CN108875205B - System availability efficient simulation method based on reachable matrix and discrete event driving - Google Patents
System availability efficient simulation method based on reachable matrix and discrete event driving Download PDFInfo
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Abstract
The invention discloses a system availability high-efficiency simulation method based on an accessible matrix and discrete event driving, which converts the available state of a system into the accessible state of each unit fault and the system after maintenance, and obtains the availability simulation value through discrete event driving and multiple times of simulation, thereby improving the efficiency and effect of the availability simulation of a complex system. The method comprises the following steps: 1, converting a reliability block diagram of the system into an adjacency matrix oriented to normal operation of the system. 2 defines the simulation convergence number. And 3, sampling the fault and maintenance time of each unit in the system, sequencing the units according to time sequence and generating a discrete event set. And 4, according to the fault event and the maintenance event of the unit, changing the element related to the unit in the adjacency matrix. And 5, solving the reachable matrix of each discrete event at the occurrence moment, and determining the available state of the system according to the reachable relation of the starting unit and the ending unit. And 6, calculating the availability of the system at each moment according to the multiple simulation results, and generating an availability simulation curve.
Description
Technical Field
The invention provides a high-efficiency simulation method for system availability based on an reachable matrix and discrete event driving, in particular to a simulation method for realizing system availability evaluation by packaging a system reliability block diagram into a reachable matrix and driving through discrete events, and belongs to the field of reliability engineering.
Background
The availability is one of the indexes for measuring the performance of the system. It represents the probability that the system is in the normal state at any time t, denoted as A (t). When the system is not repairable, the availability of the system is equal to its reliability R (t). A Reliability Block Diagram (RBD) is an effective means for solving the system availability/Reliability. When the failure distribution and maintenance distribution of the unit do not comply with the exponential distribution, the system availability cannot be solved analytically. At this time, a simulation method is generally adopted for solving. But when the system size is large or the logic relation of each unit fault is complex, the efficiency of the system availability simulation is rapidly reduced. Therefore, it is extremely important to find an efficient usability simulation algorithm.
The invention researches organic relations between various typical fault logics of units in a reliability block diagram and the reachable state of a system, invents a novel system availability simulation method, namely, a system availability high-efficiency simulation method based on reachable matrixes and discrete event driving, and can provide effective support for availability evaluation of a complex system.
Disclosure of Invention
The invention aims to provide an efficient availability simulation method for complex system evaluation, which converts the available state of a system into the reachable state of each unit fault and the maintained system, and obtains the availability simulation value through discrete event driving and multiple simulation, thereby improving the efficiency and effect of the availability simulation of the complex system.
The invention aims to provide a high-efficiency simulation method of system availability based on reachable matrix and discrete event drive, which mainly comprises the following steps:
the method comprises the following steps: transformation of Reliability Block Diagram (RBD) model into adjacency matrix
And defaulting the starting point and the end point of the RBD as a starting unit and an ending unit, and then converting the RBD block diagram of the system into an adjacent matrix Q facing the normal work of the system according to the fault logic relationship of each unit.
(1) The presence or absence of voting logic is detected. If the voting logic exists, the voting logic is packaged into a special unit, and the state of the unit is judged according to the fault condition of the internal unit;
(2) taking the starting point and the end point as special units, then checking the input-output relation among all the units according to the serial connection, parallel connection, side connection,And the bridging model is used for determining an adjacency matrix facing the normal operation of the system. When cell i has an input relationship to cell j, the element Q of matrix Q is adjoinedijOtherwise, it is 0.
Step two: defining simulation convergence times
And defining simulation convergence times n, and finishing the simulation when the simulation times reach n.
Step three: fault and repair discrete event generation and sequencing
And sampling the fault and maintenance time of each unit in the system, sequencing according to the time sequence, and determining a discrete event set according to whether the maintenance is successful and whether the task time T is reached.
(1) Sampling average fault time according to the fault distribution of each unit;
(2) sampling the average maintenance time of the maintenance distribution of each unit, and simultaneously sampling whether the maintenance is successful or not according to the success probability of the maintenance;
(3) sequencing according to the time sequence of the fault and maintenance events of each unit of the system, and writing into a discrete event set;
(4) and iterating the fault and maintenance sampling process of each unit until the task time T. There are two cases that require ending the sampling. In the first case, when the success of the repair of a unit results in a failure, the sampling is stopped and the repair event may not be added to the discrete event set. In another case, if the occurrence time of the latest discrete event exceeds the task time T, the sampling ends and the event is not added to the discrete event set.
Step four: discrete event driven adjacent matrix state change
And changing the input-output relationship related to the unit in the adjacency matrix according to the failure event and the maintenance event of the unit.
(1) When a fault event of a unit occurs, all input and output adjacency relation values aiming at the unit are changed to 0 from an initial value of 1;
(2) when a maintenance event occurs in a cell, the input and output adjacent relation value for the cell is restored to the original 1.
Step five: single availability status determination based on a reachability matrix
And solving the reachable matrix at the discrete event occurrence moment, and determining the available state of the system according to the reachable relation of the starting unit and the ending unit.
(1) Solving an reachable matrix R of the system according to the adjusted state of the adjacent matrix at the occurrence time of all discrete events before the task time is finished;
(2) it is determined whether a reachability relationship exists between the starting unit and the ending unit. When there is a reachable relationship, the system available state remains or changes to 1, and when there is no reachable relationship, the system available state remains or changes to 0.
Step six: calculating and generating a usability simulation curve
And calculating the availability of the system from T-0 to end of task T-T according to the simulation results of multiple times, and generating an availability simulation curve.
(1) The task time T is equally divided into m portions, each of which has a duration Δ T equal to T/m.
(2) Calculate A (T) for time 0, each partition point, and time T. For any one division point, set Hi(t) is the temporary value of A (t), Si(t) represents the availability of the system at time t in the ith simulation, Si(t) ═ 1 indicates that the system is usable, Si(t) ═ 0 indicates that the system is not available. Suppose H0(t) is 0, then Hi(t)＝[Hi-1(t)×(i-1)+Si(t)]And the i, i is 1,2, …, and n is the system simulation times. When i ═ n, i.e. Hn(t)＝A(t)；
(3) And (3) connecting the availability values at 0 moment, m-1 division points and T moment by taking time as an abscissa and availability as an ordinate to generate a system availability simulation curve.
Drawings
FIG. 1 is a block diagram of the overall architecture of the method of the present invention
FIG. 2 is a conversion process of the reliability block diagram and the adjacency matrix oriented to normal operation in the present invention
FIG. 3 is a process of discrete event driven neighbor matrix change in the present invention
FIG. 4 is a process for determining the available state of the system according to the reachable matrix in the present invention
Detailed Description
In order to make the technical solution, features and advantages of the present invention more clearly understood, the following detailed description is made with reference to the accompanying drawings.
The invention provides a high-efficiency simulation method for the availability of a system based on an accessible matrix and discrete event driving, which can be used for the simulation analysis of the availability of a complex system, converts the available state of the system into the accessible state of the system after the fault and the maintenance of each unit, and acquires the simulation value of the availability through the discrete event driving and multiple times of simulation. Thereby providing an efficient method for usability assessment of the system. The overall architecture of the present invention is shown in fig. 1. The specific implementation steps are as follows:
the method comprises the following steps: transformation of Reliability Block Diagram (RBD) model into adjacency matrix
And defaulting the starting point and the end point of the RBD as a starting unit and an ending unit, and then converting the RBD block diagram of the system into an adjacent matrix Q facing the normal work of the system according to the fault logic relationship of each unit.
(1) The presence or absence of voting logic is detected. If the voting logic exists, the voting logic is packaged into a special unit, and the state of the unit is judged according to the fault condition of the internal unit;
(2) and taking the starting point and the end point as special units, then checking the input-output relationship among all the units, and determining an adjacency matrix facing the normal operation of the system according to serial, parallel, side and bridging models. When cell i has an input relationship to cell j, the element Q of matrix Q is adjoinedijOtherwise, it is 0.
Example 1 a system contains 14 units, and its reliability diagram has basic logics of series connection, parallel connection, side connection, voting and bridging, etc., and converts them into a adjacency matrix facing normal operation.
As shown in fig. 2. The unit D, E, F for which there is a voting relationship is first packaged as a special unit O. The state of cell O is determined by the D, E, F state. Since the voting relationship between D, E, F is 2/3, when 2 or more than 2 cells are normal, cell O is normal, otherwise cell O is faulty. Then, an adjacency matrix is established according to the input-output relation. According to the reliability block diagram rules, all cell connections, except for bridging logic, are in the direction from the start point to the end point, in this case left to right. In the bypass relationship, the default is connected to the cell G, so that the adjacency matrix as shown in FIG. 2 can be obtained.
Step two: defining simulation convergence times
And defining simulation convergence times n, and finishing the simulation when the simulation times reach n.
Step three: fault and repair discrete event generation and sequencing
And sampling the fault and maintenance time of each unit in the system, sequencing according to the time sequence, and determining a discrete event set according to whether the maintenance is successful and whether the task time T is reached.
(1) Sampling average fault time according to the fault distribution of each unit;
(2) sampling the average maintenance time of the maintenance distribution of each unit, and simultaneously sampling whether the maintenance is successful or not according to the success probability of the maintenance;
(3) sequencing according to the time sequence of the fault and maintenance events of each unit of the system, and writing into a discrete event set;
(4) and iterating the fault and maintenance sampling process of each unit until the task time T. There are two cases where ending the sampling is required. In the first case, when the success of the repair of a unit results in a failure, the sampling is stopped and the repair event may not be added to the discrete event set. In another case, if the occurrence time of the latest discrete event exceeds the task time T, the sampling ends and the event is not added to the discrete event set.
Example 2 suppose a repairable system consists of 3 units A1，A2And A3The reliability block diagram is a series model. A. the1，A2And A3The failure rates are respectively 0.01/h,0.02/h and 0.03/h, and the maintenance distribution of each unit is subjected to normal distribution (2h,0.2h), (1.5h,0.15), (1h, 0.25). Each one ofThe repair success probabilities for the cells were 0.9,0.85, and 0.95, respectively. The task time of the system is 40h, and a discrete event set of the system is determined.
Failure and maintenance events are sampled for each unit. For cell A1Assuming that the first fault time sample is 48h, its fault time exceeds the task time, no resampling is required, and no addition to the discrete event set is made. For cell A2Assume that the first failure sampling time is 23h, the maintenance event sampling is 2.1h, and the maintenance result is successful. The second failure time sampling is 20h, and the sampling is stopped when the task time is exceeded. At the same time, the first failure and repair success is added to the discrete event set. For cell A3Assuming that the first failure sampling time is 30h, the maintenance time sampling is 1.2h, and the maintenance result is failure, the subsequent sampling is directly stopped and the first failure thereof is added to the discrete event set. The final set of discrete events is then as follows:
{23h (Unit A)2First failure), 25.2h (cell a)2End of maintenance), 30h (unit a)3First failure) }
Step four: discrete event driven adjacency matrix state change
And changing the input-output relationship related to the unit in the adjacency matrix according to the failure event and the maintenance event of the unit.
(1) When a fault event of a unit occurs, all input and output adjacency relation values aiming at the unit are changed to 0 from an initial value of 1;
(2) when a maintenance event occurs in a cell, the input and output adjacent relation value for the cell is restored to the original 1.
Example 3A System contains 3 units U1，U2，U3The reliability block diagram is a unit U2、U3After being connected in parallel with U1Are connected in series. Suppose U2Failure occurred at 40h, service was completed at 42h, and the result was successful service. And changing the state of the corresponding adjacent matrix.
As shown in FIG. 3, the initial adjacency matrix is based on the connection relationship of the system reliability block diagramElement C12，C23，C24，C35，C45Is 1, the others are 0. When U is turned2After 40 hours of failure, with U2Related C23，C35To 0. Then when the time reaches 42h, C is carried out due to the successful maintenance23，C35To 1.
Step five: single availability status determination based on a reachability matrix
And solving the reachable matrix at the discrete event occurrence moment, and determining the available state of the system according to the reachable relation of the starting unit and the ending unit.
(1) Solving an reachable matrix R of the system according to the adjusted state of the adjacent matrix at the occurrence time of all discrete events before the task time is finished;
(2) it is determined whether a reachability relationship exists between the starting unit and the ending unit. When there is a reachable relationship, the system available state remains or changes to 1, and when there is no reachable relationship, the system available state remains or changes to 0.
Example 4, example 3. Still analyze 3 units U1，U2，U3The formed series-parallel system. Suppose U2Failure occurred at 40h, service was completed at 42h, and the result was successful service. U shape3Failure occurred at 41h, maintenance was completed at 44h, and the result was successful maintenance. And determining the available states of the system at 40h, 41h, 42h and 43h according to the reachable matrix.
As shown in fig. 4. At 40h, unit U2When a fault occurs, the reachable matrix R can be obtained by solving after the adjacency matrix is updated. Element R of R15Represents the relationship from the start unit to the end unit, in this case R 151, indicating that the system is still in a usable state, which can be represented by 1. 41h, unit U2And U3While in a fault state, when R15When the system availability status is 0, the system availability status needs to be changed to 0. At 42h, U2Is repaired with only U3Is still in a fault state, when R15The system availability status needs to be changed to 1. At 43h, all cells were normal, when R was15The system can be 1The state is maintained as 1.
Step six: calculating and generating a usability simulation curve
And calculating the availability of the system from T-0 to end of task T-T according to the simulation results of multiple times, and generating an availability simulation curve.
(1) The task time T is equally divided into m portions, each of which has a duration Δ T equal to T/m.
(2) Calculate A (T) for time 0, each partition point, and time T. For any one division point, set Hi(t) is the temporary value of A (t), Si(t) represents the availability of the system at time t in the ith simulation, Si(t) ═ 1 indicates that the system is usable, S i0 denotes that the system is not available. Suppose H0(t) is 0, then Hi(t)＝[Hi-1(t)×(i-1)+Si(t)]And the i, i is 1,2, …, and n is the system simulation times. When i ═ n, i.e. Hn(t)＝A(t)；
(3) And (3) connecting the availability values at 0 moment, m-1 division points and T moment by taking time as an abscissa and availability as an ordinate to generate a system availability simulation curve.
Example 5, assuming 1000 simulations, a total of 998 available states S are available at time t-300 hi(t 300) 1, and its availability a (t 300) is determined. Then a (t 300) 998/1000 is 0.998, i.e. the system has a degree of availability of 0.998 at time t 300.
Claims (4)
1. A system availability efficient simulation method based on reachable matrix and discrete event driving comprises the following steps: it comprises the following steps:
the method comprises the following steps: converting the reliability block diagram model into an adjacency matrix, defaulting a starting point and an end point of the reliability block diagram as a starting unit and an end unit, and converting the reliability block diagram of the system into an adjacency matrix Q facing the normal work of the system according to the fault logic relationship of each unit;
(1) detecting whether a voting logic exists, if so, packaging the voting logic into a special unit, and judging the state of the unit according to the fault condition of the internal unit;
(2) will get upThe point and the end point are used as special units, then the input-output relation among all the units is checked, and an adjacency matrix facing the normal work of the system is determined according to serial, parallel, side and bridging models; when cell i has an input relationship to cell j, the element Q of matrix Q is adjoinedij1, otherwise 0;
step two: defining simulation convergence times, defining simulation convergence times n, and finishing simulation when the simulation times reach n;
step three: generating and sequencing fault and maintenance discrete events, sampling fault and maintenance time of each unit in the system, sequencing according to time sequence, and determining a discrete event set according to whether maintenance is successful and whether task time T is reached;
step four: discrete event driven adjacent matrix state change, according to unit fault event and maintenance event, change the input and output relation related to the unit in the adjacent matrix;
step five: determining a single available state based on the reachable matrix, solving the reachable matrix at the occurrence moment of the discrete event, and determining the available state of the system according to the reachable relation between the starting unit and the ending unit;
step six: calculating and generating a usability simulation curve, calculating the usability of the system from T-0 to T-T according to the simulation results of multiple times, and generating the usability simulation curve,
(1) calculating A (T) of 0 moment, each division point and T moment, and setting H for any division pointi(t) is the temporary value of A (t), Si(t) represents the availability of the system at time t in the ith simulation, Si(t) ═ 1 indicates that the system is usable, Si(t) ═ 0 indicates that the system is not available; suppose H0(t) is 0, then Hi(t)＝[Hi-1(t)×(i-1)+Si(t)]Where n is the number of system simulations, i is 1,2, …, and H is the number of system simulationsn(t)＝A(t)；
(2) And (3) connecting the availability values at 0 moment, m-1 division points and T moment by taking time as an abscissa and availability as an ordinate to generate a system availability simulation curve.
2. The method for efficient simulation of system availability based on reachable matrices and discrete event driven according to claim 1, wherein: in the step three, in the step "generation and sequencing of fault and maintenance discrete events", each unit in the system is subjected to fault and maintenance time sampling, sequencing is performed according to time sequence, and sampling is required to be finished under two conditions according to whether maintenance is successful and whether task time T is reached.
3. The method for efficient simulation of system availability based on reachable matrices and discrete event driven according to claim 1, wherein: in the "discrete event-driven state change of the adjacent matrix" in the fourth step, the input-output relationship of the adjacent matrix with respect to the cell is changed according to the occurrence of a failure event and a maintenance event of the cell,
(1) when a fault event of a unit occurs, all input and output adjacency relation values aiming at the unit are changed to 0 from an initial value of 1;
(2) when a maintenance event occurs in a cell, the input and output adjacent relation value for the cell is restored to the original 1.
4. The method for efficient simulation of system availability based on reachable matrices and discrete event driven according to claim 1, wherein: in the "single available state determination based on reachable matrix" in the fifth step, the reachable matrix is solved at the occurrence time of the discrete event, and the available state of the system is determined according to the reachable relationship between the starting unit and the ending unit,
(1) solving an reachable matrix R of the system according to the adjusted state of the adjacent matrix at the occurrence time of all discrete events before the task time is finished;
(2) and judging whether the reachable relation exists between the starting unit and the ending unit, wherein the available state of the system is kept or changed to 1 when the reachable relation exists, and the available state of the system is kept or changed to 0 when the reachable relation does not exist.
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