-03 | 2024-01-30 | 南通清浪智能科技有限公司 | Test method and system for motor driver of new energy automobile |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN113158560B (en) | Intelligent driving vehicle autonomous capability test method based on scene opposition | |
CN111105332B (en) | Highway intelligent pre-maintenance method and system based on artificial neural network | |
Sun et al. | Many-objective optimization of BEV design parameters based on gradient boosting decision tree models and the NSGA-III algorithm considering the ambient temperature | |
CN106777527A (en) | Monkey operation energy consumption analysis method based on neural network model | |
CN106869990A (en) | Coal gas Permeability Prediction method based on LVQ CPSO BP algorithms | |
CN107037373A (en) | Battery dump energy Forecasting Methodology based on neutral net | |
CN105138717A (en) | Transformer state evaluation method by optimizing neural network with dynamic mutation particle swarm | |
CN115809608A (en) | A parameter identification and optimization method for mining heavy-duty solid tires | |
CN113283173B (en) | Comprehensive inverse analysis system and method for underground engineering energy and parameters | |
CN107169205B (en) | Iron ore classification modeling method | |
CN103973221B (en) | A Photovoltaic Array Parameter Identification Method Based on Measured Data | |
CN104915515A (en) | BP neural network based GFET modeling method | |
CN108427280A (en) | A kind of overhead crane anti-swing control method based on sliding mode control theory | |
CN109492816A (en) | A kind of coal and gas prominent dynamic prediction method based on hybrid intelligent | |
CN113361090A (en) | Method for establishing strip mine slope displacement prediction model | |
CN119648041B (en) | Intelligent construction control method and system for bridge girder erection machine based on machine vision | |
CN106568647B (en) | A kind of Strength Forecast of Concrete method neural network based | |
CN118133104A (en) | Rapid identification method for lithofacies of deep sea-phase shale gas well | |
CN113743003B (en) | Method for calculating intensity of high-voltage line to ground electric field by considering influence of temperature and humidity | |
CN110570042A (en) | A method and system for short-term electric vehicle charging load prediction | |
CN117454467B (en) | Elastic conversion method, system and equipment for viscoelastic deflection basin of asphalt pavement | |
CN103983332A (en) | Method for error compensation of sensor based on HGSA-BP algorithm | |
Gheshlaghi et al. | Developing an analytical model for prediction of tyre rolling resistance on moist soils | |
CN114372353B (en) | A method for evaluating the skeleton structure of asphalt mixture based on main chain | |
CN110288726A (en) | A risk prediction method for sugarcane transport vehicles based on BP neural network |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination |