Aerodynamic noise time sequence prediction method based on VMD-ESN

Abstract

The invention discloses an aerodynamic noise time sequence prediction method based on a VMD-ESN, and relates to the technical field of hydromechanics noise prediction.The method comprises the steps that firstly, aerodynamic noise signals are collected in real time through a sound pressure sensor; secondly, performing adaptive frequency domain decomposition on the original noise signal by adopting VMD, obtaining a plurality of orthogonal narrowband intrinsic mode functions through a constraint variation optimization framework, effectively separating vortex shedding harmonic and turbulence pulsation characteristics, and inhibiting spectrum aliasing; then, inputting each IMF into an ESN, performing high-dimensional mapping on a modal time sequence evolution rule by using a dynamic reserve pool of sparse connection of a neural network, and training an output layer weight matrix through a ridge regression algorithm; and finally, linearly superposing prediction results of all modes to generate a complete aerodynamic noise time sequence. The method does not need to depend on high-resolution grid iterative calculation, and achieves the accurate prediction of the aerodynamic noise time sequence in a long time interval through a cooperation mechanism of VMD signal adaptive decomposition and ESN machine learning dynamic modeling, and greatly improves the calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the intersection of fluid dynamics noise control and machine learning, and specifically to a method and framework for aerodynamic noise time series prediction based on the collaboration of variational mode decomposition (VMD) and echo state network (ESN). Background Art

[0002] In the field of fluid mechanics and aeronautical engineering, aerodynamic noise prediction is a key step in evaluating the aerodynamic performance of aircraft and optimizing noise control. Traditional methods mainly rely on numerical simulation technologies such as computational fluid dynamics (CFD) and large eddy simulation (LES) to capture the coupling effects of flow and acoustic fields by solving the Navier-Stokes equations. However, traditional methods face great technical challenges in practical applications: in high Reynolds number flow environments, the multi-scale turbulence characteristics lead to significantly increased requirements for computational grid resolution, and a single simulation calculation can even take more than ten hours; the spectral aliasing phenomenon of non-stationary broadband noise seriously interferes with signal feature extraction, making it difficult for the accuracy of the reduced-order model to meet engineering requirements.

[0003] To improve computational efficiency, researchers have proposed using machine learning methods to construct data-driven models in recent years, circumventing complex numerical solutions by establishing a mapping relationship between input parameters and acoustic pressure responses. Although recurrent neural networks in machine learning can model short-term dependencies, the back-propagation-based training mechanism has inherent defects in long-term predictions: the vanishing and exploding gradient problems cause the prediction error to grow exponentially with the time step, and the training cost increases significantly with the modal complexity. As a variant of recurrent neural networks, ESN circumvents the vanishing gradient problem in training by fixing weights and training only the output layer, significantly reducing computational costs. However, when processing aerodynamic noise signals, standard ESNs have difficulty effectively separating low-frequency modes dominated by vortex shedding from high-frequency components dominated by turbulent pulsations, resulting in insufficient capture of key physical mechanisms. Moreover, such models have limited adaptive analytical capabilities for the transient evolution of non-stationary signals, resulting in insufficient prediction robustness under variable operating conditions. Summary of the Invention

[0004] Purpose of the invention: In order to overcome the shortcomings of existing aerodynamic noise prediction methods, the present invention proposes a method for predicting aerodynamic noise time series based on VMD-ESN. By combining the signal decomposition capability of VMD and the neural network dynamic modeling advantages of ESN, this method can efficiently extract features and model non-stationary aerodynamic noise signals, thereby achieving accurate prediction of aerodynamic noise time series.

[0005] Technical solution: The VMD-ESN-based aerodynamic noise time series prediction method of the present invention is characterized by comprising the following steps:

[0006] (1) Acquisition of aerodynamic noise signals: A high-precision sound pressure sensor is used to collect aerodynamic noise signals in real time. The signal frequency range is 20 Hz to 20 kHz. The sampling frequency must meet the Nyquist sampling theorem (i.e., the sampling frequency must be greater than or equal to twice the highest signal frequency) to ensure signal integrity and accuracy.

[0007] (2) VMD signal decomposition: The collected aerodynamic noise signal is subjected to variational modal decomposition, which decomposes it into multiple intrinsic mode functions (IMFs). VMD uses a variational optimization method to decompose the aerodynamic noise signal into a series of IMF components with specific center frequencies, thereby extracting key features from the signal and providing input data with clearer features for ESN modeling.

[0008] (3) ESN neural network modeling and training: Each IMF component is input into the echo state network for modeling and training. ESN training requires initializing the dynamic system of the reservoir first, then inputting the IMF component into the ESN for feature extraction, and finally using the ridge regression method to train the output weights;

[0009] (4) Aerodynamic noise prediction: The trained ESN model is used to predict aerodynamic noise. Each IMF component is predicted, and the prediction results of each component are integrated to obtain the final aerodynamic noise prediction value;

[0010] Preferably, in step (1), the sampling frequency f of the noise sensor is s It should be greater than or equal to twice the highest frequency of the aerodynamic noise signal, and the sampling time step is 1×10 -5 s, and a total of 3988 time steps were collected to ensure the integrity of signal sampling.

[0011] Preferably, in step (2), the modal number K used in VMD decomposition is 300, the penalty factor α is 2000, and the alternating direction multiplier method is iteratively optimized until the convergence residual is less than 1×10 -7 .

[0012] Preferably, in step (3), there are 800 neurons in the ESN reserve pool, the spectral radius SR of the reserve pool connection weight is set to 0.8, the sparsity SD of the reserve pool is set to 3, and the first 500 time steps of the sequence are discarded as a hot start process to improve the prediction performance of the machine learning model.

[0013] Beneficial Effects: The VMD-ESN-based aerodynamic noise time series prediction method requires a small aerodynamic noise database, reduces experimental costs, and reduces computational effort. This method effectively identifies aerodynamic noise trends and quantitatively analyzes noise status, enabling accurate prediction of aerodynamic noise. By monitoring noise status in real time, it ensures system stability and efficiency, reduces equipment loss, and improves overall performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is the research technology roadmap of the present invention based on VMD-ESN.

[0015] Figure 2 It is a flow chart of the VMD decomposition algorithm in the present invention.

[0016] Figure 3 This is a flow chart of the VMD-ESN prediction method of the present invention.

[0017] Figure 4 It is the noise time series prediction graph with the best prediction performance of the present invention. DETAILED DESCRIPTION

[0018] The present invention will be further described below with reference to the accompanying drawings.

[0019] The VMD-ESN-based aerodynamic noise time series prediction method of the present invention includes an aerodynamic noise sound pressure time series database module, a VMD preprocessing and feature extraction module, an ESN modeling and training module, and an aerodynamic noise prediction module. Figure 1 First, the noise pressure time series database module collects aerodynamic noise signals and establishes a database. Then, the VMD module decomposes, reduces noise, and extracts features from the signals. The ESN modeling and training module performs model training, ultimately achieving accurate prediction of aerodynamic noise.

[0020] The aerodynamic noise sound pressure time series database module is composed of aerodynamic noise signals collected by the sound pressure sensor. The aerodynamic noise signals are collected according to a preset sampling frequency, ensuring that the sampling frequency satisfies the Nyquist sampling theorem to fully capture the signal characteristics.

[0021] The VMD preprocessing and feature extraction module performs variational modal decomposition on the preprocessed aerodynamic noise signal, decomposing it into multiple intrinsic mode functions to extract key features in the signal and provide clearer and more stable input data for ESN modeling.

[0022] The ESN modeling and training module inputs each IMF component into the echo state network for modeling. By extracting features and training output weights through a dynamic reserve pool, combining the decomposition capabilities of VMD with the time series modeling advantages of ESN, the model's prediction accuracy and robustness are significantly improved.

[0023] The aerodynamic noise time series accurate prediction module uses the trained ESN model to predict each IMF component and integrates the prediction results of each component to obtain the final aerodynamic noise prediction value. By monitoring the changing trends of aerodynamic noise in real time, it provides a reliable basis for noise control and ensures the stability and efficiency of system operation.

[0024] Specific steps are as follows Figure 3 As shown:

[0025] (1) Acquisition of aerodynamic noise sound pressure time series: A high-precision sound pressure sensor is used to collect aerodynamic noise sound pressure time series at a preset sampling frequency. The sampling frequency must satisfy the Nyquist sampling theorem, that is, it must be greater than or equal to twice the highest frequency of the aerodynamic noise signal to ensure signal integrity and accuracy.

[0026] (2) VMD signal decomposition: The collected aerodynamic noise pressure time series is subjected to variational mode decomposition and decomposed into K intrinsic mode functions. VMD decomposes the aerodynamic noise signal into a series of IMF components with specific center frequencies by constructing and solving variational problems to extract key features from the signal. The VMD decomposition algorithm flow chart is shown in the figure below. Figure 2 The constructed variational model can be expressed by the following formula:

[0027]

[0028] where u k ,ω k Represent the kth mode and its center frequency respectively, {u k}={u1,...,u K},{ω k}={ω1,...,ω K} are the abbreviations for the mode set and center frequency set, respectively. δ(t) is the Dirac function, and f(t) is the original time-domain signal. Solving the above equation using an iterative optimization algorithm that combines the quadratic penalty function method, the Lagrange multiplier method, and the alternating direction multiplier method involves the following steps:

[0029] (21) Input the original sound pressure signal and set the number of modal components K, and initialize the center frequency of each modal component Modal Function and Lagrange multipliers The superscript represents the number of iterations, and the iteration counter n = 0 and the modal component index k = 1 are set;

[0030] (22) Update the iteration count \(n=n + 1\);

[0031] (23) Update the center frequency and the modal function The formulas are as follows:

[0032]

[0033] where is the Fourier transform of the original signal, is the \((n + 1)\)-th iteration result of the \(k\)-th mode in the frequency domain, is the Fourier transform of the Lagrange multiplier, is the \(n\)-th iteration result of the \(i\)-th mode in the frequency domain, \(\alpha\) is the penalty factor, is the updated center frequency of the \(k\)-th mode. After the update, set the component index \(k=k + 1\);

[0034] (24) If \(k < K\), repeat step (23);

[0035] (25) Update the Lagrange multiplier. The formula is as follows;

[0036]

[0037] where is the Fourier transform of the updated Lagrange multiplier, \(\tau\) is the penalty coefficient;

[0038] (26) Calculate the convergence error \(\varepsilon\) k , and the calculation formula is as follows:

[0039]

[0040] If the convergence residual \(\varepsilon\) k is greater than or equal to the preset residual threshold \(\varepsilon\), repeat steps (22) to (26); otherwise, finally output \(K\) optimized IMFs.

[0041] (3) ESN modeling and training: Input each IMF component obtained by decomposition into the echo state network for training and prediction. Specifically, during implementation, first initialize the dynamic system of the reservoir, then input the IMF components into the ESN for feature extraction, and finally use the ridge regression method to train the output weights to minimize the prediction error. The specific training process is as follows:

[0042] Given a signal sequence \(u(t)\), the state of the reservoir can be represented by a vector \(r(t)\in\mathbb{R}\) at discrete times \(t(t = 0,\Delta t,2\Delta t,\cdots)\), and the state update of the ESN reservoir is described by the following equation: N×1 The state update of the ESN reservoir is described by the following equation:

[0043] r(t+Δt)=g(Ar(t)+W in u(t)) (6)

[0044] Among them, g is the activation function, A is an N×N adjacency matrix that reflects the connection relationship of each element in r(t), and W in It is the mapping matrix from the input state of dimension M to the reservoir state space of dimension N.

[0045] The output vector v(t) can be obtained by the following equation:

[0046] v(t)=W out r(t) (7)

[0047] Among them, W out It is the mapping matrix from the reservoir state space of dimension N to the output state of dimension L. In general, the ridge regression algorithm can be used to introduce regularization terms to improve the stability of numerical calculations and alleviate overfitting problems.

[0048] (4) Modal prediction and fusion: predict each IMF component and linearly superimpose the prediction results of all modes, that is, Equal to the predicted value v of each mode i The algebraic sum of (t): The final aerodynamic noise sound pressure prediction value is obtained.

[0049] (5) Performance evaluation: The root mean square error (RMSE) indicator is used to evaluate the prediction performance of the model and verify the accuracy of the VMD-ESN model in aerodynamic noise prediction. Figure 4 As shown in the figure, the proposed model finally achieved good prediction results in a long time period of 150 time steps, with a prediction RMSE of only 3.32 Pa, and the computational resources required were greatly reduced compared with traditional numerical simulation methods.

[0050] In summary, this paper proposes an aerodynamic noise prediction method that integrates VMD signal preprocessing with the dynamic modeling capabilities of an ESN neural network. By analyzing the variation patterns of historical aerodynamic noise time series data and combining fluid dynamics models with machine learning algorithms, this method achieves efficient processing and accurate prediction of complex nonlinear noise data. This method only requires the acquisition of complete aerodynamic noise signals to complete noise feature decomposition and modeling, accurately determining noise variation trends and critical states. In engineering applications, this method can effectively optimize bogie noise reduction designs and reduce far-field noise impacts. In safety and early warning, it can monitor wind turbine blade noise anomalies at specific frequencies to warn of flutter risks and identify sudden changes in aircraft engine jet noise to prevent major accidents such as combustion instability. Compared to traditional methods, this method significantly reduces computational complexity and experimental costs while also providing real-time monitoring capabilities. This provides a reliable basis for aerodynamic noise prediction and control, effectively reducing equipment losses and improving overall performance while ensuring system operational stability and efficiency.

Claims

1. A method for predicting aerodynamic noise time series based on VMD-ESN, characterized by: The following steps are involved: (1) Aerodynamic noise signal acquisition: The aerodynamic noise signal under high Reynolds number flow is collected in real time through the sound pressure sensor; (2) VMD signal decomposition: The original noise signal is adaptively decomposed in the frequency domain using variational mode decomposition (VMD), and multiple orthogonal narrowband intrinsic mode functions (IMFs) are generated through a constrained variational optimization framework. (3) ESN neural network modeling: Each IMF is independently input into the ESN, and the high-dimensional state mapping is performed using the sparsely connected reservoir of the echo state network. The output layer weight matrix of the neural network is trained using the ridge regression algorithm. (4) Integration of prediction results: Linearly superimpose the prediction values ​​of each IMF to generate a complete aerodynamic noise time series.

2. The aerodynamic noise prediction method based on VMD-ESN according to claim 1, characterized in that: In step (1), the sampling frequency f of the sound pressure sensor is s ≥2·f max , where f max is the highest frequency of the aerodynamic noise signal. For a given time step △t, the highest frequency of the acoustic analysis is f max =1 / (2△t).

3. The VMD-ESN-based aerodynamic noise time series prediction method according to claim 1, characterized in that: The VMD decomposition algorithm process in step (2) includes the following steps: (21) Input the original sound pressure signal and set the number of modal components K, and initialize the center frequency of each modal component Modal Function and Lagrange multipliers The superscript indicates the number of iterations, u k With ω k Represent the kth mode and its center frequency respectively, and set the iteration counter n = 0 and the component index k = 1; (22) Then enter the main iteration loop, and in each iteration the center frequency of each modal component is updated in turn through the inner loop. and modal functions is the Fourier transform of the original signal, is the Fourier transform of the Lagrange multiplier, α is the penalty factor, and the formula is as follows: (23) After completing the update of all components, update the multiplier according to the Lagrange multiplier method And calculate the convergence error ε k ; Continue iterating until the error is lower than the preset convergence residual threshold ε, and finally output K optimized intrinsic mode functions.

4. The VMD-ESN-based aerodynamic noise time series prediction method according to claim 3, characterized in that: The optimization objective function of the VMD is: The alternating direction multiplier method is used to iteratively optimize until the convergence residual is less than the preset convergence residual threshold.

5. The VMD-ESN-based aerodynamic noise time series prediction method according to claim 1, characterized in that: The step (3) comprises the following steps: (31) The input vector u(t) is mapped to a high-dimensional dynamic system, namely the reservoir R, through the input-reservoir coupler I / R. The mapping is composed of the mapping matrix W from the input state space to the reservoir state space in accomplish; (32) The state of the reservoir r(t) is updated according to the dynamic equation: r(t+1)=g(Ar(t)+W in u(t)) Where A is the weight matrix representing the internal connection of the reservoir, and g is the activation function; (33) The high-dimensional dynamic data of the reservoir is then mapped to the output vector v(t) through the reservoir-output coupler R / O. This process is represented by the trainable output matrix W out Determine that the output is linearly related to the parameter: v(t) = W out r(t).

6. The VMD-ESN-based aerodynamic noise time series prediction method according to claim 5, characterized in that: The step (4) is the predicted value Equal to the predicted value v of each mode i The algebraic sum of (t):

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