CN105718740A - Method for determining system reliability running environment - Google Patents
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- CN105718740A CN105718740A CN201610043546.4A CN201610043546A CN105718740A CN 105718740 A CN105718740 A CN 105718740A CN 201610043546 A CN201610043546 A CN 201610043546A CN 105718740 A CN105718740 A CN 105718740A
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Abstract
The invention discloses a method for determining a system reliability running environment. The method is characterized by aiming at solving the problem of the deficiency of the processing capacity for fault data with fuzziness, randomness and discreteness of the path set domain and the cut set domain in an original SFT (space fault tree) system; a cloud model and SFT combined method is used for solving the problem. The method comprises the steps as follows: first of all, the cloud model is used for clouding an SFT characteristic function, and a clouded characteristic function is obtained; then the path set domain and the cut set domain are clouded; finally, the clouded path set domain and the clouded cut set domain are obtained. The method can be used for determining the reliability of the system running environment in a system running process.
Description
Technical field
The present invention relates to safety system engineering, particularly relate to the system running environment in system operation to reliability.
Background technology
Safety system engineering is safe and scientific important component part, wherein the core theory of fault tree theory safety system engineering especially.Fault tree theory has how each concept, while these concepts and computational methods are used widely, there is also some problems.Fault tree is a kind of fixing pattern analysis method, and the analysis of system is a kind of static state by it, it is assumed that system mode is constant.But system changes along with its working environment, although its structure is fixing, but each component reliability not ensured that in change procedure is constant.Namely how to consider that environmental factors changes system element reliability effect, and the system reliability Variation Features in the constant situation of system structure.
For this problem, propose a set of space fault tree (SpaceFaultTree, SFT) theoretical, this theory thinks that system works among environment, and it is different that the character of elementary event or physical component owing to forming system determines its fault rate worked at different conditions.The theoretical current certain system that defined of SFT, but still Shortcomings, especially for failure data analysis ability in running process.Owing to these type of data have the feature of ambiguity, randomness and discreteness (uncertainty), even if it is also difficult for using the DSFT in SFT to process.So successively propose the factor projection method such as fitting process and fuzzy structured element DSFT, but still not satisfactory.
Cloud models theory is used to combine with SFT theory, theoretical by cloud SFT characteristic function and then cloud SFT, footpath domain set domain in cloud SFT and cut set territory, form concept and the computational methods in cloud footpath domain set domain and cut set territory, thus strengthening the model disposal ability to uncertain data.
Summary of the invention
1 cloud model rationale
2.1 cloud models and numerical characteristic thereof
If U is a quantitative domain represented with exact value, C is the qualitativing concept on U, if quantitative value x ∈ U, and x is a Stochastic implementation of qualitativing concept C, the x degree of membership μ (x) ∈ [0,1] to C, is the random number with steady tendency, namely,,.Then x distribution on domain U is called that cloud is designated as C(x), each x is called a water dust (x, μ (x)).
The numerical characteristic of cloud reflects the quantitative characteristic of qualitativing concept, characterizes with expectation Ex, entropy En and super entropy He, is designated as C(Ex, En, He).Expect the most representational qualitativing concept value of Ex representation theory domain space, reflect the central value in domain space.Entropy En is the comprehensive measurement of qualitativing concept ambiguity and randomness, reflects the span of the water dust that can be accepted by qualitativing concept in domain space on the one hand, can reflect again the dispersion degree of water dust on the other hand.Super entropy He describes the uncertainty measure of entropy, reflects the cohesion degree of water dust in domain space, and He is more big, and the thickness of water dust is more big.
Cloud generator
The algorithm or the hardware that generate water dust are called cloud generator, including forward cloud, reverse cloud, X condition cloud and Y condition cloud generator.Normal Cloud Generator achieves the scope and the regularity of distribution that obtain quantitative data in the qualitative information that prophesy value is expressed, has forward direction, direct feature.Normal Cloud Generator, its water dust process generating requirement is as follows:
Input: one-dimensional qualitative features parameter (Ex, En, He) and water dust number N.
Output: N number of water dust qualitative value x and represent concept degree of certainty, q=1 ..., N.
1) generating with En for expectation, He is the normal random number En ' of standard deviation；
2) generating one with En for expectation, the absolute value of En ' is the normal random number x of standard deviationq, xqIt is called a water dust of domain space U；
3) calculate, thenForDegree of membership about C；
4) circulation 1) ~ 3), generate N number of water dust, then stop.
Backward cloud generator is that a number of exact numerical is effectively converted to appropriate qualitative Linguistic Value, has reverse, indirectly feature.Reverse cloud algorithm being improved, it is ensured that it is all arithmetic number that any water dust sample inputs calculated super entropy, reduces calculating error. algorithm specifically comprises the following steps that
Input: N number of water dust sample quantitative values。
Output: the estimated value of the qualitativing concept characteristic parameter (Ex, En, He) that water dust sample represents.
1) according to N number of water dust quantitative valuesCalculate sample mean；
2)；
3)；
4) water dust sample variance；
5)。
The cloud of 2SFT
SFT analysis foundation is the characteristic function of factor and component reliability relation.The characteristic function of DSFT is to be got by the fault data in running, but physical fault and monitoring reliability data have uncertain feature, i.e. ambiguity, randomness and discrete type it requires that characteristic function can embody these features.Original factor projection fitting process and fuzzy structured element characteristic function are also not enough for the disposal ability of this respect.
It is said that in general, component reliability data obey exponential, or peak value has the exponential (such as tub curve) of stable region.In theory by experiment or the reliability data that obtains of actual motion should be being distributed in around this curve of normal state.More big closer to curve data density, away from then reducing.The water dust that cloud model generator generates just is being curved about the data point of generator analytic expression curve normal distribution, identical with reliability data distribution characteristics.Water dust degree of membership is that [0,1] is identical with reliability codomain [0,1].Cloud model has multiple derivative form, can meet the analysis requirement of reliability data, so it is feasible for utilizing forward cloud model generator analytic expression structural feature function.Form mainly comprising the following steps of cloud characteristic function: first bring the component reliability data obtained according to certain factor into reverse cloud model generator, obtain characteristic parameter, then bringing forward cloud model generator analytic expression into, this analytic expression is subtracted as the element cloud characteristic function for this factor by 1 the most at last.Shown in forward cloud model maker analytic expression such as formula (1).Element can be used for the reliability of certain factorRepresent, and element can use for the characteristic function of this factor=1-Represent, i.e. formula (2).
(1)
(2)
In formula: d represents certain factor, x represents the numerical value of this factor, and i represents i-th element.
Expect that Ex represents factor value when component reliability is maximum in factor change procedure；Entropy En represents the dispersion degree of the reliability data in factor change procedure；Super entropy He describes the uncertainty measure of entropy.So by formula (2) representatively by characteristic function cloud, and then build the related notion in cloud characteristic function and cloud SFT frame system.
The cloud of 3 cut set territories and footpath domain set domain
Footpath collection and cut set are the definition contents in classical fault tree, and obtain corresponding development in SFT, it is proposed that the concept in footpath domain set domain and cut set territory, as follows.
As follows in give a definition footpath domain set domain and the cut set territory definition of single elementary event of SFT concept:
Cut set territory is the probability area of space (in survey region) more than the probability of predetermined or necessity that (fault) occurs single elementary event.This region is the unacceptable region of definien, and definien thinks that the fault rate in this region is too high, and this element should be made to avoid in this regional work, or takes measures to reduce fault rate.
Footpath domain set domain is the probability area of space (in survey region) less than the probability of predetermined or necessity that (fault) occurs single elementary event.This region is the receptible region of definien, and definien thinks that the fault rate in this region is not high, and this element should be made as far as possible in this regional work, need not take measures to reduce fault rate.
Border, territory PbIt is the probability contour of the predetermined or necessity described in above-mentioned definition or face or more higher-dimension form.
Footpath domain set domain, cut set territory and border, territory constitute whole survey region.Territory boundary curve or face or more higher-dimension form should be Guan Bis.The footpath domain set domain of system, cut set territory and territory boundary definition are as follows:
Cut set territory is the probability area of space (in survey region) more than the probability of predetermined or necessity that (fault) occurs top event (system).Footpath domain set domain is the probability area of space (in survey region) less than the probability of predetermined or necessity that (fault) occurs top event (system).Border, territory PbIt is the probability contour of the predetermined or necessity described in above-mentioned definition or face or more higher-dimension form.
Footpath domain set domain and cut set territory concept be not in the combination based on elementary event, but the environmental condition that system of paying close attention to works；Be not due to several elementary event simultaneous faults and cause the system failure, but due to system work under certain conditions time, elementary event is affected fault rate by these conditions and is continually changing, and the set of the condition that the system failure rate caused is continually changing.
There is the cloud of (elementary event) probability distribution in element fault under multifactor impact, and namely cloud element fault probability distribution is expressed as shown in formula (3).Under multifactor impact, cloud system fault probability distribution table is shown as shown in formula (4).
(3)
(4)
In formula: Kj(j=1,2 ..., r) represent the jth of r minimal cut set of fault tree.Represent certain factor,Expression factorConcrete numerical value.
Formula (3) and (4) can respectively obtain and use SFT and the element represented with cloud model and system failure probability of happening distribution situation, i.e. reliability distribution situation.Consider the definition on footpath domain set domain, cut set territory and border, territory, in order to use cloud SFT theory to implement the expression in cloud footpath domain set domain and cut set territory, can according to former territory border PbImplement this process.PbIt is footpath domain set domain and the demarcation line in cut set territory, represents the degrees of tolerance to system fault probability.P in cloud footpath domain set domain and cloud cut set territorybBeing still marginal effect, be different in that two territories do not have strict demarcation line, distributed areas are represented by water dust.If the components/systems probability of malfunction that water dust represents is less than Pb, i.e. Pb>(), then the region that these water dusts exist is cloud footpath domain set domain；Otherwise more than PbWater dust exist region be cloud cut set territory.
Accompanying drawing explanation
Fig. 1 difference PbLower element X1Cloud footpath domain set domain and cloud cut set territory ((a) Pb=10%(b)Pb=20%(c)Pb=30%(d)Pb=50%)
Fig. 2 difference PbThe cloud footpath domain set domain of lower system and cloud cut set territory ((a) Pb=10%(b)Pb=20%(c)Pb=30%(d)Pb=50%).
Detailed description of the invention
Electric systemThe reliability of middle 5 comprised elements is affected by temperature and humidity, and the fault of these elements in different temperatures and humidity change procedure is added up.Bring the component reliability value of different temperatures and humidity value and correspondence thereof into reverse cloud model as data, obtain these elements reliability cloud model characteristic parameter respectively about temperature and humidity.As shown in table 1.
The cloud model of table 1 component reliability
WithFor example, by C in table 11 c(20.11,6.05,1.55) and C1 h(44.37,5.11,0.55) bring formula (2) into, and then bring formula (3) into, can obtainCloud Failure probability distribution, as the formula (5).
(5)
According to formula (5) to element X1Cloud footpath domain set domain and cloud cut set territory be determined.For PbDifference, two regions water dust distribution be also different.
In Fig. 1, PbIt is respectively equal to 10%, 20%, 30%, 50% (30% is identical with the scattergram of 40%)." O " represents<PbWater dust domain of the existence, "×" represents>PbWater dust domain of the existence, namely " O " represents element X1Cloud footpath domain set domain；"×" represents element X1Cloud cut set territory.It can be seen that along with PbBe continuously increased, the fault rate of this element of tolerable is continuously increased, and represents that the water dust of cloud footpath domain set domain is ever-increasing, and this glyph closes universal law.Can determine that the environmental factors excursion that this element cloud footpath domain set domain is corresponding on the other hand, this scope can characterize this element and be suitable for the environmental factors excursion combination of work.The element worked in the domain set domain of footpath, its reliability is of a relatively high；Otherwise element manipulation is in cloud cut set territory, and its reliability is relatively low.Different from footpath domain set domain and cut set territory, cloud footpath domain set domain and cut set territory do not have clear and definite demarcation line, this surface is coarse, but has substantially reacted and analyzed the uncertainty using basic data, the i.e. ambiguity of element fault data, randomness and discreteness.So the concept of Yun Huahou can better reflect the uncertainty of initial data.
In like manner can obtain elementFailure probability distribution expression formula.In this example, system can obtain its structure through fault tree logic minimization and is:.WillCloud Failure probability distributionBring formula (4) into according to system structure, the cloud probability of malfunction variation tendency of system can be obtained, as shown in formula (6).It is determined according to the formula (6) the cloud footpath domain set domain to system and cloud cut set territory.
(6)
Note: in formulaForWrite a Chinese character in simplified form.
In Fig. 2, PbIt is respectively equal to 10%, 30%, 40%, 50% (10% is identical with the scattergram of 20%)." O " is identical with Fig. 1 with the meaning of "×".Consistent with 1 feature reflected, Fig. 2 describes the working region that this system is suitable for, i.e. cloud footpath domain set domain.In this region, the probability of malfunction of system work is relatively low, and this extra-regional cloud cut set territory then system fault probability is bigger.
By above-mentioned discussion, describe cloud footpath domain set domain and cloud cut set territory computational methods.Under original SFT, footpath domain set domain and cut set territory result of calculation have accurate Failure probability distribution and Pb, this is advantageous for for interpretation of result.It is based on accurate characteristic function, but the randomness of physical fault data, ambiguity and discreteness are obliterated in initial data handling procedure by such characteristic function.The uncertainty of data cannot be delivered to final result, and the embodiment of this inherently another kind of inexactness, so using cloud model that this (initial data) uncertainty is delivered to final result.So the concept in cloud footpath domain set domain and cloud cut set territory and computational methods are more simple, convenient and practical.
Claims (7)
1. the method determining system reliability running environment, it is characterized in that, in order to overcome original SFT system central diameter domain set domain and cut set territory to process the problem with ambiguity, randomness and discreteness fault data scarce capacity, use the method that cloud model and SFT combine to solve this problem；It comprises the steps: first by cloud model cloud SFT characteristic function, obtains cloud characteristic function, and then cloud footpath domain set domain and cut set territory, finally gives cloud footpath domain set domain and cloud cut set territory；The present invention can be used for the system running environment in system operation to reliability.
2. the step of cloud characteristic function according to claim 1, it is characterized in that, first the component reliability data obtained according to certain factor are brought into reverse cloud model generator, obtain characteristic parameter, then bringing forward cloud model generator analytic expression into, this analytic expression is subtracted as the element cloud characteristic function for this factor by 1 the most at last.
3. cut set territory according to claim 1, it is characterised in that cut set territory is the probability that occurs of the single elementary event area of space more than the probability of predetermined or necessity；This region is the unacceptable region of definien, and definien thinks that the fault rate in this region is too high, and this element should be made to avoid in this regional work, or takes measures to reduce fault rate.
4. footpath according to claim 1 domain set domain, it is characterised in that footpath domain set domain is the probability that occurs of the single elementary event area of space less than the probability of predetermined or necessity；This region is the receptible region of definien, and definien thinks that the fault rate in this region is not high, and this element should be made as far as possible in this regional work, need not take measures to reduce fault rate.
5. the method determining system reliability running environment, it is characterised in that border, territory PbIt is the probability contour of the predetermined or necessity described in above-mentioned definition or face or more higher-dimension form.
6. the method determining system reliability running environment, it is characterised in that footpath domain set domain and cut set territory concept be not in the combination based on elementary event, but the environmental condition that system of paying close attention to works；Be not due to several elementary event simultaneous faults and cause the system failure, but due to system work under certain conditions time, elementary event is affected fault rate by these conditions and is continually changing, and the set of the condition that the system failure rate caused is continually changing.
7. the method determining system reliability running environment, it is characterised in that the cloud of (elementary event) probability distribution occurs element fault under multifactor impact, and namely cloud element fault probability distribution is expressed as shown in formula (3)；Under multifactor impact, cloud system fault probability distribution table is shown as shown in formula (4)；
(3)
(4).
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