CN113656288A - Dynamic fault tree reliability analysis method based on independence coverage model - Google Patents
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Abstract
The invention relates to a dynamic fault tree reliability analysis method based on an irrelevance coverage model, which comprises the following steps: s1, analyzing the dynamic fault tree by using an algebraic frame based on the time sequence structure function, thereby obtaining an algebraic structure function based on the coverage failure event of the dynamic fault tree; s2, aiming at an algebraic structure function, obtaining the minimum irrelevant trigger of each variable by using an improved minimum irrelevant trigger calculation method; s3, acquiring a limiting expression of the basic event of the dynamic fault tree about the uncovered failure according to the minimum irrelevant trigger of each variable in the step S2; s4, obtaining an expression of the system independence coverage model based on the algebraic structure function according to the algebraic structure function in the step S2 and the expression of the uncovered failure in the step S3. The invention expands the application of the independence model in the dynamic system, is suitable for the system with any failure time distribution and the static fault tree, and has good universality.
Description
Technical Field
The invention relates to the field of software reliability engineering, in particular to a dynamic fault tree reliability analysis method based on an irrelevance coverage model.
Background
The fault tree is a classic system reliability analysis model and is commonly used for reliability analysis in the large-scale safety key field. However, with increasingly complex system architectures, particularly dynamic systems, conventional static fault trees have failed to meet reliability analysis requirements.
In fault tolerant systems, fault tolerant mechanisms assume that component failures can be perfectly identified, located, isolated, and recovered. This perfect coverage pattern becomes a perfect coverage model. However, not all component failures are perfectly fault tolerant in practice. Then, these component failures that are not recognized, isolated or recovered by the fault tolerance mechanism can propagate freely within the system and result in direct system failure. Therefore, a model that considers such a component uncovered fault becomes an incomplete coverage model. In fact, during the operation of the system, it may happen that a failure of one component causes other components to become irrelevant, and the coverage failure of this irrelevant component is not related to the system failure in the system structure, but the non-coverage failure thereof can also cause the system failure. Therefore, an incomplete coverage model considering component independence is proposed, called an independence coverage model. In the irrelevance overlay model, a component will be quarantined off immediately once it is triggered as an irrelevant component. Thus, the occurrence of an uncovered failure of a component in the model is limited before it is isolated if the component is likely to be triggered as an unrelated component.
However, the current least triggerable calculation method is based on a boolean function. Therefore, existing irrelevance overlay models are limited to analysis of static fault trees.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a dynamic fault tree reliability analysis method based on an independence coverage model, which aims at a dynamic system and considers the dynamic dependency relationship among events.
The technical scheme adopted by the invention for solving the technical problems is as follows: a dynamic fault tree reliability analysis method based on an independence covering model is constructed, and the method comprises the following steps:
s1, analyzing the dynamic fault tree by using an algebraic frame based on a time sequence structure function, thereby obtaining the basis of the dynamic fault treeAlgebraic structure function covering failure events
S2, aiming at the algebraic structure function, obtaining each variable by using the improved minimum irrelevant trigger calculation method
A minimum irrelevant trigger of;
s3, obtaining the limit expression of the basic event of the dynamic fault tree about the uncovered failure according to the minimum irrelevant trigger of each variable in the step S2
S4, obtaining an expression of the system independence coverage model based on the algebraic structure function according to the algebraic structure function in the step S2 and the expression of the uncovered failure in the step S3, wherein the general expression is as follows:
s5, obtaining a disjoint sum based on the algebraic structure function by using a disjoint sum based method according to the expression of the system independence coverage model based on the algebraic structure function in the step S4, thereby calculating the probability of the dynamic fault tree top event.
According to the scheme, the step 1 of analyzing the dynamic gate by using the algebraic frame based on the time sequence structure refers to a time sequence operator in a reference frame
"delta" represents the time sequence dependency relationship between events, namely "before" and "at the same time", the basic events at the moment are all time functions, namely time sequence variables, and the dynamic fault tree at the moment is represented as an algebraic structure function based on coverage failure.
According to the above scheme, the calculation of the minimum irrelevant trigger based on the algebraic structure function in step S2 mainly depends on the following method:
first, let
An algebraic structure function of the dynamic fault tree representing the system failure,
is a timing variable in f and represents a coverage failure for system component x,
and
respectively show when
At a certain time t equals 1 and 0
An assignment of (2). Using the following derived reduction rules (at arbitrary time t):
Respectively find out
And
an assignment of (2). A and B are time sequence variables of an algebraic structure function; then, let again
Then
All the material implications in f are expressed;
to represent
All positive inclusion in (a), i.e., inclusion of a non-variable quantity; for the
If it is not
For non-monotonic functions, all the quality implications can be derived using the consistency process and then the non-variable quality implications are excluded, so that the Minimum Independent Trigger (MIT) for the time-series variable x is
All positive substances in the product are removed
All substances in (1) imply the results of formula (la).
According to the above scheme, the limiting expression indicating that the system component x fails to be covered in step S3 is as follows:
xis a timing variable in f and represents an uncovered failure of system component x.
According to the above scheme, the (failure) expression of the system independence coverage model based on the algebraic structure function in step S4 is:
where n represents the number of components of the system and i represents the ith component of the system.
The method for analyzing the reliability of the dynamic fault tree based on the irrelevance coverage model has the following beneficial effects:
the dynamic fault tree is a fault tree model which aims at a dynamic system and considers the dynamic dependency relationship among events; the independence coverage model is expanded to the dynamic system, so that the reliability analysis of the dynamic system under the independence coverage model is realized; the invention expands the application of the independence model in the dynamic system, is suitable for a system with any failure time distribution, is also suitable for a static fault tree, and has good universality.
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The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a time diagram of an unrepairable event A in an algebraic structure function according to the present invention;
FIG. 2 is a schematic diagram of a representation of the common basic static and dynamic gates of the present invention based on algebraic structure functions;
FIG. 3 is a diagram of a dynamic fault tree according to the present invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
The invention discloses a reliability analysis method of a dynamic fault tree based on irrelevance coverage, which defines a calculation method of minimum irrelevance trigger based on time sequence logic, provides an irrelevance coverage model analysis method based on time sequence logic and combines a dynamic system of dynamic fault tree modeling, and can carry out effective reliability analysis. The method mainly comprises the following steps: firstly, modeling a system by using a dynamic fault tree, and representing the dynamic fault tree by using an algebraic frame based on a time sequence structure function so as to obtain an algebraic structure function of the dynamic fault tree based on coverage failure; then based on the improved minimum irrelevant triggering calculation method, the minimum irrelevant triggering of each coverage failure variable in the structural function is obtained, and then the uncovered failure variable of the same component is represented through the minimum irrelevant triggering limit, so that the expression of the uncovered failure variable is further obtained; and then based on the improved irrelevance covering model, an algebraic structure function of the irrelevance covering model and an expression of an uncovered failure variable are extracted to obtain a failure expression of the system based on the irrelevance covering model, and finally the expression is converted into a disjoint sum through a disjoint product based method to calculate the unreliability of the whole system.
As shown in FIGS. 1-3, in the embodiment of the method for analyzing reliability of dynamic fault tree based on independence coverage model of the present invention, an algebraic framework based on a time sequence structure is defined on the basis of a set of time sequence variables, and according to the algebraic framework, an algebraic structure function proposes three time sequence relation symbols
“Δ”，
Respectively, indicate the time sequence dependency relationship between events "before", "simultaneously", "before or simultaneously", for example, A < B indicates that event A occurs before event B, and B may or may not occur. These timing symbols can be used to represent a dynamic fault tree, including advantages for basic dynamic gatesThe first and gate, the spare part gate, the forced sequence gate and the function dependent gate can be based on the description on the time sequence relation, and the original logic relation is still reserved for the static gate.
Wherein, the general time of the irreparable event based on the algebraic structure function is shown in fig. 1, d (a) represents the time of the event a; a common representation of basic static and dynamic gates is shown in fig. 2, Sa representing the state of the standby in active mode, Sd representing the state of the standby in sleep mode, AT representing the expression causing the failure of component a, and BT representing the expression causing the failure of component B.
The following shows a common reduction rule for algebraic structure functions:
the reliability of the system is evaluated below for the dynamic fault tree shown in fig. 3 in combination with the above steps. Specifically, the fault tree includes 1 priority and gate and 2 cold standby gates: CSP1 and CSP 2. For convenience of calculation, assuming that the dynamic system is not repairable, component failures are independent of each other and the distribution of component failures based on time is continuous, the priority and gate strictly limits that left input takes precedence over right input and right input takes place, and the following steps are initiated:
s1, analyzing the dynamic fault tree by using an algebraic frame based on the time sequence structure function so as to obtain an algebraic structure function based on coverage failure of the dynamic fault tree, and combining a representation method of the algebraic frame of the time sequence structure function, wherein the algebraic structure function of the dynamic fault tree is as follows:
s2, for the algebraic structure function, the minimum irrelevant trigger of each variable is obtained by using the improved minimum irrelevant trigger calculation method, and the calculation mainly depends on the following method:
first, let
An algebraic structure function of the dynamic fault tree representing the system failure,
is a timing variable in f and represents a coverage failure for system component x,
and
respectively show when
At a certain time t equals 1 and 0
An assignment of (2). Using the following derived reduction rules (at arbitrary time t):
Respectively find out
And
an assignment of (2). A and B are time sequence variables of an algebraic structure function;
then, let again
Then
All the material implications in f are expressed;
to represent
All positive inclusion in (a), i.e., inclusion of a non-variable quantity; for the
If it is not
For non-monotonic functions, all the quality implications can be derived using the consistency process and then the non-variable quality implications are excluded, so that the Minimum Independent Trigger (MIT) for the time-series variable x is
All positive substances in the product are removed
All substances in (1) imply the results of formula (la).
According to the reduction rules (2) and (4):
according to the reduction rule (1):
the function G at this time is:
according to the reduction rules (5) and (6):
in addition, get
The substance of (a) contains the analytical formula of (b):
then
Minimum irrelevant trigger of is PPI (G) exclusion
The item of (1):
in the same way, the following can be obtained:
s3, acquiring a limiting expression of the system component not covering the failure according to the minimum irrelevant trigger of each variable in the step S2:
s4, obtaining (failure) expression F of the system independence coverage model based on the algebraic structure function according to the algebraic structure function in the step S2 and the variable expression of the uncovered failure in the step S3ICM：
S5, obtaining disjoint sum of products F 'based on algebraic structure function by combining disjoint sum of products based method according to expression in step S4'ICMThus, the calculation of the unreliability is carried out:
setting the failure time distribution of all the assemblies as index distribution, wherein the fixed risk rates are respectively as follows: λ P1 ═ λ P2 ═ λ S ═ 1.2 × 10-4The system failure probabilities at 100 days, 300 days, 500 days, and 900 days were calculated as per day, as shown in table 1 below:
TABLE 1
After repeated checking, the calculation result of the method is consistent with the result in the table, thereby demonstrating the feasibility and the correctness of the method.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A reliability analysis method for a dynamic fault tree based on an independence coverage model is characterized by comprising the following steps:
s1, analyzing the dynamic fault tree by utilizing an algebraic framework based on the time sequence structure function, thereby obtaining an algebraic structure function based on the coverage failure event of the dynamic fault tree
S2, aiming at the algebraic structure function, obtaining each variable by using the improved minimum irrelevant trigger calculation method
A minimum irrelevant trigger of;
s3, obtaining the limit expression of the basic event of the dynamic fault tree about the uncovered failure according to the minimum irrelevant trigger of each variable in the step S2
S4, obtaining an expression of the system independence coverage model based on the algebraic structure function according to the algebraic structure function in the step S2 and the expression of the uncovered failure in the step S3, wherein the general expression is as follows:
s5, obtaining a disjoint sum based on the algebraic structure function by using a disjoint sum based method according to the expression of the system independence coverage model based on the algebraic structure function in the step S4, thereby calculating the probability of the dynamic fault tree top event.
2. The method according to claim 1, wherein the step 1 of analyzing dynamic fault tree reliability by using an algebraic framework based on a time-series structure refers to a time-series operator in a reference framework
The time sequence dependency relationship between events is represented as 'before' and 'at the same time', the basic events at the moment are time functions, namely time sequence variables, and the dynamic fault tree at the moment is represented as an algebraic structure function based on coverage failure.
3. The method for analyzing reliability of dynamic fault tree based on independence coverage model as claimed in claim 1, wherein the computation of the minimum independence trigger based on algebraic structure function in step S2 depends mainly on the following method:
first, let
An algebraic structure function of the dynamic fault tree representing the system failure,
is a timing variable in f and represents a coverage failure for system component x,
and
respectively show when
At a certain time t equals 1 and 0
An assignment of (2). Using the following derived reduction rules (at arbitrary time t):
respectively find out
And
an assignment of (2). A and B are time sequence variables of an algebraic structure function; then, let again
Then
All the material implications in f are expressed;
to represent
All positive inclusion in (a), i.e., inclusion of a non-variable quantity; for the
If it is not
For non-monotonic functions, all the quality implications can be derived using the consistency process and then the non-variable quality implications are excluded, so that the Minimum Independent Trigger (MIT) for the time-series variable x is
All positive substances in the product are removed
All substances in (1) imply the results of formula (la).
4. The method for analyzing reliability of dynamic fault tree based on independence coverage model as claimed in claim 1, wherein the limiting expression in step S3 for representing uncovered failure of system component x is:
x is a timing variable in f and represents an uncovered failure of system component x.
5. The method for analyzing reliability of a dynamic fault tree based on an independence cover model as claimed in claim 1, wherein the step S4 is based on (failure) expression of system independence cover model of algebraic structure function:
where n represents the number of components of the system and i represents the ith component of the system.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110137703A1 (en) * | 2004-12-21 | 2011-06-09 | University Of Virginia Patent Foundation | Method and system for dynamic probabilistic risk assessment |
| CN104778370A (en) * | 2015-04-20 | 2015-07-15 | 北京交通大学 | Risk analyzing method based on Monte-Carlo simulation solution dynamic fault tree model |
| CN105717912A (en) * | 2016-01-27 | 2016-06-29 | 西北工业大学 | Reliability analysis method for electromechanical actuator based on fuzzy dynamic fault tree |
| CN110390147A (en) * | 2019-07-05 | 2019-10-29 | 武汉理工大学 | Phased mission systems analysis method for reliability based on unrelated overlay model |
| CN112613269A (en) * | 2020-12-28 | 2021-04-06 | 武汉理工大学 | System optimal redundancy calculation method based on irrelevance coverage model |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110137703A1 (en) * | 2004-12-21 | 2011-06-09 | University Of Virginia Patent Foundation | Method and system for dynamic probabilistic risk assessment |
| CN104778370A (en) * | 2015-04-20 | 2015-07-15 | 北京交通大学 | Risk analyzing method based on Monte-Carlo simulation solution dynamic fault tree model |
| CN105717912A (en) * | 2016-01-27 | 2016-06-29 | 西北工业大学 | Reliability analysis method for electromechanical actuator based on fuzzy dynamic fault tree |
| CN110390147A (en) * | 2019-07-05 | 2019-10-29 | 武汉理工大学 | Phased mission systems analysis method for reliability based on unrelated overlay model |
| CN112613269A (en) * | 2020-12-28 | 2021-04-06 | 武汉理工大学 | System optimal redundancy calculation method based on irrelevance coverage model |
Non-Patent Citations (1)
| Title |
|---|
| 王剑;曹宇燕;李婷;谢蓉;王新民: "基于代数模型的机电作动器Vague动态故障树分析", 西北工业大学学报, vol. 33, no. 6, 15 December 2015 (2015-12-15), pages 977 - 983 * |
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