CN103838929A - Turning repair decision optimization method for rail transit vehicle wheel sets - Google Patents

Abstract

The invention relates to a turning repair decision optimization method for rail transit vehicle wheel sets. The turning repair decision optimization method includes: subjecting eight wheel of one carriage to wheel set abrasion data preprocessing; establishing wheel set abrasion data driving models such as a wheel diameter abrasion model, a rim thickness abrasion model and a wheel set turning repair proportion coefficient distribution model; performing Monte Carlo simulation on rail transit vehicle wheel set abrasion and turning repair to acquire expected wheel set service life under the combination of different rim thickness preventing turning repair value and turning repair recovery value. By means of a genetic algorithm in the simulation, the expected rim thickness value and wheel diameter value after one specific turning repair are optimized with the optimization objectives that the wheel diameter loss is as low as possible and is possibly close to the rim thickness recovery value after turning repair; optimal turning repair decisions, namely the optimized rim thickness preventing turning repair value and turning repair recovery value, can be finally analyzed according to the expected simulated service life of the wheel sets.

Description

A decision-making optimization method for turning and repairing wheel sets of rail transit locomotives

technical field

The patent of the present invention relates to a decision-making optimization method for wheel-set repairing of rail transit locomotives and vehicles, in particular to a decision-making optimization method for wheel-set repairing of rail transit locomotives and vehicles based on a wheel-set wear data-driven model and Monte Carlo simulation.

Background technique

Entering the 21st century, my country's urban rail transit (commonly known as subway) and railway systems have entered a stage of rapid development. With the rapid development of railways and urban rail transit, higher requirements must be put forward for the maintenance and life management of related equipment such as trains and rails. The wheel set is known as one of the three major consumable parts of subway vehicles. The tread diameter and rim thickness exceed the limit faults caused by the tread and rim wear, as well as wheel scratches, tread cracks, and tread defects caused by abnormal wheel-rail contact. Faults such as delamination have an important impact on the driving safety, ride comfort and rail service life of subway vehicles. Due to the continuous wear and tear of the wheel set during use, the thickness of the rim and the diameter of the wheel (ie, the diameter of the tread) will continue to decrease, and the thickness of the rim and the diameter of the wheel have corresponding upper and lower limits. In the use of wheel sets: when the thickness of the wheel rim exceeds the limit, it must be repaired in time to restore the thickness of the wheel rim, but this repair process must be at the cost of losing part of the wheel diameter; if the wheel diameter exceeds the limit, the wheel must be repaired for replacement. In addition, the eight wheels of the same carriage must also meet the requirements for wheel diameter difference. Therefore, the decision-making problem of turning the wheel set during the use of the wheel set, that is, when the wheel set is repaired when the thickness of the wheel rim is reduced, and to what extent the thickness of the wheel set can be restored, is very important for prolonging the service life of the wheel set and reducing the subway Vehicle maintenance costs have an important impact.

After searching, no domestic and foreign patents on the decision-making optimization method for wheel set repairing of rail transit locomotives were found. The academic community has published a small number of relevant research results. Pascual and Marcos (Pascual F, Marcos J A. Wheel wear management on high-speed passenger rail: a common playground for design and maintenance engineering in the Talgo engineering cycle. Proceedings of the2004ASME/IEEE Joint RailConference for Spain, 193-1499), 2 Talgo The company's locomotive wheel set wear problem, through the rough statistical analysis of the wheel set wear measurement data for many years, it is believed that when the thickness of the wheel set rim is reduced to 27.5mm and then restored to 30.5mm through turning repairs, the wheel set Long service life. Domestic researchers such as Wang Ling (Wang Ling, Yuan Hua, Na Wenbo, Chen Xiai, Li Yuntang, Wheelset Turning Repair Strategy Optimization and Remaining Life Prediction Based on Wear Data Driven Model, System Engineering Theory and Practice, 31(6), 1143-1152, 2011.; Xu Hong, Yuan Hua, Wang Ling, Na Wenbo, Xu Wenbin, Li Yuntang, Gaussian Process-Based Modeling of Metro Vehicle Wheelset Wear and Optimization of Turning Repair Strategy, Chinese Journal of Mechanical Engineering, 46(24 ), 88-95, 2010) Aiming at the wheel set wear and repairing problems of Guangzhou subway vehicles, the corresponding wear model and the repairing decision optimization method are given, but these results only consider the turning repair decision optimization problem from the perspective of a single wheel set , which cannot be directly applied to solve the actual decision-making optimization problem of turning eight wheels of the same carriage.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies in the prior art, aim at the decision-making problem of turning eight wheels of the same carriage, provide a kind of decision-making optimization method for turning the wheel of rail transit locomotive and vehicle, so that the relevant maintenance support personnel can be based on The wheel set historical wear data and the method optimize future wheel set reconditioning decisions, thereby helping to extend the life of the wheel set.

In order to realize the purpose of the present invention, the present invention provides a method for optimizing the decision-making of turning and repairing the wheel set of rail transit locomotive and vehicle, comprising the following steps:

Step 1: For the eight wheels of a car, pre-process the wheel wear data to obtain the sample data of the wear rate of the wheel rim and wheel diameter and the turning repair ratio coefficient;

Step 2: Establish a wheel set wear data-driven model, including a wheel diameter wear model, a wheel rim thickness wear model, and a wheel set turning repair proportional coefficient distribution model, etc.;

The wheel diameter wear model adopted in the present invention is a Weibull distribution describing the probability distribution characteristic of the wheel diameter wear rate. The rim thickness wear model adopted in the present invention describes the correlation fitting relationship between the rim thickness wear rate and the corresponding rim thickness value at a certain moment, expressed as follows:

V _sd = a×S _d ² +b×S _d +c+E _vsd (1)

Where V _sd is the wear rate of the rim thickness, S _d is the value of the rim thickness, E _vsd is the random fitting difference of the wear rate of the rim thickness, E _vsd is a normal distribution random number with a mean value of zero, a, b and c is a constant. The wheel set turning repair proportional coefficient distribution model adopted in the present invention is a gamma distribution describing the probability distribution characteristic of the turning repair proportional coefficient k.

Step 3: Carry out the Monte Carlo simulation of the wheel set wear and turning repair of rail transit locomotives, and obtain the expected service life of the wheelset under the combination of the preventive turning repair value and turning repair recovery value of different wheel flange thicknesses;

In this step, the steps for simulating and calculating the expected service life of the wheel set under the combination of the preventive repair value and the repair recovery value of a specific group of rim thickness are as follows:

Step 3.1: Initialize various parameters;

Step 3.2: The simulation time step is one unit time;

Step 3.3: According to the principle of the Monte Carlo simulation method, based on the aforementioned wheel set wear data-driven model, the simulation generates the wheel diameter wear and the wheel rim thickness wear in the corresponding unit time, and according to the wheel diameter and wheel rim at the previous moment Thickness value, calculate the wheel diameter value and rim thickness value at the current moment;

Step 3.4: Determine whether the wheel diameter value is less than the lower limit of the wheel diameter, if "less than", go to step 3.5, otherwise go to step 3.8;

Step 3.5: Add 1 to the number of wheel set simulation cycles;

Step 3.6: Determine whether the number of wheel set simulation cycles is less than the set total number of wheel set simulation cycles, if "less than", go to step 3.7, otherwise the simulation optimization is over, and the simulation result is output;

Step 3.7: Update the current wheel diameter values and rim thickness values to the new wheel set wheel diameter values and rim thickness values, start the simulation of the next wheel set simulation cycle, and return to step 3.2;

Step 3.8: Determine whether each rim thickness value is less than or equal to the rim thickness preventive repair value, if "less than or equal", go to step 3.9, otherwise return to step 3.2;

Step 3.9: Optimizing the expected wheel flange thickness and wheel diameter value after a specific turning repair, that is, using the genetic algorithm, taking the wheel diameter loss as small as possible under the premise of considering the constraints of the eight wheel diameter differences, and turning the rear wheel The rim thickness value is as close as possible to the recovery value of the rim thickness as the optimization goal, and the expected rim thickness value and wheel diameter value after this turning repair are optimized;

In the above-mentioned steps of the present invention, the corresponding optimization target "the wheel diameter loss is as small as possible, and the rim thickness value after turning is as close as possible to the rim thickness recovery value" can be expressed as:

$\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; sd</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\text{<span class="notranslate"> 2</span>}<span\; class="notranslate">\; )</span>$

为t_j时刻第i个车轮镟修后的轮缘厚度值，S_dR为镟修后轮缘厚度恢复值，

为t_j时刻第k个车轮镟修前轮径值，

为t_j时刻第k个车轮镟修后轮径值，w_sd和w_D为是权重系数，满足w_sd+w_D＝1；优化约束包括同一节车厢八个车轮的轮径差约束、镟修后轮缘厚度值和轮径值不超限约束，以及镟修后的轮缘厚度值大于镟修前的的轮缘厚度值和镟修后的轮径值小于镟修前的轮径值等镟修前后轮对尺寸逻辑约束。in

is the rim thickness value of the i-th wheel at time t _j after turning, S _dR is the recovery value of the wheel rim thickness after turning,

is the wheel diameter value of the kth wheel before repairing at time t _j ,

is the wheel diameter value of the kth wheel at time t _j after turning, w _sd and w _D are the weight coefficients, satisfying w _sd +w _D =1; the optimization constraints include the wheel diameter difference constraints of the eight wheels in the same carriage, turning The rim thickness value and wheel diameter value after repairing do not exceed the constraints, and the rim thickness value after turning is greater than the rim thickness value before turning and the wheel diameter value after turning is smaller than the wheel diameter value before turning Logical constraints on the size of the wheel set before and after the repair.

Step 3.10: Based on the wheel set turning repair ratio coefficient distribution model, generate the turning repair ratio coefficient by sampling, and calculate the wheel flange thickness value and wheel diameter value after turning repair according to the expected wheel rim thickness value obtained in step 3.9 ;

Step 3.11: Accumulate the number of repairs;

Step 3.12: Determine whether each wheel diameter value is less than the lower limit of the wheel diameter, if "less than", return to step 3.5, otherwise return to step 3.2.

Step 4: Get a better repair decision, that is, compare and analyze the expected service life of the wheel set under different combinations of wheel rim thickness preventive repair value and repair recovery value, and obtain a better wheel flange thickness preventive repair value and repair value Repair the recovery value combination.

The present invention relates to a method for optimizing the repair decision-making of rail transit locomotive and vehicle wheelsets. The method is based on the historical data of rail transit locomotive and vehicle wheel wear, and after the data is preprocessed and a wheel set wear data-driven model is established, rail traffic is carried out. Monte Carlo simulation of rolling stock wheel set wear and turning repair, so as to obtain the expected service life of the wheel set under the combination of different wheel flange thickness preventive turning repair value and turning repair recovery value, and finally the expected use of the wheel set according to the simulation Based on the life results, the optimal turning repair decision can be obtained through analysis, that is, the optimal combination of wheel rim thickness preventive turning repair value and turning repair recovery value, so as to help relevant maintenance personnel optimize the wheel set turning repair decision and prolong the service life of the wheel set.

Description of drawings

Fig. 1 is a schematic diagram of steps of the present invention;

Fig. 2 is the flow chart of the wheel set's expected service life under the simulation calculation of a specific group of wheel rim thickness preventive repair value and repair recovery value combination;

Fig. 3 is the simulation calculation result of the wheel set's expected service life under different combinations of wheel rim thickness preventive turning value and turning repair recovery value in the specific embodiment of the present invention.

Detailed ways

As shown in Fig. 1, the present invention comprises four major steps: Step 1: for eight wheels of a compartment, carry out wheel pair wear data preprocessing, obtain the wheel pair rim and wheel diameter wear rate and the ratio coefficient of turning repair Sample data; Step 2: Establish a wheel set wear data-driven model, including wheel diameter wear model, rim thickness wear model, and wheel set repair proportional coefficient distribution model; Step 3: Carry out rail transit locomotive vehicle wheel set wear and turn repair The Monte Carlo simulation of different rim thicknesses obtained the expected service life of the wheel set under the combination of the preventive repair value and the repair recovery value of the wheel set; Step 4: get a better repair decision, that is, compare and analyze the preventive The expected service life of the wheelset under the combination of the repair value and the repair recovery value is obtained, and a better combination of the rim thickness prevention repair value and the repair recovery value is obtained.

In step 1 of the present invention, the preprocessing of the wheel wear data is performed on the eight wheels of a carriage, and it is required to firstly remove incomplete and obviously wrong wheel wear data. In this example, the wheel wear data records the wheel diameter and rim thickness values of the eight wheels on different dates, as well as the wheel set repair and replacement work. In this specific embodiment, 30 days is taken as a unit time, and the rim thickness and wheel diameter wear rate sample data of a certain wheel are calculated based on the following formula:

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; SD</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 30</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; 30</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

in:

v _Sd and v _D are an estimate of the wear rate of the rim thickness and tread diameter, respectively;

t _i and t _i+1 are the time values measured twice before and after the rim thickness (or wheel diameter) without turning overturning, and the unit is day;

S _{d, i} and S _{d, i+1} are the rim thickness values measured at time t _i and t _i+1 respectively;

D _i and D _i+1 are the tread diameter values measured at time t _i and t _i+1 respectively.

Calculate the sample data of the turning and repairing proportional coefficient based on the following formula:

$\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\frac{{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; +</span>}}{{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; -</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

in:

k is an estimated sample value of the repair scale factor;

D _j ^- and D _j ⁺ are the tread diameter values measured before and after the jth wheel turning repair, respectively;

S _{d, j} ^- and S _{d, j} ⁺ are the rim thickness values measured before and after the j-th wheel turning, respectively.

In step 2 of the present invention, the wheel diameter wear model is a Weibull distribution describing the probability distribution characteristics of the wheel diameter wear rate, and the v _D sample satisfies v _D ≤ 2, and according to the shape of the sample histogram, the Weibull distribution is selected to represent v _D distribution, assuming that d is a random variable representing v _D , the corresponding probability density function is:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span>}^{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

According to the sample data of the wear rate of the wheel diameter, by applying the maximum likelihood estimation method, the scale parameter β ₁ =2.3617 and the shape parameter α ₁ =4.6743 of the Weibull distribution in formula (4). According to the fitted distribution, the average value of the wheel diameter wear rate v _D is about -0.16 mm/30 days.

The rim thickness wear model used in step 2 of the present invention describes the correlation fitting relationship between the rim thickness wear rate and the corresponding rim thickness value at a certain moment. In this example, according to the sample data of the rim thickness wear rate, the rim thickness wear model can be expressed as follows:

V _sd ＝-0.02606×S _d ² +1.538×S _d -22.75+E _vsd (5)

Where V _sd is the wear rate of the rim thickness, S _d is the value of the rim thickness, E _vsd is the random fitting difference of the wear rate of the rim thickness, E _vsd is a normal distribution random number with a mean value of zero, and its standard deviation is 0.3056.

The wheel set turning repair proportional coefficient distribution model adopted in the present invention is a gamma distribution describing the probability distribution characteristic of the turning repair proportional coefficient k. Since the minimum value of the sample k of the turning repair proportional coefficient is 3.782, the γ distribution shifted to the right by 3.7 is used to characterize the distribution characteristics. Assuming that k ₁ is a random variable representing the turning repair proportional coefficient k, the probability density function is expressed as follows:

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; gampdf</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3.7</span>}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}}}{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3.7</span>}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3.7</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\frac{{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3.7</span>}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}}}{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\mathrm{<span\; class="notranslate">\; 3.7</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 3.7</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Where a ₁ >0 is the shape parameter, b ₁ >0 is the scale parameter, Γ(a ₁ ) is the gamma function:

$\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}}\mathrm{<span\; class="notranslate">\; du</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Therefore, the mean value of k ₁ is a ₁ ·b ₁ +3.7, and the variance is a ₁ ·b ₁ ² .

According to the maximum likelihood estimation method based on the sample of the modified proportional coefficient, the shape parameter of the gamma distribution about k is 1.1779, the scale parameter is 2.6615, and the average value of k is 1.1779×2.6615+3.7=6.8350.

In step 3 of the present invention, according to the simulation process shown in FIG. 2 , the expected service life of the wheel set under the combination of the specific wheel rim thickness preventive repair value S _dP and repair repair value S _dR is simulated and calculated.

Assuming that the rim thickness and wheel diameter of each wheel are measured at time t _j , denoted as S _{d, j, 1} , S _{d, j, 2} , ..., S _{d, j, 8} and D _{j, l} .. .D _{j, 8} , the subscripts 1, 2, ..., 8 correspond to the first, second, ..., eighth wheels. The first and second wheels (or third and fourth, or fifth and sixth, or seventh and eighth) are on the same axle. The first, second, third, and fourth wheels (or fifth, sixth, seventh, and eighth) are on the same bogie. In this example, the allowable lower limit of wheel diameter is 770mm, and the upper limit is 840mm; the allowable lower limit of wheel rim thickness is 26mm, and the upper limit is 32mm. At the same time, it is required that the wheel diameter difference of the coaxial wheel set shall not exceed 2mm, the wheel diameter difference of the same bogie shall not exceed 4mm, and the wheel diameter difference of the same carriage shall not exceed 7mm.

In step 3.1, "initialize various parameters", input t _j = 0, S _{d, j, i} = 32mm, D _{j, k} = 840 mm, i, k = 1, 2,..., 8, let the number of turning repairs N _Rep =0, make the number of wheel set simulation cycles N _LC =0, and set the total number of wheel set simulation cycles as N _LCtotal =50, which is large enough to be an optimal value for estimating the expected life of the wheel. Enter the S _dP and S _dR values at the same time. Furthermore, w _Sd =1 and w _D =0 are set in view of the importance of the rim thickness. The time step of the simulation is one unit time, which is 30 days.

Step 3.2 of the present invention: the simulation time stepping a unit time t _j =t _j +1;

Step 3.3: According to the principle of the Monte Carlo simulation method, based on the wheel wear data-driven model given by the aforementioned formulas (4)-(7), the simulation produces the wheel diameter wear V _D in a unit time before the time t _j , _{j, k} and rim thickness wear amount V _{Sd, j, i} , and calculate the wheel diameter value D j at the current moment based on the wheel diameter value D _{jl, k} and the rim thickness value S _{d, jl, i at} the previous moment _{, k} and rim thickness values S _{d, j, i} , expressed as follows:

D _j,k =D _jl,k +V _D,j,k ×1 (8)

S _{d, j, i} = S _{d, jl, i} + V _{Sd, j, i} × 1 (9)

where i,k=1,2,...,8

Step 3.4: Judging that D _j,k <770mm? , where k=1, 2, ..., 8, if "less than", go to step 3.5, otherwise go to step 3.8;

Step 3.5: N _LC =N _LC +1;

Step 3.6: Judging that N _LC < N _LCtotal , if “less than”, go to step 3.7, otherwise the simulation optimization ends, record the end time of simulation optimization as t _jtotal , then the expected life cycle EL of the wheel can be expressed as:

$\mathrm{<span\; class="notranslate">\; EL</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; jtotal</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; LC</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Step 3.7: The current wheel diameter values and rim thickness values are all updated to the wheel diameter values and rim thickness values of the new wheel set, that is, D _{j, k} = 840mm, S _{d, j, i} = 32mm, where i, k=1, 2, ..., 8, start the simulation of the next wheel set simulation cycle, and return to step 3.2;

Step 3.8: Determine whether S _{d, j, i} ≤ S _dP ? Wherein i=1, 2, ..., 8, if "less than or equal to", then enter step 3.9, otherwise return to step 3.2;

Step 3.9: Optimizing the expected wheel flange thickness and wheel diameter value after a specific turning repair, that is, using the genetic algorithm, taking the wheel diameter loss as small as possible under the premise of considering the constraints of the eight wheel diameter differences, and turning the rear wheel The rim thickness value is as close as possible to the rim thickness recovery value as the optimization objective, which can be expressed as:

$\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; sd</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 8</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; +</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\text{<span class="notranslate"> 11</span>}<span\; class="notranslate">\; )</span>$

为t_j时刻第i个车轮镟修后的轮缘厚度值，S_dR为镟修后轮缘厚度恢复值，

为t_j时刻第k个车轮镟修前轮径值，利用为t_j时刻第k个车轮镟修后轮径值，w_sd和w_D为是权重系数，满足w_sd+w_D＝1，本具体实施方式鉴于轮缘厚度的重要性，设定w_Sd＝1，w_D＝0。in

is the rim thickness value of the i-th wheel at time t _j after turning, S _dR is the recovery value of the wheel rim thickness after turning,

is the wheel diameter value of the kth wheel before repairing at time t _j , using is the wheel diameter value of the k-th wheel at time t _j after turning, w _sd and w _D are weight coefficients, satisfying w _sd +w _D =1, in view of the importance of the thickness of the wheel rim in this specific embodiment, w _Sd is set =1, w _D =0.

The optimization constraints are as follows:

其中u，w∈{1，2，3，4，5，6，7，8}，d，f∈{1，2，3，4}或者d，f∈{5，6，7，8}，d≠f，g，h∈{1，2，3，4，5，6，7，8}，g≠h。(a) Wheel diameter difference constraint: $0\&le;|{\mathrm{D.}}_{j,u}^{+}-{\mathrm{D.}}_{j,w}^{+}|\&le;2\mathrm{mm},0\&le;|{\mathrm{D.}}_{j,d}^{+}-{\mathrm{D.}}_{j,f}^{+}|\&le;4\mathrm{mm},$

where u, w ∈ {1, 2, 3, 4, 5, 6, 7, 8}, d, f ∈ {1, 2, 3, 4} or d, f ∈ {5, 6, 7, 8} , d≠f, g, h∈{1, 2, 3, 4, 5, 6, 7, 8}, g≠h.

(b) The value of the thickness and diameter of the wheel rim after turning is not exceeded: $770\mathrm{mm}\&le;{\mathrm{D.}}_{j,k}^{+}\&le;840\mathrm{mm},$ k=1,2,...,8

和

i，k＝1，2，…，8。(c) Logical limitation of wheel set size before and after turning:

and

i, k=1, 2, . . . , 8.

和踏面直径

i，k＝1，2，…，8。The variable to be optimized is the thickness of the rim after turning

and tread diameter

i, k=1, 2, . . . , 8.

Since the genetic algorithm is already widely known, the specific optimization process will not be repeated here.

Step 3.10: Based on the distribution model formula (6) and (7) of the ratio coefficient of wheel set turning repair, generate a turning repair ratio coefficient k by sampling, and obtain the wheel rim thickness value S _{d, j, i} after turning repair according to the result of step 3.9 ⁺ and wheel diameter value D _{j, k} ⁺ , namely

S _{d, j, i} ⁺ = S _{d, j, i} ⁺ (12)

D _{j, k} ⁺ = D _{j, k} ^- -k × (S _{d, j, i} ⁺ -S _{d, j, i} ^- ) (13)

Step 3.11: Cumulative turning times N _Rep = N _Rep +1;

Step 3.12: Judging that D _j,k <770mm? Where k=1, 2, ..., 8, if "less than", return to step 3.5, otherwise return to step 3.2.

Repeat steps 3.1 to 3.12 as many times as necessary, and calculate the expected service life of the wheel set under different combinations of rim thickness preventive repair value S _dP and repair recovery value S _dR , so as to obtain different combinations of S _dP and S _dR The expected service life EL of the wheel set below is shown in Figure 3, where 26mm≤S _dP <S _dR ≤32mm and S _dP , S _dR ∈ {26, 26.5, 27, 27.5, 28, 28.5, 29, 29.5, 30 , 30.5, 31, 31.5, 32mm}. It can be seen from Figure 3 that when {S _dP =26mm, S _dR =30mm}, {S _dP =26mm, S _dR =30.5mm}, {S _dP =26mm, S _dR =31mm}, {S _dP =26mm, When S _dR =31.5mm} and other combinations, the expected service life of the wheel set is relatively large.

Using VC++ software based on the above-mentioned steps to program, develop relevant computer software for decision-making optimization of wheel-set repairing, which can automatically realize decision-making optimization of wheel-set repairing for rail transit locomotives.

Claims (3)

1. right Xuan repaiies decision optimization method to the present invention relates to a kind of rail traffic locomotive vehicle wheel, comprises following steps:

Step 1: for eight wheels in a joint compartment, take turns abrasion data pre-service, draw the sample data that wheel is repaiied scale-up factor to wheel rim and wheel footpath wear rate and Xuan;

Step 2: set up wheel to abrasion data-driven model, comprise that wheel footpath wears away model, flange thickness abrasion model and wheel Xuan is repaiied to scale-up factor distributed model etc.

Step 3: carry out rail traffic locomotive vehicle wheel to abrasion and the Monte Carlo simulation repaiied of Xuan, show that different flange thicknesses prevention Xuan values of repairing and Xuan repair the wheel of recovery value under combining to expectation serviceable life;

In this step, to repair wheel under recovery value combination as follows to the step in expectation serviceable life for simulation calculation specific one group of flange thickness prevention Xuan value of repairing and Xuan:

Step 3.1: all kinds of parameters of initialization;

Step 3.2 a: unit interval of simulation time stepping;

Step 3.3: according to Monte Carlo simulation Method And Principle, take turns abrasion data-driven model based on aforementioned, emulation produces wheel footpath abrasion value and the flange thickness abrasion value in the corresponding unit interval, and according to wheel footpath value and the flange thickness value in a upper moment, calculated wheel footpath value and the flange thickness value of current time;

Step 3.4: judge whether wheel footpath value is less than wheel footpath lower limit, if " being less than " enters step 3.5, otherwise carry out step 3.8;

Step 3.5: wheel adds 1 to emulation periodicity;

Step 3.6: judge that wheel that whether wheel be less than setting to emulation periodicity is to emulation total number of cycles, if " being less than " enters step 3.7, otherwise simulation optimization finishes, Output simulation result;

Step 3.7: current each wheel footpath value and each flange thickness value update all are right wheel footpath value and the flange thickness value of brand-new wheel, starts the emulation of next wheel to the emulation cycle, returns to step 3.2;

Step 3.8: judge whether each flange thickness value is less than or equal to the flange thickness prevention Xuan value of repairing, if " being less than or equal to " enters step 3.9, otherwise return to step 3.2;

Step 3.9: optimize a concrete Xuan and repair rear expectation flange thickness value and wheel footpath value, utilize genetic algorithm, considering under the prerequisite of the poor constraint in eight vehicle wheel footpaths, as far as possible little with the loss of wheel footpath, and Xuan repaiies rear rim one-tenth-value thickness 1/10, and to approach as far as possible flange thickness recovery value be optimization aim, flange thickness value and wheel footpath value that this Xuan repaiied to rear expectation are optimized;

Step 3.10: based on wheel, Xuan is repaiied to scale-up factor distributed model, sampling generates Xuan and repaiies scale-up factor, and the Xuan drawing according to the step 3.9 flange thickness value of repairing rear expectation calculates Xuan and repaiies rear rim one-tenth-value thickness 1/10 and wheel footpath value;

Step 3.11: accumulation Xuan repaiies number of times;

Step 3.12: judge whether each footpath value of taking turns is less than wheel footpath lower limit, if " being less than " returned to step 3.5, otherwise return to step 3.2.

Step 4: show that preferably Xuan repaiies decision-making, i.e. comparative analysis different flange thicknesses prevention Xuan value of repairing and Xuan repair the lower wheel of recovery value combination to expecting serviceable life, obtains preferably flange thickness prevention Xuan value of repairing and Xuan and repaiies recovery value and combine.

2. the right Xuan of a kind of rail traffic locomotive vehicle wheel according to claim 1 repaiies decision optimization method, it is characterized in that, described wheel footpath abrasion model is a Weibull distribution of describing wheel footpath wear rate probability density characteristics; Described flange thickness wears away model, has portrayed the correlated fitting relation of certain moment flange thickness wear rate and corresponding flange thickness value, is expressed as follows:

V _sd＝a×S _d ²+b×S _d+c+E _vsd (1)

Wherein V _sdfor flange thickness wear rate, S _dfor flange thickness value, E _vsdfor flange thickness wear rate random fit difference, E _vsdbe that an average is zero normal distribution random number, a, b and c are constant; It is that the gamma that a description Xuan repaiies scale-up factor k probability density characteristics distributes that described wheel is repaiied scale-up factor distributed model to Xuan.

3. the right Xuan of a kind of rail traffic locomotive vehicle wheel according to claim 1 repaiies decision optimization method, it is characterized in that, the concrete Xuan of described optimization repaiies rear expectation flange thickness value and wheel footpath value, corresponding optimization aim, for wheel footpath loss is as far as possible little and Xuan repaiies rear rim one-tenth-value thickness 1/10 and approaches as far as possible flange thickness recovery value, can be expressed as:

$\min [\underset{i=1}{\overset{8}{\mathrm{\&Sigma;}}}{w}_{\mathrm{sd}}\&CenterDot;|S_{d,j,i}^{+}-S_{\mathrm{dR}}|+\underset{k=1}{\overset{8}{\mathrm{\&Sigma;}}}{w}_D\&CenterDot;(D_{j,k}^{-}-D_{j,k}^{+})]---\left(\text{2}\right)$

Wherein

for t _jflange thickness value after moment i wheel Xuan repaiies, S _dRfor Xuan repaiies rear rim caliper recovery value,

for t _jmoment, k wheel Xuan repaiied front-wheel footpath value,

for t _jmoment, k wheel Xuan repaiied trailing wheel footpath value, w _sdand w _dfor being weight coefficient, meet w _sd+ w _d=1; Optimize the poor constraint in wheel footpath, Xuan that constraint comprises eight wheels in same joint compartment and repair the constraint of not transfiniting of rear rim one-tenth-value thickness 1/10 and wheel footpath value, and the flange thickness value of Xuan after repairing before being greater than Xuan and repairing flange thickness value and the wheel footpath value of Xuan after repairing be less than Xuan and repair the Xuan such as front wheel footpath value and repair front and back wheelset profile logical constraint.

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