Spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise

Abstract

The present invention belongs to the technical field of sound propagation, and relates to a spectral wide-angle parabolic equation modeling method for non-uniform ocean wind farm noise. The method discretizes the depth operator of each layer through the Chebyshev spectrum method, divides the undulating seabed into multiple flat areas, and performs iterative solution. By analyzing the underwater noise data of the wind turbine with a single unit capacity of 5.5Mw in the Yangjiang wind farm, it is shown that the overall trend of the sound propagation law of the underwater noise of the wind farm is consistent with the theoretical model of the spectral discrete wide-angle parabolic equation model. The data and results of the present invention provide a technical reference for the environmental impact assessment of offshore wind power projects, and provide an important basis for a more comprehensive understanding of the underwater noise characteristics of offshore wind farms and their environmental impacts, as well as for optimizing engineering design and operation management. This method is of great significance for understanding and evaluating the impact of wind farms on the underwater acoustic environment, and the accurate modeling and evaluation of underwater noise will play a positive role in environmental protection and sustainable development.

Description

Technical Field

[0001] The invention belongs to the technical field of sound propagation, and in particular relates to a wide-angle parabolic equation modeling method for wind farm noise in a non-uniform ocean using a spectrum method. Background Art

[0002] At present, the rapid development of offshore wind farms has become the focus of global attention, not only because of its huge potential for renewable energy, but also because of its impact on the environment and ecosystem. In order to evaluate the impact of wind farms on the marine environment, especially on marine life, it is particularly important to accurately simulate the underwater sound propagation of wind farms.

[0003] Traditional sound propagation models include simple normal waves, wave number integrals, rays, and parabolic equation methods. Among them, simple normal waves are often used to deal with horizontally layered media, and are suitable for analyzing low-frequency far-field shallow sea sound propagation problems; the wave number integral method is also used to deal with horizontally layered media, with high calculation accuracy, and is often used as an exact solution, but it is not suitable for horizontally layered marine environments that vary with distance; the ray method is suitable for dealing with high-frequency sound propagation problems, but it is not suitable for areas where the sound field varies greatly within a wavelength range, such as acoustic shadow areas and caustic areas; the parabolic equation method is often used to deal with sound fields where the environment varies with distance, but it is not suitable for the calculation of high-frequency sound fields. For complex boundaries and complex environments, numerical methods such as finite element and finite difference methods can also be used to analyze sound propagation problems, but due to the large amount of calculation required by numerical methods, they are not suitable for high-frequency deep-sea far-field calculations.

[0004] In the context of numerical methods, spectral methods have begun to gain popularity in the computational ocean. Although, spectral methods are still numerical methods compared with finite difference and finite element methods, their exponential error convergence makes them gradually gain prominence in scientific and engineering numerical simulations. Some representative numerical experiments have demonstrated the accuracy and effectiveness of the algorithm. However, spectral methods require that the thickness of the layer does not change during the forward steps. Therefore, current spectral algorithms cannot simulate waveguides with topographic fluctuations, which is its main limitation.

[0005] The wide-angle parabola model has become one of the main numerical models for medium and low frequency sound propagation due to its balance between computational speed and accuracy. This model discretizes the wide-angle parabola model approximated by split-step Padé expansion using the Chebyshev spectral method. It only considers the forward propagation of sound waves, greatly reducing the computational complexity and being applicable to complex seabed conditions. Based on this, it is very necessary to develop a spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise, which can not only achieve a more comprehensive understanding of the underwater noise characteristics of offshore wind farms and their environmental impacts, but also provide an important basis for optimizing engineering design and operation management. Summary of the invention

[0006] The purpose of the present invention is to provide a spectral wide-angle parabolic equation modeling method for non-uniform marine wind farm noise. The depth operator of each layer is discretized by the Chebyshev spectral method, and the undulating seabed is divided into multiple flat areas. An iterative solution is performed to solve the significant limitations in dealing with complex boundaries and environmental changes, especially in high-frequency and deep-sea far-field calculations, where the finite element method and the finite difference method are difficult to apply due to the large amount of calculation.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] A spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise includes the following steps for processing wind farm noise signals:

[0009] S1. Read the noise data of the wind farm, denoise the original data, and obtain the noise data within the target time;

[0010] S2. Determine whether there is data within the target time period, perform Fourier transform, and find the frequency range of wind farm noise;

[0011] S3, extracting the sound pressure level of wind farm noise at different frequencies and distances;

[0012] S4. Draw the sound pressure of wind farm underwater noise at different distances and frequencies;

[0013] S5. Take the governing equation of sound propagation in the frequency domain, namely the Helmholtz equation, and only consider the forward propagation of sound waves. Expand and simplify the Helmholtz equation into a parabolic equation.

[0014] S6. Through Chebyshev polynomials, the conversion between physical space and spectral space is realized, and the parabolic equation is discretized;

[0015] S7, transferring the acoustic boundary conditions to the spectral space, solving the linear equations derived from the projection of the boundary conditions and the discrete control equations;

[0016] S8, after solving the first section of sound pressure, taking the first section of flat seabed sound pressure as the starting sound pressure of the next section of flat seabed for iterative solution;

[0017] S9. Import the measured data into the model and calculate the sound propagation curve.

[0018] Furthermore, step S1 specifically includes the following steps:

[0019] S11, extracting and denoising the original data to obtain the original data, and the time domain data includes the underwater noise generated during the operation period of the wind farm;

[0020] S12. Split the time domain data to keep the length of noise data at different distances consistent

[0021] Furthermore, step S2 specifically includes the following steps:

[0022] S21, removing the DC component of the noise data and performing short-time Fourier transform;

[0023] S22. Calculate the maximum sound spectrum peak in the frequency domain for the data after short-time Fourier transformation, and determine the frequency range of wind farm noise according to the frequency domain characteristics.

[0024] Further, step S5 is specifically as follows: under the condition of considering forward propagation, the undulation of the seabed is divided into multiple flat areas according to the height difference, and modeled one by one; each sub-area is merged by summation operation, and the relationship between the underwater noise of the wind farm in the study area and the distance is calculated; the Helmholtz equation of sound propagation in the frequency domain is taken, and it is simplified to the PE equation when the solution of ordinary differential equations is adopted, and it is expanded using the wide-angle paraxial approximation method.

[0025] Further, step S6, discretizing the parabolic equation through Chebyshev polynomials, specifically: setting the sea surface as a total reflection boundary, setting the uniform semi-acoustic space D as a perfect matching layer, using the following Chebyshev polynomials as basis functions, discretizing the depth operator of each layer through the Chebyshev spectral method, and then assembling them into a global matrix.

[0026] Further, step S8 is specifically as follows: the sound pressure at the end distance of the first section of flat seabed is iterated as the starting sound pressure of the next section of flat seabed, and for the plane parallel waveguide, the segmented simulation results are merged to obtain the sound propagation curve of the continuous undulating seabed.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] The present invention analyzes the underwater noise data of wind turbines with a single unit capacity of 5.5Mw in Yangjiang wind farm. The results show that the overall trend of the sound propagation law of underwater noise in wind farms is consistent with the theoretical model of the spectral discrete wide-angle parabolic equation model; it provides an important basis for a more comprehensive understanding of the underwater noise characteristics of offshore wind farms and their environmental impacts, as well as for optimizing engineering design and operation management. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0030] Figure 1A spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise;

[0031] Figure 2 It is a schematic diagram of multi-layer medium on the undulating seabed;

[0032] Figure 3 This paper presents a spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise and the sound propagation law of the model. DETAILED DESCRIPTION

[0033] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0034] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0035] like Figure 1 As shown, the present invention is directed to the spectral wide-angle parabolic equation modeling method for non-uniform ocean wind farm noise, and the wind farm noise signal processing includes the following steps:

[0036] S1. Read the wind farm noise data, denoise the original data, and obtain the noise data within the target time. Specifically, the following steps are included:

[0037] S11, extracting and denoising the original data to obtain the original data, and the time domain data includes the underwater noise generated during the operation period of the wind farm;

[0038] S12. Split the time domain data to keep the length of noise data at different distances consistent.

[0039] S2. Determine whether there is data within the target time period, perform Fourier transform, and find the frequency range of wind farm noise. Specifically, the following steps are included:

[0040] S21, removing the DC component of the noise data and performing short-time Fourier transform;

[0041] S22. Calculate the maximum sound spectrum peak in the frequency domain for the data after short-time Fourier transformation, and determine the frequency range of wind farm noise according to the frequency domain characteristics.

[0042] In the experiment, the peak frequencies of the discrete spectrum are 44Hz, 88Hz, 103Hz, 176Hz, 206Hz, and 1050Hz, and the frequencies are mainly concentrated within 1500Hz. These noises show significant attenuation when the distance increases.

[0043] S3. Extract the underwater noise intensity of wind farms at different distances and frequencies. Specifically, extract the sound pressure level of wind farm noise at different frequencies and distances. Within 4km from the site, the impact of wind farms in the 30-100Hz and 1000-1500Hz frequency bands can be measured. The overall sound pressure is significantly higher than the marine environment background, and the discrete main frequency signal is still visible.

[0044] S4. Draw the sound pressure of underwater noise at different distances and frequencies of wind farms.

[0045] S5. Take the governing equation for sound propagation in the frequency domain, the Helmholtz equation, and only consider the forward propagation of sound waves. Expand and simplify the Helmholtz equation into a parabolic equation.

[0046]

[0047] In the formula, p(r i , z) is the sound pressure corresponding to the distance and depth; n is the order of Padé approximation, a j and b j are the coefficients of the Padé approximation, k0=2πf / c0, k0 and c0 are wave number and sound speed respectively.

[0048] Specifically, under the condition of considering forward propagation, the undulation of the seabed is divided into multiple flat areas according to the height difference, and each sub-area is modeled one by one. Each sub-area is merged through addition operation, and the relationship between the underwater noise of the wind farm in the study area and the distance is calculated.

[0049] The Helmholtz equation for sound propagation in the frequency domain is taken and simplified to the PE equation when the ordinary differential equation solution is adopted and expanded using the wide-angle paraxial approximation method.

[0050] like Figure 2 This is a schematic diagram of a multi-layer medium on an undulating seabed. The continuously undulating seabed is represented by a combination of multiple flat seabeds. The underwater sound propagation medium is horizontally divided into l layers (h1, h2, …, hl, …, h l ),h l-1 The seafloor is denoted by H, and hl is the uniform acoustic half space below the seafloor, denoted by D. For the flat seafloor after segmentation, if c(r i , z), ρ(r i ,z) and α(r i,z) are the medium sound velocity, density and attenuation coefficient respectively, and the underwater sound propagation medium is divided into l layers. Solve the uniform acoustic half-space Helmholtz equation at different depths. Since the underwater noise of the fan mainly propagates along the forward direction of the installation, the Helmholtz equation can be simplified to the PE equation and expanded using the split-step Padé expansion.

[0051] S6. Based on the orthogonality of Chebyshev polynomials, the conversion between physical space and spectral space is realized. The parabolic equation is discretized by Chebyshev polynomials.

[0052] First, solve the first flat seabed r1. If we only consider the forward propagation, the sound pressure and normal vibration velocity of the particle are continuous at the interface perpendicular to the acoustic half-space direction:

[0053]

[0054] The sea surface is set as the total reflection boundary, the uniform semi-acoustic space D is set as the perfect matching layer, and the following Chebyshev polynomials are used as basis functions. The depth operator of each layer is discretized by the Chebyshev spectral method and then assembled into a global matrix. Specifically:

[0055] T0(t)=1;

[0056] T1(t) = t;

[0057] T2(t)=2t 2 -1,

[0058] T k+1 (t) = 2tT k (t)-T k-1 (t), (3)

[0059] In the formula, the Chebyshev polynomial {Tk(t)} is defined in t∈[-1,1], k=2,3,4,…. The smooth function in the interval t∈[-1,1] is approximately expanded as follows:

[0060]

[0061] In the formula, represents the spectral coefficient of u(t), and N is the spectral stage order. As N increases, the error will decrease exponentially. According to the orthogonality of Chebyshev polynomials, The spectral coefficient is expressed as formula (5). In order to improve the calculation accuracy of formula (4), Gauss–Chebyshev–Lobatto intersection is used, and the Gauss–Chebyshev–Lobatto nodes and weights are:

[0062]

[0063] The derivative of the function u(t) can be similarly expanded as shown in formula (7). Then, according to Chebyshev and its derivative, the following relationship can be obtained, as shown in formula (7).

[0064]

[0065] Formula (8) is the matrix-vector form of the derivative relationship, D N is a Legendre matrix of order N+1, Is The spectral coefficients of the product of two functions have the following relationship:

[0066]

[0067] S7, the acoustic boundary conditions are transferred to the spectral space, and the linear equations derived from the projection of the boundary conditions and the discrete control equations are solved. The wide-angle PE model is discretized using the Chebyshev spectral method. Before the spectral transformation, the solution domain [z1, z2] is first scaled to [t1, t2], t = (2z) / (z2-z1)-(z2+z1) / (z2-z1), Discretizing the density ratio χ in formula (1) yields formula (10).

[0068]

[0069] The discretized form in Chebyshev spectral space is:

[0070]

[0071] Where D N is of order N+1, C ρ , C ρ , C 1 / ρ , C k 2 is the spectral coefficient of Chebyshev discretization from physical space to spectral space, I n is a first-order unit matrix. Substitute the discretized χ into formula (1) to solve the sound pressure at different depths in the first section:

[0072]

[0073] S8. After solving the sound pressure of the first section at different depths, the sound pressure at the end distance of the first section of flat seabed is used as the starting sound pressure of the next section of flat seabed for iterative solution, that is:

[0074]

[0075] For the plane parallel waveguide, the segmented simulation results are combined to obtain the sound propagation curve of the continuous undulating seabed: the water depth is 25 meters, the sound source depth z is 10 meters, and the receiving depth is 10 meters. The seawater and the seabed are both homogeneous media, where the seawater density ρ is 1000kg / m 3 , the sound speed c0 is set to 1500m / s, and the seabed is regarded as a rigid interface.

[0076] S9. Import the measured data into the model and calculate the sound propagation curve.

[0077] Figure 3 This paper verifies a spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise. The results show that the sound pressure level of 44Hz and 2000Hz wind farm noise decreases significantly with increasing distance. When the distance exceeds 4 kilometers, it gradually approaches the ocean background noise level.

[0078] In summary, the present invention divides the horizontally undulating seabed into several flat seabed segments, iteratively solves the sound propagation curve segment by segment, and finally merges the results. Compared with the traditional finite element method and the processing method that regards the seabed as an ideal flat surface, the improved algorithm shows higher accuracy and precision in underwater noise simulation. The present invention is of great significance for understanding and evaluating the impact of wind farms on the underwater acoustic environment. With the rapid development of the offshore wind power industry, accurate modeling and evaluation of underwater noise will play a positive role in environmental protection and sustainable development.

[0079] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise, characterized in that: The processing of wind farm noise signals includes the following steps: S1. Read the noise data of the wind farm, denoise the original data, and obtain the noise data within the target time; S2. Determine whether there is data within the target time period, perform Fourier transform, and find the frequency range of wind farm noise; S3, extracting the sound pressure level of wind farm noise at different frequencies and distances; S4. Draw the sound pressure of wind farm underwater noise at different distances and frequencies; S5. Take the governing equation of sound propagation in the frequency domain, namely the Helmholtz equation, and only consider the forward propagation of sound waves. Expand and simplify the Helmholtz equation into a parabolic equation. S6. Through Chebyshev polynomials, the conversion between physical space and spectral space is realized, and the parabolic equation is discretized; S7, transferring the acoustic boundary conditions to the spectral space, solving the linear equations derived from the projection of the boundary conditions and the discrete control equations; S8, after solving the first section of sound pressure, taking the first section of flat seabed sound pressure as the starting sound pressure of the next section of flat seabed for iterative solution; S9. Import the measured data into the model and calculate the sound propagation curve.

2. The spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11, extracting and denoising the original data to obtain the original data, and the time domain data includes the underwater noise generated during the operation period of the wind farm; S12. Split the time domain data to keep the length of noise data at different distances consistent.

3. The spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise according to claim 1 is characterized in that: Step S2 specifically includes the following steps: S21, removing the DC component of the noise data and performing short-time Fourier transform; S22. Calculate the maximum sound spectrum peak in the frequency domain for the data after short-time Fourier transformation, and determine the frequency range of wind farm noise according to the frequency domain characteristics.

4. The spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise according to claim 1, characterized in that: Step S5 is specifically as follows: under the condition of considering forward propagation, the undulation of the seabed is divided into multiple flat areas according to the height difference, and each of them is modeled one by one; each sub-area is merged by summation operation, and the relationship between the underwater noise of the wind farm in the study area and the distance is calculated; the Helmholtz equation of sound propagation in the frequency domain is taken, and when the solution of ordinary differential equations is adopted, it is simplified to the PE equation, and is expanded using the wide-angle paraxial approximation method.

5. The spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise according to claim 1, characterized in that: Step S6, discretizing the parabolic equation through Chebyshev polynomials, specifically: setting the sea surface as the total reflection boundary, setting the uniform semi-acoustic space D as the perfect matching layer, using the following Chebyshev polynomials as basis functions, discretizing the depth operator of each layer through the Chebyshev spectral method, and then assembling them into a global matrix.

6. The spectral wide-angle parabolic equation modeling method for non-uniform offshore wind farm noise according to claim 1, characterized in that: Step S8 is specifically as follows: the sound pressure at the end distance of the first flat seabed is used as the starting sound pressure of the next flat seabed for iteration; for the plane parallel waveguide, the segmented simulation results are merged to obtain the sound propagation curve of the continuously undulating seabed.

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