Denoising method for GNSS monitoring data of open-pit mine slopes by integrating multi-source indicators

Abstract

The present invention discloses a method for denoising GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators. The method comprises the following steps: S1, collecting GNSS monitoring data of the slopes and detecting and interpolating large gross errors using the 3σ method, then performing wavelet decomposition to obtain low-frequency coefficients and high-frequency coefficients; reconstructing the trend term Q using the low-frequency coefficients, solving the mean square error m using the first and second layer high-frequency coefficients, and then detecting gross errors again; S2, performing empirical mode decomposition on the GNSS monitoring data of the slopes to obtain a number of slope IMFs; screening to obtain high-noise modes, low-noise modes, and residuals, reconstructing the low-noise modes and residuals to obtain a preliminary denoised slope GNSS signal result EMD_A; and S3, processing the high-noise modes of the slopes using the interval soft threshold method and synthesizing them with the slope EMD denoising result EMD_A to obtain the final slope GNSS denoising result. The present invention achieves accurate denoising of GNSS monitoring data of open-pit mine slopes, providing more reliable data support for slope stability monitoring in mining areas.

Description

Technical Field

[0001] The present invention relates to the field of mining, and in particular to a denoising method for GNSS monitoring data of open-pit mine slopes by fusing multi-source indicators. Background Art

[0002] During open-pit mining, excavation and blasting operations disrupt the original stress balance of the surrounding rock mass, easily triggering geological disasters such as slope landslides and collapses, directly threatening the safety of workers and equipment in the mining area. Therefore, long-term slope stability monitoring is crucial for open-pit mine safety management.

[0003] As an advanced means, GNSS is widely used in open-pit mine slope monitoring, and can obtain key parameters such as slope displacement, velocity and acceleration in real time. Traditional slope GNSS monitoring data denoising methods include empirical mode decomposition (EMD), Kalman filtering, wavelet transform and singular value decomposition (SVD), which have significant limitations when dealing with the special noise characteristics of open-pit mines. For example, EMD is difficult to effectively distinguish the intrinsic mode function (IMF) in a complex mining environment, resulting in the loss of deformation information; wavelet transform is limited by the choice of decomposition level and is difficult to handle sudden anomalies; Kalman filtering may lose the true deformation information of the mining area under a strong noise background; the SVD method affects the stability of the results when denoising mining area data containing trend signals due to the difficulty in selecting singular values. In response to the above problems, the present invention proposes a denoising method for open-pit mine slope GNSS monitoring data that integrates multiple source indicators. It fully considers the unique environment and complex working conditions of open-pit mines, comprehensively utilizes multiple source indicators, and significantly improves the noise suppression effect. This method can not only effectively remove high-frequency noise and gross errors from GNSS monitoring data in open-pit mines, but also preserve the true deformation trend, providing more reliable basic data for slope stability analysis, and significantly improving the reliability and practicality of mine safety monitoring. Summary of the Invention

[0004] The purpose of the present invention is to provide a denoising method for GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators. The method realizes accurate denoising of GNSS monitoring data of open-pit mine slopes and provides more reliable data support for slope stability monitoring in mining areas.

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

[0006] A denoising method for GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators, the method comprising:

[0007] S1. Collect slope GNSS monitoring data and use the 3σ method to detect large gross errors, and use the average value method to replace and interpolate the detected gross errors; perform wavelet decomposition on the interpolated slope GNSS monitoring data to obtain the corresponding low-frequency coefficients and high-frequency coefficients; reconstruct the trend term Q using the low-frequency coefficients, and solve the mean square error m using the first and second layer high-frequency coefficients. Combine the trend term Q and mean square error m and use the 3σ method to detect and eliminate gross errors in the slope GNSS monitoring data.

[0008] The 3σ method, based on the basic theory of normal distribution, detects gross errors in raw data by calculating the mean and standard deviation of the data. However, when faced with dynamically changing slope GNSS monitoring data, the 3σ method often struggles to effectively capture the complex changing trends, resulting in less than ideal gross error detection results. To address this limitation, wavelet decomposition can be combined with preprocessing of the raw slope GNSS monitoring data. Wavelet decomposition has the ability to perform multi-scale analysis and can effectively extract the different frequency components in the slope GNSS monitoring data, especially the trend term, which provides a deeper understanding of the data's changing patterns. By extracting the trend term and mean square error of the slope GNSS monitoring data and combining it with the 3σ method for gross error detection and elimination, the effectiveness of outlier detection in slope GNSS monitoring data can be significantly improved, ensuring more accurate and reliable detection results.

[0009] S2. Perform empirical mode decomposition on the slope GNSS monitoring data to obtain several slope IMFs; filter the modal decomposition results to obtain high-noise modes, low-noise modes, and residuals; reconstruct the low-noise modes and residuals to obtain the slope GNSS signal result EMD_A after preliminary denoising;

[0010] S3. The high-noise mode of the slope is processed by the interval soft threshold method and synthesized with the slope EMD denoising result EMD_A to obtain the final slope GNSS denoising result.

[0011] In order to better implement the present invention, in step S1, the 3σ method is used to detect large gross errors in the slope GNSS monitoring data. The method is as follows:

[0012] Calculate the mean value and standard deviation of the original slope GNSS monitoring data. The calculation expression is as follows:

[0013]

[0014]

[0015] Where, wi represents the i-th monitoring data in the original slope GNSS monitoring data, M represents the total number of original slope GNSS monitoring data, Represents the average value of slope GNSS monitoring data;

[0016] Construct left and right confidence intervals ul and ur, satisfying w i >ur or w i The data with the condition of <ul were judged as gross errors and removed from the original slope GNSS monitoring data;

[0017] The data at the removed positions are interpolated using the average value of the adjacent non-removed data to obtain new slope GNSS monitoring data.

[0018] Preferably, the interpolated slope GNSS monitoring data is subjected to wavelet decomposition, the method comprising:

[0019] The multi-source indicator fusion method is used to determine and obtain the optimal decomposition level of wavelet decomposition. The indicators in the multi-source indicator fusion method include the root mean square error change var_rmse, the signal-to-noise ratio change var_snr, and the smoothness change var_smooth. The calculation expression is as follows:

[0020] var_rmse(t)=rmse(t+1)-rmse(t)

[0021]

[0022] Where var_rmse(t) represents the root mean square error change between level t+1 and level t, X o Indicates slope GNSS monitoring data; X t represents the decomposed slope GNSS monitoring data corresponding to level t;

[0023] var_snr(t)=|snr(t+1)-snr(t)|

[0024]

[0025] Where var_snr(t) represents the change in signal-to-noise ratio between level t+1 and level t;

[0026] var_smooth(t)=|smooth(t+1)-smooth(t)|

[0027]

[0028] Where var_smooth(t) represents the change in smoothness between level t+1 and level t; smooth(t) represents the smoothness corresponding to level t;

[0029] Normalize the above indicators and calculate the weight of each indicator, then calculate the fusion indicator result S(t);

[0030] After obtaining the S(t) sequence, the maximum value is subtracted from the sequence data and the sequence data is reversed to obtain a new sequence. The position v where the first inflection point appears is identified, and the optimal decomposition level k=v+1.

[0031] Preferably, the high-frequency coefficients and low-frequency coefficients of the slope GNSS monitoring data are obtained after wavelet decomposition, and the deformation trend Q is reconstructed using the low-frequency coefficients. At the same time, the high-frequency coefficients of the first and second layers hfreco1 and hfreco2 are used to calculate the mean square error m. The specific method is as follows:

[0032] Calculate the energy1 and energy2 corresponding to the high-frequency coefficients of the first and second layers. The calculation method of energy1 is as follows:

[0033] For the first layer high frequency coefficient hfreco1=[c1, c2, ..., c n ], and its energy calculation formula is:

[0034]

[0035] Where c i It is the i-th coefficient in the first layer of high-frequency coefficients; the energy energy2 corresponding to the second layer of high-frequency coefficients is calculated in the same way as the energy energy1 corresponding to the first layer of high-frequency coefficients;

[0036] Calculate the mean error m using the following formula:

[0037]

[0038] Where q is the median parameter, which is 0.674; energy1 and energy2 are the energies corresponding to the high-frequency coefficients of the first and second layers respectively;

[0039] Then, the gross error is detected by combining the mean error m and the trend term Q. The calculation formula is as follows:

[0040]

[0041] If p is satisfied i >3, then X o (i) is a gross error point and needs to be eliminated.

[0042] Preferably, in step S2, the slope GNSS monitoring data is adaptively decomposed into L slope IMF components during modal decomposition, and the following formula is used to determine whether the slope IMF is qualified:

[0043]

[0044] Where SD is the threshold for stopping screening of each slope IMF. The slope IMF is qualified within the threshold range. k (t) and h k-1 (t) is the time series corresponding to the k-th slope IMF and the k-1-th slope IMF screening process.

[0045] Preferably, in step S2, the comprehensive evaluation index CEI is used to determine the optimal boundary, and the residual is used as the last slope IMF. The calculation formula is as follows:

[0046]

[0047] Where, IMF k (i) represents the i-th value corresponding to the k-th slope IMF, X o (i) represents the i-th value corresponding to the slope GNSS monitoring data;

[0048] Normalize the above two indicators and the calculation formula is as follows

[0049]

[0050] The two normalized indicators are weighted and the calculation formula is as follows:

[0051]

[0052] Where, σ wrmse and μ wrmse Represents the data sequence wrmse respectively k and wr k The standard deviation and mean of

[0053] Calculate the comprehensive evaluation index CEI, the calculation formula is as follows:

[0054] CEI=W wrmse ×wrmse+W wr ×wr

[0055] Determine the boundary threshold between noise and signal, and the calculation formula is as follows:

[0056]

[0057] Where k≥2, and when the threshold first satisfies 1≤B k-1 When ≤3, k-1 is regarded as the dividing point; that is, the K value of the truncated slope IMF function is k-1, the first k-1 slope IMF components are all regarded as noise, and the remaining slope IMF components are regarded as signals.

[0058] Preferably, in step S2, the slope GNSS signal result EMD_A is calculated using the following formula:

[0059] Where U=K.

[0060] Preferably, in step S3, the interval soft threshold processing method for the mode is as follows:

[0061] The slope IMF mode corresponding to the interval j = [VU] is subjected to interval threshold processing, and the definition of V is as follows:

[0062] V = max(1, U-1)

[0063] Calculate the threshold corresponding to each slope IMF in interval j. The calculation formula is as follows:

[0064]

[0065] Where h (1) (t) represents the sequence corresponding to the first slope IMF component, median represents the median, E1 is the energy in the first slope IMF component; β and ρ are constants with values ​​of 0.719 and 2.01 respectively;

[0066] Find all zero-crossing intervals of each slope IMF component corresponding to interval j and calculate the extreme value. If the extreme value is greater than T j , then the calculation formula for all sample values ​​in the zero-crossing interval is as follows:

[0067]

[0068] On the contrary, if the extreme value is not greater than T j , then all sample values ​​in the zero-crossing interval are set to 0, that is

[0069]

[0070] Preferably, in step S3, the processed IMF mode is finally synthesized with EMD_A to obtain the final denoising result EMD_Fin. The calculation expression is as follows:

[0071]

[0072] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0073] (1) The noise reduction method of the present invention can significantly improve the quality of slope GNSS monitoring data. Its noise reduction results can not only effectively reflect the fluctuation of the data, but also accurately capture the changing trend of the data, providing a reliable basis for the analysis of the monitoring results.

[0074] (2) By applying the technology of the present invention, the accuracy of slope GNSS monitoring data has been significantly improved; noise interference has been effectively removed, making the monitoring data more real and accurate, and providing more powerful support for slope stability analysis and early warning.

[0075] (3) The present invention applies the multi-source index fusion method to determine the optimal level of wavelet decomposition and the boundary of EMD noise signal; it overcomes the unreliability of the traditional method that relies on a single index to determine the optimal level of wavelet decomposition and the EMD modal boundary, and the comprehensive consideration of multi-source indicators significantly improves the denoising accuracy of slope GNSS monitoring data.

[0076] (4) The present invention cleverly combines the important characteristic information contained in the high-frequency IMF components, achieving data denoising while preserving these key features to the greatest extent possible, ensuring the integrity and validity of the data after denoising. This advantage enables the present invention to not only excel in denoising but also accurately reflect subtle changes in the monitoring data, providing more refined data support for slope risk assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 This is a flowchart of the method for denoising GNSS monitoring data of open-pit mine slopes of the present invention;

[0078] Figure 2 Schematic diagram of the method principle of the open-pit mine slope GNSS monitoring data denoising method of the present invention;

[0079] Figure 3 This is the slope GNSS monitoring data EMI) decomposition process in the embodiment;

[0080] Figure 4 This is the gross error detection of slope GNSS monitoring data combining wavelet decomposition and 3σ method in the embodiment;

[0081] Figure 5 This is the EMD decomposition result of the slope GNSS monitoring data in the embodiment;

[0082] Figure 6 A threshold curve diagram for determining the comprehensive evaluation index in the embodiment;

[0083] Figure 7 This is the final slope GNSS monitoring data denoising result in the embodiment. DETAILED DESCRIPTION

[0084] Below in conjunction with embodiment, the present invention is described in further detail:

[0085] Example

[0086] like Figures 1 and 2As shown in FIG, a denoising method for GNSS monitoring data of an open-pit mine slope by integrating multiple source indicators is provided, and the method includes:

[0087] S1. Collect slope GNSS monitoring data and use the 3σ method to detect large gross errors, and use the average value method to replace and interpolate the detected gross errors; perform wavelet decomposition on the interpolated slope GNSS monitoring data to obtain the corresponding low-frequency coefficients and high-frequency coefficients; reconstruct the trend term Q using the low-frequency coefficients, and solve the mean square error m using the first and second layer high-frequency coefficients. Combine the trend term Q and mean square error m and use the 3σ method to detect and eliminate gross errors in the slope GNSS monitoring data.

[0088] In some embodiments, the method for detecting large gross errors in slope GNSS monitoring data using the 3σ method in step S1 is as follows:

[0089] Calculate the mean value and standard deviation of the original slope GNSS monitoring data. The calculation expression is as follows:

[0090]

[0091] Among them, w i represents the i-th monitoring data in the original slope GNSS monitoring data, M represents the total number of original slope GNSS monitoring data, Represents the average value of the slope GNSS monitoring data. For slope monitoring, a series of GNSS monitoring stations are deployed on the open-pit mine slope. These stations collect slope monitoring data (including displacement in the north, east, and height directions, i.e., X, Y, and H) at a certain temporal resolution. A continuous period of GNSS monitoring data corresponding to one of the stations is used as the dataset for research. wi is the i-th monitoring data point in the dataset, and M represents the total number of data points in the dataset.

[0092] Construct the left and right confidence intervals ul and ur as follows:

[0093] ul=mean_value-3*std_value

[0094] ur=mean_value+3*std_value

[0095] Satisfy w i >ur or w i The data with the condition of <ul were judged as gross errors and removed from the original slope GNSS monitoring data;

[0096] The data at the removed position is interpolated with the average value of the adjacent non-removed data to obtain new slope GNSS monitoring data; for example, the data V at the removed position is i(i represents the serial number of the slope GNSS monitoring data), if the data V i There is unremoved data before and after V i-1 、V i+1 , then use the following formula to get the average value and calculate the data V i Perform interpolation:

[0097]

[0098] In some embodiments, wavelet decomposition is performed on the interpolated slope GNSS monitoring data, and the method includes:

[0099] A multi-source index fusion method is used to determine and obtain the optimal decomposition level of wavelet decomposition (the present invention performs wavelet decomposition based on the optimal decomposition level). The indicators in the multi-source index fusion method include the root mean square error change var_rmse, the signal-to-noise ratio change var_snr, and the smoothness change var_smooth. The calculation expression is as follows:

[0100] var_rmse(t)=rmse(t+1)-rmse(t)

[0101]

[0102] Where var_rmse(t) represents the root mean square error change between level t+1 and level t, X o represents the slope GNSS monitoring data, X o (i) represents the i-th monitoring data in the slope GNSS monitoring data; X t represents the decomposed slope GNSS monitoring data corresponding to level t, X t (i) represents the i-th slope GNSS monitoring data after decomposition corresponding to level t; N represents the total number of slope GNSS monitoring data after interpolation (N<M).

[0103] var_snr(t)=|snr(t+1)-snr(t)|

[0104]

[0105] Where var_snr(t) represents the change in the signal-to-noise ratio between level t+1 and level t, and snr(t) represents the signal-to-noise ratio at level t.

[0106] var_smooth(t)=|smooth(t+1)-smooth(t)|

[0107]

[0108] Where var_smooth(t) represents the change in smoothness between level t+1 and level t, and smooth(t) represents the smoothness corresponding to level t;

[0109] Normalize the above indicators (including root mean square error change var_rmse, signal-to-noise ratio change var_snr and smoothness change var_smooth) and calculate the weight of each indicator Then calculate the fusion index result S(t); the normalized expressions of the root mean square error change var_rmse, the signal-to-noise ratio change var_snr, and the smoothness change var_smooth are as follows:

[0110]

[0111] In calculating the weight of each indicator, normalized N var_rmse Taking (t) as an example (the calculation method of other indicator weights is the same), the method is as follows:

[0112]

[0113] Where L represents the length of slope GNSS monitoring data (or the number of data); G represents the entropy value; Represents weight. Calculate the fusion index result:

[0114]

[0115] After obtaining the S(t) sequence, the maximum value is subtracted from the sequence data and the sequence data is reversed to obtain a new sequence. The position v where the first inflection point appears is identified, and the optimal decomposition level k=v+1.

[0116] In this embodiment, the high-frequency coefficients and low-frequency coefficients of the slope GNSS monitoring data are obtained after wavelet decomposition. The deformation trend Q is reconstructed using the low-frequency coefficients, and the mean square error m is calculated using the high-frequency coefficients hfreco1 and hfeco2 of the first and second layers. The specific method is as follows:

[0117] Calculate the energy1 and energy2 corresponding to the high-frequency coefficients of the first and second layers. The calculation method of energy1 is as follows:

[0118] For the first layer high frequency coefficient hfreco1=[c1, c2, ..., c n ], and its energy calculation formula is:

[0119]

[0120] Where c iIt is the i-th coefficient in the first layer of high-frequency coefficients; the energy energy2 corresponding to the second layer of high-frequency coefficients is calculated in the same way as the energy energy1 corresponding to the first layer of high-frequency coefficients;

[0121] Calculate the mean error m using the following formula:

[0122]

[0123] Where q is the median parameter, which is 0.674; energy1 and energy2 are the energies corresponding to the high-frequency coefficients of the first and second layers respectively;

[0124] Then, the gross error is detected by combining the mean error m and the trend term Q. The calculation formula is as follows:

[0125]

[0126] If p is satisfied i >3, then X o (i) is a gross error point and needs to be eliminated.

[0127] This example uses the X-direction displacement of a station numbered GNSS21 at an open-pit mine in Xinjiang as an example. The data time range used is from June 27, 2023 to January 3, 2024, including N monitoring data. First, the 3σ method is used to detect large gross errors, and the average method is used for interpolation. Then, the X-direction displacement data is decomposed using wavelet decomposition to obtain its low-frequency coefficients and high-frequency coefficients. The trend term Q is reconstructed using the low-frequency coefficients, and the error m is solved using the first and second layer high-frequency coefficients. Finally, the 3σ method is used to detect gross errors again by combining the trend term Q and the mean error m. The results are as follows: Figure 4 shown.

[0128] S2. Perform empirical mode decomposition on the slope GNSS monitoring data to obtain several slope IMFs; screen the modal decomposition results to obtain high-noise modes, low-noise modes, and residuals, and reconstruct the low-noise modes and residuals to obtain the slope GNSS signal result EMD_A after preliminary denoising.

[0129] In some embodiments, as Figure 3 As shown in FIG, when performing empirical mode decomposition (EMD), the slope GNSS monitoring data is adaptively decomposed into L slope IMF components. Due to the complexity and noise interference of the monitoring data, it is difficult for the slope IMF components to strictly meet the condition that the upper and lower envelopes composed of local extreme values ​​have zero mean. To solve this problem, the present invention uses the following formula to determine whether the slope IMF is qualified:

[0130]

[0131] Where SD is the threshold for stopping screening of each slope IMF. The slope IMF is qualified within the threshold range (preferably 0.2 to 0.3 in the present invention). h k (t) and h k-1 (t) is the time series corresponding to the IMF screening process for the kth slope and the k-1th slope. When using empirical mode decomposition (EMD) to decompose the slope GNSS monitoring data, the residual is judged to be qualified by any of the following conditions: a. When the component is very small and less than a predetermined value; b. When the residual r is a monotonic function.

[0132] In some embodiments, the comprehensive evaluation index CEI is used to determine the optimal boundary (in order to effectively distinguish the noise and signal in the slope GNSS monitoring data, avoid the uncertainty of determining the boundary IMF based on a single indicator, and reduce the complexity of determining the boundary of the slope GNSS monitoring data, the present invention innovatively uses the comprehensive evaluation index CEI to determine the optimal boundary), and the residual is used as the last slope IMF. The calculation formula is as follows

[0133]

[0134] Where, IMF k (i) represents the i-th value corresponding to the k-th slope IMF (slope GNSS monitoring data will produce L slope IMF components after empirical mode decomposition, IMF k It is the kth IMF component among the L slope IMF components. k (i) is the i-th value corresponding to the k-th slope IMF component data set among the L slope IMF components), X o (i) represents the i-th value in the slope GNSS monitoring data sequence;

[0135] Normalize the above two indicators and the calculation formula is as follows

[0136]

[0137] The two normalized indicators are weighted and the calculation formula is as follows:

[0138]

[0139] Where, σ wrmse and μ wrmse Represents the data sequence wrmse respectively k and wr k The standard deviation and mean of

[0140] Calculate the comprehensive evaluation index CEI, the calculation formula is as follows:

[0141] CEI=Wwrmse ×wrmse+W wr ×wr

[0142] Determine the boundary threshold between noise and signal, and the calculation formula is as follows:

[0143]

[0144] Where k≥2, and when the threshold first satisfies 1≤B k-1 When ≤3, k-1 is regarded as the dividing point; that is, the K value of the truncated slope IMF function is k-1, the first k-1 slope IMF components are all regarded as noise, and the remaining slope IMF components are regarded as signals.

[0145] The present invention reconstructs the slope signal components to obtain the slope GNSS signal result EMD_A after preliminary denoising. The calculation formula is as follows:

[0146] Where U=K.

[0147] This embodiment takes the X-direction displacement of a measuring station numbered GNSS21 in an open-pit mine in Xinjiang as an example. According to the method of step S2 of the present invention, the X-direction displacement of the measuring station obtained after gross error elimination is subjected to EMD decomposition to obtain the IMF of each slope. The results are as follows: Figure 5 As shown. By calculating the comprehensive evaluation index, the threshold value B is determined (the comprehensive evaluation index threshold curve is drawn, as shown Figure 6 As shown), the formula is Where k≥2, and when the threshold first satisfies 1≤B k-1 When ≤3, k-1 is regarded as the dividing point; that is, the K value of the truncated slope IMF function is k-1, and the first k-1 slope IMF components (IMF j , j≤k-1) are all regarded as noise, and the slope IMF component (IMF j , j>k-1) is regarded as a signal.

[0148] S3. The high-noise mode of the slope is processed by the interval soft threshold method and synthesized with the slope EMD denoising result EMD_A to obtain the final slope GNSS denoising result.

[0149] In some embodiments, the interval soft threshold processing method for the modality is as follows:

[0150] The slope IMF mode corresponding to the interval j = [VU] is subjected to interval threshold processing, and the definition of V is as follows:

[0151] V = max(1, U-1)

[0152] Calculate the threshold corresponding to each slope IMF in interval j. The calculation formula is as follows

[0153]

[0154] Where h (1) (t) represents the sequence corresponding to the first slope IMF component, median represents the median, E1 is the energy in the first slope IMF component; β and ρ are constants with values ​​of 0.719 and 2.01, respectively.

[0155] If there are 2 IMFs in the interval, j in the second row Ej is 2, and j in the third row Tj is 1, 2.

[0156] Find all zero-crossing intervals of each slope IMF component corresponding to interval j and calculate the extreme value. If the extreme value is greater than T j , then the calculation formula for all sample values ​​in the zero-crossing interval is as follows:

[0157]

[0158] On the contrary, if the extreme value is not greater than T j , then all sample values ​​in the zero-crossing interval are set to 0, that is

[0159]

[0160] In some embodiments, in step S3, the processed high-noise IMF mode is finally synthesized with EMD_A to obtain the final denoising result EMD_Fin. The calculation expression is as follows:

[0161]

[0162] This example takes the X-direction displacement of a measuring station numbered GNSS21 in an open-pit mine in Xinjiang as an example. In this example, the boundary between the signal and the noise is determined by the comprehensive evaluation index K=4. In this example, the first K IMF components (IMF j , j≤K) are all regarded as noise, and the IMF component (IMF j , j>K) is considered as the useful part. Figure 7 As shown in Figure 2, the modes corresponding to K and K-1 are subjected to interval soft threshold processing, and the final slope GNSS denoising results are synthesized with the useful parts.

[0163] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for denoising GNSS monitoring data for open-pit mine slopes by integrating multiple source indicators, characterized by: The methods include: S1. Collect slope GNSS monitoring data and use The method is used to detect large gross errors, and the average value method is used to replace and interpolate the detected gross errors; the interpolated slope GNSS monitoring data is subjected to wavelet decomposition to obtain the corresponding low-frequency coefficients and high-frequency coefficients; the interpolated slope GNSS monitoring data is subjected to wavelet decomposition, and the method includes: The multi-source index fusion method is used to judge and obtain the optimal decomposition level of wavelet decomposition. The indicators in the multi-source index fusion method include the root mean square error change , signal-to-noise ratio change and smoothness variation , the calculation expression is as follows: ； Where, represents the change in the root mean square error between level t+1 and level t, Indicates slope GNSS monitoring data; represents the decomposed slope GNSS monitoring data corresponding to level t; ； Where, Represents the change in signal-to-noise ratio between level t+1 and level t; ； Where, Indicates the change in smoothness between level t+1 and level t; Indicates the smoothness corresponding to level t; Normalize the above indicators and calculate the weight of each indicator, then calculate the fusion indicator results ; In getting After the sequence is generated, the maximum value is subtracted from the sequence data and the new sequence is obtained by reversing it. The position v where the first inflection point appears is identified, and the optimal decomposition layer k = v+1; the trend term Q is reconstructed using the low-frequency coefficients, and the mean error m is solved using the high-frequency coefficients of the first and second layers. The trend term Q and mean error m are combined and used The method is used to detect and eliminate gross errors in slope GNSS monitoring data; S2. Perform empirical mode decomposition on the slope GNSS monitoring data to obtain several slope IMFs; filter the modal decomposition results to obtain high-noise modes, low-noise modes, and residuals; reconstruct the low-noise modes and residuals to obtain the slope GNSS signal result EMD_A after preliminary denoising; S3. The high-noise mode of the slope is processed by the interval soft threshold method and synthesized with the slope EMD denoising result EMD_A to obtain the final slope GNSS denoising result.

2. The method for denoising GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators according to claim 1 is characterized by: In step S1, use The method is to detect large gross errors in slope GNSS monitoring data as follows: Calculate the mean value and standard deviation of the original slope GNSS monitoring data. The calculation expression is as follows: ； ； in, represents the i-th monitoring data in the original slope GNSS monitoring data, Indicates the total number of original slope GNSS monitoring data, Represents the average value of slope GNSS monitoring data; Construct left and right confidence intervals ul and ur, satisfying or The data under this condition were judged as gross errors and removed from the original slope GNSS monitoring data; The data at the removed positions are interpolated using the average value of the adjacent non-removed data to obtain new slope GNSS monitoring data.

3. The method for denoising GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators according to claim 1 is characterized by: The high-frequency coefficients and low-frequency coefficients of the slope GNSS monitoring data are obtained after wavelet decomposition. The deformation trend Q is reconstructed using the low-frequency coefficients, and the high-frequency coefficients of the first and second layers are used to reconstruct the deformation trend Q. 、 To calculate the mean error m, the specific method is as follows: Calculate the energy corresponding to the high-frequency coefficients of the first and second layers 、 , The calculation method is as follows: For the first layer high frequency coefficients , and its energy calculation formula is: ； Where, is the i-th coefficient in the first layer of high-frequency coefficients; the energy corresponding to the second layer of high-frequency coefficients Energy corresponding to the high-frequency coefficients of the first layer The calculation method is the same; Calculate the mean error m using the following formula: ； ； ； Where q is the median parameter, which is 0.674; 、 are the energies corresponding to the high-frequency coefficients of the first and second layers respectively; Then, the gross error is detected by combining the mean error m and the trend term Q. The calculation formula is as follows: ； If satisfied , then it is believed that It is a gross error and needs to be removed.

4. The method for denoising GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators according to claim 1 is characterized by: In step S2, the slope GNSS monitoring data is adaptively decomposed into L slope IMF components during modal decomposition, and the following formula is used to determine whether the slope IMF is qualified: ； Where SD is the threshold for stopping screening of each slope IMF. The slope IMF is qualified if it is within the threshold range. and is the time series corresponding to the k-th slope IMF and the k-1-th slope IMF screening process.

5. The method for denoising GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators according to claim 1 is characterized by: In step S2, the comprehensive evaluation index CEI is used to determine the optimal boundary, and the residual is used as the last slope IMF. The calculation formula is as follows: ； Where, represents the i-th value corresponding to the k-th slope IMF, represents the i-th value corresponding to the slope GNSS monitoring data; Normalize the above two indicators and the calculation formula is as follows ； The two normalized indicators are weighted and the calculation formula is as follows: ， ； Where, and Represents data series and The standard deviation and mean of Calculate the comprehensive evaluation index CEI, the calculation formula is as follows: ； Determine the boundary threshold between noise and signal, and the calculation formula is as follows: ； in , and when the threshold first meets hour, is regarded as the dividing point; that is, the K value of the truncated slope IMF function is ,forward All slope IMF components are regarded as noise, and the remaining slope IMF components are regarded as signals.

6. The method for denoising GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators according to claim 1, characterized in that: In step S2, the slope GNSS signal result EMD_A is calculated as follows: , where U=K.

7. The method for denoising GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators according to claim 6 is characterized by: In step S3, the interval soft threshold processing method for the mode is as follows: The slope IMF mode corresponding to the interval j = [VU] is subjected to interval threshold processing, and the definition of V is as follows: ； Calculate the threshold corresponding to each slope IMF in interval j. The calculation formula is as follows ； Where, represents the sequence corresponding to the first slope IMF component, median represents the median, is the energy in the first slope IMF component; and The values ​​of the constants are 0.719 and 2.01 respectively; Find all zero-crossing intervals of each slope IMF component corresponding to interval j and calculate the extreme value. If the extreme value is greater than , then the calculation formula for all sample values ​​in the zero-crossing interval is as follows: ； On the contrary, if the extreme value is not greater than , then all sample values ​​in the zero-crossing interval are set to 0, that is 。 8. The method for denoising GNSS monitoring data of open-pit mine slopes by integrating multiple source indicators according to claim 1, characterized in that: In step S3, the processed IMF mode is finally synthesized with EMD_A to obtain the final denoising result. , the calculation expression is as follows, 。

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