A multi-weighted spectral ratio denoising method based on XGBoost

Abstract

The present application belongs to the technical field of urban geophysical exploration, and particularly relates to a multi-weighted spectral ratio denoising method based on XGBoost. The method is based on high-dimensional space to extract the characteristics of microtremor monitoring data, and applies XGBoost algorithm with added L2 regularization to train and analyze the data, to obtain a machine learning model that can separate signals and noise. Thus, the problem of poor signal extraction accuracy of the original denoising method in the face of high-noise complex environment is solved. Compared with the single time domain or frequency domain analysis mode in the conventional method, the multi-weighted spectral ratio denoising method based on XGBoost uses the dimension increasing function to take the characteristics of microtremor monitoring data in high-dimensional space, so that the characteristics of ground pulse are more comprehensive, and the signal-to-noise analysis model is more complete. The present application applies the supervised learning algorithm to the denoising of the original data of the microtremor HVSR method, and improves the automation degree of the denoising process and the accuracy of the denoising result.

Description

Technical Field

[0001] This invention belongs to the field of urban geophysical exploration technology, specifically relating to a method for denoising micro-motion monitoring data collected in high-noise and complex environments, and particularly to a multi-weighted spectral ratio denoising method based on XGBoost. Background Technology

[0002] The Horizontal-to-Vertical Spectral Ratio (HVSR) method is an important exploration method for obtaining urban subsurface information. However, when applied in urban environments, this method is affected by numerous factors, such as vehicle noise, electromagnetic interference from high-voltage power lines, and acoustic interference. Therefore, the data preprocessing stage has a significant impact on the accuracy of the HVSR method, and improving the signal-to-noise ratio of the original signal is extremely important.

[0003] The Short-Term Average Amplitude Ratio (STA / LTA) method is the most commonly used method for identifying transient interference in the data processing stage of the micro-motion HVSR method. The principle of the STA / LTA method is to apply short and long time windows to the original signal, calculate the STA / LTA value using the average value of the short window (STA) and the duration of the long window (LTA), and compare it with a trigger threshold to identify interfering signals. It can effectively remove transient interference to a certain extent, and is relatively simple to operate and fast to calculate. However, the STA / LTA method also has some drawbacks: 1. In complex environments with high noise, the signal extraction accuracy of this method is poor; 2. The setting of the threshold and the selection of the time window are subjective and have a significant impact on the noise reduction effect; 3. The analysis of data availability is only performed in the time domain, which leads to loopholes in the physical interpretation of its results. For example, if the duration of additive noise exceeds the period intercepted by the long time window, the noise is difficult to filter.

[0004] In addition, time-domain hierarchical clustering algorithms, frequency-domain rejection algorithms, and time-frequency domain Hilbert-Huang transforms have also been used for signal-to-noise analysis in micro-motion HVSR methods. However, these methods still have some problems: 1. Incomplete theoretical basis. For example, the empirical mode decomposition upon which the Hilbert-Huang transform relies lacks strong theoretical support; the distance evaluation function in the clustering algorithm application process still adheres to the mathematical essence of STA / LTA, thus also having the same physical basis flaws as the STA / LTA method; 2. Limited features involved in denoising decision-making. In high-noise and complex environments, the method fails if a key feature fails. In summary, traditional methods rely too heavily on single feature selection, making them difficult to denoise high-noise micro-motion data. Summary of the Invention

[0005] The purpose of this invention is to provide a micro-motion data denoising method based on the XGBoost algorithm. This method leverages high-dimensional space to mine more features from data points, addressing the problem of low denoising accuracy in the data preprocessing stage of traditional denoising methods when using micro-motion HVSR in urban geophysical exploration, especially when facing high noise levels. This invention performs dimensionality upscaling on the collected three-component time-series data to obtain quantitative evaluation criteria for the usability of micro-motion data. Based on this, the XGBoost algorithm (eXtreme Gradient Boosting) is applied to separate the signal from the noise, resulting in a new denoising method with better performance, effectively improving the data signal-to-noise ratio.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A multi-weighted spectral ratio denoising method based on XGBoost includes the following steps:

[0008] A. Based on the DFA model, quantitative analysis of signal and noise in HVSR data collected under high noise and complex environment is performed, and training set for XGBoost learning is established using the analysis results and the resonant frequency of the samples.

[0009] B. Establish a dimension-up function to separate signal and noise in HVSR data in high dimension;

[0010] C. Use XGBoost with added L2 regularization to train the model. Combine the actual collected data with the training set labeled in step A and the dimension increase function in step B for training. Set the L2 regularization coefficient through a large number of experiments to obtain a machine learning model that can separate signal and noise. Save the model for prediction.

[0011] D. Upgrade the dimensions of the sample to be analyzed and use the model trained in step C to extract the signal.

[0012] Further, step A specifically includes:

[0013] A1. From the well logging data, the peak frequency f0 of the H / V curve is obtained.

[0014]

[0015] In the formula: V s D is the weighted average shear wave velocity (m / s) of the overburden layer; ov The thickness of the loose overburden can be directly obtained from engineering data such as well logging.

[0016] A2. Starting from the mathematical and physical model established by the SPAC method and the DFA inversion model, the wave field of the underground space is regarded as a purely random process, and the wave field can be regarded as thermal noise or Gaussian white noise, with its power spectral density uniformly distributed in the frequency range and its loudness distribution following a normal distribution.

[0017] A3. For shallow ground data between 5-20Hz, the values ​​marked I∈(I0-σ,I0+σ) and f∈(f0-v1,f0+υ2) are signals of interest, and the rest are noise or useless sample points for training. In the formula, the range of values ​​of υ1 and υ2 is given according to the actual application and in combination with the well logging data used for training. I0 is a certain measure of the loudness mean of the sample points, and σ is the standard deviation of the sample loudness.

[0018] Further, step B specifically includes:

[0019] B1. Define the loudness-weighted H / V:

[0020]

[0021] In the formula: I is the Fourier amplitude of the sample point, and λ is an empirical constant, the order of magnitude of I0. The product of the orders of magnitude of the inverses of the four-dimensional amplitudes, under ideal conditions, I0 can be regarded as the mean, mode or median of the four-dimensional amplitudes. For actual data with a lot of noise, I0 should be the median, which is less affected by extreme values.

[0022] B2. Using f0, which is used to establish the training set in step A, we can define H / V under peak frequency weighting:

[0023]

[0024] In the formula: f is the frequency of the sample point, f0 is the resonance frequency obtained from the well logging data, and should be near the peak frequency of the IHV spectrum. When f0 is unknown, i.e., when processing the H / V spectrum of an unknown site, it should be replaced by the peak frequency of the IHV spectrum. μ is an empirical constant whose meaning is the same as λ above. To ensure that the frequency and H / V value are weighted on the fHV value at any point, its order of magnitude is also equal to the order of magnitude of f0. The product of the orders of magnitude of the reciprocals;

[0025] B3. From formulas (2) and (3), the mixed weighted H / V can be defined:

[0026]

[0027] B4. From formulas (2), (3), and (4), X′ can be increased in dimension to obtain:

[0028] X′(f,I,H / V,IHV,fHV,IfHV) (5)

[0029] B5. For the frequency range of interest in practical engineering and the amplitude range that should be extracted based on Gaussian white noise, X′ is located near I0 and f0, and H / V, IHV, fHV, and IfHV are all located in the support. Sample points with larger values ​​should be extracted. After dimensionality increase, the signal and noise of X′ are linearly separable in this space.

[0030] Compared with the prior art, the beneficial effects of the present invention are:

[0031] This invention is the first to apply supervised learning algorithms to denoising raw data from the micro-motion H / V method, solving the problem of low denoising accuracy in traditional methods when facing high noise levels and improving the automation of the denoising process. By utilizing an upscaling function, the dataset is easily separable in a high-dimensional space encompassing loudness, frequency, and various weighted spectral ratios. Compared to analysis modes in the single time or frequency domain, the high-dimensional space provides a more comprehensive range of ground pulse wave characteristics for decision-making, resulting in a more complete signal-to-noise analysis model. Attached Figure Description

[0032] To more clearly illustrate the technical solutions of the embodiments of the present invention, 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 the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 Flowcharts of various weighted spectral ratio denoising methods based on XGBoost;

[0034] Figure 2 Schematic diagram of the dimension-upgrading function;

[0035] Figure 3 Original data and specific morphological diagrams of the three weighted spectral ratio upscaling functions;

[0036] Figure 4a Raw data;

[0037] Figure 4b The result after STA / LTA noise reduction;

[0038] Figure 5a Raw data;

[0039] Figure 5b Data results after noise reduction and smoothing using the new method. Detailed Implementation

[0040] The present invention will be further described below with reference to embodiments:

[0041] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0042] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0043] This invention addresses the problem of traditional methods relying too heavily on single-feature selection and struggling to denoise highly noisy, micro-moving data by mining more features from data points in high-dimensional space. It introduces a supervised learning algorithm to achieve intelligent denoising, eliminating the influence of subjective factors. This invention also includes multiple weighted spectral ratio denoising methods based on XGBoost, comprising the following steps:

[0044] A. Based on the DFA (diffuse field assumption) model, quantitative analysis of signal and noise in HVSR data is performed, and the analysis results and the resonant frequencies of the samples are used to establish a training set for XGBoost learning.

[0045] From the well logging data, the peak frequency f0 of the H / V curve is obtained. Specifically,

[0046]

[0047] In the formula: V s D is the weighted average shear wave velocity (m / s) of the overburden layer; ov The thickness of the loose overburden can be directly obtained from engineering data such as well logging.

[0048] Starting from the mathematical and physical model established by the SPAC method and the DFA inversion model, the wave field of the underground space is regarded as a purely random process, and the wave field can be regarded as thermal noise or Gaussian white noise, with its power spectral density uniformly distributed in the frequency range and its loudness distribution following a normal distribution.

[0049] For shallow ground data between 5-20Hz, the values ​​labeled I∈(I0-σ,I0+σ) and f∈(f0-υ1,f0+υ2) are signals of interest, and the rest are noise or useless sample points for training. In the formula, the range of values ​​of υ1 and υ2 is given according to the actual application and in combination with the well logging data used for training. I0 is a measure of the mean loudness of the sample points, and σ is the standard deviation of the sample loudness.

[0050] B. Establish a dimension-up function to separate the signal and noise in HVSR data in a higher dimension.

[0051] Define loudness-weighted H / V:

[0052]

[0053] In the formula: I is the Fourier amplitude of the sample point, and λ is an empirical constant, the order of magnitude of I0. The product of the orders of magnitude of the four-dimensional amplitudes is ideally considered as the mean, mode, or median of the Fourier amplitudes. For real-world data with significant noise, the median, which is less affected by extreme values, should be chosen for I0.

[0054] From the f0 used to establish the training set in step A, the peak frequency weighted H / V can be defined as follows:

[0055]

[0056] In the formula: f is the frequency of the sample point, f0 is the resonance frequency obtained from the well logging data, and should be near the peak frequency of the IHV spectrum. When f0 is unknown, i.e., when processing the H / V spectrum of an unknown site, it should be replaced by the peak frequency of the IHV spectrum. μ is an empirical constant whose meaning is the same as λ above. To ensure that the frequency and H / V value are weighted on the fHV value at any point, its order of magnitude is also equal to the order of magnitude of f0. The product of the orders of magnitude of the reciprocals.

[0057] From formulas (2) and (3), the mixed-weighted H / V can be defined:

[0058]

[0059] From formulas (2), (3), and (4), X′ can be increased in dimension to obtain:

[0060] X′(f,I,H / V,IHV,fHV,IfHV) (5)

[0061] For the frequency range of interest in practical engineering and the amplitude range that should be extracted based on Gaussian white noise, X′ is located near I0 and f0, and H / V, IHV, fHV, and IfHV are all located in the support. Sample points with larger values ​​should be extracted. After dimensionality increase, the signal and noise of X′ are linearly separable in this space.

[0062] C. Use XGBoost with added L2 regularization to train the model. Combine the actual collected data with the training set labeled in step A and the dimension-increasing function in step B for training. Set the L2 regularization coefficient through a large number of experiments to obtain a machine learning model that can separate signal and noise. Save the model for prediction.

[0063] D. Upgrade the dimensions of the sample to be analyzed and use the model trained in step C to extract the signal.

[0064] Example 1

[0065] A method for denoising micro-motion HVSR data based on the XGBoost algorithm includes the following steps:

[0066] A. Establish a model training set based on the DFA model and actual needs.

[0067] Common H / V curves have a distinct peak frequency. However, single-station data cannot distinguish whether the fretting is composed of body waves or surface waves, making it difficult to determine whether the H / V peak is caused by the resonance of S-waves within the body waves in the loose sediment layer, or by the polarization of Rayleigh surface waves or the phase of Love waves. Simulation experiments show that the peak frequency of the fretting H / V curve is not significantly related to the wavefield composition, but coincides with the resonance frequency of the loose sediment layer. Furthermore, the peak frequency f0 of the H / V curve is close to or equal to the dominant frequency of the loose sediment layer. The peak frequency f0 of the H / V curve is related to the average shear wave velocity and the thickness of the loose overburden, as follows:

[0068]

[0069] In the formula: V s D is the weighted average shear wave velocity of the overburden layer (m / s); ov The thickness of the loose overburden can be directly obtained from engineering data such as well logging.

[0070] From the known well logging data, the value of f0 can be obtained. Starting from the mathematical and physical model established by the SPAC method and the DFA inversion model, the wave field in the subsurface space is regarded as a purely random process, and this wave field can be regarded as thermal noise or Gaussian white noise. Its power spectral density is uniformly distributed across the frequency range and its loudness distribution follows a normal distribution. Therefore, the Fourier amplitude spectrum of the ideal micro-motion data also follows a normal distribution and obeys Chebyshev's law of large numbers. Therefore, in samples where the data is still dominated by signals, the sample points within σ near I0 can be considered as signals. In practical applications, engineering geophysical exploration mainly focuses on shallow data between 5-20Hz. This range of data generally overlaps significantly with (f0-υ1, f0+υ2), where the values ​​of υ1 and υ2 are given according to the actual application requirements and in combination with the well logging data used for training.

[0071] Values ​​labeled I∈(I0-σ,I0+σ) and f∈(f0-υ1,f0+υ2) are signals of interest, while the rest are noise or useless sample points, and are used for training.

[0072] B. Establishing a dimension-upgrading function

[0073] Define loudness-weighted H / V:

[0074]

[0075] In the formula: I is the Fourier amplitude of the sample point, and λ is an empirical constant, the order of magnitude of I0. The product of the orders of magnitude of the four-dimensional amplitudes is ideally considered as the mean, mode, or median of the Fourier amplitudes. For real-world data with significant noise, the median, which is less affected by extreme values, should be chosen for I0.

[0076] Based on the stability characteristics of HVSR spectral lines, the weighted spectral ratio should select sampling points with stable loudness and H / V close to the peak value. Therefore, an empirical constant λ is introduced. This not only modifies the poles and simplifies the procedure, but also aligns with the meaning of the weighted spectral ratio. The weighted spectral ratio is H / V weighted by loudness, and the weighted spectral ratio value of the sampling point should be determined by both loudness and H / V values. If there are poles that cause IHV to approach infinity, the specific value of H / V has no effect on the IHV value, which does not conform to the meaning of weighting.

[0077] From the f0 used to establish the training set in step A, the peak frequency weighted H / V can be defined as follows:

[0078]

[0079] In the formula: f is the frequency of the sample point, f0 is the resonance frequency obtained from the well logging data, and should be near the peak frequency of the IHV spectrum. When f0 is unknown, i.e., when processing the H / V spectrum of an unknown site, it should be replaced by the peak frequency of the IHV spectrum. μ is an empirical constant whose meaning is the same as λ above. To ensure that the frequency and H / V value are weighted on the fHV value at any point, its order of magnitude is also equal to the order of magnitude of f0. The product of the orders of magnitude of the reciprocals.

[0080] From formulas (2) and (3), the mixed-weighted H / V can be defined:

[0081]

[0082] From formulas (2), (3), and (4), X′ can be increased in dimension to obtain:

[0083] X′(f,I,H / V,IHV,fHV,IfHV) (5)

[0084] For the frequency range of interest in practical engineering and the amplitude range that should be extracted based on Gaussian white noise, X′ is located near I0 and f0, and H / V, IHV, fHV, and IfHV are all located in the support, and sample points with larger values ​​should be extracted. Therefore, after dimensionality increase, the signal and noise in X′ are linearly separable in this space.

[0085] C. Training Model

[0086] The actual collected data were labeled according to the method in step A, and the dimensionality was increased according to the method in step B. The L2 regularization coefficient was set through a large number of experiments, and the XGBoost model was trained and obtained. After being saved, it was used for prediction.

[0087] D. After processing the micro-motion monitoring data to be analyzed using the weighting method in step B, input it into the model trained in step C for prediction. Remove sample points that are predicted as noise, smooth the data, and export the denoised data.

[0088] Calculation Example

[0089] a. such as Figure 2 As shown, the spectral ratio curve is subjected to dimensionality increase processing, allowing more features to participate in the decision-making process in a higher dimension. Figure 3 The image shows the original data and the specific forms of the three weighted spectral ratio (loudness weighted, frequency weighted, and mixed weighted) upscaling functions.

[0090] b. Comparison of original data and results after STA / LTA noise reduction (Figure 4);

[0091] c. As shown in Figure 5, the trained model is used to process the weighted spectral ratio, select sample points with stable energy and frequencies within the range of interest, and then perform spectral smoothing and plotting.

[0092] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A multi-weighted spectral ratio denoising method based on XGBoost, characterized in that, Includes the following steps: A. Based on the DFA model, quantitative analysis of signal and noise in HVSR data collected under high noise and complex environment is performed, and training set for XGBoost learning is established using the analysis results and the resonant frequency of the samples. B. Establish a dimension-up function to separate signal and noise in HVSR data in high dimension; C. Use XGBoost with added L2 regularization to train the model. Combine the actual collected data with the training set labeled in step A and the dimension increase function in step B for training. Set the L2 regularization coefficient through a large number of experiments to obtain a machine learning model that can separate signal and noise. Save the model for prediction. D. Upgrade the dimensions of the sample to be analyzed and use the model trained in step C to extract the signal; Step B, specifically: B1. Define the loudness-weighted H / V: （2） In the formula: The Fourier amplitude of the sample point. It is an empirical constant, and its order of magnitude is order of magnitude and The product of the reciprocals of orders of magnitude, under ideal conditions, It can be considered as the mean, mode, or median of the Fourier amplitudes. For real-world data with significant noise, The median, which is less affected by extreme values, should be selected. B2. The training set used in step A is used to build the training set. H / V can be defined under peak frequency weighting: （3） In the formula: The frequency of the sample points, The resonant frequency is obtained from well logging data, and should be within... Near the peak frequency of the spectrum, When dealing with H / V spectra of unknown sites, it should be done by... Replace with the peak frequency of the spectrum; This is an empirical constant, and its meaning is the same as above. To ensure that the frequency and H / V value are weighted at any point, the fHV value is also equal in magnitude. order of magnitude and The product of the orders of magnitude of the reciprocals; B3. From formulas (2) and (3), the mixed weighted H / V can be defined: （4） B4. From formulas (2), (3), and (4), we can determine... By increasing the dimensionality, we get: （5） B5. Regarding the frequency range of interest in practical engineering and the amplitude range that should be extracted based on Gaussian white noise. Central and Nearby, and Sample points that are all located within supports and have larger numerical values ​​should be extracted and then subjected to dimensionality upscaling. The signal and noise are linearly separable in space.

2. The XGBoost-based multi-weighted spectral ratio denoising method according to claim 1, characterized in that, Step A, specifically: A1. Obtain the peak frequency of the H / V curve from the well logging data. , （1） In the formula: The weighted average shear wave velocity of the overburden layer (m / s); The thickness of the loose overburden can be directly obtained from engineering data such as well logging. A2. Starting from the mathematical and physical model established by the SPAC method and the DFA inversion model, the wave field of the underground space is regarded as a purely random process, and the wave field can be regarded as thermal noise or Gaussian white noise, with its power spectral density uniformly distributed in the frequency range and its loudness distribution following a normal distribution. A3. For shallow ground data between 5-20Hz, labeling... and The value of is the signal of interest, and the rest are noise or useless sample points, used for training; where , The range of values ​​is determined based on the actual application requirements and the well logging data used in the training. A measure of the mean loudness of sample points. denoted as the standard deviation of the sample loudness.

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