Sensor data noise reduction method based on empirical wavelet decomposition

Abstract

The invention discloses a sensor data noise reduction method based on empirical wavelets, which comprises the following steps: 1) data acquisition and filtering: acquiring data of a plurality of sensors, and filtering the acquired data by adopting a Kalman filtering algorithm; 2) separating sensor axis data: separating data of different axes of different sensors; carrying out normalization processing on each separated data stream; 3) noise reduction: adopting an empirical wavelet transform (EWT) algorithm to decompose the data stream of each axis into corresponding different IMFs, and counting the Kurtosis, power spectral density (PSD) and autocorrelation function (ACF) numerical values after decomposition at the same time; 4) signal reconstruction: recombining the de-noised IMF, and reconstructing a clean signal by adopting inverse empirical wavelet transform; meanwhile, quality evaluation is carried out on the reconstructed signal, and the noise reduction effect is verified; according to the method, statistical indexes such as kurtosis, power spectral density and an autocorrelation function are utilized, noise components in the signals can be accurately separated and identified through empirical wavelet transform, and the noise processing accuracy is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and particularly relates to a method for denoising sensor data based on empirical wavelet decomposition. Background Art

[0002] With the rapid development of the Internet of Things (IoT), wearable devices, and smartphones, sensor technology is playing an increasingly important role in daily life and industrial applications. Especially in mobile devices, multi-axis sensors such as accelerometers, gyroscopes, and gravity sensors are widely used in fields such as motion detection, attitude estimation, and user interaction. However, these sensors face serious noise interference problems in practical applications, which directly affect the quality of data and the accuracy of subsequent applications.

[0003] Traditional methods for denoising sensor data mainly include: 1) Low-pass filtering: Although simple and effective, it often over-smoothes the signal, resulting in the loss of useful information. 2) Kalman filtering: Suitable for linear systems, it has a good inhibitory effect on sudden noise, but its effect is poor when dealing with non-linear and non-stationary signals. 3) Wavelet transform: It can provide time-frequency localization analysis, but traditional wavelet transform requires pre-selecting a suitable wavelet basis and lacks self-adaptability. 4) Empirical mode decomposition: It has good self-adaptability, but there are problems of mode mixing and low computational efficiency.

[0004] These methods all have certain limitations when dealing with complex multi-axis sensor data. Especially when facing non-linear and non-stationary signals, it is difficult to balance the denoising effect, computational efficiency, and signal feature retention at the same time.

[0005] Therefore, there are still many deficiencies in the prior art in terms of denoising and data processing, and new efficient, accurate, and precise denoising technologies are urgently needed to meet the requirements for data quality. In recent years, empirical wavelet transform (EWT) has attracted wide attention as a new signal processing technology. EWT combines the advantages of wavelet analysis and the self-adaptability of empirical mode decomposition, and can adaptively construct wavelet filters according to the spectral characteristics of the signal. However, the application of EWT in multi-axis sensor data processing has not been fully explored. Summary of the Invention

[0006] In view of the deficiencies of the prior art, the method for denoising sensor data based on empirical wavelet transform proposed by the present invention includes the following steps:

[0007] The technical solution of the present invention is as follows:

[0008] A method for denoising sensor data based on empirical wavelet decomposition includes the following steps:

[0009] 1) Data collection and filtering: Collect multi-sensor data and use the Kalman filter algorithm to filter the collected data, and finally generate a file F containing the xyz axis data of multiple sensors. total ;

[0010] 2) Separate sensor axis data: From F total In the file, separate the data of different axes of different sensors; normalize each separated data stream to make them have the same data range and scale;

[0011] 3) Noise reduction: The empirical wavelet transform (EWT) algorithm is used to decompose the data stream of each axis into corresponding IMFs. The kurtosis, power spectral density (PSD) and autocorrelation function (ACF) values ​​after decomposition are statistically analyzed to further determine the IMF that may be noise. Adaptive threshold processing is performed to retain the useful signal to the greatest extent while removing the noise.

[0012] 4) Signal reconstruction step: The denoised IMF is recombined and the clean signal is reconstructed using the inverse empirical wavelet transform. At the same time, the quality of the reconstructed signal is evaluated, and indicators such as the signal-to-noise ratio (SNR) and the root mean square error (RMSE) are calculated to verify the denoising effect.

[0013] Furthermore, in step 1), the detailed steps of data collection and filtering are as follows:

[0014] (1-1) Sensor data acquisition: Initialize the accelerometer, gyroscope, and gravity sensor in the Android device, and set an appropriate sampling frequency (e.g., 50, 100 Hz) to ensure sufficient time resolution.

[0015] (1-2) Data filtering: The collected data is written into the buffer (memory) in real time, and simple outlier detection is performed to remove data points that are obviously beyond the sensor range; at the same time, the collected data is filtered using a Kalman filter.

[0016] Furthermore, in step 2), the detailed steps of separating the sensor axis data are as follows:

[0017] Open and read the Ftotal file generated in step 1) and make sure the file format (CSV or binary) is correctly identified;

[0018] (2-1) According to file F total The sensor identification in the data is used to classify the data into different categories. At the same time, for each type of data, the data streams of the three axes of X, Y, and Z are further separated.

[0019] (2-2) Time series reconstruction, check the timestamps of each data stream to ensure the continuity of the time series; align the start and end times of all data streams to ensure that the data lengths of all axes are consistent;

[0020] (2-3) Data normalization process: Calculate the mean μ and standard deviation σ for the data streams of each axis respectively.

[0021] Further, in step 3), the detailed steps of noise reduction are as follows:

[0022] Explanation of the meanings of relevant parameters: In this method, there are three different signal parameters, namely: kurtosis, power spectral density, and autocorrelation function;

[0023] (3-1) EWT decomposition process: In this step, the empirical wavelet transform (EWT) technology is adopted to decompose the input signal into different frequency intervals. EWT decomposes by adaptively constructing a wavelet filter bank according to the spectral characteristics of the signal.

[0024] (3-2) Extract subband signals: Based on the EWT decomposition, this step is dedicated to accurately extracting each subband signal from the decomposition result.

[0025] (3-3) Noise identification: This step aims to conduct in-depth analysis on the extracted subband signals to distinguish useful signals and noise components.

[0026] Further, in step 4), the detailed steps of signal reconstruction are as follows:

[0027] (4-1) Inverse empirical wavelet transform: This step is the key link of signal reconstruction, aiming to recombine the subband signals that have undergone noise identification and processing into a complete and enhanced signal.

[0028] First, based on the noise identification result in step 3), the adaptive threshold technology is used to refine each subband. This adaptive threshold method can dynamically adjust the threshold level according to the characteristics of each subband, so as to retain the useful signal components to the greatest extent while effectively suppressing noise. For the subbands identified as dominated by noise, or in extreme cases, completely suppress that subband. Subsequently, we use the inverse empirical wavelet transform (IEWT) algorithm to recombine the processed subband signals.

[0029] (4-2) Effect evaluation: Calculate a series of objective indicators, such as signal-to-noise ratio (SNR) gain, mean square error (MSE), structural similarity index (SSIM), and finally evaluate the noise reduction effect.

[0030] The beneficial effects of the present invention are mainly manifested in:

[0031] 1) Significant denoising effect: Through the combination of Kalman filtering and empirical wavelet transform, the present invention achieves dual denoising in the time domain and frequency domain, effectively removes sudden noise and complex noise, and improves the clarity of the signal.

[0032] 2) Powerful adaptability: The empirical wavelet transform constructs a wavelet filter library by adaptively segmenting the Fourier spectrum of the signal, which can automatically adjust to capture various patterns and structures in the signal, enhancing the flexibility and adaptability of the system.

[0033] 3) Accurate noise identification: Using statistical indicators such as kurtosis, power spectral density and autocorrelation function, the empirical wavelet transform can accurately separate and identify the noise components in the signal, thereby improving the accuracy of noise processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Flowchart of a sensor data denoising method based on empirical wavelet decomposition. DETAILED DESCRIPTION

[0035] The present invention will be further described below in conjunction with the accompanying drawings.

[0036] Reference Figure 1 , a flow chart of a sensor data denoising method based on empirical wavelet decomposition, comprising the following steps:

[0037] Step (1) data collection and filtering, including: collecting sensor data from sensors of the Android device, such as an acceleration sensor and a gyroscope sensor; and filtering the extracted data using a Kalman filter method, and finally generating a file F containing the nine-axis data of the xyz axes of the three sensors. total ;

[0038] In step (1), the detailed steps of data collection and filtering are as follows:

[0039] (1-1) Sensor data acquisition: Initialize the accelerometer, gyroscope, and gravity sensor in the Android device, set an appropriate sampling frequency to ensure sufficient time resolution (for example, 50 Hz, 3 seconds), and the raw sensor data includes: timestamp (accurate to milliseconds), sensor type identifier (accelerometer, gyroscope, etc.), and values ​​of the three axes X, Y, and Z;

[0040] (1-2) Data filtering: The collected data is written into a buffer (e.g., memory) in real time, and a simple outlier detection is performed to remove data points that are obviously beyond the sensor range. At the same time, the collected data is filtered using a Kalman filter, and the filter parameters are as follows:

[0041] The state transfer matrix A = [1, dt; 0, 1], where dt is the sampling time interval;

[0042] The observation matrix H = [1, 0];

[0043] The process noise covariance matrix Q is set according to the sensor characteristics;

[0044] The measurement noise covariance matrix R is set according to the sensor accuracy;

[0045] Output the data stream after Kalman filtering processing, which has removed most of the high-frequency noise and sudden outliers; store the finally processed data in F total as an entire collected data file.

[0046] The steps of separating the sensor axis data in step (2) include: separating the data of different sensors and different axes from the F total file; performing normalization processing on each separated data stream to make it have the same data range and scale;

[0047] In step (2), the detailed steps of separating the sensor axis data are as follows:

[0048] (2-1) Data reading and classification: Open and read the Ftotal file generated in step (1) to ensure correct identification of the file format (CSV or binary);

[0049] (2-1-1) According to the sensor identification in the file, classify the data into different categories; at the same time, further separate the data streams of the X, Y, and Z axes for each category of data;

[0050] (2-1-2) Time series reconstruction, check the timestamps of each data stream to ensure the continuity of the time series; align the start time and end time of all data streams to ensure that the data lengths of all axes are the same.

[0051] (2-1-3) Data normalization processing Calculate the mean (μ) and standard deviation (σ) for each axis of the data stream respectively;

[0052] Use the Z-score normalization method to normalize the data:

[0053] Z = (X - μ) / σ

[0054] where X represents the data to be processed;

[0055] Step (3) Denoising step, including: using the Empirical Wavelet Transform algorithm (EWT) to decompose the data stream of each axis into corresponding different IMFs, and at the same time, statistically calculating the kurtosis, power spectral density (PSD), and autocorrelation function (ACF) values after decomposition, further determining the IMFs that may be noise, and performing adaptive threshold processing to retain the useful signal to the greatest extent while removing noise;

[0056] In step (3), the detailed denoising steps are as follows:

[0057] (3-1) Explanation of the meanings of relevant parameters:

[0058] Kurtosis calculation: Evaluate the peakedness of the signal distribution. For Gaussian noise, the kurtosis is close to 0, and a kurtosis significantly deviating from 0 may indicate that the signal contains non-Gaussian components;

[0059] Power spectral density (PSD): Analyze the energy distribution of the signal in the frequency domain. By observing the PSD, the energy distribution of the signal in the frequency domain can be understood, and the PSD of white noise should be relatively flat;

[0060] Autocorrelation function (ACF): Evaluate the periodicity and correlation of the signal. Noise usually has low autocorrelation. If the ACF rapidly decays to near zero, it may indicate that this component is more like noise;

[0061] (3-2) EWT decomposition process:

[0062] (3-2-1) Apply the Fast Fourier Transform (FFT) to each data stream to obtain its spectrum;

[0063] X(f) = FFT(x(t))

[0064] where x(t) is the input signal and X(f) is its spectrum.

[0065] (3-2-2) Use the adaptive segmentation algorithm to segment the spectrum:

[0066] First, use the local maximum detection algorithm to find the peaks of the spectrum:

[0067] f i = find_peaks(X(f))

[0068] where {f i} are the peak frequencies in the spectrum. Finding the local maxima in the spectrum indicates that the signal has significant energy at these frequencies.

[0069] Next, set the frequency band boundaries at the minimum points between adjacent peaks:

[0070] b i= find_minima(X(f), f i )

[0071] where {b i} are the band boundaries. Between every two adjacent peaks, find the local minima of the spectrum and set the band boundaries at these points.

[0072] Finally, set a minimum band-width threshold and merge overly narrow bands:

[0073] If b i+1 - b i < threshold, then merge bands

[0074] where threshold is the minimum band-width threshold. Set a minimum band-width threshold (e.g., 5% of the total bandwidth) and merge all bands smaller than this threshold.

[0075] Normalize the boundaries to the range [0, π]:

[0076]

[0077] N represents the maximum number of modes (or signal components) in the decomposition.

[0078] (3 - 2 - 3) Construct the empirical wavelet function: For each band [b n-1, bn], define the empirical scaling function Φn(b) and the empirical wavelet function ψn(b):

[0079] Empirical scaling function Φn(b):

[0080]

[0081] Empirical wavelet function ψn(b):

[0082]

[0083] where γ n is the transition-band width parameter and β(a) is a smoothing function, usually chosen as β(a) = 4(35 - 84a + 70a 2 - 20a 3 ).

[0084] (3 - 3) Extract the sub-band signals (IMFs): Using the two functions obtained in the previous step, the original signal f(b) can be decomposed into multiple sub-band signals. This process is achieved through the empirical wavelet transform, and the specific steps are as follows:

[0085] (3 - 3 - 1) Calculate the inner product to obtain the coefficients:

[0086] Approximation coefficient calculation: For each frequency band [bn-1, bn], the approximation coefficient Wfn represents the main features of the original signal within this frequency band. It can be obtained by calculating the inner product of the original signal f(b) and the empirical scaling function Φn(b):

[0087] Wfn = ∫f(b)Φn(b)db

[0088] where f(b) is the original signal and Φn(b) is the corresponding empirical scaling function.

[0089] Detail coefficient calculation: For each frequency band [bn-1, bn], the detail coefficient Wf^{n,ψ} represents the detailed variations of the original signal within this frequency band. It can be obtained by calculating the inner product of the original signal f(b) and the empirical wavelet function ψn(b):

[0090] Wf^{n,ψ} = ∫f(b)ψn(b)db

[0091] where ψn(b) is the corresponding empirical wavelet function.

[0092] (3 - 3 - 2) Reconstructing the sub - band signal:

[0093] Using the calculated approximation coefficients and detail coefficients, we can reconstruct the sub - band signal for each frequency band. The reconstruction formula is as follows:

[0094] fn(b) = WfnΦn(b)+Wf{n,ψ}ψn(b)

[0095] where fn(b) represents the nth sub - band signal, which consists of the approximation component and the detail component of this frequency band.

[0096] (3 - 4) Noise identification:

[0097] (3 - 4 - 1) For each sub - band signal, the following features are calculated:

[0098] Kurtosis (K): Kurtosis is a statistic used to describe the sharpness of the probability distribution shape. It measures the tail thickness of the data distribution and the degree to which the data concentrates towards the center;

[0099] PSD features: Peak frequency (Fp), Bandwidth (BW), Skewness (Sp);

[0100] ACF features: The position of the first zero - crossing point (Zc), Decay rate (Dr), Periodicity (Pe);

[0101] According to experience or pre - experimental results, weights are assigned to each feature:

[0102] W = [W K ,W Fp ,WBW ,W Sp ,W Zc ,W Dr ,W Pe

[0103] For each sub - band, calculate the comprehensive noise index:

[0104] NI = W K *K + W Fp *Fp + W BW *BW + W Sp *Sp + W Zc *Zc + W Dr *Dr + W Pe *Pe

[0105] (3 - 4 - 2) Use the OTSU method or K - means clustering to automatically determine the threshold of the noise index:

[0106] Perform clustering analysis on the NI values of all sub - bands (assuming two categories: noise and signal)

[0107] Calculate the segmentation point with the largest between - class variance as the threshold Th NI ;

[0108] (3 - 4 - 3) For each sub - band, if its NI > Th NI , then mark it as noise.

[0109] Step (4) Signal reconstruction step, including: recombining the denoised IMFs, and reconstructing the clean signal using the inverse empirical wavelet transform; meanwhile, perform quality assessment on the reconstructed signal, calculate indicators such as signal - to - noise ratio (SNR), root - mean - square error (RMSE), etc., to verify the denoising effect.

[0110] In step (4), the detailed steps of signal reconstruction are as follows:

[0111] (4 - 1) Inverse empirical wavelet transform: Recombine the processed IMFs in the original order. Apply IEWT to the recombined signal: f recon (t) = IEWT(ΣIMF_k(t)), where k represents the serial number of the IMF

[0112] (4 - 2) Effect evaluation:

[0113] a) Calculate the signal - to - noise ratio (SNR):

[0114] SNR = 10 * log10(Power signal / Power noise )

[0115] b) Calculate the SNR improvement degree: ​

[0116] SNR improvement = SNR after -SNR before

[0117] c) Calculate the root mean square error (RMSE):

[0118] RMSE = sqrt(mean((f original - f recon )^2))

[0119] d) Calculate the structural similarity index (SSIM) to evaluate the degree of signal structure preservation:

[0120] SSIM = (2μx * μy + C 1 )(2σxy + C 2 ) / ((μx 2 + μy 2 + C 1 )(σx 2 + σy 2 + C2))

[0121] where μx, μy are the means of the original signal and the reconstructed signal, σx 2 , σy 2 are the variances, σxy is the covariance, C 1 and C 2 are constants.

[0122] Experimental results: The improvement degree of SNR is increased, indicating that the noise is effectively suppressed. The RMSE value is decreased, indicating that the reconstructed signal is very close to the original signal. The SSIM value is increased, indicating that the structure of the signal is well preserved.

[0123] The advantages of the present invention are as follows: (1) The denoising effect is significant. By combining Kalman filtering and empirical wavelet transform, double denoising in the time domain and frequency domain is achieved. Kalman filtering effectively removes bursty noise, while empirical wavelet transform (EWT) accurately separates signal components in the frequency domain, which helps to identify and remove complex noise. (2) It has strong adaptability. EWT constructs a wavelet filter bank by adaptively segmenting the Fourier spectrum of the signal and can automatically adjust to capture various patterns and structures in the signal. (3) It can accurately identify noise. EWT can accurately separate different frequency components of the signal. Combining statistical indicators such as kurtosis, power spectral density (PSD), and autocorrelation function (ACF), it can identify the components that appear as noise in specific frequency bands. (4) It is efficient. When processing long time series data, it is efficient and suitable for real-time or near-real-time processing of continuous data streams.

Claims

1. A sensor data denoising method based on empirical wavelet, characterized in that: The steps include: 1) Data collection and filtering: Collect data from multiple sensors, use the Kalman filter algorithm to filter the collected data, and generate a file containing the xyz axis data of multiple sensors. total ; 2) Separate sensor axis data: From file F total In the process, the data of different axes of different sensors are separated; each separated data stream is normalized to have the same data range and scale; 3) Noise reduction: The empirical wavelet transform algorithm EWT is used to decompose the data stream of each axis into different intrinsic modal components IMF. At the same time, the kurtosis, power spectrum density PSD and autocorrelation function ACF values ​​after decomposition are statistically analyzed to further determine the IMF that may be noise, and perform adaptive threshold processing to remove noise to the greatest extent; 4) Signal reconstruction: The denoised IMF is recombined and the clean signal is reconstructed using the inverse empirical wavelet transform. At the same time, the quality of the reconstructed signal is evaluated to verify the denoising effect.

2. The sensor data denoising method based on empirical wavelet according to claim 1, characterized in that: The process of step 1) is as follows: 1.1) Sensor data collection: Initialize the acceleration sensor, gyroscope sensor and gravity sensor in the device, set the sampling frequency and time to collect data; the collected sensor data includes: timestamp, sensor type identification and the values ​​of the three axes of X, Y and Z; 1.2) Data filtering: The collected data is written into the buffer in real time, and outlier detection is performed at the same time to remove data points that exceed the sensor range; the collected data is filtered using a Kalman filter; 1.3) Output the data stream after Kalman filter processing, and store the final processed data in F total as a whole collection data file.

3. The sensor data denoising method based on empirical wavelet according to claim 1, characterized in that: The process of step 2) is as follows: 2.1) According to Document F total The sensor identification in the data is used to classify the data into different categories. At the same time, for each type of data, the data streams of the three axes of X, Y, and Z are further separated. 2.3) Time series reconstruction: check the timestamp of each data stream to ensure the continuity of the time series; align the start and end times of all data streams to ensure that the data length of all axes is consistent; 2.3) Data normalization: Calculate the mean μ and standard deviation σ of the data stream of each axis.

4. The sensor data denoising method based on empirical wavelet according to claim 1, characterized in that: The process of step 3) is as follows: 3.1) EWT decomposition process: The input signal is decomposed into different frequency intervals by using the empirical wavelet transform (EWT). EWT decomposes the signal according to its spectral characteristics by adaptively constructing a wavelet filter bank. 3.1.1) Apply Fast Fourier Transform FFT to each data stream to obtain its spectrum; X(f)=FFT(x(t)) Where x(t) is the input signal and X(f) is its spectrum; 3.1.2) Use adaptive segmentation algorithm to segment the spectrum; Use the local maximum detection algorithm to find the peaks of the spectrum: f i =find_peaks(X(f)) where {f i } is the peak frequency in the spectrum, find the local maximum in the spectrum; Set the band boundaries at the minimum points between adjacent peaks: b i =find_minima(X(f),f i ) Where {b i } is the frequency band boundary. Between every two adjacent peaks, the local minimum of the spectrum is found and the frequency band boundary is set; Set the minimum bandwidth threshold to merge too narrow bands: If b i+1 -b i <threshold,then merge bands Where threshold is the minimum bandwidth threshold. A minimum bandwidth threshold is set and all frequency bands smaller than the threshold are merged. Normalize the band boundaries to the range [0,π]: N represents the maximum number of modes in the decomposition; 3.1.3) Constructing empirical wavelet function: For each frequency band [b n-1, bn], define the empirical scaling function Φn(b) and the empirical wavelet function ψn(b): 3.2) Extracting sub-band signals: Based on the EWT decomposition, extract each sub-band signal from the decomposition result; 3.2.1) Calculate the inner product to obtain the coefficients: Approximate coefficient calculation: For each frequency band [bn-1, bn], the approximate coefficient Wfn represents the main characteristics of the original signal in this frequency band; it is obtained by calculating the inner product of the original signal f(b) and the empirical scaling function Φn(b): Wfn=∫f(b)Φn(b)db Among them, f(b) is the original signal, Φn(b) is the corresponding empirical scaling function; Detail coefficient calculation: For each frequency band [bn-1,bn], the detail coefficient Wf^{n,ψ} represents the detail change of the original signal within the frequency band; it is obtained by calculating the inner product of the original signal f(b) and the empirical wavelet function ψn(b): Wf^{n,ψ}=∫f(b)ψn(b)db Among them, ψn(b) is the corresponding empirical wavelet function; 3.2.2) Reconstruct subband signal: The subband signal of each frequency band is reconstructed using the calculated approximate coefficients and detail coefficients. The reconstruction formula is as follows: fn(b)=WfnΦn(b)+Wf{n,ψ}ψn(b) Wherein, fn(b) represents the nth subband signal; 3.3) Noise identification: Analyze the extracted sub-band signals to determine the noise components; 3.3.1) For each subband signal, calculate the following features: Kurtosis: Kurtosis is a statistic used to describe the sharpness of the shape of a probability distribution. It measures the thickness of the tail of the data distribution and the degree to which the data set tends to the center. PSD characteristics: peak frequency Fp, bandwidth BW, skewness Sp; ACF characteristics: first zero crossing point position Zc, decay rate Dr, periodicity Pe; Assign weights to each feature: In=[In K ,IN Fp ,IN BW ,IN Sp ,IN Zc ,IN Dr ,IN Pe ] For each subband, calculate the comprehensive noise index: NI=W K *K+W Fp *Fp+W BW *BW+W Sp *Sp+W Zc *Zc+W Dr *Dr+W Pe * Or 3.3.2) Use the OTSU method or K-means clustering to automatically determine the threshold of the noise indicator: Perform cluster analysis on the NI values ​​of all sub-bands and calculate the segmentation point with the largest inter-class variance as the threshold Th NI ; 3.3.3) For each subband, if its NI>Th NI , it is marked as noise.

5. The sensor data denoising method based on empirical wavelet according to claim 1, characterized in that: The process of step 4) is as follows: 4.1) Based on the noise identification result in step 3), each sub-band is processed by using an adaptive threshold algorithm; the processed sub-band signals are recombined by using an inverse empirical wavelet transform (IEWT) algorithm; The inverse empirical wavelet transform is: recombining the processed IMFs in the original order; applying IEWT to the recombined signal: f recon (t) = IEWT (ΣIMF_k (t)), k represents the sequence number of IMF; 4.2) Effect evaluation: Calculate a series of objective indicators and ultimately evaluate the noise reduction effect; a) Calculate the signal-to-noise ratio SNR: SNR=10*log10(Power signal / Power noise ) Among them, Power signal Indicates signal power, Power noise represents the noise power; b) Calculate the SNR improvement: SNR improvement =SNR after -SNR before Among them, SNR after Indicates the signal-to-noise ratio after system processing, SNR before represents the signal-to-noise ratio before processing; c) Calculate the root mean square error RMSE: RMSE=sqrt(mean((f original -f recon )^2)) Among them, Sqrt(*) means taking the square root of *, Mean(*) means finding the average of *, and f original represents the original signal, f recon represents the reconstruction signal; d) Calculate the structural similarity index SSIM to evaluate the degree of signal structure preservation: SSIM=(2μx*μy+C1)(2σxy+C2) / ((μx 2 +μy 2 +C1)(σx 2 +σy 2 +C2)) Where μx, μy are the means of the original signal and the reconstructed signal, σx 2 ,σy 2 is the squared difference, σxy is the covariance, and C1 and C2 are constants.

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