CN104820778B - Operational aircraft system vulnerability Allocation method - Google Patents
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Abstract
A kind of operational aircraft system vulnerability Allocation method, by setting up certain type fighter plane vulnerability model, under it is determined that threatening strike, determine vulnerability initial parameter, it is then determined that aircraft suffers the killing probability and survival probability of stricken number of times and each part after being hit, then the probability after the determination self-existent state of aircraft and each state are hit, above-mentioned the data obtained is substituted into comprehensive importance and Griffith importance calculation formula, obtain the synthesis importance and Griffith importances of all parts, finally full machine vulnerability is allocated using vulnerability Distribution Indexes method, it can obtain the vulnerability of all parts.After the vulnerability for obtaining each part distribution, vulnerability is carried out for the big part of vulnerability, its vulnerability is reduced, so as to improve the viability of aircraft.
Description
Technical field
The present invention relates to aviation operational aircraft vulnerability design field, specifically based on comprehensive importance and
The important topology degrees of Griffith carry out aircraft system vulnerability Distribution Indexes.
Background technology
Vulnerability is defined as operational aircraft under combat situation, bears the ability that artificial hostile environment is threatened.Provide aircraft
The vulnerability of part is an important process in survivability Evaluation, should just give and consider early stage airplane design.It is
Effectively improve Aircraft Survivability and guideline be provided, targetedly major design task is placed on the high part of vulnerability,
So as to reach the effectively optimizing design of Aircraft Survivability.
Development of Aircraft Vulnerability is higher, then easier when catching a packet to be killed, and can more reduce the ability that aircraft completes task.
Each part has a certain degree of vulnerability on aircraft, and the vulnerability of each part has in various degree to the vulnerability of full machine
Effect.The part that confirm which can be caused aircraft to be killed after killing or damage is estimated to vulnerability, it is confirmed
Part be exactly lethal components.Vulnerability distribution is defined as vulnerability index as defined in system reasonably distributing to composition system
Each part of system.By distribution, the weak element of aircraft can be exposed, foundation is provided to improve Development of Aircraft Vulnerability design, expects
Obtain rational vulnerability design.
The vulnerability Study of aircraft can disclose the approach for improving aircraft fight survival probability, can be provided by deducting
The vulnerability of which part is high, and aircraft will be caused seriously to injure.The vulnerability of aircraft includes many factors, and these factors determine to fly
Ability of the machine by battle injury.When the different other side's threatening environment of aircraft encounter, the threat types being subjected to are different, will lead
Vulnerability is caused to estimate also different, therefore vulnerability measure is also different, such as a kind of vulnerability measure is to use bar
Part probability represents, i.e. killing probability of the aircraft after being hit by single；Another vulnerability measure aircraft
Vulnerable Area AVCome what is represented.But the aircraft Vulnerable Area of single strike is only applicable to simply without the non-overlapping aircraft mould of remaining
Type, it or can not can not completely consider the easily worn part of complicated model aircraft (model aircraft for having remaining to have overlapping member),
For having the aircraft of remaining part, one part killing of any of which will not result in the killing of aircraft, only when this is remaining
Degree parts group killing can just cause the killing of aircraft.Therefore, the concept of equivalent single vulnerable area is suggested, and is solved well
Above mentioned problem.Vulnerability index above is the index of full machine, after the determination of full machine index, not yet there is a kind of rational at present
Method is come the Distribution Indexes to each subsystem or part.
Vulnerability includes：Remaining part, part arrangement, passive damage suppress, actively damage suppression, member shields,
Part is eliminated, and wherein part arrangement refers to carefully arrange the position of lethal components, makes the possibility and degree being damaged
Minimize.Therefore, the vulnerability of part should be considered in the airplane design starting stage, institute is obtained by vulnerability Distribution Indexes
There is a vulnerability apportioning cost of part, and then targetedly the part big to vulnerability can modify, its is reduced as far as possible easy
Damage property.Vulnerability Allocation method given herein, has taken into full account actual conditions, when aircraft is by multiple strike, flies
There are multiple states in machine, while the performance of aircraft system is also contemplated, with more generality and adaptability.Northwestern Polytechnical University exists
A kind of method sorted for aircraft components vulnerability, the party are proposed in the innovation and creation of Application No. 201410352457.9
Method provides five kinds of vulnerability sort methods, respectively structure probability importance, criticality importance (Criticality), and FV is important
Degree, RAW importances and RRW importances, but this five kinds of methods are all only suitable for two condition system, i.e., after aircraft is by hitting, fly
There is killing state and non-killing state in machine, do not account for the intermediateness of aircraft, and intermediateness will not cause aircraft to kill, but
It is the performance that can influence aircraft and the efficiency for completing task.And vulnerability importance given herein is not only allowed in aircraft
Between state also contemplate the performance of aircraft, finally provide full machine vulnerability Distribution Indexes.
The content of the invention
In order to overcome prior art to calculate the limitation of two condition system vulnerability, the present invention proposes a kind of fight and flown
Machine system vulnerability Allocation method.
The present invention detailed process be：
Step 1：Set up Development of Aircraft Vulnerability model；
Determine the lethal components of aircraft；The lethal components are pilot B, afterbody fuel tank C, Left Hand Engine D, the right side
Engine F, left hydraulic oil container G, right hydraulic oil container H, left generator I and right generator J；Wherein, pilot B, afterbody fuel tank
C, Left Hand Engine D and right engine F are non-remaining part；Left hydraulic oil container G and right hydraulic oil container H remaining part each other, it is left
Generator I and right generator J remaining part each other；
The minimal cut set of the lethal components is：{B、C、D、F、{G、H}、{I、J}}；Aircraft is drawn according to minimal cut set
Killing tree；
Step 2：Determine the direction that fighter plane is attacked；
It is 90 ° by the azimuth A of direction of attack to determine aircraft, and angle of pitch E is 0 °；
Step 3：Define vulnerability initial parameter；Described vulnerability initial parameter includes part i exposed area
Part i killing probability when threatening hitting partWith the killing probability of part i when threatening strike aircraft
By obtained part i exposed areaWith the killing probability of part i when threatening hitting partDetermine prestige
Part i killing probability during side of body strike aircraft
By exposed areaPart i killing probability when threatening hitting partBring A intoVi=APiPk/hi, obtain every
The Vulnerable Area of individual partBy obtained Vulnerable AreaWith the exposed area A of aircraftPBring intoObtain
Part i killing probability when threatening strike aircraft
The aircraft exposed area APMiddle A represents area, and subscript P represents exposure outside；Aircraft Vulnerable Area AVMiddle A is represented
Area, subscript V represents vulnerability；Part i exposed areaMiddle A represents area, and subscript P represents exposure outside, i expressed portions
Part is numbered；Part i killing probability when threatening hitting partMiddle P represents probability, and subscript k represents killing, and h represents that strike exists
On part, i represents unit number；Part i killing probability when threatening strike aircraftMiddle P represents probability, and subscript k represents to kill
Wound, H represents strike aboard, and i represents unit number；Based on the expectation cycle on exposed areaMiddle E is described
Expect cycle, subscript A represents area, and P represents exposure outside；
Step 4：It is determined that each part byKilling probability and survival probability after secondary strike；
It is determined that each part byDuring killing probability and survival probability after secondary strike, pass throughThe killing probability and survival probability of all parts are determined respectively.
For aircraft bySecondary random strike, aircraft encounter is determined using binomial approachSecondary strike back part i
Survival probability be：
In formula (1), P represents probability, and s represents existence,Represent based on the expectation cycle on exposed area, prestige
Part i killing probability during side of body strike aircraftMiddle P is represented in probability, subscript：K represents killing, and H represents strike in aircraft
On, i represents unit number；
Aircraft bySecondary strike back part i killing probability is：
In formula (2), P represents probability, and k represents killing,Represent based on the expectation cycle on exposed area, prestige
Part i killing probability during side of body strike aircraftMiddle P is represented in probability, subscript：K represents killing, and H represents strike in aircraft
On, i represents unit number；
Corresponding data in table 1 is brought into formula (1) and formula (2), obtain each part byKilling after secondary strike
Hinder probability and survival probability；
Step 5：Determine aircraft be individually present state j and aircraft byIt is described after secondary strike to be respectively individually present state
The probability of generation；All killing states of aircraft are determined using permutation and combination method；Respectively the status merging for causing aircraft to kill,
The self-existent state of each aircraft is obtained to existProbable value after secondary strike；
Step 6：Give the systematic function a of each separate statej, wherein j=0,1,2 ..., q represent aircraft independent respectively
The various states existed；
Step 7：Determine the importance VI of each part of aircraft；
The importance of each part of described aircraft includes comprehensive importance VIIIMWith Griffith importances VIG；
It is described to determine that comprehensive importance and Griffith importances are the killing probability of each part by obtaining, using public affairs
Formula (3) and formula (4) are determined；
Aircraft is making prewar, each part i availability Pi1=1；
The state space of part is { 0,1 }, wherein 0 represents killing state, 1 represents survival condition；Aircraft state space is
{ 0,1,2 ..., M }, part i synthesis importance is determined by formula (3)：
Part i Griffith importances are determined by formula (4)：
In formula (3),The conversion ratio that killing state is deteriorated to from serviceable condition, the portion are hit by single for part i
Caused by the strike threatened, therefore the conversion of part is due toDescribed serviceable condition and killing state difference
Represented with 1 and 0；
In formula (3) and formula (4)：Represent that aircraft is jth when part i is in serviceable condition
Plant shape probability of state；When representing part i killing states, aircraft is state j probability；Wherein Pr is represented
Probability,Represent based on the expectation cycle on exposed area, 1 represents intact, 0 represents killing, and X represents part vector, Φ
(1i, X) and aircaft configuration function is represented, j represents j-th of separate state of aircraft；ajRepresent systematic function；M represents aircraft independence shape
State sum；VIIIMRepresent comprehensive importance；VIGRepresent Griffith importances；
Step 8：Vulnerability Distribution Indexes；Adoption rate distribution method carries out easy to comprehensive importance and Griffith importances
The distribution of damage property index；
The synthesis importance of each part of aircraft system is VIIIM(i), Griffith importances are VIG(i)；The rapid wear of system
Property is AV, according to systematic function ajMember of imparting i weighted factor is answered during to the importance VI (i) of each part of aircraft system distribution
For ωi, the weighted factor is determined by formula (5)：
In formula (5), ωiIt is part i weighted factor, subscript i span is all 1 ..., n；
Determine that the vulnerability index that part i is distributed is by formula (6)：
AVi=ωi·AV (6)
In formula (6), AVFor the vulnerability of aircraft, AViObtained vulnerability is distributed by all parts；
So far, the distribution of operational aircraft system vulnerability index is completed.
The present invention gives the quantitative calculating of each part vulnerability of complicated system polymorphic and the method for Distribution Indexes,
The accompanying drawing 5 of the present invention is the killing tree of simplified aircraft model.It is easy to intuitively obtain when non-remaining by killing tree graph
Spend any one in pilot B, C, D, F to kill, may result in aircraft killing tree, the killing of any one remaining parts group can just be led
Cause any one part killing in aircraft killing, remaining parts group aircraft will not be caused to kill.
The present invention initially sets up certain type fighter plane vulnerability model, under it is determined that threatening strike, determines that vulnerability is initially joined
Number, it is then determined that aircraft suffers the killing probability and survival probability of stricken number of times and each part after being hit, connects
Determine the self-existent state of aircraft and each state hit after probability, by above-mentioned the data obtained substitute into comprehensive importance and
Griffith importance calculation formula, obtain the synthesis importance and Griffith importances of all parts, finally utilize rapid wear
Property Distribution Indexes method is allocated to full machine vulnerability, can obtain the vulnerability of all parts.Obtain the easy of each part distribution
After damage property, vulnerability is carried out for the big part of vulnerability, its vulnerability is reduced, so as to improve the viability of aircraft.This
Invention provides the model aircraft of certain hypothesis to verify the correctness of determination method, as shown in end product, pilot B, afterbody combustion
Fuel tank C, Left Hand Engine D, the vulnerability of right engine F distribution are than larger, and this is due to that this four parts are non-remaining parts, and
Left hydraulic oil container G, right hydraulic oil container H, left generator I, right generator J are remaining parts, therefore can be for the big portion of vulnerability
Part is improved design, reduces its vulnerability.
Brief description of the drawings
Accompanying drawing 1 is operational aircraft system vulnerability allocation process diagram；
Accompanying drawing 2 is that direction of attack is defined in figure, figure：OP represents direction of attack, and OQ is projections of the OP on coordinate surface XOZ,
OX and OQ angle is that azimuth A, OQ and OP angle are angle of pitch E；
Accompanying drawing 3 is simplified aircraft model figure front view, in figure：OP represents direction of attack, and symbol B, C, D, F, G, H, I, J are equal
For the part of aircraft, wherein B represents pilot, and C represents afterbody fuel tank, and D represents Left Hand Engine, and F represents right engine, G tables
Show left hydraulic oil container, H represents right hydraulic oil container, and I represents left generator, and J represents right generator；
Fig. 4 is simplified aircraft model figure right side elevational view on beating position, in figure：1 represents only pilot B area
Domain, 2 expressions only have the Left Hand Engine D regions overlapping with right engine F, and 3 represent only have left generator I and right generator J overlapping
Region, 4 represent there was only the left hydraulic oil container G regions overlapping with right hydraulic oil container H, and 5 represent the area that there was only afterbody fuel tank C
Domain；
Accompanying drawing 5 is the killing tree of simplified aircraft model, in figure：Symbol B represents pilot；C, D, F, G, H, I, J points of symbol
Not Wei aircraft part：C represents afterbody fuel tank, and D represents Left Hand Engine, and F represents right engine, and G represents left hydraulic oil container, H
Right hydraulic oil container is represented, I represents left generator, and J represents right generator.
Embodiment
The present embodiment is by taking certain type fighter plane as an example, to illustrate that each part of complicated system polymorphic proposed by the present invention is based on synthesis
The vulnerability of importance and Griffith importances quantitatively calculate and Distribution Indexes method.
Step 1：Set up Development of Aircraft Vulnerability model.
For certain existing type Aerodynamics Data of Fighter Models, the part that after those damages or loss aircraft can be caused to kill is determined, i.e.,
Lethal components.The model aircraft simplified in the present embodiment as shown in Figure 3, the cause for determining the model is defined by lethal components
Life property part is respectively pilot B, afterbody fuel tank C, Left Hand Engine D, right engine F, left hydraulic oil container G, right hydraulic oil container
H, left generator I and right generator J.Pilot B, afterbody fuel tank C, Left Hand Engine D and right engine F are non-remaining portion
Part.The Development of Aircraft Vulnerability model has two remaining set, wherein left hydraulic oil container G and right hydraulic oil container H remaining part each other,
Left generator I and right generator J remaining part each other.All parts for causing aircraft to kill are determined according to lethal components most
Small set, because the killing of remaining part may result in aircraft killing, and remaining part can just cause aircraft to kill when all killing, therefore
Minimal cut set in the present embodiment is：{ B, C, D, F, { G, H }, { I, J } }, draws aircraft killing according to minimal cut set and sets, that is, give
Go out the logical relation of part and the fighter plane, such as accompanying drawing 5.
Step 2：Determine the direction that fighter plane is attacked.The present embodiment is overwhelmed using on the left of aircraft and attacked as aircraft
Direction, i.e. aircraft are 90 ° by the azimuth A of direction of attack, and angle of pitch E is 0 °.
Step 3：Define vulnerability initial parameter.Determine aircraft by all parts under direction of attack and the geometry number of full machine
According to, including：Part i exposed areaPart i killing probability when threatening hitting partWith portion when threatening strike aircraft
Part i killing probabilityAs shown in table 1.Described part i exposed areaDetermined by design；The threat beating part
Part i killing probability during partObtained by inquiring about military aircraft handbook.
By obtained part i exposed areaWith the killing probability of part i when threatening hitting partDetermine prestige
Part i killing probability during side of body strike aircraftSpecifically：
When it is determined that aircraft right is hit, including overlapping region forms five key areas, five regions between part
Corresponding data it is as shown in table 1.
The related data in 1 five regions of table
By exposed areaPart i killing probability when threatening hitting partBring A intoVi=APiPk/hi, obtain each
The Vulnerable Area of partThe exposed area of aircraft is A in this directionP=55.57m2, by what is obtainedWith the exposure of aircraft
Product APBring intoPart i killing probability when obtaining threatening strike aircraftEach partWithValue is as shown in table 2.
Each part of table 2WithValue
I scope is 1~8 in the present embodiment；Determine aircraft by the full machine exposed area A on direction of attackP=55.57m2,
Full machine vulnerability is AV=3.92/m2, part expectation cycle
In viability field, aircraft exposed area APMiddle A represents area, and subscript P represents exposure outside；Aircraft rapid wear face
Product AVMiddle A represents area, and subscript V represents vulnerability；Part i exposed areaMiddle A represents area, and subscript P represents to be exposed to
Outside, i represents unit number；Part i killing probability when threatening hitting partMiddle P represents probability, and subscript k represents killing, h
Strike is represented on part, i represents unit number；Part i killing probability when threatening strike aircraftMiddle P represents probability,
Subscript k represents killing, and H represents strike aboard, and i represents unit number；Based on the expectation cycle on exposed area
Middle E is described expectation cycle, and subscript A represents area, and P represents exposure outside.
Step 4：It is determined that each part byKilling probability and survival probability after secondary strike.
For aircraft bySecondary random strike, aircraft encounter is determined using binomial approachSecondary strike back part i
Survival probability be：
In formula (1), P represents probability, and s represents existence,Represent based on the expectation cycle on exposed area, prestige
Part i killing probability during side of body strike aircraftMiddle P is represented in probability, subscript：K represents killing, and H represents strike in aircraft
On, i represents unit number.
Aircraft bySecondary strike back part i killing probability is：
In formula (2), P represents probability, and k represents killing,Represent based on the expectation cycle on exposed area, prestige
Part i killing probability during side of body strike aircraftMiddle P is represented in probability, subscript：K represents killing, and H represents strike in aircraft
On, i represents unit number.
Corresponding data in table 2 is brought into formula (1) and formula (2), obtain each part byKilling after secondary strike
Hinder probability and survival probability, as shown in table 3.
The each part of table 3 byKilling probability and survival probability after secondary strike
Step 5：Determine aircraft be individually present state j and aircraft byIt is described after secondary strike to be respectively individually present state
The probability of generation.All existences of aircraft are determined using permutation and combination method, that is, arrange and combine all states being likely to occur,
In the present embodiment, aircraft has eight critical components, and total state has 28=256 kinds, wherein representational killing state is：
The killing of only one of which part includes one kind in following 8 kinds of states：Pilot B, afterbody fuel tank C, Left Hand Engine
Part killing in D, right engine F, left hydraulic oil container G, right hydraulic oil container H, left generator I and right generator J.
There are two part killings to include one kind in following 28 kinds of states：Pilot B and afterbody fuel tank C is killed, or
Pilot B and Left Hand Engine D is killed, and either pilot B is killed with right engine F or pilot B and left hydraulic oil container G is killed
Wound, either pilot B and right hydraulic oil container H is killed or pilot B and left generator I is killed, or pilot B and right hair
Motor J is killed, and either afterbody fuel tank C and Left Hand Engine D is killed or afterbody fuel tank C and right engine F is killed, or
Afterbody fuel tank C and left hydraulic oil container G is killed, and either afterbody fuel tank C and right hydraulic oil container H is killed or afterbody fuel tank C
Killed with left generator I, either afterbody fuel tank C and right generator J is killed or Left Hand Engine D and right engine F is killed,
Either Left Hand Engine D and left hydraulic oil container G are killed or Left Hand Engine D and right hydraulic oil container H is killed, or Left Hand Engine D with
Left generator I killings, either Left Hand Engine D and right generator J is killed or right engine F and left hydraulic oil container G is killed, or
The right engine F of person and right hydraulic oil container H is killed, and either right engine F and left generator I is killed or right engine F and right hair
Motor J is killed, and either left hydraulic oil container G and right hydraulic oil container H is killed or left hydraulic oil container G and left generator I is killed, or
The left hydraulic oil container G of person and right generator J are killed, either right hydraulic oil container H and left generator I kill or right hydraulic oil container H with
Right generator J killings, or left generator I and right generator J killings.
The part killing obtained according to the permutation and combination and the method for two part killings continue to arrange and combined
All states being likely to occur, can respectively obtain three part killings and three states killed with upper-part.
Respectively the status merging for causing aircraft to kill, finally obtain the self-existent state of aircraft and have 10, i.e. j=
0,1,2,…,9.The self-existent state of each aircraft is provided to existProbable value after secondary strike, as shown in table 4.
The each state of table 4 existsProbable value after secondary strike
Step 6：Analysis determines the systematic function a of each separate statej, j=0 therein, 1,2 ..., q, in the present embodiment,
Described j represents the self-existent 10 kinds of states of aircraft respectively, therefore j=0,1,2 ..., 9.In 10 kinds of described states, when
During j=0, system is in entirely ineffective state, therefore a0=0；As j=9, system is in serviceable condition, therefore a9=1.Due to a left side
Hydraulic oil container G and right hydraulic oil container H remaining part each other, left generator I and right generator J remaining part each other, after analysis
Determine that the performance number of each state of system is as shown in table 4.
Step 7：Determine the importance VI of each part of aircraft.
The importance of each part of described aircraft includes comprehensive importance VIIIMWith Griffith importances VIG。
It is described to determine that comprehensive importance and Griffith importances are the killing probability of each part by obtaining, using public affairs
Formula (3) and formula (4) are determined.
Aircraft is making prewar, each part i availability Pi1=1.The state space of part is { 0,1 }, wherein 0 represents to kill
Hinder state, 1 represents survival condition；Aircraft state space is { 0,1,2 ..., M }, and part i synthesis importance passes through formula (3)
It is determined that：
Part i Griffith importance calculation formula are：
In formula (3),The conversion ratio that killing state is deteriorated to from serviceable condition, the part are hit by single for part i
Conversion be due to caused by the strike threatened, thereforeDescribed serviceable condition and killing state is used respectively
1 and 0 represents.
In formula (3) and formula (4)：Represent that aircraft is jth kind when part i is in serviceable condition
Shape probability of state；When representing part i killing states, aircraft is state j probability；Wherein Pr represents general
Rate,Represent based on the expectation cycle on exposed area, 1 represents intact, 0 represents killing, and X represents part vector, Φ
(1i, X) and aircaft configuration function is represented, j represents j-th of separate state of aircraft；ajRepresent systematic function；M represents aircraft independence shape
State sum；VIIIMRepresent comprehensive importance；VIGRepresent Griffith importances.
Determine pilot B killing probability：For pilot B, calculateWhen be that pilot B is intact
When the probability that exists of each state, then made in table 2Then B killing probability is 0 in table 3, and survival probability is 1, afterbody combustion
Fuel tank C, Left Hand Engine D, right engine F, left hydraulic oil container G, right hydraulic oil container H, left generator I and right generator J
Value is constant, i.e., the killing probability and survival probability of remaining each part in addition to pilot B are still the value in table 3, these values
Table 4 is brought into can obtainIt is as shown in table 5 below.AndWhen representing pilot B killings
The probability that each state is present, then make in table 2Then pilot B killing probability is 1 in table 3, and survival probability is 0, its
Remaining each partValue is constant, i.e., the killing probability and survival probability of remaining each part in addition to pilot B are still in table 3
Value, remaining described each partValue brings table 4 into, obtains each state values of pilot BSuch as
Shown in table 5.
Each state value result of calculations of the pilot B of table 5
Repeat the process of each state value for determining pilot B, determine each state value of remaining each part, it is determined that knot
Fruit is as shown in table 6~12.
The afterbody fuel tank C of table 6 each state value result of calculation
The Left Hand Engine D of table 7 each state value result of calculation
The right engine F of table 8 each state value result of calculation
The left hydraulic oil container G of table 9 each state value result of calculation
The right hydraulic oil container H of table 10 each state value result of calculation
The left generator I of table 11 each state value result of calculation
The right generator J of table 12 each state value result of calculation
Above-mentioned related data is substituted into formula (9), (10), the synthesis importance and Griffith importances of each part is obtained
And sequence is as shown in table 13.
The synthesis importance of each part of table 13 and Griffith importances and sequence
Step 8：Vulnerability Distribution Indexes.Adoption rate distribution method carries out easy to comprehensive importance and Griffith importances
The distribution of damage property index.
The synthesis importance of each part of aircraft system is VIIIM(i), Griffith importances are VIG(i)；The rapid wear of system
Property is AV, according to systematic function ajMember of imparting i weighted factor is answered during to the importance VI (i) of each part of aircraft system distribution
For ωi, the weighted factor is determined by formula (5)：
In formula (5), ωiIt is part i weighted factor, subscript i span is all 1 ..., n.
Determine that the vulnerability index that part i is distributed is by formula (6)：
AVi=ωi·AV (6)
In formula (6), AVFor the vulnerability of aircraft, AViObtained vulnerability is distributed by all parts.
In the present embodiment, full machine vulnerability is AV=3.92/m2, be based respectively on synthesis importance that above-mentioned calculating obtains and
Griffith importances carry out vulnerability distribution：For comprehensive importance, by the full machine vulnerability A of determinationV=3.92/m2Bring into
Formula (5), obtains the weighted factor of each part.Again by the full machine vulnerability A of determinationV=3.92/m2Formula (6) is brought into be flown
Office staff B, afterbody fuel tank C, Left Hand Engine D, right engine F, left hydraulic oil container G, right hydraulic oil container H, left generator I and right hair
Vulnerability value after each part distribution of motor J；Griffith is obtained using the method for carrying out vulnerability distribution with comprehensive importance
The vulnerability value of importance；Vulnerability value after each part distribution is as shown in table 14：
Each part vulnerability Distribution Indexes value of table 14
Claims (2)
1. a kind of operational aircraft system vulnerability Allocation method, it is characterised in that detailed process is：
Step 1：Set up Development of Aircraft Vulnerability model：
Determine the lethal components of aircraft；The lethal components are that pilot B, afterbody fuel tank C, Left Hand Engine D, the right side are started
Machine F, left hydraulic oil container G, right hydraulic oil container H, left generator I and right generator J；Wherein, pilot B, afterbody fuel tank C, a left side
Engine D and right engine F are non-remaining part；Left hydraulic oil container G and right hydraulic oil container H remaining part, left generating each other
Machine I and right generator J remaining part each other；
The minimal cut set of the lethal components is：{B、C、D、F、{G、H}、{I、J}}；Aircraft killing is drawn according to minimal cut set
Tree；
Step 2：Determine the direction that fighter plane is attacked：
It is 90 ° by the azimuth A of direction of attack to determine aircraft, and angle of pitch E is 0 °；
Step 3：Define vulnerability initial parameter；Described vulnerability initial parameter includes part i exposed areaThreat is beaten
Part i killing probability when hitting partWith the killing probability of part i when threatening strike aircraftPass through obtained part i
Exposed areaWith the killing probability of part i when threatening hitting partIt is determined that threatening the killing of part i when hitting aircraft
Probability
By exposed areaPart i killing probability when threatening hitting partBring A intoVi=APiPk/hi, obtain each part
Vulnerable AreaBy obtained Vulnerable AreaWith the exposed area A of aircraftPBring intoObtain threatening and beat
Part i killing probability when hitting aircraft
The aircraft exposed area APMiddle A represents area, and subscript P represents exposure outside；Aircraft Vulnerable Area AVMiddle A represents area,
Subscript V represents vulnerability；Part i exposed areaMiddle A represents area, and subscript P represents exposure outside, and i represents unit number；
Part i killing probability when threatening hitting partMiddle P represents probability, and subscript k represents killing, and h represents strike on part, i
Represent unit number；Part i killing probability when threatening strike aircraftMiddle P represents probability, and subscript k represents killing, and H is represented
Aboard, i represents unit number for strike；Based on the expectation cycle on exposed areaMiddle E is described expectation strike
Number of times, subscript A represents area, and P represents exposure outside；
Step 4：It is determined that each part byKilling probability and survival probability after secondary strike：
For aircraft bySecondary random strike, aircraft encounter is determined using binomial approachSecondary strike back part i existence
Probability is：
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>s</mi>
<mo>/</mo>
<msub>
<mi>H</mi>
<mi>i</mi>
</msub>
</mrow>
<msub>
<mi>E</mi>
<msub>
<mi>A</mi>
<mi>P</mi>
</msub>
</msub>
</msubsup>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<msub>
<mi>H</mi>
<mi>i</mi>
</msub>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>E</mi>
<msub>
<mi>A</mi>
<mi>P</mi>
</msub>
</msub>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (1), P represents probability, and s represents existence,Represent, based on the expectation cycle on exposed area, to threaten strike
Part i killing probability during aircraftMiddle P is represented in probability, subscript：K represents killing, and H represents strike aboard, and i is represented
Unit number；
Aircraft bySecondary strike back part i killing probability is：
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<msub>
<mi>H</mi>
<mi>i</mi>
</msub>
</mrow>
<msub>
<mi>E</mi>
<msub>
<mi>A</mi>
<mi>P</mi>
</msub>
</msub>
</msubsup>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>k</mi>
<mo>/</mo>
<msub>
<mi>H</mi>
<mi>i</mi>
</msub>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>E</mi>
<msub>
<mi>A</mi>
<mi>P</mi>
</msub>
</msub>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (2), P represents probability, and k represents killing,Represent that, based on the expectation cycle on exposed area, threat is beaten
Part i killing probability when hitting aircraftMiddle P is represented in probability, subscript：K represents killing, and H represents strike aboard, i tables
Show unit number；
The exposed area in each region is brought into formula (1) and formula (2), obtain each part byKilling after secondary strike
Hinder probability and survival probability；
Step 5：Determine aircraft be individually present state j and aircraft byIt is described after secondary strike to be respectively individually present what state occurred
Probability：
All killing states of aircraft are determined using permutation and combination method；Respectively the status merging for causing aircraft to kill, institute is obtained
The self-existent state of each aircraft is stated to existProbable value after secondary strike；
Step 6：Give the systematic function a of each separate statej, wherein j=0,1,2 ..., q represent aircraft and are individually present respectively
Various states；
Step 7：Determine the importance VI of each part of aircraft：
The importance of each part of described aircraft includes comprehensive importance VIIIMWith Griffith importances VIG；
It is described to determine that comprehensive importance and Griffith importances are the killing probability of each part by obtaining, using formula
(3) determined with formula (4)；
Aircraft is making prewar, each part i availability Pi1=1；
The state space of part is { 0,1 }, wherein 0 represents killing state, 1 represents survival condition；Aircraft state space for 0,1,
2 ..., M }, part i synthesis importance is determined by formula (3)：
<mrow>
<msubsup>
<mi>VI</mi>
<mn>1</mn>
<mrow>
<mi>I</mi>
<mi>I</mi>
<mi>M</mi>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msubsup>
<mi>&lambda;</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mi>i</mi>
</msubsup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>a</mi>
<mi>j</mi>
</msub>
<mo>&lsqb;</mo>
<msub>
<mi>Pr</mi>
<msub>
<mi>E</mi>
<msub>
<mi>A</mi>
<mi>P</mi>
</msub>
</msub>
</msub>
<mrow>
<mo>(</mo>
<mi>&Phi;</mi>
<mo>(</mo>
<mrow>
<msub>
<mn>1</mn>
<mi>i</mi>
</msub>
<mo>,</mo>
<mi>X</mi>
</mrow>
<mo>)</mo>
<mo>=</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>Pr</mi>
<msub>
<mi>E</mi>
<msub>
<mi>A</mi>
<mi>P</mi>
</msub>
</msub>
</msub>
<mrow>
<mo>(</mo>
<mi>&Phi;</mi>
<mo>(</mo>
<mrow>
<msub>
<mn>0</mn>
<mi>i</mi>
</msub>
<mo>,</mo>
<mi>X</mi>
</mrow>
<mo>)</mo>
<mo>=</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
Part i Griffith importances are determined by formula (4)：
<mrow>
<msubsup>
<mi>VI</mi>
<mn>1</mn>
<mi>G</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>M</mi>
</munderover>
<msub>
<mi>a</mi>
<mi>j</mi>
</msub>
<mo>&lsqb;</mo>
<msub>
<mi>Pr</mi>
<msub>
<mi>E</mi>
<msub>
<mi>A</mi>
<mi>P</mi>
</msub>
</msub>
</msub>
<mrow>
<mo>(</mo>
<mi>&Phi;</mi>
<mo>(</mo>
<mrow>
<msub>
<mn>1</mn>
<mi>i</mi>
</msub>
<mo>,</mo>
<mi>X</mi>
</mrow>
<mo>)</mo>
<mo>=</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>Pr</mi>
<msub>
<mi>E</mi>
<msub>
<mi>A</mi>
<mi>P</mi>
</msub>
</msub>
</msub>
<mrow>
<mo>(</mo>
<mi>&Phi;</mi>
<mo>(</mo>
<mrow>
<msub>
<mn>0</mn>
<mi>i</mi>
</msub>
<mo>,</mo>
<mi>X</mi>
</mrow>
<mo>)</mo>
<mo>=</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (3),The conversion ratio that killing state is deteriorated to from serviceable condition is hit by single for part i, the part
Caused by the strike threatened, therefore conversion is due toDescribed serviceable condition and killing state are respectively with 1 He
0 represents；
In formula (3) and formula (4)：Represent that aircraft is jth kind state when part i is in serviceable condition
Probability；When representing part i killing states, aircraft is state j probability；Wherein Pr represents probability,Represent based on the expectation cycle on exposed area, 1 represents intact, 0 represents killing, and X represents part vector, Φ (1i,X)
Aircaft configuration function is represented, j represents j-th of separate state of aircraft；ajRepresent systematic function；M represents that aircraft separate state is total
Number；VIIIMRepresent comprehensive importance；VIGRepresent Griffith importances；
Step 8：Vulnerability Distribution Indexes：
Adoption rate distribution method carries out the distribution of vulnerability index to comprehensive importance and Griffith importances；
The synthesis importance of each part of aircraft system is VIIIM(i), Griffith importances are VIG(i)；The vulnerability of system is
AV, according to systematic function ajThe weighted factor that member of imparting i is answered during to the importance VI (i) of each part of aircraft system distribution is
ωi, the weighted factor is determined by formula (5)：
<mrow>
<msub>
<mi>&omega;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mi>V</mi>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mi>V</mi>
<mi>I</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
2
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>&omega;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>;</mo>
</mrow>
In formula (5), ωiIt is part i weighted factor, subscript i span is all 1 ..., n；
Determine that the vulnerability index that part i is distributed is by formula (6)：
AVi=ωi·AV (6)
In formula (6), AVFor the vulnerability of aircraft, AViObtained vulnerability is distributed by all parts；
So far, the distribution of operational aircraft system vulnerability index is completed.
2. a kind of operational aircraft system vulnerability Allocation method as claimed in claim 1, it is characterised in that it is determined that each
Part byDuring killing probability and survival probability after secondary strike, pass throughEach portion is determined respectively
The killing probability and survival probability of part.
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| CN108509728B (en) * | 2018-04-04 | 2019-02-19 | 西北工业大学 | One kind weighing design method to extra large cooperation aircraft viability |
| CN108614938B (en) * | 2018-04-28 | 2019-06-18 | 西北工业大学 | A kind of Aircraft Survivability method for improving considering Campaign Process |
| CN112487558B (en) * | 2020-12-03 | 2022-08-19 | 中国航空工业集团公司沈阳飞机设计研究所 | Method for calculating vulnerability of control surface |
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