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

Weibull distribution-based marshalling station throat turnout group resource availability calculation method Download PDF

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CN108710971B
CN108710971B CN201810447519.2A CN201810447519A CN108710971B CN 108710971 B CN108710971 B CN 108710971B CN 201810447519 A CN201810447519 A CN 201810447519A CN 108710971 B CN108710971 B CN 108710971B
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薛锋
赵蕾
余潇
孙宗胜
何传磊
袁野
邹彪
吕丹
罗桂蓉
徐莉
刘珊珊
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Southwest Jiaotong University
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Abstract

The invention discloses a Weibull distribution-based method for calculating the availability of throat turnout group resources of a marshalling station, which comprises the following steps: s1, recording the execution conditions of each job in the time period t in different job time periods, and comparing the execution conditions with the job conditions obtained through actual statistics to obtain the resource vacancy degree of the resource x in the time t; s2, determining parameters for calculating the reliability of the turnout group resources in the throat area of the marshalling station, collecting and sorting corresponding index data for analysis, and obtaining the resource reliability of the resource x in the time t; and S3, calculating the resource availability according to the resource credibility and the resource vacancy. The invention considers the occupation conditions of trains, shunting machines and vehicles in the throat area of the marshalling station, designs a calculation method for the availability of the turnout group resources in the throat area of the marshalling station by using related theories such as a dynamic network resource availability measurement method and the like, can deeply analyze the utilization conditions of the turnout group resources in the throat area, and provides basis and reference for reasonable allocation of the resources of the marshalling station and further optimization of operation routes.

Description

Weibull distribution-based marshalling station throat turnout group resource availability calculation method
Technical Field
The invention belongs to the technical field of marshalling station throat area research, and particularly relates to a Weibull distribution-based method for calculating the availability of throat turnout group resources of marshalling stations.
Background
With the construction of the marshalling station integrated automation system, basic scheduling information is continuously perfected, so that a station scheduling department can conditionally utilize rich information resources to effectively monitor entity resources. The entity resources comprise outgoing line resources, hump resources, shunting line resources, pulling line resources, shunting machine resources and the like according to the sequence of the marshalling station flow process. The throat of the marshalling station controls the input and output of traffic and the running path of the shunting machine, and whether the throat normally directly influences the overall operation efficiency of the marshalling station or not. The utilization condition of the marshalling station throats is analyzed from the resource perspective, the availability of the resources in the throat area is counted, the use condition of each resource in the throat area in different time periods can be mastered by relying on the availability, and a basis is provided for further providing the utilization rate of the resources.
At present, the utilization of marshalling stations throat is studied from different angles at home and abroad. Establishing a composite hierarchical decision model of arrangement network optimization and throat operation capability of a station throat operation area, and performing theoretical verification; determining reasonable arrangement of the routes by a method of searching for the shortest path on a graph, and providing a determination method for directly obstructing a turnout group; based on cluster resource characteristics, a cluster job scheduling method based on availability is provided, and comparison and simulation prove that the cluster efficiency and job completion efficiency are improved by the algorithm. In the national intranet, when the marshalling station train is changed or sequenced, all entity resources are generally used as constraint conditions and are converted into mathematical problems to be solved, and the utilization attributes of the resources are rarely researched. Many related documents discuss calculation and optimization problems of capacities of a throat area and a turnout group of a marshalling station, but do not relate to utilization states of turnout group resources in the throat area of the marshalling station at different times, resource availability and the like.
Disclosure of Invention
Aiming at the defects in the prior art, the Weibull distribution-based method for calculating the availability of the throat turnout group resources of the marshalling station solves the problem that the utilization state and the resource availability of the throat turnout group resources of the marshalling station at different times are not calculated and analyzed in the prior art.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: the Weibull distribution-based method for calculating the availability of the resources of the throat turnout group of the marshalling station comprises the following steps of:
s1, recording the execution conditions of each job in the time period t in different job time periods, and comparing the execution conditions with the job conditions obtained through actual statistics to obtain the resource vacancy degree of the resource x in the time t;
s2, determining parameters for calculating the reliability of the turnout group resources in the throat area of the marshalling station, collecting and sorting corresponding index data for analysis, and obtaining the resource reliability of the resource x in the time t;
s3, calculating the resource availability according to the resource reliability and the resource vacancy;
in step S1, the resource idleness is a ratio of the number of task frequencies that the throat switch group can process in a time slot to the theoretical maximum use frequency;
in step S2, the resource reliability is the probability of the throat switch group completing the operation plan in a time slot, and is a variable quantity with time;
in step S3, the resource availability is a probability that the throat switch group can start a job within a time period and can complete the job under a certain time constraint;
the theoretical maximum use frequency is the number of times that one piece of equipment or facility uses in unit time by taking the maximum utilization frequency of comprehensive resources as a target under the conditions of meeting the minimum working time constraint, the working operation sequence and the operation balance of the equipment and the facility.
Further, the step S1 is specifically:
s1-1, aiming at the switch groups in the throat area of the marshalling station, analyzing operation related sequences of all the switch groups and establishing a topological network structure;
s1-2, determining a target function by using a time sequence and an optimization method according to a topological network structure, constraining according to each resource time space, and establishing a theoretical maximum use frequency calculation model of the resources in the throat area;
s1-3, according to the theoretical maximum use frequency calculation model of the resources in the throat area, counting the actual utilization condition of the resources x in a time period and the theoretical maximum use frequency condition of the resources, and according to the actual utilization condition and the time curve of the theoretical maximum use frequency of the resources, calculating the work marginal utility value of the turnout group resources x used in the time period t
Figure GDA0002542787490000031
And expected marginal utility value of working curve
Figure GDA0002542787490000032
S1-4, according to
Figure GDA0002542787490000033
And
Figure GDA0002542787490000034
calculating the resource vacancy;
the calculation formula of the resource vacancy degree is as follows:
Figure GDA0002542787490000035
in the formula (I), the compound is shown in the specification,
Figure GDA0002542787490000036
representing the actually used work curve marginal utility value of the resource x in the time period t;
Figure GDA0002542787490000037
and the marginal utility value of the working curve which is expected to be used by the resource x in the t time period is shown.
Further, the step S1-1 specifically includes:
the method comprises the steps of regarding all resources in a throat area as a point set, regarding lines among all turnout group resources as an edge set, connecting points and edges according to spatial positions and hostile access arrangement conditions, calculating according to application of a time sequence method on the basis of counting unit time occupied by all operations of a marshalling station, and obtaining operation sequences ij executed by the resources x in a working period and initial time occupied by each sequence
Figure GDA0002542787490000038
And end time
Figure GDA0002542787490000039
Calibrating the resources of each turnout group occupied by the operation sequence ij to determine the optimal operation route LijAnd an adversary access group, and a complete topological network structure is constructed.
Further, in step S1-2:
the minimum time of the operation X, Y, Z of the i-th train and the j-th train is respectively set as
Figure GDA00025427874900000310
Different operations X of the same trainij、Yij、ZijHave a certain operation precedence relationship between them, and set operation Xij、Yij、ZijRespectively of a start time and an end time of
Figure GDA00025427874900000311
And
Figure GDA00025427874900000312
if Xij、Yij、ZijAre ordered according to the sequenceOrder, then there is a spatial constraint:
Figure GDA00025427874900000313
if different jobs involve the same resource, the common resource needs to be occupied in different time periods, and the job time sequence meets the order requirements before and after the job, then there is a space constraint condition:
Figure GDA0002542787490000041
in the formula, n represents the total number of tracks, and m represents the total number of trains;
division of hostile operation groups according to principle that operation resources are not occupied simultaneously
Figure GDA0002542787490000042
Wherein
Figure GDA0002542787490000043
Representing sets of tracks and trains, respectively, then there are constraints: :
Figure GDA0002542787490000044
of formula (II) to'Working interval、t″Working interval、t″′Working intervalRespectively representing the minimum interval time between different operations, which is determined by the resource release time of the equipment resource occupied by each operation;
the objective function comprises an objective function I and an objective function II:
the first objective function is as follows:
Figure GDA0002542787490000045
in the formula
Figure GDA0002542787490000046
Indicates the ith trackEnd time occupied by the j +1 th train; gijRepresenting the starting time of the ith track occupied by the jth train;
the second objective function is:
Figure GDA0002542787490000047
in the formula (I), the compound is shown in the specification,
Figure GDA0002542787490000048
representing the starting time of resource occupation of the jth train operation of the ith track;
Figure GDA0002542787490000049
representing the ending time of the resource occupied by the j train operation of the ith track;
Figure GDA00025427874900000410
obtaining a theoretical maximum use frequency calculation model of the throat area resources according to the constraint conditions and the objective function, wherein the theoretical maximum use frequency calculation model comprises the following steps:
Figure GDA0002542787490000051
further, the marginal utility value of the working curve in the step S1-3 is: an incremental value of the workload of the device or facility when every unit time is incremented;
drawing a workload-time curve f (t) of the equipment or the facility on the basis of counting the working strength of the known equipment or facility in a certain continuous timexThe marginal utility value of the work curve of the device or facility at time T is numerically equal to the slope of the tangent to the point of the workload-time curve corresponding to time T.
Further, the calculation formula of the resource reliability in step S2 is:
Figure GDA0002542787490000052
in the formula, A' (x)tRepresenting the credibility of the resource x statistically obtained from historical data in the time period t;
Figure GDA0002542787490000053
represents the time when resource x is actually occupied while job i is performed;
Figure GDA0002542787490000054
represents the time that resource x is occupied as planned when job i is performed;
Figure GDA0002542787490000055
representing the number of times that the actual occupied time of the resource x is greater than the planned occupied time when the operation i is performed;
nt-1represents the total number of jobs executed by resource x during the t-1 period;
Tt ywrepresenting the occupied time of the resource x in the t time period due to the construction of the station according to the construction plan;
Figure GDA0002542787490000056
representing the probability of occupation of the resource x by station construction;
Tt xwrepresenting the time occupied by the resource x in the time period t for emergency maintenance construction due to the fault;
Txrepresents the projected age of resource x;
trepresenting the proportion of the resource use condition in calculating the reliability in the time period t;
A″(x)t-1representing the idleness of the resource x during the t-1 time period;
trepresenting the proportion of the resource use condition in calculating the reliability in the time period t;
the above-mentionedtThe calculation formula of (2) is as follows:
Figure GDA0002542787490000061
further, the predicted service life T of the turnout group resourcexThe probability function of the cumulative failure is the probability of failure in the period of time when the resource equipment works and is informed, and the expected service life T of the turnout group resource is obtainedxComprises the following steps:
Figure GDA0002542787490000062
wherein, f (t) represents the probability that the resource fails to complete the task in the time period t, and represents the cumulative failure probability of the resource;
the cumulative failure function is derived from the Weibull distribution as:
Figure GDA0002542787490000063
in the formula (I), the compound is shown in the specification,
Figure GDA0002542787490000064
is an estimate of the shape parameter;
t' represents the time of cumulative work of the resource since the last maintenance or replacement;
Figure GDA0002542787490000065
is an estimated value of the scale parameter;
the estimated values of the shape parameters and the scale parameters are obtained by maximum likelihood estimation as follows:
Figure GDA0002542787490000066
further, the calculation formula of the resource availability is as follows:
A(x)t＝αtA′(x)t+(1-αt)tA″(x)t(13)
in the formula, A (x)tRepresenting the availability of resource x during a time period t;
A′(x)trepresenting the credibility of the resource x statistically obtained from historical data in the time period t;
A″(x)trepresenting the relative idle degree of the resource x in the t time period;
αtrepresenting the proportion of the resource credibility in the process of calculating the resource availability;
the αtThe calculation formula of (2) is as follows:
Figure GDA0002542787490000071
the invention has the beneficial effects that: the invention considers the occupation conditions of trains, shunting machines and vehicles in the throat area of the marshalling station, designs a calculation method for the availability of the turnout group resources in the throat area of the marshalling station by using related theories such as a dynamic network resource availability measurement method and the like, can deeply analyze the utilization conditions of the turnout group resources in the throat area, and provides basis and reference for reasonable allocation of the resources of the marshalling station and further optimization of operation routes.
Drawings
Fig. 1 is a flowchart of an implementation of a method for calculating availability of throat switch group resources of a marshalling station based on weibull distribution in an embodiment of the present invention.
Fig. 2 is a flowchart of an implementation of a resource availability calculation method according to an embodiment of the present invention.
Fig. 3 is a diagram for converting the position relationship of switch groups in the throat area of a marshalling station in the embodiment provided by the invention.
Fig. 4 is a diagram illustrating the work of physical resources in the throat area of a marshalling station according to an embodiment of the present invention.
Fig. 5 is a statistical diagram of the utilization time of the switch group resources in the throat area of the marshalling station in the embodiment provided by the invention.
Fig. 6 is a schematic diagram of statistics of availability of switch group resources in the throat area of a marshalling station according to an embodiment of the present invention.
Fig. 7 is a graph showing the relationship of the enemy approach in the throat area of the north lanzhou marshalling station in the embodiment provided by the invention.
FIG. 8 is a statistical chart of total number of times of computing and operating turnout group resources in the throat area of the North Branch of Lanzhou in the embodiment provided by the invention.
FIG. 9 is a statistical chart of the total number of actual applications of the switch group resources in the throat area of the North Branch of Lanzhou, according to an embodiment of the present invention.
FIG. 10 is a statistical chart of the comprehensive resource availability of the switch groups in the throat area of the North Branch of Lanzhou, according to the embodiment of the invention.
FIG. 11 is a statistical chart of the comprehensive resource availability of the switch group in the throat area of the North Branch of Lanzhou in the embodiment provided by the present invention.
Fig. 12 is a thermodynamic diagram of the 9 o' clock throat area of the north-standing throat area of langhou in accordance with an embodiment of the present invention.
Fig. 13 is a thermodynamic diagram of the 12 o' clock throat area of the north-south pharyngeal area of Lanzhou according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
As shown in fig. 1, the method for calculating the availability of resources of the throat switch group of the marshalling station based on the weibull distribution comprises the following steps:
and S1, recording the execution conditions of each job in the time period t in different job time periods, and comparing the execution conditions with the job conditions obtained through actual statistics to obtain the resource vacancy degree of the resource x in the time t.
The resource vacancy is the ratio of the frequency of tasks which can be processed by the throat turnout group in a time period to the theoretical maximum use frequency.
As shown in fig. 2, the specific method of step S1 includes:
s1-1, aiming at the switch groups in the throat area of the marshalling station, analyzing operation related sequences of all the switch groups and establishing a topological network structure;
when the throat area of the marshalling station is operated, a certain resource of the throat area can only be occupied by one operation in space-time, and the vacancy and the maximum utilization condition of the turnout group resource of the throat area need to be counted before the availability of the turnout group resource of the throat area is calculated. The statistics generally adopts an interest rate method, a graphical method and the like, and has larger thought influence factors, so that the statistics of the vacancy degree condition of the throat turnout group resources has larger errors.
In topology, geometric figures or space can keep the constant property after continuously changing the shape, and only the position relation between the physics is considered and the shape and the size of the geometric figures or the space are not considered.
The method comprises the steps of regarding all resources in a throat area as a point set, regarding lines among all turnout group resources as an edge set, connecting points and edges according to spatial positions and hostile access arrangement conditions, calculating according to application of a time sequence method on the basis of counting unit time occupied by all operations of a marshalling station, and obtaining operation sequences ij executed by the resources x in a working period and initial time occupied by each sequence
Figure GDA0002542787490000094
And end time
Figure GDA0002542787490000095
Calibrating the resources of each turnout group occupied by the operation sequence ij to determine the optimal operation route LijAnd hostile access groups, a complete topological network structure as shown in fig. 3 can be constructed.
As shown in fig. 3, all the traversable paths of each job sequence required to be executed in the throat area of the marshalling station from the beginning to the end are sequentially the sets of tracks and switch groups which each job sequence may pass through from right to left.
S1-2, determining a target function by using a time sequence and an optimization method according to a topological network structure, constraining according to each resource time space, and establishing a theoretical maximum use frequency calculation model of the resources in the throat area;
the theoretical maximum use frequency is the number of times that one piece of equipment or facility is used in unit time by taking the maximum utilization frequency of comprehensive resources as a target under the conditions of meeting the minimum working time constraint, the working operation sequence and the working balance of the equipment and the facility.
The maximum utilization condition of the switch group resources in the throat area of the marshalling station is calculated and expanded based on the operation sequence of the throat area of the marshalling station, under the condition that the switch group and other equipment resources in the throat area of the marshalling station are limited, the time occupied by each operation of each equipment is analyzed, the idle time sequence of each resource is determined, the optimal route of each operation is determined by combining a topological network diagram, and the hostile route is screened.
The minimum time of the operation X, Y, Z of the i-th train and the j-th train is respectively set as
Figure GDA0002542787490000091
Different operations X of the same trainij、Yij、Zij.., setting operation Xij、Yij、ZijRespectively of a start time and an end time of
Figure GDA0002542787490000092
And
Figure GDA0002542787490000093
if Xij、Yij、ZijIf the data are arranged in sequence, space constraint conditions exist
Figure GDA0002542787490000101
The starting time of the subsequent operation item of the same train operation sequence must be greater than or equal to the ending time of the previous operation, and the requirement of meeting
Figure GDA0002542787490000102
Different jobs involve the same resource, the common resource needs to be occupied in different time slots, and the job time sequence meets the order requirement before and after the job, then there is space constraint condition:
Figure GDA0002542787490000103
in the formula, n represents the total number of tracks, and m represents the total number of trains;
different stock path operations may also conflict in time and space, so hostile operations need to be distinguished; only one job in the enemy job sequence group can be performed at the same time, and the job meets the constraint condition. Division of hostile operation groups according to principle that operation resources are not occupied simultaneously
Figure GDA0002542787490000104
Wherein
Figure GDA0002542787490000105
Representing sets of tracks and trains, respectively, then there are constraints:
Figure GDA0002542787490000106
of formula (II) to'Working interval、t″Working interval、t″′Working intervalRespectively representing the minimum interval time between different operations, which is determined by the resource release time of the equipment resource occupied by each operation;
the maximum time of the resources occupied in one day is 1440min, the idle time of each station track is required to be minimum under the condition of ensuring the number of the vehicles to be received, and an objective function is provided on the assumption that M is a large number
Figure GDA0002542787490000107
In the formula
Figure GDA0002542787490000108
Representing the end time of the ith track occupied by the j +1 th train; gijIndicating the starting time of the ith track occupied by the jth 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 kept relatively balanced, another objective function is provided
Figure GDA0002542787490000111
In the formula (I), the compound is shown in the specification,
Figure GDA0002542787490000112
representing the starting time of resource occupation of the jth train operation of the ith track;
Figure GDA0002542787490000113
representing the ending time of the resource occupied by the j train operation of the ith track;
Figure GDA0002542787490000114
and (3) synthesizing the utilization conditions of all the tracks to obtain a theoretical maximum use frequency calculation model of the resources in the throat area, which is as follows:
Figure GDA0002542787490000115
s1-3, according to the theoretical maximum use frequency calculation model of the resources in the throat area, counting the actual utilization condition of the resources x in a time period and the theoretical maximum use frequency condition of the resources, and according to the actual utilization condition and the time curve of the theoretical maximum use frequency of the resources, calculating the work marginal utility value of the turnout group resources x used in the time period t
Figure GDA0002542787490000116
And expected marginal utility value of working curve
Figure GDA0002542787490000117
The marginal utility of the above-mentioned operation curve is an increased value of the workload of the equipment or facility when increasing every unit time. Drawing a workload-time curve f (t) of the equipment or the facility on the basis of counting the working strength of the known equipment or facility within a certain timexWorking curve of the plant or installation at time TThe marginal utility value is numerically equal to the slope of the tangent to the point of the workload-time curve corresponding to time T.
S1-4, according to
Figure GDA0002542787490000118
And
Figure GDA0002542787490000119
calculating the resource vacancy;
the calculation formula of the resource vacancy degree is as follows:
Figure GDA00025427874900001110
in the formula (I), the compound is shown in the specification,
Figure GDA00025427874900001111
representing the actually used work curve marginal utility value of the resource x in the time period t;
Figure GDA00025427874900001112
the marginal utility value of the working curve which is used in the resource x in the time t is shown.
The actual daily working time and the predicted working time of the resources in the throat area of the marshalling station are shown in fig. 4, and the daily working time of the resources in the turnout group in the throat area of the marshalling station is often much shorter than the predicted working time due to various controllable factors such as meals, commuting shift and the like and uncontrollable factors such as scheduled delay execution, equipment failure and the like.
In FIG. 4, at time T, the utilization efficiency of a certain switch group in the throat area is numerically equal to the slope of the cumulative daily working time curve at time T, so that the utilization rate of the resources of the switch group at this time is 1-A' (x)tEqual to the ratio of the slope of the actual operating time curve to the expected operating time curve at the instant T, A' (x)tNamely the vacancy degree of the turnout group resources.
S2, determining parameters for calculating the reliability of the turnout group resources in the throat area of the marshalling station, collecting and sorting corresponding index data for analysis, and obtaining the resource reliability of the resource x in the time t;
the resource reliability is the probability of the throat turnout group completing the operation plan in a time period, and is the variable quantity along with the time;
the calculation formula of the resource reliability of step S2 is:
Figure GDA0002542787490000121
in the formula, A' (x)tRepresenting the credibility of the resource x statistically obtained from historical data in the time period t;
Figure GDA0002542787490000122
represents the time when resource x is actually occupied while job i is performed;
Figure GDA0002542787490000123
represents the time that resource x is occupied as planned when job i is performed;
Figure GDA0002542787490000124
representing the number of times that the actual occupied time of the resource x is greater than the planned occupied time when the operation i is performed;
nt-1represents the total number of jobs executed by resource x during the t-1 period;
Tt ywrepresenting the occupied time of the resource x in the t time period due to the construction of the station according to the construction plan;
Figure GDA0002542787490000125
representing the probability of occupation of the resource x by station construction;
Tt xwrepresenting the time occupied by the resource x in the time period t for emergency maintenance construction due to the fault;
Txrepresents the projected age of resource x;
trepresenting assets in a t periodThe proportion of the source usage in calculating the confidence level;
A″(x)t-1representing the idleness of the resource x during the t-1 time period;
trepresenting the proportion of the resource use condition in calculating the reliability in the time period t;
tthe calculation formula of (2) is as follows:
Figure GDA0002542787490000131
in the formula, A' (x)t-1Representing the credibility of the resource x obtained by historical data statistics in the time period t-1;
A′(x)t-2representing the relative idle degree of the resource x in the t-2 time period;
estimated service life T of the turnout group resourcexThe estimated service life T of the turnout group resource is obtained by the cumulative failure probability function of the resource, wherein the cumulative failure probability function is the probability of failure in the period of time when the resource equipment works and is informedxComprises the following steps:
Figure GDA0002542787490000132
wherein, f (t) represents the probability that the resource fails to complete the task in the time period t, and represents the cumulative failure probability of the resource;
wherein the cumulative failure function is derived from a Weibull distribution;
the Weibull distribution is obtained according to a weakest environment model or a series model, can better reflect the influence of material defects and stress concentration sources on the fatigue life of the material, has incremental failure rate, is better suitable for a distribution mode of wear accumulation failure of electromechanical products, is an expanded exponential distribution function, can be converted into exponential distribution, Rayleigh distribution, approximate normal distribution and the like, and has stronger adaptability compared with other statistical distributions;
most of the equipment in the throat area of the marshalling station is mechanical and electrical equipment, the equipment is subjected to an inspection test before use, the minimum service life of the equipment is greater than 0, the service life of the equipment is a continuous random variable, two-parameter Weibull distribution can be selected for processing according to the numerical distribution characteristics of the equipment, and the cumulative failure function expression of the two-parameter Weibull distribution is as follows:
Figure GDA0002542787490000141
in the formula (I), the compound is shown in the specification,
Figure GDA0002542787490000142
is an estimate of the shape parameter;
t' represents the time of cumulative work of the resource since the last maintenance or replacement;
Figure GDA0002542787490000143
is an estimated value of the scale parameter;
the probability density of the distribution is:
Figure GDA0002542787490000144
in the formula: gamma is a shape parameter; t' represents the time of cumulative work of the resource since the last maintenance or replacement; lambda is a scale parameter and represents the peak condition of the resource life distribution curve; according to the practical situation, the shortest working time of the resources of the throat turnout group cannot be less than 0, so that the condition that t' is more than or equal to 0 is only needed to be considered when the cumulative failure probability of the resources of the throat turnout group is calculated.
The historical fault data of each resource of the throat turnout group is analyzed, the service life time sequence of each turnout group equipment resource can be obtained, when the historical data is more comprehensive, the historical fault data of n resources can be selected for analysis, and the parameter estimation of Weibull distribution is carried out by adopting the maximum likelihood estimation.
Let the non-failure operation time sequence of a certain turnout group resource be T '═ T'1,t′2,…,t′n]Known Weibull distribution DensityThe function is f (t', lambda, gamma), x is more than or equal to 0, and the likelihood function can be obtained:
Figure GDA0002542787490000145
taking the logarithmic function as:
Figure GDA0002542787490000146
calculating the deviation of lambda and gamma, and combining
Figure GDA0002542787490000151
Obtaining:
Figure GDA0002542787490000152
from the properties of the weibull distribution, when T 'to F (λ, γ), Y ═ ln T' follows an extremal distribution, and γ ═ 1/σ, λ ═ e existu(ii) a From this, an estimate of the unknown parameters in the Weibull distribution can be obtained
Figure GDA0002542787490000153
Wherein:
Figure GDA0002542787490000154
and
Figure GDA0002542787490000155
the optimal linear invariant estimation coefficients for u and σ are shown; the cumulative failure function of the available resources of the throat turnout group is as follows:
Figure GDA0002542787490000156
in the formula (I), the compound is shown in the specification,
Figure GDA0002542787490000157
is an estimate of the shape parameter;
t' represents the time of cumulative work of the resource since the last maintenance or replacement;
Figure GDA0002542787490000158
is an estimated value of the scale parameter;
the estimated values of the shape parameters and the scale parameters are obtained by maximum likelihood estimation as follows:
Figure GDA0002542787490000159
when the data volume is further reduced, the information of the time when the equipment fails is not obtained in the data acquisition stage, the calculation of the accumulated failure function of the resources of the throat turnout group cannot be carried out by the method, and the estimation can be carried out by using the methods in the reliability evaluation and service life prediction of non-failure data; collecting a group of non-failure data T ″ ═ T ″1,t″2,…t″n]The confidence lower limit that the confidence coefficient of the switch group resource reliability life T is α is as follows:
Figure GDA00025427874900001510
wherein the confidence coefficient value is generally 85%, wherein F0Representing the probability of expected resource primary failure, gamma0And the minimum predicted shape parameter is the minimum value of the resource shape parameters of the station with the overall other data.
The confidence of the switch group resource cumulative failure probability is α, and the upper confidence limit on one side is:
Figure GDA0002542787490000161
after the throat turnout group resources are failed and maintained, the initial state is considered to be recovered, the accumulated failure probability is recovered to the original state, and the accumulated use time of the resources is counted again.
S3, calculating the resource availability according to the resource reliability and the resource vacancy;
in step S3, the resource availability is a probability that the throat switch group can start a job within a time period and can complete the job under a certain time constraint;
the calculation formula of the resource availability is as follows:
A(x)t＝αtA′(x)t+(1-αt)tA″(x)t(20)
in the formula, A (x)tRepresenting the availability of resource x during a time period t;
A′(x)trepresenting the credibility of the resource x statistically obtained from historical data in the time period t;
A″(x)trepresenting the relative idleness of the resource x during the time period t;
αtrepresenting the proportion of the resource credibility in the process of calculating the resource availability;
αtthe calculation formula of (2) is as follows:
Figure GDA0002542787490000162
wherein, A' (x)t-1Representing the credibility of the resource x obtained by historical data statistics in the time period t-1;
A′(x)t-2representing the relative idle degree of the resource x in the t-2 time period;
the availability of the switch group resources in the throat area needs to consider the idleness of the switch group resources in the throat area and also the working stability of the switch group resources, namely, the switch group resources are given certain strength in a certain time period, and whether the switch group resources can be completed with higher reliability is examined. The statistical result of the historical data used by the availability of the resources in the throat area of the marshalling station changes along with the advancing of time, and the completion condition of the historical job task influences the availability of the resources. The prior completion of the historical operation can improve the resource availability to a certain extent by being carried out at a higher quality in time, the delayed completion of the historical operation can reduce the resource availability by being carried out at a lower quality, the running time of the throat area resource and the available stock are time-varying parameters, and the use condition of the throat area of the marshalling station can be represented as shown in figure 5 and figure 6.
FIG. 5 is a diagram illustrating the statistical situation of the application time of various resources, which is calculated according to different classifications of the resources, so that the usage degree of various resources in different time periods can be visually compared, and the calculated idleness of the resources can be verified; fig. 6 is a schematic diagram of a curve of availability of multiple resources in a throat area versus time, and the availability of different resources at different times can be intuitively understood through fig. 7, so as to provide a basis for analyzing station operations.
In one embodiment of the present invention, a process for performing analysis calculation by applying the method provided by the present invention to an actual case is provided:
the data from the north lanzhou marshalling station was analyzed for a 24 hour period. The arrival field of the northern Lanzhou station has 1-6 tracks which go upwards to arrive the train and 7-12 tracks which go downwards to arrive the train. The occupied time of the vehicle receiving approach of each station is set as 10 minutes, the minimum operation time is 25 minutes, the time for pushing each station to a hump, the vehicle receiving approach section and the like is set as 5 minutes, and the operation time for disassembling the hump is set as 30 minutes. And (4) grouping switches in throat areas of northern Lanzhou stations, and determining occupation conditions of various operations.
1. Analyzing the accumulated resource application times of the throat turnout group;
as 1-6 uplink receiving operation conflicts with the disassembling operation, and 7-12 locomotive entering operation conflicts with the disassembling operation, in order to clarify the enemy relationship of each route, an enemy route relationship diagram as shown in figure 7 is established, and an enemy route group is determined.
Converting the throat area of the north Lanzhou marshalling station into a topological network structure, calculating the theoretical application condition of the turnout group in the throat area between the arrival site of the north Lanzhou marshalling station and the shunting site by using the algorithm of a formula (6), counting the turnout group in the throat area according to the calculation result in different time periods, and drawing a frequency table of the turnout group resource occupation in the throat area, wherein the frequency table is shown in a table 1.
TABLE 1 accumulated times of calculation and application of switch group resources in northern Lanzhou station throat area
Figure GDA0002542787490000181
It can be seen from table 1 that there is a certain difference in the degree of application between different switch groups, and the maximum difference value appears between switch group No. 22 and switch group No. 36, and the difference value is 182. The number of times of application of different turnout groups has a certain relationship with the spatial distribution thereof, the turnout group application at the entrance close to the throat area is relatively busy, and the turnout group on the route with more parallel routes is idle.
And carrying out time-sharing statistics on the actual application times of the turnout group in the throat area of the Lanzhou north marshalling station in one day to obtain an accumulated time table of actual application of the turnout group resource in the throat area of the Lanzhou north marshalling station.
TABLE 2 accumulated times of actual application of switch group resources in northern Lanzhou station throat area
Figure GDA0002542787490000182
It can be further confirmed from table 2 that there is a certain difference in the degree of application between different switch groups, and part of the differences are large, and the difference in the number of times between 18 switch groups with the largest cumulative number of times of application and 36 switch groups with the smallest cumulative number of times of application is 108.
Theoretical calculation use conditions and actual use conditions of all turnout groups are obtained according to statistics, and an application times accumulation graph of part turnout groups (No. 2-20) is drawn by time-sharing statistics, as shown in figures 8 and 9.
Fig. 8 and 9 are respectively the calculation and application times accumulation and actual use times accumulation of partial throat turnout groups, and the comparison shows that both the two figures show a certain linear growth trend, and the growth trend situation of each turnout group number is relatively similar. Therefore, in the actual operation environment of the marshalling station, the use of the operating resources of the turnout groups in the throat area has a certain matching relationship due to the time-space setting, and the turnout groups which are associated with each other have certain similarity in the growth trend.
2, analyzing the vacancy of the resources of the throat turnout group;
on the basis of the counted number of times of application of each time period of the switch group in the throat area, fitting an application condition curve of each throat switch group by adopting a MAT L AB curve fitting method, and calculating the application condition curve of the corresponding throat switch group at the node T of each time period
Figure GDA0002542787490000191
Dot sum
Figure GDA0002542787490000192
The slope at the point is calculated according to the formula (7) to calculate the resource vacancy of the turnout group in the throat area of the northern Lanzhou station, and the statistics are shown in the table 3.
TABLE 3 Lanzhou North station throat area Turnout group resource vacancy
Figure GDA0002542787490000193
According to the resource vacancy calculated by the turnout group No. 2-40 within 24 hours, the comprehensive vacancy of the turnout group resource in the throat area can be obtained by performing weighting calculation in combination with the frequency of the turnout group resource in the throat area of the North Lanzhou marshalling station counted in the table 1 and the table 2. The idleness is combined with the use frequency of turnout group resources, weighting statistics is carried out at different time intervals, and the integral idleness of the turnout group resources in the throat area can be better reflected. The calculated synthetic resource idleness of the throat area of the north lanzhou marshalling station is shown in table 4.
TABLE 4 Lanzhou North station throat area turnout group comprehensive resource vacancy
Figure GDA0002542787490000201
Drawing a comprehensive resource vacancy degree statistical graph of a turnout group in a throat area of a northern Lanzhou station as shown in a graph 10; as can be seen from FIG. 10, the difference of the vacancy of the switch group in the throat area is large in different time periods, and due to the complexity and the fluctuation of the operation condition, the vacancy of the throat area resource presents a certain fluctuation condition in 24 hours a day, and the distance between the wave crests is about 4 h.
3. Analyzing the availability of the resources of the throat turnout group;
averaging based on historical statistics at North Lanzhou marshalling stations, in an exemplary calculation
Figure GDA0002542787490000202
The values are all 15min, and the time is 15min,
Figure GDA0002542787490000203
the time is 20min, and the time is,
Figure GDA0002542787490000204
is 0.2, Tt ywThe average value is 5min, and the average value is 5min,
Figure GDA0002542787490000205
is 0.1, Tt xwThe time is taken to be 10min,00.5, the failure rate of the resources of the throat turnout group is low according to the historical data condition, and the resources are taken for convenient calculation
Figure GDA0002542787490000206
The value is 0.01, and A' (x) in the example is obtained according to equation (7)0Both are 66.27%.
Because the number of the turnout groups in the throat area is large, after the use frequency of different turnout groups in the throat area is counted, the comprehensive resource availability of the turnout groups in the throat area can be obtained by combining the weighted calculation of the resource availability of a single turnout group; the comprehensive resource availability of the switch group in the throat area is a probability measurement of the overall availability of the switch group resources in the throat area.
In the calculating step, the comprehensive vacancy condition of the turnout group in the throat area of the northern station of Lanzhou is obtained, and the comprehensive vacancy condition is combined with the resource availability A' (x)tAccording to the formula (7), the formula (8) and the formula (20), the comprehensive availability of the turnout group resources in the throat area of the north station of Lanzhou can be calculated as shown in the table 5.
TABLE 5 comprehensive resource availability for switch groups in North Lanzhou railway station throat area
Figure GDA0002542787490000207
As can be seen from table 5, in 24 hours a day, the maximum value of the total availability of the switch group resources in the throat area of the north lan station appears 74.06% at time period 23, the minimum value appears 28.02% at time period 16, and the difference between the maximum value and the minimum value is 46.04%, which indicates that there is a large difference in the availability of the switch group in the throat area at different time periods. The daily average value of the comprehensive availability of the resources of the turnout group in the north station throat area of Lanzhou is 51.42%, which shows that the availability of the resources in the throat area is moderate, the operation condition is moderate, and partial capacity to be used still exists. Therefore, historical change rules can be mastered by calculating the resource availability value in real time, and a basis is provided for work plan compilation.
Fig. 11 reflects the fluctuation of the comprehensive availability of the switch group resources in the throat area of the north station of lanzhou, which shows that the switch group resources have certain differences in use conditions at different time intervals in a day, the operation balance condition is not ideal, and the standard deviation of the availability is 0.1402 through calculation.
The feasibility and effectiveness of the method provided by the invention are demonstrated by the above examples, and it can be seen that:
(1) the use frequency of each turnout group resource in different time periods has certain difference in the throat area of the marshalling station due to the space configuration relationship of the turnout group resources and the time sequence condition of the operation of the turnout group resources;
(2) the resource vacancy and availability of different turnout groups in the throat area of the marshalling station have larger interpolation in the same time period, and the comprehensive resource availability of the turnout groups in the throat area also has larger difference in different time periods;
(3) the marshalling station operation has planning performance and volatility within a certain range, the comprehensive resource availability of the throat area presents a certain fluctuation condition in one day, and the distance between wave crests is about 4h-6 h;
(4) the comprehensive resource vacancy of the turnout group in the throat area of the marshalling station has great influence on available strands of the comprehensive resources, the time curve similarity of the turnout group and the available strand of the comprehensive resources is high, and the curve goodness of fit is between 70% and 85% for one section.
In one embodiment of the invention, a marshalling station throat area resource use thermodynamic diagram generation implementation method is also provided:
the marshalling station throat is used as a connection part among operation sequences of the marshalling station, a receiving train route, different shunting routes and the like all occupy the marshalling station throat area, the traditional method is that the utilization rate of the whole throat is represented by the utilization rate of one or a plurality of switches in the busiest time period all day, the traditional method is not intuitive enough, a thermodynamic diagram of the busiest degree of the operation of the throat switch area can be generated by means of a digital visualization technology, the utilization condition of the throat area resources can be better analyzed, and the specific steps are as follows:
a1, grouping the switches in the throat area according to the parallel route occupation, enemy route occupation and other throat switch grouping rules of each operation;
a2, analyzing the operation conditions of different turnout groups in different time periods, and counting the total occupied time of the turnout groups according to different turnout group numbers;
a3, calculating and counting the difference value between the maximum time and the minimum time occupied by the turnout group, setting a time scale according to the number of gradients to be adopted, and dividing the time length occupied by the turnout group;
and A4, performing region mapping according to different operation markets, and giving different color depths to turnouts in different regions, thereby generating a resource use thermodynamic diagram of the turnout group in the throat region of the marshalling station.
According to the data statistics in the above example of the north lanzhou station, the occupation of the switch group from the north lanzhou marshalling station to the throat area of the arrival yard and the shunting yard for 6 hours before work can be obtained, as shown in table 6:
TABLE 6 statistical table of occupation situation of turnout group
Figure GDA0002542787490000221
Generating a throat area resource usage thermodynamic diagram as shown in fig. 12 and 13 according to the above steps; comparing fig. 12 and fig. 13, the thermodynamic conditions of different switch groups in the same thermodynamic diagram are obviously different, and the thermodynamic diagrams of the same switch group in different time periods are also different, so that the use conditions of the switch group resources in different time periods can be more clearly mastered through the thermodynamic diagram comparison of the busy degrees of the switch group resources in the throat areas of the marshalling stations in different time periods, more intuitive estimation conditions are provided for analyzing the vacancy and the availability of the switch group resources in the throat areas in different time periods, and the resource vacancy and the availability can be finally calculated through the thermodynamic distribution condition experience of the thermodynamic diagrams in different time periods.
The invention has the beneficial effects that: the invention considers the occupation conditions of trains, shunting machines and vehicles in the throat area of the marshalling station, designs a calculation method for the availability of the turnout group resources in the throat area of the marshalling station by using related theories such as a dynamic network resource availability measurement method and the like, can deeply analyze the utilization conditions of the turnout group resources in the throat area, and provides basis and reference for reasonable allocation of the resources of the marshalling station and further optimization of operation routes.

Claims (8)

1. The method for calculating the resource availability of the throat turnout group of the marshalling station based on Weibull distribution is characterized by comprising the following steps of:
s1, recording the execution conditions of each job in the time period t in different job time periods, and comparing the execution conditions with the job conditions obtained through actual statistics to obtain the resource vacancy degree of the resource x in the time t;
s2, determining parameters for calculating the reliability of the turnout group resources in the throat area of the marshalling station, collecting and sorting corresponding index data for analysis, and obtaining the resource reliability of the resource x in the time t;
s3, calculating the resource availability according to the resource reliability and the resource vacancy;
in step S1, the resource idleness is a ratio of the number of task frequencies that the throat switch group can process in a time slot to the theoretical maximum use frequency;
in step S2, the resource reliability is a probability that the throat switch group completes the operation plan in a time slot, and is a variable quantity with time;
in step S3, the resource availability is a probability that the throat switch group can start a job within a time period and can complete the job under a certain time constraint;
the theoretical maximum use frequency is the number of times that one piece of equipment or facility uses in unit time by taking the maximum utilization frequency of comprehensive resources as a target under the conditions of meeting the minimum working time constraint, the working operation sequence and the operation balance of the equipment and the facility.
2. The method for calculating the availability of the resources of the throat switch group of the marshalling station based on the weibull distribution according to claim 1, wherein the step S1 is specifically as follows:
s1-1, aiming at the switch groups in the throat area of the marshalling station, analyzing operation related sequences of all the switch groups and establishing a topological network structure;
s1-2, determining a target function by using a time sequence and an optimization method according to a topological network structure, constraining according to each resource time space, and establishing a theoretical maximum use frequency calculation model of the resources in the throat area;
s1-3, according to the theoretical maximum use frequency calculation model of the resources in the throat area, counting the actual utilization condition of the resources x in a time period and the theoretical maximum use frequency condition of the resources, and according to the actual utilization condition and the time curve of the theoretical maximum use frequency of the resources, calculating the marginal utility value of the working curve of the turnout group resources x used in the time period t
Figure FDA0002528417730000021
And expected marginal utility value of working curve
Figure FDA0002528417730000022
S1-4, according to
Figure FDA0002528417730000023
And
Figure FDA0002528417730000024
calculating the resource vacancy;
the calculation formula of the resource vacancy degree is as follows:
Figure FDA0002528417730000025
in the formula (I), the compound is shown in the specification,
Figure FDA0002528417730000026
representing the actually used work curve marginal utility value of the resource x in the time period t;
Figure FDA0002528417730000027
and the marginal utility value of the working curve which is expected to be used by the resource x in the t time period is shown.
3. The Weibull distribution-based method for calculating the resource availability of the throat switch group of the marshalling station according to claim 2, wherein the step S1-1 is specifically as follows:
the method comprises the steps of regarding all resources in a throat area as a point set, regarding lines among all turnout group resources as an edge set, connecting points and edges according to spatial positions and hostile access arrangement conditions, calculating according to application of a time sequence method on the basis of counting unit time occupied by all operations of a marshalling station, and obtaining operation sequences ij executed by the resources x in a working period and initial time occupied by each sequence
Figure FDA0002528417730000028
And end time
Figure FDA0002528417730000029
Calibrating the resources of each turnout group occupied by the operation sequence ij to determine the optimal operation route LijAnd an adversary access group, and a complete topological network structure is constructed.
4. The Weibull distribution-based method for calculating the resource availability of the throat switch groups of the marshalling stations according to the claim 2, wherein in the step S1-2:
the minimum time of the operation X, Y, Z of the i-th train and the j-th train is respectively set as
Figure FDA00025284177300000210
Different operations X of the same trainij、Yij、ZijHave a certain operation precedence relationship between them, and set operation Xij、Yij、ZijRespectively of a start time and an end time of
Figure FDA00025284177300000211
And
Figure FDA00025284177300000212
if Xij、Yij、ZijIf the data are arranged in sequence, space constraint conditions exist:
Figure FDA0002528417730000031
if different jobs involve the same resource, the common resource needs to be occupied in different time periods, and the job time sequence meets the order requirements before and after the job, then there is a space constraint condition:
Figure FDA0002528417730000032
in the formula, n represents the total number of tracks, and m represents the total number of trains;
division of hostile operation groups according to principle that operation resources are not occupied simultaneously
Figure FDA0002528417730000033
Wherein
Figure FDA0002528417730000034
Representing sets of tracks and trains, respectively, then there are constraints:
Figure FDA0002528417730000035
of formula (II) to'Working interval、t″Working interval、t″′Working intervalRespectively representing the minimum interval time between different operations, which is determined by the resource release time of the equipment resource occupied by each operation;
the objective function comprises an objective function I and an objective function II:
the first objective function represents that the idle time of each station track is minimum under the condition of ensuring the number of the received vehicles, and specifically comprises the following steps:
Figure FDA0002528417730000036
in the formula
Figure FDA0002528417730000037
Representing the end time of the ith track occupied by the j +1 th train; gijRepresenting the starting time of the ith track occupied by the jth train; z is the idle time of each track space, and M is a coefficient related to the occupied time of the resource;
the second objective function represents that the daily workload of each track is kept relatively balanced, and specifically comprises the following steps:
Figure FDA0002528417730000038
in the formula (I), the compound is shown in the specification,
Figure FDA0002528417730000041
the daily work amount of each stock path is shown,
Figure FDA0002528417730000042
representing the starting time of resource occupation of the jth train operation of the ith track;
Figure FDA0002528417730000043
representing the ending time of the resource occupied by the j train operation of the ith track;
Figure FDA0002528417730000044
obtaining a theoretical maximum use frequency calculation model of the throat area resources according to the constraint conditions and the objective function, wherein the theoretical maximum use frequency calculation model comprises the following steps:
Figure FDA0002528417730000045
5. the Weibull distribution-based method for calculating the resource availability of the throat switch groups of the marshalling stations according to claim 2, wherein the marginal utility value of the working curve in the step S1-3 is as follows: an incremental value of the workload of the device or facility when every unit time is incremented;
drawing a workload-time curve f (t) of the equipment or the facility on the basis of counting the working strength of the known equipment or facility in a certain continuous timexThe marginal utility value of the work curve of the device or facility at time T is numerically equal to the slope of the tangent to the point of the workload-time curve corresponding to time T.
6. The Weibull distribution-based method for calculating the resource availability of the throat switch groups of the marshalling stations according to claim 2, wherein the resource reliability of step S2 is calculated by the following formula:
Figure FDA0002528417730000046
in the formula, A' (x)tRepresenting the credibility of the resource x statistically obtained from historical data in the time period t;
Figure FDA0002528417730000047
represents the time when resource x is actually occupied while job i is performed;
Figure FDA0002528417730000048
represents the time that resource x is occupied as planned when job i is performed;
Figure FDA0002528417730000049
representing the number of times that the actual occupied time of the resource x is greater than the planned occupied time when the operation i is performed;
Figure FDA00025284177300000410
representing the number of times resource x is actually occupied while performing job i;
Figure FDA0002528417730000051
representing the number of times resource x is scheduled to be occupied while performing job i;
nt-1represents the total number of jobs executed by resource x during the t-1 period;
Tt ywrepresenting the occupied time of the resource x in the t time period due to the construction of the station according to the construction plan;
Figure FDA0002528417730000052
representing the probability of occupation of the resource x by station construction;
Tt xwrepresenting the time occupied by the resource x in the time period t for emergency maintenance construction due to the fault;
Txrepresents the projected age of resource x;
trepresenting the proportion of the resource use condition in calculating the reliability in the time period t;
A″(x)t-1representing the idleness of the resource x during the t-1 time period;
trepresenting the proportion of the resource use condition in calculating the reliability in the time period t;
the above-mentionedtThe calculation formula of (2) is as follows:
Figure FDA0002528417730000053
7. the Weibull distribution-based method for calculating the resource availability of the throat switch groups of marshalling stations according to claim 6, wherein the expected service life T of the switch group resource isxThe probability function of the cumulative failure is the probability of failure in the period of time when the resource equipment works and the expected service life T of the turnout group resource is obtainedxComprises the following steps:
Figure FDA0002528417730000054
wherein, f (t) represents the probability that the resource fails to complete the task in the time period t, and represents the cumulative failure probability of the resource;
the cumulative probability of failure is obtained from the weibull distribution as:
Figure FDA0002528417730000055
in the formula (I), the compound is shown in the specification,
Figure FDA0002528417730000056
is an estimate of the shape parameter;
t' represents the time of cumulative work of the resource since the last maintenance or replacement;
Figure FDA0002528417730000061
is an estimated value of the scale parameter;
the estimated values of the shape parameters and the scale parameters are obtained by maximum likelihood estimation as follows:
Figure FDA0002528417730000062
in the formula (I), the compound is shown in the specification,
Figure FDA0002528417730000063
the shape parameter is gamma, and the accumulated working time of the resource from the last maintenance or replacement in the operation i is carried out;
t′ithe time of the cumulative operation for starting the previous maintenance or replacement of the resource at the time of the job i.
8. The Weibull distribution-based method for calculating the resource availability of the marshalling station throat turnout group according to claim 6, wherein the resource availability is calculated by the following formula:
A(x)t＝αtA′(x)t+(1-αt)tA″(x)t(13)
in the formula, A (x)tRepresenting the availability of resource x during a time period t;
A′(x)trepresenting the credibility of the resource x statistically obtained from historical data in the time period t;
A″(x)trepresenting the idleness of the resource x in the t time period;
αtrepresenting the proportion of the resource credibility in the process of calculating the resource availability;
the αtThe calculation formula of (2) is as follows:
Figure FDA0002528417730000064
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