CN105760659A - Method for assessing reliability of aircraft landing gear control system under small samples and poor information - Google Patents

Abstract

The invention relates to a method for assessing reliability of an aircraft landing gear control system under small samples and poor information. The method comprises the steps of establishing an aircraft landing gear control system failure tree according to the system principles and the failure mechanism, converting the form of a failure probability interval of each bottom event of the aircraft landing gear control system failure tree into the pangrey number expression form based on the interval and pangrey conversion rules, establishing aircraft landing gear buffer system failure transfer functions from the bottom events to top events according to the logic relation among layers of the failure tree, and calculating the aircraft landing gear buffer system failure transfer functions through pangrey four operation rules, so that the top event failure probability pangrey form is obtained; converting the top event failure probability pangrey form into the interval form based on the interval and pangrey conversion rules, so that an aircraft landing gear buffer system failure probability range based on the pangrey algorithm is obtained; according to the aircraft landing gear buffer system failure probability range, conducting reliability assessment on failure.

Description

Undercarriage extension and retraction system reliability estimation method under small sample, lean information

Technical field

The present invention relates to small sample, lean information gets off the plane the fail-safe analysis of landing-gear system, carries out fault Tree Analysis based on graying algorithm, and the more accurate reliability of the system that obtains, thus being estimated the safe coefficient of system.

Background technology

In recent years, the technology that all kinds of large-scale complicated systems use is increasingly advanced, its internal structure becomes increasingly complex, and automaticity is more and more higher, then the safety and reliability that system is run just increasingly is subject to people's attention.Undercarriage as the takeoff and anding device of aircraft, is mainly used in the taking off of aircraft, lands, ground roll-out and ground are parked.In order to reduce flight resistance, the undercarriage of present generation aircraft is usually retractable, and the effect of landing-gear system is to ensure that undercarriage is taken in fuselage interior and closes landing gear compartment by aircraft after take off smoothly, drop again before landing, fix it to certain position and pin.Related data shows, in the flight failure that aircraft occurs in recent years, 15% causes due to undercarriage fault, and in undercarriage fault, has again 23% to cause due to landing-gear system fault.2007, a Russian frame Tu-154 passenger plane cannot be opened owing to undercarriage breaks down when landing at an airport, and pilot finally have to force-land with fuselage with wiping, and causes major accident；2009, a frame Zimbabwe nationality cargo aircraft fell at Pudong International Airport in Shanghai, and when taking off, main landing gear is not packed up, and takeoff speed is crashed not.One frame AV-8B vertical take off and landing fighter of U. S. Marine Corps force-lands when failing to lay down undercarriage, and aircraft is impaired seriously；2007, a frame Boeing jumbo forward gear in Beijing to course line, Dubai was surprisingly packed up suddenly, and plane nose and part ventral lean forward and land, and causes that on machine, several personnel fall down injured.The quality of visible undercarriage extension and retraction system service behaviour directly affects the safety of the taking off of aircraft, landing data and aircraft, and the lighter's aircraft is impaired, severe one fatal crass, causes huge economic loss and casualties.Tracing it to its cause, this body structure of landing-gear system is complex, is difficult to accomplish to fully realize at design link, simultaneously because cost factor, later stage test sample is limited, thus generally presents small sample, lean information feature.Therefore, the such large-scale complicated system of the Landing Gear System being similar to failure statistics poor information is carried out reliability assessment, ensure the flight safety of aircraft, it is to avoid the generation of catastrophic failure, reduce the loss of personnel and property, have important practical significance.

Main method as Reliability evaluation, FTA is added up by the failure probability of system bottom parts, it is simultaneously based on system principle and failure mechanism obtains the logical relation between each layer parts of system, it is derived by system top level failure probability layer by layer, thus reaching system-level reliability assessment.

Fault tree analysis currently for system reliability has primarily formed based on stochastic model and the big class method of interval model two.Fault Tree Analysis based on stochastic model obtains the comparatively accurate failure probability description of bottom event by a large amount of thrashing statistical datas, in conjunction with fault tree with or gate logic relation finally give top event failure probability, and gradually built up the improved method for fault tree top event failure probability and importance of bottom incident being representative with sampling method, approximate data and non cross link method for solving in the process；Fault Tree Analysis based on interval model reflects the known degree to event with the shape in interval territory, reflect undulatory property or the departure degree of uncertainty event with size, in conjunction with fault tree with or gate logic relation and interval arithmetic rule be derived by top event failure probability layer by layer.

But it is to be noted, although the FTA based on stochastic model develops comparatively ripe, but data volume is required comparatively sensitive by the accuracy of its result, it is applicable to the class system under failure statistics data comparatively abundance is carried out fail-safe analysis, it is difficult to solve the reliability assessment problem of small sample, poor information system；Although interval model only needs the boundary of uncertainty event set, without determining its internal distribution situation, thus to the dependency of data significantly lower than stochastic model, but in carry out system top event failure probability scope solution procedure based on interval arithmetic, due to the defect that interval arithmetic itself exists, namely same expression formula causes solving, due to order of operation difference, the problem that interval is exaggerated or minimized so that the System failure probability obtained based on interval arithmetic is difficult to have stronger reference value.For the fault tree with two bottom events or door interval operator, its top event failure probability expression formula is P_Top=1-(1-p₁)(1-p₂), it is P after abbreviation_Top=p₁+p₂+p₁p₂If, assignment p₁=[0.1,0.3] and p₂=[0.4,0.8] substitution carry out interval arithmetic and solve, it has been found that the former expression formula result is [0.46,0.86], and the latter's result is [0.26,1.06].

Summary of the invention

Solve the technical problem that

Higher, interval model causes solving, due to order of operation difference, the problem that interval is exaggerated or minimized to overcome stochastic model that data volume is required, thus realizing landing-gear system more accurate reliability assessment under small sample, lean information.

Technical scheme

A kind of undercarriage extension and retraction system reliability estimation method under small sample, lean information, it is characterised in that step is as follows:

Step 1: based on system principle and failure mechanism, set up undercarriage extension and retraction system fault tree, the described each layer logical relation of undercarriage extension and retraction system fault tree: X2, X3 and X4 are constituted or gate logic tree is to M4, X5, X6 and X7 are constituted or gate logic tree is to M5, X8 and X9 constitute or gate logic tree to M6, X15, X16 and X17 constitutes or gate logic tree is to M7；X1, M4, M5 and M6 are constituted or gate logic tree is constituted to M1, X10, X11 and X12 or gate logic tree to M2, X13, X14, M7, X18, X19, X20 constitute or gate logic tree is to M3；M1, M2 and M3 are constituted or gate logic tree is to T；

Wherein, X2-piston rod clamping stagnation, X3-piston rod loosens, X4-rod fracture, X5-sealing ring mechanical failure, X6-sealing ring aging cracking, X7-sealing ring chemical attack, X8-earrings bolt fracture, X9-earrings rotates, the match spring breakage of X15-pump plunger shaft, X16-pump swivel joint leakage of oil, X17-pump motor damages, X1-pressurized strut is ruptured, M4-piston rod is abnormal, M5-sealing ring is abnormal, M6-termination earrings is abnormal, X10-pressure switch lost efficacy, X11-electromagnetic switch lost efficacy, X12-safety valve lost efficacy, X13-fluid pressure line leakage of oil, X14-vent plug, X18-oil contamination, X19-fibre conduit breaks, X20-accumulator breaks, M7-hydraulic pump is abnormal, T-landing-gear system is abnormal；

Step 2: based on the interval transformational rule with graying, by the failure probability range format of each for undercarriage extension and retraction system fault tree bottom event X1～X20It is converted into pan-grey number representationWherein,p _i For X_iFailure probability lower limit,For X_iThe failure probability upper limit；

Step 2: set up the fault tree logic sum gate operator based on graying model of monolayerLogical relation between layers according to fault tree sets up the undercarriage buffer system inefficacy transmission function X from bottom event to top event_TOP=f (X₁,X₂,...,X₂₀)；

Step 3: use graying arithmetic rule that undercarriage buffer system was lost efficacy and transmit function X_TOP=f (X₁,X₂,...,X₂₀) calculate obtain top event failure probability graying formBased on the interval transformational rule with graying, by top event failure probability graying formBe converted to range formatThus obtaining the undercarriage buffer system failure probability scope based on graying algorithm, carry out reliability assessment according to undercarriage buffer system failure probability scope to breaking down；Wherein,p _TOP For the lower limit of undercarriage buffer system failure probability,The upper limit for undercarriage buffer system failure probability.

Described graying arithmetic rule is:

If $g_1=(x_1,\[\underset{\‾}{{\mathrm{\μ}}_1},\stackrel{\‾}{{\mathrm{\μ}}_1}\]),g_2=(x_2,\[\underset{\‾}{{\mathrm{\μ}}_2},\stackrel{\‾}{{\mathrm{\μ}}_2}\]),$ Then have:

$g_1+g_2=(x_1+x_2,\[\frac{x_1\underset{\‾}{{\mathrm{\μ}}_1}+x_2\underset{\‾}{{\mathrm{\μ}}_2}}{x_1+x_2},\frac{x_1\stackrel{\‾}{{\mathrm{\μ}}_1}+x_2\stackrel{\‾}{{\mathrm{\μ}}_2}}{x_1+x_2}\]),g_1-g_2=(x_1-x_2,\[\frac{x_1\underset{\‾}{{\mathrm{\μ}}_1}-x_2\underset{\‾}{{\mathrm{\μ}}_2}}{x_1-x_2},\frac{x_1\stackrel{\‾}{{\mathrm{\μ}}_1}-x_2\stackrel{\‾}{{\mathrm{\μ}}_2}}{x_1-x_2}\]),$

$g_1\×g_2=(x_1{x}_2,\[\underset{\‾}{{\mathrm{\μ}}_1}\underset{\‾}{{\mathrm{\μ}}_2},\stackrel{\‾}{{\mathrm{\μ}}_1}\stackrel{\‾}{{\mathrm{\μ}}_2}\]),g_1/g_2=(x_1/x_2,\[\underset{\‾}{{\mathrm{\μ}}_1}/\underset{\‾}{{\mathrm{\μ}}_2},\stackrel{\‾}{{\mathrm{\μ}}_1}/\stackrel{\‾}{{\mathrm{\μ}}_2}\])$

Wherein, x₁、x₂For observation,Respectively x₁、x₂Gray information portion.

Beneficial effect

A kind of Fault Tree Analysis based on graying algorithm that the present invention proposes, it is possible to realize for the Reliability evaluation under landing-gear system each component failure statistical information inadequate i.e. small sample, lean information.

Accompanying drawing explanation

Fig. 1 undercarriage extension and retraction system fault tree

T landing-gear system is abnormal；M1 pressurized strut is abnormal；M2 controls system exception；M3 hydraulic system is abnormal；M4 piston rod is abnormal；M5 sealing ring is abnormal；M6 termination earrings is abnormal；M7 hydraulic pump is abnormal；X1 pressurized strut is ruptured；X2 piston rod clamping stagnation；X3 piston rod loosens；X4 rod fracture；X5 sealing ring mechanical failure；X6 sealing ring aging cracking；X7 sealing ring chemical attack；X8 earrings bolt fracture；X9 earrings rotates；X10 pressure switch lost efficacy；X11 electromagnetic switch lost efficacy；X12 safety valve lost efficacy；X13 fluid pressure line leakage of oil；X14 vent plug；The match spring breakage of X15 pump plunger shaft；X16 pump swivel joint leakage of oil；X17 pump motor damages；X18 oil contamination；X19 fibre conduit breaks；X20 accumulator breaks.

Fig. 2 logical AND gate symbol

Fig. 3 logic sum gate symbol

Detailed description of the invention

In conjunction with embodiment, accompanying drawing, the invention will be further described:

According to landing-gear system operation principle, form structure, failure modes etc., constructing system fault tree, as shown in Figure 1；

As shown in table 1, the failure probability simultaneously giving each bottom event of landing-gear system fault tree is interval as follows:

Table 1 landing-gear system bottom event of fault tree failure probability is interval

Make " * ", * ∈+,-,/represent the real binary operation on set of real numbers.To arbitrarilyBinary operation on interval of definition manifold I (R) is as follows:

[x] * [y]=z | z=x*y, x ∈ [x], y ∈ [y] } (1)

Then there is following arithmetic rule:

$\left\{\begin{array}{c}\[x\]+\[y\]=\[\underset{\‾}{x}+\underset{\‾}{y},\stackrel{\‾}{x}+\stackrel{\‾}{y}\]\\ \[x\]-\[y\]=\[\underset{\‾}{x}-\stackrel{\‾}{y},\stackrel{\‾}{x}-\underset{\‾}{y}\]\\ \[x\]\·\[y\]=\[\min (\underset{\‾}{x}\underset{\‾}{y},\underset{\‾}{x}\stackrel{\‾}{y},\stackrel{\‾}{x}\underset{\‾}{y},\stackrel{\‾}{x}\stackrel{\‾}{y}),\max (\underset{\‾}{x}\underset{\‾}{y},\underset{\‾}{x}\stackrel{\‾}{y},\stackrel{\‾}{x}\underset{\‾}{y},\stackrel{\‾}{x}\stackrel{\‾}{y})\]\\ \[x\]/\[y\]=\[\underset{\‾}{x},\stackrel{\‾}{x}\]\·\[1/\stackrel{\‾}{y},1/\underset{\‾}{y}\](0\∉\[y\])\end{array}\right.---\left(2\right)$

If domain U=R (set of real numbers), then claiming the graying on R to integrate as graying manifold, the element being denoted as in g (R) and title g (R) is pan-grey number, is denoted as:X ∈ R,In formula, x is observation,Gray information portion for x.

Then there is following arithmetic rule:

$g_1+g_2=(x_1+x_2,\[\frac{x_1\underset{\‾}{{\mathrm{\μ}}_1}+x_2\underset{\‾}{{\mathrm{\μ}}_2}}{x_1+x_2},\frac{x_1\stackrel{\‾}{{\mathrm{\μ}}_1}+x_2\stackrel{\‾}{{\mathrm{\μ}}_2}}{x_1+x_2}\])---\left(3\right)$

$g_1-g_2=(x_1-x_2,\[\frac{x_1\underset{\‾}{{\mathrm{\μ}}_1}-x_2\underset{\‾}{{\mathrm{\μ}}_2}}{x_1-x_2},\frac{x_1\stackrel{\‾}{{\mathrm{\μ}}_1}-x_2\stackrel{\‾}{{\mathrm{\μ}}_2}}{x_1-x_2}\])---\left(4\right)$

$g_1\×g_2=(x_1{x}_2,\[\underset{\‾}{{\mathrm{\μ}}_1}\underset{\‾}{{\mathrm{\μ}}_2},\stackrel{\‾}{{\mathrm{\μ}}_1}\stackrel{\‾}{{\mathrm{\μ}}_2}\])---\left(5\right)$

$g_1/g_2=(x_1/x_2,\[\underset{\‾}{{\mathrm{\μ}}_1}/\underset{\‾}{{\mathrm{\μ}}_2},\stackrel{\‾}{{\mathrm{\μ}}_1}/\stackrel{\‾}{{\mathrm{\μ}}_2}\])---\left(6\right)$

In actual applications, pan-grey number and interval number can convert mutually, if known pan-grey numberThen the interval number form of its correspondence isIf known interval numberIn order to facilitate computing, can be collectively expressed asForm.Bottom event failure probability interval each in fault tree is represented sequentially as Based on the interval transformational rule with graying, by each for fault tree bottom event failure probability range formatUnification is converted into pan-grey number representationAs shown in table 2；

Table 2 landing-gear system bottom event of fault tree failure probability graying represents

In fault tree logical AND gate, when all bottom event i (i=1～n) all occur, top event " AND " occurs, and under graying model with door operator isIn fault tree logic sum gate, when having at least a bottom event i (i=1～n) to occur, top event " OR " occurs, and under graying model or door operator isWherein with or gate logic symbol as shown in Figure 2,3:

Based on fault tree with or gate logic relation, obtain landing-gear system fault tree synthesis function as follows:

T=1-(1-P_M1)(1-P_M2)(1-P_M3)(7)

$\left\{\begin{array}{c}{P}_{M1}=1-(1-P_{X1})(1-P_{M4})(1-P_{M5})(1-P_{M6})\\ P_{M2}=1-(1-P_{X10})(1-P_{X11})(1-P_{X12})\\ P_{M3}=1-(1-P_{X13})(1-P_{X14})(1-P_{M7})(1-P_{X18})(1-P_{X19})(1-P_{X20})\end{array}\right.---\left(8\right)$

$\{\begin{array}{c}{P}_{M4}=1-(1-P_{X2})(1-P_{X3})(1-P_{X4})\\ P_{M5}=1-(1-P_{X5})(1-P_{X6})(1-P_{X7})\\ P_{M6}=1-(1-P_{X8})(1-P_{X9})\\ P_{M7}=1-(1-P_{X15})(1-P_{X16})(1-P_{X17})\end{array}---\left(9\right)$

Graying calculating process is as follows:

P_M4=1-(1-P_X2)(1-P_X3)(1-P_X4)

=(1, [1,1])-{ (1, [1,1])-(9.29 × 10^-5,[0.282024,1])}·{(1,[1,1])-(1.40×10^-4,[0.458571,1])}

·{(1,[1,1])-(8.85×10^-6,[0.237288,1])}

=(2.4 × 10^-4,[0.3793,1])

P_M5=1-(1-P_X5)(1-P_X6)(1-P_X7)

=(1, [1,1])-{ (1, [1,1])-(2.45 × 10^-3,[0.187755,1])}·{(1,[1,1])-(8.29×10^-4,[0.316043,1])}

·{(1,[1,1])-(9.72×10^-4,[0.251029,1])}

=(4.246 × 10^-3,[0.227505,1])

P_M6=1-(1-P_X8)(1-P_X9)

=(1, [1,1])-{ (1, [1,1])-(1.95 × 10^-3,[0.235897,1])}·{(1,[1,1])-(7.29×10^-4,[0.307270,1])}

=(2.678 × 10^-3,[0.2555464,1])

P_M7=1-(1-P_X15)(1-P_X16)(1-P_X17)

=(1, [1,1])-{ (1, [1,1])-(1.85 × 10^-4,[0.248649,1])}·{(1,[1,1])-(7.52×10^-4,[0.324468,1])}

·{(1,[1,1])-(7.72×10^-3,[0.317358,1])}

=(8.65 × 10^-3,[0.3167134,1])

Thus can try to achieve:

P_M1=1-(1-P_X1)(1-P_M4)(1-P_M5)(1-P_M6)

=(1, [1,1])-{ (1, [1,1])-(6.40 × 10^-5,[0.315625,1])}·{(1,[1,1])-(2.4×10^-4,[0.3793,1])}

·{(1,[1,1])-(4.246×10^-3,[0.227505,1])}·{(1,[1,1])-(2.678×10^-3,[0.2555464,1])}

=(7.2145 × 10^-3,[0.2431464,1])

P_M2=1-(1-P_X10)(1-P_X11)(1-P_X12)

=(1, [1,1])-{ (1, [1,1])-(8.29 × 10^-5,[0.195416,1])}·{(1,[1,1])-(8.09×10^-4,[0.264524,1])}

·{(1,[1,1])-(1.44×10^-3,[0.343750,1])}

=(2.33 × 10^-3,[0.310623,1])

P_M3=1-(1-P_X13)(1-P_X14)(1-P_M7)(1-P_X18)(1-P_X19)(1-P_X20)

=(1, [1,1])-{ (1, [1,1])-(7.20 × 10^-3,[0.363889,1])}·{(1,[1,1])-(8.25×10^-4,[0.317576,1])}

·{(1,[1,1])-(8.65×10^-3,[0.3167134,1])}·{(1,[1,1])-(9.85×10^-3,[0.283249,1])}

·{(1,[1,1])-(8.29×10^-5,[0.255730,1])}·{(1,[1,1])-(1.70×10^-4,[0.260000,1])}

=(2.65324 × 10^-2,[0.318568,1])

Finally give:

T=1-(1-P_M1)(1-P_M2)(1-P_M3)

=(1, [1,1])-{ (1, [1,1])-(7.2145 × 10^-3,[0.2431464,1])}·{(1,[1,1])-(2.33×10^-3,[0.310623,1])}

·{(1,[1,1])-(2.65324×10^-2,[0.318568,1])}

=(0.0358, [0.3044832,1])

=[0.0109,0.0358]

It is hereby achieved that, the failure probability scope of undercarriage extension and retraction system is between 0.0109～0.0358.Visible, under various parts failure probability interval value given in Table 1, the undercarriage of 100 times is packed up, is put down in process, has 1～3 time and breaks down, it is achieved thereby that the quantitative evaluation to landing-gear system functional safety degree.

Claims (2)

1. the undercarriage extension and retraction system reliability estimation method under small sample, lean information, it is characterised in that step is as follows:

Step 1: based on system principle and failure mechanism, set up undercarriage extension and retraction system fault tree, the described each layer logical relation of undercarriage extension and retraction system fault tree: X2, X3 and X4 are constituted or gate logic tree is to M4, X5, X6 and X7 are constituted or gate logic tree is to M5, X8 and X9 constitute or gate logic tree to M6, X15, X16 and X17 constitutes or gate logic tree is to M7；X1, M4, M5 and M6 are constituted or gate logic tree is constituted to M1, X10, X11 and X12 or gate logic tree to M2, X13, X14, M7, X18, X19, X20 constitute or gate logic tree is to M3；M1, M2 and M3 are constituted or gate logic tree is to T；

Wherein, X2-piston rod clamping stagnation, X3-piston rod loosens, X4-rod fracture, X5-sealing ring mechanical failure, X6-sealing ring aging cracking, X7-sealing ring chemical attack, X8-earrings bolt fracture, X9-earrings rotates, the match spring breakage of X15-pump plunger shaft, X16-pump swivel joint leakage of oil, X17-pump motor damages, X1-pressurized strut is ruptured, M4-piston rod is abnormal, M5-sealing ring is abnormal, M6-termination earrings is abnormal, X10-pressure switch lost efficacy, X11-electromagnetic switch lost efficacy, X12-safety valve lost efficacy, X13-fluid pressure line leakage of oil, X14-vent plug, X18-oil contamination, X19-fibre conduit breaks, X20-accumulator breaks, M7-hydraulic pump is abnormal, T-landing-gear system is abnormal；

Step 2: based on the interval transformational rule with graying, by the failure probability range format of each for undercarriage extension and retraction system fault tree bottom event X1～X20It is converted into pan-grey number representationWherein,p _i For X_iFailure probability lower limit,For X_iThe failure probability upper limit；

Step 2: set up the fault tree logic sum gate operator based on graying model of monolayerLogical relation between layers according to fault tree sets up the undercarriage buffer system inefficacy transmission function X from bottom event to top event_TOP=f (X₁,X₂,...,X₂₀)；

Step 3: use graying arithmetic rule that undercarriage buffer system was lost efficacy and transmit function X_TOP=f (X₁,X₂,...,X₂₀) calculate obtain top event failure probability graying formBased on the interval transformational rule with graying, by top event failure probability graying formBe converted to range formatThus obtaining the undercarriage buffer system failure probability scope based on graying algorithm, carry out reliability assessment according to undercarriage buffer system failure probability scope to breaking down；Wherein,p _TOP For the lower limit of undercarriage buffer system failure probability,The upper limit for undercarriage buffer system failure probability.

2. a kind of undercarriage extension and retraction system according to claim 1 reliability estimation method under small sample, lean information, it is characterised in that described graying arithmetic rule is:

If $g_1=(x_1,\[\underset{\‾}{{\mathrm{\μ}}_1},\stackrel{\‾}{{\mathrm{\μ}}_1}\]),g_2=(x_2,\[\underset{\‾}{{\mathrm{\μ}}_2},\stackrel{\‾}{{\mathrm{\μ}}_2}\]),$ Then have:

$g_1+g_2=(x_1+x_2,\[\frac{x_1\underset{\‾}{{\mathrm{\μ}}_1}+x_2\underset{\‾}{{\mathrm{\μ}}_2}}{x_1+x_2},\frac{x_1\stackrel{\‾}{{\mathrm{\μ}}_1}+x_2\stackrel{\‾}{{\mathrm{\μ}}_2}}{x_1+x_2}\]),g_1-g_2=(x_1-x_2,\[\frac{x_1\underset{\‾}{{\mathrm{\μ}}_1}-x_2\underset{\‾}{{\mathrm{\μ}}_2}}{x_1-x_2},\frac{x_1\stackrel{\‾}{{\mathrm{\μ}}_1}-x_2\stackrel{\‾}{{\mathrm{\μ}}_2}}{x_1-x_2}\]),$

$g_1\×g_2=(x_1{x}_2,\[\underset{\‾}{{\mathrm{\μ}}_1}\underset{\‾}{{\mathrm{\μ}}_2},\stackrel{\‾}{{\mathrm{\μ}}_1}\stackrel{\‾}{{\mathrm{\μ}}_2}\]),g_1/g_2=(x_1/x_2,\[\underset{\‾}{{\mathrm{\μ}}_1}\underset{\‾}{/{\mathrm{\μ}}_2},\stackrel{\‾}{{\mathrm{\μ}}_1}/\stackrel{\‾}{{\mathrm{\μ}}_2}\])$

Wherein, x₁、x₂For observation,Respectively x₁、x₂Gray information portion.