CN111104296B - Carrier-based aircraft carrier landing task risk control method based on GERT - Google Patents

Carrier-based aircraft carrier landing task risk control method based on GERT Download PDF

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CN111104296B
CN111104296B CN201911112609.7A CN201911112609A CN111104296B CN 111104296 B CN111104296 B CN 111104296B CN 201911112609 A CN201911112609 A CN 201911112609A CN 111104296 B CN111104296 B CN 111104296B
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execution time
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CN111104296A (en
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焦健
夏宏青
董洁
赵廷弟
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Beihang University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F11/00—Error detection; Error correction; Monitoring
    • G06F11/30—Monitoring
    • G06F11/34—Recording or statistical evaluation of computer activity, e.g. of down time, of input/output operation ; Recording or statistical evaluation of user activity, e.g. usability assessment
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    • G06F11/3419—Recording or statistical evaluation of computer activity, e.g. of down time, of input/output operation ; Recording or statistical evaluation of user activity, e.g. usability assessment for performance assessment by assessing time
    • G06F11/3423—Recording or statistical evaluation of computer activity, e.g. of down time, of input/output operation ; Recording or statistical evaluation of user activity, e.g. usability assessment for performance assessment by assessing time where the assessed time is active or idle time

Abstract

The invention relates to a GERT-based carrier aircraft carrier landing task risk control method, and belongs to the technical field of system risk analysis. The method comprises the following steps: constructing a GERT network model for introducing waiting time of resource constraint downlink for activity queuing processing and time factors of behavior activity overlapping according to the logic structure of each behavior activity of a carrier-based aircraft carrier landing task; obtaining the total execution time variance of carrier-borne aircraft carrier landing tasks and the execution time variance of each behavior activity according to the moment mother function of the GERT network model; finding out one or more behavior activities causing the change of the total execution time of the tasks according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-borne aircraft carrier landing tasks; and monitoring the one or more behavior activities as a key link of risk control so as to facilitate the safety optimization of the carrier-based aircraft landing task execution. The technical scheme of the invention realizes effective control of the carrier-based aircraft landing task risk.

Description

Carrier-based aircraft carrier landing task risk control method based on GERT
Technical Field
The invention relates to the technical field of system task risk analysis, in particular to a GERT-based carrier-based aircraft carrier landing task risk control method.
Background
The complex system task execution depends on each specific function, each function is realized by the behavior activity of a specific structure, the state represents the real-time situation of the execution, and the structure defines the basic composition units of the system and the combination mode among the units. Along with the increasingly dense task requirements, the task interval is more and more compact, and the interactive coupling relation among various behavioral activities in the system is more and more prominent, so that the user puts forward more severe requirements on the time characteristics of the system.
At present, the execution time of a carrier landing task of a carrier-based aircraft is influenced by various factors in the task execution process. First, each activity in the system needs to be executed depending on various resources, and since the number of resources in the system is limited, the system cannot guarantee that each arriving service object can be served immediately, thereby generating a waiting time caused by queuing for resource processing. Furthermore, to improve the efficiency of the execution of system tasks, there are situations where there is overlapping execution between the upstream and downstream activities in the task.
Disclosure of Invention
In view of the above analysis, the present invention aims to provide a GERT-based carrier-based aircraft landing task risk control method, so as to solve the problem that the waiting time of behavior activity queuing processing and the influence of overlapping between upstream and downstream activities are caused by neglected resource constraints in a random network model of a task flow established in the prior art.
The purpose of the invention is mainly realized by the following technical scheme:
the invention provides a GERT-based carrier-based aircraft carrier landing task risk control method, which comprises the following steps of: constructing a GERT network model for introducing waiting time of resource constraint downlink for activity queuing processing and time factors of behavior activity overlapping according to the logic structure of each behavior activity of a carrier-based aircraft carrier landing task; obtaining the total execution time variance of carrier-borne aircraft carrier landing tasks and the execution time variance of each behavior activity according to the moment mother function of the GERT network model; finding out one or more behavior activities causing the change of the total execution time of the tasks according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-borne aircraft carrier landing tasks; and monitoring the one or more behavior activities as a key link of risk control so as to facilitate the safety optimization of the carrier-based aircraft landing task execution.
Further, a calculation formula for obtaining the carrier-based aircraft landing task total execution time variance according to the moment mother function of the GERT network model is as follows:
Figure GDA0002884318170000021
σ2(T)＝E(T2)-(E(T))2；
wherein M isE(s) is the moment mother function of the GERT network model, WE(s) is the equivalent transfer function of the GERT network model, PE＝WE(0)，pEE (T) is the average value of the total execution time T of the carrier-based aircraft carrier landing tasks;
the behavioral activities AiThe execution time variance of (1) is calculated as follows:
Figure GDA0002884318170000022
Figure GDA0002884318170000023
wherein the content of the first and second substances,
Figure GDA0002884318170000024
as a function of the moment mother of the transit time between the nodes in the GERT network model,
Figure GDA0002884318170000025
behavior activity A for carrier-based aircraft landing taskiExecution time of
Figure GDA0002884318170000026
Is measured.
Further, the GERT network model comprises nodes and arrowed lines between the nodes; wherein the nodes are different states of the task, and the arrow lines among the connecting nodes represent the transmission relation among the states;
equivalent transfer function W of the GERT network modelEAnd(s) is an element corresponding to the number of rows where a terminal node j is located and the number of columns where a source node i is located in the gain matrix G of the GERT network model.
Further, a gain matrix G between any source node i and a final node j in the GERT network model is:
G＝(I-Q)-1P；
q and P are two transfer matrixes of a signal flow graph gain matrix A of the GERT network model, Q represents a transfer relation matrix between n nodes except a source node of the GERT network model, and P represents a transfer function matrix from m source nodes to the rest n nodes.
Further, the signal flow diagram gain matrix a of the GERT network model is:
Figure GDA0002884318170000031
wherein the content of the first and second substances,
Figure GDA0002884318170000032
for the transfer functions between nodes in the GERT network model,
Figure GDA0002884318170000033
as a function of the moment mother of the transit time between the nodes in the GERT network model,
Figure GDA0002884318170000034
as behavioral activity AiProbability of occurrence under the condition that the state of the leader i is realized.
Further, a moment mother function of transfer time between nodes in the GERT network model
Figure GDA0002884318170000035
The calculation formula of (a) is as follows:
Figure GDA0002884318170000036
wherein the content of the first and second substances,
Figure GDA0002884318170000037
s < lambda, s and lambda are constants,
Figure GDA0002884318170000038
a function of the moment mother of the behavioral activity service time between nodes,
Figure GDA0002884318170000039
for the time factor under the condition that the behavioral activities in the carrier-based aircraft landing task are overlapped,
Figure GDA00028843181700000310
average latency in the behavioral activity for the service object.
Further, the time factor under the condition that the behavioral activities of the carrier-based aircraft in the carrier landing task are overlapped
Figure GDA00028843181700000311
Comprises the following steps:
Figure GDA0002884318170000041
wherein the content of the first and second substances,
Figure GDA0002884318170000042
is information downstream behavior Activity Ai+1Transitive time behavior Activity AiThe time that has been executed has been elapsed,
Figure GDA0002884318170000043
representing behavioral Activity AiThe execution time of.
Further, the average waiting time of the service object in the activity comprises the behavior activity without resource sharing in the task execution processiMedium average latency and resource shared behavior Activity during task execution the kth behavior Activity is at resource R1Average latency of (1);
the behavior activity without resource sharing is a service object behavior activity A in the process of task executioniThe formula for calculating the mean average waiting time is as follows:
Figure GDA0002884318170000044
wherein λ isiFor the ith behavioral activity A in a taskiService object arrival rate of ciTo perform activity AiThe amount of resources required, ρi＝λi/μi，μiFor the ith behavioral activity AiK is the number of items of the behavioral activity;
the k-th behavior activity of the behavior activity with resource sharing in the task execution process is in the resource R1The formula for calculating the mean average waiting time is as follows:
Figure GDA0002884318170000045
wherein the content of the first and second substances,
Figure GDA0002884318170000046
to a shared resource R1The total service object arrival rate of the class k service objects,
Figure GDA0002884318170000047
for sharing resource R1With respect to the average service rate of the service object,
Figure GDA0002884318170000048
c1for sharing resource R1K is the number of items of the behavioral activity.
Further, finding out one or more behavior activities causing the total execution time variation of the tasks according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-based aircraft carrier landing tasks comprises: if the ratio is larger than a preset threshold value, judging that the influence of the execution time of the corresponding behavior activity on the total execution time fluctuation of the carrier-based aircraft carrier landing task is large, and selecting the behavior activity; otherwise, it is not selected.
Further, a calculation formula of a ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-based aircraft carrier landing task is as follows:
Figure GDA0002884318170000051
wherein the content of the first and second substances,
Figure GDA0002884318170000052
as behavioral activity AiOf the execution time variance, σ2And (T) is the total execution time variance of the carrier-based aircraft landing mission.
The beneficial effects of this technical scheme are as follows: the invention discloses a GERT-based carrier-based aircraft carrier landing task risk control method, which comprises the steps of constructing a GERT network model introducing waiting time for activity queuing processing of resource constraint downlink and time factors for behavior activity overlapping according to the logic structure of each behavior activity of a carrier-based aircraft carrier landing task; obtaining the total execution time variance of carrier-borne aircraft carrier landing tasks and the execution time variance of each behavior activity according to the moment mother function of the GERT network model; finding out one or more behavior activities causing the change of the total execution time of the tasks according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-borne aircraft carrier landing tasks; and monitoring the one or more behavior activities as a key link of risk control so as to facilitate the safety optimization of the carrier-based aircraft landing task execution. The invention solves the problems that the waiting time of behavior activity queuing processing caused by resource constraint and the influence of overlapping between upstream and downstream activities are neglected in the prior art, so that the established random network model of the task flow is closer to the real task process, and the carrier-based aircraft carrier landing task risk is effectively controlled.
Compared with the prior art, the key points of the invention are as follows:
(1) on the basis of the task execution time in an ideal state, the waiting time of behavior activity queuing and resource processing caused by resource constraint is considered, so that the established task flow model is more suitable for the real task process.
(2) In the actual task process, in order to improve the task execution efficiency, a time factor is added under the condition that some upstream and downstream activities are partially overlapped so as to correct a transfer function in the GERT network and enable the GERT network model to be more fit with the actual situation.
(3) The influence of the fluctuation of the execution time of each behavior activity in the task on the execution time of the task in the whole system is considered, so that the key links in the task process are easy to find out, and the safety of the task process is further optimized.
(4) The task flow random network model established based on the GERT has the characteristics of visualization, easiness in understanding and convenience in analysis, can be used for establishing corresponding random network models aiming at different task flows, has certain universality and supports reliability and safety analysis work.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
Fig. 1 is a flowchart of a GERT-based carrier-based aircraft carrier landing task risk control method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of basic constituent units of a GERT network model according to an embodiment of the present invention;
fig. 3 is a ship-based aircraft landing task process diagram according to the embodiment of the invention;
fig. 4 is a GERT network model diagram of a carrier-based aircraft landing task according to an embodiment of the invention;
fig. 5 is a diagram of an uncertainty analysis result of each behavior activity in the carrier-based aircraft landing task according to the embodiment of the invention.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate preferred embodiments of the invention and together with the description, serve to explain the principles of the invention and not to limit the scope of the invention.
The technical idea of the invention is as follows: in the process of executing system tasks, along with the continuous change of working environment, the state of the system is continuously changed in a certain range, and certain randomness exists in the execution of each function and the execution time of activities in the system. The GERT nodes and activities are random, the input and output logics of the nodes are diversified, and the dynamic description of the system can realize modeling analysis on system tasks. The average waiting time of the task object when executing each behavior activity is solved by adopting a queuing theory, the relation between the execution time of the upstream and downstream activities in the task is expressed by introducing a time factor, and the time parameters of each behavior activity in the GERT network branch are corrected, so that a random network model constructed by adopting a GERT method is closer to a real task process. Firstly, decomposing a carrier-based aircraft carrier landing task, and establishing a GERT network diagram of the carrier-based aircraft carrier landing task according to 6 network nodes of GERT; secondly, collecting necessary data of GERT network branches of carrier-based aircraft landing tasks, comprising the following steps: solving queuing waiting time under resource constraint based on a queuing theory, and introducing a time factor to correct the influence of activity overlapping to obtain the time spent by each node in the GERT network in transmitting; then, representing the GERT random network of carrier-based aircraft carrier landing by using a matrix form, and solving to obtain the expected value and the variance of the carrier-based aircraft carrier landing task execution time; and finally, finding out key links in the carrier landing task through solving and analyzing, and further optimizing the task process.
A specific embodiment of the present invention, as shown in fig. 1, discloses a GERT-based carrier-based aircraft carrier landing task risk control method, which includes the following steps:
s1, constructing a GERT network model introducing waiting time of resource constraint downlink for activity queuing processing and time factors of behavior activity overlapping according to the logic structure of each behavior activity of the carrier-based aircraft landing task;
specifically, each behavior activity of the carrier-based aircraft landing task comprises standby flight, approach, waiting flight, hovering flight, air refueling, gliding landing, missed approach and the like. The logical relationship among the behavioral activities represents the causal logic of the behavioral activities, and is reflected in the influence of the completion condition of local activities on other activities in the same level or high-level activities and even complex tasks at the top level. The logical relationship among the behavior activities in the task process comprises the following steps: a sequential relationship (Seq), an And relationship (And), Or relationship (Or), a conditional relationship (Cond), a concurrency relationship (Conc), a synchronization relationship (Syn), a mutual exclusion relationship (Exc), And a cyclic relationship (Cyc). Let A be { A ═ A1,A2,···,AnDenotes the set of behavioral activities in the system, Ai,AjE.g. a (i, j ≠ j) 1, 2., n, and i ≠ j),
Figure GDA0002884318170000081
and is
Figure GDA0002884318170000082
The logical structure relationship among activities in the task is shown in table 1:
TABLE 1 logical structural relationships between Activities
Figure GDA0002884318170000083
On the basis of logical relations existing among various behavior activities in the carrier-based aircraft carrier landing task process, a basic structure of a GERT network model is constructed based on 6 types of logical nodes of GERT, as shown in table 2, 1 represents that the activities are executed, and 0 represents that the activities are not executed. p represents the probability of realization of the state, t represents the execution time of the activity, piIs the probability of activation of node i, tiIs the execution time between nodes i.
TABLE 2 basic structural types of task Process stochastic networks
Figure GDA0002884318170000091
In order to facilitate the analytical calculation of the model, the AND type and OR type active nodes at the input end of the random network are converted into XOR type active nodes, the deterministic type active nodes at the output end of the random network are converted into probabilistic type active nodes, and the GERT network is converted into a typical linear system through proper logic transformation.
S2, obtaining the total execution time variance of carrier-borne aircraft carrier landing tasks and the execution time variance of each behavior activity according to the moment mother function of the GERT network model;
specifically, the execution time of each behavior activity is calculated, necessary data of network branches are collected, the execution time, the occurrence probability and the resource configuration condition of each behavior activity are included, the waiting time for execution of each activity under resource constraint is solved based on a queuing theory, the execution time of each activity in a task is obtained, and a time factor is introduced to correct the influence of activity overlapping; solving the mean value and the variance of the task execution time, representing the GERT network in a matrix form, obtaining a signal flow graph gain matrix by the GERT network, and then solving to obtain the expected value and the variance of the system task execution time by analyzing network nodes and transfer functions.
S3, finding out one or more behavior activities causing the change of the total execution time of the tasks according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-borne aircraft carrier landing tasks;
specifically, through uncertainty analysis, the influence of the fluctuation of the execution time of each behavior activity in the task process on the execution time of the whole task is obtained based on the variance, so that the key behavior activity in the system task is found out.
And S4, monitoring the one or more behavior activities as a key link of risk control so as to facilitate the safety optimization of carrier-based aircraft landing task execution.
Specifically, key links in the task process are determined, and directions and ideas are provided for further optimizing the task process.
Compared with the prior art, the method and the device have the advantages that the GERT network model of the waiting time for the activity queuing processing and the time factor for the action activity overlapping are introduced into the resource constraint downlink, so that the established random network model of the task flow is closer to the real task process, and the carrier-based aircraft carrier landing task risk is effectively controlled.
The resources are resources such as personnel and equipment, each resource is used as a service window, and due to the limited number of the resources, the system cannot ensure that each arriving service object can be immediately served by the resources, so that waiting queues are formed in front of the service windows to wait for receiving services, and the service time of the resources for the service objects is considered to be subjected to negative index distribution.
In a specific embodiment of the invention, a calculation formula for obtaining the carrier-based aircraft landing task total execution time variance according to the moment carrier function of the GERT network model is as follows:
Figure GDA0002884318170000111
σ2(T)＝E(T2)-(E(T))2；
wherein M isE(s) is the moment mother function of the GERT network model, WE(s) is the equivalent transfer function of the GERT network model, PE＝WE(0)，pEE (T) is the average value of the total execution time T of the carrier-based aircraft carrier landing tasks;
the behavioral activities AiThe execution time variance of (1) is calculated as follows:
Figure GDA0002884318170000112
Figure GDA0002884318170000113
wherein the content of the first and second substances,
Figure GDA0002884318170000114
as a function of the moment mother of the transit time between the nodes in the GERT network model,
Figure GDA0002884318170000115
behavior activity A for carrier-based aircraft landing taskiExecution time of
Figure GDA0002884318170000116
Is measured.
In a specific embodiment of the present invention, the GERT network model includes nodes and arrow lines connecting the nodes, as shown in table 2; wherein, the nodes are different states of the task, and the arrow lines between the connecting nodes represent the transfer relationship between the states, namely the transfer relationship of each behavior activity between the nodes;
specifically, each state in the task process is used as a node in the network, an arrow line connecting each node represents transmission activities among the states, namely, the quantitative relation of each behavior activity among the nodes is reflected, and a random network diagram of the task flow is constructed according to different node types of GERT by analyzing the logical relation among each behavior activity in the task process.
Specifically, the states of the carrier-based aircraft in the carrier landing task process comprise the beginning of carrier landing, the approaching of the HM, the completion of emergency landing, the completion of refueling, the standby flight, the waiting of the flight line, the hovering of the flight line, the completion of gliding after weight reduction, the successful carrier landing, the successful forced landing, the flying to the high altitude, the completion of carrier landing and the like.
Preferably, the basic building blocks of the GERT network model are shown in FIG. 2. Nodes i and j in the graph are different states in the task process, and the behavior activity AiRepresenting the transfer relationship between states, i.e. the execution process of each behavioral activity, including the execution probability of the behavioral activity and the execution time of the behavioral activity considering the resource constraint and the overlap between the upstream and downstream activities, the quantitative relationship of which is determined by the transfer function
Figure GDA0002884318170000121
And (4) showing.
Equivalent transfer function W of the GERT network modelEAnd(s) is an element corresponding to the number of rows where a terminal node j is located and the number of columns where a source node i is located in the gain matrix G of the GERT network model.
In a specific embodiment of the present invention, a gain matrix G between any source node i and any destination node j in the GERT network model is:
G＝(I-Q)-1P；
q and P are two transfer matrixes of a signal flow graph gain matrix A of the GERT network model, Q represents a transfer relation matrix between n nodes except a source node of the GERT network model, and P represents a transfer function matrix from m source nodes to the rest n nodes.
Specifically, according to the condition that the output of any node in the signal flow diagram is the sum of all inputs, the gain matrix G between any source node and any end node in the GERT network is obtained as follows:
G＝(I-Q)-1P
suppose that the equivalent transfer function W from the source node i to the final node j needs to be analyzedE(s), the equivalent transfer function W of the task flow random network is obtained by only finding out the elements corresponding to the number of rows where the node j is located and the number of columns where the node i is located in the gain matrix GE(s)。
In a specific embodiment of the present invention, the gain matrix a of the signal flow diagram of the GERT network model is:
Figure GDA0002884318170000122
wherein the content of the first and second substances,
Figure GDA0002884318170000123
for the transfer functions between nodes in the GERT network model,
Figure GDA0002884318170000124
as a function of the moment mother of the transit time between the nodes in the GERT network model,
Figure GDA0002884318170000125
as behavioral activity AiProbability of occurrence under the condition that the state of the leader i is realized.
Specifically, the gain matrix a of the signal flow diagram obtained by the GERT network is:
Figure GDA0002884318170000131
writing two transfer matrices Q from matrix An×n，Pn×mWherein Q isn×nRepresenting the transfer relationship among nodes except the source node in the GERT network, wherein n is the number of the nodes except the source node, Pn×mIs a matrix of transfer functions from m source nodes to the remaining n nodes.
In an embodiment of the present invention, the moment mother function of the transfer time between the nodes in the GERT network model
Figure GDA0002884318170000132
The calculation formula of (a) is as follows:
Figure GDA0002884318170000133
wherein the content of the first and second substances,
Figure GDA0002884318170000134
s < lambda, s and lambda are constants,
Figure GDA0002884318170000135
a function of the moment mother of the behavioral activity service time between nodes,
Figure GDA0002884318170000136
for the time factor under the condition that the behavioral activities in the carrier-based aircraft landing task are overlapped,
Figure GDA0002884318170000137
average latency in the behavioral activity for the service object.
In particular, as shown in figure 2,
Figure GDA0002884318170000138
as behavioral activity AiProbability of occurrence under the condition of state realization of the leader i;
Figure GDA0002884318170000139
indicating the time when the downstream activity starts to execute as the information is transferred to the downstream activity during the task, the upstream activity has executed
Figure GDA00028843181700001310
And
Figure GDA00028843181700001311
three components with values of
Figure GDA00028843181700001312
On the basis of
Figure GDA00028843181700001313
And
Figure GDA00028843181700001314
is corrected.
According to the function of the moment mother
Figure GDA00028843181700001315
The value of the nth derivative at s-0 equals the desired value of the argument to the power of n, i.e.:
Figure GDA00028843181700001316
the moment mother function of the transfer time between nodes in the GERT network
Figure GDA00028843181700001317
Comprises the following steps:
Figure GDA00028843181700001318
wherein, the moment mother function of the behavior activity service time between the nodes
Figure GDA00028843181700001319
Comprises the following steps:
Figure GDA00028843181700001320
for each behavior activity in the task process, the arrival of the task object is a poisson process, namely, the arrival time interval of the service object obeys negative exponential distribution, and similarly, the service time of the resource to the service object also obeys negative exponential distribution. Suppose there are n behavioral activities in a task, the ith behavioral activity AiHas an average service rate of muiThen its service time
Figure GDA0002884318170000141
Probability density function of
Figure GDA0002884318170000142
Comprises the following steps:
Figure GDA0002884318170000143
that is, the moment mother function of the behavioral activity service time between nodes in the GERT network model
Figure GDA0002884318170000144
From the above service time
Figure GDA0002884318170000145
Probability density function of
Figure GDA0002884318170000146
Obtained by Laplace transform:
Figure GDA0002884318170000147
wherein s is a constant, λi＝1/μiAverage service rate μ for a particular activityiIs a constant, i.e., muiFor the ith behavioral activity AiAverage processing speed of (2).
According to a specific embodiment of the invention, the time factor is obtained under the condition that the behavioral activities of the carrier-based aircraft in the carrier landing task are overlapped
Figure GDA0002884318170000148
Comprises the following steps:
Figure GDA0002884318170000149
wherein the content of the first and second substances,
Figure GDA00028843181700001410
is information downstream behavior Activity Ai+1Transitive time behavior Activity AiThe time that has been executed has been elapsed,
Figure GDA00028843181700001411
representing behavioral Activity AiThe execution time of.
In particular, in the case of overlap between behavioural activities in a task, a time factor is introduced
Figure GDA00028843181700001412
Figure GDA00028843181700001413
Wherein the content of the first and second substances,
Figure GDA00028843181700001414
represents activity AiThe execution time of (a) is determined,
Figure GDA00028843181700001415
represents activity Ai+1The execution time of (a) is determined,
Figure GDA00028843181700001416
is information downstream activity Ai+1Activity at delivery AiThe time of execution. It is easy to know that the method can be used for the treatment of the diseases,
Figure GDA00028843181700001417
time factor
Figure GDA00028843181700001418
Can be used for correcting the condition that the superposition exists between the behavioral activities to represent the execution time relation of the upstream and downstream activities: when in use
Figure GDA00028843181700001419
When, represented in behavioral activity AiDownstream Activity A when execution completesi+1Providing information, Activity Ai+1Starting execution when a message arrives; when in use
Figure GDA00028843181700001420
When it is shown in activity AiDownstream Activity A when partial execution completesi+1Providing information, Activity Ai+1Execution begins when a message arrives.
In a specific embodiment of the present invention, the average waiting time of the service object in the activity comprises no resource sharing behavior activity A of the service object in the behavior activity A in the task execution processiMedium average latency and resource shared behavior Activity during task execution the kth behavior Activity is at resource R1Average latency of (1);
specifically, the queuing theory is adopted to solve the waiting time of the behavior activity queuing processing caused by resource constraint in the task execution process. Suppose the ith behavioral activity A in a taskiService object arrival rate of λiActivity AiHas an average processing rate of mui. Will move AiThe required resources are used as a kind of resource module, and the number of the resource modules is ciI.e. with c in the queuing modeliService window, service object in ith action activity AiFor medium average waiting time
Figure GDA0002884318170000151
And (4) showing.
The behavior activity without resource sharing is a service object behavior activity A in the process of task executioniThe formula for calculating the mean average waiting time is as follows:
Figure GDA0002884318170000152
wherein λ isiFor the ith behavioral activity A in a taskiService object arrival rate of ciTo perform activity AiThe amount of resources required, ρi＝λi/μi，μiFor the ith behavioral activity AiK is the number of items of the behavioral activity;
in particular, for no resource coThe shared behavior activity can be regarded as a single queue type service object multi-service-station queuing problem in the system task execution process. Suppose that Activity A is performediThe required resource has ciFor the activity, it is equivalent to M/M/ciThe queuing model of (1). Let ρ bei＝λi/μiFinding the service object in the activity A by the Little formulaiAverage waiting time in (1)
Figure GDA0002884318170000153
Comprises the following steps:
Figure GDA0002884318170000154
the k-th behavior activity of the behavior activity with resource sharing in the task execution process is in the resource R1The formula for calculating the mean average waiting time is as follows:
Figure GDA0002884318170000161
wherein the content of the first and second substances,
Figure GDA0002884318170000162
to a shared resource R1The total service object arrival rate of the class k service objects,
Figure GDA0002884318170000163
for sharing resource R1With respect to the average service rate of the service object,
Figure GDA0002884318170000164
c1for sharing resource R1K is the number of items of the behavioral activity.
Specifically, for the behavior activities with resource sharing, in the system task execution process, two or more behavior activities need to use the same resource, and the service objects of each behavior activity are different, the execution time is also different, and the service objects are differentThe execution time in each action activity is the stay time in the shared resource, and can be regarded as a single queue, multiple service objects and multiple service platforms queuing problem. With shared resources R1For example, let c be common to this type of resource1If there are k behavioral activities, it needs to call this kind of resource, i.e. there are k kinds of service objects, and the arrival rate of each kind of object is lambdaiThen the total service object arrival rate for that type of resource is
Figure GDA0002884318170000165
Comprises the following steps:
Figure GDA0002884318170000166
activity of ith activity AiHas an average processing rate of muiThen share resource R1Average processing rate with respect to service objects
Figure GDA0002884318170000167
Comprises the following steps:
Figure GDA00028843181700001611
order to
Figure GDA0002884318170000168
Solving the k items of behavior activities in the resource R by the Little formula1Average waiting time in (1)
Figure GDA0002884318170000169
Comprises the following steps:
Figure GDA00028843181700001610
in a specific embodiment of the present invention, finding out one or more behavior activities that cause a change in the total execution time of the task according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-based aircraft carrier landing task includes: if the ratio is larger than a preset threshold value, judging that the influence of the execution time of the corresponding behavior activity on the total execution time fluctuation of the carrier-based aircraft carrier landing task is large, and selecting the behavior activity; otherwise, it is not selected.
In a specific embodiment of the present invention, a calculation formula of a ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-based aircraft landing task is as follows:
Figure GDA0002884318170000171
wherein the content of the first and second substances,
Figure GDA0002884318170000172
as behavioral activity AiOf the execution time variance, σ2And (T) is the total execution time variance of the carrier-based aircraft landing mission.
In particular, for a given complex task process, the variation in the time taken to execute the task due to the variation in the execution time of the behavioral activities may be separately derived. Suppose activity AiHas an execution time of TiIf the total duration of the system executing the task process is T, the uncertainty U of the activity execution time is obtainediActivity for a specific behavior AiExecution time variance of
Figure GDA0002884318170000173
Variance σ of the total duration of the task execution process2The ratio of (T) is:
Figure GDA0002884318170000174
specifically, for example, fig. 3 is a ship landing task process diagram of a carrier aircraft, which mainly includes: the method comprises the following steps of standby flight, approach, waiting for flight on an airline, hovering flight on an airline, air refueling, gliding landing, carrier landing, missed approach and other behavior activities, wherein carrier landing tasks are completed by the behavior activities in a matched mode according to a certain logic structure and a certain time sequence relation. By analyzing the logical structure relationship among the behavior activities, the carrier-based aircraft landing process is converted into a GERT network model, as shown in FIG. 4. Nodes in the model represent different states in the process of carrier landing, and arrow lines among the nodes represent various behavior activities in the carrier landing task. Wherein, 0 → 1 indicates that the carrier-based aircraft flies towards the direction close to the ship; 1 → 2 refers to air refueling under the condition of insufficient residual oil of the carrier-based aircraft; 1 → 3 refers to emergency landing when the ship-based aircraft has high threat; 1 → 4 indicates that the carrier-based aircraft flies in a standby area; 2 → 4 indicates that the shipboard aircraft flies in a standby area after oiling is finished; 4 → 5 means that the carrier-based aircraft requests to approach and fly by entering a waiting air route; 5 → 6 indicates that the carrier-based aircraft enters a hovering air route to fly; 6 → 7 indicates that the weight of the carrier-based aircraft exceeds the standard, and the redundant fuel oil needs to be discharged or the redundant bomb needs to be thrown away; 6 → 8 indicates that the carrier-based aircraft slides downwards and lands; 7 → 8 means that the shipboard aircraft is glidingly landed after weight reduction; 8 → 9 indicates the carrier-based aircraft landing; 9 → 12 indicates that the pilot stops the carrier-based aircraft to a designated parking area and finishes landing; 9 → 10 indicates that the arresting net is used for assisting the ship-based aircraft to forcedly descend under the condition that the arresting hook does not successfully arrest; 10 → 12 indicates that after the forced landing is successful, the pilot stops the carrier-based aircraft to a designated parking area, and the landing is finished; 9 → 11 indicates that under the condition that the arresting net is not successfully arrested, the pilot operates the carrier-based aircraft to fly back to the high altitude; 8 → 11 means that the descending height of the carrier is too low or too high and needs to fly to the high altitude again, and 11 → 4 means that the carrier-based aircraft enters the standby area again to wait for landing.
The execution of each behavior activity depends on some personnel, equipment and other resources, each resource is used as a service window, and due to the limited number of the resources, the system cannot ensure that each arriving service object can be immediately served by the resource, so that waiting queues are formed in front of the service windows to wait for receiving the service, and the service time of the resource to the service object is considered to be subjected to negative index distribution. The execution time (i.e. the service time of the resource to the activity), the occurrence probability and the resource demand condition of each behavior activity in the carrier-based aircraft landing task process are shown in table 3.
TABLE 3 resource demand and basic parameters during carrier-based aircraft landing mission
Figure GDA0002884318170000181
Figure GDA0002884318170000191
In the task process, activities 0 → 1, 1 → 2, 2 → 4, 4 → 5, 5 → 6 and 11 → 4 all need the communication command of an empty manager, activities 6 → 8, 7 → 8, 8 → 9, 8 → 11, 9 → 10 and 9 → 11 all need the command guidance of the LSO, the empty manager and the LSO are used as service windows, and all the behavior activities are used as service objects.
For each behavior activity in the task process, the arrival of the task object is considered as a poisson process, i.e. the time interval of the arrival of the service object obeys negative exponential distribution. And (4) calculating the average waiting time of the carrier-based aircraft in each action based on the queuing theory, wherein the average waiting time is shown in a table 4.
TABLE 4 mean waiting time of carrier-based aircraft in carrier landing mission process
Figure GDA0002884318170000192
Figure GDA0002884318170000201
In the actual carrier landing process, in order to improve the task efficiency and under the condition that partial upstream and downstream activities are overlapped, a time factor a is utilizedijThe effect of activity overlap is corrected from the perspective of information transfer between nodes. Wherein, aijThis means that the downward transfer of information triggers the execution of an upstream activity when a downstream activity is executed, whereby the effective time taken for the transfer of information between the nodes in the GERT network can be determined. Virtual nodes are added at the active branches to distinguish different overlapping conditions of the active branches, and virtual nodes 1 'and 1' are added at the node 1 to represent branch lines of three different overlapping conditions of refueling, emergency landing and entering a standby area; adding virtual nodes at node 6Point 6' to represent the branch lines for two different overlap situations of weight loss and downslide; a virtual node 8' is added at node 8 to represent a leg for two different overlap cases, drop height fair and glide height low/high.
The overlapping condition of execution time of each behavior activity in the carrier-based aircraft landing task process is mapped into a matrix form, as follows, the element representation information below the diagonal line in the matrix is transmitted from the behavior activity which occurs firstly to the back, and belongs to information feedforward, and the element representation information above the diagonal line is fed back.
Figure GDA0002884318170000202
Therefore, a transfer function W between nodes in a GERT network model of the carrier-based aircraft carrier landing task can be obtainedij(s) representing the GERT random network of the carrier aircraft landing by using a matrix form to obtain a signal flow diagram gain matrix A as follows:
Figure GDA0002884318170000211
in the GERT network model of the carrier-based aircraft carrier landing task, a source node is 0, row elements and column elements where the source node 0 is located are deleted, and a residual matrix is Q and is inherent:
Figure GDA0002884318170000212
and a matrix formed by transfer functions from the source node to the residual nodes in the GERT model is P:
Figure GDA0002884318170000213
thereby obtaining a gain matrix G from any source node to any terminal node in the GERT network, wherein the 16 th row and 1 st column elements in the matrix G are equivalent transfer functions W from the source node 0 to the terminal node 12E(s)，GERTEquivalent probability of realization of network PE＝WE(0) And respectively setting the expected value and the variance of the carrier-based aircraft landing task execution time t as follows:
Figure GDA0002884318170000214
σ2(t)＝E(t2)-(E(t))2＝161.6982min2
in order to compare the influence degree of the fluctuation of the execution time of each activity on the execution time of the whole carrier landing task in the carrier landing process of the carrier-based aircraft, the key activity is found out, the uncertainty of each behavior activity is analyzed, and the result is shown in fig. 5.
From the results of the uncertain analysis of the activity: in the carrier aircraft carrier landing process, the influence degree of the fluctuation of the execution time of each behavior activity on the carrier task execution time is roughly divided into three grades: the effects of behavioral activity corresponding to 0 → 1, 0 → 1' and 0 → 1 "are most prominent; 1 ' → 2, 1 → 4, 2 → 4, 5 → 6 ', 7 → 8 ', 10 → 12; 1 "→ 3, 4 → 5, 5 → 6, 6 ' → 7, 6 → 8 ', 8 → 9, 8 ' → 11, 9 → 10, 9 → 11, 9 → 12 and 11 → 4 are relatively weak in influence.
Therefore, the most critical activity in the carrier-based aircraft landing process is that the carrier-based aircraft flies to the HM, and because of the special conditions of insufficient residual oil and high threat in the flying process, the fluctuation of the execution time of the carrier-based aircraft is large, and the influence on the fluctuation of the execution time of the whole landing task is also maximum; secondly, activities which have great influence on the carrier landing task include: in the process of a landing task, a resource sharing mechanism has a great influence on the queuing waiting time of the activities in a resource module, so that the execution time of the landing task is influenced; the influence of the fluctuation of the execution time of other behavioral activities on the completion time of the whole carrier landing task is small. Therefore, in order to ensure that the execution time of the carrier landing task is executed within an acceptable range in the carrier landing task process of the carrier-based aircraft, the key point is to pay attention to several behavior activities with large fluctuation influence, ensure that key links in the task process do not go wrong, and effectively reduce the risk of the whole carrier landing task.
In summary, the invention discloses a GERT-based carrier-based aircraft carrier landing task risk control method, which comprises the following steps: constructing a GERT network model for introducing waiting time of resource constraint downlink for activity queuing processing and time factors of behavior activity overlapping according to the logic structure of each behavior activity of a carrier-based aircraft carrier landing task; obtaining the total execution time variance of carrier-borne aircraft carrier landing tasks and the execution time variance of each behavior activity according to the moment mother function of the GERT network model; finding out one or more behavior activities causing the change of the total execution time of the tasks according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-borne aircraft carrier landing tasks; and monitoring the one or more behavior activities as a key link of risk control so as to facilitate the safety optimization of the carrier-based aircraft landing task execution. The invention solves the problems that the waiting time of behavior activity queuing processing caused by resource constraint and the influence of overlapping between upstream and downstream activities are neglected in the prior art, so that the established random network model of the task flow is closer to the real task process, and the carrier-based aircraft carrier landing task risk is effectively controlled.
Those skilled in the art will appreciate that all or part of the processes for implementing the methods in the above embodiments may be implemented by a computer program, which is stored in a computer-readable storage medium, to instruct associated hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (8)

1. A GERT-based carrier aircraft carrier landing task risk control method is characterized by comprising the following steps:
according to the logic structure of each behavior activity of the carrier-based aircraft landing task, a GERT network model introducing waiting time for activity queuing processing of resource constraint downlink and time factors for behavior activity overlapping is constructed, and the GERT network model comprises the following steps:
time factor under condition of overlapping between behavior activities in carrier-based aircraft landing task
Figure FDA0002865008760000011
Comprises the following steps:
Figure FDA0002865008760000012
wherein the content of the first and second substances,
Figure FDA0002865008760000013
is information downstream behavior Activity Ai+1Transitive time behavior Activity AiThe time that has been executed has been elapsed,
Figure FDA0002865008760000014
representing behavioral Activity AiThe execution time of (c);
average latency of service object in Activity including resource sharing-free behavioral Activity during task executioniMedium average latency and resource shared behavior Activity during task execution the kth behavior Activity is at resource RiAverage latency of (1);
the behavior activity without resource sharing is a service object behavior activity A in the process of task executioniThe formula for calculating the mean average waiting time is as follows:
Figure FDA0002865008760000015
wherein λ isiFor the ith behavioral activity A in a taskiService object arrival ofRate, ciTo perform activity AiThe amount of resources required, ρi＝λi/μi，μiFor the ith behavioral activity AiK is the number of items of the behavioral activity;
the k-th behavior activity of the behavior activity with resource sharing in the task execution process is in the resource R1The formula for calculating the mean average waiting time is as follows:
Figure FDA0002865008760000016
wherein the content of the first and second substances,
Figure FDA0002865008760000021
Figure FDA0002865008760000022
to a shared resource R1The total service object arrival rate of the class k service objects,
Figure FDA0002865008760000023
Figure FDA0002865008760000024
for sharing resource R1With respect to the average service rate of the service object,
Figure FDA0002865008760000025
c1for sharing resource R1K is the number of items of the behavioral activity;
obtaining the total execution time variance of carrier-borne aircraft carrier landing tasks and the execution time variance of each behavior activity according to the moment mother function of the GERT network model;
finding out one or more behavior activities causing the change of the total execution time of the tasks according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-borne aircraft carrier landing tasks;
and monitoring the one or more behavior activities as a key link of risk control so as to facilitate the safety optimization of the carrier-based aircraft landing task execution.
2. The method of claim 1, wherein a calculation formula for obtaining the carrier-based aircraft landing mission total execution time variance according to the moment mother function of the GERT network model is as follows:
Figure FDA0002865008760000026
σ2(T)＝E(T2)-(E(T))2；
wherein M isE(s) is the moment mother function of the GERT network model, WE(s) is the equivalent transfer function of the GERT network model, PE＝WE(0)，pEE (T) is the average value of the total execution time T of the carrier-based aircraft carrier landing tasks;
the behavioral activities AiThe execution time variance of (1) is calculated as follows:
Figure FDA0002865008760000027
Figure FDA0002865008760000028
wherein the content of the first and second substances,
Figure FDA0002865008760000029
as a function of the moment mother of the transit time between the nodes in the GERT network model,
Figure FDA00028650087600000210
behavior activity A for carrier-based aircraft landing taskiExecution time of
Figure FDA00028650087600000211
Is measured.
3. The method according to claim 1 or 2, characterized in that the GERT network model comprises arrowed lines between nodes and connecting nodes; wherein the nodes are different states of the task, and the arrow lines among the connecting nodes represent the transmission relation among the states;
equivalent transfer function W of the GERT network modelEAnd(s) is an element corresponding to the number of rows where a terminal node j is located and the number of columns where a source node i is located in the gain matrix G of the GERT network model.
4. The method of claim 3, wherein the gain matrix G between any source node i and any destination node j in the GERT network model is:
G＝(I-Q)-1P；
q and P are two transfer matrixes of a signal flow graph gain matrix A of the GERT network model, Q represents a transfer relation matrix between n nodes except a source node of the GERT network model, and P represents a transfer function matrix from m source nodes to the rest n nodes.
5. The method of claim 4, wherein the signal flow graph gain matrix A of the GERT network model is:
Figure FDA0002865008760000031
wherein the content of the first and second substances,
Figure FDA0002865008760000032
Figure FDA0002865008760000033
for the transfer functions between nodes in the GERT network model,
Figure FDA0002865008760000034
as a function of the moment mother of the transit time between the nodes in the GERT network model,
Figure FDA0002865008760000035
as behavioral activity AiProbability of occurrence under the condition that the state of the leader i is realized.
6. The method of claim 2 or 5, wherein the moment mother function of the transit time between nodes in the GERT network model
Figure FDA0002865008760000036
The calculation formula of (a) is as follows:
Figure FDA0002865008760000037
wherein the content of the first and second substances,
Figure FDA0002865008760000038
s < lambda, s and lambda are constants,
Figure FDA0002865008760000039
a function of the moment mother of the behavioral activity service time between nodes,
Figure FDA00028650087600000310
for the time factor under the condition that the behavioral activities in the carrier-based aircraft landing task are overlapped,
Figure FDA00028650087600000311
average latency in the behavioral activity for the service object.
7. The method according to claim 1 or 2, wherein finding one or more behavior activities causing a change in the total execution time of the mission according to the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-based aircraft landing mission comprises: if the ratio is larger than a preset threshold value, judging that the influence of the execution time of the corresponding behavior activity on the total execution time fluctuation of the carrier-based aircraft carrier landing task is large, and selecting the behavior activity; otherwise, it is not selected.
8. The method according to claim 7, wherein the calculation formula of the ratio of the execution time variance of each behavior activity to the total execution time variance of the carrier-based aircraft carrier landing mission is as follows:
Figure FDA0002865008760000041
wherein the content of the first and second substances,
Figure FDA0002865008760000042
as behavioral activity AiOf the execution time variance, σ2And (T) is the total execution time variance of the carrier-based aircraft landing mission.
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