CN108875205A - 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 present invention provides a kind of system availability high efficiency simulating method based on reachability matrix and discrete event control system, especially
Refer to it is a kind of system reliability block diagram is encapsulated as reachability matrix, then driving is carried out by discrete event and realizes system availability assessment
Emulation mode, belong to Reliability Engineering field.
Background technique
Availability is one of the index of gauging system performance quality.It indicates that any moment t system is in normal condition
Probability is denoted as A (t).When system can not repair, the availability of system is equal to its reliability R (t).Reliability block diagram
(Reliability Block Diagram, RBD) is to solve for system availability/reliability effective means.When the failure of unit
When exponential distribution is disobeyed in distribution and maintenance distribution, will lead to system availability can not Analytical Solution.It is general using emulation at this time
Mode solves.But when system scale is larger or each unit fault logic relationship complexity, the effect of system availability emulation will lead to
Rate rapid decrease.Therefore finding a kind of efficient availability simulation algorithm seems increasingly important.
It is organic between a variety of typical fault logical AND system reachable states of unit in present invention research reliability block diagram
Connection, has invented a kind of novel system availability emulation mode, i.e., the system based on reachability matrix and discrete event control system can
Expenditure high efficiency simulating method can be assessed for the availability of complication system and provide effective support.
Summary of the invention
The present invention is directed to provide a kind of efficient availability emulation mode for complication system evaluation, by the available mode of system
The reachable state of system after being converted into each unit failure and repairing, then it is obtained by discrete event control system and by Multi simulation running
Availability simulation value, to improve the efficiency and effect of complication system availability emulation.
The purpose of the present invention is to propose to a kind of system availability height based on reachability matrix and discrete event control system to imitate
True method, mainly comprises the steps of：
Step 1：Reliability block diagram (RBD) model conversion is adjacency matrix
The beginning and end of RBD is defaulted as start unit and end unit, is then closed according to the fault logic of each unit
System converts the RBD block diagram of system to the adjacency matrix Q of system-oriented normal work.
(1) detect whether that there are voting logics.If there is voting logic, voting logic is encapsulated as a special list
The state of member, unit is determined according to internal element fault condition；
(2) using beginning and end as special element, the input/output relation between all units is then checked, according to string
Connection, in parallel, side connection, bridging model, determine the adjacency matrix that system-oriented works normally.It is closed when unit i has input to unit j
When being, the element q of adjacency matrix Qij=1, it is otherwise 0.
Step 2：Define simulation convergence number
Simulation convergence frequency n is defined, when simulation times reach n, emulation terminates.
Step 3：Failure and maintenance discrete event generate and sort
Failure and maintenance time sampling are carried out to each unit in system, is ranked up according to time order and function, is according to maintenance
No success and task time T whether is reached, determines discrete event set.
(1) it is distributed according to the failure of each unit and carries out mean down time sampling；
(2) average repair time sampling is carried out to the maintenance distribution of each unit, while according to the maintenance probability of success to this
Whether maintenance is successfully sampled；
(3) it is ranked up according to the time order and function of the failure of system each unit and maintenance event, discrete event set is written；
(4) iteration carries out the failure and maintenance sampling process of each unit, until task time T.There are two types of situations to need
Terminate to sample.The first situation, when certain unit maintenance whether successful result be failure, then stop sampling, and the maintenance thing
Part can be not added to discrete event set.When another situation is that the time of origin of a newest discrete event exceeds task
Between T, then sampling terminates, and the event is not added to discrete event collection.
Step 4：The adjacency matrix Status Change of discrete event control system
It is broken down event and maintenance event according to unit, will abut against input/output relation relevant to this element in matrix
Change.
(1) all to output and input syntople value by first for this element after the event of failure of unit occurs
Initial value 1 is changed to 0；
(2) after maintenance event occurs for unit, input and output syntople value for this element revert to initial
1。
Step 5：It is determined based on the single available mode of reachability matrix
Moment solution reachability matrix occurs in discrete event, and is determined according to the reachability relation of start unit and end unit
System health.
(1) moment occurs for all discrete events before task time terminates, and is solved according to adjacency matrix state adjusted
The reachability matrix R of system；
(2) determine to whether there is reachability relation between start unit and end unit.When there are reachability relation, system can
1 is kept or is changed to state, and when reachability relation is not present, system health keeps or be changed to 0.
Step 6：It calculates and generates availability simulation curve
According to Multi simulation running as a result, computing system is from t=0 to task terminates availability between t=T, and generate available
Spend simulation curve.
(1) task time T is divided into m parts, every part of duration of Δ t=T/m.
(2) 0 moment, each cut-point and the A (t) at T moment are calculated.For any one cut-point, if HiIt (t) is A
(t) nonce, Si(t) available mode of the system in t moment in i-th emulation, S are indicatedi(t)=1 indicate that system is available,
Si(t)=0 indicate that system is unavailable.It is assumed that H0(t)=0, then Hi(t)=[Hi-1(t)×(i-1)+Si(t)]/i, i=1,
2 ..., n, n are system emulation number.As i=n, i.e. Hn(t)=A (t)；
(3) using the time as abscissa, availability is ordinate, connects 0 moment, m-1 cut-point and T moment availability
Value produces system availability simulation curve.
Detailed description of the invention
Fig. 1 is the overall architecture block diagram of heretofore described method
Fig. 2 is the conversion process of reliability block diagram and the adjacency matrix towards normal work in the present invention
Fig. 3 is the process of discrete event control system adjacency matrix change in the present invention
Fig. 4 is the process for determining system health in the present invention according to reachability matrix
Specific embodiment
To better understand technical solution of the present invention, feature and advantage, below in conjunction with attached drawing, make specifically
It is bright.
The invention proposes a kind of system availability high efficiency simulating method based on reachability matrix and discrete event control system, can
For complication system availability simulation analysis, system is reachable after converting the available mode of system to each unit failure and repairing
State, then its availability simulation value is obtained by discrete event control system and Multi simulation running.To be mentioned for the availability assessment of system
For a kind of high efficiency method.Overall architecture of the invention, as shown in Figure 1.Its specific implementation step is：
Step 1：Reliability block diagram (RBD) model conversion is adjacency matrix
The beginning and end of RBD is defaulted as start unit and end unit, is then closed according to the fault logic of each unit
System converts the RBD block diagram of system to the adjacency matrix Q of system-oriented normal work.
(1) detect whether that there are voting logics.If there is voting logic, voting logic is encapsulated as a special list
The state of member, unit is determined according to internal element fault condition；
(2) using beginning and end as special element, the input/output relation between all units is then checked, according to string
Connection, in parallel, side connection, bridging model, determine the adjacency matrix that system-oriented works normally.It is closed when unit i has input to unit j
When being, the element q of adjacency matrix Qij=1, it is otherwise 0.
Certain system of example 1 includes 14 units, and there are series, parallel, other connection, voting and bridging etc. are basic for reliability block diagram
Logic is translated into the adjacency matrix towards normal work.
As shown in Fig. 2.The cells D of voting relationship will be present first, E, F are encapsulated as special element O.The state of unit O
It is determined by D, E, F state.It is 2/3, then when 2 or 2 or more units are normal, unit O due to deciding by vote relationship between D, E, F
Normally, otherwise unit O is failure.Then, adjacency matrix is established according to input/output relation.According to reliability block diagram rule, remove
Outside bridging logic, all unit connection relations are from the direction of origin-to-destination, and in this case, it is left-to-right.In other relationship,
Default connection is unit G, therefore adjacency matrix as shown in Fig. 2 can be obtained.
Step 2：Define simulation convergence number
Simulation convergence frequency n is defined, when simulation times reach n, emulation terminates.
Step 3：Failure and maintenance discrete event generate and sort
Failure and maintenance time sampling are carried out to each unit in system, is ranked up according to time order and function, is according to maintenance
No success and task time T whether is reached, determines discrete event set.
(1) it is distributed according to the failure of each unit and carries out mean down time sampling；
(2) average repair time sampling is carried out to the maintenance distribution of each unit, while according to the maintenance probability of success to this
Whether maintenance is successfully sampled；
(3) it is ranked up according to the time order and function of the failure of system each unit and maintenance event, discrete event set is written；
(4) iteration carries out the failure and maintenance sampling process of each unit, until task time T.There are two types of situations to need
Terminate to sample.The first situation, when certain unit maintenance whether successful result be failure, then stop sampling, and the maintenance thing
Part can be not added to discrete event set.When another situation is that the time of origin of a newest discrete event exceeds task
Between T, then sampling terminates, and the event is not added to discrete event collection.
Example 2 assumes certain repairable system by 3 unit A1, A2And A3It constitutes, and reliability block diagram is series model.A1, A2With
A3Failure obey exponential distribution, crash rate distinguish 0.01/h, 0.02/h and 0.03/h, each unit maintenance distribution obey normal state
It is distributed (2h, 0.2h), (1.5h, 0.15), (1h, 0.25).The maintenance probability of success of each unit is respectively 0.9,0.85 and 0.95.
The task time of system is 40h, determines the discrete event set of system.
Failure is carried out to each unit and maintenance event is sampled.For unit A1, it is assumed that the sampling of fault time first time is
48h, then its down time has exceeded task time, without sampling again, and is not added to discrete event set.For list
First A2, it is assumed that failure sample time first time is 23h, and maintenance event is sampled to 2.1h, and repairing result is successfully.Second of event
Downtime is sampled to 20h, has exceeded task time at this time, stops sampling.Meanwhile first time failure and repairing successfully be added to from
Dissipate event sets.For unit A3, it is assumed that failure sample time first time is 30h, and maintenance time is sampled to 1.2h, and repairs knot
Fruit is failure, then directly stops subsequent sampling, and its first time failure increases to discrete event set.Then final discrete event
Gather as follows：
{ 23h (unit A2First time failure), 25.2h (unit A2Maintenance terminates), 30h (unit A3First time failure) }
Step 4：The adjacency matrix Status Change of discrete event control system
It is broken down event and maintenance event according to unit, will abut against input/output relation relevant to this element in matrix
Change.
(1) all to output and input syntople value by first for this element after the event of failure of unit occurs
Initial value 1 is changed to 0；
(2) after maintenance event occurs for unit, input and output syntople value for this element revert to initial
1。
Certain system of example 3 includes 3 unit U1, U2, U3, reliability block diagram is unit U2、U3After parallel connection with U1Series connection.It is assumed that U2
It breaks down in 40h, 42h completes maintenance, and the result is that repairing successfully.To corresponding adjacency matrix, state change is performed.
As shown in Fig. 3, according to the connection relationship of system reliability block diagram, the Elements C of initial adjacency matrix12, C23, C24,
C35, C45It is 1, other are 0.Work as U2After 40 hours break down, with U2Relevant C23, C35It is changed to 0.Then when arrive 42h
When, due to repairing successfully then C23, C35It is changed to 1.
Step 5：It is determined based on the single available mode of reachability matrix
Moment solution reachability matrix occurs in discrete event, and is determined according to the reachability relation of start unit and end unit
System health.
(1) moment occurs for all discrete events before task time terminates, and is solved according to adjacency matrix state adjusted
The reachability matrix R of system；
(2) determine to whether there is reachability relation between start unit and end unit.When there are reachability relation, system can
1 is kept or is changed to state, and when reachability relation is not present, system health keeps or be changed to 0.
Example 4 connects example 3.Still 3 unit U are analyzed1, U2, U3The serial-parallel mirror system constituted.Assuming that U2Occur in 40h
Failure, 42h completes maintenance, and the result is that repairing successfully.U3Break down in 41h, 44h complete maintenance, and the result is that maintenance at
Function.Determine system in 40h, 41h, 42h, the available mode of 43h according to reachability matrix.
As shown in Fig. 4.When 40h, unit U2It breaks down, after updating adjacency matrix, can solve and obtain reachability matrix R.R
In element R15Start unit is represented to the relationship of end unit, is at this time R15=1, show that system, can still in available mode
It is indicated with 1.When 41h, unit U2And U3It is in malfunction simultaneously, at this time R15=0, show Account Dept's available mode, need by
System health is changed to 0.When 42h, U2It is repaired, only U3Still in malfunction, R at this time15=1, system can use shape
State needs to be changed to 1.When 43h, all units are normal, at this time R15=1, system health keeps 1.
Step 6：It calculates and generates availability simulation curve
According to Multi simulation running as a result, computing system is from t=0 to task terminates availability between t=T, and generate available
Spend simulation curve.
(1) task time T is divided into m parts, every part of duration of Δ t=T/m.
(2) 0 moment, each cut-point and the A (t) at T moment are calculated.For any one cut-point, if HiIt (t) is A
(t) nonce, Si(t) available mode of the system in t moment in i-th emulation, S are indicatedi(t)=1 indicate that system is available,
Si(t)=0 indicate that system is unavailable.It is assumed that H0(t)=0, then Hi(t)=[Hi-1(t)×(i-1)+Si(t)]/i, i=1,
2 ..., n, n are system emulation number.As i=n, i.e. Hn(t)=A (t)；
(3) using the time as abscissa, availability is ordinate, connects 0 moment, m-1 cut-point and T moment availability
Value produces system availability simulation curve.
Example 5, it is assumed that emulation 1000 times, at the t=300h moment, one shares 998 available mode Si(t=300)=1, really
Fixed its availability A (t=300).Then A (t=300)=998/1000=0.998, i.e. system are at t=300 moment, availability
0.998。
Claims (6)
1. a kind of system availability high efficiency simulating method based on reachability matrix and discrete event control system：It is comprised the steps of：
Step 1：Reliability block diagram (RBD) model conversion is adjacency matrix.The beginning and end of RBD is defaulted as start unit
And end unit converts system-oriented for the RBD block diagram of system and works normally then according to the fault logic relationship of each unit
Adjacency matrix Q.
Step 2：Define simulation convergence number.Simulation convergence frequency n is defined, when simulation times reach n, emulation terminates.
Step 3：Failure and maintenance discrete event generate and sort.Failure and maintenance time sampling are carried out to each unit in system,
It is ranked up according to time order and function, whether succeeds according to maintenance and whether reach task time T, determine discrete event set.
Step 4：The adjacency matrix Status Change of discrete event control system.It is broken down event and maintenance event according to unit, it will be adjacent
Connect input/output relation change relevant to this element in matrix.
Step 5：It is determined based on the single available mode of reachability matrix.Moment solution reachability matrix, and root occurs in discrete event
System health is determined according to the reachability relation of start unit and end unit.
Step 6：It calculates and generates availability simulation curve.According to Multi simulation running as a result, computing system terminates from t=0 to task
Availability between t=T, and generate availability simulation curve.
2. a kind of system availability efficient emulation side based on reachability matrix and discrete event control system according to claim 1
Method, it is characterised in that：In the first step in " reliability block diagram (RBD) model conversion is adjacency matrix ", by rising for RBD
Point and terminal are defaulted as start unit and end unit, then according to the fault logic relationship of each unit, by the RBD block diagram of system
It is converted into the adjacency matrix Q of system-oriented normal work.
(1) detect whether that there are voting logics.If there is voting logic, voting logic is encapsulated as a special element, it is single
The state of member is determined according to internal element fault condition；
(2) using beginning and end as special element, then check the input/output relation between all units, according to series connection,
In parallel, other connection, bridging model, determine the adjacency matrix that system-oriented works normally.When there are input relationships to unit j by unit i
When, the element q of adjacency matrix Qij=1, it is otherwise 0.
3. a kind of system availability efficient emulation side based on reachability matrix and discrete event control system according to claim 1
Method, it is characterised in that：In the third step in " failure and the maintenance discrete event generates and sequence ", to each unit in system
Failure and maintenance time sampling are carried out, is ranked up according to time order and function, whether succeeds according to maintenance and whether reaches task
Time T needs to terminate sampling there are two types of situation.The first situation, when certain unit maintenance whether successful result be failure, then stop
It only samples, and the maintenance event can be not added to discrete event set.Another situation is a newest discrete event
Time of origin exceeds task time T, then sampling terminates, and the event is not added to discrete event collection.
4. a kind of system availability efficient emulation side based on reachability matrix and discrete event control system according to claim 1
Method, it is characterised in that：In described in the 4th step " the adjacency matrix Status Change of discrete event control system ", occurred according to unit
Event of failure and maintenance event will abut against input/output relation change relevant to this element in matrix.
(1) all to output and input syntople value by initial value 1 for this element after the event of failure of unit occurs
It is changed to 0；
(2) after maintenance event occurs for unit, input and output syntople value for this element revert to initial 1.
5. a kind of system availability efficient emulation side based on reachability matrix and discrete event control system according to claim 1
Method, it is characterised in that：In " being determined based on the single available mode of reachability matrix " described in the 5th step, sent out in discrete event
The raw moment solves reachability matrix, and determines system health according to the reachability relation of start unit and end unit.
(1) moment occurs for all discrete events before task time terminates, according to adjacency matrix state solving system adjusted
Reachability matrix R；
(2) determine to whether there is reachability relation between start unit and end unit.When there are reachability relation, system can use shape
State keeps or is changed to 1, and when reachability relation is not present, system health keeps or be changed to 0.
6. a kind of system availability efficient emulation side based on reachability matrix and discrete event control system according to claim 1
Method, it is characterised in that：In step 6 in described " calculate and generate availability simulation curve ", according to Multi simulation running as a result,
Computing system terminates the availability between t=T from t=0 to task, and generates availability simulation curve.
(1) 0 moment, each cut-point and the A (t) at T moment are calculated.For any one cut-point, if Hi(t) for A's (t)
Nonce, Si(t) available mode of the system in t moment in i-th emulation, S are indicatedi(t)=1 indicate that system is available, Si(t)
=0 indicates that system is unavailable.It is assumed that H0(t)=0, then Hi(t)=[Hi-1(t)×(i-1)+Si(t)]/i, i=1,2 ..., n, n
For system emulation number.As i=n, i.e. Hn(t)=A (t)；
(2) using the time as abscissa, availability is ordinate, and at 0 moment of connection, m-1 cut-point and T moment can be with angle value
Produce system availability simulation curve.
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