CN114757131A - Optimization method of proxy model suitable for CFD uncertainty quantification and related equipment - Google Patents

Optimization method of proxy model suitable for CFD uncertainty quantification and related equipment Download PDF

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CN114757131A
CN114757131A CN202210660267.8A CN202210660267A CN114757131A CN 114757131 A CN114757131 A CN 114757131A CN 202210660267 A CN202210660267 A CN 202210660267A CN 114757131 A CN114757131 A CN 114757131A
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cfd
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章超
陈江涛
赵娇
肖维
张培红
赵炜
吴晓军
肖中云
沈盈盈
周晓军
吕罗庚
胡向鹏
杨福军
郭勇颜
金韬
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The invention is suitable for the technical field of CFD uncertainty quantification, and provides an optimization method and related equipment of a proxy model suitable for CFD uncertainty quantification, wherein the method comprises the following steps: acquiring an initial sample data set of CFD model input parameters; constructing a proxy model based on the initial sample data set, and evaluating the generalization error of the proxy model; if the generalization error of the agent model is larger than a preset error threshold value, updating the agent model; otherwise, ending the optimization to obtain the optimal agent model. And constructing a proxy model based on an initial sample data set of CFD model input parameters, evaluating the generalization error of the proxy model, comparing the generalized error with a preset error threshold, and if the generalization error of the proxy model is larger than the preset error threshold, acquiring new sample data to update the proxy model until the generalization error of the proxy model is smaller than the preset error threshold to obtain an optimal proxy model, thereby improving the efficiency of proxy model optimization.

Description

Optimization method of proxy model suitable for CFD uncertainty quantification and related equipment
Technical Field
The invention relates to the technical field of CFD uncertainty quantification, in particular to an optimization method of a proxy model suitable for CFD uncertainty quantification and related equipment.
Background
CFD (Computational Fluid Dynamics) plays an increasingly important role in the fields of aerospace, energy power, transportation and delivery, and the like. However, due to reasons such as insufficient cognition, the CFD has non-negligible uncertain parameters such as turbulence model parameters and material thermophysical parameters. These uncertain parameters lead to significant uncertainty in the simulation results, which can bring potential risks to the decision. NASA has investigated 2500 on-track aircraft faults, of which about 52% are caused by uncertainty factors. It is therefore desirable to quantify the effect of parameter uncertainty on the CFD numerical simulation.
In the field of CFD uncertainty quantification, a proxy model is an important method for representing uncertainty propagation, and has achieved certain success in engineering. However, in the prior art, because each sample data obtained by sampling needs to be solved by calling a CFD program in the process of constructing and optimizing the proxy model, when many sample data need to be sampled and solved for practical engineering application, under the condition of limited computing resources, the computation amount is very large, the computation time is long, and the efficiency is low. Therefore, a more efficient proxy model optimization method is urgently needed to be developed, and a feasible solution is provided for the problem of parameter uncertainty quantification in engineering under limited computing resources.
Disclosure of Invention
The invention aims to provide an optimization method of a proxy model suitable for CFD uncertainty quantification, and the efficiency of proxy model optimization in the CFD parameter uncertainty quantification process is improved.
In a first aspect, an embodiment of the present invention provides an optimization method for a proxy model suitable for CFD uncertainty quantization, including:
s1, obtaining an initial sample data set of CFD model input parameters;
s2, constructing a proxy model based on the initial sample data set, and evaluating the generalization error of the proxy model;
s3, if the generalization error of the proxy model is larger than a preset error threshold, updating the proxy model; otherwise, ending the optimization to obtain the optimal agent model.
Further, the obtaining the initial sample data set of CFD model input parameters includes:
and performing Latin hypercube sampling on the CFD model input parameters to obtain the initial sample data set, wherein the initial sample data set comprises N sample point sequences.
Further, the constructing a proxy model based on the initial sample data set includes:
inputting the N sample point sequences into a CFD solver, and correspondingly obtaining N response vector sequences;
and constructing the proxy model by a Gaussian regression algorithm based on a sample pool consisting of the N sample point sequences and the corresponding N response vector sequences.
Further, the step of updating the proxy model includes:
constructing an acquisition function based on the initial sample data set;
solving the minimum value of the acquisition function to obtain a new sample point;
inputting the new sample point into a CFD solver to obtain a new response quantity, and adding the new sample point and the new response quantity into the sample pool;
updating the proxy model based on the pool of samples.
Further, after the step of updating the proxy model based on the sample pool, the step of updating the proxy model further comprises:
and calculating the generalization error of the updated proxy model, and comparing the generalization error with the preset error threshold.
Further, the method further comprises:
if the generalization error of the updated proxy model is larger than the preset error threshold, repeating the step of updating the proxy model until the generalization error of the updated proxy model is smaller than the preset error threshold, and obtaining the optimal proxy model.
Further, the solving of the minimum value of the acquisition function to obtain a new sample point includes:
and solving the minimum value of the acquisition function through a genetic algorithm to obtain the new sample point.
In a second aspect, an embodiment of the present invention provides an apparatus for optimizing a proxy model suitable for CFD uncertainty quantization, including:
the acquisition module is used for acquiring an initial sample data set of CFD model input parameters;
the building and evaluating module is used for building a proxy model based on the initial sample data set and evaluating the generalization error of the proxy model;
the optimization module is used for updating the proxy model if the generalization error of the proxy model is larger than a preset error threshold; otherwise, ending the optimization to obtain the optimal agent model.
In a third aspect, an embodiment of the present invention provides a computer device, including: the device comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the steps in the optimization method of the proxy model suitable for CFD uncertainty quantification when executing the computer program.
In a fourth aspect, the embodiment of the present invention provides a computer-readable storage medium, where a computer program is stored, and when the computer program is executed by a processor, the computer program implements the steps in the optimization method of the proxy model suitable for CFD uncertainty quantification.
Compared with the prior art, the embodiment of the invention mainly has the following beneficial effects: the method comprises the steps of constructing a proxy model based on an initial sample data set of CFD (computational fluid dynamics) model input parameters through a Gaussian regression algorithm, evaluating the generalization error of the proxy model, comparing the generalized error with a preset error threshold, and if the generalization error of the proxy model is larger than the preset error threshold, circularly constructing an acquisition function to obtain new sample data and updating the proxy model until the generalization error of the proxy model is smaller than the preset error threshold to obtain an optimal proxy model.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the embodiments of the present invention or the description of the prior art will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of one embodiment of a method for optimizing a proxy model for CFD uncertainty quantification of the present invention;
FIG. 2 is a schematic structural diagram illustrating an embodiment of an optimization apparatus of a proxy model for CFD uncertainty quantization according to the present invention;
fig. 3 is a schematic diagram of the basic structure of a computer device of the present invention.
Detailed Description
The following description provides many different embodiments, or examples, for implementing different features of the invention. The particular examples set forth below are illustrative only and are not intended to be limiting.
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.
Fig. 1 is a flowchart of an embodiment of an optimization method of a proxy model suitable for CFD uncertainty quantization according to the present invention, where the optimization method of the proxy model suitable for CFD uncertainty quantization includes the following steps:
s1, obtaining an initial sample data set of CFD model input parameters;
s2, constructing a proxy model based on the initial sample data set, and evaluating the generalization error of the proxy model;
s3, if the generalization error of the proxy model is larger than a preset error threshold, updating the proxy model; otherwise, ending the optimization to obtain the optimal agent model.
Examples of the inventionIn the above-mentioned CFD model, the input parameters have uncertainty, and may be one, two or more of the multiple parameters of the CFD model, and taking the CFD model as an aircraft wing type turbulence model as an example, the model mainly includes 9 parameters
Figure DEST_PATH_IMAGE001
The input parameters of the CFD model may be one or more of them; then, a Latin hypercube sampling method is used for sampling in a high-dimensional space formed by the CFD model input parameters to obtain a sample point sequence comprising N sample points
Figure 446377DEST_PATH_IMAGE002
An initial sample data set of composition.
Further, constructing a proxy model based on the initial sample data set specifically includes:
inputting the N sample point sequences into a CFD solver, and correspondingly obtaining N response vector sequences;
and constructing the proxy model by a Gaussian regression algorithm based on a sample pool consisting of the N sample point sequences and the corresponding N response vector sequences.
In the embodiment of the invention, N sample point sequences obtained by sampling input parameters
Figure 753730DEST_PATH_IMAGE002
The output quantity of interest of each sample point can be obtained by transmitting the output quantity to a CFD solver, namely a sequence consisting of N response vectors is correspondingly obtained
Figure DEST_PATH_IMAGE003
Forming a sample pool by the N sample point sequences and the corresponding response vector sequences; then randomly removing a sample point from the sample pool
Figure 956304DEST_PATH_IMAGE004
And its response vector
Figure DEST_PATH_IMAGE005
Using the remaining sampleThe data establishes a proxy model representing the discrete relation between input and output by a Gaussian regression algorithm
Figure 476147DEST_PATH_IMAGE006
And circulating the process to obtain N proxy models which are respectively recorded as
Figure DEST_PATH_IMAGE007
. Finally, generalized error of the proxy model is evaluated
Figure 651039DEST_PATH_IMAGE008
。
Further generalizing the proxy model
Figure DEST_PATH_IMAGE009
With a predetermined error threshold
Figure 145605DEST_PATH_IMAGE010
Make a comparison if
Figure 334010DEST_PATH_IMAGE009
Is less than
Figure 470593DEST_PATH_IMAGE010
If the agent model meets the requirement, the optimization process is terminated; if it is not
Figure 827887DEST_PATH_IMAGE009
Is greater than
Figure 555672DEST_PATH_IMAGE010
Updating and optimizing the proxy model by the following steps:
constructing an acquisition function based on the initial sample data set;
solving the minimum value of the acquisition function to obtain a new sample point;
inputting the new sample point into a CFD solver to obtain a new response quantity, and adding the new sample point and the new response quantity into the sample pool;
updating the proxy model based on a pool of samples;
calculating the generalization error of the updated agent model, and comparing the generalization error with a preset error threshold;
if the generalization error of the updated proxy model is larger than the preset error threshold, repeating the step of updating the proxy model until the generalization error of the updated proxy model is smaller than the preset error threshold, and obtaining the optimal proxy model.
In the embodiment of the invention, any input parameter sample in the initial sample data set
Figure DEST_PATH_IMAGE011
An acquisition function of the form:
Figure 434635DEST_PATH_IMAGE012
wherein
Figure DEST_PATH_IMAGE013
；
Then solving the minimum value of the acquisition function through a genetic algorithm to obtain a new sample point
Figure 797745DEST_PATH_IMAGE014
. Inputting new sample points of parameters
Figure 508081DEST_PATH_IMAGE014
Transmitting to CFD solver to obtain corresponding sample output quantity
Figure DEST_PATH_IMAGE015
I.e. new response, and new sample points
Figure 564024DEST_PATH_IMAGE014
And new response
Figure 477754DEST_PATH_IMAGE015
Adding to the sample pool, adding 1 to the number of sample points N, further based on the new sample points contained
Figure 939828DEST_PATH_IMAGE014
Reconstructing the proxy model by a Gaussian regression algorithm to obtain a new proxy model; computing generalization error of new proxy model
Figure 520982DEST_PATH_IMAGE016
And the predetermined error threshold
Figure 590569DEST_PATH_IMAGE010
Comparing, if the new proxy model has generalized error
Figure 7906DEST_PATH_IMAGE016
Greater than a predetermined error threshold
Figure 758825DEST_PATH_IMAGE010
Repeating the above steps of updating and optimizing the proxy model until the generalization error of the new proxy model is obtained
Figure 443753DEST_PATH_IMAGE016
Less than a predetermined error threshold
Figure 153083DEST_PATH_IMAGE010
And stopping the updating optimization process of the proxy model, and taking the corresponding new proxy model as the optimal proxy model.
Taking an aircraft airfoil turbulence model as an example, the model mainly comprises 9 parameters
Figure 588874DEST_PATH_IMAGE001
The input parameters of the CFD model described above may be two of them, i.e., 2-dimensional uncertain input parameters.
The method comprises the following steps: firstly, sampling in a 2-dimensional input parameter space by using Latin hypercube sampling to obtain data of 6 initial sample points; sequentially transmitting the 6 initial sample point data to a CFD program to obtain sample output, correspondingly obtaining a sequence comprising 6 response vectors and containing 6 initial sample point sequencesThe columns and the corresponding sequence of 6 response vectors constitute a pool of samples; randomly selecting 1 sample point from a sample pool as a test set, using the remaining 5 sample points as a training set, constructing an agent model by using a Gaussian regression process algorithm and the training set, and calculating a prediction error of the agent model on the test set; circulating for 6 times, and calculating to obtain the generalization error of the initial proxy model
Figure 409063DEST_PATH_IMAGE009
=0.4496, greater than the preset error threshold of 0.1, so a subsequent model update optimization process needs to be performed to get the optimal proxy model.
Step two: and further constructing an acquisition function related to input parameters based on the initial sample data set, solving the minimization problem of the acquisition function through a genetic algorithm, obtaining new sample points, transmitting the new sample points to a CFD program, correspondingly obtaining new response, and adding the new response into a sample pool, wherein the sample pool contains 7 sample point data.
Step three: and randomly selecting 1 sample point from the sample pool as a test set, using the remaining 6 sample points as a training set, reconstructing a new agent model by using a Gaussian regression process algorithm and the training set, and calculating the prediction error of the agent model on the test set. Circulating for 7 times, and calculating to obtain the generalization error of the new proxy model
Figure 948497DEST_PATH_IMAGE009
=0.30558, still greater than the preset error threshold value of 0.1. And step two and step three are circulated again, and after 5 sample points are added into the sample pool, the generalization error of the new proxy model
Figure 563150DEST_PATH_IMAGE009
=0.095137, if the error is smaller than a preset error threshold value 0.1, the updating optimization process is terminated; there are only 12 sample points data in the final sample pool.
To test the advantages of the method of the present invention, the above process is repeated 100 times, the average value of the final sample pool number is taken, the average sample size required by the method of the present invention is 13.72, and on the premise of achieving the same one-way error (error threshold 0.1), the average sample size required by the original latin hypercube sampling method repeated 100 times is 22.68, as shown in table 1, table 1 is the sample size comparison of the method of the present invention and the original sampling method under the requirement of the one-way error of 0.1:
Figure 735505DEST_PATH_IMAGE018
TABLE 1
The method reduces the number of the required sample points by 39.5 percent under the condition of ensuring the precision, so that the calculation time required by establishing the high-fidelity agent model by the method is about 60 percent of that of the original method, the calculation time is greatly saved, the calculation resources are saved, and the efficiency of agent model optimization in the CFD parameter uncertainty quantification process is improved; the agent model optimization method does not depend on the type of the agent model at the bottom layer, and has universality.
In summary, in the embodiment of the present invention, an agent model is constructed based on an initial sample data set of CFD model input parameters through a gaussian regression algorithm, a generalization error of the agent model is evaluated and then compared with a preset error threshold, if the generalization error of the agent model is greater than the preset error threshold, a collection function is cyclically constructed to obtain new sample data and update the agent model until the generalization error of the agent model is less than the preset error threshold to obtain an optimal agent model.
It should be understood that, although the steps in the flowcharts of the figures are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and may be performed in other orders unless explicitly stated herein. Moreover, at least a portion of the steps in the flow chart of the drawings may include multiple sub-steps or multiple stages, which are not necessarily performed at the same time or on the same device or machine, but may be performed at different times and different places, which are not necessarily performed in sequence, but may be performed alternately or alternatingly with other steps or at least a portion of the sub-steps or stages of other steps.
In a second aspect, as shown in fig. 2, as an implementation of the method for optimizing the proxy model applicable to CFD uncertainty quantization shown in fig. 1, the present invention provides an embodiment of an apparatus for optimizing the proxy model applicable to CFD uncertainty quantization, where the embodiment of the apparatus corresponds to the embodiment of the method shown in fig. 1, and the apparatus for optimizing the proxy model applicable to CFD uncertainty quantization can be applied to various computer devices.
Fig. 2 is a schematic structural diagram illustrating an optimization apparatus of a proxy model suitable for CFD uncertainty quantization according to an embodiment of the present invention, where the apparatus 200 specifically includes:
an obtaining module 201, configured to obtain an initial sample data set of CFD model input parameters;
a constructing and evaluating module 202, configured to construct a proxy model based on the initial sample data set, and evaluate a generalization error of the proxy model;
the optimization module 203 is configured to update the proxy model if the generalization error of the proxy model is greater than a preset error threshold; otherwise, ending the optimization to obtain the optimal agent model.
The optimization device of the proxy model suitable for CFD uncertainty quantization provided in the embodiment of the present invention can implement each implementation manner in the method embodiment of fig. 1 and corresponding beneficial effects, and is not described here again in order to avoid repetition.
In a third aspect, an embodiment of the present invention provides a computer device, including: the device comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the steps in the optimization method of the proxy model suitable for CFD uncertainty quantification when executing the computer program.
In a fourth aspect, the present invention provides a computer readable storage medium, where a computer program is stored, where the computer program, when executed by a processor, implements the steps in the optimization method for a proxy model suitable for CFD uncertainty quantization.
Specifically, referring to fig. 3, fig. 3 is a schematic diagram of a basic structure of a computer device according to an embodiment of the present invention. The computer device 300 includes a memory 301, a processor 302, and a network interface 303 communicatively coupled to each other via a system bus. It is noted that only a computer device 300 having components 301 and 303 is shown, but it is understood that not all of the shown components are required and that more or fewer components may be implemented instead. As will be understood by those skilled in the art, the computer device is a device capable of automatically performing numerical calculation and/or information processing according to a preset or stored instruction, and the hardware includes, but is not limited to, a microprocessor, an Application Specific Integrated Circuit (ASIC), a Programmable Gate Array (FPGA), a Digital Signal Processor (DSP), an embedded device, and the like.
The computer device can be a desktop computer, a notebook, a palm computer, a cloud server and other computing devices. The computer equipment can carry out man-machine interaction with a user through a keyboard, a mouse, a remote controller, a touch panel or voice control equipment and the like.
The memory 301 includes at least one type of readable storage medium including a flash memory, a hard disk, a multimedia card, a card-type memory (e.g., SD or DX memory, etc.), a Random Access Memory (RAM), a Static Random Access Memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the storage 301 may be an internal storage unit of the computer device 300, such as a hard disk or a memory of the computer device 300. In other embodiments, the memory 301 may also be an external storage device of the computer device 300, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), or the like, provided on the computer device 300. Of course, the memory 301 may also include both internal and external storage devices of the computer device 300. In this embodiment, the memory 301 is generally used to store an operating system installed in the computer device 300 and various types of application software, such as program codes of an optimization method of a proxy model suitable for CFD uncertainty quantification. In addition, the memory 301 may also be used to temporarily store various types of data that have been output or are to be output.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present application may be embodied in the form of a software product, which is stored in a storage medium (such as ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal device (such as a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present application.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (10)

1. A method for optimizing a proxy model suitable for CFD uncertainty quantization is characterized by comprising the following steps:
s1, acquiring an initial sample data set of CFD model input parameters;
s2, constructing a proxy model based on the initial sample data set, and evaluating the generalization error of the proxy model;
s3, if the generalization error of the proxy model is larger than a preset error threshold, updating the proxy model; otherwise, ending the optimization to obtain the optimal agent model.
2. The method of claim 1, wherein said obtaining an initial sample data set of CFD model input parameters comprises:
and performing Latin hypercube sampling on the CFD model input parameters to obtain the initial sample data set, wherein the initial sample data set comprises N sample point sequences.
3. The method of claim 2, wherein said building a proxy model based on said initial set of sample data comprises:
inputting the N sample point sequences into a CFD solver, and correspondingly obtaining N response vector sequences;
and constructing the proxy model by a Gaussian regression algorithm based on a sample pool consisting of the N sample point sequences and the corresponding N response vector sequences.
4. The method of claim 3, wherein the step of updating the proxy model comprises:
constructing an acquisition function based on the initial sample data set;
solving the minimum value of the acquisition function to obtain a new sample point;
inputting the new sample point into a CFD solver to obtain a new response quantity, and adding the new sample point and the new response quantity into the sample pool;
updating the proxy model based on the pool of samples.
5. The method of claim 4, wherein after the step of updating the proxy model based on the sample pool, the step of updating the proxy model further comprises:
and calculating the generalization error of the updated agent model, and comparing the generalization error with the preset error threshold.
6. The method of claim 5, wherein the method further comprises:
if the generalization error of the updated proxy model is larger than the preset error threshold, repeating the step of updating the proxy model until the generalization error of the updated proxy model is smaller than the preset error threshold, and obtaining the optimal proxy model.
7. The method of claim 6, wherein solving for the minima of the acquisition function to obtain new sample points comprises:
and solving the minimum value of the acquisition function through a genetic algorithm to obtain the new sample point.
8. An optimization apparatus of a proxy model suitable for CFD uncertainty quantization, comprising:
the acquisition module is used for acquiring an initial sample data set of CFD model input parameters;
the building and evaluating module is used for building a proxy model based on the initial sample data set and evaluating the generalization error of the proxy model;
the optimization module is used for updating the proxy model if the generalization error of the proxy model is larger than a preset error threshold value; otherwise, ending the optimization to obtain the optimal agent model.
9. A computer device, comprising: memory, processor and computer program stored on the memory and executable on the processor, the processor implementing the steps in the method for optimizing a proxy model for CFD uncertainty quantification according to any one of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium, having stored thereon a computer program which, when being executed by a processor, carries out the steps of the method for optimizing a proxy model for CFD uncertainty quantization according to any one of claims 1 to 7.
CN202210660267.8A 2022-06-13 2022-06-13 Optimization method of proxy model suitable for CFD uncertainty quantification and related equipment Pending CN114757131A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116842853A (en) * 2023-09-01 2023-10-03 中国空气动力研究与发展中心计算空气动力研究所 Missile aerodynamic characteristic prediction model construction method for uncertainty quantization

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116842853A (en) * 2023-09-01 2023-10-03 中国空气动力研究与发展中心计算空气动力研究所 Missile aerodynamic characteristic prediction model construction method for uncertainty quantization
CN116842853B (en) * 2023-09-01 2023-11-28 中国空气动力研究与发展中心计算空气动力研究所 Missile aerodynamic characteristic prediction model construction method for uncertainty quantization

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Application publication date: 20220715