Noise spectrum prediction method, equipment and medium

Abstract

The invention discloses a noise spectrum prediction method, equipment and a medium, and relates to the field of design optimization. The noise spectrum prediction method comprises the following steps: acquiring a data set of sound power level spectrum data of an underwater vehicle based on numerical simulation; performing frequency spectrum order reduction on the acquired data set based on eigen-orthogonal decomposition, and screening modal coefficients with high energy ratio as output parameters; gradient prior information under the discrete sample condition in the data set after frequency spectrum order reduction is obtained based on a local linear regression gradient estimation method; a gradient-enhanced multi-output Gaussian process regression agent model is selected to construct a mapping relation between the control surface structure parameters of the underwater vehicle and the radiation noise sound power level spectrum according to the output parameters; and performing stern rudder flow noise spectrum prediction of the underwater vehicle according to the mapping relation. According to the noise spectrum prediction method, the flow noise spectrum of the stern rudder of the underwater vehicle can be rapidly and accurately predicted.

Description

Technical Field

[0001] This application relates to the field of design optimization, and more specifically, to a noise spectrum prediction method, device, and medium. Background Technology

[0002] In complex engineering equipment operating under adverse pressure gradients and unsteady shear flow fields, the flow noise generated by appendage structures is complex, encompassing not only turbulent boundary layer noise but also tip vortex noise and horseshoe vortex noise generated by eddies at the structure's tip and root, respectively. Rapid and accurate prediction of the impact of different geometric configurations on flow noise is of significant engineering value for achieving low-noise structural design. However, given the aforementioned complex flow noise generation mechanisms, establishing a mapping relationship between geometric configurations and noise spectra using methods suitable for engineering design remains a major technical challenge that needs to be addressed.

[0003] Current research on the aforementioned flow noise mainly relies on theoretical models and semi-empirical formulas, numerical simulations, and traditional multi-input single-output surrogate models. However, theoretical models and semi-empirical formulas are limited by simplification and assumptions, making it difficult to predict the impact of some important factors on noise. While high-precision numerical simulations can reveal the mechanisms of multi-source noise, their high computational cost makes them difficult to apply to rapid engineering design. Traditional multi-input single-output surrogate models can predict the overall noise level, but their spectrum prediction is constrained by the complexity of multi-dimensional input and multi-dimensional output mapping. Although all three methods can predict rudder noise to some extent, it is still difficult to simultaneously balance computational efficiency and prediction accuracy. Summary of the Invention

[0004] The purpose of this application is to provide a noise spectrum prediction method, device and medium that can achieve efficient and accurate prediction of the noise sound power level spectrum under different combinations of geometric parameters, and meet the needs of efficient evaluation and optimization design in engineering applications.

[0005] This application is implemented as follows: This application provides a noise spectrum prediction method, including the following steps: Data set of acoustic power level spectrum data of underwater vehicles obtained by numerical simulation; The obtained dataset is subjected to spectral order reduction based on intrinsic orthogonal decomposition, and modal coefficients with high energy proportions are selected as output parameters. Prior gradient information under discrete sample conditions within the dataset after spectral reduction is obtained based on the local linear regression gradient estimation method. A gradient-enhanced multi-output Gaussian process regression surrogate model was selected to construct the mapping relationship between the control surface structural parameters of the underwater vehicle and the radiated noise sound power level spectrum based on the output parameters. Predict the stern rudder flow noise spectrum of underwater vehicles based on the mapping relationship.

[0006] In some alternative implementations, the dataset of acoustic power level spectrum data of an underwater vehicle obtained by numerical simulation includes the following steps: obtaining wall pressure pulsation data by performing unsteady flow numerical simulation of the underwater vehicle, and then calculating the acoustic power level spectrum of the stern rudder radiation based on the frequency domain acoustic integral method.

[0007] In some alternative implementations, when calculating the acoustic power level spectrum of the stern radiated by the frequency domain acoustic integration method, the unsteady pressure on the stern surface is used as the sound source information to calculate the radiated sound pressure and sound velocity in the frequency domain. The sound intensity is then integrated on a closed integral surface with the geometric center of the underwater vehicle model as the center and radius R to obtain the sound power at different frequencies, thereby obtaining the acoustic power level spectrum.

[0008] In some alternative implementations, spectral reduction of the acquired dataset based on intrinsic orthogonal decomposition includes the following steps: Select Sound power level spectrum data of each sample Decompose into average value and pulsation value The superposition is as follows: ; In the formula, The number of discrete frequency points. For the first Sample , For the first discrete frequency points The average value is defined as: ; Then, the pulsation value It can be decomposed into a linear combination of a set of orthogonal modes and their corresponding mode coefficients: ; In the formula, To truncate the modal order, ; Indicates the i-th sample and the i-th sample. Modal coefficients; Represents the first in the frequency domain Individual POD modes; POD mode set It is orthogonal and normalized in the discrete frequency domain, satisfying: , and Index representing the POD mode, For the Kronecker function; The correlation matrix is ​​calculated based on the sound power level spectrum matrix. , where the matrix Defined as:

[0009] because Since this is a symmetric matrix, all its eigenvalues ​​are non-negative. We can perform eigenvalue decomposition on this matrix as follows: ; In the formula, For the correlation matrix The One eigenvalue; To and The corresponding eigenvector, which corresponds to the first eigenvector in the frequency domain. A POD mode can be represented as: ; and the The corresponding POD mode is the 1st The modal coefficients of a sample can be obtained through projection: ; For eigenvalues The energy distribution of each mode is determined by sorting the modes by size.

[0010] In some alternative implementations, for eigenvalues After sorting by size to determine the energy distribution of each mode, the mode coefficient with the highest energy distribution ratio is used as the output parameter.

[0011] In some optional implementations, obtaining prior gradient information for discrete samples within the dataset after spectral reduction based on the local linear regression gradient estimation method includes the following steps: At the target sample point Selecting nearby The nearest neighbor sample points have inputs and outputs respectively. Within this local neighborhood, construct the following linear model: ; In the formula, For the dimension of the input parameters, in Neighborhood selection Nearest neighbor sample points The corresponding output is , For the intercept term of the local linear model, For the local linear model with respect to the th The regression coefficients of each input component. , , For nearest neighbor sample index, , The value of is usually chosen as the dimension of the input parameter. 2 times; Substituting neighboring samples into the above linear model yields the matrix form of least squares: ; In the formula, The neighborhood input sample matrix; Let be the corresponding output vector; its least squares solution is ; The j-th component in the regression coefficient vector For output For input gradient prior information : ; In the formula, Indicates at sample points The gradient prior information constructed at that location.

[0012] In some alternative implementations, selecting a gradient-enhanced multi-output Gaussian process regression surrogate model to construct the mapping relationship between the control surface structural parameters of the underwater vehicle and the radiated noise acoustic power level spectrum based on the output parameters includes the following steps: Prior function values ​​of a Gaussian process with zero mean and gradient The covariance is defined as: ; In the formula, Indicates the first The correlation matrix of each kernel component in the output space; Represents the Kronecker product; This represents the number of kernel components of the covariance in the linear model. Indicates the first The covariance kernel matrix of each kernel component in the input space; It consists of four parts, which can be represented as follows: ; In the formula, For the output index, For sample index, For the input dimension index, This indicates that the outputs s and t are in and Cross covariance between , These are the cross-covariances between the function values ​​and the gradient, respectively. The gradient-gradient covariance can be represented by the kernel function. The partial derivative with respect to the input components is obtained; The input space kernel function is: ; In the formula, the diagonal matrix Containing elements Defined as the feature length scale; Will The four parts are combined to obtain the joint covariance matrix used for training: ; In the formula, This is a matrix representing the correlation between outputs, which is parameterized using Cholesky decomposition. , It is a positive semi-definite matrix; The joint distribution between the predicted values ​​and function values ​​on the test set is as follows: ; In the formula, The covariance matrix between the training set and the test set. The covariance matrix between the test sets, It is a diagonal noise matrix. This represents a joint observation vector containing function values ​​and gradient observations; The hyperparameter set is analyzed by minimizing the negative log marginal likelihood (NLML). Optimize to obtain the optimal value: ; In the formula, express , elements and In ; By analyzing the output y The posterior distribution is derived by using the joint Gaussian prior: ; The predicted mean and variance of the test set are expressed as follows: .

[0013] In some optional implementations, stern rudder structural parameters are used as input parameters, and modal coefficients with high energy proportions after spectral order reduction of the acquired dataset based on intrinsic orthogonal decomposition are used as output parameters. The gradient prior information corresponding to the modal coefficients and the modal coefficient function values ​​are jointly used as observations to participate in model training. A multi-output covariance structure is introduced into the Gaussian process regression model to explicitly characterize the correlation between different modal coefficients. During the model training phase, the dataset is divided into training and testing sets in a 9:1 ratio. The mapping relationship between the rudder structural parameters of the underwater vehicle and the radiated noise sound power level spectrum is constructed by analyzing the model kernel function parameters, output correlation parameters, and noise parameters.

[0014] This application also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0015] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0016] The beneficial effects of this application are as follows: The noise spectrum prediction method provided by this application includes the following steps: obtaining a dataset of acoustic power level spectrum data of an underwater vehicle based on numerical simulation; reducing the spectrum order of the obtained dataset based on intrinsic orthogonal decomposition and selecting modal coefficients with high energy proportions as output parameters; obtaining gradient prior information under discrete sample conditions in the dataset after spectrum reduction based on the local linear regression gradient estimation method; selecting a gradient-enhanced multi-output Gaussian process regression surrogate model to construct a mapping relationship between the rudder structure parameters of the underwater vehicle and the radiated noise acoustic power level spectrum based on the output parameters; and predicting the stern rudder flow noise spectrum of the underwater vehicle based on the mapping relationship. The noise spectrum prediction method provided in this application reduces the order of high-dimensional sound power level spectrum data by introducing intrinsic orthogonal decomposition, transforming the original high-dimensional spectrum into a small number of modal coefficients with main energy characteristics, thereby significantly reducing the output dimension and model complexity. On this basis, a gradient-enhanced multi-output Gaussian process regression model is constructed. While considering the correlation between different modal coefficients, gradient information is introduced to constrain the input-output mapping relationship to improve the prediction accuracy and stability of the surrogate model under small sample conditions, thereby achieving rapid and accurate prediction of the stern rudder flow noise spectrum of underwater vehicles. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart illustrating the noise spectrum prediction method provided in the embodiments of this application; Figure 2 A local structural parameter diagram of the research object of the noise spectrum prediction method provided in the embodiments of this application; Figure 3 A structural parameter diagram of the research object for the noise spectrum prediction method provided in the embodiments of this application; Figure 4 A diagram showing the local structural parameters of the stern rudder, the research object of the noise spectrum prediction method provided in this application embodiment; Figure 5 A graph showing the cumulative energy percentage of the first 50 modes in the noise spectrum prediction method provided in this application embodiment; Figure 6 Comparison of the reconstructed sound power level spectrum of the first 8 modal coefficients with numerical simulation results in the noise spectrum prediction method provided in the embodiments of this application; Figure 7 A graph showing the prediction results of the first-order mode coefficients of the training set in the noise spectrum prediction method provided in the embodiments of this application; Figure 8 The image shows the prediction results of the second-order mode coefficients of the training set in the noise spectrum prediction method provided in the embodiments of this application. Figure 9 The image shows the prediction results of the third-order mode coefficients of the training set in the noise spectrum prediction method provided in the embodiments of this application. Figure 10 A graph showing the prediction results of the fourth-order mode coefficients of the training set in the noise spectrum prediction method provided in the embodiments of this application; Figure 11 A graph showing the prediction results of the fifth-order mode coefficients of the training set in the noise spectrum prediction method provided in the embodiments of this application; Figure 12 A graph showing the prediction results of the sixth-order mode coefficients of the training set in the noise spectrum prediction method provided in the embodiments of this application; Figure 13 A graph showing the prediction results of the 7th-order mode coefficients of the training set in the noise spectrum prediction method provided in the embodiments of this application; Figure 14 The image shows the prediction results of the 8th-order mode coefficients of the training set in the noise spectrum prediction method provided in the embodiments of this application. Figure 15 A comparison of the sound power level spectrum prediction results and numerical simulation results for scheme 13 in the test set of the gradient-enhanced multi-output Gaussian process regression surrogate model in the noise spectrum prediction method provided in the embodiments of this application; Figure 16 A comparison of the sound power level spectrum prediction results and numerical simulation results for scheme 19 in the test set of the gradient-enhanced multi-output Gaussian process regression surrogate model in the noise spectrum prediction method provided in the embodiments of this application; Figure 17 A comparison of the sound power level spectrum prediction results and numerical simulation results for scheme 25 in the test set of the gradient-enhanced multi-output Gaussian process regression surrogate model in the noise spectrum prediction method provided in the embodiments of this application; Figure 18 A comparison of the sound power level spectrum prediction results and numerical simulation results of scheme 34 in the test set of the gradient-enhanced multi-output Gaussian process regression surrogate model in the noise spectrum prediction method provided in the embodiments of this application; Figure 19 A comparison of the sound power level spectrum prediction results and numerical simulation results for scheme 45 in the test set of the gradient-enhanced multi-output Gaussian process regression surrogate model in the noise spectrum prediction method provided in the embodiments of this application; Figure 20 The graph shows a comparison of the predicted spectrum and numerical simulation results of the same sample using different methods for structural parameters in the noise spectrum prediction method provided in the embodiments of this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this application, but not all embodiments.

[0020] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0021] The following detailed description of the features and performance of the noise spectrum prediction method, device and medium of this application is provided in conjunction with embodiments.

[0022] like Figure 1 As shown in the figure, this application provides a noise spectrum prediction method based on POD order reduction and gradient enhancement Gaussian process, including the following steps: Step S1: Obtain a dataset of acoustic power level spectrum data of underwater vehicles based on numerical simulation.

[0023] Step S2: Perform spectral order reduction on the acquired dataset based on intrinsic orthogonal decomposition (POD) and select modal coefficients with high energy proportions as output parameters.

[0024] Step S3: Obtain the gradient prior information of discrete samples in the dataset after spectral reduction using the Local Linear Regression Gradient Estimation (LLR) method.

[0025] Steps S2-S3 lay the groundwork for step S4, aiming to obtain the outputs and corresponding gradient information of the gradient-enhanced multi-output Gaussian process regression model through intrinsic orthogonal decomposition and local linear regression gradient estimation methods, thereby enabling rapid and accurate prediction of the stern rudder flow noise spectrum of underwater vehicles.

[0026] Step S4: Select a gradient-enhanced multi-output Gaussian process regression surrogate model and construct the mapping relationship between the control surface structural parameters of the underwater vehicle and the radiated noise sound power level spectrum based on the output parameters.

[0027] Step S5: Predict the stern rudder flow noise spectrum of the underwater vehicle based on the mapping relationship between the rudder surface structure parameters and the radiated noise sound power level spectrum.

[0028] The technical solution of this application is described in detail below. The mapping relationship between the control surface structural parameters of the underwater vehicle and the radiated noise sound power level spectrum described in step S1 is as follows: S101: Research Subjects like Figure 2 , Figure 3 and Figure 4 As shown, this application takes the single rudder and tail cone connection section of the SUBOFF standard model as the research object. The model is mainly composed of a quarter-axis symmetric streamlined rotating body and a rudder. The total length of the model is L=4.356m, the maximum diameter of the rotating body is D=0.508m, and the length of the truncated model selected in the actual calculation is l=L / 2. The tail edge of the rudder is located at x / l=0.952.

[0029] S102: Dataset Acquisition After performing unsteady flow numerical simulations of the underwater vehicle and obtaining wall pressure fluctuation data, the acoustic power level spectrum radiated by the stern rudder is further calculated based on the frequency domain acoustic integration method. Specifically, using the unsteady pressure on the stern rudder surface as the sound source information, the radiated sound pressure and sound velocity are calculated in the frequency domain. The sound intensity is then integrated on a closed integration surface with the geometric center of the model as the center and a radius R = 10m to obtain the sound power at different frequencies, and further, the acoustic power level spectrum is obtained. For each set of geometric configuration samples, a corresponding set of acoustic power level spectrum data is obtained. In other optional embodiments, the radius R can also be 7.5m, 12.5m, 15m, or other values.

[0030] Step S2: Based on the intrinsic orthogonal decomposition, the obtained dataset is subjected to spectral order reduction, and modal coefficients with high energy proportions are selected as output parameters. The specific method is as follows: S201: POD Order Reduction Principle Intrinsic Orthogonal Decomposition (POD) can significantly reduce data dimensionality while preserving key energy features. Its basic principle is to decompose the data matrix into eigenvectors and then sort the resulting eigenvalues ​​and eigenvectors according to their energy magnitude, thereby extracting the dominant modes that reflect the main features of the spectrum. The specific steps are as follows: First, select Sound power level spectrum data of each sample Decompose it into average value and pulsation value The superposition of, that is: (1) In the formula, The number of discrete frequency points. For the first Sample , For the first discrete frequency points The average value is defined as: (2) Then, the pulsation value It can be decomposed into a linear combination of a set of orthogonal modes and their corresponding modal coefficients, that is: (3) In the formula, To truncate the modal order, , Indicates the i-th sample and the i-th sample. Modal coefficients, Represents the first in the frequency domain A set of POD modes. It is orthogonal and normalized in the discrete frequency domain, satisfying: , and Index representing the POD mode, For the Kronecker function; The correlation matrix is ​​calculated based on the sound power level spectrum matrix. , where the matrix Defined as: (4) because Since this is a symmetric matrix, all its eigenvalues ​​are non-negative. We can perform eigenvalue decomposition on this matrix as follows: (5) In the formula, For the correlation matrix The 1 eigenvalue, To and The corresponding eigenvector, which corresponds to the first eigenvector in the frequency domain. A POD mode can be represented as: ; and the The corresponding POD mode is the 1st The modal coefficients of a sample can be obtained through projection: (6) Finally, for eigenvalues By sorting the modes by size, the energy distribution of each mode can be determined. The top few modes with the highest energy percentage are the dominant modes, representing the most significant energy characteristics in the numerical simulation results.

[0031] S202: POD order reduction of stern rudder flow noise spectrum The dataset obtained in step S102 of this application takes 50 samples as an example, but is not limited to 50 samples. The sound power level spectrum of all samples is extracted and constructed into a sample matrix. Then, the POD reduction method in step S201 above is used to decompose and reduce the dimensionality of the matrix, such as... Figure 5 The figure shows the cumulative energy percentage of the first 50 modes, from Figure 5 As can be seen, the energy of the first 8 modes accounts for approximately 96.0%. Figure 6The image shows the reconstruction of the first 8 modal coefficients and a comparison with the numerical simulation results. The results show that the total sound power level reconstructed from the first 8 modal coefficients is 93.45 dB, compared to 93.48 dB in the numerical simulation, with an error of 0.03 dB. This indicates that the number of modes at this point can adequately characterize the main energy features. Considering both the reconstruction accuracy and the computational complexity of the subsequent multi-output surrogate model, the first 8 modal coefficients were ultimately selected as the output parameters for constructing the sound power level spectrum surrogate model.

[0032] Step S3: Obtain the gradient prior information of the discrete samples in the dataset after spectral order reduction based on the local linear regression gradient estimation method. The specific method is as follows: The Local Linear Regression Gradient Estimation (LLR) method constructs a locally linear approximation model near the target sample point, simultaneously estimating function values ​​and gradient information. It should be noted that the gradient information in this application is not used to approximate the point derivative in a strict sense, but rather as prior gradient information in the gradient-enhanced Gaussian process regression model, used to constrain the local variation trend of the surrogate model and improve modeling stability.

[0033] Specifically, at the target sample points Selecting nearby The nearest neighbor sample points have inputs and outputs respectively. Within this local neighborhood, the following linear model is constructed: (7) In the formula, For the dimension of the input parameters, in Neighborhood selection Nearest neighbor sample points The corresponding output is , For the intercept term of the local linear model, For the local linear model with respect to the th The regression coefficients of each input component. , , For nearest neighbor sample index, , The value of is usually chosen as the dimension of the input parameter. This is doubled to improve the numerical stability of gradient estimation while ensuring the solvability of the local linear regression problem. It should be noted that the above equation describes the output within the neighborhood of the target sample point. The model describes the local linear variation trend of the input parameters, rather than the point derivative model in the sense of first-order Taylor expansion.

[0034] Substituting the neighboring samples into equation (7), we can obtain the least squares in matrix form: (8) In the formula, The neighborhood input sample matrix; Let be the corresponding output vector; its least squares solution is .

[0035] Regression coefficient vector In, the j-th component For output For input gradient prior information : (9) In the formula, Indicates at sample points The gradient prior information constructed at that point is used in the gradient-enhanced Gaussian process regression model, and this quantity reflects the output. Within a local neighborhood, the input parameters The average linear sensitivity is not the point derivative in the strict sense.

[0036] Step S4, based on the modal coefficients and gradient information obtained in steps S2 and S3, uses a gradient-enhanced multi-output Gaussian process regression surrogate model to construct the mapping relationship between the control surface structural parameters of the underwater vehicle and the radiated noise sound power level spectrum according to the output parameters. The specific method is as follows: S401: Principle of Gradient-Enhanced Multi-Output Gaussian Process Regression Surrogate Model The gradient-enhanced multi-output Gaussian process regression model (GEMOGP) can not only capture the correlation between multiple outputs in small sample scenarios, but also use sample gradient information to improve the local accuracy and global generalization ability of prediction.

[0037] In having One input parameter and In the predicted scenario of each output, in each training sample The output function value can be obtained at the same time. and its gradient with respect to the input Treating gradients as additional observations can create augmented training datasets that include function values ​​and gradients.

[0038] Assuming function value and gradient The covariance of a prior Gaussian process with zero mean is defined as: (10) In the formula, Indicates the first The correlation matrix of each kernel component in the output space Represents the Kronecker product. This represents the number of kernel components of the covariance in the linear model. Indicates the first The covariance kernel matrix of each kernel component in the input space. It consists of four parts, which can be represented as follows: (11) In the formula, For the output index, For sample index, For the input dimension index, This indicates that the outputs s and t are in and Cross covariance between , These are the cross-covariances between the function values ​​and the gradient, respectively. The gradient-gradient covariance can be represented by the kernel function. The partial derivative with respect to the input component is obtained.

[0039] The input space kernel function is: (12) In the formula, the diagonal matrix Containing elements Defined as the feature length scale.

[0040] Combining the four parts of equation (9) yields the joint covariance matrix used for training: (13) In the formula, This is a matrix representing the correlation between outputs, which is parameterized using Cholesky decomposition. , It is a positive semi-definite matrix.

[0041] Since a Gaussian process can be viewed as a set of random variables, and any finite number of random variables follow a joint Gaussian distribution, the joint distribution between the predicted values ​​and the function values ​​on the test set is: (14) In the formula, The covariance matrix between the training set and the test set. The covariance matrix between the test sets, This is a diagonal noise matrix. This represents a joint observation vector containing function values ​​and gradient observations.

[0042] To maximize the predictive performance of the multi-output Gaussian process model, the hyperparameter set is optimized by minimizing the negative log-marginal likelihood (NLML). Optimize to obtain the optimal value: (15) In the formula, express , elements and In .

[0043] By deriving the joint Gaussian prior of the output y, its posterior distribution can be obtained: (16) Accordingly, the predicted mean and variance of the test set can be expressed as: (17) S402: Construction of a Gradient-Boosted Multi-Output Gaussian Process Regression Surrogate Model Based on the dominant modal coefficients of the sound power level spectrum obtained in step S2 and the prior information of discrete sample gradients constructed in step S3, a gradient-enhanced multi-output Gaussian process regression model is selected as the surrogate model framework to establish the mapping relationship between the rudder surface structural parameters and the modal coefficients of the sound power level spectrum. Specifically, the stern rudder structural parameters are used as input parameters, and the first 8 modal coefficients after POD reduction are used as output parameters. In the Gaussian process regression model, a multi-output covariance structure is introduced to explicitly characterize the correlation between different modal coefficients, thereby avoiding the correlation loss problem caused by modeling each modal coefficient independently. At the same time, the gradient prior information corresponding to the modal coefficients and the modal coefficient function values ​​are jointly used as observations to participate in model training, so as to constrain the local variation trend in the input parameter space, thereby improving the prediction accuracy and generalization ability of the model under small sample conditions. In the model training stage, the dataset is divided into training set and test set in a 9:1 ratio. By jointly optimizing the model kernel function parameters, output correlation parameters and noise parameters, the gradient-enhanced multi-output Gaussian process regression surrogate model is completed.

[0044] Step S5 involves using the mapping relationship between the rudder surface structural parameters and the radiated noise sound power level spectrum of the underwater vehicle constructed in steps S2, S3 and S4 to predict the rudder flow noise spectrum for different structural parameters.

[0045] By changing the structural parameters of the stern rudder (span, chord length, maximum relative thickness, relative position of the maximum thickness, leading edge tilt angle), the mapping relationship between the rudder surface structural parameters of the underwater vehicle and the radiated noise sound power level spectrum can be used to predict the stern rudder flow noise spectrum.

[0046] Figure 7The image shows the prediction results of the first 8 modal coefficients of the training set using a gradient-enhanced multi-output Gaussian process regression surrogate model (LLR-GEMOGP) based on a local linear regression gradient estimation strategy. Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 , Figure 13 , Figure 14 As shown in the figure, the prediction results of the surrogate model are generally highly consistent with the reference values, and can stably and accurately characterize the changing trends of the modal coefficients of each order. Furthermore, evaluating the prediction using the coefficient of determination R², the coefficients of determination for each output modal coefficient are all greater than 0.77, indicating that the surrogate model has good fitting accuracy and prediction reliability.

[0047] like Figure 15 , Figure 16 , Figure 17 , Figure 18 and Figure 19 The figure shows a comparison between the sound power level spectrum prediction results and the numerical simulation results of the gradient-enhanced multi-output Gaussian process regression surrogate model based on the local linear regression gradient estimation strategy on the test set. It can be seen that the predicted spectrum can reconstruct the main features of the numerical simulation results relatively accurately. It maintains good consistency with the numerical simulation results in terms of overall trend and macroscopic direction of energy distribution, and no systematic deviation occurs.

[0048] Furthermore, Table 1 verifies the above conclusions from the perspective of total sound power level. The results show that the prediction error of the total sound power level of each sample in the test set does not exceed 0.3dB, indicating that the method can achieve high-precision prediction of the stern rudder flow noise spectrum and its overall sound power level.

[0049] Table 1 Comparison of total acoustic power levels in the test set of the gradient-enhanced Gaussian process regression surrogate model.

[0050] To verify the prediction accuracy and effectiveness of this method, the structural parameters of the same sample were selected as input. The sound power level spectrum was predicted using a traditional Gaussian process regression surrogate model, a gradient-enhanced Gaussian process regression surrogate model, and the Howe theory model, respectively. The results were then compared with numerical simulation results. The comparison results of the sound power level spectrum and the total sound power level are shown below. Figure 20 As shown in Table 2: Table 2 Comparison of prediction accuracy of different algorithms

[0051] from Figure 20As can be seen, the gradient-enhanced Gaussian process regression surrogate model predicts the spectrum with a high degree of consistency with the numerical simulation results in terms of both amplitude level and spectral variation trend across the entire frequency band. The traditional Gaussian process regression surrogate model can reflect the variation law of the numerical simulation results in terms of overall trend, but there is a certain deviation between the overall amplitude and the numerical simulation results. In contrast, the Howe theoretical model predicts the spectrum with a higher amplitude in the low frequency band than the numerical simulation results, while it is significantly lower in the mid-to-high frequency band, failing to reflect the main energy distribution characteristics of the numerical simulation results.

[0052] Table 2 provides a quantitative analysis. The total sound power level predicted by the numerical simulation is 96.06 dB, while the total sound power level predicted by the gradient-enhanced Gaussian process regression surrogate model is 96.18 dB, a difference of only 0.12 dB. This indicates that the gradient-enhanced Gaussian process regression surrogate model is more reliable in overall energy prediction and can accurately reconstruct the true sound radiation energy level. In contrast, the total sound power level predicted by the traditional Gaussian process regression surrogate model is 94.47 dB, an underestimation of 1.59 dB compared to the numerical simulation result. The total sound power level predicted by the Howe theoretical model is only 89.66 dB, a deviation of 6.40 dB compared to the numerical simulation result.

[0053] The noise spectrum prediction method provided in this application reduces the order of high-dimensional sound power level spectrum data by introducing intrinsic orthogonal decomposition, transforming the original high-dimensional spectrum into a small number of modal coefficients with main energy characteristics, thereby significantly reducing the output dimension and model complexity. Based on this, a gradient-enhanced multi-output Gaussian process regression model is constructed. While considering the correlation between different modal coefficients, gradient information is introduced to constrain the input-output mapping relationship to improve the prediction accuracy and stability of the surrogate model under small sample conditions. This method can effectively achieve rapid prediction of radiated noise spectrum from stern and rudder structural parameters with high accuracy, greatly saving computational resources and time costs.

[0054] This method can quickly predict the radiated noise spectrum from the structural parameters of the stern and rudder with high accuracy, greatly saving computing resources and time costs.

[0055] This application also provides a computer device, which may include a processor with one or more processing cores, a memory with one or more computer-readable storage media, a power supply, and an input unit, etc.

[0056] Although not shown, the computer device may also include a display unit, etc., which will not be described in detail here. Specifically, in this embodiment, the processor in the computer device loads the executable files corresponding to the processes of one or more applications into the memory according to the following instructions, and the processor runs the applications stored in the memory, thereby implementing the steps in the above method embodiment.

[0057] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be performed by instructions, or by instructions controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor.

[0058] Therefore, embodiments of this application provide a computer-readable storage medium having a computer program stored thereon, the computer program being loaded by a processor to execute the steps of any of the methods provided in embodiments of this application.

[0059] For details on the implementation of each of the above operations, please refer to the previous examples, which will not be repeated here.

[0060] The computer-readable storage medium may include: read-only memory, random access memory, disk or optical disk, etc.

[0061] Since the computer program stored in the computer-readable storage medium can execute the steps of any of the methods provided in the embodiments of this application, the beneficial effects that any of the methods provided in the embodiments of this application can achieve can be realized, as detailed in the preceding embodiments, and will not be repeated here.

[0062] The embodiments described above are some, but not all, of the embodiments of this application. The detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A noise spectrum prediction method, characterized in that, Includes the following steps: Data set of acoustic power level spectrum data of underwater vehicles obtained by numerical simulation; The obtained dataset is subjected to spectral order reduction based on intrinsic orthogonal decomposition, and modal coefficients with high energy proportions are selected as output parameters. Prior gradient information under discrete sample conditions within the dataset after spectral reduction is obtained based on the local linear regression gradient estimation method. A gradient-enhanced multi-output Gaussian process regression surrogate model was selected to construct the mapping relationship between the control surface structural parameters of the underwater vehicle and the radiated noise sound power level spectrum based on the output parameters. Predict the stern rudder flow noise spectrum of underwater vehicles based on the mapping relationship.

2. The noise spectrum prediction method according to claim 1, characterized in that, The dataset for obtaining the acoustic power level spectrum data of an underwater vehicle based on numerical simulation includes the following steps: after obtaining wall pressure fluctuation data through unsteady flow numerical simulation of the underwater vehicle, the acoustic power level spectrum of the stern rudder radiation is calculated based on the frequency domain acoustic integral method.

3. The noise spectrum prediction method according to claim 2, characterized in that, When calculating the acoustic power level spectrum of the stern rudder radiation using the frequency domain acoustic integral method, the unsteady pressure on the stern rudder surface is used as the sound source information to calculate the radiated sound pressure and sound velocity in the frequency domain. The sound intensity is then integrated on a closed integral surface with the geometric center of the underwater vehicle model as the center and radius R to obtain the sound power at different frequencies, thereby obtaining the acoustic power level spectrum.

4. The noise spectrum prediction method according to claim 1, characterized in that, The spectral reduction of the obtained dataset based on intrinsic orthogonal decomposition includes the following steps: Select Sound power level spectrum data of each sample Decompose into average value and pulsation value The superposition is as follows: ； In the formula, The number of discrete frequency points. For the first Sample , For the first discrete frequency points The average value is defined as: ； Then, the pulsation value It can be decomposed into a linear combination of a set of orthogonal modes and their corresponding mode coefficients: ； In the formula, To truncate the modal order, ; Indicates the i-th sample and the i-th sample. Modal coefficients; Represents the first in the frequency domain One POD mode; POD mode set It is orthogonal and normalized in the discrete frequency domain, satisfying: , and Index representing the POD mode, For the Kronecker function; The correlation matrix is ​​calculated based on the sound power level spectrum matrix. , where the matrix Defined as: because Since this is a symmetric matrix, all its eigenvalues ​​are non-negative. We can perform eigenvalue decomposition on this matrix as follows: ； In the formula, For the correlation matrix The One eigenvalue; To and The corresponding eigenvector, which corresponds to the first eigenvector in the frequency domain. A POD mode can be represented as: ; and the The corresponding POD mode is the 1st The modal coefficients of a sample can be obtained through projection: ； For eigenvalues The energy distribution of each mode is determined by sorting the modes by size.

5. The noise spectrum prediction method according to claim 4, characterized in that, For eigenvalues After sorting by size to determine the energy distribution of each mode, the mode coefficient with the highest energy distribution ratio is used as the output parameter.

6. The noise spectrum prediction method according to claim 1, characterized in that, Obtaining prior gradient information for discrete samples within the dataset after spectral reduction using the local linear regression gradient estimation method includes the following steps: At the target sample point Selecting nearby The nearest neighbor sample points have inputs and outputs respectively. Within this local neighborhood, construct the following linear model: ； In the formula, For the dimension of the input parameters, in Neighborhood selection Nearest neighbor sample points The corresponding output is , For the intercept term of the local linear model, For the local linear model with respect to the th The regression coefficients of each input component. , , For nearest neighbor sample index, , The value of is usually chosen as the dimension of the input parameter. 2 times; Substituting neighboring samples into the above linear model yields the matrix form of least squares: ； In the formula, The neighborhood input sample matrix; Let be the corresponding output vector; its least squares solution is ; The j-th component in the regression coefficient vector For output For input gradient prior information : ； In the formula, Indicates at sample points The gradient prior information constructed at that location.

7. The noise spectrum prediction method according to claim 1, characterized in that, Selecting a gradient-enhanced multi-output Gaussian process regression surrogate model, and constructing the mapping relationship between the control surface structural parameters of the underwater vehicle and the radiated noise sound power level spectrum based on the output parameters, includes the following steps: Prior function values ​​of a Gaussian process with zero mean and gradient The covariance is defined as: ； In the formula, Indicates the first The correlation matrix of each kernel component in the output space; Represents the Kronecker product; This represents the number of kernel components of the covariance in the linear model. Indicates the first The covariance kernel matrix of each kernel component in the input space; It consists of four parts, which can be represented as follows: ； In the formula, For the output index, For sample index, For the input dimension index, This indicates that the outputs s and t are in and Cross covariance between , These are the cross-covariances between the function values ​​and the gradient, respectively. The gradient-gradient covariance can be represented by the kernel function. The partial derivative with respect to the input components is obtained; The input space kernel function is: ； In the formula, the diagonal matrix Containing elements Defined as the feature length scale; Will The four parts are combined to obtain the joint covariance matrix used for training: ； In the formula, This is a matrix representing the correlation between outputs, which is parameterized using Cholesky decomposition. , It is a positive semi-definite matrix; The joint distribution between the predicted values ​​and function values ​​on the test set is as follows: ； In the formula, The covariance matrix between the training set and the test set. The covariance matrix between the test sets, This is a diagonal noise matrix. This represents a joint observation vector containing function values ​​and gradient observations; The hyperparameter set is analyzed by minimizing the negative log marginal likelihood (NLML). Optimize to obtain the optimal value: ； In the formula, express , elements and In ; By analyzing the output y The posterior distribution is derived by using the joint Gaussian prior: ； The predicted mean and variance of the test set are expressed as follows: 。 8. The noise spectrum prediction method according to claim 7, characterized in that, Using stern rudder structural parameters as input parameters, and the modal coefficients with high energy proportions after spectral order reduction of the obtained dataset based on intrinsic orthogonal decomposition as output parameters, the gradient prior information corresponding to the modal coefficients and the modal coefficient function values ​​are combined as observations to participate in model training. A multi-output covariance structure is introduced into the Gaussian process regression model to explicitly characterize the correlation between different modal coefficients. During the model training phase, the dataset is divided into training and testing sets in a 9:1 ratio. The mapping relationship between the control surface structural parameters and the radiated noise sound power level spectrum of the underwater vehicle is constructed by analyzing the model kernel function parameters, output related parameters, and noise parameters.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method according to any one of claims 1 to 8.

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