CN106156478A - A kind of electrical system method for evaluating reliability based on binary accident tree - Google Patents
A kind of electrical system method for evaluating reliability based on binary accident tree Download PDFInfo
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- CN106156478A CN106156478A CN201510205508.XA CN201510205508A CN106156478A CN 106156478 A CN106156478 A CN 106156478A CN 201510205508 A CN201510205508 A CN 201510205508A CN 106156478 A CN106156478 A CN 106156478A
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Abstract
The invention discloses a kind of electrical system method for evaluating reliability based on binary accident tree, feature is just to affect two key factors of electrical equipment reliability: the reliability of discrete component is analyzed by working time (t) and operating temperature (c), when the working time of the most each element and appropriate working temperature are different, it is difficult for using traditional methods analyst system reliability.The reliability mainly including electrical equipment determines, the fail-safe analysis of electrical system.The present invention can represent system structure by accident tree, by accident tree, system structure is carried out abbreviation, obtains considering that the system fault probability under the influence of t and c Binary Factor is distributed.Can be widely used for analyzing under binary even multiple factors influence condition, analyze the feature of electrical malfunction probability, and then study its system reliability.
Description
Technical field
The present invention relates to electrical system reliability, particularly relate to use a kind of method based on binary accident tree can to electrical system
It is evaluated by property.
Background technology
Electrical system is modal system in present every field, and its reliability directly affects the overall performance of place system.
From system perspective analysis, its reliability can be divided into two parts to study.One is the primary element of composition system, these elements
Character be applied to self reliability, and then affect the reliability of this electrical system.Two is the structure of system itself, it is simply that
The building form of primary element, the difference of building form will directly determine the effect degree of elements affect system reliability.Whole system
The reliability of system is both combinations.But these researchs do not consider under conditions of multifactor impact, element itself
Failure probability distribution, more do not study the Failure probability distribution situation of the constituted system of these elements.
For the diode element in electric system, its probability of malfunction just with the length of working time, the size of operating temperature,
Direct relation is had by electric current and voltage etc..Assume that the system failure causes due to component wear, and carry out by changing element
Failture evacuation.So use time of element will become the key factor affecting component reliability, and this factor affects probability of malfunction
Degree obey exponential expression.Another factor is exactly operating temperature, it will be apparent that, too high and too low for electrical equipment temperature
The decline of its reliability and the rising of fault rate will be caused, substantially obey cosine curve.First build electric elements based on making
With the probability of malfunction space of time (t) He operating temperature (c), then use accident tree that system composition structure is described,
And then Simplification System structure, finally according to the probability of malfunction space of the probability of malfunction space drafting whole system of each original paper.Show,
Under the conditions of classical accident tree cannot represent multifactor impact, the failure condition of discrete component.The most polynary accident of binary can only be used
Tree could describe the element fault situation under multifactor impact, and then describes the distribution of the probability of malfunction of multiple element composition system.
Summary of the invention
For being preferably described invention, designing simple electric system here and be described, this system is constituted by a diode,
The rated operation of diode is affected by many factors, the most importantly t and c.For the electrical equipment affected by the two factor
System is as object of study.System has five primary element X1、X2、X3、X4、X5, and it is set to be had by t and c bright
The element that development rings, shown in its classical accident tree Fig. 1.The accident tree abbreviation of this system obtains: T=X1X2X3+X1X4+X3X5。
1. the fail-safe analysis of electrical equipment
5 essential electronic element X in system1、X2、X3、X4、X5Probability of malfunction, be all affected by the shadow of t and c
Ring, i.e. the probability of malfunction P of elementi(t, c), wherein i ∈ { under 1,2,3,4,5} is same, is t and the c function as independent variable.As t and
During one of c two aspect fault, element just breaks down, according to logic or concept Pi(t, c) as shown in formula (1).
Pi(t, c)=1-(1-Pi t(t))(1-Pi c(c)) (1)
Determine Pi(t, c), it is necessary to first determine Pi t(t) and Pi c(c).If can not repair after in system, discrete component breaks down, system is arranged
Except fault realizes by changing element.Then Pi tT () may be considered the cell failure probability of not repairable system, and set fault and reach
To 0.9999 element should change (these data can be obtained by given system failure rate back analysis, generally little than this value must
Many), as shown in Equation 2.
Pi t(t)=0.9999=1-e-λt；λ t=9.2103 (2)
In formula: λ is cell failure rate.
For Pi cC (), the normal work of electric elements will have certain operating temperature range, higher or lower than this temperature range unit
Part just breaks down, and this rule is expressed as cosine curve, as shown in Equation 3.
In formula: A is range of temperature.
The element of actually distinct type has different use time lifetimes and the scope of appropriate working temperature.
2. the fail-safe analysis of electrical system
Being obtained by Fig. 1 systematic failures tree abbreviation, formula (4) is as follows:
T=X1x2X3+X1X4+X3X5 (4)
The system failure (top event) probability of happening is obtained, as shown in formula (5) by classical accident tree theory:
PT(t, c)=P1P2P3+P1P4+P3P5-P1P2P3P4-P1P3P4P5-P1P2P3P5+P1P2P3P4P5(5)
From formula (5), PT(t, is c) function reflecting electrical malfunction probability, and this function is by P1～5(t, c) determines, again by formula (1),
Understand PT(t, c) be byWithI.e. PT(t is c) by the function of t and c, by PT(t, c), t and c constitute three-dimensional
Probability space distribution and equivalent curve thereof.
Accompanying drawing explanation
The accident tree of Fig. 1 electrical system
Fig. 2 X1～5Probability of malfunction spatial distribution and equivalent curve
The distribution of Fig. 3 system failure three-dimensional probability space and equivalent curve thereof
Detailed description of the invention
Embodiment is the electrical system shown in Fig. 1.
1. the fail-safe analysis of electrical equipment
5 essential electronic element X in system1、X2、X3、X4、X5Probability of malfunction, be all affected by the shadow of t and c
Ring, i.e. the probability of malfunction P of elementi(t, c), wherein i ∈ { under 1,2,3,4,5} is same, is t and the c function as independent variable.As t and
During one of c two aspect fault, element just breaks down, according to logic or concept Pi(t, c) such as following formula:
Pi(t, c)=1-(1-Pi t(t))(1-Pi c(c)) (1)
Determine Pi(t, c), it is necessary to first determine Pi t(t) and Pi c(c).If can not repair after in system, discrete component breaks down, system is arranged
Except fault realizes by changing element.Then Pi tT () may be considered the cell failure probability of not repairable system, and set fault and reach
To 0.9999 element should change (these data can be obtained by given system failure rate back analysis, generally little than this value must
Many), as shown in Equation 2.For Pi cC (), the normal work of electric elements will have certain operating temperature range, be higher than or low
Just break down in this temperature range element, this rule is expressed as cosine curve, as shown in Equation 3.
Pi t(t)=0.9999=1-e-λt；λ t=9.2103 (2)
In formula: λ is cell failure rate, A is range of temperature.
The element of actually distinct type has different use time lifetimes and the scope of appropriate working temperature, it has been assumed that they make
With scope, working time scope t ∈ [0, the 100] sky of research, operating temperature interval c ∈ [0,50] DEG C.And according to formula (2) and formula
(3) it is calculated Pi t(t) and Pi c(c) expression functional relationship in the range of each.Pi t(t) and Pi cC () is in respective research range
It not continuous print, but piecewise function.The segmentation of each function represents as shown in table 1.
System element X can be constructed by table 2 and formula (1)1～5Probability of malfunction spatial distribution and equivalent curve, such as Fig. 2 institute
Show.
Table 1Pi t(t) and Pi c(c) expression formula in survey region
In Fig. 2, X1-5Probability of malfunction spatial distribution and equivalent curve be all different, this is the shadow due to itself t and c
Sound causes.For working time t in the search time region of each element, probability of malfunction spatial distribution map has two or
Trizonal probability of malfunction substantially reduces, and causes owing to changing new element when element reaches probability of malfunction 0.9999.Actual
Probability of malfunction during this replacing upper can use polynary accident tree Space Theory inverting by setting the probability of malfunction of whole system
Obtaining, the probability of malfunction that Practical Calculation obtains is much smaller.For operating temperature c, owing to using cosine curve as expression
Function, the position of probability of malfunction minimum is in the middle of adaptive temperature scope.From image, the portion that element fault probability is less
Position concentrates on the zone line of temperature range.But, element accident probability acceptable scope is less on figure, and this is
Owing to using binary accident tree to represent the inevitable outcome of element fault probability.The superposition of two probability makes element total breakdown probability increase
Adding, this phenomenon uses classical accident tree to analyze.Certainly, also there is the reason of element replacement excessive cycle.
The fail-safe analysis of 2 electrical systems
Being obtained by Fig. 1 systematic failures tree abbreviation, formula (4) is as follows:
T=X1X2X3+X1X4+X3X5 (4)
The system failure (top event) probability of happening is obtained, as shown in formula (5) by classical accident tree theory:
PT(t, c)=P1P2P3+P1P4+P3P5-P1P2P3P4-P1P3P4P5-P1P2P3P5+P1P2P3P4P5(5)
From formula (5), PT(t, is c) function reflecting electrical malfunction probability, and this function is by P1～5(t, c) determines, again by formula (1),
Understand PT(t, c) be byWithI.e. PT(t is c) by the function of t and c, by PT(t, c), t and c constitute three-dimensional
Probability space distribution and equivalent curve thereof are as shown in Figure 3.
Knowable to the left figure of Fig. 3, system fault probability is minimum near the t=0 moment, main cause be in system all elements at t=0
Moment simultaneously enters use state, and the probability of malfunction of each element is the lowest during this period of time, makes the probability of malfunction of whole system reduce.
In terms of using temperature, the use temperature of majority element is all at 20 DEG C to 30 DEG C, so system works in this temperature range
Probability of malfunction relatively low.But development over time, the probability of malfunction of element constantly increases, and begins with element and is replaced,
Other elements also maintain original probability of malfunction curvilinear trend to continue development simultaneously, make the new element of replacing reduce system fault probability
Effect be cancelled.The ability that each replacement of element cycle difference causes new element to improve system reliability is cancelled out each other, and makes except t=0
Outside near, the system failure rate in other regions is the highest.The right figure of Fig. 3 can be seen that, each probability of malfunction forms isolated island, except being analyzed above
Feature outside, the center in temperature of each isolated island is not consistent, and this also reflects has changed element and these yuan in this moment
The adaptive temperature scope of part is the most different.
It practice, the analysis that binary accident tree is to system fault probability, the spatial probability distribution figure obtained, it is fully applicable to
Practical problem analysis the most widely.Such as can adjust each replacement of element cycle according to distribution results right for Fig. 3, make
In the range of Time Continuous, system fault probability preserves less than certain value always, and this value is probably outer bound pair system reliability
Requirement.Further, it is possible to by, in the scheme of all replacing elements of the reliability that meets this outer bound pair system requirements, finding out
Replacement cycle is the longest, the prescription case that i.e. replacement frequency is minimum, thus reduces expenses.This is also important to actual system.
Above-mentioned analytical proof binary or polynary accident tree are comprehensive to the analysis of electrical system, concrete, it can be seen that each element and
Whole system is for working time t and the distribution relation of use temperature c, thus is applied in the problem of more reality.
Claims (1)
1. the present invention relates to electrical system reliability, particularly relate to use a kind of method based on binary accident tree to electrical system
Reliability is evaluated.It is characterized in that, for preferably invention being described, design simple electric system here and discuss
Stating, this system is constituted by a diode, and the rated operation of diode is affected by many factors, the most importantly t and c.
For the electric system affected by the two factor as object of study.System has five primary element X1、X2、X3、X4、
X5, and it is set to the element being had a significant effect by t and c, shown in its classical accident tree Fig. 1.The accident tree abbreviation of this system obtains:
T=X1X2X3+X1X4+X3X5。
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| CN108364115A (en) * | 2018-01-04 | 2018-08-03 | 浙江大学 | A kind of quick multimode Power System Reliability computational methods |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108364115A (en) * | 2018-01-04 | 2018-08-03 | 浙江大学 | A kind of quick multimode Power System Reliability computational methods |
| CN108364115B (en) * | 2018-01-04 | 2020-07-10 | 浙江大学 | Rapid multi-state power system reliability calculation method |
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Application publication date: 20161123 |