CN117633491B - Pneumatic data uncertainty quantitative evaluation method, electronic device and storage medium - Google Patents
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Abstract
A quantitative evaluation method for uncertainty of pneumatic data, electronic equipment and a storage medium belong to the field of aerodynamics. In order to improve the quantitative evaluation efficiency of the uncertainty of the pneumatic data, the invention sets the input variable and the output variable of the pneumatic data and obtains the input variable sample and the output variable sample of the pneumatic data; setting a pneumatic data uncertainty quantization parameter, and collecting samples of an input variable sample of pneumatic data and a pneumatic data output variable sample based on a distribution form of the pneumatic data uncertainty quantization parameter to obtain a test set; constructing a pneumatic data uncertainty quantitative evaluation model based on a symbolic regression method; inputting the test set into a pneumatic data uncertainty quantitative evaluation model to obtain an output value of the pneumatic data uncertainty quantitative evaluation model, constructing an expansion, calculating mathematical statistics of the expansion, and finishing pneumatic data uncertainty quantitative evaluation. The invention establishes the mathematical function expression of the input variable and the output variable based on a small number of samples, thereby greatly improving the calculation efficiency.
Description
Technical Field
The invention belongs to the field of aerodynamics, and particularly relates to a pneumatic data uncertainty quantitative evaluation method, electronic equipment and a storage medium.
Background
As a main acquisition path of aerodynamic data of the aircraft, numerical calculation and wind tunnel test are modeling of real natural phenomena, and errors and uncertainty exist in the modeling of the real natural phenomena. In the numerical calculation method, parameters such as Mach number, attack angle and the like are considered as the most critical influencing factors of aerodynamic data, and geometrical appearance parameters (such as model manufacturing tolerance, model static deformation and the like) and numerical calculation solving parameters (including grid generation, space discrete format, time discrete format selection and the like) also cause uncertainty of the aerodynamic data; the wind tunnel test data has high precision, but has the influence of parameters such as hole wall interference, bracket interference, reynolds number, aeroelasticity and the like. Therefore, if uncertainty of parameters under real conditions is not considered, pneumatic performance of an aircraft with a real appearance under a complex incoming flow condition cannot be accurately estimated, uncertainty estimation is a basis of safe flight of the aircraft, and is a premise of effective action of a flight control system, and uncertainty estimation on acquired pneumatic data is very important.
Uncertainty quantization assessment is to quantify the uncertainty of the response caused by an input parameter. Common uncertainty quantitative assessment methods include: a Monte Carlo method, a perturbation method, a moment equation method, a random configuration method and a polynomial chaos method. The Monte Carlo method is widely used because of simple structure and convenient use. The method obtains the statistical characteristics of the result by randomly sampling a large amount of problems to be solved so as to quantify the uncertainty of the evaluation parameters. The higher the accuracy of the monte carlo method, the higher the number of samples required, and therefore a large number of samples are required to obtain accurate calculation results, however, for pneumatic data, random samples at a large number of sampling points cannot be obtained.
Disclosure of Invention
The invention aims to improve the quantitative evaluation efficiency of the uncertainty of pneumatic data and provides a quantitative evaluation method of the uncertainty of the pneumatic data, electronic equipment and a storage medium.
In order to achieve the above purpose, the present invention is realized by the following technical scheme:
a pneumatic data uncertainty quantitative evaluation method comprises the following steps:
s1, setting an input variable and an output variable of pneumatic data, and acquiring an input variable sample and an output variable sample of the pneumatic data;
s2, setting uncertainty quantization parameters of pneumatic data, and collecting samples of input variable samples of the pneumatic data and output variable samples of the pneumatic data obtained in the step S1 based on distribution forms of the uncertainty quantization parameters of the pneumatic data to obtain a test set;
s3, constructing a pneumatic data uncertainty quantitative evaluation model based on a symbolic regression method;
s4, inputting the test set obtained in the step S2 into the pneumatic data uncertainty quantitative evaluation model constructed in the step S3 to obtain an output value of the pneumatic data uncertainty quantitative evaluation model;
s5, constructing an expansion for the output value of the pneumatic data uncertainty quantitative evaluation model obtained in the step S4, and then calculating mathematical statistics of the expansion to complete pneumatic data uncertainty quantitative evaluation.
Further, the specific implementation method of the step S1 includes the following steps:
s1.1, setting pneumatic data input variables: the pneumatic data input variables are incoming flow parameters or model geometric shape parameters, the incoming flow parameters comprise attack angles, sideslip angles, mach numbers and Reynolds numbers, and the model geometric shape parameters comprise model span, front edge sweepback angles, rear edge sweepback angles and torsion angles;
s1.2, setting a pneumatic data output variable: the aerodynamic data output variable is a lift coefficient or a drag coefficient.
Further, the specific implementation method of the step S2 includes the following steps:
s2.1, setting uncertainty quantization parameters of pneumatic data, wherein the uncertainty quantization parameters comprise incoming flow parameters or model geometric shape parameters;
s2.2, setting distribution forms of the pneumatic data uncertainty quantization parameters to comprise uniform distribution or normal distribution, wherein a sample acquisition method comprises one of Sobol sampling, dual variable sampling and Halton sampling.
Further, in step S2.2, the quantization parameter of uncertainty of the pneumatic data is normally distributed, and the sampling method is Sobol sampling.
Further, the specific implementation method of the step S3 includes the following steps:
s3.1, setting a to-be-selected symbol set of a symbol regression method, wherein the symbols of the to-be-selected symbol set comprise: ++, -,/, or, and mod, sin, cos, tan, exp, square, cube, absolute, log10, root mark;
s3.2, setting an adaptability function of a symbolic regression method as a mean square error MSE, and calculating an expression as follows:
；
wherein,nfor the number of samples to be taken,y i is the firstiThe pneumatic data output variables of the individual samples,is the firstiPneumatic data input variable of individual samples, +.>Is the firstiA functional expression of a sign regression method of the individual samples;
s3.3, setting basic parameters and iteration conditions of a symbolic regression method, wherein the basic parameters are functional expressions of the symbolic regression method, the maximum length is 10, and the iteration conditions are genetic evolution iterations and the number is 40;
s3.4, constructing a function expression of the symbolic regression method based on the symbolic regression method programmed by genetic expression according to the symbol set to be selected in the step S3.1, the basic parameters and the iteration conditions of the symbolic regression method in the step S3.3.
Further, the specific implementation method of the step S5 includes the following steps:
s5.1. Determining the expansion by a non-embedded chaotic polynomial expansion methodThe computational expression is:
；
wherein,for the orthogonal basis functions, < > is determined according to the Askey scheme>For the coefficient of expansion according to ∈ ->And +.>Corresponding->Obtaining，N PC Total number of items for truncation;
s5.2. CalculationkIndividual samplesThe mathematical statistics comprise mean, variance, mean of mathematical statistics +.>The mathematical expression of (2) is:
；
variance of mathematical statisticsThe mathematical expression of (2) is:
。
an electronic device comprising a memory and a processor, the memory storing a computer program, said processor implementing the steps of said method for quantitatively evaluating the uncertainty of pneumatic data when executing said computer program.
A computer readable storage medium having stored thereon a computer program which when executed by a processor implements the method of quantitatively evaluating pneumatic data uncertainty.
The invention has the beneficial effects that:
according to the pneumatic data uncertainty quantitative evaluation method, aiming at the problem that the conventional Monte Carlo method cannot acquire random samples at a large number of sampling points, a mathematical function expression between an input variable and an output variable is established through a symbolic regression method based on a small number of samples, and corresponding output values at the sampling points are acquired, so that mathematical statistics are calculated, uncertainty quantization is completed, calculation efficiency is greatly improved, and calculation cost is reduced.
Drawings
FIG. 1 is a flow chart of a method for quantitatively evaluating uncertainty of pneumatic data according to the present invention;
fig. 2 is a diagram of Sobol sampling point distribution diagram in a pneumatic data uncertainty quantization and evaluation method according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings and detailed description. It should be understood that the embodiments described herein are for purposes of illustration only and are not intended to limit the invention, i.e., the embodiments described are merely some, but not all, of the embodiments of the invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein can be arranged and designed in a wide variety of different configurations, and the present invention can have other embodiments as well.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, are intended to fall within the scope of the present invention.
For further understanding of the invention, the following detailed description is to be taken in conjunction with fig. 1 and 2, in which:
embodiment one:
a pneumatic data uncertainty quantitative evaluation method comprises the following steps:
s1, setting an input variable and an output variable of pneumatic data, and acquiring an input variable sample and an output variable sample of the pneumatic data;
further, the specific implementation method of the step S1 includes the following steps:
s1.1, setting pneumatic data input variables: the pneumatic data input variables are incoming flow parameters or model geometric shape parameters, the incoming flow parameters comprise attack angles, sideslip angles, mach numbers and Reynolds numbers, and the model geometric shape parameters comprise model span, front edge sweepback angles, rear edge sweepback angles and torsion angles;
s1.2, setting a pneumatic data output variable: the pneumatic data output variable is a lift coefficient or a resistance coefficient;
s2, setting uncertainty quantization parameters of pneumatic data, and collecting samples of input variable samples of the pneumatic data and output variable samples of the pneumatic data obtained in the step S1 based on distribution forms of the uncertainty quantization parameters of the pneumatic data to obtain a test set;
further, the specific implementation method of the step S2 includes the following steps:
s2.1, setting uncertainty quantization parameters of pneumatic data, wherein the uncertainty quantization parameters comprise incoming flow parameters or model geometric shape parameters;
s2.2, setting distribution forms of the pneumatic data uncertainty quantization parameters to comprise uniform distribution or normal distribution, wherein a sample acquisition method comprises one of Sobol sampling, dual variable sampling and Halton sampling;
further, in step S2.2, the quantization parameter of uncertainty of the pneumatic data is normally distributed, and the sampling method is Sobol sampling;
s3, constructing a pneumatic data uncertainty quantitative evaluation model based on a symbolic regression method;
further, the specific implementation method of the step S3 includes the following steps:
s3.1, setting a to-be-selected symbol set of a symbol regression method, wherein the symbols of the to-be-selected symbol set comprise: ++, -,/, or, and mod, sin, cos, tan, exp, square, cube, absolute, log10, root mark;
s3.2, setting an adaptability function of a symbolic regression method as a mean square error MSE, and calculating an expression as follows:
；
wherein,nfor the number of samples to be taken,y i is the firstiThe pneumatic data output variables of the individual samples,is the firstiPneumatic data input variable of individual samples, +.>Is the firstiA functional expression of a sign regression method of the individual samples;
s3.3, setting basic parameters and iteration conditions of a symbolic regression method, wherein the basic parameters are functional expressions of the symbolic regression method, the maximum length is 10, and the iteration conditions are genetic evolution iterations and the number is 40;
s3.4, constructing a function expression of a symbol regression method based on the symbol regression method programmed by genetic expression according to the symbol set to be selected in the step S3.1, the basic parameters and the iteration conditions of the symbol regression method in the step S3.3;
s4, inputting the test set obtained in the step S2 into the pneumatic data uncertainty quantitative evaluation model constructed in the step S3 to obtain an output value of the pneumatic data uncertainty quantitative evaluation model;
s5, constructing an expansion for the output value of the pneumatic data uncertainty quantitative evaluation model obtained in the step S4, and then calculating mathematical statistics of the expansion to complete the pneumatic data uncertainty quantitative evaluation;
according to the non-embedded chaotic polynomial expansion method, a proper orthogonal basis function is selected according to a probability density distribution function of input parameters, then the output of the random process is expanded in a spectrum space formed by the basis functions, and a problem core is converted into an orthogonal polynomial coefficient determination problem in the spectrum space;
further, the specific implementation method of the step S5 includes the following steps:
s5.1. Determining the expansion by a non-embedded chaotic polynomial expansion methodThe computational expression is:
；
wherein,for the orthogonal basis functions, < > is determined according to the Askey scheme>For the coefficient of expansion according to ∈ ->And +.>Corresponding->Obtaining，N PC Total number of items for truncation;
s5.2. CalculationkIndividual samplesThe mathematical statistics comprise mean, variance, mean of mathematical statistics +.>The mathematical expression of (2) is:
；
variance of mathematical statisticsThe mathematical expression of (2) is:
。
further, the mathematical expression of the test function for constructing the pneumatic data uncertainty quantization parameter is:
；
wherein,p 1 a first pneumatic data input variable that is a test function of the pneumatic data uncertainty quantization parameter,p 2 a second pneumatic data input variable of the test function of the pneumatic data uncertainty quantization parameter, q is a pneumatic data output variable of the test function of the pneumatic data uncertainty quantization parameter;
further, in step S3, based on 100 samples, verification is performed on the test function based on symbolic regression, and the expression of the test function after symbolic regression is:
；
firstly, selecting an individual with good adaptability in the first generation as a parent individual, and carrying out genetic operation (crossing and mutation) on the parent individual to generate a new individual, namely the next generation individual. Iteratively performing the steps until reaching the iteration condition, and stopping to finally obtain the individual with the best adaptability;
in the pneumatic data uncertainty quantitative evaluation method according to the present embodiment, the mathematical statistics calculation result of the test function is shown in table 1:
table 1 comparison table of mathematical statistics calculation results
As can be seen from Table 1, the uncertainty result of the sign regression and non-embedded chaotic polynomial expansion method based on the invention is consistent, which illustrates the accuracy of the method in the embodiment, and the method in the embodiment only needs 100 samples, thus greatly improving the calculation efficiency and reducing the calculation cost.
Embodiment two:
an electronic device comprising a memory and a processor, the memory storing a computer program, the processor implementing the steps of a pneumatic data uncertainty quantitative assessment method according to embodiment one of the present invention when executing the computer program.
The computer device of the present invention may be a device including a processor and a memory, such as a single chip microcomputer including a central processing unit. And the processor is used for realizing the steps of the pneumatic data uncertainty quantitative evaluation method when executing the computer program stored in the memory.
The processor may be a central processing unit (Central Processing Unit, CPU), other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program (such as a sound playing function, an image playing function, etc.) required for at least one function, and the like; the storage data area may store data (such as audio data, phonebook, etc.) created according to the use of the handset, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as a hard disk, memory, plug-in hard disk, smart Media Card (SMC), secure Digital (SD) Card, flash Card (Flash Card), at least one disk storage device, flash memory device, or other volatile solid-state storage device.
Embodiment III:
a computer readable storage medium having a computer program stored thereon, wherein the computer program when executed by a processor implements a pneumatic data uncertainty quantitative assessment method according to embodiment one.
The computer readable storage medium of the present invention may be any form of storage medium that is readable by a processor of a computer device, including but not limited to, nonvolatile memory, volatile memory, ferroelectric memory, etc., on which a computer program is stored, and when the processor of the computer device reads and executes the computer program stored in the memory, the steps of a pneumatic data uncertainty quantization evaluation method described above may be implemented.
The computer program comprises computer program code which may be in source code form, object code form, executable file or in some intermediate form, etc. The computer readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), an electrical carrier signal, a telecommunications signal, a software distribution medium, and so forth. It should be noted that the computer readable medium contains content that can be appropriately scaled according to the requirements of jurisdictions in which such content is subject to legislation and patent practice, such as in certain jurisdictions in which such content is subject to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals.
It is noted that relational terms such as "first" and "second", and the like, are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
Although the present application has been described hereinabove with reference to specific embodiments, various modifications thereof may be made and equivalents may be substituted for elements thereof without departing from the scope of the application. In particular, the features of the embodiments disclosed in this application may be combined with each other in any way as long as there is no structural conflict, and the exhaustive description of these combinations is not given in this specification merely for the sake of omitting the sake of brevity and saving resources. Therefore, it is intended that the present application not be limited to the particular embodiments disclosed, but that the present application include all embodiments falling within the scope of the appended claims.
Claims (6)
1. A method for quantitatively evaluating uncertainty of pneumatic data, comprising the steps of:
s1, setting an input variable and an output variable of pneumatic data, and acquiring an input variable sample and an output variable sample of the pneumatic data;
s2, setting uncertainty quantization parameters of pneumatic data, and collecting samples of input variable samples of the pneumatic data and output variable samples of the pneumatic data obtained in the step S1 based on distribution forms of the uncertainty quantization parameters of the pneumatic data to obtain a test set;
the specific implementation method of the step S2 comprises the following steps:
s2.1, setting uncertainty quantization parameters of pneumatic data including incoming flow parameters or model geometric shape parameters;
s2.2, setting distribution forms of the pneumatic data uncertainty quantization parameters to comprise uniform distribution or normal distribution, wherein a sample acquisition method comprises one of Sobol sampling, dual variable sampling and Halton sampling;
s3, constructing a pneumatic data uncertainty quantitative evaluation model based on a symbolic regression method;
the specific implementation method of the step S3 comprises the following steps:
s3.1, setting a to-be-selected symbol set of a symbol regression method, wherein the symbols of the to-be-selected symbol set comprise: ++, -,/, or, and mod, sin, cos, tan, exp, square, cube, absolute, log10, root mark;
s3.2, setting an adaptability function of a symbolic regression method as a mean square error MSE, wherein a calculation expression is as follows:
where n is the number of samples, y i Output variable, x, for pneumatic data of the ith sample i The pneumatic data input variable for the ith sample, f (x i ) A functional expression of a symbolic regression method for the ith sample;
s3.3, setting basic parameters and iteration conditions of a symbolic regression method, wherein the basic parameters are functional expressions of the symbolic regression method, the maximum length is 10, and the iteration conditions are genetic evolution iterations and the number is 40;
s3.4, constructing a function expression of a symbol regression method based on the symbol regression method programmed by genetic expression according to the symbol set to be selected in the step S3.1, the basic parameters and the iteration conditions of the symbol regression method in the step S3.3;
s4, inputting the test set obtained in the step S2 into the pneumatic data uncertainty quantitative evaluation model constructed in the step S3 to obtain an output value of the pneumatic data uncertainty quantitative evaluation model;
s5, constructing an expansion for the output value of the pneumatic data uncertainty quantitative evaluation model obtained in the step S4, and then calculating mathematical statistics of the expansion to complete pneumatic data uncertainty quantitative evaluation.
2. The method for quantitatively evaluating uncertainty of pneumatic data according to claim 1, wherein the specific implementation method of step S1 comprises the steps of:
s1.1, setting a pneumatic data input variable: the pneumatic data input variables are incoming flow parameters or model geometric shape parameters, the incoming flow parameters comprise attack angles, sideslip angles, mach numbers and Reynolds numbers, and the model geometric shape parameters comprise model span, front edge sweepback angles, rear edge sweepback angles and torsion angles;
s1.2, setting a pneumatic data output variable: the aerodynamic data output variable is a lift coefficient or a drag coefficient.
3. The method according to claim 2, wherein the pneumatic data uncertainty quantization parameter in step S2.2 is a normal distribution, and the sampling method is Sobol sampling.
4. A method for quantitatively evaluating uncertainty of pneumatic data as set forth in claim 3, wherein the specific implementation method of step S5 includes the steps of:
s5.1, determining an expansion R (ζ) by a non-embedded chaotic polynomial expansion method, wherein the calculation expression is as follows:
wherein, psi is j (ζ) is an orthogonal basis function, α, determined according to the Askey scheme j For the expanded coefficients, according to ψ j (ζ) and x at the sampling point i Corresponding y i Obtained N PC Total number of items for truncation;
s5.2. calculating k samples R k (xi) mathematical statistics including mean, variance, mean of mathematical statisticsThe mathematical expression of (2) is:
mathematics systemVariance sigma of the metric 2 The mathematical expression of (2) is:
5. an electronic device comprising a memory and a processor, the memory storing a computer program, the processor implementing the steps of a pneumatic data uncertainty quantization assessment method according to any one of claims 1-4 when executing the computer program.
6. A computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements a pneumatic data uncertainty quantitative assessment method according to any of claims 1-4.
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| WO2006104838A2 (en) * | 2005-03-25 | 2006-10-05 | Lockheed Martin Corporation | Lifting body tuned for passive re-entry |
| CN115809504A (en) * | 2022-11-14 | 2023-03-17 | 中国运载火箭技术研究院 | Multi-source pneumatic data uncertainty quantitative evaluation method and system |
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