A method for reducing noise of MHD angular velocity sensor signal

Abstract

The present invention relates to a noise reduction method, and in particular to a signal noise reduction method for an MHD angular velocity sensor, in order to solve the problems in the prior art that some IMF components after CEEMDAN decomposition are easily ignored as noise components, resulting in limited improvement of the signal-to-noise ratio, and that the threshold criterion and threshold function in the method of joint denoising of CEEMDAN and wavelet packet threshold have poor adaptability, resulting in destruction of high-frequency details of the signal and causing signal distortion. A signal noise reduction method for an MHD angular velocity sensor comprises the following steps: S1. performing CEEMDAN decomposition on the original signal, S2. selecting relevant IMF components, S3. denoising the relevant IMF components, S4. combining the denoised relevant IMF components to obtain a denoised signal; in S3, using an improved threshold criterion to use different adjustment factors for the frequency band where the vibration signal and the noise are located, effectively improving the signal-to-noise ratio.

Description

Technical Field

[0001] The invention relates to a noise reduction method, and in particular to a noise reduction method for MHD angular velocity sensor signals. Background Art

[0002] The reaction flywheel and control moment gyro on the spacecraft will generate micro-angular vibrations of different frequencies when working, which are mainly manifested as steady-state sinusoidal response, angle jitter of attenuated oscillation, etc. Modern high-precision spacecraft have extremely high requirements for attitude stability and pointing accuracy. Some deep space exploration remote sensing spacecraft have requirements for pointing and tracking accuracy reaching sub-micro-radian level. The passive vibration isolation system will increase the volume and mass of the terminal, increase the structural complexity of the communication terminal, and there will often be vibration residuals after vibration isolation, which cannot achieve the required pointing and tracking accuracy. These limitations make it unsatisfactory for some practical systems, especially those for small satellites. Therefore, the on-orbit detection and compensation control of micro-angular vibrations of space structures has become a key technology in the design of high-precision spacecraft.

[0003] The MHD angular velocity sensor is a new type of sensor based on magnetohydrodynamics. It has a wide measurement bandwidth range, usually 1Hz-1kHz, and can effectively obtain micro-angular vibration information within the kilohertz bandwidth. However, the output signal of this sensor is very weak. When the sensor input angular velocity is at the milliradian level, the output signal of the sensor header is at the microvolt level; when the detected angular velocity is at the sub-microradian level, the output signal of the sensor header is only at the nanovolt level. Such a weak signal cannot be collected and must be amplified. However, some hardware noises such as installation errors, sensor noise, errors caused by AD reference voltage fluctuations, and AD output noise will also be amplified, resulting in a low signal-to-noise ratio of the output signal, which seriously affects the detection accuracy.

[0004] The angular vibration of the satellite has the characteristics of high frequency and low amplitude and low amplitude and high frequency. The conventional complete ensemble empirical mode decomposition (CEEMDAN) of adaptive noise can decompose the vibration signals of different frequencies into one or several intrinsic mode components (IMF components), but the existing method of determining the IMF components where the effective signal is located does not take into account that the vibration signal of a certain frequency may be decomposed into several IMF components, resulting in a low amplitude. This part of the IMF components is easily ignored as noise components, which limits the improvement of the signal-to-noise ratio. The existing methods of combining CEEMDAN with wavelet packet threshold denoising mostly denoise all IMF components, and the hard threshold function used is discontinuous, while the deviation between the soft threshold function and the hard threshold function is large, the threshold criterion and the threshold function have poor adaptability, and the high-frequency vibration with relatively weak amplitude is easily filtered out as noise, and the high-frequency details of the signal are less retained, so that the high-frequency details of the signal are destroyed, causing signal distortion. Therefore, the existing methods have great limitations on the improvement of the signal-to-noise ratio, and it is difficult to retain the high-frequency details of the signal. Summary of the invention

[0005] The purpose of the present invention is to solve the problems in the prior art that some IMF components after CEEMDAN decomposition are easily ignored as noise components, resulting in limited improvement of the signal-to-noise ratio, and the threshold criterion and threshold function in the method of joint denoising of CEEMDAN and wavelet packet threshold have poor adaptability, which destroys the high-frequency details of the signal and causes signal distortion, and to provide a method for denoising the signal of an MHD angular velocity sensor.

[0006] To achieve the above objectives, the technical solutions provided by the present invention are as follows:

[0007] A method for reducing noise of MHD angular velocity sensor signals is characterized in that it comprises the following steps:

[0008] S1. Perform adaptive noise complete set empirical mode decomposition on the original signal to obtain multiple IMF components;

[0009] S2. Calculate the autocorrelation coefficient R of each IMF component separately c,τ1 and its root mean square r 1,c , filter out relevant IMF components and remove irrelevant IMF components; among them, the relevant IMF component is r 1,c ≥β 1 The corresponding IMF component is r 1,c <β 1 The corresponding IMF component when 1 is the first threshold set, c is the number of IMF components, τ 1 is the delay of the set IMF component;

[0010] S3. De-noise each relevant IMF component obtained in S2 by wavelet packet threshold processing, specifically:

[0011] S3.1. Perform wavelet packet decomposition on each relevant IMF component, with the decomposition layer number being J layers, and obtain multiple frequency bands of the Jth layer in the relevant IMF component and their corresponding wavelet packet coefficient sequences;

[0012] S3.2. Calculate the autocorrelation coefficient of the wavelet packet coefficient sequence of each frequency band in the Jth layer and its root mean square r 2,I ; Where I is the frequency band number of the J-th layer band decomposition sequence, I = 0, 1, 2, 3, 4, ..., 2 J -1;

[0013] S3.3. Calculate the wavelet packet coefficient thresholds of each frequency band in the Jth layer using the threshold criterion;

[0014] The threshold criterion is an improved threshold criterion:

[0015]

[0016] Where, T J,I is the wavelet packet coefficient threshold of the Jth layer and the Ith frequency band, σ is the standard deviation of the noise in the estimated IMF component, N is the data length of the IMF component, β 2 is the second threshold set, d and b are adjustment coefficients, d>0, b>0;

[0017] S3.4 performs threshold denoising on each frequency band of the Jth layer using the wavelet packet coefficient threshold of each frequency band of the Jth layer through a threshold function;

[0018] S3.5. Reconstruct each frequency band denoised in S3.4 to obtain denoised related IMF components;

[0019] S4. Combine the denoised related IMF components obtained in S3.5 to obtain a denoised signal.

[0020] Further, in S3.4, the threshold function is an improved threshold function, as shown in the following formula:

[0021]

[0022] In the formula, w J,I (f) is the wavelet packet coefficient sequence of the fth point in the I frequency band at the decomposition level J; is the wavelet packet coefficient sequence after denoising at the fth point in the I frequency band at the decomposition level J, λ J,I,f is the threshold adjustment factor.

[0023] Furthermore, in S3.4, the threshold adjustment factor λ J,I,f Specifically:

[0024]

[0025] In the formula, w J,I (f) is the wavelet packet coefficient sequence of the fth point in the I frequency band at the decomposition level J; α is the adjustment parameter, α>0.

[0026] Furthermore, in S3.4, the value range of α is 0-1.

[0027] Furthermore, in S2, 0<β 1 <0.01.

[0028] Furthermore, in S3.3, d>10, b>10.

[0029] Furthermore, in S3.3, 0<β 2 <0.01.

[0030] Furthermore, in S2, β1 The value of is 0.005;

[0031] In S3.3, d = 100, b = 100;

[0032] In S3.3, β 2 The value of is 0.005.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. The present invention utilizes the autocorrelation characteristic of micro-angular vibration signals, determines the relevant IMF components of the vibration signal according to the root mean square of the autocorrelation coefficients of each IMF component, and directly removes the irrelevant components, so that the vibration signal can be quickly and adaptively screened out, and then the relevant IMF components are denoised, and the denoised IMF components are combined to obtain a denoised signal, thereby improving the signal-to-noise ratio.

[0035] 2. The present invention uses an improved threshold criterion, by setting and As a regulating factor. In the frequency band where the vibration signal is located, Adjust the wavelet packet coefficient threshold of this frequency band to reduce the value, so as to avoid the IMF component containing weak vibration signal being filtered out as noise after wavelet packet threshold processing, which is beneficial to protect signal details. By adjusting the wavelet packet coefficient threshold of the frequency band to increase, the noise can be removed as much as possible and the signal-to-noise ratio can be improved. Therefore, in the improved threshold criterion, the root mean square and β of the autocorrelation coefficient of each frequency band are used. 2 After comparison, different wavelet packet coefficient thresholds are set for different frequency bands by adjusting factors, where d>0 and b>0.

[0036] 3. The improved threshold function of the present invention is provided with λ J,I,f and Ensure that the improved threshold function is within the wavelet packet coefficient threshold ±T J,I is continuous at |w, and at infinity, the deviation between the improved threshold function and the hard threshold function is zero, and α>0 ensures that the improved threshold function is J,I (f)|≥T J,I The improved threshold function approaches the hard threshold function under the condition of . By adjusting α, the speed at which the improved threshold function approaches the hard threshold function can be changed. The smaller α is, the faster the approximation speed is, so that the deviation between the improved threshold function and the hard threshold function approaches zero faster. Therefore, compared with the hard threshold function, the improved threshold function is J,IIt has continuity, and compared with the soft threshold function, the deviation from the hard threshold tends to zero, which shows that the improved threshold function improves the shortcomings of the traditional threshold function; the improved threshold function can enhance the smoothness of the denoised signal, and will not easily produce additional oscillations like the hard threshold, and effectively protect the high-frequency details of the vibration signal; unlike the soft threshold, it will not constantly compress the wavelet packet coefficient sequence greater than the wavelet packet coefficient threshold, causing signal distortion after reconstruction; therefore, the present invention can effectively retain high-frequency details, improve the signal-to-noise ratio, and achieve better denoising effect.

[0037] 4. In the present invention, the value range of α is preferably 0<α<1, which allows the improved threshold function to approach the hard threshold function more quickly. Different values ​​make the threshold function applicable to signals under different working conditions.

[0038] 5. The regulatory factors provided by the present invention and In the above, the threshold of wavelet packet coefficient is adjusted by adjusting d and b. Since some vibration signals of the same frequency may be decomposed into different IMF components, the amplitude of IMF components is small. In addition, the amplitude of high-frequency micro-angular vibration itself is small. In these two cases, after the IMF components are decomposed by wavelet packets, r 2,I It is relatively small, so in the present invention, d>10, b>10, and the regulating effect on the wavelet packet coefficient threshold is more obvious.

[0039] 6. In the present invention, β 1 and β 2 The values ​​of take into account the lower amplitude IMF components and high-frequency low-amplitude angular vibration signals. The preferred value range is: 0<β 1 <0.01, 0<β 2 <0.01, which can effectively retain more vibration signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of a first embodiment of a method for reducing noise of an MHD angular velocity sensor signal according to the present invention;

[0041] Figure 2 is a flow chart of performing denoising on relevant IMF components using an improved threshold function in Embodiment 1 of the present invention;

[0042] Figure 3 is a denoising characteristic curve diagram of the improved threshold function in the first embodiment of the present invention;

[0043] Figure 4 This is a denoising effect diagram of the low-frequency analog output signal of the MHD sensor with 5 Hz, 0.0600 V and a signal-to-noise ratio of 5 dB in the first embodiment of the present invention;

[0044] Figure 5This is an error curve diagram of the low-frequency analog output signal of the MHD sensor with 5 Hz, 0.0600 V and a signal-to-noise ratio of 5 dB in the first embodiment of the present invention;

[0045] Figure 6 This is a diagram showing the denoising effect of the intermediate frequency analog output signal of the MHD sensor with a signal-to-noise ratio of 50 Hz, 0.0350 V and 5 dB in the second embodiment of the present invention;

[0046] Figure 7 This is an error curve diagram of the intermediate frequency analog output signal of the MHD sensor with 50 Hz, 0.0350 V and a signal-to-noise ratio of 5 dB in the second embodiment of the present invention;

[0047] Figure 8 This is a denoising effect diagram of the high-frequency analog output signal of the MHD sensor with 185Hz, 0.0150V and a signal-to-noise ratio of 5dB in Example 3 of the present invention;

[0048] Fig. 9 This is an error curve diagram of the high-frequency analog output signal of the MHD sensor at 185 Hz, 0.0150 V, and a signal-to-noise ratio of 5 dB in Example 3 of the present invention;

[0049] Fig.10 A diagram showing the denoising effect of mixed analog output signals of 5 Hz, 50 Hz and 185 Hz MHD sensors with a signal-to-noise ratio of 5 dB in the fourth embodiment of the present invention;

[0050] Fig.11 Error curve diagram of mixed analog output signals of the MHD sensor at 5 Hz, 50 Hz and 185 Hz with a signal-to-noise ratio of 5 dB in the fourth embodiment of the present invention;

[0051] Fig.12 RMS graph of IMF autocorrelation coefficients of mixed analog output signals of the MHD sensor at 5 Hz, 50 Hz and 185 Hz with a signal-to-noise ratio of 5 dB in the fourth embodiment of the present invention;

[0052] Fig.13 IMF component diagram of the mixed analog output signals of the MHD sensor at 5 Hz, 50 Hz and 185 Hz with a signal-to-noise ratio of 5 dB in the fourth embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0054] Embodiment 1

[0055] like Figure 1 As shown, a method for reducing noise of an MHD angular velocity sensor signal of the present invention comprises the following steps:

[0056] S1. Processing the original signal by CEEMDAN to obtain multiple IMF components; the original signal contains vibration signals and noise;

[0057] The original signal is processed by CEEMDAN, such as Figure 1 As shown in the dotted box, specifically:

[0058] S1.1. Add E groups of positive and negative Gaussian white noise to the original signal x(k), and perform EMD decomposition on the signal after each addition of Gaussian white noise to obtain 2E IMFs 1 z (k), the standard deviation of the positive and negative Gaussian white noise is 0.2, and the first IMF component IMF is calculated by the following formula 1 (k) and the first residual r 1 (k):

[0059]

[0060] r 1 (k) = x(k) - IMF 1 (k)

[0061] Where z is the number of times positive and negative Gaussian white noise is added, and its value is 1, 2, ..., 2E, and k is the sequence of the signal;

[0062] S1.2. Repeat the operation of S1.1 several times until there are no more than two extreme points of the residual, and then get the IMF c (k) and r c (k) specifically:

[0063] In the previous residual r c-1 (k) Add E groups of positive and negative Gaussian white noise, and add positive and negative Gaussian white noise to r c-1 (k) Perform EMD decomposition to obtain 2E And the cth IMF component IMF is calculated by the following formula c (k) and residual r c (k):

[0064]

[0065] r c (k) = r c-1 (k)-IMF c (k)

[0066] Where c is the number of IMF components, which can be 1, 2, …, K;

[0067] The Kth IMF component IMF K (k) is as follows:

[0068]

[0069] The original signal x(k) after CEEMDAN decomposition is as follows:

[0070]

[0071] In this embodiment, the number of groups of positive and negative Gaussian white noise added is 50, and the iterative calculation is stopped until the number of extreme points of the residual does not exceed two or the number of iterations does not exceed 100. In other embodiments of the present invention, the number of groups of positive and negative Gaussian white noise added and the maximum number of iterations can be adjusted according to the intensity of the noise; the amplitude of the Gaussian white noise can generally be selected as 0.01-0.5 times the standard deviation of the original signal amplitude, or can be appropriately adjusted and increased with the intensity of the noise to achieve a better denoising effect.

[0072] S2. Calculate the autocorrelation coefficient and root mean square of each IMF component respectively, use the root mean square of the autocorrelation coefficient of each IMF component to determine whether it is a related IMF component, and remove irrelevant IMF components;

[0073] Specifically:

[0074] S2.1. Set the delay of the IMF component to τ 1 , the autocorrelation coefficient of each IMF component is calculated by the following formula:

[0075]

[0076] In the formula, R c,τ is the cth one, with a delay of τ 1 The autocorrelation coefficient of the IMF component, τ 1 =0,1,2,…,N; N is the data length of the IMF component, μ is the mean value of the IMF component;

[0077] S2.2. Calculate the root mean square of the autocorrelation coefficient of each IMF component by the following formula: 1,c ; and through r 1,c Determine whether the IMF component is a relevant component;

[0078]

[0079] Among them, R c,τ is the cth one, with a delay of τ 1 The autocorrelation coefficient of the IMF component; N is the data length of the IMF component.

[0080] When 1,c ≥β 1 , the component is a relevant component, otherwise it is an irrelevant component; retain the relevant component and remove the irrelevant component;

[0081] Among them, β 1 is the first threshold set; β 1 The value of is related to the root mean square of the autocorrelation coefficient of the IMF component. The best value can be obtained through multiple experiments. Considering that some vibration signals of the same frequency may be decomposed into different IMF components, the amplitude of the IMF component is small; at the same time, the amplitude of the high-frequency angular vibration in the vibration signal is smaller than that of other frequency vibrations. In these two cases, r 1,c It is also relatively small compared to other cases, so in the present invention, 0<β 1 <0.01, in this embodiment, β 1 Set to 0.005.

[0082] S3. De-noising each relevant IMF component obtained in S2 by wavelet packet threshold processing;

[0083] like Figure 2 As shown, specifically:

[0084] S3.1. Perform wavelet packet decomposition on each relevant IMF component to obtain multiple frequency bands of the Jth layer in the relevant IMF component and their corresponding wavelet packet coefficient sequences: The sampling frequency of the original signal is f s , the number of layers of wavelet packet decomposition is J, and the analysis frequency band of wavelet packet decomposition is f s / 2, then each IMF component has 2 J frequency bands;

[0085] In this embodiment, considering factors such as support length, symmetry and vanishing moment, the wavelet packet decomposition uses the sym6 wavelet basis function, and the decomposition layer number J is 8. Discrete wavelet packet decomposition is performed by the following formula:

[0086]

[0087] Where J is the number of decomposition layers, j = 1, 2, ..., J; i is the frequency band number with decomposition sequence, i = 0, 1, 2, 3, 4, ..., 2 j -1;w j,2i (m) and w j,2i+1 (m) is the wavelet packet coefficient sequence of the 2ith and 2i+1th frequency bands of the IMF component at the jth decomposition level; w j-1,i (n) is the wavelet packet coefficient sequence of the i-th frequency band of the IMF component at the j-1th decomposition level; when j = 1, w 0,i (n) is the sequence of x(k) in the i-th frequency band; w(n) is the wavelet packet coefficient sequence on the layer to be decomposed, w(m) is the wavelet packet coefficient sequence after decomposition; l is the number of data in the wavelet packet coefficient sequence of each frequency band in the j-th layer, l = N / 2 j; h(l) is the coefficient of the high-pass filter, and g(l) is the coefficient of the low-pass filter.

[0088] In other embodiments of the present invention, other wavelet basis functions may be used and other decomposition levels may be selected. As the number of decomposition levels increases, the wavelet packet coefficient sequence of the frequency band where the noise is located decreases, and the wavelet packet coefficient sequence of the frequency band where the vibration signal is located tends to be stable.

[0089] S3.2. Calculate the autocorrelation coefficient of the wavelet packet coefficient sequence of each frequency band in the Jth layer by the following formula: and its root mean square r 2,I :

[0090]

[0091] Where I is the frequency band number of the J-th layer band decomposition sequence, I = 0, 1, 2, 3, 4, ..., 2 J -1; τ 2 is the delay of the set wavelet packet coefficient sequence, τ 2 =0,1,2,…,l, where l is the number of data in the wavelet packet coefficient sequence; is the last layer of frequency band I, with a delay of τ 2 The autocorrelation coefficient of the wavelet packet coefficient sequence, μ is the mean value of the wavelet packet coefficient sequence in this frequency band, and w J,I (k) is the wavelet packet coefficient sequence of the Jth layer and the Ith frequency band; r 2,I is the root mean square of the autocorrelation coefficient of the Jth layer and the Ith frequency band.

[0092] S3.3. Calculate the wavelet packet coefficient thresholds of each frequency band in the Jth layer using the improved threshold criterion;

[0093] The improved threshold criterion is:

[0094]

[0095] in,

[0096]

[0097] Where, T J,I is the wavelet packet coefficient threshold of the Jth layer and the Ith frequency band, σ is the standard deviation of the noise in the estimated IMF component, N is the data length of the IMF component, β 2 is the second threshold set, d and b are adjustment coefficients, d>0, b>0, It is the median of all high-frequency wavelet coefficients on the decomposition layer number J. In the present invention, when the values ​​of d and b satisfy d>10 and b>10, the regulating effect on the wavelet packet coefficient threshold is more obvious. In this embodiment, d is 100 and b is 100.

[0098] If r is satisfied 2,I ≥β 2 , indicating that the frequency band contains vibration signals. In the frequency band where the vibration signal is located, Adjustment reduces the wavelet packet coefficient threshold to prevent the IMF component containing weak vibration signals from being filtered out as noise during denoising, which is beneficial to protecting signal details. 2,I <β 2 , then this frequency band is the noise frequency band, through Adjustment increases the wavelet packet coefficient threshold to remove as much noise as possible and improve the signal-to-noise ratio.

[0099] Considering that some vibration signals of the same frequency may be decomposed into different IMF components, and then decomposed by wavelet packets, the wavelet packet coefficients are relatively small; at the same time, the wavelet packet coefficients of the IMF components where high-frequency angular vibrations are located are relatively small. 2,I is also relatively small, so in the present invention, 0<β 2 <0.01, in this embodiment, β 2 Set it to 0.005 to avoid treating vibration signals as noise.

[0100] S3.4. The threshold value of each frequency band of the Jth layer is used to perform threshold denoising on each frequency band of the Jth layer through a threshold function; the improved threshold function used in this embodiment is as follows:

[0101]

[0102] in,

[0103]

[0104] In the formula, w J,I (f) is the wavelet packet coefficient sequence of the fth point in the I frequency band at the decomposition level J; is the wavelet packet coefficient sequence after denoising at the fth point in the I frequency band at the decomposition level J, λ J,I,f is the threshold adjustment factor, α is the adjustment parameter, α>0, by adjusting α, the improved threshold function can be changed in |w J,I (f)|≥T J,I The speed of approximating the hard threshold function under the condition of α, the smaller the value of α, the faster the approximation speed; when 0<α<1, the improved threshold function can be applied to signals under more working conditions. In this embodiment, α is set to 0.01;

[0105] Figure 3 The figure shows the denoising characteristic curve of the improved threshold function. It can be seen that the deviation between the improved threshold function image of the present invention and the hard threshold function is close to zero, and at T J,I and -T J,I The positions are continuous;

[0106] S3.5. Reconstruct each frequency band denoised in S3.4 to obtain denoised related IMF components;

[0107] S4. Combine the denoised related IMF components obtained in S3.5 to obtain a denoised signal.

[0108] Noise does not have autocorrelation, but micro-angular vibration signals have autocorrelation. The root mean square of the autocorrelation coefficient of the IMF component containing the vibration signal is larger than the root mean square of the autocorrelation coefficient of the noise component. Therefore, in S2.2, the root mean square of the autocorrelation coefficient of each IMF component is used to determine whether it is a correlated IMF component.

[0109] In this embodiment, the original signal is sampled at a sampling frequency of 10kHz and a sampling time of 1 second. After sampling, a 5Hz, 0.060V original signal with a signal-to-noise ratio of 5dB is obtained. After S1-S4, a denoised signal is obtained as follows: Figure 4 As shown, the ideal signal is a 5Hz, 0.060V signal without noise. It can be seen that the signal curve obtained by the present invention is close to the ideal signal curve. The signal-to-noise ratio of the original signal is 5.0000dB, and the signal-to-noise ratio of the signal processed by the method of the present invention is 29.6236dB; the root mean square error of the original signal is 0.0238V, and the root mean square error after using the method of the present invention is 0.0014V. The comparison of the error curves is as follows: Figure 5 shown.

[0110] In this embodiment, the original signal is a sine angular velocity signal. In other embodiments of the present invention, the method can also perform noise reduction on a cosine angular velocity signal and other types of signals, and the steps are the same as those in this embodiment.

[0111] Embodiment 2

[0112] The difference between this embodiment and the first embodiment is that the original signal is different. In the present invention, the original signal of 50Hz, 0.0350V with a signal-to-noise ratio of 5dB is obtained by sampling. After S1-S4, the denoised signal is obtained as follows: Figure 6 As shown, the signal-to-noise ratio of the original signal is 5.0000dB, and the signal-to-noise ratio after using the method of the present invention is 28.9028dB; the root mean square error of the original signal is 0.0139V, and the root mean square error after using the method of the present invention is 0.0009V. The comparison of the error curves is as follows Figure 7 shown.

[0113] Embodiment 3

[0114] The difference between this embodiment and the first embodiment is that the original signal is different. In the present invention, the original signal of 185Hz and 0.0150V with a signal-to-noise ratio of 5dB is obtained by sampling. After S1-S4, the denoised signal is obtained as follows: Figure 8 As shown, the signal-to-noise ratio of the original signal is 5.0000dB, and the signal-to-noise ratio after using the method of the present invention is 23.7653dB; the root mean square error of the original signal is 0.0060V, and the root mean square error after using the method of the present invention is 0.0007V. The comparison of the error curves is as follows Fig. 9 shown.

[0115] Embodiment 4

[0116] The difference between this embodiment and the first embodiment is that the original signal is different. The original signal in the present invention is a mixed frequency micro-angular vibration signal of 5 Hz, 55 Hz and 185 Hz with a signal-to-noise ratio of 5 dB. The multiple IMF components obtained by S1 decomposition are as follows: Fig.13 As shown, IMF6, IMF7, IMF8, IMF11 and IMF12 are related IMF components, and the root mean square of the autocorrelation coefficient of the IMF component is as follows: Fig.12 As shown. After S1-S4 processing of the relevant IMF components, the denoised signal is obtained as follows Fig.10 As shown, the signal-to-noise ratio of the original signal is 5.0000dB, and the signal-to-noise ratio after using the method of the present invention is 25.1879dB; the root mean square error of the original signal is 0.0282V, and the root mean square error after using the method of the present invention is 0.0028V. The comparison of the error curves is as follows Fig.11 shown.

[0117] It can be proved through multiple embodiments that the method of the present invention can significantly improve the problem that small angular vibration signals are easily interfered by noise, which is beneficial to improving the signal-to-noise ratio of the signal, reducing signal errors, and can better preserve the detailed information of small angular vibrations.

Claims

1. A method for reducing noise of MHD angular velocity sensor signal, characterized in that: The following steps are involved: S1. Perform adaptive noise complete set empirical mode decomposition on the original signal to obtain multiple IMF components; S2. Calculate the autocorrelation coefficient of each IMF component separately and its root mean square r 1,c , filter out relevant IMF components and remove irrelevant IMF components; among them, the relevant IMF component is r 1,c ≥β1 corresponding to the IMF component; the irrelevant component is r 1,c <β1 corresponding to the IMF component; where β1 is the first threshold set, c is the number of IMF components, and τ1 is the delay of the set IMF component; S3. De-noise each relevant IMF component obtained in S2 by wavelet packet threshold processing, specifically: S3.

1. Perform wavelet packet decomposition on each relevant IMF component, with the decomposition layer number being J layers, and obtain multiple frequency bands of the Jth layer in the relevant IMF component and their corresponding wavelet packet coefficient sequences; S3.

2. Calculate the autocorrelation coefficient of the wavelet packet coefficient sequence of each frequency band in the Jth layer and its root mean square r 2,I ; Where I is the frequency band number of the J-th layer band decomposition sequence, I = 0, 1, 2, 3, 4, ..., 2 J -1; S3.

3. Calculate the wavelet packet coefficient thresholds of each frequency band in the Jth layer using the threshold criterion; The threshold criterion is an improved threshold criterion: Where, T J,I is the wavelet packet coefficient threshold of the Jth layer and the Ith frequency band, σ is the standard deviation of the noise in the estimated IMF component, N is the data length of the IMF component, β2 is the set second threshold, d and b are adjustment coefficients, d>0, b>0; S3.4 performs threshold denoising on each frequency band of the Jth layer using the wavelet packet coefficient threshold of each frequency band of the Jth layer through a threshold function; the threshold function is an improved threshold function, as shown in the following formula: In the formula, w J,I (f) is the wavelet packet coefficient sequence of the fth point in the I frequency band at the decomposition level J; is the wavelet packet coefficient sequence after denoising at the fth point in the I frequency band at the decomposition level J, λ J,I,f is the threshold adjustment factor; S3.

5. Reconstruct each frequency band denoised in S3.4 to obtain denoised related IMF components; S4. Combine the denoised related IMF components obtained in S3.5 to obtain a denoised signal.

2. The method for reducing noise of an MHD angular velocity sensor signal according to claim 1, characterized in that: In S3.4, the threshold adjustment factor λ J,I,f Specifically: In the formula, w J,I (f) is the wavelet packet coefficient sequence of the fth point in the I frequency band at the decomposition level J; α is the adjustment parameter, α>0.

3. The method for reducing noise of MHD angular velocity sensor signals according to claim 2, characterized in that: In S3.4, the value range of α is 0-1.

4. A method for reducing noise of MHD angular velocity sensor signals according to any one of claims 1 to 3, characterized in that: In S2, 0<β1<0.

01.

5. The method for reducing noise of MHD angular velocity sensor signals according to claim 4, characterized in that: In S3.3, d>10, b>10.

6. The method for reducing noise of MHD angular velocity sensor signals according to claim 5, characterized in that: In S3.3, 0<β2<0.

01.

7. The method for reducing noise of MHD angular velocity sensor signals according to claim 6, characterized in that: In S2, the value of β1 is 0.005; In S3.3, d = 100, b = 100; In S3.3, the value of β2 is 0.005.

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