CN108710971B - Weibull distribution-based marshalling station throat turnout group resource availability calculation method - Google Patents

Abstract

The invention discloses a method for calculating the availability of resources of a marshalling yard throat turnout group based on Weibull distribution, comprising the following steps: S1. In different operation periods, record the execution conditions of each operation in the time period t, and obtain the operation conditions with actual statistics. By comparison, the resource vacancy degree of resource x within time t is obtained; S2. Determine the parameters for resource reliability calculation of turnout group in the throat area of the marshalling yard, and collect and sort out the corresponding index data for analysis, and obtain the resource x within time t. Resource reliability; S3. Calculate resource availability according to resource reliability and resource idleness. The invention considers the occupancy of trains, machines and vehicles in the throat area of the marshalling yard, and uses the dynamic network resource availability measurement method and other related theories to design a method for calculating the resource availability of the turnout group in the throat area of the marshalling yard, and can deeply analyze the resource utilization of the throat area. , to provide a basis and reference for the rational allocation of marshalling yard resources and further optimization of the operation route.

Description

Calculation method of resource availability of marshalling yard throat turnout group based on Weibull distribution

technical field

The invention belongs to the technical field of research on the throat area of a marshalling yard, and in particular relates to a method for calculating the availability of resources of a marshalling yard throat turnout group based on Weibull distribution.

Background technique

With the construction of the marshalling yard integrated automation system, the basic dispatching information has been continuously improved, so that the station dispatching department has the conditions to use the abundant information resources to effectively monitor the physical resources. Entity resources include arrival and departure line resources, hump resources, shunting line resources, pull-out line resources, and machine shunting resources according to the order of the marshalling yard. The throat of the marshalling yard controls the input and output of the traffic flow and the running path of the engine, which usually directly affects the overall operation efficiency of the marshalling yard. From the perspective of resources, analyze the utilization of the throat of the marshalling station, count the availability of resources in the throat area, and based on this, you can master the use of each resource in the throat area by time period, and provide a basis for further utilization of resources.

At present, the utilization of the throat of the marshalling yard has been studied from different angles at home and abroad. A composite hierarchical decision-making model for network optimization of station throat operation area and throat operation capacity is established, and the theoretical verification is carried out; the reasonable arrangement of the route is determined by finding the shortest path on the graph, and the method of directly hindering the turnout group is given. Determination method; based on the characteristics of cluster resources, a cluster job scheduling method based on availability is proposed, and the comparison simulation proves that the algorithm improves the efficiency of the cluster and the efficiency of job completion. When solving the change or ordering of trains in marshalling yards, domestic network usually regards each entity resource as a constraint condition and converts it into a mathematical problem to solve, and rarely studies the utilization attributes of resources. There are many relevant literatures on the capacity calculation and optimization of the throat area and turnout group of the marshalling yard, but they do not involve the utilization status and resource availability of the turnout group resources in the throat area of the marshalling station at different times.

SUMMARY OF THE INVENTION

In view of the above deficiencies in the prior art, the Weibull distribution-based method for calculating the resource availability of the turnout group in the throat area of the marshalling yard solves the problem that the prior art does not have the utilization status of the resources of the turnout group in the throat area of the marshalling yard at different times. The problem of computational analysis of resource availability.

In order to achieve the above purpose of the invention, the technical solution adopted in the present invention is: a method for calculating the resource availability of a marshalling yard throat switch group based on Weibull distribution, comprising the following steps:

S1. In different operation periods, record the execution status of each job in time period t, and compare it with the operation status obtained from actual statistics to obtain the resource idleness of resource x within time t;

S2. Determine the parameters for calculating the reliability of the resources of the turnout group in the throat area of the marshalling station, and collect and sort out the corresponding index data for analysis to obtain the resource reliability of the resource x within the time t;

S3. Calculate resource availability according to resource credibility and resource idleness;

In the step S1, the resource idleness is the ratio of the number of tasks that can be handled by the throat switch group in a period of time to the theoretical maximum frequency of use;

In the step S2, the reliability of the resource is the probability that the throat switch group completes the operation plan in a time period, which is an amount that changes with time;

In the step S3, the resource availability is the probability that the throat switch group can start a job within a time period and complete the job under a certain time constraint;

The theoretical maximum frequency of use is the number of times a piece of equipment or facility is used per unit time with the goal of the maximum utilization frequency of comprehensive resources under the conditions of meeting the minimum working time constraints of equipment and facilities, work sequence, and work balance.

Further, the step S1 is specifically:

S1-1. For the turnout groups in the throat area of the marshalling station, analyze the operation-related sequences of each turnout group, and establish a topology network structure;

S1-2. According to the topology network structure, use time series and optimization method to determine the objective function, and according to the constraints of each resource time and space, establish a theoretical maximum use frequency calculation model of throat resources;

和预计使用的工作曲线边际效用值

S1-3. According to the calculation model of the theoretical maximum frequency of use of resources in the throat area, count the actual utilization of resources in x time periods and the theoretical maximum frequency of use of resources, and calculate the turnout according to the actual utilization and the time curve of the theoretical maximum frequency of use of resources. The marginal utility value of work that group resource x is used in time period t

and expected to use the marginal utility value of the working curve

和

计算资源空闲度；S1-4, according to

and

Idleness of computing resources;

The calculation formula of the resource idleness is:

表示资源x在t时间段内被实际使用的工作曲线边际效用值；In the formula,

Represents the marginal utility value of the work curve that the resource x is actually used in the t time period;

表示资源x在t时间段内预计使用的工作曲线边际效用值。

represents the marginal utility value of the work curve expected to be used by resource x in time period t.

Further, the step S1-1 is specifically:

和结束时间

将作业序列ij占用各项道岔组资源进行标定，确定作业最优进路L_ij及敌对进路组，构建完整的拓扑网络结构。Each resource in the throat area is regarded as a point set, and the lines between the resources of each turnout group are regarded as an edge set, and the points and edges are connected according to the spatial position and the arrangement of the hostile approach, and each operation in the statistical marshalling station occupies a unit time basis Above, according to the application of the time series method, the calculation is performed to obtain the job sequence ij executed by the resource x in a working cycle, and the starting time occupied by each sequence

and end time

The operation sequence ij is used to calibrate the resources of each turnout group, and the optimal operation route _{Li ij} and the adversarial route group are determined, and a complete topology network structure is constructed.

Further, it is characterized in that, in the step S1-2:

同一列车不同作业X_ij、Y_ij、Z_ij之间存在一定的作业先后关系，设作业X_ij、Y_ij、Z_ij的开始时间和结束时间分别为

和

Assume that the minimum time of operation X, Y, and Z of the jth train of track i are respectively

There is a certain operation sequence relationship between different operations X _ij , _{Yi ij} , and Z _ij on the same train, and the start time and end time of the operations X _ij , _{Yi ij} , and Z _ij are set as

and

If X _ij , Y _ij , and Z _ij are arranged in order, there are space constraints:

If different jobs involve the same resource, the common resource needs to be occupied in different time periods, and the job time series meets the requirements of the job sequence, there are space constraints:

In the formula, n represents the total number of tracks, and m represents the total number of trains;

其中

分别表示股道和列车的集合，则存在约束条件：：Divide hostile operation groups according to the principle of different occupation of operation resources at the same time

in

Representing the sets of tracks and trains, respectively, there are constraints:

In the formula, t' _{job interval} , t" _{job interval} , and t"' _{job interval} respectively represent the minimum interval time between different jobs, which is determined by the resource release time of the equipment resources occupied by each job;

The objective function includes objective function one and objective function two:

The first objective function is:

表示第i条股道被第j+1列车占用的结束时间；G_ij表示第i条股道被第j列车占用的起始时间；in the formula

Represents the end time when the i-th track is occupied by the j+1th train; G _ij represents the start time when the i-th track is occupied by the j-th train;

The second objective function is:

表示第i条股道第j列车作业占用资源的开始时间；

表示第i条股道第j列车作业占用资源的结束时间；

In the formula,

Indicates the start time of the resource occupied by the operation of the jth train on the i-th track;

Indicates the end time of the resource occupied by the operation of the jth train of the i-th track;

According to the constraints and the objective function, the theoretical maximum usage frequency calculation model of the throat area resources is obtained as:

Further, the marginal utility value of the working curve in the step S1-3 is: the increased value of the equipment or facility workload when each unit of time is increased;

On the basis of statistics of the working intensity of known equipment or facilities in a certain continuous time, the workload-time curve f(t) _x of the equipment or facility is drawn. The marginal utility value of the working curve of the equipment or facility at time T is numerically equal to The slope of the tangent line at the point corresponding to the workload-time curve at time T.

Further, it is characterized in that the calculation formula of the resource credibility of the step S2 is:

In the formula, A'(x) _t represents the reliability of resource x obtained from historical data statistics in the t time period;

表示在进行作业i时资源x实际被占用的时间；

Represents the time that resource x is actually occupied when job i is performed;

表示在进行作业i时资源x按计划被占用的时间；

Represents the time that resource x is occupied according to plan when job i is performed;

表示进行作业i时资源x实际被占用时间大于计划占用时间的次数；

Indicates the number of times that the actual occupied time of resource x is greater than the planned occupied time during job i;

n _t-1 represents the total number of jobs executed by resource x during the t-1 period;

T _t ^yw represents the time that the resource x is occupied due to the construction of the station according to the construction plan in the time period t;

表示资源x被车站施工所占用的概率；

Represents the probability that resource x is occupied by station construction;

T _t ^xw represents the time occupied by the emergency maintenance construction of resource x due to failure in the t time period;

T _x represents the expected useful life of resource x;

ε _t represents the proportion of resource usage in the calculation of credibility in time period t;

A"(x) _t-1 represents the idleness of resource x in the time period of t-1;

ε _t represents the proportion of resource usage in the calculation of credibility in time period t;

The calculation formula of the ε _t is:

Further, the estimated service life T _x of the resources of the turnout group is obtained from the cumulative failure probability function of the resource, and the cumulative failure probability function is the probability of failure within the time period when the resource equipment has been notified. The estimated useful life T _x is:

In the formula, F(t) represents the probability that the resource fails to complete the task within the time period t, and represents the cumulative failure probability of the resource;

The cumulative failure function is obtained from the Weibull distribution as:

为形状参数的估计值；In the formula,

is the estimated value of the shape parameter;

t' represents the cumulative work time of the resource since the last maintenance or replacement;

为刻度参数的估计值；

is the estimated value of the scale parameter;

The estimated values of the shape parameter and scale parameter are obtained by maximum likelihood estimation as:

Further, the calculation formula of the resource availability is:

A(x) _t = α _t A′(x) _t +(1-α _t ) _t A″(x) _t (13)

In the formula, A(x) _t represents the availability of resource x in time period t;

A'(x) _t represents the reliability of resource x obtained from historical data statistics in time period t;

A″(x) _t represents the relative idleness of resource x in time period t;

α _t represents the proportion of resource credibility in the process of calculating resource availability;

The calculation formula of the α _t is:

The beneficial effects of the invention are as follows: the invention considers the occupancy of trains, machines and vehicles in the throat area of the marshalling yard, and uses the dynamic network resource availability measurement method and other related theories to design a method for calculating the resource availability of the turnout group in the throat area of the marshalling yard, which can be analyzed in depth. The resource utilization of the turnout group in the throat area provides a basis and reference for the rational allocation of marshalling yard resources and further optimization of the operation route.

Description of drawings

FIG. 1 is a flowchart for realizing a method for calculating the availability of resources of a marshalling yard throat switch group based on Weibull distribution in an embodiment provided by the present invention.

FIG. 2 is a flowchart for realizing a method for calculating a resource availability in an embodiment provided by the present invention.

FIG. 3 is a transformation diagram of the positional relationship of the turnout groups in the throat area of the marshalling station in the embodiment provided by the present invention.

FIG. 4 is a working curve diagram of entity resources in the throat area of a marshalling station in an embodiment provided by the present invention.

FIG. 5 is a statistical diagram of the utilization time of the turnout group resources in the throat area of the marshalling station in the embodiment provided by the present invention.

FIG. 6 is a schematic diagram of the availability statistics of the turnout group resources in the throat area of the marshalling station in the embodiment provided by the present invention.

FIG. 7 is a diagram showing the relationship between the enemy routes in the throat area of the Lanzhou North marshalling station in the embodiment provided by the present invention.

FIG. 8 is a statistical diagram of the total number of times of calculating and using the resources of the turnout group in the throat area of Lanzhou North Station in the embodiment provided by the present invention.

FIG. 9 is a statistical diagram of the total number of actual utilization times of the resources of the turnout group in the throat area of Lanzhou North Station in the embodiment provided by the present invention.

FIG. 10 is a statistical diagram of the comprehensive resource vacancy degree of the turnout group in the throat area of Lanzhou North Station in the embodiment provided by the present invention.

FIG. 11 is a statistical diagram of comprehensive resource availability of a turnout group in the throat area of Lanzhou North Station in an embodiment provided by the present invention.

12 is a heat map of the throat area at 9 o'clock in the throat area of Lanzhou North Station in the embodiment provided by the present invention.

13 is a heat map of the throat area at 12 o'clock in the throat area of Lanzhou North Station in the embodiment provided by the present invention.

Detailed ways

The specific embodiments of the present invention are described below to facilitate those skilled in the art to understand the present invention, but it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes Such changes are obvious within the spirit and scope of the present invention as defined and determined by the appended claims, and all inventions and creations utilizing the inventive concept are within the scope of protection.

As shown in Figure 1, the calculation method of the resource availability of the marshalling yard throat turnout group based on Weibull distribution includes the following steps:

S1. In different operation periods, record the execution status of each job in the time period t, and compare it with the operation status obtained from the actual statistics to obtain the resource idleness of the resource x within the time t.

The above-mentioned resource idleness is the ratio of the frequency of tasks that the throat switch group can handle in a time period to the theoretical maximum frequency of use.

As shown in Figure 2, the specific method of the above step S1 is:

S1-1. For the turnout groups in the throat area of the marshalling station, analyze the operation-related sequences of each turnout group, and establish a topology network structure;

When the throat area of the marshalling station is operating, a certain resource in the throat area can only be occupied by one operation in time and space. Use statistics. This kind of statistics generally adopts the interest rate method, graphical method, etc., and there are large factors that are considered to be influential, which makes the statistics of the resource idleness of the throat turnout group have a large error.

In topology, geometry or space can remain unchanged after changing shape continuously, and only consider the physical position relationship without considering their shape and size.

和结束时间

将作业序列ij占用各项道岔组资源进行标定，确定作业最优进路L_ij及敌对进路组，可以构建如图3所示的完整的拓扑网络结构。Each resource in the throat area is regarded as a point set, and the lines between the resources of each turnout group are regarded as an edge set, and the points and edges are connected according to the spatial position and the arrangement of the hostile approach, and each operation in the statistical marshalling station occupies a unit time basis Above, according to the application of the time series method, the calculation is performed to obtain the job sequence ij executed by the resource x in a working cycle, and the starting time occupied by each sequence

and end time

The operation sequence ij occupies the resources of each switch group for calibration, and the optimal operation path _{Li ij} and the adversarial path group are determined, and a complete topology network structure as shown in Fig. 3 can be constructed.

As shown in Figure 3, all possible paths of each operation sequence to be executed in the throat area of the marshalling yard from start to finish are all feasible paths.

S1-2. According to the topology network structure, use time series and optimization method to determine the objective function, and according to the constraints of each resource time and space, establish a theoretical maximum use frequency calculation model of throat resources;

The theoretical maximum frequency of use is the number of times a piece of equipment or facility is used per unit of time with the goal of the maximum utilization frequency of comprehensive resources under the conditions of meeting the minimum working time constraints of equipment and facilities, work sequence, and work balance.

The maximum utilization of turnout group resources in the throat area of the marshalling yard is calculated based on the operation sequence of the throat area of the marshalling yard. When the resources of the turnout group and other equipment in the throat area of the marshalling yard are limited, the time occupied by each equipment is analyzed and determined. The resource idle time sequence, combined with the topology network diagram, determines the optimal route of each job, and conducts adversarial route screening.

同一列车不同作业X_ij、Y_ij、Z_ij...之间存在一定的作业先后关系，设作业X_ij、Y_ij、Z_ij的开始时间和结束时间分别为

和

Assume that the minimum time of operation X, Y, and Z of the jth train of track i are respectively

There is a certain operation sequence relationship between different operations X _ij , _{Yi ij} , Z _ij ... on the same train, and the start time and end time of the operations X _ij , _{Yi ij} , and Z _ij are set as

and

If X _ij , Y _ij , and Z _ij are arranged in order, there are space constraints

不同作业涉及到同一资源，共同资源需要在不同的时间段被占用，且作业时间序列满足作业前后顺序要求，则存在空间约束条件：The start time of the subsequent operation items of the same train operation sequence must be greater than or equal to the end time of the previous operation, and it should meet the following requirements:

Different jobs involve the same resource, common resources need to be occupied in different time periods, and the job time sequence meets the requirements of the sequence of jobs before and after, there are space constraints:

In the formula, n represents the total number of tracks, and m represents the total number of trains;

其中

分别表示股道和列车的集合，则存在约束条件：Different track operations may also conflict in time and space, so it is necessary to distinguish adversarial operations; only one operation in the hostile operation sequence group can be performed at the same time, and this operation satisfies the above constraints. Divide hostile operation groups according to the principle of different occupation of operation resources at the same time

in

represent the sets of tracks and trains, respectively, there are constraints:

In the formula, t' _{job interval} , t" _{job interval} , and t"' _{job interval} respectively represent the minimum interval time between different jobs, which is determined by the resource release time of the equipment resources occupied by each job;

The maximum time that the above resources are occupied in a day is 1440min. In the case of ensuring the number of vehicles to be picked up, the idle time of each lane is required to be the least. Assuming that M is a large number, there is an objective function.

表示第i条股道被第j+1列车占用的结束时间；G_ij表示第i条股道被第j列车占用的起始时间。in the formula

represents the end time of the i-th track being occupied by the j+1th train; G _ij represents the starting time of the i-th track being occupied by the j-th train.

In order to ensure that the workload of each track is not too high, and the daily workload of each track needs to be relatively balanced, there is another objective function.

表示第i条股道第j列车作业占用资源的开始时间；

表示第i条股道第j列车作业占用资源的结束时间；

In the formula,

Indicates the start time of the resource occupied by the operation of the jth train on the i-th track;

Indicates the end time of the resource occupied by the operation of the jth train of the i-th track;

Based on the utilization of each strand, the theoretical maximum usage frequency calculation model of the throat area resources is obtained as follows:

和预计使用的工作曲线边际效用值

S1-3. According to the calculation model of the theoretical maximum frequency of use of resources in the throat area, count the actual utilization of resources in x time periods and the theoretical maximum frequency of use of resources, and calculate the turnout according to the actual utilization and the time curve of the theoretical maximum frequency of use of resources. The marginal utility value of work that group resource x is used in time period t

and expected to use the marginal utility value of the working curve

The marginal utility of the above working curve is the increase in the workload of the equipment or facility for each additional unit of time. On the basis of statistics of the working intensity of the known equipment or facilities in a certain period of time, draw the workload-time curve f(t) _x of the equipment or facility, the marginal utility value of the working curve of the equipment or facility at time T is numerically equal to the work The slope of the tangent line at the point corresponding to the quantity-time curve at time T.

和

计算资源空闲度；S1-4, according to

and

Idleness of computing resources;

The calculation formula of the resource idleness is:

表示资源x在t时间段内被实际使用的工作曲线边际效用值；In the formula,

Represents the marginal utility value of the work curve that the resource x is actually used in the t time period;

表示资源x在t时间内预计使用的工作曲线边际效用值。

represents the marginal utility value of the work curve expected to be used by resource x in time t.

The daily actual working time and estimated working time of the resources in the throat area of the marshalling yard are shown in Figure 4. Due to various controllable factors such as meals and shift shifts, as well as uncontrollable factors such as delayed execution of plans and equipment failures, the throat area of the marshalling yard has been affected. The daily working hours of turnout group resources are often much less than the expected working hours.

In Figure 4, at time T, the resource utilization efficiency of a turnout group in the throat area is numerically equal to the slope of the cumulative curve of daily working hours at time T, so the resource utilization of this turnout group at this time is 1-A″(x) _t Equal to the ratio of the slope of the actual working time curve to the estimated working time curve at time T, A″(x) _t is the idleness of the switch group resources.

S2. Determine the parameters for calculating the reliability of the resources of the turnout group in the throat area of the marshalling station, and collect and sort out the corresponding index data for analysis to obtain the resource reliability of the resource x within the time t;

Resource reliability is the probability that the throat turnout group completes the work plan in a period of time, which is a quantity that changes with time;

The calculation formula of the resource credibility in step S2 is:

In the formula, A'(x) _t represents the reliability of resource x obtained from historical data statistics in the t time period;

表示在进行作业i时资源x实际被占用的时间；

Represents the time that resource x is actually occupied when job i is performed;

表示在进行作业i时资源x按计划被占用的时间；

Represents the time that resource x is occupied according to plan when job i is performed;

表示进行作业i时资源x实际被占用时间大于计划占用时间的次数；

Indicates the number of times that the actual occupied time of resource x is greater than the planned occupied time during job i;

n _t-1 represents the total number of jobs executed by resource x during the t-1 period;

T _t ^yw represents the time that the resource x is occupied due to the construction of the station according to the construction plan in the time period t;

表示资源x被车站施工所占用的概率；

Represents the probability that resource x is occupied by station construction;

T _t ^xw represents the time occupied by the emergency maintenance construction of resource x due to failure in the t time period;

T _x represents the expected useful life of resource x;

ε _t represents the proportion of resource usage in the calculation of credibility in time period t;

A"(x) _t-1 represents the idleness of resource x in the time period of t-1;

ε _t represents the proportion of resource usage in the calculation of credibility in time period t;

The formula for calculating _εt is:

In the formula, A'(x) _t-1 represents the reliability of resource x obtained from historical data statistics in the time period of t-1;

A'(x) _t-2 represents the relative idleness of resource x in the time period of t-2;

The estimated service life T _x of the above turnout group resources is obtained from the cumulative failure probability function of the resources. The cumulative failure probability function is the probability of failure within the notified period of resource equipment operation, and the estimated service life T _x of the turnout group resources is obtained. for:

In the formula, F(t) represents the probability that the resource fails to complete the task within the time period t, and represents the cumulative failure probability of the resource;

Among them, the cumulative failure function is obtained from the Weibull distribution;

The Weibull distribution is obtained according to the weakest environment model or the series model, which can better reflect the influence of material defects and stress concentration sources on the fatigue life of the material, and has an increasing failure rate, which is better suitable for the wear accumulation of electromechanical products. The distribution mode of failure, the cumulative distribution function of Weibull distribution is an extended exponential distribution function, and can be transformed into exponential distribution, Rayleigh distribution and approximate normal distribution, etc. Compared with other statistical distributions, Weibull distribution has a strong adaptability;

The equipment in the throat area of the marshalling yard is mostly mechanical and electrical equipment. The equipment has been checked and tested before use. Its minimum life is greater than 0, and the life is a continuous random variable. According to its numerical distribution characteristics, a two-parameter Weibull distribution can be used for Processing, the cumulative failure function expression of the two-parameter Weibull distribution is:

为形状参数的估计值；In the formula,

is the estimated value of the shape parameter;

t' represents the cumulative work time of the resource since the last maintenance or replacement;

为刻度参数的估计值；

is the estimated value of the scale parameter;

The probability density of the distribution is:

In the formula: γ is the shape parameter; t' represents the cumulative working time of the resource since the last maintenance or replacement; λ is the scale parameter, representing the peak condition of the resource life distribution curve; according to the actual situation, the shortest resource of the throat switch group The working time cannot be less than 0, so when calculating the cumulative failure probability of the throat turnout group resources, only the case of t'≥0 should be considered.

By analyzing the historical fault data of each resource of the throat turnout group, the life time sequence of the equipment resources of each turnout group can be obtained. When the historical data is relatively comprehensive, the historical fault data of n resources can be selected for analysis, and the maximum likelihood estimation can be used for the analysis. Parameter estimates for the Weibull distribution.

Let the fault-free running time series of a certain type of switch group resource be T′=[t′ ₁ ,t′ ₂ ,…,t′ _n ], and the known Weibull distribution density function is f(t′,λ,γ) , x≥0, the likelihood function can be obtained:

Take the logarithmic function as:

Find partial derivatives with respect to λ, γ, and let

get:

其中：

和

所示u和σ的最优线性不变估计系数；可得咽喉道岔组资源的累积失效函数为：According to the properties of the Weibull distribution, when T′～F(λ,γ), Y=ln T′ obeys the extreme value distribution, and there is γ=1/σ, λ=e ^u ; from this, the Weibull distribution can be obtained Estimation of unknown parameters in

in:

and

The optimal linear invariant estimation coefficients of u and σ are shown; the cumulative failure function of the throat turnout group resources can be obtained as:

为形状参数的估计值；In the formula,

is the estimated value of the shape parameter;

t' represents the cumulative work time of the resource since the last maintenance or replacement;

为刻度参数的估计值；

is the estimated value of the scale parameter;

The estimated values of shape parameter and scale parameter are obtained by maximum likelihood estimation as:

When the amount of data is further reduced, the time information of equipment failure is not obtained in the data collection stage. At this time, it is impossible to calculate the cumulative failure function of the resources of the throat turnout group through the above method. It can be used in the reliability evaluation and life prediction without failure data. method for estimation; collecting a set of non-failure data T″=[t″ ₁ , t″ ₂ ,…t″ _n ], the lower confidence limit of the confidence of the reliable life T of the turnout group resource is α is:

The confidence value is generally 85%, where F ₀ represents the original failure probability of the expected resource, γ ₀ is the minimum expected shape parameter, and the value is the minimum value of the shape parameter of this type of resource compared with other data in the whole station.

The one-sided upper confidence limit of α for the confidence of the cumulative failure probability of the switch group resources is:

After the resources of the throat turnout group are faulty and repaired, it is considered that the initial state is restored, the cumulative failure probability is restored to the original state, and the cumulative use time of the resource starts to be counted again.

S3. Calculate resource availability according to resource credibility and resource idleness;

In the step S3, the resource availability is the probability that the throat switch group can start a job within a time period and complete the job under a certain time constraint;

The calculation formula of the above resource availability is:

A(x) _t = α _t A′(x) _t +(1-α _t ) _t A″(x) _t (20)

In the formula, A(x) _t represents the availability of resource x in time period t;

A'(x) _t represents the reliability of resource x obtained from historical data statistics in time period t;

A″(x) _t represents the relative idleness of resource x in time period t;

α _t represents the proportion of resource credibility in the process of calculating resource availability;

The formula for calculating a _t is:

Among them, A'(x) _t-1 represents the reliability of resource x obtained from historical data statistics in the time period of t-1;

A'(x) _t-2 represents the relative idleness of resource x in the time period of t-2;

The availability of resources of the turnout group in the throat area should not only consider the idleness of the resources of the turnout group in the throat area, but also consider the stability of its work, that is, give resources a certain intensity in a certain period of time, and check whether the resources can be completed with high reliability. . The statistical results of historical data used in the resource availability in the throat area of the marshalling yard change over time, and the completion of historical tasks will affect the availability of the resource. The early completion of historical jobs, or on-time completion with high quality can improve the availability of resources to a certain extent, while the delayed completion of historical jobs or completion with poor quality will also reduce the availability of resources, and resources in the throat area The running time of and its available stocks are time-varying parameters, and the utilization of the throat area of the marshalling yard can be expressed as shown in Figure 5 and Figure 6.

Figure 5 is a schematic diagram of the statistical situation of the utilization time of various resources. According to the different classification of resources, statistics can be cleaned and intuitively compared to the usage levels of various resources in different time periods, and the calculated resource idleness can also be verified; Figure 6 It is a schematic diagram of the multi-resource availability-time curve in the throat area. Figure 7 can intuitively understand the availability of different resources at different times, which provides a basis for analyzing station operations.

In one embodiment of the present invention, a process of analyzing and calculating by applying the method provided by the present invention to a practical case is provided:

The data of Lanzhou North marshalling station is used for analysis, and the cycle is 24 hours. Lanzhou North Railway Station Arrival Field 1-6 trains are connected to the ascending trains, and 7-12 trains are connected to the descending trains. It is assumed that the time occupied by each track to pick up the vehicle and enter the road is 10 minutes, the minimum operation time is 25 minutes, the time for each track to be pushed to the hump, pick up and enter the section is 5 minutes, and the operation time of the hump disintegration is 30 minutes. Group the turnouts in the throat area of Lanzhou North Station, and determine the occupancy of each operation.

1. Analysis of the cumulative times of resource utilization of the throat turnout group;

Due to the conflict between the locomotive pick-up operation and the dismantling operation of lanes 1-6, and the conflict between the locomotive entry operation and the dismantling operation of lanes 7-12, in order to clarify the hostile relationship between each approach, establish the relationship diagram of the hostile approach as shown in Figure 7, and determine Hostile approach group.

The throat area of Lanzhou North marshalling station is transformed into a topological network structure, and the algorithm of formula (6) is used to calculate the theoretical application of the turnout group in the throat area between the arrival yard and the shunting yard of Lanzhou North Station. Draw the resource occupancy frequency table of the turnout group in the throat area, as shown in Table 1.

Table 1 Cumulative times of resource calculation and application of turnout group resources in the throat area of Lanzhou North Station

It can be seen from Table 1 that there is a certain difference in the degree of application between different turnout groups. The largest difference appears between the No. 22 turnout group and the No. 36 turnout group, and the difference value is 182. There is a certain relationship between the use times of different turnout groups and their spatial distribution. The use of turnout groups near the entrance and exit of the throat area is relatively busy, while the turnout groups on the approach with many parallel approaches are relatively idle.

The actual utilization times of turnout groups in the throat area of Lanzhou North marshalling station are counted by time period in a day, and a table of actual utilization cumulative times of turnout groups resources in the throat area of Lanzhou North marshalling station can be obtained.

Table 2. The cumulative times of actual utilization of the resources of the turnout group in the throat area of Lanzhou North Station

From Table 2, it can be further confirmed that there are certain differences in the degree of use between different turnout groups, and some of them are quite different. It can be seen from the actual data statistics that there is a certain relationship between the use times of different turnout groups and their spatial distribution. The use of turnout groups near the entrance and exit of the throat area is relatively busy, while the turnout groups on the approach with many parallel routes are relatively idle. rule.

According to the statistics, the theoretical calculation usage and actual usage of each turnout group are obtained, and some turnout groups (No. 2-20) are selected to count and draw the cumulative graph of their usage times by time period, as shown in Figure 8 and Figure 9.

Figures 8 and 9 show the cumulative number of calculated and actual use times of some throat switch groups, respectively. The comparison shows that both figures show a certain linear growth trend, and the growth trend of each turnout group number is relatively similar. It can be seen that in the actual operating environment of the marshalling yard, the use of operating resources of the turnout group in the throat area has a certain proportioning relationship due to the space-time setting, and there is a certain similarity in the growth trend of the interconnected turnout groups.

2. Analysis of resource idleness of throat turnout group;

点和

点处的斜率，按照公式(7)所示计算兰州北站咽喉区道岔组资源空闲度，统计如表3所示。On the basis of the statistics of the number of times of use in each time period of the turnout group in the throat area, the MATLAB curve fitting method is used to fit the usage curve of each throat switch group, and the corresponding operation of the throat switch group at node T in each time period is calculated. situation curve

point sum

The slope at the point is calculated according to the formula (7) to calculate the resource vacancy degree of the turnout group in the throat area of Lanzhou North Station, and the statistics are shown in Table 3.

Table 3 Resource vacancy degree of turnout group in the throat area of Lanzhou North Station

According to the resource vacancy degree calculated by No. 2-40 turnout group in 24 hours by time period, combined with the statistics of table 1 and table 2 of the resource usage frequency of the turnout group in the throat area of the Lanzhou North marshalling station, the weighted calculation can be carried out to obtain the turnout in the throat area. The overall idleness of group resources. The vacancy degree is combined with the frequency of use of turnout group resources, and weighted statistics are carried out in different time periods, which can better reflect the overall idle situation of turnout group resources in the throat area. The calculated idleness of comprehensive resources in the throat area of Lanzhou North Marshalling Station is shown in Table 4.

Table 4 Comprehensive resource vacancy degree of turnout group in the throat area of Lanzhou North Station

Figure 10 shows the comprehensive resource vacancy statistics chart of the turnout group in the throat area of Lanzhou North Station; it can be seen from Figure 10 that the resource vacancy degree of the turnout group in the throat area in different time periods varies greatly, and due to the complexity and fluctuation of the operation situation The availability of resources in the throat area shows a certain fluctuation in 24 hours a day, and the interval between the peaks is about 4 hours.

3. Analysis of resource availability of throat turnout group;

值均为15min，

为20min，

为0.2，T_t ^yw均值为5min，

为0.1，T_t ^xw均取为10min，ε₀为0.5，根据历史数据情况，咽喉道岔组资源的失效率较低，为了计算便捷，取

值为0.01，根据公式(7)可得示例中A′(x)₀均为66.27％。According to the historical statistical data of Lanzhou North marshalling station, the average value is taken in the calculation of the example.

The value is 15min,

is 20min,

is 0.2, the mean value of T _t ^yw is 5min,

is 0.1, T _t ^xw is taken as 10min, ε ₀ is 0.5, according to the historical data, the failure rate of the throat turnout group resources is low, for the convenience of calculation, take

The value is 0.01, and according to formula (7), A'(x) ₀ in the example is 66.27%.

Due to the large number of turnout groups in the throat area, after counting the frequency of use of different switch groups in the throat area, the comprehensive resource availability of the turnout group in the throat area can be obtained by combining the resource availability weighted calculation of a single switch group; the comprehensive resource availability of the switch group in the throat area is the throat A probabilistic measure of the overall availability of resources in a district switch group.

In the above calculation steps, the comprehensive availability of resources of the turnout group in the throat area of Lanzhou North Station has been obtained. Combined with the resource availability A'(x) _t , it can be calculated according to formula (7), formula (8) and formula (20). The comprehensive availability of turnout group resources in the throat area of Lanzhou North Station is shown in Table 5.

Table 5 Comprehensive resource availability of turnout group in the throat area of Lanzhou North Station

It can be seen from Table 5 that in 24 hours a day, the maximum resource comprehensive availability of the turnout group in the throat area of Lanzhou North Station occurs at the time period 23, which is 74.06%, and the minimum value occurs at the time period 16, and the minimum value is 28.02%. , the difference between the maximum value and the minimum value is 46.04%, indicating that there is a big difference in the availability of turnout groups in the throat area in different time periods. The daily average value of comprehensive availability of turnout group resources in the throat area of Lanzhou North Station is 51.42%, indicating that the availability of resources in the throat area is moderate, the operation situation is moderate, and there is still some capacity to be used. In this way, the resource availability value can be calculated in real time, the historical change law can be grasped, and the basis for the preparation of the operation plan can be provided.

Figure 11 reflects the fluctuation of the comprehensive availability of turnout group resources in the throat area of Lanzhou North Station, indicating that there are certain differences in the utilization of turnout group resources at different times of the day, and the operation balance is not ideal. It can be seen from the calculation that the standard deviation of availability is 0.1402 .

The feasibility and effectiveness of the method provided by the invention have been proved by the above examples, and it can be seen that:

(1) In the throat area of marshalling station, due to the spatial configuration of turnout group resources and the time series of operations, there is a certain difference in the use frequency of each turnout group resource in different periods;

(2) In the throat area of the marshalling station, there is a large interpolation of the resource availability and availability of different turnout groups in the same time period, and the comprehensive resource availability of the turnout groups in the throat area also has a large difference in different time periods;

(3) The marshalling yard operation is planned and fluctuated within a certain range. The comprehensive resource availability in the throat area fluctuates to a certain extent throughout the day, and the interval between the peaks is about 4h-6h;

(4) The vacancy degree of comprehensive resources of turnout group in the throat area of marshalling station has a great influence on the available stocks of comprehensive resources. The similarity between the time curves of the two is relatively high, and the coincidence degree of the curve is between 70% and 85%.

In an embodiment of the present invention, there is also provided a method for generating a heat map for resource usage in the throat area of a marshalling yard:

The throat of the marshalling yard is the connecting part between the various operation sequences of the marshalling yard. The incoming and outgoing trains, different shunting routes, etc. will occupy the throat area of the marshalling yard. The traditional method is to use one or several turnouts throughout the day. The utilization rate during the busy period is not intuitive enough to represent the utilization rate of the entire throat. Now, with the help of digital visualization technology, a heat map of the busyness of the operation in the throat switch area can be generated, which can better analyze the utilization of resources in the throat area. The specific steps are as follows :

A1. Group the switches in the throat area according to the occupation of the parallel approach, the occupation of the hostile approach and other throat switch grouping rules;

A2. Analyze the operation conditions of different turnout groups in different time periods, and make statistics on the total time occupied by different turnout group numbers;

A3. Calculate the difference between the maximum occupied time and the minimum time of the turnout group obtained by statistics, and set the time scale according to the number of gradients to be used, and divide the occupied time length of the turnout group;

A4. Perform regional mapping according to different job markets, and assign different color depths to turnouts in different regions, thereby generating a heat map of resource usage of turnout groups in the throat area of the marshalling yard.

According to the statistical results of the above Lanzhou North Station example, the occupancy of the turnout group 6 hours before a shift at the Lanzhou North marshalling station to the arrival yard and the throat area of the shunting yard can be obtained, as shown in Table 6:

Table 6 Occupancy statistics of turnout groups

According to the above steps, the heat map of resource usage in the throat area is generated as shown in Figure 12 and Figure 13; compared with Figure 12 and Figure 13, the thermal conditions of different switch groups in the same heat map are significantly different, and the same switch group in different time periods There are also some differences in the heat map of the turnout group. By comparing the heat map of the resource busyness of the turnout group in the throat area of the marshalling station in different time periods, it is possible to more clearly grasp the use of the turnout group resources in different time periods. The idleness and availability of different time periods provide more intuitive estimation conditions, and the resource idleness and availability can also be finally calculated through experience of the heat distribution of the heat map in different time periods.

The beneficial effects of the invention are as follows: the invention considers the occupancy of trains, machines and vehicles in the throat area of the marshalling yard, and uses the dynamic network resource availability measurement method and other related theories to design a method for calculating the resource availability of the turnout group in the throat area of the marshalling yard, which can be analyzed in depth. The resource utilization of the turnout group in the throat area provides a basis and reference for the rational allocation of marshalling yard resources and further optimization of the operation route.

Claims (8)

1. the calculation method of the marshalling yard throat switch group resource availability based on Weibull distribution, is characterized in that, comprises the following steps: S1. In different operation periods, record the execution status of each job in time period t, and compare it with the operation status obtained from actual statistics to obtain the resource idleness of resource x within time t; S2. Determine the parameters for calculating the reliability of the resources of the turnout group in the throat area of the marshalling station, and collect and sort out the corresponding index data for analysis to obtain the resource reliability of the resource x within the time t; S3. Calculate resource availability according to resource credibility and resource idleness; In the step S1, the resource idleness is the ratio of the number of tasks that can be handled by the throat switch group in a period of time to the theoretical maximum frequency of use; In the step S2, the reliability of the resource is the probability that the throat switch group completes the operation plan in a time period, which is an amount that changes with time; In the step S3, the resource availability is the probability that the throat switch group can start a job within a time period and complete the job under a certain time constraint; The theoretical maximum frequency of use is the number of times a piece of equipment or facility is used per unit time with the goal of the maximum utilization frequency of comprehensive resources under the conditions of meeting the minimum working time constraints of equipment and facilities, work sequence, and work balance. 2. the method for calculating the resource availability of the marshalling yard throat switch group based on Weibull distribution according to claim 1, is characterized in that, described step S1 is specifically: S1-1. For the turnout groups in the throat area of the marshalling station, analyze the operation-related sequences of each turnout group, and establish a topology network structure; S1-2. According to the topology network structure, use time series and optimization method to determine the objective function, and according to the constraints of each resource time and space, establish a theoretical maximum use frequency calculation model of throat resources; S1-3. According to the calculation model of the theoretical maximum frequency of use of resources in the throat area, count the actual utilization of resources in x time periods and the theoretical maximum frequency of use of resources, and calculate the turnout according to the actual utilization and the time curve of the theoretical maximum frequency of use of resources. The marginal utility value of the work curve that the group resource x is used in time period t

and expected to use the marginal utility value of the working curve

S1-4, according to

and

Idleness of computing resources; The calculation formula of the resource idleness is:

In the formula,

Represents the marginal utility value of the work curve that the resource x is actually used in the t time period;

represents the marginal utility value of the work curve expected to be used by resource x in time period t. 3. the method for calculating the resource availability of marshalling yard throat switch group based on Weibull distribution according to claim 2, is characterized in that, described step S1-1 is specifically: Each resource in the throat area is regarded as a point set, and the lines between the resources of each turnout group are regarded as an edge set, and the points and edges are connected according to the spatial position and the arrangement of the hostile approach, and each operation in the statistical marshalling station occupies a unit time basis Above, according to the application of the time series method, the calculation is performed to obtain the job sequence ij executed by the resource x in a working cycle, and the starting time occupied by each sequence

and end time

The operation sequence ij is used to calibrate the resources of each turnout group, and the optimal operation route _{Li ij} and the adversarial route group are determined, and a complete topology network structure is constructed. 4. the method for calculating the availability of marshalling yard throat switch group resources based on Weibull distribution according to claim 2, is characterized in that, in described step S1-2: Assume that the minimum time of operation X, Y, and Z of the jth train of track i are respectively

There is a certain operation sequence relationship between different operations X _ij , _{Yi ij} , and Z _ij on the same train, and the start time and end time of the operations X _ij , _{Yi ij} , and Z _ij are set as

and

If X _ij , Y _ij , and Z _ij are arranged in order, there are space constraints:

If different jobs involve the same resource, the common resource needs to be occupied in different time periods, and the job time series meets the requirements of the job sequence, there are space constraints:

In the formula, n represents the total number of tracks, and m represents the total number of trains; Divide hostile operation groups according to the principle of different occupation of operation resources at the same time

in

represent the sets of tracks and trains, respectively, there are constraints:

In the formula, t' _{job interval} , t" _{job interval} , and t"' _{job interval} respectively represent the minimum interval time between different jobs, which is determined by the resource release time of the equipment resources occupied by each job; The objective function includes objective function one and objective function two: The objective function 1 indicates that under the condition of ensuring the number of vehicles to be picked up, the idle time of each track is the least, which is specifically:

in the formula

Represents the end time when the i-th track is occupied by the j+1th train; G _ij represents the start time when the i-th track is occupied by the j-th train; Z is the idle time of each track space, and M is the resource occupied time-dependent coefficients; The second objective function indicates that the daily workload of each track is relatively balanced, which is specifically:

In the formula,

Indicates the daily workload of each stock,

Indicates the start time of the resource occupied by the operation of the jth train on the i-th track;

Indicates the end time of the resource occupied by the operation of the jth train of the i-th track;

According to the constraints and the objective function, the theoretical maximum usage frequency calculation model of the throat area resources is obtained as:

5. The method for calculating the availability of marshalling yard throat switch group resources based on Weibull distribution according to claim 2, wherein the marginal utility value of the working curve in the step S1-3 is: when each additional unit The added value of the workload of the equipment or facility over time; On the basis of statistics of the working intensity of known equipment or facilities in a certain continuous time, the workload-time curve f(t) _x of the equipment or facility is drawn. The marginal utility value of the working curve of the equipment or facility at time T is numerically equal to The slope of the tangent line at the point corresponding to the workload-time curve at time T. 6. the computing method of the marshalling yard throat switch group resource availability based on Weibull distribution according to claim 2, is characterized in that, the computing formula of described step S2 resource reliability is:

In the formula, A'(x) _t represents the reliability of resource x obtained from historical data statistics in the t time period;

Represents the time that resource x is actually occupied when job i is performed;

Represents the time that resource x is occupied according to plan when job i is performed;

Indicates the number of times that the actual occupied time of resource x is greater than the planned occupied time during job i;

Represents the number of times the resource x is actually occupied during job i;

Represents the number of times the resource x plan is occupied during job i; n _t-1 represents the total number of jobs executed by resource x during the t-1 period; T _t ^yw represents the time that the resource x is occupied due to the construction of the station according to the construction plan in the time period t;

Represents the probability that resource x is occupied by station construction; T _t ^xw represents the time occupied by the emergency maintenance construction of resource x due to failure in the t time period; T _x represents the expected useful life of resource x; ε _t represents the proportion of resource usage in the calculation of credibility in time period t; A"(x) _t-1 represents the idleness of resource x in the time period of t-1; ε _t represents the proportion of resource usage in the calculation of credibility in time period t; The calculation formula of the ε _t is:

7. The method for calculating the availability of resources of marshalling yard throat turnout groups based on Weibull distribution according to claim 6, wherein the estimated service life T _x of the resources of the turnout group is determined by the cumulative failure probability function of the resources It can be obtained that the cumulative failure probability function is the probability of failure within the notified period of resource equipment operation, and the estimated service life T _x at the turnout group resource is obtained as:

In the formula, F(t) represents the probability that the resource fails to complete the task within the time period t, and represents the cumulative failure probability of the resource; The cumulative failure probability is obtained from the Weibull distribution as:

In the formula,

is the estimated value of the shape parameter; t' represents the cumulative work time of the resource since the last maintenance or replacement;

is the estimated value of the scale parameter; The estimated values of the shape parameter and scale parameter are obtained by maximum likelihood estimation as:

In the formula,

The shape parameter is γ, the accumulated work time of the last maintenance or replacement of the resource when the job i is performed; t' _i is the accumulated work time of the last maintenance or replacement of the resource when the job i is performed. 8. The method for calculating the resource availability of the marshalling yard throat switch group based on Weibull distribution according to claim 6, wherein the calculation formula of the resource availability is: A(x) _t = α _t A′(x) _t +(1-α _t ) _t A″(x) _t (13) In the formula, A(x) _t represents the availability of resource x in time period t; A'(x) _t represents the reliability of resource x obtained from historical data statistics in time period t; A″(x) _t represents the idleness of resource x in time period t; α _t represents the proportion of resource credibility in the process of calculating resource availability; The calculation formula of the α _t is:

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