A Machine Learning-Based Method for Estimating the Average Wave Period of Coherent X-Band

Abstract

This invention relates to a machine learning-based method for estimating the average wave period of coherent X-band microwave radar. The steps are as follows: acquiring the Doppler spectrum and temporal Doppler spectrum of a single sea surface echo; obtaining the left and right boundaries from the echo Doppler spectrum and extracting the Doppler frequency shift of the echo Doppler spectrum; acquiring the spatiotemporal sequence of radial velocity and extracting feature parameters of wave characteristics; calculating the minimum peak distance of wave characteristics based on the average wave period data; inputting the feature parameters and minimum peak distance into a random forest and linear regression ensemble model for training; subsequently, inputting the feature parameters into the trained ensemble model for prediction; identifying wave peaks and troughs based on the prediction results, thereby estimating the average wave period. This invention establishes a direct relationship between the spatiotemporal sequence of radar echo velocity and wave period parameters, solving the problems of high computational load, long processing time, and low accuracy of traditional methods. It is unaffected by the quality of historical data due to extreme weather conditions, thus improving the accuracy of average wave period estimation.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and more specifically to a method for estimating the average wave period of coherent X-band based on machine learning. Background Technology

[0002] Ocean wave parameters are crucial for marine engineering, hazard prediction, and oceanographic research in marine monitoring. Coherent microwave radar, as an effective ocean detection tool, extracts Doppler velocity information from echoes and uses the relationship between wave trajectory velocity and wave height to obtain wave parameters such as wave spectrum and mean wave period. However, due to the influence of breaking waves, nonlinear characteristics such as group lines and higher harmonic energy in the wave number frequency spectrum measured by radar reduce the accuracy of wave parameter inversion, especially the estimation of the mean wave period.

[0003] Current methods for estimating the mean wave period using coherent microwave radar neglect the uncertainty of nonlinear wave energy and energy distribution of different frequency components in radar echoes, resulting in significant measurement errors. Predicting wave parameters through machine learning requires substantial computational resources and input data, and long-term wave parameter prediction is inefficient. Data-driven models for short-term and long-term wave parameter forecasting using historical wave data suffer from significant errors in predicting nonlinear and non-stationary wave parameters due to data variability and limitations imposed by linearity and stationarity assumptions. Summary of the Invention

[0004] The technical problem of this invention is to provide a coherent X-band mean wave period estimation method based on machine learning, which estimates the mean wave period from the perspective of velocity spatiotemporal sequence and machine learning, improves the accuracy and precision of coherent microwave radar in predicting the mean wave period, and provides a more accurate method for inverting ocean wave parameters.

[0005] The purpose of this invention is to solve the above-mentioned problems. The technical solution of this invention is a coherent X-band average wave period estimation method based on machine learning, which includes the following steps:

[0006] S1: Obtain the Doppler spectrum and time Doppler spectrum of a single echo from the sea surface using coherent X-band radar;

[0007] S2: Obtain the left and right boundaries from the echo Doppler spectrum, and extract the Doppler frequency shift of the echo Doppler spectrum using the moment estimation method;

[0008] S3: Obtain the spatiotemporal sequence of radial velocity through Doppler frequency shift, divide it into training dataset and test dataset, and then extract the feature parameters of wave features to obtain training dataset D1 and test dataset D2;

[0009] S4: Calculate the minimum peak distance of wave characteristics based on the average wave period data, and then input the dataset D1 and the minimum peak distance into the random forest and linear regression ensemble model for training;

[0010] S5: Input the dataset D2 into the trained ensemble model to predict the minimum peak distance of wave features, identify the positions of wave peaks and troughs based on the prediction results, and then estimate the average wave period based on the relationship between wavelength and period.

[0011] Preferably, step S2 includes calculating the center frequency using the echo Doppler spectrum, and the calculation formula is:

[0012] ;

[0013] In the formula, Indicates the Doppler frequency. This represents the Doppler spectrum.

[0014] Furthermore, in S3, feature parameters of wave features are extracted, specifically the mean, standard deviation, maximum and minimum values ​​of wave features.

[0015] Preferably, the formula for calculating the space-time sequence of radial velocity is:

[0016] ;

[0017] In the formula, Indicates electromagnetic wavelength. Indicates radial distance. f represents the sampling time. d This represents the average Doppler frequency shift.

[0018] Furthermore, step S4 also includes: performing correlation analysis on the fluctuation characteristics in dataset D1, screening out a subset of features that are significantly related to the target variable, and then removing low-correlation feature values ​​by setting a correlation threshold.

[0019] Preferably, the ensemble model of random forest and linear regression, wherein the random forest sub-model enhances the robustness to noise and outliers, as well as the prediction accuracy and stability, by integrating multiple independent regression trees and a Bagging strategy; the linear regression sub-model introduces regularization methods, including Lasso or Ridge regression. The calculation formula for the ensemble model of random forest and linear regression is as follows:

[0020] ;

[0021] In the formula, This represents the nonlinear prediction of a random forest. Indicates the number of decision trees. Indicates the input feature value. Represents independent and identically distributed random variables. This represents the output of the decision tree. This represents the linear prediction of linear regression. These are regression coefficients, representing the impact of each feature on the target variable. Indicates the error term. and These represent the weights for random forest regression and linear regression, respectively.

[0022] Furthermore, the average wave period is estimated based on the relationship between wavelength and period. Specifically, the average wave period is calculated using linear wave theory, and the formula is as follows:

[0023] ;

[0024] In the formula, Indicates wavelength. Indicates period, This indicates the phase velocity of the wave.

[0025] Compared with the prior art, the beneficial effects of the present invention include:

[0026] 1) The coherent X-band average wave period estimation method proposed in this invention extracts wave feature parameters by analyzing the velocity spatiotemporal sequence and inputs them into the constructed random forest and linear regression ensemble model to predict the minimum peak distance of the wave features. It establishes a direct relationship between the radar echo velocity spatiotemporal sequence and the wave period parameter, solving the problems of large computation, long time consumption and low accuracy in traditional methods. Moreover, it is not affected by the quality of historical data caused by extreme weather conditions, thus improving the accuracy of average wave period estimation.

[0027] 2) The random forest and linear regression ensemble model proposed in this invention effectively identifies the locations of wave peaks and troughs, and accurately evaluates the average wave period by utilizing the relationship between wavelength and period, thereby improving the accuracy of average wave period estimation in ocean remote sensing by coherent microwave radar and enhancing the effectiveness of remote sensing data.

[0028] 3) This invention retains most of the echo information while effectively removing interference, balancing noise suppression and information preservation, ensuring the efficiency and accuracy of wave parameter estimation, and providing more valuable data support for marine engineering and monitoring. Attached Figure Description

[0029] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0030] Figure 1 This is a schematic diagram of the average wave period estimation method according to an embodiment of the present invention.

[0031] Figure 2This is a radar illumination sea surface scattering geometry diagram according to an embodiment of the present invention.

[0032] Figure 3 This is a single echo Doppler spectrum obtained from the echo signal of the sea surface detected by the coherent microwave radar in an embodiment of the present invention.

[0033] Figure 4 The time Doppler spectrum of the echo signal obtained by the coherent microwave radar detecting the sea surface in this embodiment of the invention.

[0034] Figure 5 This is a simulated sea surface displacement time-space sequence according to an embodiment of the present invention.

[0035] Figure 6 This is a simulated sea surface velocity space-time sequence according to an embodiment of the present invention.

[0036] Figure 7 This is a comparison chart showing the results of evaluating the sea surface mean wave period using the method of this embodiment of the invention, as well as the Berbi and simulation methods. Detailed Implementation

[0037] The data used in this invention for marine detection comes from the dataset "Radar Marine Detection Data, Vol. 1, 2022" published in the Journal of Radar.

[0038] like Figure 1 As shown, the machine learning-based method for estimating the average wave period of the coherent X-band includes the following steps:

[0039] S1: Obtain the Doppler spectrum and time Doppler spectrum of a single echo from the sea surface using coherent multi-band radar;

[0040] like Figure 2 As shown, the radar's range resolution is set to 2.5m, and the Doppler spectrum sampling rate is 0.0005s. Water particles on the sea surface propagate in the form of continuous waves, and their orbital motion causes a frequency shift in the Doppler spectrum.

[0041] The formula for calculating radar orbital velocity is:

[0042] ;

[0043] In the formula, Let represent the radial distance, t represent time, u() represent the horizontal component of the orbital velocity, and w() represent the vertical component of the orbital velocity.

[0044] ;

[0045] ;

[0046] In the formula, U0 represents the initial velocity of the radar illuminating the sea surface, k represents the wave number, and w represents the wave approaching or moving away from the radar.

[0047] Radial velocity of radar echo and center frequency of Doppler spectrum The expression for the relationship between them is:

[0048] ;

[0049] In the formula, Indicates the radial velocity of the radar echo. The center frequency of the Doppler spectrum.

[0050] The single echo Doppler spectrum and time Doppler spectrum obtained by coherent microwave radar detecting echo signals from the sea surface are as follows: Figure 3 and Figure 4 shown.

[0051] S2: Obtain the left and right boundaries from the echo Doppler spectrum, and extract the Doppler frequency shift of the echo Doppler spectrum using the moment estimation method;

[0052] Step S2 includes calculating the center frequency using the echo Doppler spectrum. The calculation formula is as follows:

[0053] ;

[0054] In the formula, Indicates the Doppler frequency. Represents the Doppler spectrum. Indicates the left boundary. Indicates the right boundary.

[0055] S3: Obtain the spatiotemporal sequence of radial velocity through Doppler frequency shift, divide it into training dataset and test dataset, and then extract the feature parameters of wave features to obtain training dataset D1 and test dataset D2;

[0056] The displacement sequence of the sea surface reflects the wave characteristics of the sea surface. The spatiotemporal sequence of the simulated radial velocity of the sea surface is as follows: Figure 3 As shown;

[0057] The simulated space-time sequence of sea surface velocity is as follows Figure 6 As shown, the feature parameters of the wave feature are then extracted, specifically the mean, standard deviation, maximum value and minimum value of the wave feature.

[0058] The mean wave period data were obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF).

[0059] The formula for calculating the space-time sequence of radial velocity is:

[0060] ;

[0061] In the formula, Indicates electromagnetic wavelength. Indicates radial distance. f represents the sampling time. d This represents the average Doppler frequency shift.

[0062] S4: Calculate the minimum peak distance of wave characteristics based on the average wave period data, and then input the dataset D1 and the minimum peak distance into the random forest and linear regression ensemble model for training;

[0063] Step S4 also includes: performing correlation analysis on the fluctuation characteristics in dataset D1, screening the feature subsets that are significantly related to the target variable, and then removing low-correlation feature values ​​through a set correlation threshold;

[0064] The ensemble model of random forest and linear regression combines multiple independent regression trees and a Bagging strategy to enhance its resilience to noise and outliers, as well as its prediction accuracy and stability. The linear regression sub-model incorporates regularization methods, including Lasso or Ridge regression. The calculation formula for the ensemble model is as follows:

[0065] ;

[0066] In the formula, This represents the nonlinear prediction of a random forest. Indicates the number of decision trees. Indicates the input feature value. Represents independent and identically distributed random variables. This represents the output of the decision tree. This represents the linear prediction of linear regression. These are regression coefficients, representing the impact of each feature on the target variable. Indicates the error term. and These represent the weights for random forest regression and linear regression, respectively.

[0067] S5: Input the dataset D2 into the trained ensemble model to predict the minimum peak distance of wave features, identify the positions of wave peaks and troughs based on the prediction results, and then estimate the average wave period based on the relationship between wavelength and period.

[0068] The average wave period is estimated based on the relationship between wavelength and period. Specifically, the average wave period is calculated using linear wave theory, and the formula is as follows:

[0069] ;

[0070] In the formula, Indicates wavelength. Indicates period, This indicates the phase velocity of the wave.

[0071] like Figure 7 As shown in Table 1, in order to verify the effectiveness of the proposed method for estimating the mean wave period, the evaluation results of the proposed method are compared with those of the Berbi method.

[0072] Table 1

[0073]

[0074] The correlation coefficient (CC), absolute error (AMD), and root mean square error (RMSD) of this invention are 0.9642, 0.0935, and 0.1098, respectively; while the correlation coefficient (CC), absolute error (AMD), and root mean square error (RMSD) of the Berbi method are 0.9115, 0.1341, and 0.1619, respectively. This invention outperforms the Berbi method in terms of correlation coefficient (CC), absolute error (AMD), and root mean square error (RMSD).

[0075] Experimental results show that this invention can not only accurately capture the nonlinear characteristics of waves, but also maintain high prediction accuracy in complex wave phenomena, proving the effectiveness of the improved method presented in this paper. By combining the advantages of multiple algorithms, this integrated model significantly improves the estimation accuracy of wave periods, providing reliable technical support for practical applications.

[0076] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be the technical solution described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for estimating the average wave period of a coherent X-band based on machine learning, characterized in that, The following steps are involved: S1: Obtain the Doppler spectrum and time Doppler spectrum of a single echo from the sea surface using coherent X-band radar; S2: Obtain the left and right boundaries from the echo Doppler spectrum, and extract the Doppler frequency shift of the echo Doppler spectrum using the moment estimation method; S3: Obtain the spatiotemporal sequence of radial velocity through Doppler frequency shift, divide it into training dataset and test dataset, and then extract the feature parameters of wave features to obtain training dataset D1 and test dataset D2; S4: Calculate the minimum peak distance of wave characteristics based on the average wave period data, and then input the dataset D1 and the minimum peak distance into the random forest and linear regression ensemble model for training; S5: Input the dataset D2 into the trained ensemble model to predict the minimum peak distance of wave features, identify the positions of wave peaks and troughs based on the prediction results, and then estimate the average wave period based on the relationship between wavelength and period.

2. The method for estimating the average wave period of a coherent X-band based on machine learning according to claim 1, characterized in that, Step S2 includes calculating the center frequency using the echo Doppler spectrum, and the calculation formula is as follows: ； In the formula, Indicates the Doppler frequency. Represents the Doppler spectrum. Indicates the left boundary. Indicates the right boundary.

3. The method for estimating the average wave period of a coherent X-band based on machine learning according to claim 1, characterized in that, In step S3, the feature parameters for extracting wave features specifically include extracting the mean, standard deviation, maximum value, and minimum value of the wave features.

4. The method for estimating the average wave period of a coherent X-band based on machine learning according to claim 3, characterized in that, The formula for calculating the space-time sequence of radial velocity is: ； In the formula, Indicates electromagnetic wavelength. Indicates radial distance. f represents the sampling time. d This represents the average Doppler frequency shift.

5. The method for estimating the average wave period of a coherent X-band based on machine learning according to claim 1, characterized in that, Step S4 also includes: performing correlation analysis on the fluctuation characteristics in dataset D1, screening the feature subsets that are significantly related to the target variable, and then removing low-correlation feature values ​​by setting a correlation threshold.

6. The method for estimating the average wave period of a coherent X-band based on machine learning according to claim 5, characterized in that, The ensemble model of random forest and linear regression, with the random forest sub-model integrating multiple independent regression trees and the Bagging strategy, is used to enhance the tolerance to noise and outliers, as well as the prediction accuracy and stability. The linear regression sub-model incorporates regularization methods, and the calculation formulas for the random forest and linear regression ensemble model are as follows: ； In the formula, This represents the nonlinear prediction of a random forest. Indicates the number of decision trees. Indicates the input feature value. Represents independent and identically distributed random variables. This represents the output of the decision tree. This represents the linear prediction of linear regression. These are regression coefficients, representing the impact of each feature on the target variable. Indicates the error term. and These represent the weights for random forest regression and linear regression, respectively.

7. The method for estimating the average wave period of a coherent X-band based on machine learning according to claim 1, characterized in that, The estimation of the average wave period based on the relationship between wavelength and period specifically involves calculating the average wave period using linear wave theory. The calculation formula is as follows: ； In the formula, Indicates wavelength. Indicates period, This indicates the phase velocity of the wave.

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