CN114429036A - Dynamic simulation result verification method based on feature extraction and area measurement - Google Patents

Dynamic simulation result verification method based on feature extraction and area measurement Download PDF

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CN114429036A
CN114429036A CN202111629335.6A CN202111629335A CN114429036A CN 114429036 A CN114429036 A CN 114429036A CN 202111629335 A CN202111629335 A CN 202111629335A CN 114429036 A CN114429036 A CN 114429036A
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张欢
李伟
杨明
马萍
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Harbin Institute of Technology
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Abstract

The invention discloses a dynamic simulation result verification method based on feature extraction and area measurement, and belongs to the technical field of computer simulation. Specifically, the method adopts discrete orthogonal polynomials to extract the characteristics of the time sequence, such as the mean value, the slope, the curvature and the like, further calculates the probability distribution area difference of each characteristic, and finally synthesizes to obtain a verification result. The invention can solve the problem of simulation result verification of dynamic output with uncertainty. Meanwhile, the characteristic coefficients have definite physical meanings, and the characteristic coefficients to be extracted can be selected according to the orthogonal polynomial fitting effect and the actual physical meanings of dynamic output.

Description

Dynamic simulation result verification method based on feature extraction and area measurement
Technical Field
The invention relates to a dynamic simulation result verification method based on feature extraction and area measurement, and belongs to the technical field of computer simulation.
Background
The simulation technology becomes an important means for realizing and modifying the objective world after theoretical research and experimental research, and is widely applied to the fields of industry, agriculture, medicine, economy, aerospace, aviation and the like due to the advantages of economy, safety, repeatability, no destructiveness, no limitation of weather conditions, no limitation of site space and the like. With the wide application and rapid development of simulation technology, the credibility of simulation results is also more and more concerned by people. In the late stage of the fifties of the twentieth century, the problem of the reliability of a simulation model is firstly proposed, certain research is carried out, and a series of classical simulation result verification methods such as Turing test, TIC method, hypothesis test and the like appear. In the twenty-first century, with the increase of the complexity of a simulation system, the simulation output also presents the characteristics of diversity, uncertainty, relevance and the like, and scholars represented by Oberkampf, Mahadevan and the like successively provide simulation result verification methods such as probability distribution area difference, interval estimation, Bayesian hypothesis testing and the like.
This is relatively little studied with respect to the dynamic output of simulation systems. The learners take each time point in the time sequence as a variable, and convert the simulation result verification problem of the dynamic time sequence into the simulation result verification problem of the multi-element static variable, but due to the autocorrelation and high dimensionality of the time sequence, the method has large calculation amount and inaccurate result; in addition, the verification method of the simulation result of dynamic output mainly focuses on extracting the characteristics of the time sequence by adopting a characteristic extraction method, and then consistency analysis is performed on the characteristics, such as a simulation result verification method based on the combination of probability principal component analysis and Bayesian factors, a dynamic output verification method based on KL Transformation (Karhunen-Loe've Transformation), and the like, but the physical meaning of the extracted characteristics by adopting principal component analysis or probability principal component analysis and the like in the existing method is not clear; related scholars at home and abroad also provide a model verification method based on wavelet transformation, a reliability criterion on a time domain and the like.
Disclosure of Invention
The invention aims to provide a dynamic simulation result verification method based on feature extraction and area measurement, which aims to solve the problems that the extracted features are ambiguous in physical meaning, large in calculated amount, inaccurate in result and the like in the existing method by adopting principal component analysis or probabilistic principal component analysis and the like.
A dynamic simulation result verification method based on feature extraction and area measurement assumes that a dynamically output simulation time sequence is expressed as Y ═ Y i1,2, M, with reference to the time series denoted R ═ R i1, 2.. M, the dynamically output simulation data and reference data comprise a plurality of time series. The dynamic simulation result verification method is divided into a single verification point and a multi-verification point,
at a single verification point, the verification of the dynamic output simulation result comprises the following steps:
s100, obtaining the dynamic output Y of the simulation model at the single verification point xl，l＝1,2,...,NsThe actual observed data is Rk， k＝1,2,...,Nr；
S200, fitting the time sequence by adopting a discrete Chebyshev polynomial to obtain orthogonal expansion coefficients of the simulation data and the reference data, wherein the orthogonal expansion coefficients are respectively { alpha [ + ]sl}qAnd { alphark}qQ1.. Q, where Q is the number of orthogonal expansion coefficients, thereby obtaining { α ·sl}qHas a cumulative distribution function of Fsq(α)，{αrk}qHas an empirical cumulative distribution function of Frq(α)；
S300, calculating F by adopting area measurementsq(. alpha.) and FrqThe area difference of (alpha) is dqI.e. by
Figure BDA0003439773780000021
And normalizing the area difference to obtain the consistency c of the simulation data and the reference data of each orthogonal expansion coefficientqThe normalized calculation formula of the area difference is as follows:
Figure BDA0003439773780000022
wherein
Figure BDA0003439773780000023
xmaxAnd xminMaximum and minimum values in the simulation and reference data of the corresponding orthogonal expansion coefficient respectively;
s400, integrating the consistency of each orthogonal expansion coefficient, and calculating to obtain a verification result of dynamic output
Figure BDA0003439773780000024
Wherein omegaqIs the weight of each orthogonal expansion coefficient and
Figure BDA0003439773780000025
at multiple verification points, the verification of the dynamic output simulation result comprises the following steps:
s500, at verification point { x1,x2,...,xPGet the dynamic output of the simulation model as
Figure BDA0003439773780000026
The actual observed data are
Figure BDA0003439773780000027
Wherein l 1,2s，k＝1,2,...,Nr，j＝1,2,...,P；
S600, fitting the time sequence by adopting a discrete Chebyshev polynomial to obtain orthogonal expansion coefficients of simulation data and reference data respectively
Figure BDA0003439773780000031
And
Figure BDA0003439773780000032
q1.., Q, where Q is the number of orthogonal expansion coefficients;
s700, calculating orthogonal expansion coefficients of simulation data
Figure BDA0003439773780000033
Cumulative distribution function of { F }j}qCumulative distribution function of each coefficient { F) according to probability integral transformationj}qConversion to uniformly distributed U (0)1), while, the orthogonal expansion coefficient of the reference data
Figure BDA0003439773780000034
According to { F of the corresponding coefficientj}qIs converted into a series of u values in the relationship of
Figure BDA0003439773780000035
S800, calculating each coefficient
Figure BDA0003439773780000036
Area difference from uniformly distributed U (0,1)
Figure BDA0003439773780000037
Wherein F (u)qIs composed of
Figure BDA0003439773780000038
And normalizing the area difference to obtain the consistency c of the simulation data and the reference data of each orthogonal expansion coefficientqThe normalized calculation formula of the area difference is as follows: c. Cq＝1-2*dq；
S900, obtaining a verification result of dynamic output by integrating consistency calculation of each orthogonal expansion coefficient
Figure BDA0003439773780000039
Wherein ω isqIs the weight of each orthogonal expansion coefficient and
Figure BDA00034397737800000310
the beneficial effects of the invention are as follows: the invention provides a dynamic simulation result verification method based on feature extraction and area measurement. Aiming at the problem of verification of a simulation result of dynamic output, firstly, extracting characteristic coefficients such as a mean value, a slope, curvature and the like of a time sequence by adopting an orthogonal polynomial; secondly, because the characteristic coefficients of the time sequence are mutually independent, the difference of the characteristic coefficients is measured by adopting a probability distribution area difference method; and finally, synthesizing the difference of the characteristic coefficients to obtain a verification result of dynamic output. The method can solve the problem of simulation result verification of dynamic output with uncertainty. Meanwhile, the characteristic coefficients have definite physical meanings, and the characteristic coefficients to be extracted can be selected according to the orthogonal polynomial fitting effect and the actual physical meanings of dynamic output.
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FIG. 1 is a flow chart of a single verification point dynamic output simulation result verification method;
FIG. 2 is a flow chart of a verification method for dynamically outputting simulation results at multiple verification points;
FIG. 3 is a schematic view of a line of sight, wherein FIG. 3(a) is the line of sight; FIG. 3(b) is a 2 nd order orthopolynomial fitting line of sight angle;
fig. 4 is a schematic diagram of area measurement of a candidate model, wherein fig. 4(a) is the area measurement of the feature coefficient 1, (b) is the area measurement of the feature coefficient 2, and (c) is the area measurement of the feature coefficient 3;
FIG. 5 is a schematic diagram of the U-pooling metric of a candidate model, wherein FIG. 5(a) is the U-pooling metric of a feature coefficient of 1; FIG. 5(b) is a U-pooling metric for a characteristic coefficient of 2; FIG. 5(c) is a U-pooling metric for the characteristic coefficient 3.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a dynamic simulation result verification method based on feature extraction and area measurement, which aims to solve the problems that the extracted features are ambiguous in physical meaning, large in calculated amount, inaccurate in result and the like in the existing method by adopting principal component analysis or probabilistic principal component analysis and the like.
A dynamic simulation result verification method based on feature extraction and area measurement assumes that a dynamically output simulation time sequence is expressed asY＝{ y i1,2, M, with reference to the time series denoted R ═ R i1, 2.. M, the dynamically output simulation data and reference data comprise a plurality of time series. The dynamic simulation result verification method is divided into a single verification point and a multi-verification point,
referring to fig. 1, at a single verification point, the verification of the dynamic output simulation result includes the following steps:
s100, obtaining the dynamic output Y of the simulation model at a single verification point xl，l＝1,2,...,NsThe actual observed data is Rk， k＝1,2,...,Nr；
S200, fitting the time sequence by adopting a discrete Chebyshev polynomial to obtain orthogonal expansion coefficients of the simulation data and the reference data, wherein the orthogonal expansion coefficients are respectively { alpha [ + ]sl}qAnd { alphark}qQ1.. Q, where Q is the number of orthogonal expansion coefficients, thereby obtaining { α ·sl}qHas a cumulative distribution function of Fsq(α)，{αrk}qHas an empirical cumulative distribution function of Frq(α)；
S300, calculating F by adopting area measurementsq(. alpha.) and FrqThe area difference of (alpha) is dqI.e. by
Figure BDA0003439773780000051
And normalizing the area difference to obtain the consistency c of the simulation data and the reference data of each orthogonal expansion coefficientqThe normalized calculation formula of the area difference is as follows:
Figure BDA0003439773780000052
wherein
Figure BDA0003439773780000053
xmaxAnd xminMaximum and minimum values in the simulation and reference data of the corresponding orthogonal expansion coefficient respectively;
s400, integrating the consistency of each orthogonal expansion coefficient, and calculating to obtain a verification result of dynamic output
Figure BDA0003439773780000054
Wherein ω isqIs the weight of each orthogonal expansion coefficient and
Figure BDA0003439773780000055
referring to fig. 2, at a multi-verification point, the verification of the dynamic output simulation result comprises the following steps:
s500, at verification point { x1,x2,...,xPGet the dynamic output of the simulation model as
Figure BDA0003439773780000056
The actual observed data are
Figure BDA0003439773780000057
Wherein l 1,2s，k＝1,2,...,Nr，j＝1,2,...,P；
S600, fitting the time sequence by adopting a discrete Chebyshev polynomial to obtain orthogonal expansion coefficients of simulation data and reference data respectively
Figure BDA0003439773780000058
And
Figure BDA0003439773780000059
q1.., Q, where Q is the number of orthogonal expansion coefficients;
s700, calculating orthogonal expansion coefficients of simulation data
Figure BDA00034397737800000510
Cumulative distribution function of { F }j}qCumulative distribution function of each coefficient { F, according to probability integral transformationj}qConverted into uniformly distributed U (0,1) and, at the same time, the orthogonal expansion coefficient of the reference data
Figure BDA00034397737800000511
According to { F of the corresponding coefficientj}qIs converted into a series of u values in the relationship of
Figure BDA00034397737800000512
S800, calculating each coefficient
Figure BDA00034397737800000513
Area difference from uniformly distributed U (0,1)
Figure BDA00034397737800000514
Wherein F (u)qIs composed of
Figure BDA00034397737800000515
And normalizing the area difference to obtain the consistency c of each orthogonal expansion coefficient simulation data and reference dataqThe normalized calculation formula of the area difference is as follows: c. Cq＝1-2*dq；
S900, obtaining a verification result of dynamic output by integrating consistency calculation of each orthogonal expansion coefficient
Figure BDA0003439773780000061
Wherein ω isqIs the weight of each orthogonal expansion coefficient and
Figure BDA0003439773780000062
the following are specific examples of the present invention:
the effectiveness of the invention is illustrated by taking the verification of the simulation result output by the terminal guidance sight angle of an aircraft as an example.
1. Candidate model and time series data processing
Uncertainty such as atmospheric density, lift coefficient, drag coefficient and the like is usually existed in the terminal guidance process of an aircraft. Assuming an initial mass of 750kg for the aircraft, the initial mass for each candidate model for single and multiple verification points is shown in Table 1.
Figure BDA0003439773780000063
TABLE 1 initial quality of candidate models
Before simulation result verification is carried out, the order of an orthogonal polynomial fitting the line-of-sight angle time sequence needs to be determined firstly. And 2-order orthogonal polynomials are selected to fit the line of sight angle by comparing the fitting effect of each order polynomial with the actual physical meaning of the line of sight angle. Fig. 3 shows an example of fitting the viewing angle by using a 2 nd order orthogonal polynomial, and as can be seen from the figure, the fitting effect of the 2 nd order orthogonal polynomial is better, and further, the coefficients of the orthogonal polynomial are extracted as the characteristic coefficients, i.e., the characteristic coefficients 1,2, and 3.
2. Single verification point
At a single verification point, 1000 groups of simulation data and 100 groups of observation data are obtained, the simulation result is verified by adopting the method, the area difference of each characteristic coefficient of the line-of-sight angle is shown in fig. 4, and the result is shown in table 2. Therefore, if the verification results of the candidate models are 0.9635, 0.8633, 0.7485, respectively, the accuracy of the candidate models is ranked as model 1> model 2> model 3, which is consistent with the actual situation.
Figure BDA0003439773780000071
TABLE 2 area measurement results and verification results for candidate models
3. Multiple authentication points
At multiple verification points, 50 verification points are extracted according to the probability distribution of the initial quality of the candidate model, 1000 groups of simulation data and 100 groups of observation data are obtained at each verification point, the simulation result is verified by adopting the method, the area difference of each characteristic coefficient of the line-of-sight angle is shown in figure 5, and the result is shown in table 3. Therefore, the verification results of the candidate models are 0.9853, 0.9544 and 0.8905 respectively, and the accuracy of the candidate models is ranked as model 1> model 2> model 3, which is consistent with the actual situation.
Figure BDA0003439773780000072
TABLE 3U-pooling metric and validation results for candidate models
From the above example verification, the dynamic simulation result verification method based on feature extraction and area measurement provided by the invention is reasonable and effective.
Although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made therein by those skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (1)

1. A dynamic simulation result verification method based on feature extraction and area measurement assumes that a dynamically output simulation time sequence is expressed as Y ═ Yi1,2, M, with reference to the time series denoted R ═ Ri1,2, M, the dynamically output simulation data and reference data comprise a plurality of time sequences, the dynamic simulation result verification method is divided into a single verification point and a plurality of verification points,
at a single verification point, the verification of the dynamic output simulation result comprises the following steps:
s100, obtaining the dynamic output Y of the simulation model at a single verification point xl，l＝1,2,...,NsThe actual observed data is Rk，k＝1,2,...,Nr；
S200, fitting the time sequence by adopting a discrete Chebyshev polynomial to obtain orthogonal expansion coefficients of the simulation data and the reference data, wherein the orthogonal expansion coefficients are respectively { alpha [ + ]sl}qAnd { alphark}qQ1.. Q, where Q is the number of orthogonal expansion coefficients, thereby obtaining { α ·sl}qHas a cumulative distribution function of Fsq(α)，{αrk}qHas an empirical cumulative distribution function of Frq(α)；
S300, calculating F by adopting area measurementsq(. alpha.) and FrqThe difference in area of (. alpha.) is dqI.e. by
Figure FDA0003439773770000011
And normalizing the area difference to obtain the consistency c of the simulation data and the reference data of each orthogonal expansion coefficientqThe normalized calculation formula of the area difference is as follows:
Figure FDA0003439773770000012
wherein
Figure FDA0003439773770000013
xmaxAnd xminMaximum and minimum values in the simulation and reference data of the corresponding orthogonal expansion coefficient respectively;
s400, integrating the consistency of each orthogonal expansion coefficient, and calculating to obtain a verification result of dynamic output
Figure FDA0003439773770000014
Wherein ω isqIs the weight of each orthogonal expansion coefficient and
Figure FDA0003439773770000015
at multiple verification points, the verification of the dynamic output simulation result comprises the following steps:
s500, at verification point { x1,x2,...,xPGet the dynamic output of the simulation model as
Figure FDA0003439773770000016
The actual observed data are
Figure FDA0003439773770000017
Wherein l 1,2s，k＝1,2,...,Nr，j＝1,2,...,P；
S600, fitting the time sequence by adopting a discrete Chebyshev polynomial to obtain orthogonal expansion coefficients of the simulation data and the reference data respectively
Figure FDA0003439773770000021
And
Figure FDA0003439773770000022
wherein Q is the number of orthogonal expansion coefficients;
s700, calculating orthogonal expansion coefficients of simulation data
Figure FDA0003439773770000023
Cumulative distribution function of { F }j}qCumulative distribution function of each coefficient { F) according to probability integral transformationj}qConverted into uniformly distributed U (0,1) and, at the same time, the orthogonal expansion coefficient of the reference data
Figure FDA0003439773770000024
According to { F of the corresponding coefficientj}qIs converted into a series of u values in the relationship of
Figure FDA0003439773770000025
S800, calculating each coefficient
Figure FDA0003439773770000026
Area difference from uniformly distributed U (0,1)
Figure FDA0003439773770000027
Wherein F (u)qIs composed of
Figure FDA0003439773770000028
And normalizing the area difference to obtain the consistency c of the simulation data and the reference data of each orthogonal expansion coefficientqThe normalized calculation formula of the area difference is as follows: c. Cq＝1-2*dq；
S900, obtaining a verification result of dynamic output by integrating consistency calculation of each orthogonal expansion coefficient
Figure FDA0003439773770000029
Wherein ω isqFor each orthogonal spreadWeights of open coefficients and
Figure FDA00034397737700000210
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