Signal denoising method and system based on improved empirical mode decomposition and wavelet threshold function

Abstract

The present invention discloses a signal denoising method based on improved empirical mode decomposition and wavelet threshold function, which relates to the field of signal denoising, including: curve fitting the monitored original signal through replaced fully adaptive noise set empirical mode decomposition to solve the envelope, and obtaining the modal component group of the original signal through the envelope; filtering out the modal components that meet the coefficient standard in the modal component group as the target modal components through the preset correlation coefficient; obtaining the target wavelet threshold function through the hard threshold function and the soft threshold function using the preset adjustment parameters; performing wavelet decomposition on each target modal component, and filtering out the wavelet coefficients within the preset amplitude range using the target wavelet threshold function; and reconstructing the filtered wavelet coefficients using the inverse wavelet transform to obtain the denoised signal. The present invention performs double denoising on the signal by combining the improved CEEMDAN with the improved wavelet threshold function, which greatly improves the denoising effect of the signal.

Description

Technical Field

[0001] The present invention relates to the field of signal denoising, and in particular to a signal denoising method and system based on improved empirical mode decomposition and wavelet threshold function. Background Art

[0002] The design of hardware and acquisition software can reduce the influence of noise to a certain extent during the signal acquisition process, but it cannot completely avoid the interference of noise data. Compared with other research methods in the same field, there are methods that directly collect data for big data analysis or extract several commonly used time-frequency domain feature quantities for analysis after collecting data. For the former, the information richness of the data set is guaranteed, but there are irrelevant noise signals that interfere with data analysis; for the latter, although the amount of data calculation is reduced, only limited manual feature quantity selection is used, which is easy to lose a lot of information in the signal, and there may be other highly correlated features that are not extracted.

[0003] In traditional signal processing, Empirical Mode Decomposition (EMD) is widely used. It can adaptively decompose signals into signal components of different scales, avoiding the trouble of manually selecting wavelet basis and decomposition level in wavelet decomposition. However, it also has obvious disadvantages, such as modal confusion and endpoint effect, which makes the same intrinsic mode function (IMF) component contain signals of obviously different scales or different IMF components contain signals of obviously the same scale. To solve this problem, some people have proposed the average empirical mode decomposition method and complementary set mode decomposition method. They are both optimizations of empirical mode decomposition, and the introduction of complementary noise is aimed at eliminating the influence of added noise. Based on these methods, some scholars have proposed an improved algorithm - Complete EEMD with Adaptive Noise (CEEMDAN). The difference between it and other algorithms is that the modal components of auxiliary noise are added to the residual components of the solved signal, and the modal components obtained after empirical mode decomposition are averaged overall. After continuous optimization, CEEMDAN performs better than EMD in signal decomposition, but in the process of solving the envelope, CEEMDAN still uses cubic spline interpolation. The second-order derivative of this method is continuous, which may cause over-envelope or under-envelope phenomenon in the process of solving the envelope, which is particularly obvious in non-stationary signals. Therefore, it is urgent to improve the CEEMDAN method to improve the denoising effect.

[0004] In addition, wavelet threshold denoising in the prior art is widely used in the field of signal denoising. After the original signal is decomposed by wavelet, the wavelet coefficients with larger amplitudes are mostly effective components, while the wavelet coefficients with smaller amplitudes are generally noise components. Since the effective components and noise components have been separated from the original signal by wavelet transform, we only need to set a reasonable wavelet coefficient threshold, retain the wavelet coefficients larger than the threshold, discard the wavelet coefficients smaller than the threshold, and finally use the inverse wavelet transform to process the filtered wavelet coefficients to reconstruct a clean signal with the noise filtered out. The idea of ​​the wavelet threshold denoising process is to select a suitable threshold and a threshold function combined with the threshold, calculate the wavelet coefficients through the threshold function, and automatically filter the wavelet coefficients. The threshold function and the wavelet threshold are related to the selection of effective components and noise components. Reasonable settings can obtain ideal noise reduction effects. Threshold function is the core component of wavelet denoising, and commonly used ones are hard threshold function and soft threshold function. Although the soft and hard threshold methods are the most commonly used, they also have some defects. For the hard threshold method, since the function is discontinuous, the reconstructed signal will show oscillation and fluctuation, and there will be a large deviation; for the soft threshold method, although the function is continuous, there is always a deviation between the reconstructed signal and the real effective signal, so it is urgent to improve the wavelet threshold function to improve the noise reduction effect.

[0005] Although the improved CEEMDAN method can decompose the signal into the eigenmode function well, the obtained high frequency is directly discarded to achieve the denoising effect. However, although such a denoising method filters out part of the noise, it also discards the high frequency components in the original signal at the same time, and there are still some noise signals in other order modal components. Therefore, the present invention combines the improved CEEMDAN method with the improved wavelet threshold function while improving the CEEMDAN method and the wavelet threshold function to achieve the best denoising effect. Summary of the invention

[0006] In order to solve the problem that the CEEMDAN method may cause over-envelope or under-envelope phenomena in the process of solving the envelope line, and the problem that the function is discontinuous in the soft and hard threshold methods of the wavelet threshold denoising method, and there is always a deviation between the reconstructed signal and the real effective signal, while solving the problem that the improved CEEMDAN method discards the high-frequency components in the original signal at the same time, and there are still some noise signals in other modal components, the present invention combines the improved CEEMDAN method with the improved wavelet threshold function, and proposes a signal denoising method based on improved empirical mode decomposition and wavelet threshold function, which is used to denoise the monitored original signal, including the steps of:

[0007] S01: Use the piecewise cubic Hermite interpolation method to replace the cubic spline interpolation method in the fully adaptive noise ensemble empirical mode decomposition, perform curve fitting on the monitored original signal through the replaced fully adaptive noise ensemble empirical mode decomposition to solve the envelope, and obtain the modal component group of the original signal through the envelope; select the modal component that meets the coefficient standard in the modal component group as the target modal component through the preset correlation coefficient;

[0008] S02: Obtaining a target wavelet threshold function by using a hard threshold function and a soft threshold function with preset adjustment parameters;

[0009] S03: performing wavelet decomposition on each target modal component to obtain its corresponding wavelet coefficient, and using the target wavelet threshold function to filter out the wavelet coefficients within the preset amplitude range; using the inverse wavelet transform to reconstruct the filtered wavelet coefficients to obtain a denoised signal.

[0010] Furthermore, the modal component group includes modal components of several orders;

[0011] The preset correlation coefficient in step S01 is the correlation coefficient between the modal component and the original signal, and its formula expression is:

[0012]

[0013] Where L represents the length of the original signal in the modal component, n = 1, 2, ..., L, k represents the order of the modal component in the modal component group, s(n) represents the original signal at the nth point, and IMF k (n) represents the modal component corresponding to the n-th point original signal in the k-th modal component; r is the correlation coefficient between the k-th modal component and the original signal.

[0014] Furthermore, the target modal component includes modal components of several orders, and the formula expression of the target wavelet threshold function in step S02 is:

[0015]

[0016] In the formula, m is the preset adjustment parameter, j is the number of wavelet decompositions, k is the order of the modal component in the target modal component, λ is the preset threshold, and w j,k is the wavelet coefficient of the target wavelet threshold function of the k-th order modal component at the j-th wavelet decomposition, and tanh is the hyperbolic tangent function.

[0017] Furthermore, the specific method for solving the envelope in step S01 is:

[0018] Obtain the maximum point, minimum point and extreme symmetric point of the signal time domain spectrum through the original signal;

[0019] The envelope is obtained by using the maximum, minimum and extreme symmetric points of the signal time domain spectrum through the piecewise cubic Hermite interpolation method.

[0020] Furthermore, the screening method in step S01 is specifically as follows:

[0021] Obtain each modal component except the first and last order as the intermediate modal components;

[0022] It is determined in turn whether the correlation coefficients of the intermediate-order modal components are all smaller than the correlation coefficients of the upper and lower-order modal components. If so, the intermediate-order modal component is taken as the local modal component, the next-order modal component of the local modal component is taken as the boundary modal component, and the local modal component and the boundary modal component are taken as the target modal components.

[0023] The present invention also proposes a signal denoising system based on improved empirical mode decomposition and wavelet threshold function, which is used to denoise the monitored original signal, including:

[0024] The empirical mode decomposition module is used to replace the cubic spline interpolation method in the fully adaptive noise ensemble empirical mode decomposition with the piecewise cubic Hermite interpolation method, and to perform curve fitting on the monitored original signal through the replaced fully adaptive noise ensemble empirical mode decomposition to solve the envelope, and to obtain the modal component group of the original signal through the envelope; and to select the modal component that meets the coefficient standard in the modal component group as the target modal component through the preset correlation coefficient;

[0025] A wavelet threshold function module is used to obtain a target wavelet threshold function by using a hard threshold function and a soft threshold function with preset adjustment parameters;

[0026] The denoising module is used to obtain the corresponding wavelet coefficients by performing wavelet decomposition on each target modal component, and to select the wavelet coefficients within the preset amplitude range using the target wavelet threshold function; and to reconstruct the selected wavelet coefficients using the inverse wavelet transform to obtain the denoised signal.

[0027] Furthermore, the modal component group includes modal components of several orders;

[0028] The preset correlation coefficient in the empirical mode decomposition module is the correlation coefficient between the modal component and the original signal, and its formula expression is:

[0029]

[0030] Where L represents the length of the original signal in the modal component, n = 1, 2, ..., L, k represents the order of the modal component in the modal component group, s(n) represents the original signal at the nth point, and IMF k(n) represents the modal component corresponding to the n-th point original signal in the k-th modal component; r is the correlation coefficient between the k-th modal component and the original signal.

[0031] Furthermore, the target modal component includes modal components of several orders, and the formula expression of the target wavelet threshold function in the wavelet threshold function module is:

[0032]

[0033] In the formula, m is the preset adjustment parameter, j is the number of wavelet decompositions, k is the order of the modal component in the target modal component, λ is the preset threshold, and w j,k is the wavelet coefficient of the target wavelet threshold function of the k-th order modal component at the j-th wavelet decomposition, and tanh is the hyperbolic tangent function.

[0034] Furthermore, the specific method for solving the envelope line in the empirical mode decomposition module includes: an extreme value acquisition unit, which is used to obtain the maximum points, minimum points and extreme symmetric points of the signal time domain spectrum through the original signal; an envelope line acquisition unit, which is used to obtain the envelope line using the maximum points, minimum points and extreme symmetric points of the signal time domain spectrum through the piecewise cubic Hermite interpolation method.

[0035] Furthermore, the screening method in the empirical mode decomposition module is specifically as follows: obtaining each order modal component except the first order and the last order as the intermediate order modal component; judging in turn whether the correlation coefficient of each intermediate order modal component is smaller than the correlation coefficient of its upper and lower order modal components; if so, taking the intermediate order modal component as the local modal component, taking the next order modal component of the local modal component as the boundary modal component, and taking the local modal component and the boundary modal component as the target modal components.

[0036] Compared with the prior art, the present invention has at least the following beneficial effects:

[0037] (1) The cubic Hermite interpolation method can fit the curve well. Compared with the cubic spline interpolation method, it has better approximation ability and high fitting accuracy. The present invention uses piecewise cubic Hermite interpolation to solve the envelope. Compared with the traditional cubic spline interpolation method, as long as the first-order derivative of the interpolation point is reasonably selected, the interpolation curve can remain monotonous, avoiding the phenomenon of over-envelope and under-envelope, and improving the denoising effect;

[0038] (2) The present invention obtains the target wavelet threshold function by using a hard threshold function and a soft threshold function with preset adjustment parameters, which better combines the hard and soft threshold functions, and solves the problem that in the hard threshold method, the reconstructed signal shows oscillation and fluctuation due to the discontinuity of the function, resulting in a large deviation; and in the soft threshold method, although the function is continuous, there is always a deviation between the reconstructed signal and the real effective signal;

[0039] (3) The present invention combines the improved CEEMDAN method with the improved wavelet threshold function to solve the problem that although the improved CEEMDAN can decompose the signal into the eigenmode function well and directly discard the obtained high frequency to achieve the denoising effect, such denoising method filters out part of the noise, but also discards the high frequency components in the original signal at the same time, and there are still some noise signals in other order modal components, which greatly improves the denoising effect of the signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A method flow chart of a signal denoising method based on improved empirical mode decomposition and wavelet threshold function;

[0041] Figure 2 It is the system structure diagram of the signal denoising system based on improved empirical mode decomposition and wavelet threshold function;

[0042] Figure 3 It is the modal component diagram corresponding to the radial vibration signal. DETAILED DESCRIPTION

[0043] The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solution of the present invention, but the present invention is not limited to these embodiments.

[0044] Embodiment 1

[0045] At present, since the automatic tool changing technology of CNC machine tools is relatively mature, what is lacking is the accurate judgment of the tool status. If the tool wear status information is not grasped in time, and unqualified tools are continued to be used when the tools should be replaced, it will cause the quality of the processed products to be unqualified, and even cause the tool to break and the machine tool to be damaged. In order to realize the effective monitoring of the tool wear status, the key is to reasonably select and accurately obtain the monitoring signal of the tool wear, and reduce the noise after obtaining it to accurately obtain the tool wear status. Therefore, this embodiment selects to use the vibration signal (including radial vibration signal, tangential vibration signal, axial vibration signal) and sound signal monitored during the operation of the CNC machine tool as the denoising object for illustration. Although the vibration signal and the sound signal also have the disadvantage of being easily affected by environmental interference, the denoising method of the present invention can greatly reduce their disadvantages and expand their advantages.

[0046] In order to solve the problem that the improved CEEMDAN method discards the high-frequency components in the original signal at the same time, and other order modal components still have some noise signals, and the problem that the function is discontinuous in the soft and hard threshold methods of the wavelet threshold denoising method, and there is always a deviation between the reconstructed signal and the real effective signal, the present invention combines the improved CEEMDAN method with the improved wavelet threshold function, such as Figure 1 As shown, the present invention proposes a signal denoising method based on improved empirical mode decomposition and wavelet threshold function.

[0047] It is used to denoise the original signal monitored, including the steps of:

[0048] S01: Use the piecewise cubic Hermite interpolation method to replace the cubic spline interpolation method in the fully adaptive noise ensemble empirical mode decomposition, perform curve fitting on the monitored original signal through the replaced fully adaptive noise ensemble empirical mode decomposition to solve the envelope, and obtain the modal component group of the original signal through the envelope; select the modal component that meets the coefficient standard in the modal component group as the target modal component through the preset correlation coefficient;

[0049] In this embodiment, the specific method of obtaining the modal component group of the original signal through the replaced fully adaptive noise ensemble empirical mode decomposition (CEEMDAN) includes the following steps:

[0050] Step 1: Add the positive and negative paired auxiliary Gaussian white noise signals to the signal to be decomposed (i.e. the original signal) s(t) to obtain a new signal s(t)+(-1) q a0n i (t); t is the time variable (time in the signal time domain, s(t) is a continuous signal), s(t) represents the original signal corresponding to time t;

[0051] Obtain the maximum point, minimum point and extreme symmetric point of the signal time domain spectrum through the new signal;

[0052] The envelope is obtained by using the maximum, minimum and extreme symmetric points of the signal time domain spectrum through the piecewise cubic Hermite interpolation method, and the modal component group is obtained by using the envelope (the application of the cubic Hermite interpolation method to EMD decomposition can further improve the CEEMDAN algorithm and retain more original signal information), specifically:

[0053] Perform N EMD decompositions on the new signal, thereby calculating N first-order modal components

[0054] s(t)+(-1) q a0n i (t) = IMF1i (t)+r1 i (t) (Formula 1);

[0055] Where n i (t) is the auxiliary Gaussian white noise signal added during the i-th EMD decomposition, (i=1,2,…,N); a0 is the noise amplitude; q is 1 or 2, which is used to ensure that the added auxiliary Gaussian white noise signal is a positive and negative pair; is the first-order residual signal of the ith EMD decomposition, and the final first-order modal component That is, N IMF1 i The average value of (t):

[0056]

[0057] From equations 1 and 2, we can see that the added auxiliary Gaussian white noise signals are positive and negative pairs, and their interference with the decomposition process is offset, so that The noise contained is greatly reduced. At the same time, the final first-order residual signal is obtained as:

[0058]

[0059] Step 2: The j-1th order residual signal r obtained after decomposition j-1 (t) Continue to add specific positive and negative pairs of auxiliary Gaussian white noise signals to obtain the signal: r j-1 (t)+(-1) q a j-1 Ex -1 (n i (t)), and then continue to perform EMD decomposition N times using the piecewise cubic Hermite interpolation method to obtain N j-th order eigenmode components

[0060] r j-1 (t)+(-1) q a j-1 E j-1 (n i (t)) = IMF j i (t)+r j i (t) (Formula 4);

[0061] Where j represents the order of the modal component, E j-1 (n i (t)) represents the auxiliary Gaussian white noise signal n added during the i-th decomposition i (t) Perform EMD decomposition using piecewise cubic Hermite interpolation method, where i = 1, 2, ..., N; a j-1is the noise amplitude, is the j-th order residual signal of the i-th EMD decomposition; for N IMF j i (t) Take the average value to get the final j-th order modal component

[0062]

[0063] Repeat step 2 continuously until the residual signal (assuming it is r k When the number of extreme points of (t)) is less than 2, K-order modal components and the final residual signal R(t) are obtained. It should be noted that the original signal can be represented by the calculated K-order modal components and the final residual signal R(t):

[0064] In the formula, represents the final k-th order modal component (i.e., taking the average of N k-th order modal components);

[0065] By improving the algorithm flow of the above CEEMDAN, the cubic Hermite interpolation method is more ideal for solving the signal envelope. By adding an auxiliary Gaussian white noise signal during decomposition, the interference to the residual signal of each layer is greatly reduced, so the decomposition result is more accurate and the signal denoising effect is improved.

[0066] The modal component group includes modal components of several orders, and the modal components of several orders include high-frequency modal components;

[0067] The preset correlation coefficient in step S01 is the correlation coefficient between the modal component and the original signal, and its formula expression is:

[0068]

[0069] Where L represents the length of the original signal in the modal component, n = 1, 2, ..., L (represents the number of sampling points), k represents the order of the modal component in the modal component group, s(n) represents the original signal at the nth point (sampling point signal), and IMF k (n) represents the modal component corresponding to the n-th point original signal in the k-th order modal component; It represents the average value of the modal component corresponding to the n-th point original signal in the k-th modal component; r is the correlation coefficient between the k-th modal component and the original signal.

[0070] This embodiment is now described by taking the radial vibration signal, tangential vibration signal, axial vibration signal and sound signal monitored during the operation of a numerical control machine tool as an example ( Figure 3The modal component group (IMF1-IMF10) and the final residual remainder diagram (indicated as R in the figure) obtained after the monitored radial vibration signal, i.e., the original signal, is decomposed and processed in the above steps of the present invention, the numbers on each modal component in the figure are signal amplitudes, and the number of sampling points is 2000), and the correlation coefficients corresponding to each type of signal are obtained by processing each signal in the above steps of the present invention as shown in the following Table 1 (IMF1 in Table 1 represents the first-order modal component, IMF2 represents the second-order modal component, and so on):

[0071] Radial vibration signal Tangential vibration signal Axial vibration signal Sound signal IMF1 0.7568 0.7570 0.6843 0.0274 IMF2 0.4746 0.3990 0.5301 0.0208 IMF3 0.4015 0.3843 0.2923 0.0176 IMF4 0.2346 0.3900 0.5794 0.1363 IMF5 0.2577 0.2351 0.1809 0.2301 IMF6 0.0450 0.1222 0.1281 0.4626 IMF7 0.1535 0.1454 0.1350 0.4786 IMF8 0.0752 0.1535 0.1383 0.7040 IMF9 0.0017 0.0428 0.1259 0.3634 IMF10 0.0039 0.0130 0.0451 0.2526

[0072] The modal components that meet the coefficient standard in the modal component group are screened out by preset correlation coefficients as target modal components, wherein the screening method is specifically as follows:

[0073] Obtain each modal component except the first and last order as the intermediate modal components;

[0074] It is determined in turn whether the correlation coefficients of the intermediate-order modal components are all smaller than the correlation coefficients of the upper and lower-order modal components (smaller than the correlation coefficients of the upper and lower-order modal components is the coefficient standard). If so, the intermediate-order modal component is taken as the local modal component, the next-order modal component of the local modal component is taken as the boundary modal component, and the local modal component and the boundary modal component are taken as the target modal components, and the target modal component also includes a preset number of high-frequency modal components.

[0075] In the table, IMF4 corresponding to the radial vibration signal is a local modal component, and thus IMF5 is a boundary modal component; IMF3 corresponding to the tangential vibration signal, axial vibration signal and sound signal is a local modal component, and thus IMF4 is a boundary modal component. Considering that there are slight differences in the signals of each sampling point, in order to ensure that the noisy modal components are denoised as much as possible (among which IMF1 and IMF2 are high-frequency modal components), this embodiment selects the modal components of IMF1 to IMF5 as the signal data for the next wavelet denoising process, so as to solve the problem that the improved CEEMDAN method discards the high-frequency components in the original signal at the same time, and there are still some noise signals in other modal components.

[0076] S02: Obtaining a target wavelet threshold function by using a hard threshold function and a soft threshold function with preset adjustment parameters;

[0077] The formula expression of the hard threshold function is:

[0078]

[0079] The formula expression of the soft threshold function is:

[0080]

[0081] In the formula, sgn(·) is the sign function, λ is the threshold value. Through the calculation of the threshold function, the wavelet coefficients whose absolute values ​​are less than the threshold value are set to zero, which plays the role of filtering the noise component. The formula for obtaining the threshold value is:

[0082]

[0083] Where σ is the noise variance, and the estimation formula is:

[0084]

[0085] The soft and hard threshold methods are the most commonly used, but they also have some defects. For the hard threshold method, w j，k There is discontinuity at ±λ, which will make the reconstructed signal show oscillation and fluctuation, with large deviation; for the soft threshold method, although w j，k Continuous at ±λ, but at |w j，k |≥λ interval, the original w j，k With the new j，k There is always a difference of λ, which will also cause the reconstructed signal to always have a deviation from the real effective signal. j，k Continuous at ±λ, let the new w j，k In |w j，k |≥λ interval with the original w j，k If the values ​​of the target wavelet threshold function are equal, the noise reduction achieved by wavelet denoising will be more accurate. Therefore, the present invention designs a target wavelet threshold function to solve the above technical problems.

[0086] The target modal component includes modal components of several orders, and the formula expression of the target wavelet threshold function in step S02 is:

[0087]

[0088] In the formula, m is the preset adjustment parameter, j is the number of wavelet decompositions, k is the order of the modal component in the target modal component, λ is the preset threshold, and w j,k is the wavelet coefficient of the target wavelet threshold function of the k-th order modal component at the j-th wavelet decomposition, and tanh is the hyperbolic tangent function.

[0089] In the formula, m is the preset adjustment parameter. When m→0, μ→1. At this time, the function image is very close to the soft threshold function. The difference is that it uses the hyperbolic tangent function to replace the sign function, and applies nonlinear functions to gradually compress the wavelet coefficients outside the threshold absolute value range to make the function more continuous. When m→∞, μ→0, at this time, the function image is very close to the hard threshold function. m takes a certain constant, and |w j，k|=λ, then μ→1, w j，k →0, that is, w j，k Continuous at ±λ; when |w j，k When |→∞, μ→0, w j，k →w j，k It can be seen that the target wavelet threshold function of the present invention skillfully combines the advantages of the soft and hard threshold functions, which can make the function continuous and also make the original w j，k With the new j，k The deviation between them is no longer constant. When |w j，k When |-λ is large enough, μ→0, and the difference between the new wavelet coefficient and the original wavelet coefficient is basically zero, which can effectively reduce the deviation between the denoised signal and the real effective signal. A smooth transition curve is set in the target wavelet threshold function, and its asymptote coincides with the hard threshold function, which retains the advantages of soft and hard thresholds while overcoming their respective defects and improving the denoising effect of the signal.

[0090] S03: performing wavelet decomposition on each target modal component to obtain its corresponding wavelet coefficient, and using the target wavelet threshold function to filter out the wavelet coefficients within the preset amplitude range; using the inverse wavelet transform to reconstruct the filtered wavelet coefficients to obtain a denoised signal.

[0091] In this embodiment, the db4 wavelet is used to perform a six-layer decomposition on the selected IMF1 to IMF5 modal components. The present invention denoises the original signal based on the improved empirical mode decomposition and the improved wavelet threshold function, which retains more features in the original signal (it does not discard the high-frequency components in the original signal at the same time, and retains the high-frequency modal components), and selects the wavelet coefficients within the preset amplitude range through the wavelet threshold function. Finally, the selected wavelet coefficients are processed by the inverse wavelet transform to reconstruct a clean signal (i.e., the denoised signal) with the noise filtered out.

[0092] In order to further quantify the denoising effect of this method, taking the radial vibration signal as an example, two evaluation criteria, root mean square error (RMSE) and signal to noise ratio (SNR), are introduced to compare the actual effects of the six denoising methods. The calculation formulas are:

[0093]

[0094]

[0095] Where y(n) is the original signal, is the denoised signal, and L is the signal length. The signal-to-noise ratio (SNR) is the ratio of signal to noise. The larger the signal-to-noise ratio, the better the denoising effect. The root mean square error (RMSE) is the root of the ratio of the square of the difference between the original signal and the denoised signal to the number of sampling points. The smaller the root mean square error, the better the denoising effect. The following table (Table 2) compares the denoising indicators of different denoising methods.

[0096]

[0097] Compared with several other denoising algorithms, the denoising method of the present invention has a higher signal-to-noise ratio, indicating that more useful components are retained; the root mean square error is smaller, indicating that more noise components are filtered out, so the denoising method of the present invention has a better noise reduction effect.

[0098] The present invention combines the improved CEEMDAN with the improved wavelet threshold function to perform double denoising on the signal, thereby greatly improving the denoising effect of the signal.

[0099] Embodiment 2

[0100] like Figure 2 As shown, the present invention also proposes a signal denoising system based on improved empirical mode decomposition and wavelet threshold function, which is used to denoise the monitored original signal, including:

[0101] The empirical mode decomposition module is used to replace the cubic spline interpolation method in the fully adaptive noise ensemble empirical mode decomposition with the piecewise cubic Hermite interpolation method, and to perform curve fitting on the monitored original signal through the replaced fully adaptive noise ensemble empirical mode decomposition to solve the envelope, and to obtain the modal component group of the original signal through the envelope; and to select the modal component that meets the coefficient standard in the modal component group as the target modal component through the preset correlation coefficient;

[0102] The cubic Hermite interpolation method can fit the curve very well, and has better approximation ability and high fitting accuracy than the cubic spline interpolation method. The present invention uses piecewise cubic Hermite interpolation to solve the envelope line. Compared with the traditional cubic spline interpolation method, as long as the first-order derivative of the interpolation point is reasonably selected, the interpolation curve can remain monotonic, avoiding the phenomenon of over-envelope and under-envelope, and improving the denoising effect.

[0103] A wavelet threshold function module is used to obtain a target wavelet threshold function by using a hard threshold function and a soft threshold function with preset adjustment parameters;

[0104] The present invention obtains the target wavelet threshold function by using preset adjustment parameters through the hard threshold function and the soft threshold function, which better combines the hard and soft threshold functions, and solves the problem that in the hard threshold method, due to the discontinuity of the function, the reconstructed signal shows oscillation and fluctuation, resulting in a large deviation; and in the soft threshold method, although the function is continuous, there is always a deviation between the reconstructed signal and the real effective signal.

[0105] The denoising module is used to obtain the corresponding wavelet coefficients by performing wavelet decomposition on each target modal component, and to select the wavelet coefficients within the preset amplitude range using the target wavelet threshold function; and to reconstruct the selected wavelet coefficients using the inverse wavelet transform to obtain the denoised signal.

[0106] The modal component group includes modal components of several orders;

[0107] The preset correlation coefficient in the empirical mode decomposition module is the correlation coefficient between the modal component and the original signal, and its formula expression is:

[0108]

[0109] Where L represents the length of the original signal in the modal component, n = 1, 2, ..., L, k represents the order of the modal component in the modal component group, s(n) represents the original signal at the nth point, and IMF k (n) represents the modal component corresponding to the n-th point original signal in the k-th order modal component; r is the correlation coefficient between the k-th order modal component and the original signal.

[0110] The target modal component includes modal components of several orders, and the formula expression of the target wavelet threshold function in the wavelet threshold function module is:

[0111]

[0112] In the formula, m is the preset adjustment parameter, j is the number of wavelet decompositions, k is the order of the modal component in the target modal component, λ is the preset threshold, and w j,k is the wavelet coefficient of the target wavelet threshold function of the k-th order modal component at the j-th wavelet decomposition, and tanh is the hyperbolic tangent function.

[0113] The specific method for solving the envelope line in the empirical mode decomposition module includes: an extreme value acquisition unit, which is used to obtain the maximum point, minimum point and extreme symmetric point of the signal time domain spectrum through the original signal; an envelope line acquisition unit, which is used to obtain the envelope line using the maximum point, minimum point and extreme symmetric point of the signal time domain spectrum through the piecewise cubic Hermite interpolation method.

[0114] The screening method in the empirical mode decomposition module is specifically as follows: obtaining each order modal component except the first order and the last order as the intermediate order modal component; judging in turn whether the correlation coefficient of each intermediate order modal component is smaller than the correlation coefficient of its upper and lower order modal components; if so, taking the intermediate order modal component as the local modal component, taking the next order modal component of the local modal component as the boundary modal component, and taking the local modal component and the boundary modal component as the target modal components.

[0115] The present invention combines the improved CEEMDAN method with the improved wavelet threshold function to solve the problem that although the improved CEEMDAN can well decompose the signal into the eigenmode function and directly discard the obtained high frequency to achieve the denoising effect, such denoising method filters out part of the noise, but also discards the high frequency components in the original signal at the same time, and there are still some noise signals in other order modal components, thereby greatly improving the denoising effect of the signal.

[0116] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0117] In addition, in the present invention, descriptions such as "first", "second", "one", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0118] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0119] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

Claims

1. A signal denoising method based on improved empirical mode decomposition and wavelet threshold function, characterized in that: It is used to denoise the original signal monitored, including the steps of: S01: Using the piecewise cubic Hermite interpolation method to replace the cubic spline interpolation method in the fully adaptive noise ensemble empirical mode decomposition, curve fitting is performed on the monitored original signal through the replaced fully adaptive noise ensemble empirical mode decomposition to solve the envelope, and the modal component group of the original signal is obtained through the envelope; the modal component that meets the coefficient standard in the modal component group is screened out as the target modal component through the preset correlation coefficient; the modal component group contains modal components of several orders; The preset correlation coefficient in step S01 is the correlation coefficient between the modal component and the original signal, and its formula expression is: Where L represents the length of the original signal in the modal component, n = 1, 2, ..., L, k represents the order of the modal component in the modal component group, s(n) represents the original signal at the nth point, and IMF k (n) represents the modal component corresponding to the original signal at the nth point in the kth modal component; r is the correlation coefficient between the kth modal component and the original signal; S02: Obtain a target wavelet threshold function by using a hard threshold function and a soft threshold function with preset adjustment parameters; the target modal component includes modal components of several orders, and the formula expression of the target wavelet threshold function in step S02 is: In the formula, m is the preset adjustment parameter, j is the number of wavelet decompositions, k is the order of the modal component in the target modal component, λ is the preset threshold, and w j,k is the wavelet coefficient of the target wavelet threshold function of the k-th order modal component at the j-th wavelet decomposition, and tanh is the hyperbolic tangent function; S03: performing wavelet decomposition on each target modal component to obtain its corresponding wavelet coefficient, and using the target wavelet threshold function to screen out the wavelet coefficient within a preset amplitude range; The selected wavelet coefficients are reconstructed using inverse wavelet transform to obtain the denoised signal.

2. The signal denoising method based on improved empirical mode decomposition and wavelet threshold function according to claim 1, characterized in that: The specific method for solving the envelope in step S01 is: Obtain the maximum point, minimum point and extreme symmetric point of the signal time domain spectrum through the original signal; The envelope is obtained by using the maximum, minimum and extreme symmetric points of the signal time domain spectrum through the piecewise cubic Hermite interpolation method.

3. The signal denoising method based on improved empirical mode decomposition and wavelet threshold function according to claim 1, characterized in that: The screening method in step S01 is specifically as follows: Obtain each modal component except the first and last order as the intermediate modal components; It is determined in turn whether the correlation coefficients of the intermediate-order modal components are all smaller than the correlation coefficients of the upper and lower-order modal components. If so, the intermediate-order modal component is taken as the local modal component, the next-order modal component of the local modal component is taken as the boundary modal component, and the local modal component and the boundary modal component are taken as the target modal components.

4. A signal denoising system based on improved empirical mode decomposition and wavelet threshold function, characterized in that: It is used to denoise the original monitored signal, including: An empirical mode decomposition module is used to replace the cubic spline interpolation method in the fully adaptive noise set empirical mode decomposition with the piecewise cubic Hermite interpolation method, perform curve fitting on the monitored original signal through the replaced fully adaptive noise set empirical mode decomposition to solve the envelope, and obtain the modal component group of the original signal through the envelope; select the modal component that meets the coefficient standard in the modal component group as the target modal component through the preset correlation coefficient; the modal component group contains modal components of several orders; The preset correlation coefficient in the empirical mode decomposition module is the correlation coefficient between the modal component and the original signal, and its formula expression is: Where L represents the length of the original signal in the modal component, n = 1, 2, ..., L, k represents the order of the modal component in the modal component group, s(n) represents the original signal at the nth point, and IMF k (n) represents the modal component corresponding to the original signal at the nth point in the kth modal component; r is the correlation coefficient between the kth modal component and the original signal; A wavelet threshold function module is used to obtain a target wavelet threshold function by using a hard threshold function and a soft threshold function with preset adjustment parameters; The target modal component includes modal components of several orders, and the formula expression of the target wavelet threshold function in the wavelet threshold function module is: In the formula, m is the preset adjustment parameter, j is the number of wavelet decompositions, k is the order of the modal component in the target modal component, λ is the preset threshold, and w j,k is the wavelet coefficient of the target wavelet threshold function of the k-th order modal component at the j-th wavelet decomposition, and tanh is the hyperbolic tangent function; The denoising module is used to obtain the corresponding wavelet coefficients by performing wavelet decomposition on each target modal component, and to select the wavelet coefficients within the preset amplitude range using the target wavelet threshold function; and to reconstruct the selected wavelet coefficients using the inverse wavelet transform to obtain the denoised signal.

5. The signal denoising method based on improved empirical mode decomposition and wavelet threshold function according to claim 4 is characterized in that: The specific method for solving the envelope line in the empirical mode decomposition module includes: an extreme value acquisition unit, which is used to obtain the maximum point, minimum point and extreme symmetric point of the signal time domain spectrum through the original signal; an envelope line acquisition unit, which is used to obtain the envelope line using the maximum point, minimum point and extreme symmetric point of the signal time domain spectrum through the piecewise cubic Hermite interpolation method.

6. The signal denoising system based on improved empirical mode decomposition and wavelet threshold function according to claim 4, characterized in that: The screening method in the empirical mode decomposition module is specifically as follows: obtaining each order modal component except the first order and the last order as the intermediate order modal component; judging in turn whether the correlation coefficient of each intermediate order modal component is smaller than the correlation coefficient of its upper and lower order modal components; if so, taking the intermediate order modal component as the local modal component, taking the next order modal component of the local modal component as the boundary modal component, and taking the local modal component and the boundary modal component as the target modal components.

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