CN112183755A - Markov model construction simplification method and system applied to complex system - Google Patents

Markov model construction simplification method and system applied to complex system Download PDF

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CN112183755A
CN112183755A CN202011132772.2A CN202011132772A CN112183755A CN 112183755 A CN112183755 A CN 112183755A CN 202011132772 A CN202011132772 A CN 202011132772A CN 112183755 A CN112183755 A CN 112183755A
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markov model
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张庆
马权
刘明星
许标
吴礼银
王远兵
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Abstract

The invention discloses a Markov model construction simplification method and system applied to a complex system, relating to the technical field of Markov model construction and solving the problem of combined explosion when the Markov model is established in the existing complex system, and the key points of the technical scheme are as follows: detecting states in the Markov model, and screening out states with the same transfer rate to form a simplified state group; the member states in the simplified state group are merged and simplified into one state by the principle that the entry rate is added and the exit rate is kept unchanged. Before simplification, the state of the equipment needs to be divided, the equipment is taken as a whole and divided according to the influence condition of an external system, and the states with the same or similar influence are combined; the number of states can be greatly reduced in the construction process of the Markov model, so that the constructed Markov model is simplified.

Description

Markov model construction simplification method and system applied to complex system
Technical Field
The invention relates to the technical field of Markov model construction, in particular to a Markov model construction simplification method and a Markov model construction simplification system applied to a complex system.
Background
The markov model is a state transition diagram representing the system using a markov chain. If the model is completely built, the Markov model can completely express all normal states of the system, all degraded states of the system and all failure states of the system. The probability of a state in a markov model transitioning to another state depends only on the current state of the system, regardless of the state in which it has historically been. The Markov model is characterized by not only clearly expressing the next state transition condition of each state of the system under a certain condition, but also clearly reflecting the returned state of the system under a certain function degradation state after effective maintenance treatment, and is greatly recognized in various industries.
However, when the markov model is built for a complex system with a large number of states, the built markov model is extremely large, and the problem of state combination explosion is easily caused, which is also an important factor for restricting the application of the markov method. Therefore, how to design a simplified method and system for constructing a markov model applied to a complex system is an urgent problem to be solved at present.
Disclosure of Invention
The invention aims to solve the problem of combined explosion when a Markov model is established in the existing complex system, such as a nuclear power plant DCS platform, and provides a Markov model construction simplification method and system applied to the complex system.
The technical purpose of the invention is realized by the following technical scheme:
in a first aspect, a simplified method for constructing a markov model applied to a complex system is provided, which includes the following steps:
detecting states in the Markov model, and screening out states with the same transfer rate to form a simplified state group;
the member states in the simplified state group are merged and simplified into one state by the principle that the entry rate is added and the exit rate is kept unchanged.
Further, the transfer rate determination specifically includes: the probability of entering different states is the same, and the probability of going out different states is the same, namely the states with the same transition rate.
Further, the calculation of the transfer rate specifically comprises:
Pn(t+Δt)＝Pn(t)+λn-1ΔtP1(t)-λΔtPn(t)
in the formula, Pn(t + Δ t) is the probability that the complex system is in state n at time t + Δ t; pn(t) is the probability that the complex system is in state n at time t; p1(t) is the probability that the complex system is in state 1 at time t, λn-1Δ t. is the transition probability from state 1 to state n of the complex system; λ Δ t is the transition probability of complex system state 2 to state n + 1.
Further, the merging and simplifying calculation of the simplified state group specifically includes:
P2(t+Δt)+P3(t+Δt)+......+Pn(t+Δt)＝[P2(t)+P3(t)+......+Pn(t)]+(λ1+λ2+......+λn-1)ΔtP1(t)-λΔt[P2(t)+P3(t)+......+Pn(t)]
in the formula, P2(t+Δt)+P3(t+Δt)+......+Pn(t + Δ t) is the sum of the probabilities of the complex system from state 2 to state n at time t + Δ t; [ P ]2(t)+P3(t)+......+Pn(t)]The sum of the probabilities of the state 2 to the state n of the complex system at the time t; (lambda1+λ2+......+λn-1) Δ t is the sum of transition probabilities for complex system state 2 to state n.
Further, the complex system is a nuclear power plant DCS system.
In a second aspect, a simplified markov model construction system applied to a complex system is provided, including:
the state confirmation module is used for detecting states in the Markov model, screening out the states with the same transfer rate and then forming a simplified state group;
and the simplified merging module is used for merging and simplifying the member states in the simplified state group into one state by the principle of adding the entry rates and keeping the exit rate unchanged.
In a third aspect, there is provided a computer terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements a simplified markov model construction method applied to complex systems as described in any one of the first aspects when executing the computer program.
In a fourth aspect, there is provided a processor for executing a computer program which, when executed, performs a simplified markov model construction method as set forth in any of the first aspects applied to a complex system.
In a fifth aspect, there is provided a computer readable medium having stored thereon a computer program for execution by a processor to implement a simplified markov model construction method applicable to complex systems as claimed in any one of the first aspects.
In a sixth aspect, there is provided a computer program executable by a processor for implementing a simplified markov model construction method applicable to complex systems as claimed in any one of the first aspects.
Compared with the prior art, the invention has the following beneficial effects:
before simplification, the state of the equipment needs to be divided, the equipment is taken as a whole and divided according to the influence condition of an external system, and the states with the same or similar influence are combined; the method can greatly reduce the number of states in the process of building the Markov model, simplify the built Markov model and solve the problem of state combination explosion to a certain extent.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a diagram illustrating transition types applicable to homogeneous merge states in an embodiment of the present invention;
FIG. 2 is a schematic diagram of a 1oo2 system architecture;
FIG. 3 is a conventional Markov model of the 1oo2 architecture;
FIG. 4 is a simplified Markov model diagram of the post-1 oo2 framework in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail in the following with reference to examples 1 to 3 and accompanying drawings 1 to 4, and the exemplary embodiments and descriptions thereof are only for explaining the present invention and are not to be construed as limiting the present invention.
Example 1: a simplified method for constructing a Markov model applied to a complex system comprises the following steps:
the method comprises the following steps: as shown in fig. 1, when the complex system is analyzed, it is found that the complex system in this embodiment is a nuclear power plant DCS system, and in an actual operation process of the system, different devices have the same influence on system variables and the next stage (system) in the same fault mode. In the process of establishing the conventional Markov model, the state transition needs to be established for different failure modes of each board, so that the traditional Markov model often has the problem of combinatorial explosion. In the invention, the situation can be simplified, the state of the equipment or the system can be analyzed, the equipment as a whole is divided according to the influence situation of the external system, and the states with the same or similar influence are combined, namely the principle of similar combination provided by the invention.
And detecting states in the Markov model, and screening out the states with the same transfer rate to form a simplified state group. The simplified state groups are independent of each other, and the number of members in each simplified state group is not less than two. The probability of entering different states is the same, and the probability of going out different states is the same, namely, the states with the same transition rate.
The transfer rate calculation specifically comprises:
P2(t+Δt)＝P2(t)+λ1ΔtP1(t)-λΔtP2(t) (1)
equation (1) shows that the probability P that the system is in state 2 at time t + Δ t2(t + Δ t) equals: probability P of state 2 at time t2(t) first adding the probability P of state 1 at time t1(t) multiplied by the transition probability λ to state 21Δ t, and subtracting the probability P of state 2 at time t2(t) is multiplied by the transition probability λ Δ t to state 4.
By analogy, for state n, one can get:
Pn(t+Δt)＝Pn(t)+λn-1ΔtP1(t)-λΔtPn(t) (2)
in the formula, Pn(t + Δ t) is the probability that the complex system is in state n at time t + Δ t; pn(t) is the probability that the complex system is in state n at time t; p1(t) is the probability that the complex system is in state 1 at time t, λn-1Δ t. is the transition probability from state 1 to state n of the complex system; λ Δ t. is the transition probability of complex system state 2 to state n + 1.
Step two: the member states in the simplified state group are merged and simplified into one state by the principle that the entry rate is added and the exit rate is kept unchanged.
The merging and simplifying calculation of the simplified state group specifically includes:
Figure BDA0002735689980000041
in the formula, P2(t+Δt)+P3(t+Δt)+......+Pn(t + Δ t) is the sum of the probabilities of the complex system from state 2 to state n at time t + Δ t; [ P ]2(t)+P3(t))+.....+Pn(t)]Is a complex systemSumming the probabilities from state 2 to state n at time t; (lambda1+λ2+......+λn-1) Δ t) is the sum of transition probabilities for complex system state 2 to state n. The results verify that when multiple states have the same transition rate, the multiple states can be merged into one state, the entry rates are added, and the exit rates remain unchanged.
Example 2: a simplified Markov model building system applied to a complex system comprises a state confirmation module and a simplified combination module. And the state confirmation module is used for detecting the states in the Markov model, and forming a simplified state group after screening out the states with the same transfer rate. And the simplified merging module is used for merging and simplifying the member states in the simplified state group into one state by the principle of adding the entry rates and keeping the exit rate unchanged.
Example 3: the present embodiment takes the 1oo2 (1 is taken as 2) architecture as an example to explain a simplified method for constructing a markov model applied to a complex system.
As shown in fig. 2, the 1oo2 architecture consists of two channels in parallel, either of which can perform security functions. The safety function is disabled on demand if and only if both channels are subject to dangerous failure.
As shown in fig. 3, according to the system architecture of 1oo2, system model establishment is performed according to a conventional markov model to obtain a markov model, and a corresponding state transition matrix P0 can be obtained, where P0 is an 8-level state transition matrix, specifically:
Figure BDA0002735689980000051
as can be seen from the conventional 1oo2 structure markov model analysis shown in fig. 3, the state 1 and the state 3 have the same transition rate, i.e. the probability of entering the state 1 and the state 3 is the same, and the probability of going out from the state 1 and the state 3 is the same, which satisfies the simplified principle proposed by the present invention. Similarly, state 2 and state 4 also satisfy the simplified principle proposed by the present invention.
As shown in fig. 4, according to the simplification principle proposed by the present invention, states 1 and 3, and states 2 and 4 respectively satisfy the simplification principle, and are subjected to simplified combination, i.e., "same kind of combination". Combining the state 1 and the state 3 into one state, adding the input rates, and keeping the output rate unchanged; combining the state 2 and the state 4 into one state, adding the input rates, keeping the output rate unchanged, and setting the corresponding state transition probability matrix as P, specifically:
Figure BDA0002735689980000061
by comparing the two Markov models before and after simplification and the state transition matrix, the simplification method provided by the invention is applied to simplify the original 8-order model matrix to a 6-order model matrix.
This embodiment is only for a simple 1oo2 architecture, and the simplification will be very significant when applied to more complex systems.
The working principle is as follows: before simplification, the state of the equipment needs to be divided, the equipment is taken as a whole and divided according to the influence condition of an external system, and the states with the same or similar influence are combined; the method can greatly reduce the number of states in the process of building the Markov model, simplify the built Markov model and solve the problem of state combination explosion to a certain extent.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A Markov model construction simplification method applied to a complex system is characterized by comprising the following steps:
detecting states in the Markov model, and screening out states with the same transfer rate to form a simplified state group;
the member states in the simplified state group are merged and simplified into one state by the principle that the entry rate is added and the exit rate is kept unchanged.
2. The method of claim 1, wherein the transition rate determination is specifically: the probability of entering different states is the same, and the probability of going out different states is the same, namely the states with the same transition rate.
3. The method of claim 1, wherein the computation of the transition rate is specifically:
Pn(t+Δt)＝Pn(t)+λn-1ΔtP1(t)-λΔtPn(t)
in the formula, Pn(t + Δ t) is the probability that the complex system is in state n at time t + Δ t; pn(t) is the probability that the complex system is in state n at time t; p1(t) is the probability that the complex system is in state 1 at time t, λn-1Δ t is the transition probability from state 1 to state n of the complex system; λ Δ t is the transition probability of complex system state 2 to state n + 1.
4. The method of claim 3, wherein the simplified combination of states is calculated by:
P2(t+Δt)+P3(t+Δt)+......+Pn(t+Δt)＝[P2(t)+P3(t)+......+Pn(t)]+(λ1+λ2+......+λn-1)ΔtP1(t)-λΔt[P2(t)+P3(t)+......+Pn(t)]
in the formula, P2(t+Δt)+P3(t+Δt)+......+Pn(t + Δ t) is the state 2 to the state of the complex system at the time t + Δ tn is the sum of the probabilities; [ P ]2(t)+P3(t)+......+Pn(t)]The sum of the probabilities of the state 2 to the state n of the complex system at the time t; (lambda1+λ2+......+λn-1) Δ t is the sum of transition probabilities for complex system state 2 to state n.
5. The simplified markov model construction method applied to a complex system according to claim 1, wherein the complex system is a nuclear power plant DCS system.
6. A simplified system for constructing a Markov model applied to a complex system is characterized by comprising the following components:
the state confirmation module is used for detecting states in the Markov model, screening out the states with the same transfer rate and then forming a simplified state group;
and the simplified merging module is used for merging and simplifying the member states in the simplified state group into one state by the principle of adding the entry rates and keeping the exit rate unchanged.
7. A computer terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing a simplified markov model construction method for complex systems as claimed in any one of claims 1 to 5 when executing the program.
8. A processor, characterized in that the processor is adapted to run a computer program which when run performs a markov model construction simplification method for complex systems as claimed in any one of the claims 1 to 5.
9. A computer-readable medium, on which a computer program is stored which, when being executed by a processor, is adapted to carry out a markov model construction reduction method applicable to complex systems as claimed in any one of claims 1 to 5.
10. A computer program for implementing a simplified markov model construction method for complex systems according to any one of claims 1 to 5, by means of a processor.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115277444A (en) * 2022-07-05 2022-11-01 中国人民解放军陆军炮兵防空兵学院 Dynamic modeling method for communication system, storage medium and computer system

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103440393A (en) * 2013-09-18 2013-12-11 江苏大学 State space reduction method for continuous time Markov chain
CN104680549A (en) * 2015-03-24 2015-06-03 西安电子科技大学 SAR (synthetic aperture radar) image change detection method based on high-order neighborhood TMF (triplet Markov random field) model
CN109241583A (en) * 2018-08-17 2019-01-18 北京航空航天大学 Man-machine interactive system Reliability Solution method based on Markov
CN110110395A (en) * 2019-04-18 2019-08-09 江苏理工学院 A kind of multi-state System Reliability appraisal procedure based on markov and general generating function
CN110147306A (en) * 2019-04-26 2019-08-20 北京航空航天大学 A kind of fault-tolerant software reliability and performance estimating method considering relevant failure
CN111125551A (en) * 2019-11-12 2020-05-08 杭州电子科技大学 User position prediction method based on Markov model with selective memory

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103440393A (en) * 2013-09-18 2013-12-11 江苏大学 State space reduction method for continuous time Markov chain
CN104680549A (en) * 2015-03-24 2015-06-03 西安电子科技大学 SAR (synthetic aperture radar) image change detection method based on high-order neighborhood TMF (triplet Markov random field) model
CN109241583A (en) * 2018-08-17 2019-01-18 北京航空航天大学 Man-machine interactive system Reliability Solution method based on Markov
CN110110395A (en) * 2019-04-18 2019-08-09 江苏理工学院 A kind of multi-state System Reliability appraisal procedure based on markov and general generating function
CN110147306A (en) * 2019-04-26 2019-08-20 北京航空航天大学 A kind of fault-tolerant software reliability and performance estimating method considering relevant failure
CN111125551A (en) * 2019-11-12 2020-05-08 杭州电子科技大学 User position prediction method based on Markov model with selective memory

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
HAITAO GUO等: "《Automatic creation of Markov models for reliability assessment ofsafety instrumented systems》", 《SCIENCEDIRECT》 *
吴礼银 等: "《基于马尔可夫计算核电厂安全级DCS可用性的研究》", 《仪器仪表用户》 *
沈继忱 等: "《控制系统可靠性评估方法》", 《控制系统》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115277444A (en) * 2022-07-05 2022-11-01 中国人民解放军陆军炮兵防空兵学院 Dynamic modeling method for communication system, storage medium and computer system
CN115277444B (en) * 2022-07-05 2023-06-02 中国人民解放军陆军炮兵防空兵学院 Dynamic modeling method for communication system, storage medium and computer system

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