A flow field data modal decomposition method, device and equipment suitable for aircraft non-stationary flow field and a storage medium

Abstract

The application discloses a flow field data modal decomposition method and device suitable for an aircraft non-stationary flow field, equipment and a storage medium, relates to the technical field of fluid dynamics, and comprises the following steps: acquiring the space-time data of the aircraft non-stationary flow field, determining a physical representation form, decomposing the physical representation form into a plurality of low-order dynamic process components composed of a space mode and a time evolution coefficient by using a frequency modulation technology, constructing a frequency modulation operator, converting the time evolution coefficient of each component into a narrow-band frequency modulation component time sequence signal, taking the minimization of the bandwidth of the narrow-band signal as an optimization target, combining a flow field reconstruction constraint and a frequency modulation structure constraint to construct a to-be-solved variation optimization problem, and iteratively solving the time evolution coefficient, the instantaneous frequency, the instantaneous amplitude and the space mode by using an alternating direction multiplier method to determine a modal decomposition result based on a solving result, so that the adaptive extraction and dynamic characteristic description of the non-stationary flow field are realized, and the modal separation precision of the non-stationary flow field and the extraction efficiency of the nonlinear and transient characteristics are improved.

Description

Technical Field

[0001] This invention relates to the field of fluid dynamics, and in particular to a method, apparatus, device, and storage medium for modal decomposition of flow field data applicable to non-stationary flow fields of aircraft. Background Technology

[0002] Currently, in complex fluid dynamics systems, flow fields generally exhibit significant multi-scale characteristics and non-stationary transient structures. Traditional mode decomposition techniques, such as intrinsic orthogonal decomposition (POD) and dynamic mode decomposition (DMD), often show limitations when processing flow field data with strong nonlinear and non-stationary characteristics, making it difficult to simultaneously capture the multi-scale features and transient dynamic behaviors during spatiotemporal evolution.

[0003] Furthermore, although reduced-order variational mode decomposition (RVMD) exhibits significant advantages in flow field analysis, its core limitation cannot be ignored: this method inherently relies strictly on the narrowband assumption of the time-series signal. This fundamental constraint requires each time mode to be decomposed to have a compact spectral distribution and a definite center frequency, which significantly limits the effectiveness of RVMD when facing complex flow fields with rich broadband spectral characteristics (especially nonlinear time-varying frequency evolution). Although its adaptive variational framework can effectively identify the center frequency and bandwidth of different modes, when there are significant broadband energy distributions or strongly nonlinear dynamic behaviors in the flow field, the limitations of the narrowband assumption will directly restrict the applicability and accuracy of the method, seriously hindering its widespread application in more complex flow problems.

[0004] As can be seen from the above, improving the mode separation accuracy and extraction efficiency of nonlinear and transient features of non-stationary flow fields during the mode decomposition process of flow field data applicable to non-stationary flow fields of aircraft is an urgent problem to be solved. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method, apparatus, device, and storage medium for mode decomposition of flow field data suitable for non-stationary flow fields of aircraft, which can improve the mode separation accuracy and the extraction efficiency of nonlinear and transient features of non-stationary flow fields during mode decomposition of flow field data suitable for non-stationary flow fields of aircraft. The specific solution is as follows:

[0006] Firstly, this application provides a method for modal decomposition of flow field data applicable to non-stationary flow fields of aircraft, including:

[0007] Acquire spatiotemporal flow field data, including spatial and temporal coordinates, in the non-stationary flow field of an aircraft;

[0008] A physical representation form corresponding to the spatiotemporal flow field data is determined, so as to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components using frequency modulation technology and based on the physical representation form; the basic low-order dynamic process components are mathematical representations constructed based on spatial modes and time evolution coefficients.

[0009] A frequency modulation operator with demodulation and modulation functions is constructed, and the time evolution coefficients in each of the basic low-order dynamic process components are converted into time-series signals of each narrowband frequency modulation component to be processed, including a first narrowband frequency modulation component and a second narrowband frequency modulation component, using each frequency modulation operator.

[0010] The optimization objective is to minimize the sum of the bandwidths of the time-series signals of each of the narrowband frequency-modulated components to be processed, and the flow field reconstruction constraints and frequency modulation structure constraints are determined, so as to construct the variational optimization problem to be solved based on the optimization objective, the flow field reconstruction constraints and the frequency modulation structure constraints.

[0011] The variational optimization problem to be solved is iteratively solved using the alternating direction multiplier method to obtain solution results including flow field time evolution coefficients, instantaneous frequency, instantaneous amplitude and spatial modes. Based on the solution results, the mode decomposition results corresponding to the flow field of the aircraft are determined. The mode decomposition results include time-frequency analysis results of flow field time evolution.

[0012] Optionally, determining the physical representation form corresponding to the spatiotemporal flow field data, and using frequency modulation technology and based on the physical representation form to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components, includes:

[0013] Determine the physical representation form corresponding to the spatiotemporal flow field data, and use frequency modulation technology to construct mathematical representations corresponding to each basic low-order dynamic process component based on the spatial modes and time evolution coefficients of the flow field in the physical representation form;

[0014] A frequency modulation term corresponding to the time evolution coefficient in the mathematical representation of each of the basic low-order dynamic process components is determined, and a frequency modulation operation is performed on each of the basic low-order dynamic process components having an amplitude-frequency modulation function expression based on the frequency modulation term; the frequency modulation term is a frequency modulation function based on the instantaneous frequency being nonlinearly variable with time.

[0015] Optionally, the frequency modulation operator with demodulation and modulation functions includes:

[0016] A Hilbert transform is performed on the time evolution coefficient signal with broadband characteristics in the spatiotemporal flow field data to obtain the corresponding time analytical signal, and the instantaneous frequency function of the frequency modulation term that matches the instantaneous frequency of the time analytical signal is determined.

[0017] Determine whether the instantaneous frequency function of the frequency modulation term matches the instantaneous frequency function of the time signal, obtain the matching result, and when the matching result indicates a successful match, construct a demodulation operator based on the instantaneous frequency and the preset carrier frequency, and then perform a complex conjugate operation on the demodulation operator to obtain the corresponding modulation operator.

[0018] Optionally, the step of using each of the frequency modulation operators to convert the time evolution coefficients in each of the basic low-order dynamic process components into a time-series signal of a narrowband frequency modulation component to be processed, including a first narrowband frequency modulation component and a second narrowband frequency modulation component, includes:

[0019] Extract the time evolution coefficients corresponding to the basic low-order dynamic process components;

[0020] The time evolution coefficients are subjected to equivalent trigonometric function transformation to obtain the transformation result, and the first narrowband frequency modulation component time signal and the second narrowband frequency modulation component time signal are determined based on the transformation result and the sine function and cosine function in the frequency modulation operator, respectively.

[0021] Construct a narrowband frequency modulation component timing signal to be processed, which includes the first narrowband frequency modulation component and the second narrowband frequency modulation component.

[0022] Optionally, the step of setting the minimization of the sum of bandwidths of the time-series signals of the narrowband frequency-modulated components to be processed as the optimization objective, and determining the flow field reconstruction constraints and the frequency modulation structure constraints, to construct the variational optimization problem to be solved based on the optimization objective, the flow field reconstruction constraints, and the frequency modulation structure constraints, includes:

[0023] Determine the sum of squares of the L2 norms of the second-order time derivatives of the first narrowband frequency modulation component and the second narrowband frequency modulation component, and set the sum of squares as the bandwidth expression;

[0024] The flow field reconstruction error expression is determined based on the spatiotemporal flow field data and the basic low-order dynamic model.

[0025] Determine the product between the spatial mode and the time evolution coefficient corresponding to each of the basic low-order dynamic process components of the target, and determine the flow field reconstruction constraints based on the sum of the product results.

[0026] The first product of the first narrowband frequency modulation component and the cosine function in the frequency modulation operator is determined, and the cosine function of the frequency modulation operator is determined to have a sine function with the same phase and frequency, so as to determine the second product between the sine function and the second narrowband frequency modulation component signal. Then, the frequency modulation structure constraint conditions are determined based on the sum of the first product and the second product.

[0027] Based on the optimization objective, the flow field reconstruction constraints, and the frequency modulation structure constraints, a variational optimization problem to be solved is constructed.

[0028] Optionally, the iterative solution of the variational optimization problem to be solved using the alternating direction multiplier method yields solution results including flow field time evolution coefficients, instantaneous frequencies, instantaneous amplitudes, and spatial modes. Based on these solution results, the modal decomposition results corresponding to the flow field of the aircraft are determined, including:

[0029] The variational optimization problem to be solved is transformed into several sub-convex optimization problems using the alternating direction multiplier method. Under the conditions of fixed spatial modes, time evolution coefficients and instantaneous frequency, the time-series signal of the narrowband frequency-modulated component to be processed in the sub-convex optimization problem is updated to obtain the target narrowband frequency-modulated component time-series signal.

[0030] Under the condition of fixed narrowband frequency modulation component timing signal, instantaneous frequency and spatial mode, update the time evolution coefficients in the subconvex optimization problem to obtain the target time evolution coefficients;

[0031] The spatial modes are updated under the conditions of fixed narrowband frequency modulated component time-series signal, time evolution coefficient and instantaneous frequency to obtain the target spatial mode;

[0032] Based on the timing signals of each target narrowband frequency-modulated component, the increment and amplitude of the instantaneous frequency are determined. The instantaneous frequency is then updated based on each increment to obtain the instantaneous frequency of each target. The initial Lagrange multiplier is then updated to obtain the target Lagrange multiplier. Then, based on the target instantaneous frequency and the target instantaneous amplitude, the target time evolution coefficient signal is determined. Based on the target time evolution coefficient signal, the target spatial mode, the target time evolution coefficient, and the target Lagrange multiplier, the mode decomposition result corresponding to the flow field of the aircraft is determined.

[0033] Optionally, the step of determining the increment and instantaneous amplitude of the instantaneous frequency based on the timing signals of each of the target narrowband frequency-modulated components, and updating the instantaneous frequency based on each increment to obtain the instantaneous frequency of each target, includes:

[0034] Determine the ratio between the first target narrowband frequency modulation component and the second target narrowband frequency modulation component in each of the target narrowband frequency modulation component signals, and use the arctangent function to determine the derivative with respect to the time variable corresponding to the ratio, so as to obtain the increment and instantaneous amplitude of each instantaneous frequency.

[0035] Based on the smoothness assumption of each target instantaneous frequency, an auxiliary optimization sub-model corresponding to the increment is constructed. Then, the increment is iteratively updated using the auxiliary optimization sub-model and based on the variational method to obtain the updated increment. Then, the instantaneous frequency is updated based on each updated increment to obtain the instantaneous frequency to be processed. Finally, each target instantaneous frequency is determined based on the preset step size coefficient and each instantaneous frequency to be processed.

[0036] Secondly, this application provides a flow field data mode decomposition device suitable for non-stationary flow fields of aircraft, comprising:

[0037] The spatiotemporal flow field data acquisition module is used to acquire spatiotemporal flow field data, including spatial and temporal coordinates, in the non-stationary flow field of an aircraft.

[0038] The spatiotemporal flow field data decomposition module is used to determine the physical representation form corresponding to the spatiotemporal flow field data, so as to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components based on the physical representation form using frequency modulation technology; the basic low-order dynamic process components are mathematical representations constructed based on spatial modes and time evolution coefficients.

[0039] A frequency modulation operator construction module is used to construct a frequency modulation operator with demodulation and modulation functions, and to use each of the frequency modulation operators to convert the time evolution coefficients in each of the basic low-order dynamic process components into a narrowband frequency modulation component time-series signal to be processed, including a first narrowband frequency modulation component and a second narrowband frequency modulation component.

[0040] The constraint determination module is used to set minimizing the sum of bandwidths of the time-series signals of the narrowband frequency-modulated components to be processed as the optimization objective, and to determine the flow field reconstruction constraints and the frequency modulation structure constraints, so as to construct the variational optimization problem to be solved based on the optimization objective, the flow field reconstruction constraints and the frequency modulation structure constraints.

[0041] The problem iterative solution module is used to iteratively solve the variational optimization problem to be solved using the alternating direction multiplier method, and obtain the solution results including the flow field time evolution coefficient, instantaneous frequency, instantaneous amplitude and spatial modes, so as to determine the mode decomposition result corresponding to the flow field of the aircraft based on the solution results; the mode decomposition result includes the time-frequency analysis result of the flow field time evolution.

[0042] Thirdly, this application provides an electronic device, comprising:

[0043] Memory, used to store computer programs;

[0044] A processor is used to execute the computer program to implement the aforementioned method for modal decomposition of flow field data applicable to non-stationary flow fields of aircraft.

[0045] Fourthly, this application provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned method for modal decomposition of flow field data applicable to non-stationary flow fields of aircraft.

[0046] As can be seen from the above, before performing mode decomposition of flow field data applicable to non-stationary flow fields of aircraft, this application needs to acquire spatiotemporal flow field data including spatial and temporal coordinates in the non-stationary flow field of the aircraft; determine the physical representation form corresponding to the spatiotemporal flow field data, so as to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components using frequency modulation technology and based on the physical representation form; the basic low-order dynamic process components are mathematical representations constructed based on spatial modes and time evolution coefficients; construct a frequency modulation operator with demodulation and modulation functions, and use the frequency modulation operator to convert the time evolution coefficients in each basic low-order dynamic process component into a first narrowband frequency modulation component. The time-series signal of the narrowband frequency-modulated component to be processed is obtained by combining the quantity and the second narrowband frequency-modulated component. The optimization objective is to minimize the sum of the bandwidths of the time-series signal of the narrowband frequency-modulated component to be processed, and the flow field reconstruction constraints and frequency modulation structure constraints are determined. Based on the optimization objective, flow field reconstruction constraints and frequency modulation structure constraints, a variational optimization problem to be solved is constructed. The variational optimization problem to be solved is iteratively solved using the alternating direction multiplier method to obtain the solution results including the flow field time evolution coefficients, instantaneous frequency, instantaneous amplitude and spatial modes. Based on the solution results, the modal decomposition results corresponding to the flow field of the aircraft are determined. The modal decomposition results include the time-frequency analysis results of the flow field time evolution.

[0047] Therefore, this application first acquires spatiotemporal flow field data, including spatial and temporal coordinates, in the non-stationary flow field of an aircraft; determines the physical representation form corresponding to the spatiotemporal flow field data, and uses frequency modulation technology and based on the physical representation form to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components; secondly, the basic low-order dynamic process components are mathematical representations constructed based on spatial modes and time evolution coefficients; constructs a frequency modulation operator with demodulation and modulation functions, and uses the frequency modulation operator to convert the time evolution coefficients in each basic low-order dynamic process component into a narrowband frequency modulation component including a first narrowband frequency modulation component and a second narrowband frequency modulation component. The process begins with a time-series signal containing frequency-modulated (FM) components. The optimization objective is to minimize the sum of bandwidths of the narrowband FM components. Flow field reconstruction constraints and FM structure constraints are then determined. Based on these constraints, a variational optimization problem is constructed. Finally, the alternating direction multiplier method is used to iteratively solve the variational optimization problem, yielding results including flow field time evolution coefficients, instantaneous frequencies, instantaneous amplitudes, and spatial modes. These results are then used to determine the modal decomposition results corresponding to the aircraft's flow field. The modal decomposition results include time-frequency analysis of the flow field's time evolution. This approach improves the efficiency of modal decomposition of data in nonlinear and non-stationary flow fields, thereby enhancing the user experience. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0049] Figure 1 This application discloses a flow field data mode decomposition method applicable to non-stationary flow fields of aircraft.

[0050] Figure 2 This application discloses a specific set of real components and their corresponding spectrograms;

[0051] Figure 3 This is a specific example of the present application and a schematic diagram illustrating the separation of nonlinear frequency-modulated broadband signals using the VMD method.

[0052] Figure 4 This is a schematic diagram of the flow field data mode decomposition device disclosed in this application, which is suitable for non-stationary flow fields of aircraft.

[0053] Figure 5This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0054] 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.

[0055] Currently, in complex fluid dynamics systems, flow fields generally exhibit significant multi-scale characteristics and non-stationary transient structures. Traditional mode decomposition techniques, such as intrinsic orthogonal decomposition (POD) and dynamic mode decomposition (DMD), often show limitations when processing flow field data with strong nonlinear and non-stationary characteristics, making it difficult to simultaneously capture multi-scale features and transient dynamic behaviors during spatiotemporal evolution. Therefore, this application provides a flow field data mode decomposition method suitable for non-stationary flow fields in aircraft, which can improve the accuracy of mode separation and the efficiency of transient feature extraction in the process of mode decomposition of flow field data for non-stationary flow fields in aircraft.

[0056] See Figure 1 As shown in the figure, this invention discloses a method for modal decomposition of flow field data applicable to non-stationary flow fields of aircraft, including:

[0057] Step S11: Obtain spatiotemporal flow field data, including spatial and temporal coordinates, in the non-stationary flow field of the aircraft.

[0058] In this embodiment, during the process of performing flow field data mode decomposition applicable to non-stationary flow fields of aircraft, this application embodiment combines the frequency modulation technique of VNCMD (Variational Non-linear Chirp Mode Decomposition), the ELD characterization of the flow field in RVMD (Reduced-order variational mode decomposition), and the variational optimization principle. It breaks through the narrow-band limitation of the time evolution coefficient in RVMD and can decompose complex flow fields with broadband characteristics of time evolution coefficients that are difficult for RVMD to handle.

[0059] First, the frequency modulation technique used in the embodiments of this application is as follows: In one specific implementation, assume the timing signal It is a broadband signal ( It is a nonlinear function), and its transformation process based on frequency modulation technology is as follows: Analytical signal based on Hilbert transform:

[0060] ;

[0061] in, Let Hilbert represent the Hilbert transform, and the corresponding expression is: ,in, It is Cauchy's principal value constant. This represents the convolution operation. Indicates the imaginary part unit. It is the instantaneous amplitude function of the signal. It is the input real number signal.

[0062] Subsequently, a demodulation operator (DO) is constructed. Modulation Operator (MO) :

[0063] ;

[0064] ;

[0065] in, and satisfy .

[0066] Subsequently, the demodulated and narrowband signals are obtained:

[0067] ;

[0068] when hour, It is a center frequency of Narrowband signals. Therefore, the core of frequency modulation is: constructing the instantaneous frequency function of the modulation operator. .

[0069] Then, modulation and reconstruction of the original signal are performed:

[0070] ;

[0071] Then, by taking the real part of both sides of the above complex function equation, we can obtain the corresponding trigonometric identity:

[0072] ;

[0073] ;

[0074] in, A signal function with narrowband characteristics obtained through frequency modulation (FM) technology is called a frequency-modulated (FM) signal. It is the instantaneous frequency function of the frequency modulation operator. That is, to find the optimal approximation function of the instantaneous frequency of the real signal component.

[0075] Step S12: Determine the physical representation form corresponding to the spatiotemporal flow field data, so as to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components based on the frequency modulation technique and the physical representation form; the basic low-order dynamic process components are mathematical representations constructed based on spatial modes and time evolution coefficients.

[0076] In this embodiment, based on the above-mentioned conversion of broadband time signals into narrowband signals by frequency modulation, this application embodiment first constructs a frequency modulation technique and a mathematical expression of the mode decomposition model for the spatiotemporal flow field matrix data. That is, it constructs a basic low-order dynamic process and, based on the decomposition and physical interpretation of the flow field in POD and DMD, combined with the definition of IMF in VMD, constructs a model that can characterize the spatiotemporal evolution process of nonlinear and non-stationary flow field. Here, ELD is defined as a spatiotemporal field.

[0077] In this embodiment, the present application considers a more general case and performs spatiotemporal flow field decomposition based on the AM-FM function: First, starting from the more generalized AM-FM function, the spatiotemporal flow field is considered. The decomposition of a function is assumed to be obtained by superimposing a finite number of the following basic component functions:

[0078] ;

[0079] in, For a basic component function to satisfy certain constraints, the constraints are given by the set of... The limitations are given. Here, embodiments of this application require... Change ratio Much slower, that is:

[0080] ;

[0081] Furthermore, regarding the quantity The frequency modulation process and the time signal The analysis process is similar; only special attention needs to be paid to choosing the appropriate two-dimensional Hilbert transform form (Bi-orthogonal Hilbert). and frequency modulation operator:

[0082] ;

[0083] ;

[0084] in, It is the overall Hilbert transform. These are the Hilbert transforms in the time direction (t) and the spatial direction (x), respectively. It is a biorthogonal two-dimensional Hilbert transform that combines global and directional Hilbert transforms.

[0085] Specifically, determining the physical representation form corresponding to the spatiotemporal flow field data, and using frequency modulation technology based on the physical representation form to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components, may include: determining the physical representation form corresponding to the spatiotemporal flow field data, and using frequency modulation technology based on the physical representation form to model the flow field as a superposition of various basic low-order dynamic process components, where each basic low-order dynamic process component corresponds to a mathematical representation of the product of a spatial mode function and a time evolution coefficient, and the mathematical representation is in the form of an amplitude modulation-frequency modulation function; determining the frequency modulation term corresponding to each time evolution coefficient, and performing frequency modulation operation on each basic low-order dynamic process component with amplitude modulation-frequency modulation function based on each frequency modulation term; the frequency modulation term is a frequency modulation function based on the fact that the instantaneous frequency can change nonlinearly with time.

[0086] Step S13: Construct frequency modulation operators with demodulation and modulation functions, and use each frequency modulation operator to convert the time evolution coefficients in each of the basic low-order dynamic process components into a time-series signal of the narrowband frequency modulation component to be processed, which includes the first narrowband frequency modulation component and the second narrowband frequency modulation component.

[0087] In this embodiment, based on the aforementioned frequency modulation, the optimization problem for general spatiotemporal flow field decomposition can be obtained:

[0088] ;

[0089] The frequency-modulated narrowband signal is as follows:

[0090] .

[0091] Specifically, constructing a frequency modulation operator with demodulation and modulation functions may include: performing Hilbert transform on each time evolution coefficient signal containing broadband characteristics in the spatiotemporal flow field data to obtain the corresponding time analytical signal, and determining the instantaneous frequency function of the frequency modulation term that matches the instantaneous frequency of the time analytical signal; determining whether the instantaneous frequency function of the frequency modulation term matches the instantaneous frequency function of the time signal, obtaining the matching result, and when the matching result indicates a successful match, constructing a demodulation operator based on the instantaneous frequency and a preset carrier frequency, and then performing a complex conjugate operation on the demodulation operator to obtain the modulation operator corresponding to each time coefficient.

[0092] Furthermore, by using each frequency modulation operator to convert the time evolution coefficients in each basic low-order dynamic process component into time-series signals of each narrowband frequency modulation component to be processed, including the first narrowband frequency modulation component and the second narrowband frequency modulation component, this can include: extracting the time evolution coefficients corresponding to each basic low-order dynamic process component; performing equivalent trigonometric function transformations on each time evolution coefficient to obtain the transformation results; and determining the time signals of the first narrowband frequency modulation component and the second narrowband frequency modulation component based on the transformation results and the sine and cosine functions in each frequency modulation operator, respectively; and constructing time-series signals of each narrowband frequency modulation component to be processed, including the first narrowband frequency modulation component and the second narrowband frequency modulation component.

[0093] Step S14: Set minimizing the bandwidth of the time-series signal of the narrowband frequency-modulated component to be processed as the optimization objective, and determine the flow field reconstruction constraints and the frequency modulation structure constraints, so as to construct the variational optimization problem to be solved based on the optimization objective, the flow field reconstruction constraints and the frequency modulation structure constraints.

[0094] In this embodiment, for solving the above-mentioned optimization problem, this application embodiment chooses to use the ADMM framework to solve the optimization problem. Furthermore, the above process is completely similar to the solution steps for the spatiotemporally coupled flow field described below. The detailed steps can be referred to the solution of the following model: First, based on the spatiotemporal flow field decomposition using ELD, that is, considering the physical meaning of the flow field (the spatiotemporal flow field can be decomposed into the product of spatial modes and time evolution coefficients, ELD), i.e. Time evolution coefficient It can be a wideband nonlinear frequency-modulated signal, therefore .

[0095] Subsequently, for the decomposition model based on the AM-FM function, the embodiments of this application introduce more physical constraints, namely, taking... Furthermore, substituting the above conditions into the optimization problem, we construct the following mode decomposition model for nonlinear, nonstationary spatiotemporal coupled flow field data:

[0096] ;

[0097] in, It is a spatial mode. It is a time evolution function, that is, an ELD of the flow field, with the first term being a regularization term. Narrowband constraints are used to represent the frequency modulation operator for each modal component, and the last two equality constraints are reconstruction conditions for the original flow field. Spatiotemporal sampling is performed. The following discrete model can be obtained:

[0098] ;

[0099] in, It is a second-order difference matrix. It is a flow field data matrix.

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] in, This represents the discretized diagonal matrix, with the diagonal elements being... and i=1,2,…,T, It is an instantaneous phase function, which needs to be discretized into a T-dimensional vector over time t. ,and These are two Lagrange multipliers in matrix and vector form, respectively.

[0107] Specifically, minimizing the bandwidth of each narrowband frequency-modulated component's time-series signal is set as the optimization objective, and flow field reconstruction constraints and frequency modulation structure constraints are determined. Based on the optimization objective, flow field reconstruction constraints, and frequency modulation structure constraints, a variational optimization problem to be solved is constructed. This may include: setting the minimization of the sum of the bandwidths of each narrowband frequency-modulated component's time-series signal as the optimization objective, determining the sum of squares of the L⁻² norms of the second-order time derivatives of each first and second narrowband frequency-modulated component, and setting this sum as the bandwidth estimation formula for the time evolution coefficients; and determining the expression of the flow field reconstruction error based on spatiotemporal flow field data and each basic low-order dynamic model. The formula is as follows: The product between the spatial mode and the time evolution coefficient corresponding to each basic low-order dynamic process component is determined, and the flow field reconstruction constraint is determined based on the sum of the product results; the first product between each first narrowband frequency-modulated component and the cosine function in the corresponding frequency-modulated operator is determined, and the cosine function of the frequency-modulated operator is determined to have a sine function with the same phase and frequency, so as to determine the second product between the sine function and the corresponding second narrowband frequency-modulated component signal; then, the frequency modulation structure constraint for each time coefficient is determined based on the sum of the first and second products; and the variational optimization problem to be solved is constructed based on the optimization objective, the flow field reconstruction constraint, and the frequency modulation structure constraint.

[0108] Step S15: Iteratively solve the variational optimization problem to be solved using the alternating direction multiplier method to obtain the solution results including the flow field time evolution coefficient, instantaneous frequency, instantaneous amplitude and spatial modes, so as to determine the mode decomposition result corresponding to the flow field of the aircraft based on the solution results; the mode decomposition result includes the time-frequency analysis result of the flow field time evolution.

[0109] In this embodiment, the ADMM method is used to solve the above model. First, Lagrange multipliers are introduced. and The penalty item is:

[0110] ;

[0111] in, yes The penalty factor parameter of the penalty item, This is also a penalty parameter.

[0112] In other words, by using the alternating direction iterative method, the above optimization can be transformed into the following sub-optimization problems:

[0113] ;

[0114] ;

[0115] It is worth mentioning that, for The instantaneous phase function increment of the frequency modulation operator can be obtained by using the arctangent technique, and further differentiation yields the instantaneous frequency increment:

[0116]

[0117] in, The instantaneous frequency difference between the frequency modulation operator and the true mode, ideally, should be a constant or a linear function of time, then we have: Therefore, assuming The fit is close around a certain center frequency, denoted as Modeling is possible:

[0118] ;

[0119] Therefore, in this embodiment of the application, it is only necessary to select a suitable initial iteration value for the instantaneous frequency. You can then obtain:

[0120] ;

[0121] in, It is a coefficient used to stabilize the algorithm.

[0122] It is worth mentioning that the above sub-optimization problem can be solved using the variational method (with partial derivatives of 0).

[0123] The detailed process of using the ADMM framework described above is as follows: First, in the initialization phase, this embodiment of the application needs to perform parameter initialization: setting penalty parameters. proportionality coefficient Maximum number of iterations Then initialize the variables: , Secondly, the iterative update phase begins:

[0124] ;

[0125] ;

[0126] ;

[0127] ;

[0128] in, It is a second-order difference matrix. It is the diagonal matrix in the discretized model.

[0129] Finally, we move on to the output stage: outputting the optimal spatial mode. Time coefficient Instantaneous frequency With instantaneous amplitude .

[0130] Specifically, the iterative solution of the variational optimization problem to be solved using the alternating direction multiplier method yields solution results including flow field time evolution coefficients, instantaneous frequencies, instantaneous amplitudes, and spatial modes. Based on these results, the mode decomposition results corresponding to the flow field of the aircraft are determined. This can include: transforming the variational optimization problem to be solved into several sub-convex optimization problems using the alternating direction multiplier method; updating the time series signal of the narrowband frequency-modulated component to be processed in the sub-problems under the condition of fixed spatial modes, time evolution coefficients, and instantaneous frequencies to obtain the target narrowband frequency-modulated component time series signal; and updating the time series signal of the sub-problems under the condition of fixed narrowband frequency-modulated component time series signal, instantaneous frequency, and spatial modes. The evolution coefficients are used to obtain the target time evolution coefficients. Under the condition of fixed narrowband frequency modulation component time-series signal, time evolution coefficients and instantaneous frequency, the spatial mode is updated to obtain the target spatial mode. Based on the target narrowband frequency modulation component time-series signal, the increment and instantaneous amplitude of the instantaneous frequency are determined, and the instantaneous frequency is updated based on the increment to obtain the target instantaneous frequency. The initial Lagrange multiplier is updated to obtain the target Lagrange multiplier. Then, based on the target instantaneous frequency and the target instantaneous amplitude, the target time evolution coefficient signal is determined. Based on the target time evolution coefficient signal, the target spatial mode, the target time evolution coefficients and the target Lagrange multiplier, the mode decomposition result corresponding to the flow field of the aircraft is determined.

[0131] Furthermore, determining the increment and instantaneous amplitude of the instantaneous frequency based on the target narrowband frequency-modulated component time-series signal, and updating the instantaneous frequency based on the increment to obtain the target instantaneous frequency, may include: determining the ratio between the first target narrowband frequency-modulated component and the second target narrowband frequency-modulated component in the target narrowband frequency-modulated component signal, and using the arctangent function to determine the derivative of the ratio with respect to the time variable, thereby obtaining the corresponding increment and instantaneous amplitude of the instantaneous frequency; constructing an auxiliary optimization sub-model corresponding to the increment based on the smoothness assumption of the target instantaneous frequency, then using the auxiliary optimization sub-model and the variational method to iteratively update the increment to obtain the updated increment, then updating the instantaneous frequency based on the updated increment to obtain the instantaneous frequency to be processed, and finally determining the target instantaneous frequency based on the preset step size coefficient and the instantaneous frequency to be processed.

[0132] Subsequently, numerical verification is required for the embodiments of this application. Based on the above ADMM algorithm flow, the method proposed in the embodiments of this application has been verified in numerical examples. That is, the embodiments of this application adopt a generalized spatiotemporal flow field model:

[0133] ;

[0134] Subsequently, the above expression is degenerated into a model that incorporates physical constraints, and the specific mathematical expression is as follows:

[0135] ;

[0136] in, Represents Gaussian noise, and .

[0137] In this embodiment, the specific results obtained by using the above algorithm model are illustrated as follows: Figure 2 and Figure 3 As shown, where, Figure 2 For each true component and its corresponding spectrum, Figure 3 This diagram illustrates the present application and the separation of a nonlinear frequency-modulated broadband signal using the VMD method, where the brightness of the grayscale represents the amplitude of the frequency. That is, by... Figure 3 It can be seen that the method proposed in this application has better separation effect and frequency resolution for nonlinear frequency modulated broadband signals, while the VMD method will have mode aliasing and cannot accurately separate different components in the spectrum.

[0138] As can be seen from the above, the embodiments of this application first need to acquire spatiotemporal flow field data, including spatial and temporal coordinates, in the non-stationary flow field of the aircraft; determine the physical representation form corresponding to the spatiotemporal flow field data, so as to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components using frequency modulation technology and based on the physical representation form; secondly, construct a frequency modulation operator with demodulation and modulation functions, and use the frequency modulation operator to convert the time evolution coefficients in each basic low-order dynamic process component into a time-series signal of a narrowband frequency modulation component to be processed, including a first narrowband frequency modulation component and a second narrowband frequency modulation component; then, The optimization objective is to minimize the sum of bandwidths of the time-series signals of the narrowband frequency-modulated components to be processed. Flow field reconstruction constraints and frequency modulation structure constraints are determined, and a variational optimization problem is constructed based on these constraints. Finally, the alternating direction multiplier method is used to iteratively solve the variational optimization problem, yielding results including flow field time evolution coefficients, instantaneous frequencies, instantaneous amplitudes, and spatial modes. These results are then used to determine the modal decomposition results corresponding to the aircraft's flow field. The modal decomposition results include time-frequency analysis of the flow field's time evolution. This improves the efficiency of modal decomposition of data in nonlinear and non-stationary flow fields applicable to non-stationary flow fields of aircraft, thereby enhancing the user experience.

[0139] Accordingly, see Figure 4 As shown, this application also provides a flow field data mode decomposition device suitable for non-stationary flow fields of aircraft, comprising:

[0140] The spatiotemporal flow field data acquisition module 11 is used to acquire spatiotemporal flow field data, including spatial coordinates and time coordinates, in the non-stationary flow field of the aircraft.

[0141] The spatiotemporal flow field data decomposition module 12 is used to determine the physical representation form corresponding to the spatiotemporal flow field data, so as to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components based on the physical representation form using frequency modulation technology; the basic low-order dynamic process components are mathematical representations constructed based on spatial modes and time evolution coefficients.

[0142] Frequency modulation operator construction module 13 is used to construct frequency modulation operators with demodulation and modulation functions, and to use each of the frequency modulation operators to convert the time evolution coefficients in each of the basic low-order dynamic process components into time-series signals of each narrowband frequency modulation component to be processed, including a first narrowband frequency modulation component and a second narrowband frequency modulation component.

[0143] The constraint determination module 14 is used to set the sum of the bandwidths of the time-series signals of each of the narrowband frequency-modulated components to be processed as the optimization objective, and to determine the flow field reconstruction constraint and the frequency modulation structure constraint, so as to construct the variational optimization problem to be solved based on the optimization objective, the flow field reconstruction constraint and the frequency modulation structure constraint.

[0144] The problem iterative solution module 15 is used to iteratively solve the variational optimization problem to be solved using the alternating direction multiplier method, and obtain the solution results including the flow field time evolution coefficient, instantaneous frequency, instantaneous amplitude and spatial modes, so as to determine the mode decomposition result corresponding to the flow field of the aircraft based on the solution results; the mode decomposition result includes the time-frequency analysis result of the flow field time evolution.

[0145] In some specific embodiments, the spatiotemporal flow field data decomposition module 12 may specifically include:

[0146] The physical representation form determination unit is used to determine the physical representation form corresponding to the spatiotemporal flow field data, so as to use frequency modulation technology and model the flow field as the superposition of each basic low-order dynamic process component based on the physical representation form. Each basic low-order dynamic process component corresponds to the mathematical representation of the product of spatial mode function and time evolution coefficient, and the mathematical representation is in the form of amplitude modulation-frequency modulation function.

[0147] A process component frequency modulation unit is used to determine the frequency modulation term corresponding to each of the time evolution coefficients, so as to perform frequency modulation operation on each of the basic low-order dynamic process components with amplitude modulation-frequency modulation function based on each of the frequency modulation terms; the frequency modulation term is a frequency modulation function based on the instantaneous frequency being nonlinearly variable with time.

[0148] In some specific embodiments, the frequency modulation operator construction module 13 may specifically include:

[0149] The instantaneous frequency function determination unit is used to perform Hilbert transform on each time evolution coefficient signal containing broadband characteristics in the spatiotemporal flow field data to obtain the corresponding time analytical signal, and to determine the instantaneous frequency function of the frequency modulation term that matches the instantaneous frequency of the time analytical signal.

[0150] The matching result determination unit is used to determine whether the instantaneous frequency function of the frequency modulation term matches the instantaneous frequency function of the time signal, obtain the matching result, and when the matching result indicates that the matching is successful, construct a demodulation operator based on the instantaneous frequency and the preset carrier frequency, and then perform a complex conjugate operation on the demodulation operator to obtain the modulation operator corresponding to each time coefficient.

[0151] In some specific embodiments, the frequency modulation operator construction module 13 may specifically include:

[0152] The time evolution coefficient extraction unit is used to extract the time evolution coefficients corresponding to each of the basic low-order dynamic process components.

[0153] The transformation result generation unit is used to perform equivalent trigonometric function transformation on each of the time evolution coefficients to obtain the transformation result, and to determine the first narrowband frequency modulation component time signal and the second narrowband frequency modulation component time signal based on the transformation result and the sine function and cosine function in each of the frequency modulation operators, respectively.

[0154] The timing signal construction unit is used to construct timing signals for each narrowband frequency modulation component to be processed, including the first narrowband frequency modulation component and the second narrowband frequency modulation component.

[0155] In some specific embodiments, the constraint determination module 14 may specifically include:

[0156] A bandwidth estimation generation unit is used to set the sum of the bandwidths of the timing signals of each of the narrowband frequency modulation components to be processed as the optimization objective, and to determine the sum of squares of the L-2 norms of the second-order time derivatives of each of the first narrowband frequency modulation components and each of the second narrowband frequency modulation components, and to set the sum of squares as the bandwidth estimation formula for the time evolution coefficients.

[0157] The reconstruction error expression determination unit is used to determine the flow field reconstruction error expression based on the spatiotemporal flow field data and the basic low-order dynamic models.

[0158] The product result determination unit is used to determine the product result between the spatial mode and the time evolution coefficient corresponding to each of the basic low-order dynamic process components, and to determine the flow field reconstruction constraint conditions based on the sum of the product results.

[0159] The frequency modulation structure constraint determination unit is used to determine the first product of each first narrowband frequency modulation component and the cosine function in the corresponding frequency modulation operator, and to determine that the cosine function of the frequency modulation operator has a sine function with the same phase and frequency, so as to determine the second product between the sine function and the corresponding second narrowband frequency modulation component signal, and then determine the frequency modulation structure constraint of each time coefficient based on the sum of the first product and the second product.

[0160] The variational optimization problem construction unit is used to construct the variational optimization problem to be solved based on the optimization objective, the flow field reconstruction constraints, and the frequency modulation structure constraints.

[0161] In some specific embodiments, the problem iterative solution module 15 may specifically include:

[0162] The variational optimization problem transformation unit is used to transform the variational optimization problem to be solved into several sub-convex optimization problems using the alternating direction multiplier method. Under the conditions of fixed spatial modes, time evolution coefficients and instantaneous frequency, the unit updates the time-series signal of the narrowband frequency-modulated component to be processed in the sub-convex optimization problem to obtain the target narrowband frequency-modulated component time-series signal.

[0163] The time evolution coefficient update unit is used to update the time evolution coefficients in the subconvex optimization problem under the condition of fixed narrowband frequency modulation component timing signal, instantaneous frequency and spatial mode, so as to obtain the target time evolution coefficients.

[0164] The spatial mode update unit is used to update the spatial mode under the conditions of fixed narrowband frequency modulated component timing signal, time evolution coefficient and instantaneous frequency to obtain the target spatial mode;

[0165] The instantaneous frequency update unit is used to determine the increment and instantaneous amplitude of the instantaneous frequency based on the timing signals of each target narrowband frequency-modulated component, update the instantaneous frequency based on each increment to obtain the instantaneous frequency of each target, update the initial Lagrange multiplier to obtain the target Lagrange multiplier, and then determine the target time evolution coefficient signal based on the target instantaneous frequency and the target instantaneous amplitude, and determine the mode decomposition result corresponding to the flow field of the aircraft based on the target time evolution coefficient signal, the target spatial mode, the target time evolution coefficient, and the target Lagrange multiplier.

[0166] In some specific embodiments, the problem iterative solution module 15 may specifically include:

[0167] The ratio determination unit is used to determine the ratio between the first target narrowband frequency modulation component and the second target narrowband frequency modulation component in each of the target narrowband frequency modulation component signals, and to determine the derivative with respect to the time variable corresponding to the ratio using the arctangent function, so as to obtain the increment and instantaneous amplitude of each instantaneous frequency.

[0168] The incremental update unit is used to construct an auxiliary optimization sub-model corresponding to the increment based on the smoothness assumption of each target instantaneous frequency, then use the auxiliary optimization sub-model and the variational method to iteratively update the increment to obtain the updated increment, then update the instantaneous frequency based on each updated increment to obtain the instantaneous frequency to be processed, and finally determine each target instantaneous frequency based on the preset step size coefficient and each instantaneous frequency to be processed.

[0169] Furthermore, embodiments of this application also disclose an electronic device, Figure 5 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the flow field data mode decomposition method for non-stationary flow fields of aircraft disclosed in any of the foregoing embodiments. Furthermore, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0170] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0171] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0172] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the flow field data mode decomposition method for non-stationary flow fields of aircraft disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0173] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned method for modal decomposition of flow field data applicable to non-stationary flow fields of aircraft. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0174] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0175] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0176] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0177] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0178] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for modal decomposition of flow field data applicable to non-stationary flow fields of aircraft, characterized in that, include: Acquire spatiotemporal flow field data, including spatial and temporal coordinates, in the non-stationary flow field of an aircraft; Determine the physical representation form corresponding to the spatiotemporal flow field data, so as to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components using frequency modulation technology and based on the physical representation form; The basic low-order dynamic process components are mathematical representations constructed based on spatial modes and time evolution coefficients; A frequency modulation operator with demodulation and modulation functions is constructed, and the time evolution coefficients in each of the basic low-order dynamic process components are converted into time-series signals of each narrowband frequency modulation component to be processed, including a first narrowband frequency modulation component and a second narrowband frequency modulation component, using each frequency modulation operator. The optimization objective is to minimize the sum of the bandwidths of the time-series signals of each of the narrowband frequency-modulated components to be processed, and the flow field reconstruction constraints and frequency modulation structure constraints are determined, so as to construct the variational optimization problem to be solved based on the optimization objective, the flow field reconstruction constraints and the frequency modulation structure constraints. The variational optimization problem to be solved is iteratively solved using the alternating direction multiplier method to obtain the solution results including the flow field time evolution coefficient, instantaneous frequency, instantaneous amplitude and spatial modes, so as to determine the mode decomposition result corresponding to the flow field of the aircraft based on the solution results; The modal decomposition results include time-frequency analysis results of the flow field time evolution.

2. The flow field data mode decomposition method applicable to non-stationary flow fields of aircraft according to claim 1, characterized in that, The step of determining the physical representation form corresponding to the spatiotemporal flow field data, and using frequency modulation technology and based on the physical representation form to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components, includes: Determine the physical representation form corresponding to the spatiotemporal flow field data, so as to use frequency modulation technology and model the flow field as the superposition of each basic low-order dynamic process component based on the physical representation form. Each basic low-order dynamic process component corresponds to the mathematical representation of the product of spatial mode function and time evolution coefficient, and the mathematical representation is in the form of amplitude modulation-frequency modulation function. A frequency modulation term corresponding to each of the time evolution coefficients is determined, and frequency modulation operation is performed on each of the basic low-order dynamic process components with amplitude modulation-frequency modulation function based on each of the frequency modulation terms; the frequency modulation term is a frequency modulation function based on the fact that the instantaneous frequency can change nonlinearly with time.

3. The flow field data mode decomposition method applicable to non-stationary flow fields of aircraft according to claim 2, characterized in that, The constructed frequency modulation operator with demodulation and modulation functions includes: Hilbert transform is performed on each time evolution coefficient signal containing broadband characteristics in the spatiotemporal flow field data to obtain the corresponding time analytical signal, and the instantaneous frequency function of the frequency modulation term that matches the instantaneous frequency of the time analytical signal is determined. Determine whether the instantaneous frequency function of the frequency modulation term matches the instantaneous frequency function of the time signal, obtain the matching result, and when the matching result indicates a successful match, construct a demodulation operator based on the instantaneous frequency and the preset carrier frequency, and then perform a complex conjugate operation on the demodulation operator to obtain the modulation operator corresponding to each time coefficient.

4. The flow field data mode decomposition method applicable to non-stationary flow fields of aircraft according to claim 3, characterized in that, The step of converting the time evolution coefficients in each of the basic low-order dynamic process components into time-series signals of each narrowband frequency-modulated component to be processed, including a first narrowband frequency-modulated component and a second narrowband frequency-modulated component, using the frequency modulation operators respectively includes: Extract the time evolution coefficients corresponding to each of the basic low-order dynamic process components; Equivalent trigonometric function transformations are performed on each of the time evolution coefficients to obtain the transformation results. Based on the transformation results and the sine and cosine functions in each of the frequency modulation operators, the time signals of the first narrowband frequency modulation component and the second narrowband frequency modulation component are determined respectively. Construct timing signals for each narrowband frequency modulation component to be processed, including the first narrowband frequency modulation component and the second narrowband frequency modulation component.

5. The flow field data mode decomposition method applicable to non-stationary flow fields of aircraft according to claim 4, characterized in that, The optimization objective is to minimize the sum of the bandwidths of the time-series signals of each of the narrowband frequency-modulated components to be processed, and the flow field reconstruction constraints and frequency modulation structure constraints are determined. Based on the optimization objective, the flow field reconstruction constraints, and the frequency modulation structure constraints, a variational optimization problem to be solved is constructed, including: The optimization objective is to minimize the sum of the bandwidths of the timing signals of each of the narrowband frequency modulation components to be processed, and to determine the sum of squares of the L-2 norms of the second-order time derivatives of each of the first narrowband frequency modulation components and each of the second narrowband frequency modulation components, and to set the sum of squares as the bandwidth estimation formula for the time evolution coefficients. The flow field reconstruction error expression is determined based on the spatiotemporal flow field data and the components of each basic low-order dynamic process. The product between the spatial mode and the time evolution coefficient corresponding to each of the basic low-order dynamic process components is determined, and the flow field reconstruction constraints are determined based on the sum of the product results. Determine the first product of each first narrowband frequency modulation component and the cosine function in the corresponding frequency modulation operator, and determine that the cosine function of the frequency modulation operator has a sine function with the same phase and frequency, so as to determine the second product between the sine function and the corresponding second narrowband frequency modulation component signal, and then determine the frequency modulation structure constraint condition of each time coefficient based on the sum of the first product and the second product; Based on the optimization objective, the flow field reconstruction constraints, and the frequency modulation structure constraints, a variational optimization problem to be solved is constructed.

6. The flow field data mode decomposition method applicable to non-stationary flow fields of aircraft according to claim 5, characterized in that, The iterative solution of the variational optimization problem using the alternating direction multiplier method yields solution results including flow field time evolution coefficients, instantaneous frequencies, instantaneous amplitudes, and spatial modes. Based on these solution results, the modal decomposition results corresponding to the flow field of the aircraft are determined, including: The variational optimization problem to be solved is transformed into several sub-convex optimization problems using the alternating direction multiplier method. Under the conditions of fixed spatial modes, time evolution coefficients and instantaneous frequency, the time-series signal of the narrowband frequency-modulated component to be processed in the sub-convex optimization problem is updated to obtain the target narrowband frequency-modulated component time-series signal. Under the condition of fixed narrowband frequency modulation component timing signal, instantaneous frequency and spatial mode, update the time evolution coefficients in the subconvex optimization problem to obtain the target time evolution coefficients; The spatial modes are updated under the conditions of fixed narrowband frequency modulated component time-series signal, time evolution coefficient and instantaneous frequency to obtain the target spatial mode; Based on the timing signals of each target narrowband frequency-modulated component, the increment and amplitude of the instantaneous frequency are determined. The instantaneous frequency is then updated based on each increment to obtain the instantaneous frequency of each target. The initial Lagrange multiplier is then updated to obtain the target Lagrange multiplier. Then, based on the target instantaneous frequency and the target instantaneous amplitude, the target time evolution coefficient signal is determined. Based on the target time evolution coefficient signal, the target spatial mode, the target time evolution coefficient, and the target Lagrange multiplier, the mode decomposition result corresponding to the flow field of the aircraft is determined.

7. The flow field data mode decomposition method applicable to non-stationary flow fields of aircraft according to claim 6, characterized in that, The step of determining the instantaneous frequency increment and instantaneous amplitude based on the timing signals of each of the target narrowband frequency-modulated components, and updating the instantaneous frequency based on each increment to obtain the instantaneous frequency of each target, includes: Determine the ratio between the first target narrowband frequency modulation component and the second target narrowband frequency modulation component in each of the target narrowband frequency modulation component signals, and use the arctangent function to determine the derivative with respect to the time variable corresponding to the ratio, so as to obtain the increment and instantaneous amplitude of each instantaneous frequency. Based on the smoothness assumption of each target instantaneous frequency, an auxiliary optimization sub-model corresponding to the increment is constructed. Then, the increment is iteratively updated using the auxiliary optimization sub-model and based on the variational method to obtain the updated increment. Then, the instantaneous frequency is updated based on each updated increment to obtain the instantaneous frequency to be processed. Finally, each target instantaneous frequency is determined based on the preset step size coefficient and each instantaneous frequency to be processed.

8. A flow field data mode decomposition device suitable for non-stationary flow fields of aircraft, characterized in that, include: The spatiotemporal flow field data acquisition module is used to acquire spatiotemporal flow field data, including spatial and temporal coordinates, in the non-stationary flow field of an aircraft. The spatiotemporal flow field data decomposition module is used to determine the physical representation form corresponding to the spatiotemporal flow field data, so as to decompose the spatiotemporal flow field data into a superposition of several basic low-order dynamic process components based on the physical representation form and using frequency modulation technology. The basic low-order dynamic process components are mathematical representations constructed based on spatial modes and time evolution coefficients; A frequency modulation operator construction module is used to construct a frequency modulation operator with demodulation and modulation functions, and to use each of the frequency modulation operators to convert the time evolution coefficients in each of the basic low-order dynamic process components into time-series signals of each narrowband frequency modulation component to be processed, including a first narrowband frequency modulation component and a second narrowband frequency modulation component. The constraint determination module is used to set minimizing the sum of bandwidths of the time-series signals of each of the narrowband frequency-modulated components to be processed as the optimization objective, and to determine the flow field reconstruction constraints and the frequency modulation structure constraints, so as to construct the variational optimization problem to be solved based on the optimization objective, the flow field reconstruction constraints and the frequency modulation structure constraints. The problem iterative solution module is used to iteratively solve the variational optimization problem to be solved using the alternating direction multiplier method, and obtain the solution results including the flow field time evolution coefficient, instantaneous frequency, instantaneous amplitude and spatial modes, so as to determine the mode decomposition result corresponding to the flow field of the aircraft based on the solution results; The modal decomposition results include time-frequency analysis results of the flow field time evolution.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor is configured to execute the computer program to implement the flow field data mode decomposition method for non-stationary flow fields of aircraft as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the flow field data mode decomposition method for non-stationary flow fields of aircraft as described in any one of claims 1 to 7.

Images