A method and system for denoising vibration signals of hydropower units based on cross entropy

Abstract

The present invention discloses a method and system for denoising a vibration signal of a hydropower unit based on cross entropy, which relates to the technical field of signal processing and comprises the following steps: using an empirical mode decomposition method to decompose and process the original vibration signal to obtain a number of modal components; calculating the cross entropy of the several modal components and the original vibration signal and calculating the threshold value to screen the effective component; using a singular value decomposition method to perform secondary denoising on the effective component to obtain a secondary denoised component; reconstructing the secondary denoised component to obtain a denoised vibration signal. The present invention combines the empirical mode decomposition method and the singular value decomposition method to perform denoising on the vibration signal, has a certain robustness, and can avoid the loss of effective information in the signal.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and more particularly to a method and system for reducing noise of vibration signals of hydropower units based on cross entropy. Background Art

[0002] The hydropower unit is the heart of hydropower, and regular fault diagnosis is the premise for ensuring the healthy operation of the hydropower industry. Most of the fault information of the hydropower unit is hidden in the vibration signal, but it is often submerged in the many noises in the operation of the hydropower unit, so that most of the signal distortion cannot obtain the exact fault information. Therefore, before the subsequent fault diagnosis work, it is a necessary step to pre-process the vibration signal of the hydropower unit to reduce the noise.

[0003] Therefore, how to effectively reduce the noise of vibration signals, simplify the calculation process, and avoid the loss of effective information is a technical problem that technical personnel in this field urgently need to solve. Summary of the invention

[0004] In view of this, the present invention provides a method and system for denoising vibration signals of hydropower units based on cross entropy, which combines empirical mode decomposition and singular value decomposition to perform denoising on vibration signals, has certain robustness, and reduces the loss of effective information in the signal.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for reducing noise of vibration signals of a hydropower unit based on cross entropy comprises the following steps:

[0007] The original vibration signal is decomposed and processed using the empirical mode decomposition method to obtain several modal components;

[0008] Calculating the cross entropy between several modal components and the original vibration signal and calculating the threshold value to screen the effective components;

[0009] Performing secondary denoising on the effective component by using a singular value decomposition method to obtain a secondary denoised component;

[0010] The components after secondary noise reduction are reconstructed to obtain a vibration signal after noise reduction.

[0011] The technical effect achieved by the above technical solution is: combining the empirical mode decomposition method and the singular value decomposition method can effectively reduce the noise of the signal, and has a certain robustness, solving the problem of loss of effective information in the noise reduction process.

[0012] Optionally, the obtaining of a plurality of modal components specifically comprises the following steps:

[0013] Determine all the maximum and minimum points of the original vibration signal within the analysis period, and use cubic splines to connect all the maximum and minimum points with smooth line segments to form an upper envelope and a lower envelope; the upper envelope and the lower envelope include all the maximum and minimum points;

[0014] Calculate the mean of the upper envelope and the lower envelope to obtain the first signal h1:

[0015] h1=x(t)-m1 (1);

[0016] Determine whether the first signal h1 satisfies a preset condition. If so, use the first signal h1 as the first intrinsic mode function, denoted as c1(t); if not, repeat the above operation until the preset condition is satisfied;

[0017] Separate c1(t) from the original vibration signal to obtain the second signal r1:

[0018] r1=x(t)-c1 (2);

[0019] Repeat the above operations to obtain several modal components:

[0020]

[0021] The loop ends when a monotonic function is obtained and the intrinsic mode function cannot be extracted from the signal:

[0022]

[0023] In the formula, r n (t) is the residual function, which indicates the stable trend of the signal; x(t) is the original vibration signal; m1 is the mean of the upper and lower envelopes.

[0024] Optionally, the preset condition is:

[0025] During the analysis period, the number of extreme value points and the number of zero-crossing points are equal or differ by at most 1;

[0026] At any time, the average value between the upper envelope formed by the maximum value point and the lower envelope formed by the minimum value point in the analysis period is zero, that is, the signal of the analysis period is locally symmetrical up and down based on the time axis.

[0027] Optionally, the screening effective component is specifically:

[0028] If a random variable has two independent probability distributions P(x) and Q(x), The cross entropy is expressed as:

[0029]

[0030] When both probability distributions obey Gaussian distribution, the cross entropy can be expressed as:

[0031]

[0032] Where μ1, μ2, σ1, and σ2 represent the mean and standard deviation of two probability density distribution functions respectively;

[0033] Assuming that the sub-band logarithmic energy distribution of the useful signal and background noise in the processed signal conforms to the Gaussian distribution, the logarithmic energy probability distribution of the useful signal is recorded as P S , the logarithmic energy probability distribution of the background noise signal is recorded as P N , and their means are μ S , μ N , and the standard deviations are σ S , σ N , the measurement expression is specified as:

[0034]

[0035] The threshold expression is:

[0036]

[0037] In the formula, E(·) represents the mean; ρ S,N represents the final symmetric cross entropy measure, n represents the number of modal components, H i represents the correlation coefficient between the i-th modal component and the original signal;

[0038] Components above the threshold are selected as suspicious components and secondary denoising is performed.

[0039] Optionally, obtaining the component after secondary noise reduction specifically includes the following steps:

[0040] Reconstruct the time series of length N into an m×n Hankle matrix as follows:

[0041]

[0042] According to the orthogonalization method:

[0043] K=UDV T (10);

[0044] In the formula, N = m + n + 1, m and n represent the order of the matrix, U∈R m×m , V∈R n×n , D∈R m×n , D=(diag(σ1,σ2,...,σ q), 0), 0 represents the zero matrix; q = min(m,n); σ1≥σ2≥...≥σ q >0 represents the singular value of the matrix;

[0045] Based on the singular value difference spectrum, the maximum mutation point is determined as the dividing point between effective information and noise information, and the part before the dividing point is selected for superposition and reconstruction to obtain the component after secondary denoising.

[0046] The technical effect achieved by the above technical solution is: using singular value decomposition (SVD) method to perform secondary noise reduction to reduce the loss of effective signal information.

[0047] The present invention also discloses a hydropower unit vibration signal denoising system based on cross entropy, comprising: a first decomposition module, a screening module, a second decomposition module, and a reconstruction module, and each structure is connected in sequence;

[0048] The first decomposition module decomposes the original vibration signal using an empirical mode decomposition method to obtain a number of modal components;

[0049] The screening module is used to calculate the cross entropy between several modal components and the original vibration signal and calculate the threshold value to screen the effective components;

[0050] The second decomposition module performs secondary denoising on the effective component by using a singular value decomposition method to obtain a secondary denoised component;

[0051] The reconstruction module is used to reconstruct the components after the secondary noise reduction to obtain the vibration signal after noise reduction.

[0052] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method and system for denoising vibration signals of hydropower units based on cross entropy, which decomposes vibration signals based on empirical mode decomposition and cross entropy, selects effective components, and uses singular value decomposition to perform secondary denoising to reduce the loss of effective information of the signal; introduces the concept of cross entropy and simplifies the calculation process, and uses it as a criterion for effective component screening. This technical solution combines empirical mode decomposition and singular value decomposition, can effectively denoise vibration signals, and has a certain degree of robustness, solving the problem of effective information loss during denoising. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0054] Figure 1 It is a flow chart of the method for denoising the vibration signal of a hydropower unit based on cross entropy;

[0055] Figure 2(a) and Figure 2(b) are the frequency graph after processing by the improved EMD method and the frequency graph after denoising based on cross entropy, respectively;

[0056] Figure 3 This is the structural diagram of the hydropower unit vibration signal denoising system based on cross entropy. DETAILED DESCRIPTION

[0057] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] Example 1

[0059] In order to perform noise reduction processing on the vibration signal of a hydropower unit, the embodiment of the present invention discloses a noise reduction method for the vibration signal of a hydropower unit based on cross entropy, such as Figure 1 As shown, the following steps are included:

[0060] The original vibration signal is decomposed and processed using the empirical mode decomposition method to obtain several modal components;

[0061] Calculating the cross entropy between several modal components and the original vibration signal and calculating the threshold value to screen the effective components;

[0062] Performing secondary denoising on the effective component by using a singular value decomposition method to obtain a secondary denoised component;

[0063] The components after secondary noise reduction are reconstructed to obtain a vibration signal after noise reduction.

[0064] Next, the technical solution is described in more detail to further understand the noise reduction process of the vibration signal of the hydropower unit.

[0065] (1) The original vibration signal is decomposed using the empirical mode decomposition (EMD) method to obtain several modal components, which specifically includes the following steps:

[0066] Firstly, all the maximum and minimum points of the original vibration signal in the analysis period are determined, and all the maximum and minimum points are connected by smooth line segments using cubic splines to form an upper envelope and a lower envelope; the upper envelope and the lower envelope include all the maximum and minimum points;

[0067] Calculate the mean of the upper envelope and the lower envelope to obtain the first signal h1:

[0068] h1=x(t)-m1 (1);

[0069] Determine whether the first signal h1 satisfies a preset condition. If so, use the first signal h1 as the first intrinsic mode function, denoted as c1(t); if not, repeat the above operation until the preset condition is satisfied;

[0070] Separate c1(t) from the original vibration signal to obtain the second signal r1:

[0071] r1=x(t)-c1 (2);

[0072] Repeat the above operations to obtain several modal components:

[0073]

[0074] The loop ends when a monotonic function is obtained and the intrinsic mode function cannot be extracted from the signal:

[0075]

[0076] In the formula, r n (t) is the residual function, which indicates the stable trend of the signal; x(t) is the original vibration signal; m1 is the mean of the upper and lower envelopes.

[0077] The preset conditions are:

[0078] During the analysis period, the number of extreme points and the number of zero-crossing points are equal or differ by at most 1;

[0079] At any time, the average value between the upper envelope formed by the maximum value point and the lower envelope formed by the minimum value point in the analysis period is zero, that is, the signal of the analysis period is locally symmetrical up and down based on the time axis.

[0080] (2) Calculate the cross entropy between several modal components and the original vibration signal and calculate the threshold value to screen the effective components, specifically:

[0081] If a random variable has two independent probability distributions P(x) and Q(x), The cross entropy is expressed as:

[0082]

[0083] When both probability distributions obey Gaussian distribution, the cross entropy can be expressed as:

[0084]

[0085] Where μ1, μ2, σ1, and σ2 represent the mean and standard deviation of two probability density distribution functions respectively;

[0086] Assuming that the sub-band logarithmic energy distribution of the useful signal and background noise in the processed signal conforms to the Gaussian distribution, the logarithmic energy probability distribution of the useful signal is recorded as P S , the logarithmic energy probability distribution of the background noise signal is recorded as P N , and their means are μ S , μ N , and the standard deviations are σ S , σ N , the measurement expression is specified as:

[0087]

[0088] The threshold expression is:

[0089]

[0090] In the formula, E(·) represents the mean; ρ S,N represents the final symmetric cross entropy measure, n represents the number of modal components, H i represents the correlation coefficient between the i-th modal component and the original signal;

[0091] Components above the threshold are selected as suspicious components and secondary denoising is performed.

[0092] (3) performing secondary denoising on the effective component by using a singular value decomposition (SVD) method to obtain a secondary denoised component, specifically comprising the following steps:

[0093] Reconstruct the time series of length N into an m×n Hankle matrix as follows:

[0094]

[0095] According to the orthogonalization method:

[0096] K=UDV T (10);

[0097] In the formula, N = m + n + 1, m and n represent the order of the matrix, U∈R m×m , V∈R n×n , D∈R m×n , D=(diag(σ1,σ2,...,σ q ), 0), 0 represents the zero matrix; q = min(m,n); σ1≥σ2≥...≥σ q >0 represents the singular value of the matrix;

[0098] Based on the singular value difference spectrum, the maximum mutation point is determined as the dividing point between effective information and noise information, and the part before the dividing point is selected for superposition and reconstruction to obtain the component after secondary denoising.

[0099] (4) Reconstruct the components after the secondary noise reduction to obtain the vibration signal after noise reduction.

[0100] Next, the vibration signal denoising results of this technical solution are analyzed through specific experiments. The Chirp function is used to simulate the signal, and noise with signal-to-noise ratios of 0dB, 5dB, 10dB, and 15dB are added respectively. The EMD+wavelet threshold denoising method is introduced for comparison. The results are shown in Table 1. The cross entropy-based denoising method performs well in different signal-to-noise ratio environments, not only improving the signal-to-noise ratio of the noisy signal, but also reducing the root mean square error of the signal.

[0101] Table 1 Denoising results based on cross entropy method and EMD+wavelet denoising method

[0102]

[0103] It can be seen more intuitively from the frequency diagrams of Figure 2(a) and Figure 2(b) that the characteristics of the fault signal are more prominent when the signal is denoised using the cross entropy-based denoising method.

[0104] Example 2

[0105] The embodiment of the present invention discloses a hydropower unit vibration signal noise reduction system based on cross entropy, such as Figure 3 As shown, it includes: a first decomposition module, a screening module, a second decomposition module, and a reconstruction module, and each structure is connected in sequence;

[0106] The first decomposition module decomposes the original vibration signal using an empirical mode decomposition method to obtain a number of modal components;

[0107] The screening module is used to calculate the cross entropy between several modal components and the original vibration signal and calculate the threshold value to screen the effective components;

[0108] The second decomposition module performs secondary denoising on the effective component by using a singular value decomposition method to obtain a secondary denoised component;

[0109] The reconstruction module is used to reconstruct the components after the secondary noise reduction to obtain the vibration signal after noise reduction.

[0110] Based on the empirical mode decomposition method and cross entropy, the vibration signal is decomposed and the effective components are selected, and the singular value decomposition method is used for secondary noise reduction to reduce the loss of effective information of the signal; the concept of cross entropy is introduced and the calculation process is simplified, and it is used as the judgment standard for effective component screening. This technical solution combines the empirical mode decomposition method and the singular value decomposition method, which can effectively reduce the noise of the vibration signal and has a certain degree of robustness, solving the problem of loss of effective information in the noise reduction process.

[0111] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0112] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for denoising vibration signals of hydropower units based on cross entropy, characterized in that: The following steps are involved: The original vibration signal is decomposed and processed using the empirical mode decomposition method to obtain several modal components; Calculating the cross entropy between several modal components and the original vibration signal and calculating the threshold value to screen the effective components; Performing secondary denoising on the effective component by using a singular value decomposition method to obtain a secondary denoised component; Reconstructing the components after secondary noise reduction to obtain a vibration signal after noise reduction; The screening effective component is specifically: If a random variable has two independent probability distributions P(x) and Q(x), The cross entropy is expressed as: When both probability distributions obey Gaussian distribution, the cross entropy can be expressed as: Where μ1, μ2, σ1, and σ2 represent the mean and standard deviation of two probability density distribution functions respectively; Assuming that the sub-band logarithmic energy distribution of the useful signal and background noise in the processed signal conforms to the Gaussian distribution, the logarithmic energy probability distribution of the useful signal is recorded as P S , the logarithmic energy probability distribution of the background noise signal is recorded as P N , and their means are μ S , μ N , and the standard deviations are σ S , σ N , the measurement expression is specified as: The threshold expression is: In the formula, E(·) represents the mean; ρ S,N represents the final symmetric cross entropy measure, n represents the number of modal components, H i represents the correlation coefficient between the i-th modal component and the original signal; Components above the threshold are selected as suspicious components and secondary denoising is performed.

2. According to a cross entropy-based hydropower unit vibration signal denoising method according to claim 1, it is characterized in that: The obtaining of the plurality of modal components specifically comprises the following steps: Determine all the maximum and minimum points of the original vibration signal within the analysis period, and use cubic splines to connect all the maximum and minimum points with smooth line segments to form an upper envelope and a lower envelope; the upper envelope and the lower envelope include all the maximum and minimum points; Calculate the mean of the upper envelope and the lower envelope to obtain the first signal h1: h1=x(t)-m1 (1); Determine whether the first signal h1 satisfies a preset condition. If so, take the first signal h1 as the first intrinsic mode function, denoted as c1(t); if not, repeat the above operation until the preset condition is satisfied; Separate c1(t) from the original vibration signal to obtain the second signal r1: r1=x(t)-c1 (2); Repeat the above operations to obtain several modal components: The loop ends when a monotonic function is obtained and the intrinsic mode function cannot be extracted from the signal: In the formula, r n (t) is the residual function, which indicates the stable trend of the signal; x(t) is the original vibration signal; m1 is the mean of the upper and lower envelopes.

3. A method for denoising a vibration signal of a hydropower unit based on cross entropy according to claim 2, characterized in that: The preset conditions are: During the analysis period, the number of extreme value points and the number of zero-crossing points are equal or differ by at most 1; At any time, the average value between the upper envelope formed by the maximum value point and the lower envelope formed by the minimum value point in the analysis period is zero, that is, the signal of the analysis period is locally symmetrical up and down based on the time axis.

4. A method for denoising a vibration signal of a hydropower unit based on cross entropy according to claim 1, characterized in that: The step of obtaining the secondary noise reduction component specifically includes the following steps: Reconstruct the time series of length N into an m×n Hankle matrix as follows: According to the orthogonalization method: K=UDV T (10); In the formula, N = m + n + 1, m and n represent the order of the matrix, U∈R m×m , V∈R n×n , D∈R m×n , D=(diag(σ1,σ2,...,σ q ), 0), 0 represents the zero matrix; q = min(m,n); σ1≥σ2≥...≥σ q >0 represents the singular value of the matrix; Based on the singular value difference spectrum, the maximum mutation point is determined as the dividing point between effective information and noise information, and the part before the dividing point is selected for superposition and reconstruction to obtain the component after secondary denoising.

5. A hydropower unit vibration signal denoising system based on cross entropy, using the hydropower unit vibration signal denoising method based on cross entropy as described in any one of claims 1 to 4, characterized in that: include: A first decomposition module, a screening module, a second decomposition module, and a reconstruction module, and each structure is connected in sequence; The first decomposition module decomposes the original vibration signal using an empirical mode decomposition method to obtain a number of modal components; The screening module is used to calculate the cross entropy between several modal components and the original vibration signal and calculate the threshold value to screen the effective components; The second decomposition module performs secondary denoising on the effective component by using a singular value decomposition method to obtain a secondary denoised component; The reconstruction module is used to reconstruct the components after the secondary noise reduction to obtain the vibration signal after noise reduction.

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