PCA (Principal Component Analysis)-based rear duct variable area ejector generation method, device and equipment and storage medium
By using PCA to parameterize the ejector shape and perform principal component analysis, the problem of low sample generation efficiency in high-dimensional parameter space is solved, and efficient generation and uniform design of the ejector shape are achieved.
Patent Information
- Application Number
- CN202511968617.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-24
- Publication Date
- 2026-03-20
AI Technical Summary
In existing designs of variable area ejectors with a rear duct, the high dimensionality of parameters leads to problems such as low sample generation efficiency and uneven exploration of the design space.
The ejector shape was parameterized using PCA, and perturbation shape samples were generated using CST parameterization method. Principal component analysis was performed to extract the principal mode matrix of shape deformation. The top K principal modes were selected, and uniform sampling was performed in the low-dimensional modal coefficient space using Latin hypercube sampling. Finally, the target ejector shape coordinate data were reconstructed.
While ensuring the physical rationality of the shape, the efficiency of ejector shape generation has been significantly improved, achieving uniform coverage of the design space and efficient exploration.
Smart Images
Figure CN121706259A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of aero-engines, and in particular to a method, apparatus, device, and storage medium for generating a PCA-based variable area ejector with a rear duct. Background Technology
[0002] Variable area ejectors are crucial rectifying devices in aero-engine propulsion systems. The geometry of their internal flow channels directly determines the mixing efficiency, pressure distribution, and flow regulation characteristics of the gases in the inner and outer bypass ducts. The throat and expansion section curves of the rear-bypass variable area ejector are particularly critical. These curves are hydrodynamically equivalent to two-dimensional aerodynamic curves with continuous smooth boundaries, exhibiting aerodynamic characteristics highly similar to traditional airfoils. In existing geometric design processes for rear-bypass variable area ejectors, designers typically need to generate a large number of ejector curve samples to support subsequent aerodynamic simulations, optimization iterations, and uncertainty analysis.
[0003] However, ejector curves have a high dimensionality in their parameterization description. For example, when using the CST parameterization method, a single curve typically requires more than ten parameters for description. When designers need to generate a well-covered set of curve samples in a high-dimensional parameter space, they face problems such as uneven sample distribution and high computational resource consumption. Specifically, if all CST parameters are randomly perturbed and sampled directly, due to a lack of understanding of the main direction of curve deformation, the generated samples often cluster in local regions of the parameter space, with minimal differences between a large number of samples, while the truly representative curve deformation patterns are not adequately covered. This forces designers to generate an extremely large number of samples to effectively explore the ejector curve design space, which is not only computationally inefficient but also makes it difficult to guarantee the diversity and physical rationality of the samples.
[0004] In view of the above, this application is hereby submitted. Summary of the Invention
[0005] This invention discloses a method, apparatus, device, and storage medium for generating a post-duct variable area ejector based on PCA, aiming to solve the technical problems of low sample generation efficiency and uneven design space exploration caused by the high parameter dimensionality in the shape design of existing post-duct variable area ejectors. The first embodiment of the present invention provides a method for generating a post-duct variable area ejector based on PCA, comprising: Obtain the original coordinate data of the shapes of multiple basic ejectors, and perform interpolation processing on the original coordinate data to obtain standardized shape coordinate data; The standardized shape coordinate data were fitted using the CST parameterization method to obtain the CST fitting parameters corresponding to the shape of each basic ejector. Based on the CST fitting parameters, the shapes of each basic ejector are perturbed to generate perturbed shape samples, and the perturbed shape samples are converted into shape coordinate matrices. Principal component analysis was performed on the shape coordinate matrix to extract the principal mode matrix of shape deformation and the modal coefficients corresponding to each disturbed shape sample; Based on the variance contribution rate of the principal mode matrix of the external shape deformation, the first K principal modes of external shape deformation are selected, and the range of values of the modal coefficients is calculated to determine the K-dimensional modal coefficient space. The Latin hypercube sampling method is used to uniformly sample within the K-dimensional modal coefficient space to obtain multiple sets of target modal coefficients; Based on the target modal coefficients and the principal modal matrix of the shape deformation, inverse principal component analysis transformation is performed to reconstruct the target ejector shape coordinate data.
[0006] Preferably, the interpolation process uses a linear interpolation method to uniformly interpolate the original coordinate data of each basic ejector shape to the same number of sampling points to obtain the standardized shape coordinate data.
[0007] Preferably, the CST parameterization method uses the following formula to represent the ejector outline: y(x) = C(x) * S(x) Where C(x) is a class function used to guarantee the endpoint conditions of the ejector shape; S(x) is a shape function, which uses polynomial expansion to represent the shape of the ejector shape, and its expression is:
[0008] in, Here are the CST fitting parameters, and N is the polynomial order. Let i be the i-th power of the normalized chord coordinates of each point on the ejector's outer surface.
[0009] Preferably, the parameter perturbation includes: The perturbable range is calculated based on the sensitivity of each CST fitting parameter, and the perturbable range is calculated according to the following formula:
[0010] in, Let be the perturbation range of the i-th CST fitting parameters, and let target_y_change be the change in the target ordinate. The sensitivity of the i-th CST fitting parameter; Random perturbation values are generated within the perturbation range and superimposed on the CST fitting parameters to obtain the perturbed CST parameters; The perturbated CST parameters are converted into longitudinal coordinate points of the ejector shape to generate the perturbated shape sample. The conversion formula is: j=1...,m; in, For the k-th perturbation shape sample at the sampling point The ordinate at that location, Let i be the CST parameter of the k-th perturbation shape sample. The sampling points are equidistant from the chord length, and m is the total number of sampling points. Let be the i-th power of the x-coordinate of the j-th sampling point.
[0011] Preferably, the principal component analysis of the external coordinate matrix specifically involves: Calculate the covariance matrix of the external shape coordinate matrix. The formula for calculating the covariance matrix is as follows:
[0012] Where Y is the external coordinate matrix, Let be the mean of the shape coordinate matrix, and n be the number of perturbed shape samples; perform eigenvalue decomposition on the covariance matrix to obtain the eigenvector matrix V and the eigenvalue matrix D, whose eigenvalue equation is: ; The eigenvector matrix V constitutes the principal mode matrix of the external shape deformation, and the diagonal elements of the eigenvalue matrix D characterize the variance contribution of each principal mode of external shape deformation.
[0013] Preferably, the range of the modal coefficients is determined by statistically analyzing the maximum and minimum values of the projection values of each disturbed airfoil sample in the direction of each airfoil deformation principal mode.
[0014] Preferably, the variance contribution rate of each principal mode of external deformation is calculated according to the following formula:
[0015] in, Let be the variance contribution rate of the i-th principal mode of external shape deformation. For the i-th eigenvalue, The sum of all eigenvalues is used. When the cumulative variance contribution rate of the current K main modes of shape deformation reaches a preset threshold, the value of K stops increasing.
[0016] A second embodiment of the present invention provides a PCA-based variable area ejector generation device for a post-ducted duct, comprising: The data preprocessing module is used to acquire the original coordinate data of multiple basic ejector shapes, and to perform interpolation processing on the original coordinate data to obtain standardized shape coordinate data. The CST parameterization module is used to fit the standardized shape coordinate data using the CST parameterization method to obtain the CST fitting parameters corresponding to the shape of each basic ejector. The perturbation sample generation module is used to perturb the parameters of each basic ejector shape based on the CST fitting parameters, generate perturbation shape samples, and convert the perturbation shape samples into shape coordinate matrices. The principal component analysis module is used to perform principal component analysis on the shape coordinate matrix and extract the principal mode matrix of shape deformation and the modal coefficients corresponding to each disturbed shape sample. The K-dimensional modal coefficient space determination module is used to select the first K main modes of external deformation based on the variance contribution rate of the main mode matrix of external deformation, and to calculate the value range of the modal coefficients to determine the K-dimensional modal coefficient space. The sampling module is used to uniformly sample within the K-dimensional modal coefficient space using the Latin hypercube sampling method to obtain multiple sets of target modal coefficients; The shape reconstruction module is used to perform inverse principal component analysis transformation based on the target modal coefficients and the shape deformation principal mode matrix to reconstruct the target ejector shape coordinate data.
[0017] The third embodiment of the present invention provides a PCA-based variable area ejector generation device, including a memory and a processor. The memory stores a computer program, which can be executed by the processor to implement the PCA-based variable area ejector generation method as described in any of the above embodiments.
[0018] The fourth embodiment of the present invention provides a computer-readable storage medium, characterized in that it stores a computer program, which can be executed by a processor of the device in which the computer-readable storage medium is located, to implement a PCA-based variable area ejector generation method as described in any of the above claims.
[0019] This invention provides a PCA-based method, apparatus, device, and storage medium for generating a post-duct variable area ejector. The method converts the original coordinate data of the basic ejector shape into low-dimensional controllable parameters using the CST parameterization method. Based on this, the CST fitted parameters are perturbed to generate a large number of perturbed shape samples. Principal component analysis is then used to extract the principal mode matrix of the shape deformation, compressing the high-dimensional parameter space into a low-dimensional modal coefficient space composed of a few principal modes. Furthermore, the top K principal modes are selected based on the variance contribution rate, and the value range of the modal coefficients is determined. Uniform sampling is performed within this K-dimensional modal coefficient space using the Latin hypercube sampling method. Finally, inverse principal component analysis is used to reconstruct the target modal coefficients obtained from the sampling into the target ejector shape coordinate data. This method, while ensuring the physical rationality of the ejector shape, achieves uniform coverage and efficient exploration of the design space with a smaller number of samples, significantly improving the efficiency of ejector shape generation. Attached Figure Description
[0020] Figure 1 This is a flowchart illustrating a PCA-based variable area ejector generation method according to the first embodiment of the present invention. Figure 2 This is a schematic diagram of the original coordinate input format provided by the present invention; Figure 3 This is a schematic diagram of an example of CST parameter fitting provided by the present invention; Figure 4 This is a schematic diagram of the variance contribution rate provided by the present invention; Figure 5 This is a schematic diagram of the mode 1 coefficient distribution provided by the present invention; Figure 6 This is a schematic diagram of 8-dimensional Latin hypercube sampling provided by the present invention; Figure 7 This is a schematic diagram of a PCA-based variable area ejector generation device provided in the second embodiment of the present invention. Detailed Implementation
[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0022] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0023] This invention discloses a method, apparatus, device, and storage medium for generating a post-duct variable area ejector based on PCA, aiming to solve the technical problems of low sample generation efficiency and uneven design space exploration caused by the high parameter dimensionality in the shape design of existing post-duct variable area ejectors. Please see Figure 1 The first embodiment of the present invention provides a method for generating a PCA-based variable area ejector, which can be executed by a generation device or system, specifically by one or more processors within the generation device or system, to at least implement the following steps: S101, Obtain the raw coordinate data of multiple basic ejector shapes (the format is as follows). Figure 2 As shown, the original coordinate data is interpolated to obtain standardized shape coordinate data; In this embodiment, the generating device can be a desktop computer, laptop computer, server, or other terminal with data processing capabilities. The auxiliary device can be equipped with a corresponding operating system and application software, and the functions required in this embodiment can be realized through the combination of the operating system and application software.
[0024] In this embodiment, the initial step is to obtain the raw coordinate data of multiple basic ejector shapes as the data basis for subsequent processing. Since the outer wall curve of the ducted variable area ejector is equivalent to a two-dimensional aerodynamic curve with a continuous smooth outer boundary in terms of hydrodynamic characteristics, and is highly similar to traditional airfoils, mature airfoil data can be used as the basic ejector shape. Specifically, a new Excel spreadsheet named "airfoils.xlsx" is created in the program's folder. Nine blank sheets are created within this spreadsheet and named "airfoil1, airfoil2, ..., airfoil9". The raw coordinate data of the corresponding basic ejector shape is entered into each sheet, where the first column is the x-coordinate and the second column is the corresponding y-coordinate. During program execution, the coordinate points in the Excel spreadsheet are read and converted into a .mat file format suitable for MATLAB operations. Because the number and distribution of sampling points in the raw coordinate data of basic ejector shapes from different sources may vary, interpolation processing of the raw coordinate data is required to ensure consistency in the point correspondence between different samples during subsequent CST fitting and principal component analysis. This embodiment uses a linear interpolation method to uniformly interpolate the original coordinate data of each basic ejector shape to the same number of sampling points, thereby obtaining standardized shape coordinate data, thus obtaining a smooth ejector shape curve with a consistent number of points, providing standardized data input for subsequent parameterization processing.
[0025] S102, The standardized shape coordinate data is fitted using the CST parameterization method to obtain the CST fitting parameters corresponding to the shape of each basic ejector. Please see Figure 3 After obtaining standardized shape coordinate data, the Class-Shape Transformation (CST) parameterization method is used to fit it, converting the ejector shape coordinates into a small number of controllable parameters. The CST method is a classic and efficient curve parameter description method that can describe a complete complex curve with only a few parameters. This not only ensures the integrity of the curve features but also facilitates subsequent parameter perturbation to generate diverse curve samples. Specifically, each ejector shape profile is represented by the CST method as y(x) = C(x) * S(x), where C(x) is a class function used to ensure the endpoint conditions of the ejector shape, and S(x) is a shape function, represented by a polynomial expansion, with the expression: ,in Here are the CST fitting parameters, and N is the polynomial order. The normalized chord coordinates of all points on the ejector's shape are raised to the power of i. The effectiveness of CST parametric fitting is determined by three key parameters: the leading-edge fitting parameter N1, the trailing-edge fitting parameter N2, and the polynomial order N. The leading-edge and trailing-edge fitting parameters N1 and N2 are generally determined based on engineering experience. For ejectors used at the end of an outer bypass duct, where the airflow velocity is typically 250 to 340 meters per second (not exceeding the speed of sound), a value of 0.5 for N1 and 1.0 for N2 are appropriate. For applications involving high-speed conditions such as low-bypass engines in specific scenarios, N1 can be reduced to 0.2, and N2 can be reduced accordingly. The selection of the polynomial order N requires balancing fitting accuracy and curve smoothness. Practical testing revealed that when N is too large, especially at the rear end of the ejector shape, a small, sharp protrusion occurs, resulting in an uneven curve; when N is too small, the curve details are not fully represented, and the difference from the basic shape is too large. After comprehensive consideration, a polynomial order of 7 is chosen as having good versatility, ensuring both fitting accuracy and curve smoothness. Using the CST parameterization method described above, the program calls the CST fitting function to process the standardized shape coordinate data, obtaining the CST fitting parameters corresponding to the shapes of each basic ejector. This maps the original coordinate data to the parameter space, forming operable shape design parameters.
[0026] S103, based on the CST fitting parameters, the shape of each basic ejector is perturbed to generate perturbed shape samples, and the perturbed shape samples are converted into shape coordinate matrices; After obtaining the CST fitting parameters corresponding to each basic ejector shape, it is necessary to perturb these parameters to generate a large number of perturbed shape samples, providing a sufficient data foundation for subsequent principal component analysis. Utilizing the parameterization characteristics of the CST method, the ejector shape can be efficiently perturbed by changing the values of the CST fitting parameters to generate shape samples with different geometric features. Specifically, for the sensitivity of each CST fitting parameter, the program calculates its perturbable range. The formula for calculating the perturbable range of each CST fitting parameter based on its sensitivity is as follows: ,in, Let be the perturbation range of the i-th CST fitting parameters, and let target_y_change be the change in the target ordinate. Let be the sensitivity of the i-th CST fitting parameter. Sensitivity reflects the degree to which the parameter's change affects the ejector's ordinate. A parameter with higher sensitivity has a smaller perturbation range to avoid excessively drastic shape changes. After determining the perturbation range of each parameter, random perturbation values at equal points are generated within this range. These random perturbation values are then superimposed onto the original CST fitting parameters to obtain the perturbed CST parameters. Simultaneously, a validity check is performed to ensure that the generated perturbed parameters are within a reasonable range, avoiding abnormal ejector shapes. Subsequently, the perturbed CST parameters are converted back into the ejector's ordinate points to generate perturbed shape samples. The conversion formula is as follows: ,j=1...,m; where, For the k-th perturbation shape sample at the sampling point The ordinate at that location, Let i be the CST parameter of the k-th perturbation shape sample. Here, m represents the chord-length equidistant sampling points, and m is the total number of sampling points. Using chord-length equidistant sampling points ensures consistent point correspondences between different perturbation shape samples, allowing the generated shape data to be directly used for subsequent statistical analysis and principal component analysis. After the above perturbation process, a large number of perturbation shape samples can be generated based on multiple basic ejector shapes. The coordinate data of all perturbation shape samples are arranged in rows to form a shape coordinate matrix, providing input data for subsequent principal component analysis.
[0027] S104, perform principal component analysis on the shape coordinate matrix to extract the main mode matrix of shape deformation and the mode coefficients corresponding to each disturbed shape sample; After obtaining the shape coordinate matrix, principal component analysis (PCA) is used to process it and extract the main modes of ejector shape deformation. PCA is an effective dimensionality reduction technique that can extract the most representative feature directions from high-dimensional data, decomposing complex shape changes into several mutually orthogonal main deformation modes. Specifically, the covariance matrix of the shape coordinate matrix is first calculated. The formula for calculating the covariance matrix is as follows: Where Y is the external coordinate matrix, Let be the mean of the shape coordinate matrix, and n be the number of perturbed shape samples. The covariance matrix reflects the correlation and variation magnitude among the dimensions of the shape coordinates and is the core input for principal component analysis. Subsequently, eigenvalue decomposition is performed on the covariance matrix to solve for the eigenvalues and eigenvectors; its eigenvalue equation is: In this matrix, V is the eigenvector matrix and D is the eigenvalue matrix. Each column of the eigenvector matrix V represents a principal component direction, i.e., a principal mode of shape deformation. Therefore, the eigenvector matrix V constitutes the principal mode matrix of shape deformation. The eigenvalue matrix D is a diagonal matrix, and its diagonal elements are the eigenvalues, representing the variance contribution of the corresponding principal mode of shape deformation. The larger the eigenvalue, the stronger the explanatory power of the mode for the overall shape variation. After extracting the principal mode matrix of shape deformation, the modal coefficients corresponding to each perturbed shape sample are further calculated. The modal coefficients describe the amplitude variation of each sample in each principal component direction, and their calculation formula is score = Y·V, where score is the modal coefficient matrix, Y is the shape coordinate matrix, and V is the principal mode matrix of shape deformation. Through the above principal component analysis process, the original high-dimensional shape coordinate data is transformed into a low-dimensional feature space represented by modal coefficients.
[0028] S105, Based on the variance contribution rate of the principal mode matrix of the external shape deformation, select the first K principal modes of external shape deformation, and calculate the range of values of the mode coefficients to determine the K-dimensional mode coefficient space. S106, The Latin hypercube sampling method is used to uniformly sample in the K-dimensional modal coefficient space to obtain multiple sets of target modal coefficients; Please combine Figure 4 After extracting the principal mode matrix and modal coefficients of the ejector shape deformation, it is necessary to select the top K principal modes that have the most significant impact on the shape deformation based on the variance contribution rate, and determine the boundary range of the modal coefficient space. The variance contribution rate reflects the explanatory power of each principal component for the overall ejector shape variation, and its calculation formula is as follows: ;in, Let be the variance contribution rate of the i-th principal mode of external shape deformation. For the i-th eigenvalue, This represents the sum of all eigenvalues. By calculating the variance contribution rate of each principal mode and plotting the cumulative variance contribution rate curve, the number of principal modes to be retained can be intuitively determined. According to actual calculation results, the first 10 principal modes can basically describe all the ejector shape characteristics. Parameters after the 10th mode have almost no significant impact on the shape characteristics and can be ignored. Furthermore, verification revealed that when the modal coefficients reach the 9th and 10th values, the corresponding modal coefficient range is close to zero and clutter exists. Therefore, in practical applications, selecting the first 8 principal modes is sufficient, i.e., K is set to 8, and 1000 values are uniformly selected within this space, such as... Figure 6As shown. To verify the correctness of principal component analysis (PCA) dimensionality reduction, the first K principal modes and their corresponding modal coefficients can be used for inverse reconstruction. The reconstructed shape coordinate data is then compared with the original shape coordinates to calculate the reconstruction error. When the reconstruction error is zero or infinitesimal, it proves that PCA dimensionality reduction is basically correct, and the number of selected principal modes can sufficiently characterize the geometric features of the original shape. After determining the number of principal modes, it is necessary to statistically determine the range of modal coefficient values to define the boundary of the K-dimensional modal coefficient space. The range of modal coefficient values is determined by statistically analyzing the maximum and minimum values of the projections of each disturbed shape sample onto the directions of each shape deformation principal mode.
[0029] Specifically, during principal component analysis (PCA) dimensionality reduction, the coordinates of the perturbation shape sample are expanded along each principal component direction to obtain the modal coefficient score. By plotting the histogram distribution of each modal coefficient, the maximum and minimum values of each modal coefficient can be obtained. These extreme values represent the maxima and minima of the perturbation along that modal direction. Please refer to... Figure 5 Taking the first mode as an example, histogram analysis reveals that its modal coefficient has a minimum value of 0.472 and a maximum value of 1.546. The same applies to the other seven modes. Through the above process, the K-dimensional modal coefficient space consisting of the first K principal modes and the value boundaries of each dimension are determined, providing a clear sampling region for subsequent Latin hypercube sampling.
[0030] S107, Based on the target modal coefficients and the principal modal matrix of the shape deformation, perform inverse principal component analysis transformation to reconstruct the target ejector shape coordinate data.
[0031] It should be noted that after obtaining multiple sets of target modal coefficients through Latin hypercube sampling, these modal coefficients need to be converted back into ejector shape coordinate data to generate the target ejector shape that can be used for subsequent simulation and optimization. This process is achieved through inverse principal component analysis transformation, which is similar in principle to data decompression, restoring the coefficients in the low-dimensional modal space to the shape data in the high-dimensional coordinate space.
[0032] Specifically, the data obtained after Latin hypercube sampling is a 1000×8 matrix, representing 1000 new ejector shapes, each described by 8 modal coefficients. Based on actual needs, a set of target modal coefficients corresponding to a specified row number is extracted from this matrix. This is then combined with the shape deformation principal modal matrix obtained from the previous principal component analysis to perform inverse principal component analysis (IPA). The inverse transformation is calculated by multiplying the target modal coefficients by the transpose of the shape deformation principal modal matrix, and adding the mean of the shape coordinate matrix to reconstruct the coordinate data of the target ejector shape. Entering any integer between 1 and 1000 in the row number edit box of the program interface will extract the target modal coefficients for the corresponding row and perform the inverse transformation, generating the corresponding target ejector shape coordinate data. After calculation, the program will output a file named "airfoil_points_%d.txt", where %d is the row number entered by the user. This file contains the complete coordinate data of the corresponding target ejector shape. Through the above inverse principal component analysis transformation process, the mapping from the low-dimensional modal coefficient space to the high-dimensional shape coordinate space is realized. The sampled abstract modal coefficients are restored into ejector shape curve coordinates with clear geometric meaning, providing directly usable shape data for subsequent 3D modeling, aerodynamic simulation and optimization analysis.
[0033] Please see Figure 7 The second embodiment of the present invention provides a PCA-based variable area ejector generation device for a rear duct, comprising: The data preprocessing module 201 is used to acquire the original coordinate data of multiple basic ejector shapes, and to perform interpolation processing on the original coordinate data to obtain standardized shape coordinate data. CST parameterization module 202 is used to fit the standardized shape coordinate data using the CST parameterization method to obtain the CST fitting parameters corresponding to the shape of each basic ejector. The perturbation sample generation module 203 is used to perturb the parameters of each basic ejector shape based on the CST fitting parameters, generate perturbation shape samples, and convert the perturbation shape samples into shape coordinate matrices. Principal component analysis module 204 is used to perform principal component analysis on the shape coordinate matrix and extract the principal mode matrix of shape deformation and the mode coefficients corresponding to each disturbed shape sample. The K-dimensional modal coefficient space determination module 205 is used to select the first K main modes of shape deformation based on the variance contribution rate of the main mode matrix of shape deformation, and to calculate the value range of the modal coefficients to determine the K-dimensional modal coefficient space. Sampling module 206 is used to uniformly sample within the K-dimensional modal coefficient space using the Latin hypercube sampling method to obtain multiple sets of target modal coefficients; The shape reconstruction module 207 is used to perform inverse principal component analysis transformation based on the target modal coefficients and the shape deformation principal mode matrix to reconstruct the target ejector shape coordinate data.
[0034] The third embodiment of the present invention provides a PCA-based variable area ejector generation device, including a memory and a processor. The memory stores a computer program, which can be executed by the processor to implement the PCA-based variable area ejector generation method as described in any of the above embodiments.
[0035] The fourth embodiment of the present invention provides a computer-readable storage medium, characterized in that it stores a computer program, which can be executed by a processor of the device in which the computer-readable storage medium is located, to implement a PCA-based variable area ejector generation method as described in any of the above claims.
[0036] This invention provides a PCA-based method, apparatus, device, and storage medium for generating a post-duct variable area ejector. The method converts the original coordinate data of the basic ejector shape into low-dimensional controllable parameters using the CST parameterization method. Based on this, the CST fitted parameters are perturbed to generate a large number of perturbed shape samples. Principal component analysis is then used to extract the principal mode matrix of the shape deformation, compressing the high-dimensional parameter space into a low-dimensional modal coefficient space composed of a few principal modes. Furthermore, the top K principal modes are selected based on the variance contribution rate, and the value range of the modal coefficients is determined. Uniform sampling is performed within this K-dimensional modal coefficient space using the Latin hypercube sampling method. Finally, inverse principal component analysis is used to reconstruct the target modal coefficients obtained from the sampling into the target ejector shape coordinate data. This method, while ensuring the physical rationality of the ejector shape, achieves uniform coverage and efficient exploration of the design space with a smaller number of samples, significantly improving the efficiency of ejector shape generation.
[0037] Exemplary examples show that the computer program described in the third and fourth embodiments of the present invention can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in implementing a PCA-based post-duct variable area ejector generation device. For example, the apparatus described in the second embodiment of the present invention.
[0038] The processor referred to can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the PCA-based back-duct variable-area ejector generation method, connecting various parts of the entire PCA-based back-duct variable-area ejector generation method through various interfaces and lines.
[0039] The memory can be used to store the computer program and / or modules. The processor implements various functions of a PCA-based post-duct variable area ejector generation method by running or executing the computer program and / or modules stored in the memory, and by calling data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, text conversion function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, text message data, etc.). In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.
[0040] If the implemented module is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.
[0041] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.
[0042] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for generating a post-duct variable area ejector based on PCA, characterized in that, include: Obtain the original coordinate data of the shapes of multiple basic ejectors, and perform interpolation processing on the original coordinate data to obtain standardized shape coordinate data; The standardized shape coordinate data were fitted using the CST parameterization method to obtain the CST fitting parameters corresponding to the shape of each basic ejector. Based on the CST fitting parameters, the shapes of each basic ejector are perturbed to generate perturbed shape samples, and the perturbed shape samples are converted into shape coordinate matrices. Principal component analysis was performed on the shape coordinate matrix to extract the principal mode matrix of shape deformation and the modal coefficients corresponding to each disturbed shape sample; Based on the variance contribution rate of the principal mode matrix of the external shape deformation, the first K principal modes of external shape deformation are selected, and the range of values of the modal coefficients is calculated to determine the K-dimensional modal coefficient space. The Latin hypercube sampling method is used to uniformly sample within the K-dimensional modal coefficient space to obtain multiple sets of target modal coefficients; Based on the target modal coefficients and the principal modal matrix of the shape deformation, inverse principal component analysis transformation is performed to reconstruct the target ejector shape coordinate data.
2. The method for generating a PCA-based variable area ejector for a post-duct system according to claim 1, characterized in that, The interpolation process employs a linear interpolation method, which interpolates the original coordinate data of each basic ejector shape to the same number of sampling points to obtain the standardized shape coordinate data.
3. The method for generating a PCA-based variable area ejector for a post-duct system according to claim 1, characterized in that, The CST parameterization method uses the following formula to represent the ejector outline: y(x) = C(x) * S(x) Where C(x) is a class function used to guarantee the endpoint conditions of the ejector shape; S(x) is a shape function, which uses polynomial expansion to represent the shape of the ejector shape, and its expression is: in, Here are the CST fitting parameters, and N is the polynomial order. Let i be the i-th power of the normalized chord coordinates of each point on the ejector's outer surface.
4. The method for generating a PCA-based variable area ejector for a post-duct system according to claim 1, characterized in that, The parameter perturbation includes: The perturbable range is calculated based on the sensitivity of each CST fitting parameter, and the perturbable range is calculated according to the following formula: in, Let be the perturbation range of the i-th CST fitting parameters, and let target_y_change be the change in the target ordinate. The sensitivity of the i-th CST fitting parameter; Random perturbation values are generated within the perturbation range and superimposed on the CST fitting parameters to obtain the perturbed CST parameters; The perturbated CST parameters are converted into longitudinal coordinate points of the ejector shape to generate the perturbated shape sample. The conversion formula is: j=1...,m; in, For the k-th perturbation shape sample at the sampling point The ordinate at that location, Let i be the CST parameter of the k-th perturbation shape sample. Let be the x-coordinate of the j-th equidistant sampling point along the chord length, and m be the total number of sampling points. Let be the i-th power of the x-coordinate of the j-th sampling point.
5. The method for generating a PCA-based variable area ejector for a post-duct system according to claim 1, characterized in that, The principal component analysis of the external coordinate matrix is specifically performed as follows: Calculate the covariance matrix of the external shape coordinate matrix. The formula for calculating the covariance matrix is as follows: Where Y is the external coordinate matrix, Let be the mean of the shape coordinate matrix, and n be the number of perturbed shape samples; perform eigenvalue decomposition on the covariance matrix to obtain the eigenvector matrix V and the eigenvalue matrix D, whose eigenvalue equation is: ; The eigenvector matrix V constitutes the principal mode matrix of the external shape deformation, and the diagonal elements of the eigenvalue matrix D characterize the variance contribution of each principal mode of external shape deformation.
6. The method for generating a PCA-based variable area ejector for a post-duct system according to claim 1, characterized in that, The range of modal coefficients is determined by statistically analyzing the maximum and minimum values of the projection values of each disturbed airfoil sample in the direction of each airfoil deformation principal mode.
7. The method for generating a PCA-based variable area ejector for a post-duct system according to claim 1, characterized in that, The variance contribution rate of each principal mode of external deformation is calculated using the following formula: in, Let be the variance contribution rate of the i-th principal mode of external shape deformation. For the i-th eigenvalue, The sum of all eigenvalues is used. When the cumulative variance contribution rate of the current K principal modes of shape deformation reaches a preset threshold, the value of K stops increasing.
8. A PCA-based variable area ejector generation device for a rear duct, characterized in that, include: The data preprocessing module is used to acquire the original coordinate data of multiple basic ejector shapes, and to perform interpolation processing on the original coordinate data to obtain standardized shape coordinate data. The CST parameterization module is used to fit the standardized shape coordinate data using the CST parameterization method to obtain the CST fitting parameters corresponding to the shape of each basic ejector. The perturbation sample generation module is used to perturb the parameters of each basic ejector shape based on the CST fitting parameters, generate perturbation shape samples, and convert the perturbation shape samples into shape coordinate matrices. The principal component analysis module is used to perform principal component analysis on the shape coordinate matrix and extract the principal mode matrix of shape deformation and the modal coefficients corresponding to each disturbed shape sample. The K-dimensional modal coefficient space determination module is used to select the first K main modes of external deformation based on the variance contribution rate of the main mode matrix of external deformation, and to calculate the value range of the modal coefficients to determine the K-dimensional modal coefficient space. The sampling module is used to uniformly sample within the K-dimensional modal coefficient space using the Latin hypercube sampling method to obtain multiple sets of target modal coefficients; The shape reconstruction module is used to perform inverse principal component analysis transformation based on the target modal coefficients and the shape deformation principal mode matrix to reconstruct the target ejector shape coordinate data.
9. A PCA-based variable area ejector generation device, comprising a memory and a processor, wherein the memory stores a computer program that can be executed by the processor to implement a PCA-based variable area ejector generation method as described in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, The device contains a computer program that can be executed by a processor of the device in which the computer-readable storage medium is located, to implement a PCA-based method for generating a variable area ejector in a duct as described in any one of claims 1 to 7.