An α-stable distribution estimation method for the distance characteristics of underwater noise in a wind farm

Abstract

The present invention belongs to the technical field of wind farm noise, and particularly relates to a method for estimating the α-stable distribution of the distance characteristics of underwater noise in a wind farm. This method first preprocesses the wind farm noise to obtain the time-domain waveform diagrams of the wind farm noise at different distances; then, according to the parameter characteristics of the α-stable distribution, the value ranges of the stable distribution a and γ are determined, and the value range of ω0 is selected in combination with the range of the simulation data; to solve the problem of relatively large estimation error of the γ parameter, a new estimation method based on the semi-probability scale parameter is combined, and the time-domain waveform data of the wind farm noise at different distances are estimated through a new parameter estimation formula. The method for estimating the α-stable distribution of the distance characteristics of underwater noise in a wind farm according to the present invention can more accurately describe the characteristics of the underwater noise in a wind farm changing with distance, and provides an effective means for the evaluation and management of the underwater noise in a wind farm.

Description

Technical Field

[0001] The present invention belongs to the technical field of wind farm noise, and in particular relates to a method for describing the distance characteristics of underwater noise from a wind farm based on α-stable distribution. Background Art

[0002] With the continuous advancement of global offshore renewable energy technology and the urgent need for international energy conservation and emission reduction, the offshore wind farm industry is experiencing rapid development. However, the noise issues generated during the construction and operation phases have attracted widespread attention. Noise issues are a significant problem throughout the entire life cycle of offshore wind farms.

[0003] During the operational phase, wind turbine rotation and mechanical vibrations within the nacelle continuously generate noise, a process that persists until the wind farm ceases operations. This noise can propagate up to several kilometers from the source. Furthermore, mechanical vibration noise during the operational phase persists the longest and has the most significant impact on underwater noise. The α-stable distribution is well suited to describe this non-Gaussian noise. However, the α-stable distribution lacks a closed characteristic function, making existing estimation methods unable to meet the accuracy requirements for wind farm underwater noise. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for describing the distance characteristics of underwater noise in wind farms based on α stable distribution, and to complete the γ estimation combined with semi-probability to solve the problem of low accuracy in underwater noise estimation in the interval α∈(1,2].

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A method for estimating the α-stable distribution of wind farm underwater noise distance characteristics comprises the following steps:

[0007] S1. Read wind farm noise data, perform wavelet denoising on the original data, and obtain time domain waveform data of underwater noise at wind farms at different distances;

[0008] S2. Determine the effective time-frequency waveform data within the target time period and calculate the mathematical expectation of the noise data at different distances;

[0009] S3. Select the value range of ω0 based on the simulation data range; it is necessary to determine whether the standard deviation of different ω0 is the smallest, and discard the value range that does not meet the conditions;

[0010] S4. After selecting the value range of ω0, the parameter estimation optimization is performed in combination with the semi-probability formula to give a new scale estimation algorithm;

[0011] S5. Through the new estimation algorithm, the distance characteristics of the wind farm underwater noise are given, and the relationship between the wind farm underwater noise and the α stable distribution parameter at different distances is obtained.

[0012] Furthermore, step S1 specifically includes the following steps:

[0013] S11. Extract the original data of the wind farm noise for wavelet denoising to obtain the original waveform data. The time-domain data includes the underwater noise generated during the operation period of the wind farm;

[0014] S12. Segment the time-domain data to make the lengths of the noise data at different distances consistent, and obtain the time-domain waveform data of the underwater noise of the wind farm at different distances.

[0015] Furthermore, step S3 specifically includes the following steps:

[0016] S31. Use the characteristic function of the stable random variable to describe its distribution characteristics and corresponding parameter estimation, which is expressed by the following formula;

[0017]

[0018] In the formula, ω = 1 and ω = ω0 represent two characteristic function points, and sign(·) represents the sign function. α is the characteristic exponent, and its value range is 0 < α ≤ 2. β is the skewness parameter, which determines the skewness degree of the distribution, and its value range is -1 ≤ β ≤ 1. γ is the scale parameter, also known as the dispersion coefficient and deviation, which describes the degree to which the stable distribution random variable deviates from the mean or median. γ can be any positive number, similar to the variance in the Gaussian distribution. δ is the location parameter, which determines the position of the peak of the probability density function of the α-stable distribution, and its value range is -∞ < δ < ∞.

[0019] S32. Estimate the expressions of the α characteristic parameter and the γ scale parameter, such as the formula;

[0020]

[0021] where N is the length of the observed sample X, X = {x1, x2, x3, … x i , …, x N [[ID= / / 32]]}; ω0 in the characteristic function of the stable distribution is closely related to the accuracy of the parameter estimation, and its value range is 0 < ω0 < 0.5 and 1 < ω0 < 3. Analyze the estimation accuracy of the statistical characteristics of the underwater noise of the wind farm for different value ranges of ω0; if α ∈ (0, 2] is set, simulate with the key parameter of the input stable distribution data.

[0022] S33. Set the range of the scale parameter γ value in the simulation to be in the interval (0.0001, 0.001).

[0023] Furthermore, step S4 specifically includes the following steps:

[0024] Note: There seems to be an incomplete expression in line 32 of the original text (the part after "x N}"). The translation is provided as far as possible based on the existing content.S41. Set α ∈ (0, 2] and γ ∈ (0.0001, 0.001), and estimate by combining the method based on the semi - probability scale parameter;

[0025] S42. Compare with the simulation data, and the new parameter estimation algorithm is the following formula;

[0026]

[0027] H(·) is a piece - wise function. When α ∈ (1, 2], the function value is 0. At this time, x i : P(|X|>x i ) = 0.5; when α ∈ (0, 1], the function value is 1.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0029] The present invention uses the improved α - stable distribution to describe the noise characteristics. Statistical analysis shows that as the distance increases, the pulse characteristics of the underwater noise time - domain waveform gradually weaken. The maximum values of the scale parameter γ in the two experiments are 0.00094 and 0.00087 respectively, and it decreases with the increase of distance; γ measures the deviation degree of the random variable from the mathematical expectation in the time - domain waveform, which implies that the amplitude of the time - domain waveform is more stable as the distance increases; the sound propagation law is consistent with the overall trend of the scale parameter; the present invention improves the distance - characteristic estimation algorithm for describing the underwater noise of the wind farm by the α - stable distribution, making the complexity lower and the estimation accuracy higher during estimation; this method can accurately estimate the distance characteristics of the underwater noise of the wind farm, which helps to more comprehensively understand the underwater noise characteristics of the offshore wind farm and its environmental impact, and provides an important basis for optimizing engineering design and operation management. Description of the Drawings

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. It should be understood that the following drawings only show some embodiments of the present invention, so they should not be regarded as limiting the scope. For those of ordinary skill in the art, without creative efforts, other related drawings can also be obtained based on these drawings.

[0031] Figure 1 It is a flow - chart of the steps of the α - stable distribution estimation method for the distance characteristics of the underwater noise of the wind farm of the present invention;

[0032] Figures 2a - 2b It is a comparison diagram of the improved estimation method. Detailed Embodiments

[0033] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present invention, rather than limiting the present invention. In addition, it should be noted that for the convenience of description, only the parts related to the present invention rather than all the structures are shown in the accompanying drawings.

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

[0035] As Figure 1 shown, a method for estimating the α-stable distribution of the underwater noise distance characteristics of a wind farm includes the following steps:

[0036] S1. Obtain the wind farm noise signal within the target time period, select time-frequency signals with the same time length according to different distances, read the wind farm noise data, and perform wavelet denoising on the original data to obtain the underwater noise time-domain waveform data of the wind farm at different distances. Specifically, it includes the following steps:

[0037] S11. Extract the original data of the wind farm noise and perform wavelet denoising to obtain the original waveform data. The time-domain data includes the underwater noise generated during the operation period of the wind farm;

[0038] S12. Segment the time-domain data to make the noise data lengths at different distances consistent, and obtain the underwater noise time-domain waveform data of the wind farm at different distances.

[0039] S2. Determine the effective time-frequency waveform data within the target time period, and calculate the mathematical expectation of the noise data at different distances.

[0040] S3. Select the value range of ω0 in combination with the simulation data range. It is necessary to judge whether the standard deviation of different ω0 is the smallest, and discard the value ranges that do not meet the conditions. Specifically, it includes the following steps:

[0041] S31. Use the characteristic function of the stable random variable to describe its distribution characteristics and corresponding parameter estimation, which is expressed by the following formula;

[0042]

[0043] Where ω = 1 and ω = ω0 represent two characteristic function points, and sign(·) represents the sign function. α is the strength of the stable distribution pulse characteristic and the tail thickness of the probability density function, and its value range is 0 < α ≤ 2. β is the skewness parameter, which determines the skewness degree of the distribution, and its value range is -1 ≤ β ≤ 1. γ is the scale parameter, which describes the degree to which the stable distribution random variable deviates from the mean or median. γ is any positive number, similar to the variance in the Gaussian distribution. δ is the location parameter, which determines the position of the peak of the α-stable distribution probability density function, and its value range is -∞ < δ < ∞.

[0044] S32. Estimate the expressions of the α characteristic parameter and the γ scale parameter, such as the formula;

[0045]

[0046]

[0047] Where N is the length of the observed sample X, X = {x1, x2, x3, … x i , …, x N}. ω0 in the characteristic function of the stable distribution is closely related to the accuracy of parameter estimation, and its value range is 0 < ω0 < 0.5 and 1 < ω0 < 3. Analyze the estimation accuracy of the statistical characteristics of the underwater noise of the wind farm for different value ranges of ω0. If α ∈ (0, 2] is set, simulations are carried out for the key parameters of the input stable distribution data.

[0048] S33. The simulation sets the value range of the scale parameter γ in the interval (0.0001, 0.001). In this interval, the error of the scale parameter γ estimated by the original method is relatively large. To solve the problem of the large estimation error of the scale parameter of the wind farm noise, a new scale estimation method is given by combining the estimation method based on the semi-probability scale parameter.

[0049] As Figure 2a shown, the blue is the true value of α, and the green and red are the results estimated by the formula for 0 < ω0 < 0.5 and 1 < ω0 < 3 respectively. The horizontal axis is the value of α ∈ (0, 2], and the vertical axis is the standard deviation of α. When the range of ω0 is 1 < ω0 < 3, the estimated standard deviation of α is smaller.

[0050] S4. After selecting the value range of ω0, combine the semi-probability formula to optimize the parameter estimation and give a new scale estimation algorithm. Specifically, it includes the following steps:

[0051] S41. Set α ∈ (0, 2], γ ∈ (0.0001, 0.001) and combine the method based on the semi-probability scale parameter for estimation;

[0052] S32. Combine the simulation data for comparison. The new parameter estimation method is the following formula;

[0053]

[0054] H(·) is a piecewise function. When α ∈ (1, 2], the function value is 0. At this time, x i :P(X|>x i ) = 0.5; when α ∈ (0, 1], the function value is 1.

[0055] Figure 2b Among them, the gray line is the value of the scale parameter in (0.0001, 0.001), and the green is the estimated value of the improved formula. It can be seen that the error of the estimated scale parameter is relatively large in this interval. The red line is the estimation comparison within the range of α ∈ (1, 2] and γ ∈ (0.0001, 0.001). It can be seen that within the entire effective range of α, the error of the estimated value of γ is the smallest.

[0056] S5. Through the new estimation algorithm, the distance characteristics of the underwater noise of the wind farm are given, and the relationship between the underwater noise of the wind farm and the α-stable distribution parameters at different distances is obtained.

[0057] In summary, the statistical analysis using the improved α-stable distribution to describe the noise characteristics shows that this method can accurately estimate the distance characteristics of the underwater noise of the wind farm, which helps to more comprehensively understand the underwater noise characteristics of the offshore wind farm and its environmental impact, and provides an important basis for optimizing the engineering design and operation management.

[0058] Note that the above is only the preferred embodiment of the present invention and the applied technical principle. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described here. Various obvious changes, re-adjustments and substitutions can be made by those skilled in the art without departing from the protection scope 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. Without departing from the concept of the present invention, more other equivalent embodiments can be included, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A method for estimating the α-stable distribution of the underwater noise distance characteristics of a wind farm, characterized in that, It includes the following steps: S1. Read the wind farm noise data, perform wavelet denoising on the original noise data, and obtain the time-domain waveform data of the underwater noise of the wind farm at different distances; S11. Extract the original noise data of the wind farm noise and perform wavelet denoising to obtain the original waveform data. The time-domain waveform data includes the underwater noise generated during the operation period of the wind farm; S12. Segment the time-domain waveform data to make the noise data lengths at different distances consistent, and obtain the time-domain waveform data of the underwater noise of the wind farm at different distances; S2. Determine the effective time-domain waveform data within the target time period, and calculate the mathematical expectation of the noise data at different distances; S3. Select the value range of ω0 in combination with the simulation data range; it is necessary to judge whether the standard deviation of different ω0 is the smallest, and discard the value ranges that do not meet the conditions; S4. After selecting the value range of ω0, perform parameter estimation optimization in combination with the semi-probability formula, and give a new scale estimation algorithm; S41. Set α ∈ (0, 2], γ ∈ (0.0001, 0.001), and perform estimation in combination with the method based on the semi-probability scale parameter; S42. Compare with the simulation data, and the new parameter estimation algorithm is the following formula; H(·) is a piecewise function. When α ∈ (1, 2], the function value is 0; at this time, x i : P(|X| > x i ) = 0.5; when α ∈ (0, 1], the function value is 1; S5. Through the new scale estimation algorithm, give the distance characteristics of the underwater noise of the wind farm, and obtain the relationship between the underwater noise of the wind farm at different distances and the α-stable distribution; 2. The α-stable distribution estimation method for the underwater noise distance characteristics of a wind farm according to claim 1, characterized in that Step S3 specifically includes the following steps: S31. Use the characteristic function of the stable random variable to describe its distribution characteristics and the corresponding parameter estimation, which is expressed by the following formula; In the formula, ω = 1 and ω = ω0 represent two characteristic function points, sign(·) represents the sign function; α is the characteristic exponent, and its value range is 0 < α ≤ 2; β is the skewness parameter, which determines the skewness degree of the distribution, and its value range is -1 ≤ β ≤ 1; γ is the scale parameter, also known as the dispersion coefficient and deviation, which describes the degree to which the stable distribution random variable deviates from the mean or median; δ is the location parameter, which determines the position of the peak of the probability density function of the α-stable distribution, and its value range is -∞ < δ < ∞; S32. Estimate the expressions of the α characteristic parameter and the γ scale parameter, such as the formula; where N is the length of the observed sample X, and X = {x1, x2, x3, … x i , …, x N}; ω0 in the characteristic function of the stable distribution is closely related to the accuracy of parameter estimation, and its value range is 0 < ω0 < 0.5 and 1 < ω0 < 3; analyze the estimation accuracy of the statistical characteristics of the underwater noise of the wind farm for different value ranges of ω0; if α ∈ (0, 2] is set, simulate the key parameters of the input stable distribution data; S33. Set the value range of the scale parameter γ in the simulation to be in the interval (0.0001, 0.001).

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