Pulsating pressure field multi-frequency comprehensive feature extraction method and device and storage medium

Abstract

The application discloses a pulsating pressure field multi-frequency comprehensive feature extraction method and device and a storage medium, and relates to the technical field of experimental fluid mechanics and aeroacoustics. A three-dimensional pressure snapshot is converted into a two-dimensional snapshot matrix, the two-dimensional snapshot matrix is blocked and frequency-shifted according to a dominant fundamental frequency, a global circularly stationary data matrix containing a complete set of frequencies is constructed, and a joint eigenvalue of the coupling matrix is uniformly solved. The obtained mode retains multi-frequency components, is a phase-locked space-time wave packet, can completely restore the space-time evolution characteristics of the circularly stationary flow, provides a global feature view of a noise source, and provides a complete basis for analyzing a nonlinear aerodynamic noise generation mechanism. The whole process is adapted to a pressure-sensitive paint measurement system, is easy to program and implement, and is suitable for experimental analysis of aerodynamic noise of high-speed jets, rotating machines and the like.

Description

Technical Field

[0001] This application relates to the fields of experimental fluid mechanics and aeroacoustics, specifically to a method, apparatus, and storage medium for multi-frequency comprehensive feature extraction of pulsating pressure fields. Background Technology

[0002] In experimental fluid mechanics and aeroacoustics, dynamic unsteady pressure field measurement techniques based on pressure-sensitive paint (PSP) have become an important means of obtaining the spatiotemporal distribution of pressure on complex flowing surfaces. To extract dominant coherent modes from unsteady-state data, the Spectral Proper Orthogonal Decomposition (SPOD) method is widely used. Traditional techniques typically analyze time-varying pressure fields acquired by PSPs using SPOD to identify the energy-optimal coherent modes at each individual frequency. However, the theoretical basis of the standard SPOD method rests on the assumption of wide stationarity, requiring that the statistical characteristics of the signal do not change over time. This premise has fundamental limitations in cyclostationary signal processing.

[0003] Cyclostationary signals are widely found in high-speed impinging jets, rotating machinery (such as compressors and turbines), and flows dominated by feedback loops (such as whistling tones). Their statistical characteristics (such as mean and correlation function) are periodically modulated with the fundamental frequency (such as rotational frequency and impingement feedback frequency). When a signal has cyclostationary characteristics, the standard SPOD cannot utilize the phase correlation across frequencies. It treats each frequency component as an independent statistical entity for analysis, thus severing multiple harmonic energies that were originally generated by the same physical mechanism and had a fixed phase relationship. This results in dispersed modal energy and makes it difficult to extract the "comprehensive characteristics" that reflect the complete physical process. Summary of the Invention

[0004] The purpose of this application is to provide a method, device and storage medium for multi-frequency comprehensive feature extraction of pulsating pressure fields, in order to solve the problems of modal energy dispersion and fragmented harmonic features in traditional experimental fluid mechanics data processing methods for unsteady pulsating pressure fields.

[0005] To achieve the above objectives, the first aspect of this application provides a method for extracting multi-frequency comprehensive features of a pulsating pressure field, comprising: The wall pulsating pressure field during the jet impact process is obtained, and full-field three-dimensional pressure snapshot data containing spatial coordinates and time series is obtained. Each frame of pressure image in the full-field three-dimensional pressure snapshot data is expanded into a column vector, and the column vectors at all times are arranged in chronological order to construct the two-dimensional snapshot matrix; Identify the dominant fundamental frequency of the jet impact, determine the corresponding target harmonic frequencies, construct a target frequency set, divide the two-dimensional snapshot matrix into blocks and frequency shift according to the dominant fundamental frequency, reorganize the Fourier coefficients distributed in different data blocks and different frequency shifts according to the target frequency set, and construct a global cyclic stationary data matrix coupled with the fundamental frequency and multiple harmonics. Eigenvalue decomposition or singular value decomposition is performed on the global cyclic stationary data matrix to extract dominant eigenvalues ​​and dominant eigenvectors; Based on the dominant eigenvalues ​​and dominant eigenvectors, the coherent modes of the flow field are reconstructed to obtain cross-frequency bound synthetic modes.

[0006] A second aspect of this application provides a device for multi-frequency integrated feature extraction of pulsating pressure fields, comprising: The acquisition module is used to acquire the wall pulsating pressure field during the jet impact process, and obtain full-field three-dimensional pressure snapshot data containing spatial coordinates and time series. The dimension reduction module is used to expand each frame of pressure image in the full-field three-dimensional pressure snapshot data into a column vector, and arrange the column vectors of all times in chronological order to construct the two-dimensional snapshot matrix; A construction module is used to identify the dominant fundamental frequency of the jet impact, determine the corresponding target harmonic frequencies, construct a target frequency set, divide the two-dimensional snapshot matrix into blocks and frequency shift according to the dominant fundamental frequency, and reorganize the Fourier coefficients distributed in different data blocks and different frequency shifts according to the target frequency set to construct a global cyclic stationary data matrix coupled with the fundamental frequency and multiple harmonics. The decomposition module is used to perform eigenvalue decomposition or singular value decomposition on the global cyclic stationary data matrix to extract dominant eigenvalues ​​and dominant eigenvectors. The reconstruction module is used to reconstruct the coherent modes of the flow field based on the dominant eigenvalues ​​and dominant eigenvectors, and obtain cross-frequency bound synthetic modes.

[0007] A third aspect of this application provides a computer-readable storage medium storing a program that can be loaded by a processor and executed by the above-described method for multi-frequency comprehensive feature extraction of pulsating pressure fields.

[0008] The beneficial effects of this application are: This application transforms a three-dimensional pressure snapshot into a two-dimensional snapshot matrix, unifying the dimensions of subsequent calculations and reducing computational redundancy. Based on the dominant fundamental frequency, the two-dimensional snapshot matrix is ​​divided into blocks and frequency-shifted, stacking multi-harmonic frequency domain coefficients to construct a global cyclic stationary data matrix containing the entire frequency set. Then, by uniformly solving the joint eigenvalues ​​of this coupling matrix, the cross-frequency composite modes bound to multiple harmonics are directly extracted. This application can aggregate the pulsating energy dispersed in the fundamental frequency and harmonics, solving the problems of frequency harmonic fragmentation and mode confusion in traditional SPOD, achieving a one-to-one correspondence between periodic flow structures and modes, and accurately locating aerodynamic noise sources. Simultaneously, the obtained modes retain multi-frequency components and are phase-locked spatiotemporal wave packets, capable of completely restoring the spatiotemporal evolution characteristics of cyclic stationary flow, providing a global characteristic view of the noise source, and providing a complete basis for analyzing the nonlinear aerodynamic noise generation mechanism. The entire process is compatible with pressure-sensitive paint measurement systems, easy to program, and suitable for experimental analysis of aerodynamic noise in high-speed jets, rotating machinery, etc.

[0009] Other features and advantages of this application will be described in detail in the following detailed description section. Attached Figure Description

[0010] Figure 1 This is a flowchart illustrating a multi-frequency comprehensive feature extraction method for pulsating pressure fields provided in an embodiment of this application. Figure 2 This is a schematic diagram of the structure of a fast-response pressure-sensitive coating wall pressure measuring device provided in the embodiments of this application; Figure 3 This is a schematic diagram comparing the modal energy captured at the target frequency by a multi-frequency comprehensive feature extraction method for pulsating pressure fields and the SPOD method provided in the embodiments of this application. Figure 4 This is a schematic diagram of the structure of a multi-frequency integrated feature extraction device for pulsating pressure fields provided in the embodiments of this application.

[0011] Explanation of reference numerals in the attached figures: 1. Flat panel model; 2. Pressure-sensitive coating; 3. Pulsating pressure sensor; 4. Ultraviolet light source; 5. Camera; 6. Nozzle system; 400. Multi-frequency integrated feature extraction device for pulsating pressure field; 401. Acquisition module; 402. Dimensionality reduction module; 403. Construction module; 404. Decomposition module; 405. Reconstruction module. Detailed Implementation

[0012] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0013] In the description of this application, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified. Details are set forth in the following description for illustrative purposes. It should be understood that those skilled in the art will recognize that this application can be implemented without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid unnecessarily obscuring the description of this application. Therefore, this application is not intended to be limited to the embodiments shown, but rather to be consistent with the broadest scope of the principles and features disclosed herein.

[0014] Figure 1 This is a flowchart illustrating a multi-frequency comprehensive feature extraction method for pulsating pressure fields provided in an embodiment of this application. Figure 1 As shown, the method may include steps 101-105, which will be described in detail below.

[0015] Step 101: Obtain the wall pulsating pressure field during the jet impact process, and obtain full-field three-dimensional pressure snapshot data containing spatial coordinates and time series.

[0016] Three-dimensional pressure snapshot data is a pressure field dataset that simultaneously contains two-dimensional planar spatial coordinates and a temporal dimension. Each frame corresponds to the full-field pressure distribution on the wall at a specific moment. All time-series images are combined to form three-dimensional spatiotemporal data, which serves as the raw input. Temporal fluorescence images of jet impacting a flat plate wall are acquired using optical full-field pressure measurement methods. After image correction, intensity ratio calculation, pressure inversion, and removal of the time-averaged component, transient pulsating pressure images are obtained time-by-time. The pulsating pressure field is a non-steady pressure distribution that fluctuates periodically with time due to the continuous impact of the jet on the wall, distinct from a static pressure field that does not change over time. The combination of all time-series pulsating pressure images forms full-field three-dimensional pressure snapshot data that simultaneously carries spatial coordinates and temporal series information.

[0017] This step completes the acquisition of spatiotemporal information of flow field pressure, generating a standardized three-dimensional time-series pressure dataset. This provides a complete and static-free original data base for subsequent matrix construction and frequency domain coupling analysis, ensuring that the subsequent modal extraction results truly reflect the flow pulsation characteristics.

[0018] Step 102: Expand each frame of pressure image in the full-field three-dimensional pressure snapshot data into a column vector, and arrange the column vectors of all times in chronological order to construct a two-dimensional snapshot matrix.

[0019] The column vector is obtained by straightening all spatial grid point values ​​of a single-frame two-dimensional planar pressure image in a fixed order, transforming it into a one-dimensional array, thus completely preserving the spatial pressure distribution information of the entire field at a single moment. Each two-dimensional pressure image within the three-dimensional pressure snapshot is unfolded pixel-by-pixel into a one-dimensional spatial column vector. Following the chronological order of image acquisition, the column vectors corresponding to all moments are sequentially concatenated horizontally to form a unified two-dimensional snapshot matrix. The two-dimensional snapshot matrix is ​​a two-dimensional matrix formed by concatenating the spatial column vectors corresponding to the single-frame pressure image as matrix columns, arranged in chronological order of image acquisition, achieving a standardized transformation of three-dimensional spatiotemporal data into a two-dimensional standard matrix. In this way, all spatiotemporal information of the original data can be completely preserved without data loss, and the dimensionality of subsequent operations such as block segmentation, frequency shifting, and Fourier transform is unified.

[0020] For example, the two-dimensional planar pressure image at each time step can be expanded into a one-dimensional column vector based on spatial grid points. Assuming a two-dimensional plane pressure image in Axial direction and The number of pixels along the axis are respectively and ,but The length is , .Will The column vectors at each time point are arranged in chronological order to form a two-dimensional snapshot matrix. ,Right now: .

[0021] Step 103: Identify the dominant fundamental frequency of the jet impact, determine the corresponding target harmonic frequencies, construct the target frequency set, divide the two-dimensional snapshot matrix into blocks and frequency shift according to the dominant fundamental frequency, reorganize the Fourier coefficients distributed in different data blocks and different frequency shifts according to the target frequency set, and construct a global cyclic stationary data matrix coupled with the fundamental frequency and multiple harmonics.

[0022] The dominant fundamental frequency is the reference frequency of periodic flow oscillations formed by the jet impact feedback effect, and it is the core frequency for the smooth modulation of the flow field. The target harmonic frequencies are integer multiples of the dominant fundamental frequency, generated synchronously with the fundamental frequency by the same flow physics mechanism. Spectral analysis is performed on the pressure time-series signal to extract the oscillation frequency with the highest energy as the dominant fundamental frequency. Then, the effective harmonics of each order are selected and combined to form the target frequency set. The target frequency set is a complete frequency combination integrating the dominant fundamental frequency and the target harmonics, covering all effective frequency components generated by the same flow excitation.

[0023] Then, the window length is set according to the complete cycle of the dominant fundamental frequency, and the time dimension of the two-dimensional snapshot matrix is ​​divided into sliding blocks. Frequency shift modulation is performed on the time-series data of each block to achieve unified processing of multiple harmonic components, and then Fourier coefficients corresponding to the target frequency set are extracted by Fourier transform. The frequency domain coefficients under different data blocks and different frequency shifts are stacked and recombined to construct a globally cyclically stationary data matrix that simultaneously couples the fundamental frequency and multiple harmonics. The globally cyclically stationary data matrix is ​​a coupling matrix formed by integrating the Fourier coefficients corresponding to the target frequency set under all segmented data and all frequency shifts, which can achieve unified binding of fundamental frequency and harmonic frequency domain information.

[0024] This step breaks through the limitations of traditional single-frequency independent analysis, unifying the fundamental frequency and harmonic components generated by the same physical mechanism into the same matrix carrier, fully preserving the inherent phase correlation between different frequencies, and aggregating the pulsating energy dispersed across multiple harmonics at the data level, thus solving the problems of fragmented multi-frequency characteristics and energy dispersion in traditional methods.

[0025] Step 104: Perform eigenvalue decomposition or singular value decomposition on the globally cyclic stationary data matrix to extract dominant eigenvalues ​​and dominant eigenvectors.

[0026] The magnitude of the eigenvalue corresponds to the total energy contribution of the mode within the entire target frequency set; a higher value indicates a stronger dominant role of the mode in the flow field fluctuations. Eigenvectors characterize the coupling relationships between different data blocks and different frequency shift components, serving as the fundamental carrier for reconstructing the coherent structure of the flow field. Dominant eigenvalues ​​and dominant eigenvectors are sorted from highest to lowest energy. The preceding eigenvalues ​​and their corresponding eigenvectors best represent the core fluctuation energy of the flow field; low-energy components, corresponding to random noise, are discarded.

[0027] Eigenvalue decomposition or singular value decomposition is performed on the globally cyclic stationary data matrix to obtain an eigenvalue sequence arranged in descending order of eigenvalues ​​and a one-to-one matching eigenvector. The eigenvalues ​​and corresponding eigenvectors with the highest energy proportions are selected as the dominant eigenvalues ​​and dominant eigenvectors to filter out random noise interference in the flow field and quickly lock the core coherent structure of the control jet impact pulsation and noise.

[0028] Step 105: Reconstruct the coherent modes of the flow field based on the dominant eigenvalues ​​and dominant eigenvectors to obtain cross-frequency bound synthetic modes.

[0029] Cross-frequency bound synthetic modes are composite flow field modes obtained by mapping dominant eigenvalues ​​and eigenvectors back to the original physical space. They simultaneously carry the full-field spatial distribution of the fundamental frequency and all harmonics, with each frequency component maintaining a fixed phase difference and amplitude ratio. Flow field modes are reconstructed using the selected dominant eigenvalues ​​and eigenvectors, mapping the abstract frequency domain eigenvectors back to the original flow field physical space, generating a composite structure that simultaneously contains the spatial distribution of multiple harmonics and is phase-locked, i.e., cross-frequency bound synthetic modes.

[0030] It outputs complete spatiotemporal flow field wave packets coupled across multiple frequencies, unlike traditional methods that can only output local flow field slices at a single frequency. It fully reconstructs the evolution of periodic flow across the entire time scale, establishes a one-to-one correspondence between flow physics mechanisms and modes, achieves precise spatiotemporal localization of aerodynamic noise sources, and fully reveals the noise generation mechanism of cyclic steady flow.

[0031] This application transforms a three-dimensional pressure snapshot into a two-dimensional snapshot matrix, unifying the subsequent computational dimensions and reducing computational redundancy. Based on the dominant fundamental frequency, the two-dimensional snapshot matrix is ​​divided into blocks and frequency-shifted, and the frequency domain coefficients of various harmonics are stacked to construct a global cyclic stationary data matrix containing the entire frequency set. Then, by uniformly solving the joint eigenvalues ​​of this coupling matrix, the cross-frequency composite modes bound to multiple harmonics are directly extracted. This application can aggregate the pulsating energy dispersed in the fundamental frequency and harmonics, solving the problems of frequency doubling and mode confusion in traditional SPOD, achieving a one-to-one correspondence between periodic flow structures and modes, and accurately locating aerodynamic noise sources. Simultaneously, the obtained modes retain multi-frequency components and are phase-locked spatiotemporal wave packets, capable of completely restoring the spatiotemporal evolution characteristics of cyclic stationary flow, providing a global characteristic view of the noise source, and providing a complete basis for analyzing the nonlinear aerodynamic noise generation mechanism. The entire process is compatible with pressure-sensitive paint measurement systems, easy to program, and suitable for experimental analysis of aerodynamic noise in high-speed jets, rotating machinery, etc.

[0032] In this embodiment of the application, the full-field three-dimensional pressure snapshot data is acquired by a fast-response pressure-sensitive coating wall pressure measurement device. In step 101, a fast-response pressure-sensitive coating wall pressure measurement device is constructed. This device is used to acquire time-series fluorescence images under jet impact conditions. After registration, repair, and pressure conversion, the three-dimensional pressure snapshot dataset required by the algorithm is output. Figure 2 This is a schematic diagram of a fast-response pressure-sensitive coating wall pressure measuring device provided in an embodiment of this application. Figure 2 As shown, the fast-response pressure-sensitive coating wall pressure measurement device may include a flat plate model 1, a pressure-sensitive coating 2, a pulsating pressure sensor 3, an ultraviolet light source 4, a camera 5, and a nozzle system 6.

[0033] The flat plate model 1 serves as the test platform for the jet impact test and is the main body to be tested by the fast-response pressure-sensitive coating wall pressure measurement device. The entire surface of the flat plate model 1 is coated with pressure-sensitive coating 2, and a pulsating pressure sensor 3 is embedded in the surface. Pressure-sensitive coating 2 is a fast-response optical sensing medium sprayed onto the surface of the flat plate model 1. It fluoresces when excited by ultraviolet light, and the fluorescence intensity changes with the wall pressure, forming the core sensing layer for achieving full-field non-contact pressure measurement. The pulsating pressure sensor 3 is a single-point pressure acquisition element embedded in the test area of ​​the flat plate model, outputting a single-point pressure time-domain signal for subsequent analysis of the flow field signal fundamental frequency.

[0034] The ultraviolet light source 4 is an excitation light source that matches the excitation wavelength of the pressure-sensitive coating. It directionally illuminates the test area of ​​the flat plate model 1, causing the pressure-sensitive coating 2 to continuously generate fluorescence signals that can be captured by the camera. The camera 5 is a high-speed image acquisition device, positioned directly opposite the test surface of the flat plate model 1, used to simultaneously acquire full-field fluorescence images under baseline and jet impact conditions. The nozzle system 6 is a jet generation and control component that can precisely control the airflow velocity and pressure, directionally ejecting airflow to form a circulating and stable jet field impacting the flat plate model.

[0035] The nozzle system 6 is positioned facing the surface of the flat plate model 1, enabling directional output of impinging airflow. The ultraviolet light source 4 is obliquely aligned with the area of ​​the flat plate model 1 coated with pressure-sensitive paint 2, ensuring uniform excitation across the entire coating area. The camera 5 is mounted directly facing the surface of the flat plate model 1 to capture complete fluorescence imaging of the coating. The pulsating pressure sensor 3 is embedded within the area of ​​the flat plate model 1 to be measured, coplanar with the area covered by the pressure-sensitive paint 2. The single-point pressure time-domain signal acquired by the pulsating pressure sensor 3 and the fluorescence image sequence output by the camera are uniformly transmitted to the back-end data processing terminal to complete the entire process of image correction and pressure conversion.

[0036] Dynamic unsteady pressure field measurement technology based on PSP is an important means to obtain the spatiotemporal distribution of pressure on complex flowing surfaces. Its measurement principle follows the Stern-Volmer relation, which can be stated as follows: the luminescence intensity of the pressure-sensitive paint is inversely proportional to the local oxygen partial pressure, i.e.: ; in, Fluorescence intensity Light intensity The corresponding pressure (pressure to be determined). For reference pressure The reference light intensity below, and This is the calibration coefficient, which can be obtained through static calibration. The fluorescence intensity distribution can be converted into a pressure distribution using this formula.

[0037] Before data acquisition, system parameters were set, including the distance from nozzle system 6 to flat plate model 1, jet Mach number, camera frame rate 5, and sampling frequency of pulsating pressure sensor 3. The first two parameters determine the jet flow conditions, while the latter two control the spatiotemporal resolution of the measurement. During the acquisition process, reference light intensity needed to be collected for each condition under windless conditions. After the jet stabilizes, single-point pulsating pressure (collected by a pulsating pressure sensor) and fluorescence intensity are collected. It is also necessary to record the reference pressure under the reference environment. This serves as a benchmark for pressure conversion. The reference image is used to correct for errors caused by uneven lighting and differences in coating thickness.

[0038] The nozzle system 6 generates a jet that impacts the plate model 1, and the ultraviolet light source 4 excites the pressure-sensitive coating 2 to emit light. A camera 5 captures a reference fluorescence image under windless conditions and a dynamic fluorescence image after the jet has stabilized. The reference image is used to correct for system measurement errors caused by uneven illumination and coating thickness differences. With the nozzle system 6 closed, in a windless reference environment, the camera 5 captures a reference fluorescence image, which is used to correct for system measurement errors caused by uneven illumination and coating thickness differences. The nozzle system 6 is then activated to generate a stable jet that continuously impacts the plate model 1, and the ultraviolet light source 4 continuously excites the pressure-sensitive coating to emit light. After the jet flow has completely stabilized, the camera 5 continuously captures multiple frames of dynamic fluorescence images.

[0039] During jet imaging, camera shake and optical distortion can cause pixel misalignment between the reference image and the dynamic image. Using pre-defined markers on the surface of the flat plate model 1 as positioning references, spatial registration is performed frame-by-frame on the reference fluorescence image and the dynamic fluorescence image to ensure pixel alignment of the same spatial grid point in different images. After registration, the two types of images are divided pixel-by-pixel to obtain a light intensity ratio image sequence. To address the local data loss caused by the presence of markers in the light intensity ratio image sequence, a fast traversal method is used for interpolation reconstruction to eliminate data gaps and obtain a complete light intensity ratio image sequence.

[0040] The complete light intensity ratio image sequence and pressure-sensitive coating calibration parameters and Substituting the values ​​into the Stern-Volmer formula yields the time-series transient pressure image. The difference between each frame of the transient pressure image and the time-averaged pressure image is calculated to remove static pressure components that do not change over time, generating a time-series pulsating pressure image. All time-series pulsating pressure images are then integrated to form a full-field three-dimensional pressure snapshot data containing both two-dimensional spatial coordinates and time-series information, serving as the raw input for subsequent multi-frequency feature extraction algorithms.

[0041] Utilizing a fast-response pressure-sensitive coating wall pressure testing device, a full-field, non-contact, high-resolution pressure measurement of the wall surface is achieved. Multiple methods, including reference image correction, image registration, missing region repair, and time-averaged component difference calculation, eliminate multiple interferences from optics, equipment, and static pressure, outputting a high-precision, distortion-free three-dimensional time-series pressure snapshot. A unified raw data storage format provides a complete and reliable raw data foundation for subsequent two-dimensional snapshot matrix construction and frequency domain coupling analysis, reducing the distortion of modal extraction results caused by the downward propagation of measurement errors.

[0042] In step 103, a single-point time-domain pressure signal can be extracted first, the dominant fundamental frequency and target harmonics can be identified, and a target frequency set can be constructed.

[0043] Specifically, a pulsating pressure sensor 3 installed on the flat plate model 1 is used to synchronously acquire single-point time-domain pressure signals during the jet impact process. The single-point time-domain pressure signal is the time-series data of single-point pressure on the wall surface synchronously collected by the pulsating pressure sensor 3 embedded in the flat plate model 1, used for global flow field spectral characteristic calibration. Spectral analysis is performed on the single-point time-domain pressure signal to calculate the power spectral density, and the frequency with the largest power spectral density amplitude is determined as the dominant fundamental frequency.

[0044] Using the dominant fundamental frequency or its integer multiples as a benchmark, the search proceeds outwards at integer multiples of frequency to filter out all non-wideband harmonic frequencies in the power spectrum. In other words, the harmonic components in the power spectrum with amplitudes higher than the noise floor and belonging to discrete narrowband characteristics are filtered out, and the continuous frequency bands corresponding to wideband turbulence noise are eliminated.

[0045] The dominant fundamental frequency and the selected non-wideband harmonic frequencies are used as target harmonic frequencies of each order. The target harmonic frequencies are integer harmonic components of the dominant fundamental frequency, with energy significantly higher than the noise floor and not belonging to the discrete harmonics of wideband turbulent noise. They are generated synchronously with the dominant fundamental frequency by the same flow physics mechanism, thus constructing the target frequency set.

[0046] For example, the dominant fundamental frequency extracted from a single-point pulsating pressure signal. Construct frequency sets , can be represented as: ; in, Indicates the frequency around the target The neighborhood frequency is usually taken as , It is a positive integer.

[0047] Then, the two-dimensional snapshot matrix is ​​periodically slid-blocked and overlapped based on the dominant fundamental frequency.

[0048] Specifically, based on the dominant fundamental frequency Calculate the corresponding reference period. The reference period is the complete oscillation duration corresponding to the dominant fundamental frequency, and it serves as the window design reference for time series data block partitioning. The impingement jet exhibits statistical characteristics of periodic modulation, requiring the entire time series to be divided into multiple data blocks containing an integer number of periods to satisfy the ergodicity assumption. Power spectrum analysis is performed on the single-point pulsating pressure signal acquired by the pressure sensor to identify the discrete frequency component with the highest sound pressure level, and this frequency is determined as the fundamental frequency to be analyzed. And calculate its corresponding reference period as Determine the number of snapshots contained in each data block. Number of snapshots Set as the base period Image sampling time interval An integer multiple of the ratio. The image sampling time interval refers to the interval between the acquisition of two consecutive frames of pulsating pressure images by the camera, which is determined by the camera frame rate.

[0049] For example, ,in, Indicates rounding down. Represents positive integers. The time interval between two adjacent time series images, i.e., the image sampling frequency. The derivative of . In this way, it can be ensured that each data block covers the complete oscillation cycle.

[0050] To improve statistical convergence, a window length is set with a defined data overlap rate. The two-dimensional snapshot matrix is ​​then truncated to obtain multiple time-series data blocks. Each time-series data block is a segmented set of time-series snapshots truncated along the time axis of the two-dimensional snapshot matrix, with a window length that is an integer multiple of the reference period. Each block contains an integer number of complete flow oscillation cycles. A preset number of overlapping images are maintained between adjacent time-series data blocks.

[0051] For example, there are adjacent data blocks The overlapping images. Data blocks It can be represented as: ; in, This indicates the index offset, ensuring that blocks slide according to the set overlap ratio. It is the single-frame spatial column vector corresponding to the i-th time step in the original two-dimensional snapshot matrix. This is the time-series index. The total number of time-series data blocks obtained after sliding block partitioning. , , It is the total number of time series in the original two-dimensional snapshot matrix.

[0052] A window function is applied to each group of time-series data blocks. The window function is a weighted function (Hanning window / Hamming window) applied to the time-domain snapshot of a single block to eliminate spectral leakage caused by suppressing the truncation of the time-domain signal.

[0053] Next, frequency shift modulation and Fourier transform are performed to extract the Fourier coefficients of the target frequency set.

[0054] Specifically, for each snapshot data block, a complex exponential function is used as the frequency shift operator to modulate the snapshot data, shifting each frequency component in the target frequency set to near an integer multiple of the fundamental frequency, thus obtaining the frequency-shifted time-domain data. The frequency shift operator is a complex exponential modulation function that performs frequency-domain shifting on the time-domain signal.

[0055] For example, for the first Data blocks The first in A snapshot Apply frequency shift ( (This is the frequency shift index, taking values ​​of 0, ±1, ±2, ...). For the first The absolute sampling time corresponding to each snapshot is used to obtain the frequency-shifted time-domain data: .

[0056] Perform a Fast Fourier Transform on the frequency-shifted time-domain data to extract the Fourier coefficients corresponding to each frequency component. Traverse all time-series data blocks and all frequency shifts to extract the Fourier coefficients of frequencies belonging to the target frequency set in all frequency-domain data blocks.

[0057] For example, calculate the first Fourier coefficients of each frequency component : ; in, It is a window function used to reduce spectral leakage.

[0058] Construct a spliced ​​frequency data matrix according to the frequency shift index order. The spliced ​​frequency data matrix is ​​a complex matrix obtained by vertically stacking all time-series data blocks and the Fourier coefficients corresponding to the target frequency set at all frequency shifts. The data is distributed across different frequency shifts. Fourier coefficients in different data blocks according to target frequency set Reorganize the data. Extract all frequencies belonging to this frequency set (i.e., those satisfying the given conditions) from all data blocks. The Fourier coefficients of ). Index these coefficients by frequency shift. The data are stacked sequentially to form a large spliced ​​frequency data matrix. , its first The column is the first Fourier coefficient vectors obtained from data blocks at different frequency shifts.

[0059] in, .

[0060] Then splice the frequency data matrix Weighted inner product operations are performed to obtain the globally cyclically stationary data matrix. In one example, the cyclically stationary data matrix... Satisfy the following formula: ; in, Represents a positive definite spatial weighting matrix; This is the conjugate transpose of the spliced ​​frequency data matrix. Physical weight correction of the full-field spatial grid pressure data is achieved using a positive definite weighting matrix. Combined with the conjugate transpose operation, a second-order statistical covariance matrix of the flow field is constructed, realizing the global coupling and binding of fundamental frequency and multi-harmonic frequency domain information.

[0061] In step 104, singular value decomposition or eigenvalue decomposition is performed on the global cyclic stationary data matrix to obtain an eigenvalue sequence sorted by eigenvalue size and a corresponding eigenvector sequence. The eigenvalue sequence is a set of scalar values ​​obtained after decomposition. The magnitude of the value corresponds to the total pulsating energy contribution of the mode within the entire target frequency set. The higher the value, the stronger the dominant effect of the coherent flow structure on the flow field pulsation. The eigenvalue with the largest value in the eigenvalue sequence is selected as the dominant eigenvalue, and the eigenvector corresponding to the dominant eigenvalue is selected as the dominant eigenvector. This step performs joint decomposition of the global matrix of coupled multi-harmonics. The eigenvalues ​​directly represent the aggregated total energy of the entire target frequency set, and the energy values ​​can intuitively distinguish between the core flow structure controlling aerodynamic noise and random turbulent noise. Only the dominant components before the cumulative energy proportion reaches the target are retained, and the eigenvectors corresponding to low-energy noise are directly discarded. This reduces the computational load of subsequent mode reconstruction without losing the core flow characteristics, thus improving the algorithm's computational efficiency.

[0062] In step 105, the dominant feature vector is mapped to physical space to obtain a matrix containing spatial distribution information, which serves as the cross-frequency bound synthesis mode. The cross-frequency bound synthesis mode includes the spatial distribution at the center frequency and its neighboring offset frequencies, used to characterize the coherent structure at multiple harmonic frequencies.

[0063] Taking the eigenvalue decomposition of a globally cyclically stationary data matrix as an example, the eigenvalue decomposition satisfies the following formula: ; in, This represents a diagonal eigenvalue matrix, where the diagonal elements are... Arranged in descending order, representing the first First mode in the target frequency set The energy contained in it. The dominant eigenvectors in a cyclic stationary data matrix are its column vectors. It is the eigenvector corresponding to the eigenvalue.

[0064] ; .

[0065] in, The maximum value indicates that its reconstructed mode is the optimal mode. Fourier transform results from different data blocks and different frequency shifts can be linearly combined to reconstruct the first... 1st mode.

[0066] Arrange all eigenvalues ​​and eigenvectors in descending order of energy, select the dominant components, and construct the dominant eigenvectors from the dominant eigenvectors. The dominant diagonal matrix is ​​formed by the corresponding dominant eigenvalues. Projecting the dominant eigenvectors back into the original high-order physical space yields an interpretable mode matrix: ; in, For interpretable modal matrices, This is a spliced ​​frequency data matrix. An interpretable mode matrix. The reconstructed modality matrix, whose column vectors are... That is, the first First mode in the target frequency set Frequency domain representation. Each mode It is a composite vector, and its structure is as follows: .

[0067] Includes center frequency and its vicinity offset frequency (±) ,± The spatial distribution at (, ...), a mode simultaneously describes the coherent structure at multiple harmonic frequencies and their fixed phase relationships.

[0068] An interpretable modal matrix is ​​used to map abstract features in the frequency domain to the original physical space of the flow field, generating a composite matrix carrying complete two-dimensional spatial coordinate distribution information. This composite matrix is ​​a cross-frequency bound synthetic mode, which carries the full-field spatial coherence structure corresponding to the central dominant fundamental frequency and the neighboring offset harmonics of each order within the mode, with each frequency component being strictly phase-locked.

[0069] This application provides a method for extracting common features of the fundamental frequency and its harmonic frequencies from a time-series image. Its core advantage lies in its ability to solve the coupling eigenvalue problem across the entire frequency set, thereby directly extracting coherent modes spanning multiple harmonic frequencies. Specific beneficial effects and their causal relationships are analyzed below.

[0070] First, mode confusion must be eliminated to establish a clear physical mapping. Standard SPOD solves independently at a single discrete frequency point, and the extracted modes are frequency-decoupled. This means that pressure fluctuations generated by the same physical mechanism, with energy distributed at the fundamental frequency and its harmonics, will be treated by SPOD as multiple statistically independent modes with separate physical meanings, leading to "mode confusion." As a result, it is impossible to accurately correspond the extracted modes to specific periodic physical mechanisms (such as vortex impacts and shear layer feedback).

[0071] The embodiments of this application extract modes by solving the joint eigenvalue problem on the frequency set, and the extracted modes are forcibly associated with multiple harmonic frequencies. The modal energy is the total contribution of all frequency components in the frequency set, and each extracted mode directly corresponds to a complete periodic physical process. Figure 3 This diagram illustrates a comparison of modal energies captured at a target frequency by a multi-frequency comprehensive feature extraction method for pulsating pressure fields and the SPOD method, as provided in this embodiment of the application. Figure 3 As shown, the horizontal axis represents the modal order. The vertical axis is the front The cumulative energy percentage of the first-order eigenvalues ​​is labeled as follows: .

[0072] It is the sum of the previous largest eigenvalues. It is the sum of all eigenvalues.

[0073] The white circle indicates that the energy of the first 5 modes captured at the target frequency is significantly higher than that of the SPOD method (gray circle). This fundamentally solves the modal confusion problem and achieves a direct mapping from "one physical mechanism to a clear mode".

[0074] Secondly, multi-frequency synthesis features were extracted, revealing a complete physical picture. The standard SPOD mode is a single-frequency, standing wave spatial structure that loses the fixed phase relationship between cross-frequency components. However, noise generation often depends on coherent interference between different frequency components (such as the generation mechanism of impulse sounds).

[0075] The output mode of this embodiment is a cross-frequency, phase-locked spatiotemporal wave packet, the mathematical form of which ensures... , , The synchronous oscillation of equal components with a fixed amplitude ratio and phase difference essentially extracts the comprehensive characteristics of all frequency components simultaneously modulated by a periodic physical mechanism. This wave packet accurately describes the complete spatiotemporal evolution of the physical mechanism, rather than merely a "slice" projection of it at a single frequency. This provides a global view of the complete spatiotemporal characteristics of the noise source and is key to understanding the generation mechanisms of complex nonlinear noise.

[0076] Figure 4 This is a schematic diagram of a multi-frequency integrated feature extraction device for pulsating pressure fields provided in an embodiment of this application. Figure 4 As shown, the multi-frequency integrated feature extraction device 400 for pulsating pressure fields may include an acquisition module 401, a dimensionality reduction module 402, a construction module 403, a decomposition module 404, and a reconstruction module 405.

[0077] The acquisition module 401 is used to acquire the wall pulsating pressure field during the jet impact process, and obtain full-field three-dimensional pressure snapshot data containing spatial coordinates and time series.

[0078] The dimension reduction module 402 is used to expand each frame of pressure image in the full-field three-dimensional pressure snapshot data into a column vector, and arrange the column vectors of all times in chronological order to construct a two-dimensional snapshot matrix.

[0079] The construction module 403 is used to identify the dominant fundamental frequency of the jet impact, determine the corresponding target harmonic frequencies, construct a target frequency set, divide the two-dimensional snapshot matrix into blocks and frequency shift according to the dominant fundamental frequency, and reorganize the Fourier coefficients distributed in different data blocks and different frequency shifts according to the target frequency set to construct a global cyclic stationary data matrix coupled with the fundamental frequency and multiple harmonics.

[0080] The decomposition module 404 is used to perform eigenvalue decomposition or singular value decomposition on the global cyclic stationary data matrix to extract the dominant eigenvalues ​​and dominant eigenvectors.

[0081] The reconstruction module 405 is used to reconstruct the coherent modes of the flow field based on the dominant eigenvalues ​​and dominant eigenvectors to obtain cross-frequency bound synthetic modes.

[0082] The acquisition module 401, dimensionality reduction module 402, construction module 403, decomposition module 404, and reconstruction module 405 can be used to execute steps 101-105 in the embodiments of the above-mentioned multi-frequency comprehensive feature extraction method for pulsating pressure fields. For the specific implementation methods of these modules and more details, please refer to the corresponding method section, which will not be elaborated here.

[0083] This application also provides a computer-readable storage medium storing a program that can be loaded by a processor and executed by any of the pulsating pressure field multi-frequency integrated feature extraction methods in this application.

[0084] Those skilled in the art will understand that all or part of the functions of the various methods in the above embodiments can be implemented by hardware or by computer programs. When all or part of the functions in the above embodiments are implemented by computer programs, the program can be stored in a computer-readable storage medium, which may include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to achieve the above functions. For example, the program can be stored in the memory of a device, and when the program in the memory is executed by the processor, all or part of the above functions can be achieved. In addition, when all or part of the functions in the above embodiments are implemented by computer programs, the program can also be stored in a server, another computer, disk, optical disk, flash drive, or external hard drive, etc., and can be downloaded or copied to the memory of a local device, or the system of the local device can be updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be achieved.

[0085] The above examples illustrate this application only to aid understanding and are not intended to limit its scope. Those skilled in the art to which this application pertains can make various simple deductions, modifications, or substitutions based on the ideas presented.

Claims

1. A method for extracting multi-frequency comprehensive features of a pulsating pressure field, characterized in that, include: The wall pulsating pressure field during the jet impact process is obtained, and full-field three-dimensional pressure snapshot data containing spatial coordinates and time series is obtained. Each frame of pressure image in the full-field three-dimensional pressure snapshot data is expanded into a column vector, and the column vectors at all times are arranged in chronological order to construct a two-dimensional snapshot matrix; Identify the dominant fundamental frequency of the jet impact, determine the corresponding target harmonic frequencies, construct a target frequency set, divide the two-dimensional snapshot matrix into blocks and frequency shift according to the dominant fundamental frequency, reorganize the Fourier coefficients distributed in different data blocks and different frequency shifts according to the target frequency set, and construct a global cyclic stationary data matrix coupled with the fundamental frequency and multiple harmonics. Eigenvalue decomposition or singular value decomposition is performed on the global cyclic stationary data matrix to extract dominant eigenvalues ​​and dominant eigenvectors; Based on the dominant eigenvalues ​​and dominant eigenvectors, the coherent modes of the flow field are reconstructed to obtain cross-frequency bound synthetic modes.

2. The method for extracting multi-frequency comprehensive features of pulsating pressure fields according to claim 1, characterized in that, The process of acquiring the wall pulsating pressure field during the jet impact process, obtaining full-field three-dimensional pressure snapshot data including spatial coordinates and time series, includes: A fast-response pressure-sensitive coating wall pressure measurement device is constructed. The fast-response pressure-sensitive coating wall pressure measurement device includes a flat plate model, an ultraviolet light source, a camera, and a nozzle system. The surface of the flat plate model is coated with pressure-sensitive coating and equipped with a pulsating pressure sensor for analyzing the fundamental frequency of the signal. The nozzle system generates a jet that impacts the flat plate model, and the ultraviolet light source excites the pressure-sensitive coating to emit light. The camera is used to acquire reference fluorescence images under windless conditions and dynamic fluorescence images after the jet has stabilized. Based on the marker points in the model, the reference fluorescence image and the dynamic fluorescence image are registered and divided to obtain the light intensity ratio image sequence; To address the local data loss caused by the presence of marker points in the light intensity ratio image sequence, a fast traversal method is used for interpolation reconstruction to obtain a complete light intensity ratio image sequence. Substituting the complete light intensity ratio image sequence and the pressure-sensitive coating calibration parameters into the Stern-Volmer formula yields a time-series transient pressure image. This image is then compared with the time-averaged pressure image to generate a time-series pulsating pressure image, which serves as the full-field three-dimensional pressure snapshot data.

3. The method for extracting multi-frequency comprehensive features of pulsating pressure fields according to claim 2, characterized in that, The process of identifying the dominant fundamental frequency of the jet impact, determining the corresponding target harmonic frequencies, and constructing a target frequency set includes: Using the pulsating pressure sensor mounted on the flat plate model, the single-point time-domain pressure signal during the jet impact process is acquired synchronously. The single-point time-domain pressure signal is subjected to spectral analysis to calculate the power spectral density, and the frequency with the largest power spectral density amplitude is determined as the dominant fundamental frequency. Using the dominant fundamental frequency or its integer multiples as a reference, search outwards at integer multiples of frequency to filter out all non-wideband harmonic frequencies in the power spectrum; The dominant fundamental frequency and the selected non-wideband harmonic frequencies are used as the target harmonic frequencies of each order to construct a target frequency set.

4. The method for extracting multi-frequency comprehensive features of pulsating pressure fields according to claim 1, characterized in that, Based on the dominant fundamental frequency, the two-dimensional snapshot matrix is ​​divided into blocks, including: The corresponding reference period is calculated based on the dominant fundamental frequency, and the number of snapshots contained in each data block is determined. The number of snapshots is set to an integer multiple of the ratio of the reference period to the image sampling time interval to ensure that each data block covers the complete oscillation period. By setting the window length according to a certain data overlap rate, the two-dimensional snapshot matrix is ​​slidably truncated to obtain multiple time-series data blocks. A preset number of overlapping images are retained between adjacent time-series data blocks to improve statistical convergence. A window function is applied to the time-series data block to eliminate spectral leakage.

5. The method for extracting multi-frequency comprehensive features of pulsating pressure fields according to claim 4, characterized in that, The step of dividing the two-dimensional snapshot matrix into blocks and frequency shifting based on the dominant fundamental frequency, and reorganizing the Fourier coefficients distributed in different data blocks and frequency shifts according to the target frequency set to construct a globally cyclically stationary data matrix coupled with the fundamental frequency and multiple harmonics includes: For each snapshot data in the time-series data block, the snapshot data is modulated using a complex exponential function as a frequency shift operator, and the frequency components in the target frequency set are shifted to near an integer multiple of the fundamental frequency to obtain the frequency-shifted time-domain data. Perform a fast Fourier transform on the frequency-shifted time-domain data to extract the Fourier coefficients corresponding to each frequency component; Extract the Fourier coefficients of frequencies belonging to the target frequency set from all frequency domain data blocks, and construct a spliced ​​frequency data matrix according to the frequency shift index order; The global cyclic stationary data matrix is ​​obtained by performing a weighted inner product operation on the spliced ​​frequency data matrix.

6. The method for extracting multi-frequency comprehensive features of pulsating pressure fields according to claim 5, characterized in that, The cyclically stationary data matrix satisfies the following formula: ； in, For the cyclically stationary data matrix, This represents a positive definite spatial weighting matrix; The splicing frequency data matrix; It is the conjugate transpose of the spliced ​​frequency data matrix.

7. The method for extracting multi-frequency comprehensive features of pulsating pressure fields according to claim 1, characterized in that, The step of performing eigenvalue decomposition or singular value decomposition on the globally cyclically stationary data matrix to extract dominant eigenvalues ​​and dominant eigenvectors includes: Singular value decomposition or eigenvalue decomposition is performed on the global cyclic stationary data matrix to obtain an eigenvalue sequence sorted by eigenvalue size and an eigenvector sequence corresponding to the eigenvalue sequence. The feature value with the largest value in the feature value sequence is selected as the dominant feature value, and the feature vector corresponding to the dominant feature value is selected as the dominant feature vector.

8. The method for extracting multi-frequency comprehensive features of pulsating pressure fields according to claim 7, characterized in that, The process of reconstructing the coherent modes of the flow field based on the dominant eigenvalues ​​and dominant eigenvectors to obtain cross-frequency bound synthetic modes includes: The dominant feature vector is mapped to the physical space to obtain a matrix containing spatial distribution information, which serves as the cross-frequency bound synthetic mode. The cross-frequency bound synthetic mode includes the spatial distribution of the center frequency and the neighboring offset frequencies of the center frequency, which is used to characterize the coherent structure at multiple harmonic frequencies.

9. A device for extracting multi-frequency integrated features of a pulsating pressure field, characterized in that, include: The acquisition module is used to acquire the wall pulsating pressure field during the jet impact process, and obtain full-field three-dimensional pressure snapshot data containing spatial coordinates and time series. The dimensionality reduction module is used to expand each frame of pressure image in the full-field three-dimensional pressure snapshot data into a column vector, and arrange the column vectors of all times in chronological order to construct a two-dimensional snapshot matrix; A construction module is used to identify the dominant fundamental frequency of the jet impact, determine the corresponding target harmonic frequencies, construct a target frequency set, divide the two-dimensional snapshot matrix into blocks and frequency shift according to the dominant fundamental frequency, and reorganize the Fourier coefficients distributed in different data blocks and different frequency shifts according to the target frequency set to construct a global cyclic stationary data matrix coupled with the fundamental frequency and multiple harmonics. The decomposition module is used to perform eigenvalue decomposition or singular value decomposition on the global cyclic stationary data matrix to extract dominant eigenvalues ​​and dominant eigenvectors. The reconstruction module is used to reconstruct the coherent modes of the flow field based on the dominant eigenvalues ​​and dominant eigenvectors to obtain cross-frequency bound synthetic modes.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that can be loaded by a processor and executed as described in any one of claims 1 to 8.

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