CN103150446B - Near space vehicle modelling verification and Simulation Methods - Google Patents

Abstract

The present invention relates near space vehicle technology.For provide based near space vehicle model dynamic time sequence export, the New model checking system of system-level consistency check, the qualutative model provided based on monte carlo method is verified, venture analysis is carried out to model, comprehensively treat verification model and carry out conforming inspection, and provide and verify criterion intuitively, the technical scheme that the present invention takes is: near space vehicle modelling verification and Simulation Methods, comprises the steps: 1. to carry out qualitative checking based on Monte Carlo simulation method to it; 2. the quantitative model based on Time Domain Analysis is verified; 3. the quantitative model based on venture analysis is verified, model parameter is considered as risk, providing the criterion of quantitative model checking intuitively, provide model standard of comparison when there is multiple model to be verified, and can verification model being used with and providing the scope of safe handling safely.The present invention is mainly used near space vehicle design.

Description

Near space vehicle modelling verification and Simulation Methods

Technical field

The present invention relates near space vehicle technology, relate to the modelling verification problem of aerospace field.Relate generally to qualitative, the quantitative model checking of near space vehicle complex model.Specifically, near space vehicle modelling verification and Simulation Methods is related to.

Background technology

Near space vehicle structural design, material behavior, mechanical characteristic, high-speed air fluid are all different from projectile flight device or traditional aircraft to the impact of body.In order to describe the near space vehicle characteristics of motion in detail and clearly, need to describe hypersonic fluid behaviour, engine characteristics, structural elasticity characteristic, pneumatic/propelling/structure Coupling characteristic, topworks's characteristic etc. in modeling process comprehensively.Modelling verification work is the follow-up study content of modeling work, on the one hand, can error be there is in modeling process, although modeling work person wish model to set up more accurately better, require modeling personnel to provide to fit like a glove that the mathematical model of realistic model output characteristics is unpractical.The model set up always and between true model there are differences.On the other hand, model simplification process can make model simplify, and inevitably introduces model error simultaneously, makes to there are differences between simplified model and master pattern.In addition, due to the X factor of external environment, parameter error and measuring error etc., also can cause the mathematical model being finally supplied to user to depart from real system model.Therefore need research model proof theory, pass judgment on the size of difference between institute's Modling model and true model, and with the reliability of this evaluation model.

Early stage modeling personnel have recognized the validity taking certain measure that the mathematical model oneself provided is described, the method of most employing is the output of the model of foundation exported with true model intuitively to contrast in a graphical form, or only from certain part of model start with (as engine, actuator etc.) do the comparative analysis of data, do not form a set of independently modelling verification theoretical system being applicable near space vehicle.More not from the angle of model user, consider the reliability of institute's Modling model, consistance and security from the angle of overall system performance comprehensively.But, it is necessary for setting up the modelling verification theoretical system being independently applicable near space mathematical model, reason mainly contains following three aspects: 1. the theory of modeling work librarian use mostly is Analysis on Mechanism or simulation wind tunnel test methods, if model simplification work also will apply other way of thinking of theories, and modelling verification work can not be subject to the constraint of modeling method, do not rely on these theoretical systems.2. set up a set of independently modelling verification theoretical system, modelling verification work objective and fair more can be made, be widely used in the work of evaluation model.3. not only can modeling personnel pay close attention to mathematical model and reflect true model, and the user of model is often concerned about the reliability that modeling personnel supply a model more, therefore, needs that independently modelling verification is theoretical objectively connects modeling work personnel and model user of service.Therefore, the research and development of modelling verification theory, not only will contribute to the development of modeling work, more provide theoretical foundation by the reliable use for model.

At present, the research of modelling verification work is at the early-stage not yet to depart from modeling work, particularly for the near space vehicle of complexity, lack suitable model verification method, be applicable to the modelling verification theoretical system that can provide Qualitative and quantitative analysis result of near space vehicle requirement in practical systems simultaneously in the urgent need to one.This technology can to supply a model the feedback suggestion of checking angle for modeling work, for controlling to provide design and decision-making foundation, thus can for aircraft final safe, stable, reliably fly and give security.

Summary of the invention

The present invention is intended to overcome the deficiencies in the prior art, provides to export based near space vehicle model dynamic time sequence, the New model of system-level consistency check checking system.While providing the qualutative model checking based on monte carlo method, respectively from the regularity of distribution, development trend, the quantitative model that the angle of metric space provides based on time-domain analysis is verified, finally venture analysis is carried out to model, comprehensively treat verification model and carry out conforming inspection, and provide and verify criterion intuitively, for achieving the above object, the technical scheme that the present invention takes is: near space vehicle modelling verification and Simulation Methods, comprise the steps: 1. to carry out qualitative checking based on Monte Carlo simulation method to it, answer the problem that can model to be verified react the dynamic perfromance of master pattern strictly according to the facts, 2. the quantitative model based on Time Domain Analysis is verified, respectively from the regularity of distribution, development trend, metric space three angles, provides model to be verified and master pattern consistency check with quantitative form comprehensively, 3. the quantitative model based on venture analysis is verified, model parameter is considered as risk, providing the criterion of quantitative model checking intuitively, provide model standard of comparison when there is multiple model to be verified, and can verification model being used with and providing the scope of safe handling safely.

1. step is specially further: first determine its regularity of distribution according to the concrete physical meaning and acquiring way that comprise uncertain parameter, and according to 3 δ principles, determine the span of parameter, after determining Monte Carlo simulation number of times, each emulation, all according to the stochastic distribution rule random value of these parameters, generates curve of output race; Then the qualitative master pattern that compares exports the curve of data and model output data curve race to be verified, if the two differs greatly, then need further correction model, if the two difference is little, illustrate that the output of simplified model can reflect the statistical property that master pattern exports; And then, carry out Monte Carlo simulation convergence, obtain the gang's curve of output about simplified model, for the output valve outside 90%, be referred to as the boundary value of output quantity, this region is just called bounds, the some Output rusults of random selecting in this bounds, and take out the value of the uncertain combination of sensitivity corresponding to these several groups output, utilize the value of these uncertain combinations and the simulation times of its correspondence, further aircraft can be carried out at loop simulation.

2. step is specially further: first, adopts fiducial interval consistency check method, and from the angle of Statistical Distribution, in conjunction with the method for test of hypothesis in statistical inference, rational judgment dynamic time sequence to be verified exports the consistance of Data distribution8 rule; Secondly, adopt Grey Incidence Analysis, from the angle of development trend and spatial shape, response curve consistance is assessed; Finally, adopt Distance Test Method, from space length angle, use statistical study and hypothesis testing method, provide response curve distance consistency check result.

Respectively from the regularity of distribution, development trend and metric space three angles treat verification model dynamic time sequence export carry out quantitative time domain checking concrete steps be:

1. regularity of distribution consistance is checked: obtain master pattern sample output sequence X={x (t), t=1,2 ..., n} and simplified model sample group output sequence Y _i={ y _i(t), t=1,2 ..., n}, i=1,2 ..., m, sample size meets statistical demand, wherein n represents master pattern and simplified model output sampling number, and m represents simplified model output sample number, the fiducial interval size in each moment of node-by-node algorithm, repeat this process, the fiducial interval completing each moment calculates, and carries out Jarque--Bera statistics control, if data meet normal distribution for t data, then construct the fiducial interval of normalized set t as follows, first definition, simple model output sample average and variance as follows:

$\stackrel{\‾}{y}\left(t\right)=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{y}_i\left(t\right),t=\mathrm{1,2},...n$

${\mathrm{\σ}}^2\left(t\right)=\frac{1}{m-1}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{[y_i\left(t\right)-\stackrel{\‾}{y}\left(t\right)]}^2,t=\mathrm{1,2},...,n$

s(t)＝σ(t)

Wherein, representative sample average, σ ²(t) representative sample variance, s (t) representative sample standard deviation, export for simplification y (t) model meeting normal distribution, under given level of significance α, its confidence upper limit is:

$Y_u\left(t\right)=\stackrel{\‾}{y}\left(t\right)+\sqrt{\frac{m+1}{m}}{t}_{\mathrm{\α}/2}(m-1)s\left(t\right)$

Confidence lower limit is:

$Y_l\left(t\right)=\stackrel{\‾}{y}\left(t\right)-\sqrt{\frac{m+1}{m}}{t}_{\mathrm{\α}/2}(m-1)s\left(t\right)$

If statistics control does not meet normal distribution hypothesis, then by simplified model output sample group Y _i={ y _i(t), t=1,2,, n}, i=1,2,, m at each moment t according to sorting from big to small, for given confidence level γ, the value subscript p of confidence lower limit is p=[γ m+1], wherein, ' [] ' represents rounding operation, the value subscript q of confidence upper limit be q=[(1-γ) (m+1)] so the confidence upper limit of t be: y _pt (), namely the confidence upper limit of t is the p large sample numerical value of t sample sequence, and confidence lower limit is: y _q(t), namely the confidence lower limit of t is the q large sample numerical value of t sample sequence, draw fiducial interval distribution plan, by observation and analysis fiducial interval distribution plan, judge whether master pattern and simplified model Output rusults meet regularity of distribution consistance;

2. development trend consistance is checked: definition Δ _oibe the different information between 2:

Δ _oi＝|x _o(k)-x _i(k)|,i∈I,k∈{1,2,...n}

In above formula, I refers to output sample space, and k is emulation sequential, and master pattern exports as x ₀, difference space is: Δ={ Δ _oi(k) }, if only have simulation data, so an I={1}, difference space lower limit parameter is: also environmental parameter on the two poles of the earth of i.e. difference; Difference space lower limit parameter is: also be environmental parameter under the two poles of the earth of difference, resolution ratio: ξ ∈ [0,1], according to minimum information principle, gets 0.05, under the condition meeting grey correlation four axiom, and structure grey correlation space Δ _gR=(Δ, ξ, Δ _oi(max), Δ _oi(min)) grey incidence coefficient can be defined in grey correlation space as follows, original grey incidence coefficient:

$r(x_o\left(k\right),x_i\left(k\right))={(\frac{\underset{i}{\min }\underset{k}{\min }{\mathrm{\Δ}}_{\mathrm{oi}}\left(k\right)+\mathrm{\ξ}\underset{i}{\max }\underset{k}{\max }{\mathrm{\Δ}}_{\mathrm{oi}}\left(k\right)}{{\mathrm{\Δ}}_{\mathrm{oi}}\left(k\right)+\mathrm{\ξ}\underset{i}{\max }\underset{k}{\max }{\mathrm{\Δ}}_{\mathrm{oi}}\left(k\right)}\×e^{-{\mathrm{\η}}_{\mathrm{oi}}\left(k\right)})}^{\frac{1}{2}}$

Wherein η _oi(k)=2 × Δ _oi(k)/| x _o(k)+x _i(k) |, the output of master pattern is x _ok (), k is the integer from time point 1 to n, and n counts in the sampling time, and the output of simplified model is x _i(k), the implication of k is the same, and i represents i-th simplified model output sample, and the average grey incidence coefficient of curve is:

$\mathrm{\γ}(x_o,x_i)=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\γ}(x_o\left(k\right),x_i\left(k\right))$

The average grey incidence coefficient of the overall situation and each moment grey incidence coefficient size, sampling number, and number of samples is correlated with, and draws grey correlation trend map, analyzes grey correlation trend map and calculates ensemble average grey incidence coefficient, drawing consistency check conclusion;

3. metric space consistance is checked: first obtain m ₁individual model output sample to be verified i=1,2 ..., m ₁, calculate master pattern output time series X and simplified model output time series average between mahalanobis distance

$D(X,\stackrel{\‾}{Y^1})=\sqrt{\frac{1}{n}(X-\stackrel{\‾}{Y^1})S^{-1}{(X-\stackrel{\‾}{Y^1})}^T}$

S-matrix is the covariance matrix of simplified model output sample, and then obtains m ₂individual model output sample to be verified; i=1,2 ..., m ₂, calculate with between Mean Mahalanobis distance

$D(Y_i^2,\stackrel{\‾}{Y^1})=\sqrt{\frac{1}{n}(Y_i^2-\stackrel{\‾}{Y^1})S^{-1}{(Y_i^2-\stackrel{\‾}{Y^1})}^T}$

If d is i=1,2 ..., m ₂in meet formula 's number, for given level of significance α, if then can conclude that between master pattern and simplified model, response curve metric space exists significant difference, namely not accept former consistance hypothesis.

Can the quantitative model checking based on venture analysis be specially further: model uncertain parameter is considered as risk factors, uses safely, y from the angle verification model of model user _r(x, θ) represents the output of simplified model, is subject to model state x and uncertain parameter θ=[θ ₁..., θ _i..., θ _p] ^timpact, illustrate in modeling process, simplified model may comprise multiple uncertain parameter, model export be y is that m dimension is compacted.When Model Parameter is in certain limit during interior random value, p is uncertain parameter number, and Θ represents that initial parameter span is provided by modeling personnel, the output of system will change, θ belongs to this random vector compacted, and illustrates the uncertain parameter in modeling process, by Multi-dimensional probability density function f _θx () describes, y _r(x, θ), under the impact of stray parameter vector θ, for belonging to the random vector compacting Y, tabular form model to be verified exports, and in order to analyze the performance that simplified model exports, provides the definition of performance index:

The performance index that model exports are the function of model output, contain the information of quantity of state, have expressed aircraft in the flight path expected (expectedflightenvelope), performance (vehicleperformance) quality of operation, concrete form of Definition is as follows:

Here y (x) represents the output quantity of master pattern, y _r(x, θ) represents the output quantity of simplified model, wherein, for k ties up performance function, illustrate the concrete constraint to performance function, represent lower bound requirement, represent upper bound requirement, first consider the upper bound requirement of performance index the probability that model output meets upper bound performance index requirement can be expressed as p _y(Ω _y), wherein represent model output set when meeting upper bound performance index needs; Simplify the Probability p that system performance to be verified meets upper bound performance index requirement _y(Ω _y) computing formula is:

$p_Y\left({\mathrm{\Ω}}_y\right)={\∫}_{\mathrm{\θ}}{\underset{\‾}{\mathrm{\δ}}}_y\left[y_r(x,\mathrm{\θ})\right]d_{\mathrm{\θ}}\left(\mathrm{\θ}\right)\mathrm{d\θ}$

In above formula, be defined as following two-valued function:

Sampling emulation mode is utilized to estimate above formula:

Wherein, n ' _sMn _sMrepresent sampling number, calculate model to be verified according to the following formula and export the probability meeting performance index:

And then consider the lower bound requirement of performance index system exports the probability meeting the requirement of performance index lower bound and can be expressed as computing formula is:

$p_Y\left({\mathrm{\Ω}}_y^c\right)={\∫}_{\mathrm{\θ}}{\stackrel{\‾}{\mathrm{\δ}}}_y\left[y_r(x,\mathrm{\θ})\right]d_{\mathrm{\θ}}\left(\mathrm{\θ}\right)\mathrm{d\θ}$

Sampling emulation mode is utilized to estimate above formula:

$p_Y\left({\mathrm{\Ω}}_y^c\right)\≅\underset{i=1}{\overset{n_{\mathrm{SM}}^{\′}}{\mathrm{\Σ}}}{\stackrel{\‾}{\mathrm{\δ}}}_y\left[y_{r,i}(x,\mathrm{\θ})\right]/n_{\mathrm{SM}}^{\′}$

Wherein, n ' _sMrepresent emulation sampling number.In above formula, be defined as following two-valued function:

Consider the upper bound and the lower bound requirement of performance index, after calculating, be simplified the probability that model output performance function meets performance index requirement, when time, illustrate that corresponding uncertain parameter value can cause model to use dangerous, will meet the output valve record of performance requirement, and record corresponding uncertain parameter value θ ^*, represent the output of the system when uncertain parameter gets particular value; N ' will be emulated _sM+ n _sMin secondary, undesirable data point is removed, and obtains wherein for n ' _sMthe simulation times selected in secondary emulation, for n _sMthe simulation times selected in secondary emulation; Now, the reduced-order model after screening exports the probability of meeting property index request $p_Y\left({\mathrm{\Ω}}_y\right)+p_Y\left({\mathrm{\Ω}}_y^c\right)\≅\underset{i=1}{\overset{{\tilde{n}}_{\mathrm{SM}}^{\′}}{\mathrm{\Σ}}}{\underset{\‾}{\mathrm{\δ}}}_y\left[y_{r,i}(x,\mathrm{\θ})\right]/{\tilde{n}}_{\mathrm{SM}}^{\′}+\underset{i=1}{\overset{{\tilde{n}}_{\mathrm{SM}}}{\mathrm{\Σ}}}{\stackrel{\‾}{\mathrm{\δ}}}_y\left[y_{r,i}(x,\mathrm{\θ})\right]/{\tilde{n}}_{\mathrm{SM}}=1,$ Generate these multi-Dimensional parameters valued space exported owing to can ensure that output performance meets the demands, this multi-C parameter space is the operational envelope of model to be verified, is expressed as

Technical characterstic of the present invention and effect:

This modelling verification theoretical system may be used for the checking of near space vehicle mathematical model, be not subject to the restriction of model form, can be applied in the following aspects: 1, checking adopts the near space vehicle mathematical model that simulation wind tunnel methods is set up, and verifies that can this experimental mathematics model react the dynamic perfromance of real system strictly according to the facts.2, checking adopts the near space vehicle mathematical model that mechanism based method analysis is set up, and verifies that can this mechanism mathematical model react the dynamic perfromance of real system strictly according to the facts.3, distinguish and compare by multiple mechanism or seminar, adopting the near space vehicle mathematical model that distinct methods provides, application quantitative model verification method obtains quantitative comparative result, and for model, user provides decision-making foundation.4, on the basis of known high-fidelity mathematical model, application model short-cut method carries out simplification to this high-fidelity model and is simplified model, the consistance of checking simplified model and master pattern.

In application in above three, the modelling verification theoretical system that the present invention provides, can provide the modelling verification conclusion of following four aspects for model user for model to be verified:

1, can mathematical model to be verified react the dynamic perfromance of real system strictly according to the facts: the method adopting qualutative model checking, in the mode of statistical test, from the angle of figure, be the ability of the actual near space vehicle flight data dispose of model prediction to be verified, provide preliminary modelling verification result.

2, the time domain consistance of mathematical model dynamical output to be verified and true model: respectively from the angle of the regularity of distribution, development trend, metric space, adopt time domain quantitative model verification method, on the basis tentatively providing qualitative checking conclusion, the time domain consistency checking conclusion of quantitative.

3, can mathematical model to be verified be used safely: be considered as the uncertain parameter in model affecting the risk factors that model uses, and the user for model supplies a model range of safety operation, to reduce for the purpose of model application risk, provides comprehensive modelling verification.

Social benefit and economic benefit: the research of the present invention near space vehicle has very important promotion meaning.The present invention can provide effective Model Simplification Method and model verification method, not only alleviate the contradiction of mathematical model increasingly sophisticated at present and the existence between model analysis and Controller gain variations, contribute to the model credibility improving the close to space vehicle system development initial stage simultaneously, for the reliability application of model provides foundation, accelerate the process that new model comes into operation, reduce application risk, shorten research cycle, not only rapidly and efficiently but also reduce expenses.Near space vehicle, as potential manned and means of transport in future, promotes that flow of research is accelerated in the development of its correlation technique, will have higher economic worth.

Accompanying drawing explanation

Accompanying drawing 1 near space vehicle modelling verification system figure.

Accompanying drawing 2 qualutative model checking process flow diagram.

Accompanying drawing 3 quantitative model checking process flow diagram.

Accompanying drawing 4 is based on the modelling verification process flow diagram of venture analysis.

Accompanying drawing 5 modelling verification software simulating surface chart.

Embodiment

The object of the invention is to the modelling verification theoretical system comprehensively and reliably proposing to be applicable near space vehicle, and realize the modelling verification software that can be used for evaluation near space vehicle mathematical model.

Along with the research of close to space vehicle technology is goed deep into, multi-modeling method and Model Simplification Method obtain development in various degree, because the cost of flight test is extremely expensive, insecure mathematical model brings potential application risk to system, therefore be badly in need of the modelling verification theoretical system that is applicable near space vehicle feature comprehensively reliably, ensure that model is before use by comprehensive modelling verification.Fundamental purpose of the present invention is just to provide and exports based near space vehicle model dynamic time sequence, the New model of system-level consistency check checking system.While providing the qualutative model checking based on monte carlo method, the quantitative model provided based on time-domain analysis from the angle of the regularity of distribution, development trend, metric space is respectively verified, finally also will carry out venture analysis to model, comprehensively treat verification model and carry out conforming inspection, and provide and verify criterion intuitively.Complex model checking for experimentation costliness is provided feasible thinking by the present invention, advance the Analysis and design process of near space vehicle, foundation for novel near space vehicle model provides comprehensively model verification method reliably, for the safe handling of model provides safeguard, reduce the risk that near space vehicle model uses, save cost of development, there is good application prospect and economic worth.

The present invention is integrated as main research means with theoretical method and Virtual Simulation, near space vehicle modelling verification problem, proposes the qualutative model verification method being not limited to model form; The Model in Time Domain verification method of multianalysis is carried out from the regularity of distribution, space length, development trend three angles; From the risk analysis model verification method that model user angle is carried out; And a whole set of modelling verification theoretical system that will set up, embed existing near space vehicle emulation platform, and Method Of Accomplishment software simulating and simulating, verifying.

The New model verification method first step that the present invention proposes is qualutative model checking.In the uncertain situation of model parameter, by the research to output quantity statistical law, the difference of visual representation reduced-order model and master pattern, tentatively provides modelling verification result from angle qualitatively.Three parts are mainly divided into the research of the qualitative checking work of model: first, tested by a large amount of Monte Carlo simulation, the statistical law of simulation reduced-order model output quantity when uncertain parameter random value, and then generate curve of output race.Whether dropping within simplified model curve of output race to be verified by observing master pattern curve of output, judging the difference that simplified model and master pattern export intuitively.Secondly, the convergence of research Monte Carlo simulation method, supports later stage simulation study to reduce simulation times.Finally, be simplified model output when getting boundary value, corresponding sensitive parameter combination, the combination of these sensitive parameters can provide Data Source for the aircraft carrying out limited number of times at loop simulation.Model user of service can utilize these sensitive parameters of limited group to combine, and carries out aircraft at loop semi matter emulation.

The New model verification method second step that the present invention proposes is quantitative model checking.By time-domain analysis technology, by observing the output response curve of master pattern and reduced-order model, show that master pattern and reduced-order model are exporting the conclusion in response consistance.Respectively from the regularity of distribution, development trend, metric space three angle quantitative modelling verification conclusions: first, adopt fiducial interval consistency check method, from the angle of Statistical Distribution, in conjunction with the method for test of hypothesis in statistical inference, rational judgment dynamic time sequence to be verified exports the consistance of Data distribution8 rule.Secondly, adopt Grey Incidence Analysis, from the angle of development trend and spatial shape, response curve consistance is assessed.Finally, adopt Distance Test Method, from space length angle, use statistical study and hypothesis testing method, provide response curve distance consistency check result.

New model verification method the 3rd step that the present invention proposes is quantitative risk analysis.On the basis providing qualitative and quantitative verification result, consider the practical application request of model to be verified, the uncertain parameter in model is considered as the risk factors affecting model safety use.According to the actual demand of model user, the parameter area of computation model safe operation.

Modelling verification program has been built based on dSPACE real-time simulation machine, this set of model verification method is embedded existing near space vehicle emulation platform, this simulated program can realize treating verification model based on qualitative, quantitatively and the modelling verification work of venture analysis.By means of this computer virtual simulation program, simulating, verifying is carried out to this patent institute extracting method.Result demonstrates the validation problem that carried model verification method may be used near space vehicle mathematical model, under this theoretical system, can provide the checking conclusion that model to be verified is qualitative and quantitative.

This modelling verification theoretical system may be used for the checking of near space vehicle mathematical model, be not subject to the restriction of model form, can be applied in the following aspects: 1, checking adopts the near space vehicle mathematical model that simulation wind tunnel methods is set up, and verifies that can this experimental mathematics model react the dynamic perfromance of real system strictly according to the facts.2, checking adopts the near space vehicle mathematical model that mechanism based method analysis is set up, and verifies that can this mechanism mathematical model react the dynamic perfromance of real system strictly according to the facts.3, distinguish and compare by multiple mechanism or seminar, adopting the near space vehicle mathematical model that distinct methods provides, application quantitative model verification method obtains quantitative comparative result, and for model, user provides decision-making foundation.4, on the basis of known high-fidelity mathematical model, application model short-cut method carries out simplification to this high-fidelity model and is simplified model, the consistance of checking simplified model and master pattern.

In application in above three, the modelling verification theoretical system that the present invention provides, can provide the modelling verification conclusion of following four aspects for model user for model to be verified:

1, can mathematical model to be verified react the dynamic perfromance of real system strictly according to the facts: the method adopting qualutative model checking, in the mode of statistical test, from the angle of figure, be the ability of the actual near space vehicle flight data dispose of model prediction to be verified, provide preliminary modelling verification result.

2, the time domain consistance of mathematical model dynamical output to be verified and true model: respectively from the angle of the regularity of distribution, development trend, metric space, adopt time domain quantitative model verification method, on the basis tentatively providing qualitative checking conclusion, the time domain consistency checking conclusion of quantitative.

3, can mathematical model to be verified be used safely: be considered as the uncertain parameter in model affecting the risk factors that model uses, and the user for model supplies a model range of safety operation, to reduce for the purpose of model application risk, provides comprehensive modelling verification.

For the longitudinal model of near space vehicle elasticity typical disclosed in USAF laboratory, the model to be verified that the Model Simplification Method using Ohio State University to propose is simplified for this high-fidelity mathematical model, the New model verification method that application the present invention proposes, successfully gives comprehensively qualitative, quantitative verification conclusion.Prove that this proof theory system is applicable to the checking work of near space vehicle mathematical model.

Choose this model flight height 85000-86000 foot and speed 7846-8846 feet per second cruising flight phase as the effective working stage of model.First the qualutative model verification method based on Monte Carlo simulation technology is applied, can when there is Parameter uncertainties in model, whether dropping within simplified model curve of output race to be verified by observing master pattern curve of output, judging the difference that simplified model and master pattern export intuitively.Simultaneously by the constringent research of Monte Carlo simulation, and the asking for of sensitive parameter combination, support later stage hardware and test at loop-around test in loop and aircraft.Greatly reduce the input of later stage test.Secondly, apply quantitative Model in Time Domain verification method, can utilize the consistance that test of hypothesis Technical Analysis Model dynamic time sequence exports, from the regularity of distribution, development trend, metric space three angles are quantitative checking conclusion respectively.Finally, application quantitative risk analysis method, is considered as risk factors by the uncertain parameter in model, according to the working stage actual performance requirement of model, calculates the model safety working range of hyperspace form.While comprehensive verification model, the user for model provides quantitative reliable analysis data, for the safe handling of model provides theoretical foundation, accelerates the process of near space vehicle exploitation, can effectively reduce model application risk simultaneously.

Social benefit and economic benefit: the research of the present invention near space vehicle has very important promotion meaning.The present invention can provide effective Model Simplification Method and model verification method, not only alleviate the contradiction of mathematical model increasingly sophisticated at present and the existence between model analysis and Controller gain variations, contribute to the model credibility improving the close to space vehicle system development initial stage simultaneously, for the reliability application of model provides foundation, accelerate the process that new model comes into operation, reduce application risk, shorten research cycle, not only rapidly and efficiently but also reduce expenses.Near space vehicle, as potential manned and means of transport in future, promotes that flow of research is accelerated in the development of its correlation technique, will have higher economic worth.

The invention will be further described by reference to the accompanying drawings.

See Fig. 1, the model verification method that the present invention provides, comprises three key steps, in the process of carrying out modelling verification, order is carried out, the conclusion iterative method that three checking links provide, supports mutually, finally forms the comprehensive modelling verification result under block mold proof theory system.This modelling verification theoretical system considers the Parameter uncertainties problem existed in model, can verify from qualitative and quantitative angle the model to be verified provided respectively.The verification method that the present invention proposes has wide range of applications, do not limit to the concrete form of model, model to be verified for linear/non-linear form all can use, and can verify simplified model with master pattern, the mathematical model that can also obtain with practical flight data verification test or Analysis on Mechanism.For given model to be verified, modelling verification work will divide three steps to carry out: 1. carry out qualitative checking based on Monte Carlo simulation method to it, answer the problem that can model to be verified react the dynamic perfromance of master pattern strictly according to the facts.2. the quantitative model based on Time Domain Analysis is verified, respectively from the regularity of distribution, development trend, metric space three angles, provides model to be verified and master pattern consistency check with quantitative form comprehensively.3. based on the quantitative model verification method of venture analysis, model parameter is considered as risk, providing the criterion of quantitative model checking intuitively, provide model standard of comparison when there is multiple model to be verified, and can verification model being used with and providing the scope of safe handling safely.

See Fig. 2, qualutative model checking work is for model to be verified, and ABC intuition provides the result in a graphical form.Consider the uncertain parameter in model, as aerodynamic parameter, environmental parameter, physical parameter etc. reflect in modeling process and systematic risk source in model use procedure, first determine its regularity of distribution by modeling work person according to the concrete physical meaning of parameter and acquiring way, as Gaussian distribution, be evenly distributed.And according to 3 δ principles, determine the span of parameter.After determining Monte Carlo simulation number of times, emulate all according to the stochastic distribution rule random value of these parameters at every turn, generate curve of output race.Then the qualitative master pattern that compares exports the curve of data and model output data curve race to be verified, if the two differs greatly, then needs further correction model.If the two difference is little, illustrate that the output of simplified model can reflect the statistical property that master pattern exports.And then, carry out Monte Carlo simulation convergence, not only can verify whether selected simulation times has been enough to this emulation experiment, the simulation study that simulation times supports the later stage can also be reduced.After completing the Monte Carlo simulation of a large amount of number of times is carried out to set up near space vehicle simplified model, the gang's curve of output about simplified model can be obtained.For the output valve outside 90%, be referred to as the boundary value of output quantity, this region is just called bounds.The some Output rusults of random selecting in this bounds, and the value of taking out the uncertain combination of sensitivity corresponding to these several groups output.Utilize the value of these uncertain combinations and the simulation times of its correspondence, further aircraft can be carried out at loop simulation.

See Fig. 3, treat the output of verification model dynamic time sequence from the regularity of distribution, development trend and metric space three angles respectively and carry out quantitative time domain checking.

1. regularity of distribution consistance is checked: obtain master pattern sample output sequence X={x (t), t=1,2 ..., n} and simplified model sample group output sequence Y _i={ y _i(t), t=1,2 ..., n}, i=1,2 ..., m, sample size meets statistical demand, wherein n represents master pattern and simplified model output sampling number, and m represents simplified model output sample number, the fiducial interval size in each moment of node-by-node algorithm, repeat this process, the fiducial interval completing each moment calculates, and carries out Jarque--Bera statistics control, if data meet normal distribution for t data, then construct the fiducial interval of normalized set t as follows, first definition, simple model output sample average and variance as follows:

$\stackrel{\‾}{y}\left(t\right)=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{y}_i\left(t\right),t=\mathrm{1,2},...n$

${\mathrm{\σ}}^2\left(t\right)=\frac{1}{m-1}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{[y_i\left(t\right)-\stackrel{\‾}{y}\left(t\right)]}^2,t=\mathrm{1,2},...,n$

s(t)＝σ(t)

Wherein, representative sample average, σ ²(t) representative sample variance, s (t) representative sample standard deviation, export for simplification y (t) model meeting normal distribution, under given level of significance α, its confidence upper limit is:

$Y_u\left(t\right)=\stackrel{\‾}{y}\left(t\right)+\sqrt{\frac{m+1}{m}}{t}_{\mathrm{\α}/2}(m-1)s\left(t\right)$

Confidence lower limit is:

$Y_l\left(t\right)=\stackrel{\‾}{y}\left(t\right)-\sqrt{\frac{m+1}{m}}{t}_{\mathrm{\α}/2}(m-1)s\left(t\right)$

If statistics control does not meet normal distribution hypothesis, then by simplified model output sample group Y _i={ y _i(t), t=1,2,, n}, i=1,2,, m at each moment t according to sorting from big to small, for given confidence level γ, the value subscript p of confidence lower limit is p=[γ m+1], wherein, ' [] ' represents rounding operation, the value subscript q of confidence upper limit be q=[(1-γ) (m+1)] so the confidence upper limit of t be: y _pt (), namely the confidence upper limit of t is the p large sample numerical value of t sample sequence, and confidence lower limit is: y _q(t), namely the confidence lower limit of t is the q large sample numerical value of t sample sequence, draw fiducial interval distribution plan, by observation and analysis fiducial interval distribution plan, judge whether master pattern and simplified model Output rusults meet regularity of distribution consistance;

2. development trend consistance is checked: definition Δ _oibe the different information between 2:

Δ _oi＝|x _o(k)-x _i(k)|,i∈I,k∈{1,2,...n}

In above formula, I refers to output sample space, and k is emulation sequential, and master pattern exports as x ₀, difference space is: Δ={ Δ _oi(k) }, if only have simulation data, so an I={1}.Difference space lower limit parameter is: also environmental parameter on the two poles of the earth of i.e. difference; Difference space lower limit parameter is: also be environmental parameter under the two poles of the earth of difference, resolution ratio: ξ ∈ [0,1], according to minimum information principle, gets 0.05, under the condition meeting grey correlation four axiom, and structure grey correlation space Δ _gR=(Δ, ξ, Δ _oi(max), Δ _oi(min)) grey incidence coefficient can be defined in grey correlation space as follows, original grey incidence coefficient:

$r(x_o\left(k\right),x_i\left(k\right))={(\frac{\underset{i}{\min }\underset{k}{\min }{\mathrm{\Δ}}_{\mathrm{oi}}\left(k\right)+\mathrm{\ξ}\underset{i}{\max }\underset{k}{\max }{\mathrm{\Δ}}_{\mathrm{oi}}\left(k\right)}{{\mathrm{\Δ}}_{\mathrm{oi}}\left(k\right)+\mathrm{\ξ}\underset{i}{\max }\underset{k}{\max }{\mathrm{\Δ}}_{\mathrm{oi}}\left(k\right)}\×e^{-{\mathrm{\η}}_{\mathrm{oi}}\left(k\right)})}^{\frac{1}{2}}$

Wherein η _oi(k)=2 × Δ _oi(k)/| x _o(k)+x _i(k) |, the output of master pattern is x _ok (), k is the integer from time point 1 to n, and n counts in the sampling time, and the output of simplified model is x _i(k), the implication of k is the same, and i represents i-th simplified model output sample, and the average grey incidence coefficient of curve is:

$\mathrm{\γ}(x_o,x_i)=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{\γ}(x_o\left(k\right),x_i\left(k\right))$

The average grey incidence coefficient of the overall situation and each moment grey incidence coefficient size, sampling number, and number of samples is correlated with, and draws grey correlation trend map, analyzes grey correlation trend map and calculates ensemble average grey incidence coefficient, drawing consistency check conclusion;

3. metric space consistance is checked: first obtain m ₁individual model output sample to be verified i=1,2 ..., m ₁, calculate master pattern output time series X and simplified model output time series average between mahalanobis distance

$D(X,\stackrel{\‾}{Y^1})=\sqrt{\frac{1}{n}(X-\stackrel{\‾}{Y^1})S^{-1}{(X-\stackrel{\‾}{Y^1})}^T}$

S-matrix is the covariance matrix of simplified model output sample.And then obtain m ₂individual model output sample to be verified. i=1,2 ..., m ₂, calculate with between Mean Mahalanobis distance

$D(Y_i^2,\stackrel{\‾}{Y^1})=\sqrt{\frac{1}{n}(Y_i^2-\stackrel{\‾}{Y^1})S^{-1}{(Y_i^2-\stackrel{\‾}{Y^1})}^T}$

If d is i=1,2 ..., m ₂in meet formula 's number, for given level of significance α, if then can conclude that between master pattern and simplified model, response curve metric space exists significant difference, namely not accept former consistance hypothesis.

See Fig. 4, can the quantitative model checking based on venture analysis be specially further: model uncertain parameter is considered as risk factors, uses safely from the angle verification model of model user.Y _r(x, θ) represents the output of simplified model, is subject to model state x and uncertain parameter θ=[θ ₁..., θ _i..., θ _p] ^timpact, illustrate in modeling process, simplified model may comprise multiple uncertain parameter.Model exports y is that m dimension is compacted.When Model Parameter is in certain limit during interior random value, p is uncertain parameter number, and Θ represents that initial parameter span is provided by modeling personnel, and the output of system will change.θ belongs to this random vector compacted, and illustrates the uncertain parameter in modeling process, by Multi-dimensional probability density function f _θx () describes, y _r(x, θ), under the impact of stray parameter vector θ, for belonging to the random vector compacting Y, tabular form model to be verified exports.In order to analyze the performance that simplified model exports, provide the definition of performance index:

The performance index that model exports are the function of model output, contain the information of quantity of state.Have expressed aircraft in the flight path expected (expectedflightenvelope), performance (vehicleperformance) quality of operation.Concrete form of Definition is as follows:

Here y (x) represents the output quantity of master pattern, y _r(x, θ) represents the output quantity of simplified model, wherein, for k ties up performance function, illustrate the concrete constraint to performance function, represent lower bound requirement, represent upper bound requirement.First the upper bound requirement of performance index is considered system exports the probability meeting upper bound performance index requirement can be expressed as p _y(Ω _y), wherein represent model output set when meeting upper bound performance index needs.Simplify the Probability p that system performance to be verified meets upper bound performance index requirement _y(Ω _y) computing formula is:

$p_Y\left({\mathrm{\Ω}}_y\right)={\∫}_{\mathrm{\θ}}{\underset{\‾}{\mathrm{\δ}}}_y\left[y_r(x,\mathrm{\θ})\right]d_{\mathrm{\θ}}\left(\mathrm{\θ}\right)\mathrm{d\θ}$

In above formula, be defined as following two-valued function:

Sampling emulation mode is utilized to estimate above formula:

Wherein, n ' _sMn _sMrepresent sampling number, calculate model to be verified according to the following formula and export the probability meeting performance index:

And then consider the lower bound requirement of performance index system exports the probability meeting the requirement of performance index lower bound and can be expressed as computing formula is:

$p_Y\left({\mathrm{\Ω}}_y^c\right)={\∫}_{\mathrm{\θ}}{\stackrel{\‾}{\mathrm{\δ}}}_y\left[y_r(x,\mathrm{\θ})\right]d_{\mathrm{\θ}}\left(\mathrm{\θ}\right)\mathrm{d\θ}$

Sampling emulation mode is utilized to estimate above formula:

$p_Y\left({\mathrm{\Ω}}_y^c\right)\≅\underset{i=1}{\overset{n_{\mathrm{SM}}^{\′}}{\mathrm{\Σ}}}{\stackrel{\‾}{\mathrm{\δ}}}_y\left[y_{r,i}(x,\mathrm{\θ})\right]/n_{\mathrm{SM}}^{\′}$

Wherein, n ' _sMrepresent emulation sampling number.In above formula, be defined as following two-valued function:

Consider the upper bound and the lower bound requirement of performance index, the probability that model output performance function meets performance index requirement can be simplified after calculating, when time, illustrate that corresponding uncertain parameter value can cause model to use dangerous, will meet the output valve record of performance requirement, and record corresponding uncertain parameter value θ ^*, represent the output of the system when uncertain parameter gets particular value; N ' will be emulated _sM+ n _sMin secondary, undesirable data point is removed, and obtains wherein for n ' _sMthe simulation times selected in secondary emulation, for n _sMthe simulation times selected in secondary emulation.Now, the reduced-order model after screening exports the probability of meeting property index request $p_Y\left({\mathrm{\Ω}}_y\right)+p_Y\left({\mathrm{\Ω}}_y^c\right)\≅\underset{i=1}{\overset{{\tilde{n}}_{\mathrm{SM}}^{\′}}{\mathrm{\Σ}}}{\underset{\‾}{\mathrm{\δ}}}_y\left[y_{r,i}(x,\mathrm{\θ})\right]/{\tilde{n}}_{\mathrm{SM}}^{\′}+\underset{i=1}{\overset{{\tilde{n}}_{\mathrm{SM}}}{\mathrm{\Σ}}}{\stackrel{\‾}{\mathrm{\δ}}}_y\left[y_{r,i}(x,\mathrm{\θ})\right]/{\tilde{n}}_{\mathrm{SM}}=1,$ Generate these multi-Dimensional parameters valued space exported owing to can ensure that output performance meets the demands, this multi-C parameter space is the operational envelope of model to be verified, is expressed as

See Fig. 5, modelling verification main control software interface adopts MFC design, and realize being connected by Matlab engine technique and main control software, overall software function is embedded in existing near space vehicle simulation and verification platform.Comprise four functional areas in interface: region 1 is model verification method setting area, comprise the acquisition of master pattern and model data to be verified, Matlab/Sinulink functional entrance and initial simulated conditions and arrange; Region 2 is qualutative model checking district, comprises the setting of Monte Carlo simulation number of times, the checking of qualitative the result, convergence and border value analytic function; Region 3 is the quantitative model validation region based on time-domain analysis, comprises the development trend consistency checking based on Grey Incidence Analysis, the regularity of distribution consistency checking based on fiducial interval method and the space length consistency checking function based on distance calculating method; Region 4 is the modelling verification region based on venture analysis, comprises risk factors setting, performance index requirement and analysis result Presentation Function.

Claims (4)

1. near space vehicle modelling verification and a Simulation Methods, is characterized in that, comprises the steps: 1. to carry out qualitative checking based on Monte Carlo simulation method to it, answers the problem that can model to be verified react the dynamic perfromance of master pattern strictly according to the facts; 2. the quantitative model based on Time Domain Analysis is verified, respectively from the regularity of distribution, development trend, metric space three angles, provides model to be verified and master pattern consistency check with quantitative form comprehensively; 3. the quantitative model based on venture analysis is verified, model parameter is considered as risk, providing the criterion of quantitative model checking intuitively, provide model standard of comparison when there is multiple model to be verified, and can verification model being used with and providing the scope of safe handling safely; Respectively from the regularity of distribution, development trend and metric space three angles treat verification model dynamic time sequence export carry out quantitative time domain checking concrete steps be:

1. regularity of distribution consistance is checked: obtain master pattern sample output sequence X={x (t), t=1,2 ..., n} and simplified model sample group output sequence Y _i={ y _i(t), t=1,2 ..., n}, i=1,2 ..., m, sample size meets statistical demand, wherein n represents master pattern and simplified model output sampling number, and m represents simplified model output sample number, the fiducial interval size in each moment of node-by-node algorithm, repeat this process, the fiducial interval completing each moment calculates, and carries out Jarque--Bera statistics control, if data meet normal distribution for t data, then construct the fiducial interval of normalized set t as follows, first definition, simple model output sample average and variance as follows:

$\stackrel{\‾}{y}\left(t\right)=\frac{1}{m}\underset{i=1}{\overset{m}{\Σ}}{y}_i\left(t\right),t=1,2,...,n$

${\mathrm{\σ}}^2\left(t\right)=\frac{1}{m-1}\underset{i=1}{\overset{m}{\Σ}}{\[y_i\left(t\right)-\stackrel{\‾}{y}\left(t\right)\]}^2,t=1,2,...,n$

s(t)＝σ(t)

Wherein, representative sample average, σ ²(t) representative sample variance, s (t) representative sample standard deviation, export for simplification y (t) model meeting normal distribution, under given level of significance α, its confidence upper limit is:

$Y_u\left(t\right)=\stackrel{\‾}{y}\left(t\right)+\sqrt{\frac{m+1}{m}}{t}_{\mathrm{\α}/2}(m-1)s\left(t\right)$

Confidence lower limit is:

$Y_l\left(t\right)=\stackrel{\‾}{y}\left(t\right)-\sqrt{\frac{m+1}{m}}{t}_{\mathrm{\α}/2}(m-1)s\left(t\right)$

If statistics control does not meet normal distribution hypothesis, then by simplified model output sample group Y _i={ y _i(t), t=1,2,, n}, i=1,2,, m at each moment t according to sorting from big to small, for given confidence level γ, the value subscript p of confidence upper limit is p=[γ m+1], wherein, ' [] ' represents rounding operation, and the value subscript q of confidence lower limit is q=[(1-γ) (m+1)]; So the confidence upper limit of t is: y _p(t), namely the confidence upper limit of t is the p large sample numerical value of t sample sequence; Confidence lower limit is: y _q(t), namely the confidence lower limit of t is the q large sample numerical value of t sample sequence, draw fiducial interval distribution plan, by observation and analysis fiducial interval distribution plan, judge whether master pattern and simplified model Output rusults meet regularity of distribution consistance;

2. development trend consistance is checked: definition Δ _oibe the different information between 2:

Δ _oi＝|x _o(k)-x _i(k)|,i∈I,k∈{1,2,...n}

In above formula, I refers to output sample space, and k is emulation sequential, and master pattern exports as x ₀, difference space is: Δ={ Δ _oi(k) }, if only have simulation data, so an I={1}, difference space upper limit parameter is: also environmental parameter on the two poles of the earth of i.e. difference; Difference space lower limit parameter is: also be environmental parameter under the two poles of the earth of difference, resolution ratio: ξ ∈ [0,1], according to minimum information principle, gets 0.05, under the condition meeting grey correlation four axiom, and structure grey correlation space Δ _gR=(Δ, ξ, Δ _oi(max), Δ _oi(min)) grey incidence coefficient can be defined in grey correlation space as follows, original grey incidence coefficient:

$r\left(x_o\right(k),x_i(k\left)\right)={(\frac{\underset{i}{min}\underset{k}{min}{\mathrm{\Δ}}_{oi}\left(k\right)+\mathrm{\ξ}\underset{i}{\max }\underset{k}{\max }{\mathrm{\Δ}}_{oi}\left(k\right)}{{\mathrm{\Δ}}_{oi}\left(k\right)+\mathrm{\ξ}\underset{i}{max}\underset{k}{max}{\mathrm{\Δ}}_{oi}\left(k\right)}\×e^{-{\mathrm{\η}}_{oi}\left(k\right)})}^{\frac{1}{2}}$

Wherein η _oi(k)=2 × Δ _oi(k)/| x _o(k)+x _i(k) |, the output of master pattern is x _ok (), k is the integer from time point 1 to n, and n counts in the sampling time, and the output of simplified model is x _i(k), the implication of k is the same, and i represents i-th simplified model output sample, and the average grey incidence coefficient of curve is:

$\mathrm{\γ}(x_o,x_i)=\frac{1}{n}\underset{k=1}{\overset{n}{\Σ}}\mathrm{\γ}\left(x_o\right(k),x_i(k\left)\right)$

The average grey incidence coefficient of the overall situation and each moment grey incidence coefficient size, sampling number, and number of samples is correlated with, and draws grey correlation trend map, analyzes grey correlation trend map and calculates ensemble average grey incidence coefficient, drawing consistency check conclusion;

3. metric space consistance is checked: first obtain m ₁individual model output sample Y to be verified _i ¹={ y _i(t), t=1,2 ..., n}, i=1,2 ..., m ₁, calculate master pattern output time series X and simplified model output time series average between mahalanobis distance

$D(X,\stackrel{\‾}{Y^1})=\sqrt{\frac{1}{n}(X-\stackrel{\‾}{Y^1})S^{-1}{(X-\stackrel{\‾}{Y^1})}^T}$

S-matrix is the covariance matrix of simplified model output sample, and then obtains m ₂individual model output sample to be verified; Y _i ²={ y _i(t), t=1,2 ..., n} .i=1,2 ..., m ₂, calculate Y _i ²with between Mean Mahalanobis distance

$D(Y_i^2,\stackrel{\‾}{Y^1})=\sqrt{\frac{1}{n}(Y_i^2-\stackrel{\‾}{Y^1})S^{-1}{(Y_i^2-\stackrel{\‾}{Y^1})}^T}$

If d is i=1,2 ..., m ₂in meet formula $D(Y_i^2,\stackrel{\‾}{Y^1})\≥D(X,\stackrel{\‾}{Y^1})$ 's number, for given level of significance α, if then can conclude that between master pattern and simplified model, response curve metric space exists significant difference, namely not accept former consistance hypothesis.

2. near space vehicle modelling verification as claimed in claim 1 and Simulation Methods, it is characterized in that, 1. step is specially further: first determine its regularity of distribution according to the concrete physical meaning and acquiring way that comprise uncertain parameter, and according to 3 δ principles, determine the span of parameter, after determining Monte Carlo simulation number of times, emulate all according to the stochastic distribution rule random value of these parameters at every turn, generate curve of output race; Then the qualitative master pattern that compares exports the curve of data and model output data curve race to be verified, if the two differs greatly, then need further correction model, if the two difference is little, illustrate that the output of simplified model can reflect the statistical property that master pattern exports; And then, carry out Monte Carlo simulation convergence, obtain the gang's curve of output about simplified model, for the output valve outside 90%, be referred to as the boundary value of output quantity, this region is just called bounds, the some Output rusults of random selecting in this bounds, and take out the value of the uncertain combination of sensitivity corresponding to these several groups output, utilize the value of these uncertain combinations and the simulation times of its correspondence, further aircraft can be carried out at loop simulation.

3. near space vehicle modelling verification as claimed in claim 1 and Simulation Methods, it is characterized in that, 2. step is specially further: first, adopt fiducial interval consistency check method, from the angle of Statistical Distribution, in conjunction with the method for test of hypothesis in statistical inference, rational judgment dynamic time sequence to be verified exports the consistance of Data distribution8 rule; Secondly, adopt Grey Incidence Analysis, from the angle of development trend and spatial shape, response curve consistance is assessed; Finally, adopt Distance Test Method, from space length angle, use statistical study and hypothesis testing method, provide response curve distance consistency check result.

4. can near space vehicle modelling verification as claimed in claim 1 and Simulation Methods, is characterized in that, model uncertain parameter is considered as risk factors, use safely, y from the angle verification model of model user _r(x, θ) represents the output of simplified model, is subject to model state x and uncertain parameter θ=[θ ₁..., θ _i..., θ _p] ^timpact, illustrate in modeling process, simplified model may comprise multiple uncertain parameter, model export be y is that m dimension is compacted; When Model Parameter is in certain limit during interior random value, p is uncertain parameter number, and Θ represents that initial parameter span is provided by modeling personnel, the output of system will change, θ belongs to this random vector compacted, and illustrates the uncertain parameter in modeling process, by Multi-dimensional probability density function f _θx () describes, y _r(x, θ), under the impact of stray parameter vector θ, for belonging to the random vector compacting Y, tabular form model to be verified exports, and in order to analyze the performance that simplified model exports, provides the definition of performance index:

The performance index that model exports are the function of model output, contain the information of quantity of state, have expressed aircraft expectedflightenvelope in the flight path expected, the performance vehicleperformance quality of operation, concrete form of Definition is as follows:

Here y (x) represents the output quantity of master pattern, y _r(x, θ) represents the output quantity of simplified model, wherein, for k ties up performance function, illustrate the concrete constraint to performance function, represent lower bound requirement, represent upper bound requirement, first consider the upper bound requirement of performance index the probability that model output meets upper bound performance index requirement can be expressed as p _y(Ω _y), wherein represent model output set when meeting upper bound performance index needs; Simplify the Probability p that system performance to be verified meets upper bound performance index requirement _y(Ω _y) computing formula is:

$p_Y\left({\mathrm{\Ω}}_y\right)={\∫}_{\mathrm{\θ}}{\underset{\‾}{\mathrm{\δ}}}_y\[y_r(x,\mathrm{\θ})\]d_{\mathrm{\θ}}\left(\mathrm{\θ}\right)d\mathrm{\θ}$

In above formula, δ _ybe defined as following two-valued function:

Sampling emulation mode is utilized to estimate above formula:

Wherein, n ' _sMn _sMrepresent sampling number, calculate model to be verified according to the following formula and export the probability meeting performance index:

And then consider the lower bound requirement of performance index system exports the probability meeting the requirement of performance index lower bound and can be expressed as computing formula is:

$p_Y\left({\mathrm{\Ω}}_y^c\right)={\∫}_{\mathrm{\θ}}{\stackrel{\‾}{\mathrm{\δ}}}_y\[y_r(x,\mathrm{\θ})\]d_{\mathrm{\θ}}\left(\mathrm{\θ}\right)d\mathrm{\θ}$

Sampling emulation mode is utilized to estimate above formula:

$p_Y\left({\mathrm{\Ω}}_y^c\right)\≅\underset{i=1}{\overset{n_{SM}^{\′}}{\Σ}}{\stackrel{\‾}{\mathrm{\δ}}}_y\[y_{r,i}(x,\mathrm{\θ})\]/n_{SM}^{\′}$

Wherein, in above formula, be defined as following two-valued function:

Consider the upper bound and the lower bound requirement of performance index, after calculating, be simplified the probability that model output performance function meets performance index requirement, when time, illustrate that corresponding uncertain parameter value can cause model to use dangerous, will meet the output valve record of performance requirement, and record corresponding uncertain parameter value θ ^*, represent the output of the system when uncertain parameter gets particular value; N ' will be emulated _sM+ n _sMin secondary, undesirable data point is removed, and obtains wherein for n ' _sMthe simulation times selected in secondary emulation, for n _sMthe simulation times selected in secondary emulation; Now, the reduced-order model after screening exports the probability of meeting property index request $p_Y\left({\mathrm{\Ω}}_y\right)+p_Y\left({\mathrm{\Ω}}_y^c\right)\≅\underset{i=1}{\overset{{\tilde{n}}_{SM}^{\′}}{\Σ}}{\underset{\‾}{\mathrm{\δ}}}_y\[y_{r,i}(x,\mathrm{\θ})\]/{\tilde{n}}_{SM}^{\′}+\underset{i=1}{\overset{{\tilde{n}}_{SM}}{\Σ}}{\stackrel{\‾}{\mathrm{\δ}}}_y\[y_{r,i}(x,\mathrm{\θ})\]/{\tilde{n}}_{SM}=1,$ Generate these multi-Dimensional parameters valued space exported owing to can ensure that output performance meets the demands, this multi-C parameter space is the operational envelope of model to be verified, is expressed as ${\mathrm{\Θ}}_s=\left\{\mathrm{\θ}\right|p_Y\left({\mathrm{\Ω}}_y\right)+p_Y\left({\mathrm{\Ω}}_y^c\right)=1\}.$