CN114970602A - Signal denoising method and system based on improved empirical mode decomposition and wavelet threshold function - Google Patents
Signal denoising method and system based on improved empirical mode decomposition and wavelet threshold function Download PDFInfo
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Abstract
The invention discloses a signal denoising method based on improved empirical mode decomposition and wavelet threshold function, which relates to the field of signal denoising and comprises the following steps: performing curve fitting on the monitored original signal through the replaced fully adaptive noise set empirical mode decomposition to solve an envelope curve, and acquiring a mode component group of the original signal through the envelope curve; screening out modal components meeting the coefficient standard in the modal component group as target modal components through a preset correlation coefficient; acquiring a target wavelet threshold function by using preset adjusting parameters through a hard threshold function and a soft threshold function; performing wavelet decomposition on each target modal component, and screening out wavelet coefficients in a preset amplitude range by using a target wavelet threshold function; and reconstructing the screened wavelet coefficients by utilizing wavelet inverse transformation to obtain denoised signals. The invention carries out double denoising on the signal by combining the improved CEEMDAN and the improved wavelet threshold function, thereby greatly improving the denoising effect of the signal.
Description
Technical Field
The invention relates to the field of signal denoising, in particular to a signal denoising method and system based on improved empirical mode decomposition and a wavelet threshold function.
Background
The influence of noise can be reduced to a certain extent by the design of hardware and acquisition software in the acquisition process of the signal, but the interference of noise data cannot be completely avoided. Compared with other research methods in the same field, the method has the advantages that data are directly collected to carry out big data analysis or a plurality of common time frequency domain characteristic quantities are extracted after the data are collected to carry out analysis. For the former, the information richness of the data set is ensured, but irrelevant noise signals exist to cause interference to data analysis; in the latter case, although the amount of data calculation is reduced, a large amount of information in the signal is easily lost by using only limited manual feature quantity selection, and other highly correlated features may not be extracted.
In the traditional signal processing, the application of Empirical Mode Decomposition (EMD) is wide, the signal can be decomposed into signal components with different scales in a self-adaptive manner, and the trouble that wavelet basis and Decomposition level need to be selected manually in wavelet Decomposition is avoided. However, it also has the obvious disadvantage of modal aliasing and end-point effects, so that the same Intrinsic Mode Function (IMF) component contains signals with obviously different scales or different IMF components contain signals with obviously the same scale. In order to solve this problem, an average empirical mode decomposition method and a complementary ensemble mode decomposition method have been proposed, which are both optimized for empirical mode decomposition, and complementary noise is introduced to eliminate the influence of added noise. Based on these methods, another scholars has proposed an improved algorithm, namely, a fully Adaptive Noise ensemble empirical mode decomposition (CEEMDAN), which is distinguished from other algorithms by adding the modal components of the auxiliary Noise to the residual components of the signal to be solved, and by performing ensemble averaging on the modal components obtained after the empirical mode decomposition. Through continuous optimization, CEEMDAN performs better in signal decomposition than EMD, but in the process of solving the envelope curve, CEEMDAN adopts a cubic spline interpolation method. The second derivative of the method is continuous, and the over-enveloping or under-enveloping phenomenon can be caused in the process of solving the envelope curve, and is particularly obvious in a non-stationary signal, so that the CEEMDAN method is urgently needed to be improved to improve the denoising effect.
In addition, wavelet threshold denoising in the prior art is widely used in the field of signal denoising. The original signal is decomposed by wavelet, the wavelet coefficient with larger amplitude is mostly effective component, and the wavelet coefficient with smaller amplitude is noise component. Since the effective component and the noise component are already separated from the original signal by wavelet transform, we only need to set a reasonable wavelet coefficient threshold, retain the wavelet coefficient larger than the threshold, discard the wavelet coefficient smaller than the threshold, and finally use wavelet inverse transform to process the screened wavelet coefficient, so as to reconstruct and obtain the clean signal with noise filtered. The idea of the wavelet threshold denoising process is to select a suitable threshold and a threshold function combined with the threshold, calculate wavelet coefficients through the threshold function, and automatically screen the wavelet coefficients. The threshold function and the wavelet threshold are related to the selection of the effective component and the noise component, and the setting is reasonable, so that an ideal noise reduction effect can be obtained. The threshold function is used as a core component of wavelet denoising, and a hard threshold function and a soft threshold function are commonly used. Soft and hard threshold methods, while most commonly used, all have some respective drawbacks. For the hard threshold method, due to the discontinuous function, the reconstructed signal shows oscillation fluctuation, and a large deviation exists; 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 the wavelet threshold function is to be improved urgently to improve the noise reduction effect.
The improved CEEMDAN method can well decompose the signal into an intrinsic mode function, and directly abandon the obtained high frequency to achieve the denoising effect. However, although such a denoising method filters a part of noise, high frequency components in the original signal are also simultaneously removed, and other order modal components still have a part of noise signal. Therefore, the invention improves the CEEMDAN method and the wavelet threshold function, and combines the improved CEEMDAN method and the improved wavelet threshold function to achieve the optimal noise reduction effect.
Disclosure of Invention
In order to solve the problems that an over-envelope phenomenon or an under-envelope phenomenon may be caused in the process of solving an envelope curve in a CEEMDAN method, and a function is discontinuous in a soft-hard threshold method of a wavelet threshold denoising method, a reconstructed signal always has a deviation with a real effective signal, and simultaneously solve the problems that a high-frequency component in an original signal is simultaneously discarded and other order modal components still have partial noise signals in the improved CEEMDAN method, the invention combines the improved CEEMDAN method with an improved wavelet threshold function, and provides a signal denoising method based on improved empirical mode decomposition and the wavelet threshold function, which is used for denoising a monitored original signal, and comprises the following steps:
s01: replacing a cubic spline interpolation method in the empirical mode decomposition of the fully adaptive noise set by using a segmented cubic Hermite interpolation method, carrying out curve fitting on the monitored original signal by the replaced empirical mode decomposition of the fully adaptive noise set so as to solve an envelope curve, and acquiring a mode component group of the original signal by the envelope curve; screening out modal components meeting the coefficient standard in the modal component group as target modal components through a preset correlation coefficient;
s02: acquiring a target wavelet threshold function by using preset adjusting parameters through a hard threshold function and a soft threshold function;
s03: wavelet decomposition is carried out on each target modal component to obtain a corresponding wavelet coefficient, and the wavelet coefficient in a preset amplitude range is screened out by utilizing a target wavelet threshold function; and reconstructing the screened wavelet coefficients by utilizing wavelet inverse transformation to obtain denoised signals.
Further, the modal component group comprises modal components of several orders;
the preset correlation coefficient in step S01 is a correlation coefficient between the modal component and the original signal, and the formula expression thereof is:
where L denotes the length of the original signal in the modal component, n is 1,2, …, L, k denotes the order of the modal component in the modal component group, s (n) denotes the nth point original signal, IMF k (n) representing a modal component corresponding to the nth point original signal in the kth order modal component; and r is the correlation coefficient of the k-th order modal component and the original signal.
Further, the target modal component includes modal components of several orders, and the formula expression of the target wavelet threshold function in step S02 is as follows:
in the formula (I), the compound is shown in the specification,
m is a preset adjusting parameter, j is the number of wavelet decomposition, k is the order of the modal component in the target modal component, lambda is a preset threshold value, w j,k And (4) taking the wavelet coefficient of a target wavelet threshold function of the kth order modal component in the jth wavelet decomposition, wherein tanh is a hyperbolic tangent function.
Further, the specific method for solving the envelope curve in step S01 is as follows:
acquiring a maximum point, a minimum point and an extreme value symmetrical point of a signal time domain spectrum through an original signal;
and acquiring an envelope curve by using a maximum point, a minimum point and an extremum symmetric point of a signal time domain spectrum through a three-stage Hermite interpolation method.
Further, the screening method in step S01 specifically includes:
acquiring modal components of all orders except the first order and the last order as intermediate-order modal components;
and sequentially judging whether the correlation coefficient of each intermediate-order modal component is smaller than the correlation coefficients of the upper and lower-order modal components, if so, taking the intermediate-order modal component as a local modal component, taking the next-order modal component of the local modal component as a boundary modal component, and taking the local modal component and the boundary modal component as target modal components.
The invention also provides a signal denoising system based on the improved empirical mode decomposition and the wavelet threshold function, which is used for denoising the monitored original signal and comprises the following steps:
the empirical mode decomposition module is used for replacing a cubic spline interpolation method in the empirical mode decomposition of the fully adaptive noise set by using a segmented cubic Hermite interpolation method, performing curve fitting on the monitored original signal through the replaced fully adaptive noise set empirical mode decomposition to solve an envelope curve, and acquiring a mode component group of the original signal through the envelope curve; screening out modal components meeting the coefficient standard in the modal component group as target modal components through a preset correlation coefficient;
the wavelet threshold function module is used for acquiring a target wavelet threshold function by using preset adjusting parameters through a hard threshold function and a soft threshold function;
the de-noising module is used for performing wavelet decomposition on each target modal component to obtain a corresponding wavelet coefficient, and screening out the wavelet coefficient in a preset amplitude range by using a target wavelet threshold function; and reconstructing the screened wavelet coefficients by utilizing wavelet inverse transformation to obtain denoised signals.
Further, the modal component group comprises modal components of several orders;
the preset correlation coefficient in the empirical mode decomposition module is a correlation coefficient between a modal component and an original signal, and a formula expression of the preset correlation coefficient is as follows:
where L denotes the length of the original signal in the modal component, n is 1,2, …, L, k denotes the order of the modal component in the modal component group, s (n) denotes the nth point original signal, IMF k (n) representing a modal component corresponding to the nth point original signal in the kth order modal component; r is the k-th modeThe correlation coefficient of the component with the original signal.
Further, the target modal component includes modal components of several orders, and a formula expression of a target wavelet threshold function in the wavelet threshold function module is as follows:
in the formula (I), the compound is shown in the specification,
m is a preset adjusting parameter, j is the number of wavelet decomposition, k is the order of the modal component in the target modal component, lambda is a preset threshold value, w j,k And (4) taking the wavelet coefficient of a target wavelet threshold function of the kth order modal component in the jth wavelet decomposition, wherein tanh is a hyperbolic tangent function.
Further, the specific method for solving the envelope in the empirical mode decomposition module includes: the extreme value acquisition unit is used for acquiring a maximum point, a minimum point and an extreme value symmetrical point of a signal time domain spectrum through an original signal; and the envelope acquiring unit is used for acquiring the envelope by utilizing a maximum point, a minimum point and an extremum symmetric point of the signal time domain spectrum through a segmented cubic Hermite interpolation method.
Further, the screening method in the empirical mode decomposition module specifically includes: acquiring modal components of all orders except the first order and the last order as intermediate-order modal components; and sequentially judging whether the correlation coefficient of each intermediate-order modal component is smaller than the correlation coefficients of the upper and lower-order modal components, if so, taking the intermediate-order modal component as a local modal component, taking the next-order modal component of the local modal component as a boundary modal component, and taking the local modal component and the boundary modal component as target modal components.
Compared with the prior art, the invention at least has the following beneficial effects:
(1) compared with the cubic spline interpolation method, the envelope curve can be kept monotonous as long as the first derivative of an interpolation point is reasonably selected, the phenomena of over-enveloping and under-enveloping are avoided, and the denoising effect is improved;
(2) according to the method, the target wavelet threshold function is obtained through the hard threshold function and the soft threshold function by utilizing the preset adjusting parameters, the soft threshold function and the hard threshold function are better combined, and the problem that in a hard threshold method, due to the fact that the functions are discontinuous, a reconstructed signal shows oscillation fluctuation, and large deviation exists is solved; in the soft threshold method, although the function is continuous, a reconstructed signal and a real effective signal always have a deviation problem;
(3) the invention combines the improved CEEMDAN method with the improved wavelet threshold function, solves the problems that although the improved CEEMDAN can well decompose the signal into an intrinsic mode function, the obtained high frequency is directly abandoned, and the denoising effect is achieved, although the denoising mode filters part of the noise, the high frequency component in the original signal is simultaneously abandoned, and other order mode components still have part of noise signals, and greatly improves the denoising effect of the signal.
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FIG. 1 is a flow chart of a method for signal denoising based on improved empirical mode decomposition and wavelet threshold function;
FIG. 2 is a system diagram of a signal denoising system based on improved empirical mode decomposition and wavelet threshold function;
fig. 3 is a diagram of the modal components corresponding to the radial vibration signal.
Detailed Description
The following are specific embodiments of the present invention and are further described with reference to the drawings, but the present invention is not limited to these embodiments.
Example one
At present, because the automatic tool changing technology of a numerical control machine tool is mature, what is lacking is the accurate judgment of the tool state, if the tool wear state information is not grasped in time, the unqualified tool is continuously used when the tool is to be replaced, the quality of the processed product is unqualified, even the tool is broken and the machine tool is damaged, the key to realizing the effective monitoring of the tool wear state lies in reasonably selecting and accurately acquiring the monitoring signal of the tool wear, and the noise is reduced after the monitoring signal is acquired, so that the wear state of the tool is accurately obtained, therefore, the embodiment selects the vibration signal (including the radial vibration signal, the tangential vibration signal and the axial vibration signal) and the sound signal which are monitored when the numerical control machine tool operates as the object of noise reduction for illustration, although the vibration signal and the sound signal also have the defect of easy environmental interference, but the denoising method of the invention can greatly reduce the defects and expand the advantages of the defects and the advantages.
In order to solve the problems that the improved CEEMDAN method simultaneously discards high-frequency components in an original signal and partial noise signals exist in other order modal components, and the problems that the function is discontinuous and a reconstructed signal always has a deviation with a real effective signal in the soft-hard threshold method of the wavelet threshold denoising method, the invention combines the improved CEEMDAN method with the improved wavelet threshold function, as shown in figure 1, the invention provides a signal denoising method based on improved empirical mode decomposition and the wavelet threshold function,
the method is used for denoising a monitored original signal, and comprises the following steps:
s01: replacing a cubic spline interpolation method in the empirical mode decomposition of the fully adaptive noise set by using a segmented cubic Hermite interpolation method, carrying out curve fitting on the monitored original signal by the replaced empirical mode decomposition of the fully adaptive noise set so as to solve an envelope curve, and acquiring a mode component group of the original signal by the envelope curve; screening out modal components meeting the coefficient standard in the modal component group as target modal components through a preset correlation coefficient;
in this embodiment, the specific method for obtaining the modal component set of the original signal through the replaced fully adaptive noise ensemble empirical mode decomposition (CEEMDAN) includes the steps of:
the method comprises the following steps: auxiliary white Gaussian noise formed by pairing positive and negativeAdding sound signal into the signal to be decomposed (original signal) s (t) to obtain new signal s (t) + (-1) q a 0 n i (t); t is a time variable (time in the signal time domain, s (t) is a continuous signal), and s (t) represents the corresponding original signal at the time t;
acquiring a maximum point, a minimum point and an extreme value symmetrical point of a signal time domain spectrum through a new signal;
the envelope curve is obtained by utilizing the maximum point, the minimum point and the extremum symmetric point of the signal time domain spectrum through the segmented cubic Hermite interpolation method, and the modal component group is obtained by utilizing the envelope curve (the cubic Hermite interpolation method is applied to EMD decomposition, the CEEMDAN algorithm can be further improved, more original information of the signal is reserved), and the method specifically comprises the following steps:
performing EMD decomposition on the new signal for N times, thereby obtaining N first-order modal components
s(t)+(-1) q a 0 n i (t)＝IMF 1 i (t)+r 1 i (t) (formula 1);
in the formula, n i (t) is an auxiliary white gaussian noise signal added at the ith EMD decomposition, (i ═ 1,2, …, N); a is 0 Is the noise amplitude; q is 1 or 2, and is used for ensuring that the added auxiliary white Gaussian noise signal is in positive and negative pairings;
is the first order residual margin signal of the ith EMD decomposition, and the final first order modal component
I.e. N IMFs 1 i Average value of (t):
as can be seen from the equations 1 and 2, the added auxiliary white Gaussian noise signal has positive and negative valuesIn pairs, their interference with the decomposition process is counteracted, so that
The noise contained is greatly reduced. And simultaneously obtaining a final first-order residual margin signal as follows:
step two: decomposing the obtained j-1 th order residual signal r j-1 (t) continuously adding a specific positive and negative paired auxiliary white Gaussian noise signal to obtain a signal: r is j-1 (t)+(-1) q a j-1 Ex -1 (n i (t)), and continuing to perform EMD decomposition on the N-time-series composite material by adopting a segmented thrice Hermite interpolation method to obtain N j-th-order intrinsic mode components
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);
wherein j represents the order of the modal component, E j-1 (n i (t)) represents the auxiliary white Gaussian noise signal n added at the i-th decomposition i (t) performing EMD decomposition using three-pass Hermite interpolation, wherein i is 1,2, …, N; a is j-1 In order to be the amplitude of the noise,
the residual signal of the j th order in the ith EMD decomposition is obtained; for N IMFs j i (t) taking the average value to obtain the final j-th order modal component
Continuously repeating the second step to obtain the residual signal (assuming as r) k (t)) when the number of extreme points is less than 2, obtaining K-order modal components and a final residual signal r (t), wherein the original signal can be represented by the K-order modal components and the final residual signal r (t) obtained by calculation:
by improving the CEEMDAN algorithm flow, the envelope curve of the signal is more ideal to be solved by the three-time Hermite interpolation method, and the interference to residual signals of each hierarchy is greatly reduced by adding an auxiliary white Gaussian noise signal during decomposition, so that the decomposition result is more accurate, and the signal denoising effect is improved.
The modal component group comprises modal components of a plurality of orders, and the modal components of the plurality of orders comprise high-frequency modal components;
the preset correlation coefficient in step S01 is a correlation coefficient between the modal component and the original signal, and the formula expression thereof is:
where L denotes the length of the original signal in the modal component, n is 1,2, …, L (representing the number of sampling points), k denotes the order of the modal component in the modal component group, s (n) denotes the nth point original signal (sampling point signal), IMF k (n) representing a modal component corresponding to the nth point original signal in the kth order modal component;
representing the corresponding modal score of the n-th original signal in the k-th modal componentAn average value of the amounts; and r is a correlation coefficient of the k-th order modal component and the original signal.
In this embodiment, a radial vibration signal, a tangential vibration signal, an axial vibration signal, and a sound signal monitored during operation of a numerical control machine are exemplified (fig. 3 is a graph (R) of modal components (IMF1 to IMF10) obtained by performing decomposition processing of the above steps on a monitored radial vibration signal, that is, an original signal, and a final residual margin (R) in the graph, where the number on each modal component in the graph is a signal amplitude and the number of sampling points is 2000), and correlation coefficients corresponding to various signals obtained by performing processing of the above steps of the present invention on each signal are shown in table 1 below (IMF1 in table 1 represents a first-order modal component, IMF2 represents a second-order modal component, and so on):
| 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 |
The method comprises the following steps of screening modal components meeting a coefficient standard in a modal component group as target modal components by presetting a correlation coefficient, wherein the screening method specifically comprises the following steps:
acquiring modal components of all orders except the first order and the last order as intermediate-order modal components;
whether the correlation coefficient of each intermediate-order modal component is smaller than the correlation coefficient of the upper-order modal component and the lower-order modal component (the correlation coefficient smaller than the upper-order modal component is a coefficient standard) is sequentially judged, if yes, the intermediate-order modal component is used as a local modal component, the next-order modal component of the local modal component is used as a boundary modal component, the local modal component and the boundary modal component are used as target modal components, and the target modal components further comprise preset high-frequency modal components.
In the table, the IMF4 corresponding to the radial vibration signal is the local modal component, and thus the IMF5 is the boundary modal component; the IMF3 corresponding to the tangential vibration signal, the axial vibration signal, and the acoustic signal is a local mode component, and thus the IMF4 is a boundary mode component. Considering that there are some differences in signals of each sampling point, in order to ensure that noise-containing modal components are denoised as much as possible (where IMF1 and IMF2 are high-frequency modal components), in this embodiment, the modal components of IMF1 to IMF5 are selected as signal data for the next wavelet denoising process, so as to solve the problem that the improved CEEMDAN method simultaneously discards high-frequency components in an original signal, and other order modal components still have partial noise signals.
S02: acquiring a target wavelet threshold function by using preset adjusting parameters through a hard threshold function and a soft threshold function;
the formula expression of the hard threshold function is as follows:
the formula expression of the soft threshold function is as follows:
wherein sgn (-) is a sign function, λ is a threshold, the wavelet coefficient whose wavelet coefficient absolute value is smaller than the threshold is set to zero by the calculation of the threshold function, which plays a role of filtering noise components, and the obtaining formula of the threshold is:
wherein σ is the noise variance, and the estimation formula is as follows:
soft and hard threshold methods are most commonly used, but all have some drawbacks. For the hard threshold method, w j，k Discontinuity is caused at +/-lambda, so that the reconstructed signal shows oscillation fluctuation and has larger deviation; for the soft threshold method, although w j，k Continuous at + - λ, but at | w j，k In the range of | ≧ λ, original w j，k And new w j，k Always differ by lambda, which also leads to reconstructionThere is always a deviation of the signal from the true valid signal. If can let w both j，k Continuing at + -lambda and letting new w j，k At | w j，k In the interval of | ≧ lambda j，k Equal, the noise reduction achieved by wavelet denoising is more accurate. Therefore, the invention designs a target wavelet threshold function to solve the technical problem.
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 (I), the compound is shown in the specification,
m is a preset adjusting parameter, j is the number of wavelet decomposition, k is the order of the modal component in the target modal component, lambda is a preset threshold value, w j,k And (4) taking the wavelet coefficient of a target wavelet threshold function of the kth order modal component in the jth wavelet decomposition, wherein tanh is a hyperbolic tangent function.
In the formula, m is used as a preset adjusting parameter, when m → 0, the value is mu → 1, at this time, the function image is very close to the soft threshold function, the difference is that a hyperbolic tangent function is adopted to replace a sign function, and a nonlinear function is applied to wavelet coefficients outside a threshold absolute value range to carry out gradual compression, so that the function continuity is better; when m → ∞, then μ → 0, at which point the functional image is very close to the hard threshold function. m is a constant and | w j，k When | ═ λ, then μ → 1, w j，k → 0, i.e. w j，k Continuous at + -lambda; when | w j，k | → ∞ time, μ → 0, w j，k →w j，k . Therefore, the target wavelet threshold function skillfully combines the respective advantages of the soft threshold function and the hard threshold function, and can ensure that the functions are continuous and the original w is also ensured j，k And new w j，k The deviation between them is not constant, when | w j，k When | - λ is large enough, μ → 0, at which time the new wavelet coefficients are smaller than the original onesThe difference between the wave coefficients is substantially zero, so that the deviation between the noise reduction signal and the true effective signal can be effectively reduced. The smooth transition curve is set in the target wavelet threshold function, the asymptote of the smooth transition curve is overlapped with the hard threshold function, the advantages of soft and hard thresholds are kept, the respective defects of the soft and hard thresholds are overcome, and the signal denoising effect is improved.
S03: wavelet decomposition is carried out on each target modal component to obtain a corresponding wavelet coefficient, and the wavelet coefficient in a preset amplitude range is screened out by utilizing a target wavelet threshold function; and reconstructing the screened wavelet coefficients by utilizing wavelet inverse transformation to obtain denoised signals.
In the embodiment, db4 wavelet is adopted to carry out six-layer decomposition on the screened IMF 1-IMF 5 modal components. The invention denoises the original signal based on the improved empirical mode decomposition and the improved wavelet threshold function, reserves more characteristics in the original signal (does not discard high-frequency components in the original signal at the same time and reserves high-frequency modal components), and screens out the wavelet coefficient in a preset amplitude range through the wavelet threshold function. Finally, the wavelet coefficient after screening is processed by utilizing wavelet inverse transformation, and a clean signal (namely a denoised signal) with noise filtered out can be reconstructed.
In order to further quantify and explain the noise reduction effect of the method, taking a radial vibration signal as an example, two evaluation criteria of Root Mean Square Error (RMSE) and signal to noise ratio (SNR) are introduced to compare the actual effects of the six noise reduction methods, and the calculation formulas are respectively:
wherein 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 a signal to noise, and the larger the signal-to-noise ratio is, the better the noise reduction effect is; the root mean square error RMSE is a ratio of the square of the difference value of the original signal and the denoised signal to the number of sampling points is taken as a root, and the smaller the root mean square error is, the better the denoising effect is. The following table (table 2) shows the comparison of the denoising indicators of different denoising methods.
Compared with other denoising algorithms, the denoising method has higher signal-to-noise ratio, and represents that more useful components are reserved; the root mean square error is smaller, which means that more noise components are filtered, so the denoising method of the invention has better denoising effect.
The invention carries out double denoising on the signal by combining the improved CEEMDAN and the improved wavelet threshold function, thereby greatly improving the denoising effect of the signal.
Example two
As shown in fig. 2, the present invention further provides a signal denoising system based on improved empirical mode decomposition and wavelet threshold function, which is used for denoising the monitored original signal, and includes:
the empirical mode decomposition module is used for replacing a cubic spline interpolation method in the empirical mode decomposition of the fully adaptive noise set by using a segmented cubic Hermite interpolation method, performing curve fitting on the monitored original signal through the replaced fully adaptive noise set empirical mode decomposition to solve an envelope curve, and acquiring a mode component group of the original signal through the envelope curve; screening out modal components meeting the coefficient standard in the modal component group as target modal components through a preset correlation coefficient;
the cubic Hermite interpolation method can well fit a curve, and has better approximation capability and high fitting precision compared with a cubic spline interpolation method.
The wavelet threshold function module is used for acquiring a target wavelet threshold function by using preset adjusting parameters through a hard threshold function and a soft threshold function;
according to the method, the target wavelet threshold function is obtained by utilizing the preset adjusting parameters through the hard threshold function and the soft threshold function, the soft threshold function and the hard threshold function are better combined, and the problem that in a hard threshold method, due to the fact that the functions are discontinuous, a reconstructed signal shows oscillation fluctuation, and large deviation exists is solved; and in the soft threshold method, although the function is continuous, the reconstructed signal and the real effective signal always have a deviation problem.
The de-noising module is used for performing wavelet decomposition on each target modal component to obtain a corresponding wavelet coefficient, and screening out the wavelet coefficient in a preset amplitude range by using a target wavelet threshold function; and reconstructing the screened wavelet coefficients by utilizing wavelet inverse transformation to obtain denoised signals.
The modal component group comprises modal components of a plurality of orders;
the preset correlation coefficient in the empirical mode decomposition module is a correlation coefficient between a modal component and an original signal, and a formula expression of the preset correlation coefficient is as follows:
where L denotes the length of the original signal in the modal component, n is 1,2, …, L, k denotes the order of the modal component in the modal component group, s (n) denotes the nth point original signal, IMF k (n) representing a modal component corresponding to the nth point original signal in the kth order modal component; and r is a correlation coefficient of the k-th order modal component and the original signal.
The target modal component comprises modal components of a plurality of orders, and the formula expression of the target wavelet threshold function in the wavelet threshold function module is as follows:
in the formula (I), the compound is shown in the specification,
m is a preset adjusting parameter, j is the number of wavelet decomposition, k is the order of the modal component in the target modal component, lambda is a preset threshold value, w j,k And (4) taking the wavelet coefficient of a target wavelet threshold function of the kth order modal component in the jth wavelet decomposition, wherein tanh is a hyperbolic tangent function.
The specific method for solving the envelope curve in the empirical mode decomposition module comprises the following steps: the extreme value acquisition unit is used for acquiring a maximum point, a minimum point and an extreme value symmetrical point of a signal time domain spectrum through an original signal; and the envelope curve acquisition unit is used for acquiring the envelope curve by using a maximum point, a minimum point and an extremum symmetric point of the signal time domain spectrum through a piecewise cubic Hermite interpolation method.
The screening method in the empirical mode decomposition module specifically comprises the following steps: acquiring modal components of all orders except the first order and the last order as intermediate-order modal components; and sequentially judging whether the correlation coefficient of each intermediate-order modal component is smaller than the correlation coefficients of the upper and lower-order modal components, if so, taking the intermediate-order modal component as a local modal component, taking the next-order modal component of the local modal component as a boundary modal component, and taking the local modal component and the boundary modal component as target modal components.
The invention combines the improved CEEMDAN method with the improved wavelet threshold function, solves the problems that although the improved CEEMDAN can well decompose the signal into an intrinsic mode function, the obtained high frequency is directly abandoned, and the denoising effect is achieved, although the denoising mode filters part of the noise, the high frequency component in the original signal is simultaneously abandoned, and other order mode components still have part of noise signals, and greatly improves the denoising effect of the signal.
It should be noted that all the directional indicators (such as up, down, left, right, front, and rear … …) in the embodiment of the present invention are only used to explain the relative position relationship between the components, the movement situation, etc. in a specific posture (as shown in the drawing), and if the specific posture is changed, the directional indicator is changed accordingly.
Moreover, descriptions of the present invention as relating to "first," "second," "a," etc. are for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicit ly indicating a number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "connected," "secured," and the like are to be construed broadly, and for example, "secured" may be a fixed connection, a removable connection, or an integral part; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In addition, the technical solutions in the embodiments of the present invention may be combined with each other, but it must be based on the realization of those skilled in the art, and when the technical solutions are contradictory or cannot be realized, such a combination of technical solutions should not be considered to exist, and is not within the protection scope of the present invention.
Claims (10)
1. A signal denoising method based on improved empirical mode decomposition and wavelet threshold function is characterized in that the method is used for denoising a monitored original signal and comprises the following steps:
s01: replacing a cubic spline interpolation method in the empirical mode decomposition of the fully adaptive noise set by using a segmented cubic Hermite interpolation method, carrying out curve fitting on the monitored original signal by the replaced empirical mode decomposition of the fully adaptive noise set so as to solve an envelope curve, and acquiring a mode component group of the original signal by the envelope curve; screening out modal components meeting the coefficient standard in the modal component group as target modal components through a preset correlation coefficient;
s02: acquiring a target wavelet threshold function by using preset adjusting parameters through a hard threshold function and a soft threshold function;
s03: wavelet decomposition is carried out on each target modal component to obtain a corresponding wavelet coefficient, and the wavelet coefficient in a preset amplitude range is screened out by utilizing a target wavelet threshold function; and reconstructing the screened wavelet coefficients by utilizing wavelet inverse transformation to obtain denoised signals.
2. The method for signal denoising based on improved empirical mode decomposition and wavelet threshold function of claim 1, wherein the set of modal components comprises several orders of modal components;
the preset correlation coefficient in step S01 is a correlation coefficient between the modal component and the original signal, and the formula expression thereof is:
wherein, L represents the length of original signal in modal component, n is 1,2, …, L, k represents the order of modal component in modal component group, s (n) represents the n-th original signal, IMF k (n) representing a modal component corresponding to the nth point original signal in the kth order modal component; and r is a correlation coefficient of the k-th order modal component and the original signal.
3. The method for denoising a signal based on improved empirical mode decomposition and wavelet threshold function of claim 1, wherein the target modal component comprises several orders of modal components, and the formula expression of the target wavelet threshold function in step S02 is:
in the formula (I), the compound is shown in the specification,
m is a preset adjusting parameter, j is the number of wavelet decomposition, k is the order of the modal component in the target modal component, lambda is a preset threshold value, w j,k And (4) taking the wavelet coefficient of a target wavelet threshold function of the kth order modal component in the jth wavelet decomposition, wherein tanh is a hyperbolic tangent function.
4. The method for denoising signals based on improved empirical mode decomposition and wavelet threshold function according to claim 1, wherein the specific method for solving the envelope in step S01 is:
acquiring a maximum point, a minimum point and an extreme value symmetrical point of a signal time domain spectrum through an original signal;
and acquiring an envelope curve by using a maximum point, a minimum point and an extremum symmetric point of a signal time domain spectrum through a three-stage Hermite interpolation method.
5. The method for denoising a signal based on improved empirical mode decomposition and wavelet threshold function according to claim 2, wherein the screening method in step S01 is specifically:
obtaining modal components of each order except the first order and the last order as intermediate-order modal components;
and sequentially judging whether the correlation coefficient of each intermediate-order modal component is smaller than the correlation coefficients of the upper and lower-order modal components, if so, taking the intermediate-order modal component as a local modal component, taking the next-order modal component of the local modal component as a boundary modal component, and taking the local modal component and the boundary modal component as target modal components.
6. A signal denoising system based on improved empirical mode decomposition and wavelet threshold function is characterized in that the system is used for denoising a monitored original signal and comprises:
the empirical mode decomposition module is used for replacing a cubic spline interpolation method in the empirical mode decomposition of the fully adaptive noise set by using a segmented cubic Hermite interpolation method, performing curve fitting on the monitored original signal through the replaced fully adaptive noise set empirical mode decomposition to solve an envelope curve, and acquiring a mode component group of the original signal through the envelope curve; screening out modal components meeting the coefficient standard in the modal component group as target modal components through a preset correlation coefficient;
the wavelet threshold function module is used for acquiring a target wavelet threshold function by using preset adjusting parameters through a hard threshold function and a soft threshold function;
the de-noising module is used for performing wavelet decomposition on each target modal component to obtain a corresponding wavelet coefficient, and screening out the wavelet coefficient in a preset amplitude range by using a target wavelet threshold function; and reconstructing the screened wavelet coefficients by utilizing wavelet inverse transformation to obtain denoised signals.
7. The system for denoising a signal based on improved empirical mode decomposition and wavelet threshold function of claim 6, wherein the set of modal components comprises several orders of modal components;
the preset correlation coefficient in the empirical mode decomposition module is a correlation coefficient between a modal component and an original signal, and a formula expression of the preset correlation coefficient is as follows:
where L denotes the length of the original signal in the modal component, n is 1,2, …, L, k denotes the order of the modal component in the modal component group, s (n) denotes the nth point original signal, IMF k (n) representing a modal component corresponding to the nth point original signal in the kth order modal component; and r is the correlation coefficient of the k-th order modal component and the original signal.
8. The system of claim 6, wherein the target modal component comprises several orders of modal components, and the wavelet threshold function module is a formula of a target wavelet threshold function:
in the formula (I), the compound is shown in the specification,
m is a preset adjusting parameter, j is the number of wavelet decomposition, k is the order of the modal component in the target modal component, lambda is a preset threshold value, w j,k And (4) taking the wavelet coefficient of a target wavelet threshold function of the kth order modal component in the jth wavelet decomposition, wherein tanh is a hyperbolic tangent function.
9. The method for denoising a signal based on improved empirical mode decomposition and wavelet threshold function according to claim 6, wherein the specific method for solving the envelope in the empirical mode decomposition module comprises: the extreme value acquisition unit is used for acquiring a maximum point, a minimum point and an extreme value symmetrical point of a signal time domain spectrum through an original signal; and the envelope acquiring unit is used for acquiring the envelope by utilizing a maximum point, a minimum point and an extremum symmetric point of the signal time domain spectrum through a segmented cubic Hermite interpolation method.
10. The system for denoising a signal based on improved empirical mode decomposition and wavelet threshold function of claim 7, wherein the filtering method in the empirical mode decomposition module is specifically: acquiring modal components of all orders except the first order and the last order as intermediate-order modal components; and sequentially judging whether the correlation coefficient of each intermediate-order modal component is smaller than the correlation coefficients of the upper and lower-order modal components, if so, taking the intermediate-order modal component as a local modal component, taking the next-order modal component of the local modal component as a boundary modal component, and taking the local modal component and the boundary modal component as target modal components.
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