CN105608251A - BNSobol method for sensitivity analysis on precision of Helicopter fire control system - Google Patents

BNSobol method for sensitivity analysis on precision of Helicopter fire control system Download PDF

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CN105608251A
CN105608251A CN201510872978.1A CN201510872978A CN105608251A CN 105608251 A CN105608251 A CN 105608251A CN 201510872978 A CN201510872978 A CN 201510872978A CN 105608251 A CN105608251 A CN 105608251A
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高晓光
贺楚超
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Northwestern Polytechnical University
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Abstract

The invention provides a BNSobol method for sensitivity analysis on the precision of a Helicopter fire control system. The method comprises the steps of performing global sensitivity analysis of the influence of error sources on the precision of the fire control system by combining a Bayesian network and a Sobol index; establishing the Bayesian network according to priori knowledge; learning related parameters in the network through Bayesian estimation to obtain a probability that the precision of the fire control system reaches a specified level under the condition of taking different values for the error sources; and finally processing a probability result by utilizing Sobol method variance decomposition to obtain sensitivity coefficients of the error sources. The invention proposes a new sensitivity analysis mechanism combining the Bayesian network and the Sobol index method, thereby providing reference and theoretical support for performing the sensitivity analysis on the precision of the Helicopter fire control system under the condition of insufficient sample quantity, and providing an uncertain quick quantitative analysis concept for other large-sized complicated systems.

Description

The BNSobol method of helicopter fire control system precision sensitivity analysis
Technical field
The present invention relates to avionic fire control and intelligent decision and optimization field, especially helicopter fire control system field.
Background technology
Armed helicopter, by feat of its maneuverability, is being played the part of more and more important role in modernized war. MachineRifle, gun and rocket projectile etc. have proposed higher requirement without control weapon to the precision of helicopter fire control system, in reality is fought,Due to the complexity of battlefield surroundings, Prerequisite and target travel etc., cause fire control system precision to be subject to the shadow of many factorsRing. Analyze impact and the influence degree of these factors on attack precision very important to improving fire control system performance. Both at home and abroad allExisting research and analyse the impact of different error sources on helicopter fire control system precision, and provided and reduce error and carry high-precisionMeasure. But, each error source be not independent role in fire control system, often multiple error exists simultaneously and has stronger friendship therebetweenCoupling effect mutually. Therefore, carry out the sensitivity analysis of fire control system precision, thereby find out the phase between main error source and error sourceMutual effect just seems very necessary to the impact of final precision.
According to sphere of action, Sensitivity Analysis can be divided into local sensitivity analysis method and global sensitivity analysisMethod. Local sensitivity analysis is only checked the influence degree of single attribute to model; Global sensitivity analysis is checked multiple genusProperty total impact that model result is produced, and interaction between the analytic attribute impact on model output. The mould that it is exploredThe type input space is large, and analysis result has good robustness, therefore can be used as helicopter fire control system precision sensitiveness and dividesThe method of analysing. Several conventional global sensitivity analysis methods have: regression analysis (RA), Fourier's amplitude sensitiveness method of inspection(FAST), Response Surface Method (RSM), mutual information index method (MII) and Sobol index method etc. Wherein Sobol method relies on becomingThe distribution character of the stronger ability of group input factor analysis and linearity, monotonicity and the input to Effectiveness Evaluation Model etc. is wantedThe wide in range property of asking, becomes a kind of comparatively feasible method of carrying out weaponry sensitivity analysis. Sobol method is decomposed based on modelThought obtain respectively parameter 1,2 times and the susceptibility of high order more, can carry out the contribution proportion of output variance by parameterSensitiveness classification. In the time processing the combination of single variable or a little variable, calculate rapidly, workable. But because it isBased on the method for statistics, therefore when it come to more multivariable combination, amount of calculation is large, and operation is more difficult in actual applications. ThisOutward, its computational analysis is to carry out on a large amount of sample data bases, and this, answers especially aspect military project in a lot of fieldsUse and can have any problem.
Bayesian network (BayesianNetwork) can represent random uncertainty and the correlation of variable well, andCan carry out uncertain inference, not only can realize forward reasoning, derive posterior probability by prior probability, be derived by reasonAs a result, also can utilize formula to derive prior probability by posterior probability, derive reason by result. Research both domestic and external has respectivelyBayesian network is applied to the importance degree of the assessment of Model in Reliability Evaluation of Power Systems, Reliability of Mechanical System and element and sensitiveDuring degree is analyzed, and all obtain good result.
Summary of the invention
At military industry field, because Cost Problems is often difficult to for analysis and research provide a large amount of sample datas, this makes to passThe sensitivity analysis method of system is restricted, and cannot ensure precision of analysis.
In order to overcome the deficiencies in the prior art, the present invention creatively proposes to use and refers to based on Bayesian network and SobolThe BNSobol method that number combines is carried out the global sensitivity analysis of error source to fire control system Accuracy, utilizes BayesThe feature of network reasoning, sets up Bayesian network according to priori, by relevant parameter in Bayesian Estimation learning network, entersAnd reasoning obtains getting at each error source the probability that under different value condition, fire control system precision reaches specific grade, finally utilizeThe thought that Sobol method variance is decomposed is processed the sensitivity coefficient that just can obtain each error source to reasoning gained probability results.
The present invention can be good at solving the sensitivity analysis problem of system accuracy under the insufficient condition of data volume, and ensuresThe precision of analysis result.
The technical solution adopted for the present invention to solve the technical problems is:
Step 1: determine precision sensitivity analysis index
Adopt Sobol index method defined sensitiveness index, decompose by variance, model be decomposed into single parameter andThe mutual function of combination between parameter, the shadow of the variance by calculating single input parameter or input parameter collection to total output varianceRing the interaction between importance and the parameter of analytical parameters;
The each sensitiveness index definition of Sobol index method is as follows:
(1) main effect, also referred to as single order sensitiveness Index Definition isFor Xi" alone " to YThe contribution of variance, it is worth in [0,1];
(2) second order interaction is defined asFor the mutual effect of the twoThe impact of reply output;
Step 2: the Bayesian network model of setting up the sensitivity analysis of helicopter fire control system precision
Determine accuracy class according to error source size, set up naive Bayesian network:
Y represents accuracy evaluation index, and X1,…,X4Represent respectively different error sources, to variables set X={X1,X2,X3,X4, wherein XiThe codomain of ∈ X or state setriFor the state number of each child node, i.e. the value district of error sourceBetween number; D={C1,…,CnBe data sample, i.e. data set or database, ClBe an example, i.e. single test situation or dataA record in storehouse, refers to throw-off practice data one time at this;For the parametric variable of prior probability,Be illustrated in user and there is the hypothesis that state of knowledge ξ, network structure are S, XiFather node collection Pa there is the prerequisite of j stateUnder, variable XiGet the objective probability of k value,The codomain of Pa is { pa1,…paq, what q was Pa is allThe number of possible state, i.e. the number of degrees of precision index, note?
Following 3 hypothesis are proposed:
(1). random sample D is complete, in D, there is no the data of losing;
(2). parameter vector is separate, that is:
(3). parameter vector is that Dirichle distributes, that is:
Wherein, N 'ijkIndex coefficient or super parameter that > 0 distributes for Dirichle;
Step 3: utilize BNSobol method to carry out the precision sensitivity analysis of fire control system
First carry out Bayesian network parameter learning:
(1). the prior distribution of parameter
Wherein,
(2). the posteriority of parameter distributes:
Wherein, NijkTo meet in database DAnd the quantity of the situation of pa=j;
Want that by calculating the probability process of calculating is called Bayesian inference, is obtained by parameter learning in Bayesian networkLocal conditional probability distribution function, can draw accordingly with all error source intervals and combine corresponding specific precisionThe probability of index grade,Wherein j=1 ..., q, ki＝1,…,ri；
Calculate sensitiveness index:
(1) main effect
According to Sobol index method XiThe definition of main effectObtain in conjunction with Bayesian Network InferenceThe each probable value going out can directly be calculated main effect
V(Y)＝E(Y2)-E2(Y)(5)
In formula, n is error source value combination subscript,The value of i error source under the combination of n kind, in like manner:
In formulaThe k of i error sourceiIndividual value, andExcept xiN value group of outer other error sourceClose;
Formula (5～9) is brought intoJust can try to achieve error source XiMain effect;
(2) second order interaction
XiWith XjThe interaction of the two is defined asWherein,WithAll can obtain;
(x in formulaixj)kBe i and combine with k value of j error source, andExcept xiAnd xjOuter itsN the value combination of its error source;
Formula (10), (11) are brought intoDefinition can try to achieve XiWith XjThe interaction of the two.
Beneficial effect of the present invention is:
(1). establish the multiple main error source of helicopter fire control system precision, and considered that environmental factor is under rotorThe impact of wash and RANDOM WIND, makes analysis result have more practical significance.
(2). adopt the defined each sensitiveness index of Sobol index method, and utilize in the specific implementation Sobol method varianceThe thought of decomposing is carried out global sensitivity analysis, makes analysis result more comprehensively.
(3). by setting up the Bayesian network model of helicopter fire control system precision sensitivity analysis, according to sample dataCarry out network parameter study, and then according to the required probability of learning outcome reasoning, thereby in meeting required precision, reduceAnalyze required sample data amount, reduced to analyze required cost.
In a word, the present invention proposes a kind of new sensitivity analysis mechanism that combines Bayesian network and Sobol index method, forUnder the insufficient condition of sample size, carrying out the sensitivity analysis of helicopter fire control system precision provides reference and theoretical support, simultaneouslyA kind of thinking of uncertain rapid measuring fractional analysis is also provided for other large-scale complicated system.
Brief description of the drawings
Fig. 1 is the naive Bayesian network of fire control system precision of the present invention sensitivity analysis.
Fig. 2 is Bayesian Network Inference procedure chart of the present invention, and wherein, Y represents accuracy evaluation index, and X1,X2,X3,X4Represent respectively different error sources.
Fig. 3 is error source graph of a relation of the present invention.
Fig. 4 is rotor downwash flow field figure of the present invention.
Fig. 5 is RANDOM WIND FIELD simulation result figure of the present invention.
Fig. 6 is that attack from horizon level CCIP of the present invention aims at schematic diagram.
Fig. 7 is simulation analysis flow chart of the present invention.
Fig. 8 is the two kinds of each error source main effect of analytic approach gained comparison diagrams of the present invention.
Fig. 9 is the second order interaction comparison diagram between two kinds of each error sources of analytic approach gained of the present invention.
Detailed description of the invention
Below in conjunction with drawings and Examples, the present invention is further described.
Step 1: determine helicopter Error of FCS source and accuracy evaluation index
Adopt Sobol index method defined sensitiveness index, decompose by variance, model be decomposed into single parameter andThe mutual function of combination between parameter, the shadow of the variance by calculating single input parameter or input parameter collection to total output varianceRing the interaction between importance and the parameter of analytical parameters.
The each sensitiveness index definition of Sobol index method is as follows:
(1) main effect, also referred to as single order sensitiveness Index Definition isX has been describedi" alone "The contribution of the variance to Y, it is worth in [0,1], according to the size of main effect, each variable is carried out to sensitiveness sequence, main effectIndex is larger, shows that the variation of this variable is larger to the influence of change of output, therefore, controls the variation of output, and emphasis is justControl the variation of the input that main effect index is large;
(2) second order interaction is defined asThe friendship of the two has been describedThe impact of effect on output mutually;
One, determine error source
The error source that the present invention mainly studies is as follows: sensor (radar laydown error), inertial navigation (measure error), hanger(jitter error), environmental error (RANDOM WIND, rotor down-wash flow), because environmental error cannot manual control, therefore be taken as fixedValue, other error is all superimposed upon in standard value as white noise, and wherein between each error source, relation is as shown in Figure 3.
Under floating state, because rocket projectile is suspended on the below of Helicopter Main rotor, when rotor wing rotation, wash under generationFlow field, rocket projectile changes passing through the flight force and moment that this flow field makes to act on rocket projectile leaving after emitterThereby affect its initial trajectory track. Therefore lifting airscrew purling can not be ignored the impact of rocket bomb transmitting trajectory,In the time carrying out solution of fire control, should be taken into account. And for gun, because its initial velocity is larger, pass through the flow field time usedShort, and gun bullet volume is little, and therefore rotor down-wash flow is ignored compared with I its effect, and rotor downwash flow field is as shown in Figure 4.
The Mathematical Modeling of RANDOM WIND FIELD:
Due to wind to affect mechanism very complicated, thereby mainly in real work consider beam wind and range wind, and think horizontalWind and range wind are Normal Distribution, according to theoretical research and experiment test, obtain the covariance function of wind field:
Range wind:
Beam wind:
Simulation of Wind Field model according to covariance function formula (12), (13):
In formula: Kx(τ),Ky(τ) be the covariance function of range wind and beam wind random quantity; Sx(ω),Sy(ω) be range wind and horizontal strokeThe spectral density of wind random quantity; L is the period of change of simulation wind field; W1For calculating the excessive variable of wind-field model; V is bullet fortuneMoving speed; WxFor range wind wind speed; WyFor beam wind wind speed; ξx、ξyFor Normal DistributionStochastic variable; σwFor wind speedMean square deviation.
During taking V=100m/s, RANDOM WIND FIELD is example, σwValue is 5m/s, through emulation, obtains the emulation knot of RANDOM WIND FIELDFruit sees Fig. 5.
Two, determine accuracy evaluation index
Accuracy evaluation index adopts circular error probable (CEP), and helicopter is being attacked with the weapon such as gun, rocket projectileTime, what conventionally adopt is burst-firing, i.e. the multiple shell of disposable transmitting, and due to random errors such as RANDOM WIND and hanger shakesImpact can make these shells impact plane form scatter. Conventionally the CEP, solving by closeness assessment method falls apart relativelyCloth center, but not relative aiming point. Accuracy at target should be the relative aiming point dispersion level of bullet drop point, and size equals to aim atPoint is the center of circle, the round territory radius r that impact probability is 0.5.
Step 2: set up helicopter fire control system model
In precision analysis, C represents a series of grades of precision index, A1,…,AnRepresentative affects the error source of precision, rootDetermine accuracy class according to error source size, set up naive Bayesian network as shown in Figure 1 for this reason:
In Fig. 1, Y represents accuracy evaluation index, and X1,…,X4Represent respectively different error sources, to variables set X={X1,X2,X3,X4, wherein XiThe codomain of ∈ X or state setriFor the state number of each child node, i.e. error sourceInterval number; D={C1,…,CnBe data sample, i.e. data set or database, ClBe an example, i.e. single test situationOr a record of database, refer to throw-off practice data one time at this;For the ginseng of prior probabilityNumber variable, is illustrated in user and has the hypothesis that state of knowledge ξ, network structure are S, XiFather node collection Pa there is j statePrerequisite under, variable XiGet the objective probability of k value,The codomain of Pa is { pa1,…paq, q is PaThe number of all possible states, i.e. the number of degrees of precision index, note?
Following 3 hypothesis are proposed:
(1). random sample D is complete, in D, there is no the data of losing;
(2). parameter vector is separate, that is:
(3). parameter vector is that Dirichle distributes, that is:
Wherein, N 'ijkIndex coefficient or super parameter that > 0 distributes for Dirichle;
Attack over the ground Fire Control Theory CCIP
Continuously computed impact point (ContinouslyComputedImpactPoint, CCIP) aims at principle, is to look squarelyWhen demonstration/weapon-aiming system, integrated fire control system are implemented bombing and air-to-ground fire, the one generally adopting aims at formerReason.
Shown in Fig. 6, be at (OXYZ)HMutual alignment and the movement relation of carrier aircraft in the coordinate system of course, bullet, target.Aircraft velocity vector and XHAxially consistent. Carrier aircraft fire control computer is according to carrier aircraft flying height H, air speed V1, weapons and ammunitions performanceThe Prerequisites such as parameter and wind velocity U, wind angle ε, if calculate continuously current projection, this bullet point of impact C on the groundPosition, on head-up display, show, pilot, by observing point of impact C, forms sight line. Use at O place, incident pointSight line run-home M point projection, bullet hit M point after bullet fall time T.
Point of impact C claims again demolition point or bullet drop point. Aiming point B refers to the intersection point on sight line and ground, is not aiming atWhen error, aiming point is point of impact C in fact namely.
The position of point of impact C, can be with C point at course coordinate system (OXYZ)HIn 3 coordinates represent,
Longitudinally range: AXH＝A0+UTcosε(15)
Side direction range: AYH＝UTsinε(16)
Vertical range: AZH＝H(17)
In formula
A0---the calm range of-----bullet;
T---------bullet lowering time.
The position of point of impact C, also can use range vectorVirtual course coordinate system (OXYZ)HXHTwo corners of axleRepresent range vector with the mould of vectorX relativelyHAxle (is V1Direction) adopt Y-Z-X mode to turn over angle μCH-νCH-0，Be easy to obtain following result according to Fig. 6, that is:
Negative sign in formula, illustrates by the right-hand rule, diagram μCHAngle should be negative value.
Without control weapon motion model
In the time separating gun, rocket projectile etc. without control weapon center of mass motion, hypothesis below comprehensive proposition:
(1). within the whole flight time of bullet, establish its movement velocity direction and overlap with playing the axle direction of motion all the time, be i.e. nutatingAngle δ ≈ 0, air drag position is by barycenter, and direction is contrary with velocity attitude. Just can be by Projectile Motion based on this hypothesisRegarding as is the motion of a particle;
(2). establish thrust P or thrust acceleration a by barycenter, its direction is identical with velocity attitude, that is rocket projectile motorIt is complete ideal situation;
(3). because range is little, thereby can suppose that acceleration of gravity is a constant, direction is vertical downwards;
(4). earth curvature and Corioli's acceleration are all ignored;
(5). pressure, temperature, humidity and the proportion of air is standard value on ground, and they are also marks by the distribution of heightAccurate;
Under supposed premise, specify: meteorological condition is air arm's standard meteorological conditions. Gravity acceleration g=9.806m/s2; Ground standard atmospheric pressure value h0=760 millimetress of mercury; Ground standard virtual temperature τ0=288.4 ° of K; Thermograde G=5.862×10-3Degree/rice; Air gas constant R=29.27 rice/degree; Ground air proportion standard value γON＝1.225kg/m3。
1.. gun motion model
Gun center of mass motion equation:
Known according to aviation exterior ballistics again:
J＝CHτ(y1)G(vτ)v(22)
τ＝288.4-5.862×10-3×y1(25)
Primary condition: in the time of t=0, x=0, y=0, z=0, v0For gun launch velocity degree.
By subsidiary equation (22)～(29) and according toTable and corresponding primary condition, available runge kutta method solutionDifferential equation group draws the theoretical trajectory drop point set of data.
In equation, J is air drag acceleration above, and γ is air specific weight, and v is velocity of shot, and τ is virtual temperature, and y isThe displacement of gun vertical movement, direction is vertical, and h is air pressure downwards, and C is ballistic coefficient, and a is the velocity of sound of bullet height of living in,y1For bullet is apart from ground level. WhereinFor the resistance coefficient of bullet, its value is relevant with velocity of shot, can be byTable is carriedThe resistance coefficient when partial data of confession utilizes Lagrange's interpolation to try to achieve bullet arbitrary speed.
Because the gun carriage on helicopter is movable, gun carriage is rotatable, therefore at the beginning of gun carriage is rotated down and makes weaponVelocity and carrier aircraft velocity form weapon angle of site μwTime, only need to change initial transmissions condition: in the time of t=0, x＝0,y＝0,z＝0，voy＝v0sinμw，
2.. rocket projectile motion model
Rocket projectile motion model is similar to gun, after transmitting, all in without control state, does difference according to different launching conditionsThe parabolic motion of dive angle. But it and gun have again difference, rocket bomb transmitting initial velocity is less than gun, but rocketBullet itself is from carrying fuel, and the motion after transmitting is divided into powered phase and post-boost phase two parts. Powered phase utilizes fuel combustion to produceThrust is done accelerated motion, and the motion of post-boost phase is identical with gun.
In formula:
Wherein:
ω is explosive payload; q0For bullet starting weight; tKFor the burning duration; ueFor effective exhaust velocity.
v0For rocket bomb transmitting initial velocity (speed while penetrating slide rail section), primary condition and solve trajectory data methodThe same with gun. A thrust acceleration only acts on powered phase, and when post-boost phase, its value is zero.
Step 3: utilize BNSobol method to carry out the precision sensitivity analysis of fire control system
First carry out Bayesian network parameter learning:
(1). parameter prior distribution
Wherein,
(2). the posteriority of parameter distributes:
Wherein, NijkTo meet in database DAnd the quantity of the situation of pa=j;
Want that by calculating the probability process of calculating is called Bayesian inference in Bayesian network, in theory by Joint DistributionCan infer any in Bayesian network inquisitive probability, obtained local conditional probability by parameter learning and dividedCloth function, accordingly can reasoning draws with all error source intervals and combines the general of corresponding specific precision index gradeRate,Wherein j=1 ..., q, ki＝1,…,ri; Its inference method is (this process as shown in Figure 2By means of the Bayesian tool box of Matlab):
In Fig. 2, reasoning evidence (evidence) is corresponding error source value combination, and class is accuracy evaluation index.
Calculate each sensitiveness index:
(1) main effect
According to Sobol index method XiThe definition of main effectObtain in conjunction with Bayesian Network InferenceThe each probable value going out can directly be calculated
V(Y)＝E(Y2)-E2(Y)(5)
In formula, n is error source value combination subscript,The value of i error source under the combination of n kind, in like manner:
In formulaThe k of i error sourceiIndividual value, andExcept xiN value group of outer other error sourceClose;
Formula (5～9) is brought intoJust can try to achieve error source XiMain effect;
(2) second order interaction
XiWith XjThe interaction of the two is defined asWherein,WithAll can obtain;
(x in formulaixj)kBe i and combine with k value of j error source, andExcept xiAnd xjOuter itsN the value combination of its error source;
Formula (10), (11) are brought intoDefinition can try to achieve XiWith XjThe interaction of the two.
Replace corresponding error source and interaction with following symbol:
x1--carrier aircraft yaw angle measure error;
x2--hanger randomized jitter error;
x3--target distance measurement error;
x4--target bearing collimating fault;
This sentences helicopter in hover rocket projectile and attacks over the ground as example, and the emulation of other attack condition similarly.
Entirety simulation analysis flow process is as Fig. 7.
(1), initial parameter setting
Table 1 emulation initial parameter arranges
The poor scope setting of the each error mean square of table 2
x1 x2 x3 x4
0～0.5 0～0.5 0～2 0～0.5
(2), the Sobol index sensitiveness index based on Monte Carlo is calculated
If each error mean square difference is obeyed and is uniformly distributed in the listed scope of upper table, first, adopt the method for random samplingGenerate two input matrix A, B, each provisional capital in two matrixes is the concrete value combination of a group of four kinds of error sources.
Note C3The 3rd row of matrix B are changed into the 3rd row gained matrix of matrix A; Note C-3Change the 3rd row of matrix A into matrixThe matrix of the 3rd row gained of B.
In like manner definable C1,C2,C4,C-1,C-2,C-4And C1,2,C-1,-2Deng. Using these matrixes as error source data, foldedBe added in standard value and bring simulation model into, the output vector that just can obtain model is precision index CEP. Note yA,yB,yCBe respectivelyCorresponding output column vector corresponding to input matrix.
Can obtain following estimation by Monte Carlo method:
Note
The estimation of sensitiveness index is carried out as follows:
Error source x3Main effect indexEstimation:
Error source x1With x3Second order interaction indexEstimation:
Adopt repeatedly not several error source data on the same group of random sampling of said method, bring model emulation into and calculate, can obtain respectivelyThe susceptibility sequence of error source on the impact of rocket projectile accuracy at target. Find to level off to 5000 groups time in data volume, analysis result byGradually closing is held back, and lists herein each error source main effect and the second order of 5000 groups of data and 500 groups of data analysis gained are imitated alternatelyThe result of calculation of answering:
Each error source main effect sequence under table 35000 group data
Second order interaction under table 45000 group data between each error source
x1 x2 x3 x4
x1 -- 0.109 0.217 0.155
x2 0.109 -- 0.182 0.179
x3 0.217 0.182 -- 0.366
x4 0.155 0.179 0.366 --
Each error source main effect sequence under table 5500 group data
Error source Main effect Sequence
x1 0.208 3
x2 0.598 1 14 -->
x3 0.598 1
x4 0.503 2
Second order interaction under table 6500 group data between each error source
x1 x2 x3 x4
x1 -- 0.251 0.048 0.1755
x2 0.251 -- 0.438 0.295
x3 0.048 0.438 -- 0.4025
x4 0.1755 0.295 0.4025 --
(3), the sensitiveness index based on BNSobol method is calculated
Input and output discretization, turns to following interval by discrete each error source value:
The each error source interval of table 7
Be divided into two grades by the large young pathbreaker's precision index of CEP:
Table 8 precision index grade classification
On the basis of above-mentioned processing, repeatedly randomly draw and do not count on the same group simulation sample data as true target practice data,Carry out parameter learning by means of MatLab Bayesian Networks Toolbox (BayesianNetorksToolbox, BNT), findData volume is greater than at 400 o'clock, and result restrains gradually. Get 500 groups of sample datas at this and analyze acquired results, under each parameter of network is shown inTable:
Table 9 network parameter learning outcome table
θ in tableijkValue Representative errors source xiIn the time of the each interval of k, CEP reaches the probability of the each accuracy class of j. FromIn table, can find out that in network, each parameter value not presents monotonic increase or the relation of successively decreasing, each error source in this explanation initial dataBetween there is coupling interaction effect. The parameter being obtained by study is carried out reasoning and just can be acquired under 256 kinds of error source value combinationsAccuracy at target, and then can obtain each sensitiveness index.
Result contrast by two kinds of precision sensitivity analysis methods is known:
Although (1). can find out that from analysis result comparison diagram 8 and Fig. 9 two kinds of analytical method acquired results are not to kiss completelyClose, but all can draw following 2 conclusions: 1.. while acting on fire control system in multiple error source, carrier aircraft yaw angle is measured mistake simultaneouslyPoor and target bearing collimating fault has material impact to rocket projectile shooting precision, is main error source; 2.. between each error source, all depositAt stronger second order interaction, wherein carrier aircraft yaw angle measure error and target bearing collimating fault mutual effect between the twoShould be the most remarkable.
(2) the statistical analysis of .Sobol method needs a large amount of sample datas, and this is difficult to accomplish in actual applications sometimes. With directlyRising the precision analysis of machine fire control system is example, in the time that data volume is abundant, provides under 5000 groups of data cases Sobol method to analyzeTo correct conclusion. And in the time that data volume is insufficient, only provide 500 groups of data, traditional Sobol method is analyzed acquired results changeIt is no longer accurate to obtain. In military project, the data of especially practicing shooting, each group has all consumed a large amount of funds, and itself is just very rare. HereinOnly 4 kinds of error sources are analyzed, when error source increases or when model is more complicated, the required sample size of Sobol method is very fastIncrease, therefore the method should use and obviously become very difficult. But BNSobol method is analyzed and is drawn in the time only having 500 groups of dataApply the approximate result of traditional Sobol index method when abundant with data volume, therefore greatly reduced to analyze required cost.

Claims (1)

1. a BNSobol method for helicopter fire control system precision sensitivity analysis, is characterized in that comprising the steps:
Step 1: determine precision sensitivity analysis index
Adopt the defined sensitiveness index of Sobol index method, decompose by variance, model is decomposed into single parameter and parameterBetween the mutual function of combination, by the variance of calculating single input parameter or input parameter collection, the impact of total output variance is comeInteraction between importance and the parameter of analytical parameters;
The each sensitiveness index definition of Sobol index method is as follows:
(1) main effect, also referred to as single order sensitiveness Index Definition isFor Xi" alone " side to YPoor contribution, it is worth in [0,1];
(2) second order interaction is defined asFor the interaction pair of the twoThe impact of output;
Step 2: the Bayesian network model of setting up the sensitivity analysis of helicopter fire control system precision
Determine accuracy class according to error source size, set up naive Bayesian network:
Y represents accuracy evaluation index, and X1,…,X4Represent respectively different error sources, to variables set X={X1,X2,X3,X4}，Wherein XiThe codomain of ∈ X or state setriFor the state number of each child node, the i.e. interval of error sourceNumber; D={C1,…,CnBe data sample, i.e. data set or database, ClBe an example, i.e. single test situation or databaseA record, refer to throw-off practice data one time at this;For the parametric variable of prior probability,Be illustrated in user and there is the hypothesis that state of knowledge ξ, network structure are S, XiFather node collection Pa there is the prerequisite of j stateUnder, variable XiGet the objective probability of k value,The codomain of Pa is { pa1,…paq, what q was Pa is allThe number of possible state, i.e. the number of degrees of precision index, note?
Following 3 hypothesis are proposed:
(1). random sample D is complete, in D, there is no the data of losing;
(2). parameter vector is separate, that is:
(3). parameter vector is that Dirichle distributes, that is:
Wherein, N 'ijkIndex coefficient or super parameter that > 0 distributes for Dirichle;
Step 3: utilize BNSobol method to carry out the precision sensitivity analysis of fire control system
First carry out Bayesian network parameter learning:
(1). the prior distribution of parameter
Wherein,
(2). the posteriority of parameter distributes:
Wherein, NijkTo meet in database DAnd the quantity of the situation of pa=j;
Want that by calculating the probability process of calculating is called Bayesian inference, has obtained office by parameter learning in Bayesian networkThe conditional probability distribution function of portion, can draw accordingly with all error source intervals and combine corresponding specific precision indexThe probability of grade,Wherein j=1 ..., q, ki＝1,…,ri；
Calculate sensitiveness index:
(1) main effect
According to Sobol index method XiThe definition of main effectDraw in conjunction with Bayesian Network InferenceEach probable value can directly be calculated main effect
V(Y)＝E(Y2)-E2(Y)(5)
In formula, n is error source value combination subscript,The value of i error source under the combination of n kind, in like manner:
In formulaThe k of i error sourceiIndividual value, andExcept xiN value combination of outer other error source;
Formula (5～9) is brought intoJust can try to achieve error source XiMain effect;
(2) second order interaction
XiWith XjThe interaction of the two is defined asWherein,WithAll can obtain;
(x in formulaixj)kBe i and combine with k value of j error source, andExcept xiAnd xjOuter otherN value combination of error source;
Formula (10), (11) are brought intoDefinition can try to achieve XiWith XjThe interaction of the two.
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