A blind deconvolution method based on candidate fault frequency

Abstract

The application discloses a blind deconvolution method based on candidate fault frequency, and belongs to the field of rotating machinery state monitoring and fault diagnosis. Firstly, the measured signal is decomposed into different frequency bands to obtain a series of narrow-band signals with different center frequencies and bandwidths; then, based on the local features of the square envelope spectrum of the narrow-band signal, candidate fault frequencies possibly related to faults are identified, and then an optimal objective function is constructed by using the candidate fault frequencies; finally, an iterative solution strategy is adopted to solve the blind deconvolution filter, so that the bearing transient cyclic impact fault feature extraction is realized. Compared with existing deconvolution methods, the method fully excavates the time-frequency characteristics of the vibration signal, can effectively extract the local defect fault feature information of the rotating machinery, and is suitable for bearing fault diagnosis under the working condition of missing shaft rotating speed information.

Description

Technical Field

[0001] This invention relates to the field of health monitoring of rotating machinery structures, and specifically to a blind deconvolution method based on candidate fault frequencies. Background Technology

[0002] Rolling bearings are extremely precise components in modern industrial systems. Their primary function is to convert the sliding friction between the drive shaft and the bearing housing into rolling friction, ensuring the normal operation of the mechanical system. Under complex service conditions, localized damage to bearings can easily be induced, affecting the safe operation of mechanical equipment. When a damaged bearing component periodically passes through the load area, it can trigger a series of transient cyclic impacts. However, the measured bearing vibration signal is only partially represented, and fault characteristics are difficult to identify under strong background noise interference. Therefore, extracting weak impact fault characteristics from the measured vibration signal is crucial for achieving early bearing fault diagnosis.

[0003] Blind deconvolution is a typical method for extracting bearing impact fault features. This method utilizes finite impulse response (FIR) filters to extract axle box fault features, typically selecting an index sensitive to fault impulses as the optimization objective to solve for the filter parameters, thereby extracting impact features from the signal. The 2012 paper "Maximum correlated kurtosis deconvolution and application on gear tooth chip fault detection," published in *Mechanical Systems and Signal Processing*, designed an iterative strategy for solving the filter by maximizing the correlation kurtosis of the filtered signal, proposing maximum correlation kurtosis deconvolution, which can be used to extract periodic fault impulses from the signal. The 2017 paper "MultipointOptimal Minimum Entropy Deconvolution and Convolution Fix: Application tovibration fault detection," also published in *Mechanical Systems and Signal Processing*, uses the multipoint D-norm of the filtered signal as the optimization objective, proposing multipoint D-norm blind deconvolution. To improve filter solution strategies, the 2018 paper "Application of an improved minimum entropy deconvolution method for railway rolling element bearing fault diagnosis," published in the *Journal of Sound and Vibration*, proposed a filter solution strategy applicable to various blind deconvolution methods based on generalized spherical coordinate transformation and particle swarm optimization. The aforementioned methods all construct an optimal objective function in the time domain to solve the filter, making them susceptible to interference from strong background noise. To enhance the fault feature extraction performance of deconvolution methods, the 2018 paper "Blinddeconvolution based on cyclostationarity maximization and its application to fault identification," also published in the *Journal of Sound and Vibration*, for the first time extended the optimal objective function from the time domain to the frequency spectrum. Based on the cyclostationarity of rotating machinery fault characteristics, it proposed a method to enhance transient impacts of a specific period by maximizing the second-order cyclostationarity of the filtered signal.The methods described above all require bearing fault cycle information when constructing the optimization objective function. Therefore, when bearing speed information is lacking, these methods cannot be used for bearing impact fault feature extraction. To address this, fully exploring the features hidden in the vibration signal and constructing an optimization objective function independent of fault cycle information is key to expanding the application scenarios of blind deconvolution algorithms and realizing the extraction of weak impact fault features even when bearing speed information is missing. Summary of the Invention

[0004] To address the aforementioned shortcomings in the prior art, this invention provides a blind deconvolution method based on candidate fault frequencies.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0006] A blind deconvolution method based on candidate fault frequencies includes the following steps:

[0007] S1. Collect the vibration acceleration signal of rotating machinery and decompose the vibration acceleration signal into narrowband signals with different center frequencies and bandwidths;

[0008] S2. Calculate the squared envelope spectrum of each narrowband signal, and construct a time-frequency information matrix using the squared envelope spectra of all narrowband signals.

[0009] S3. Identify candidate fault frequencies based on the local features of the square envelope spectrum of the narrowband signal;

[0010] S4. Construct the optimization objective function based on the candidate frequencies and solve the blind deconvolution filter;

[0011] S5. Calculate the blind deconvolution filter signal and extract the fault characteristics of rotating machinery.

[0012] Furthermore, the squared envelope spectrum of the narrowband signal in S2 is calculated as follows:

[0013]

[0014] Where Δf is the frequency interval, m = 1,...,M, and j is the imaginary unit. For narrowband signal c k,l (t n The envelope of ).

[0015] Furthermore, step S3 specifically includes the following steps:

[0016] S31. Construct an indicator vector based on the squared envelope spectrum of the narrowband signal:

[0017] Id k,l =[Id k,l (1),Id k,l(2),...,Id k,l (M)] T

[0018] Where k represents the k-th decomposition layer in the acceleration signal decomposition process, l represents the l-th narrowband signal of the k-th layer, and Id *,l M is the number of indicator vectors;

[0019] S32. Calculate the number η(m) of narrowband envelope spectra that take a local maximum at frequency m·Δf based on the constructed indicator vector, expressed as:

[0020]

[0021] B k K represents the number of narrowband signals in the k-th decomposition layer during the acceleration signal decomposition process, where K is the number of decomposition layers.

[0022] Arrange η(m) in descending order into a vector to obtain the vector

[0023] S33. Calculate the frequencies of the top D candidate faults based on the vectors arranged in descending order in S32.

[0024] Furthermore, in S31, the indicator vector indicates the local maximum information value in the narrowband signal envelope spectrum.

[0025]

[0026] Where P is a positive integer and m is the m-th indicator vector.

[0027] Furthermore, the calculation method for the first D candidate fault frequencies in S33 is as follows:

[0028]

[0029] Where, α d Let d be the fault frequency.

[0030] Furthermore, step S4 specifically includes the following steps:

[0031] S41. Construct a blind deconvolution filter h = [h0,...,h...] S-1 ] T Where S is the filter length, the filtered signal y of the blind deconvolution filter is expressed as:

[0032]

[0033] Where x = [x(t0),...,v(t)] N-1 )] TGiven the original signal, y = [y(t0), ..., y(t)]. N-1 )] T , t=[t0,...,t N-1 ] T Where S is the sampling time, S is the filter length, and N is the signal length. (Each parameter needs to be explained here.)

[0034] S42. Calculate the cyclic stability index based on the candidate fault frequency according to the filtered signal. The calculation method is as follows:

[0035]

[0036] Among them, E * and E T These are the conjugate matrix and transpose matrix of matrix E, respectively. Matrix E is represented as:

[0037]

[0038] S43, By maximizing the cyclic stability index Solve for the filter.

[0039] The present invention has the following beneficial effects:

[0040] 1. This invention fully explores the time-frequency features of vibration signals to identify candidate fault frequencies that may be related to the fault, and then constructs an optimized objective function to solve a blind deconvolution filter. It does not rely on fault period information and solves the problem of fault feature extraction when shaft speed information is missing.

[0041] 2. This invention can more effectively extract minor fault feature information of rotating machinery, has good anti-interference ability, and has a wide range of applications. Attached Figure Description

[0042] Figure 1 This is a flowchart of the blind deconvolution method based on candidate fault frequency in this invention.

[0043] Figure 2 This is the time-domain waveform of the filtered signal in the blind deconvolution method based on candidate fault frequencies in this invention.

[0044] Figure 3 This is a schematic diagram of the candidate fault feature frequency in the blind deconvolution method based on candidate fault frequency in this invention.

[0045] Figure 4 It is the optimal filter obtained in the blind deconvolution method based on candidate fault frequencies in this invention.

[0046] Figure 5 It is the blind deconvolution filtering signal in the blind deconvolution method based on candidate fault frequency in this invention. Detailed Implementation

[0047] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0048] A blind deconvolution method based on candidate fault frequencies, such as Figure 1 As shown, it includes the following steps:

[0049] S1. Collect the vibration acceleration signal of rotating machinery and decompose the vibration acceleration signal into narrowband signals with different center frequencies and bandwidths;

[0050] The measured vibration signal x(t) n ), The signal n = 0, 1, ..., N-1 (where N is the signal length and Fs is the signal sampling frequency) is decomposed into narrowband signals with different center frequencies and bandwidths, and all narrowband signals have a length of N. A binary tree or 1 / 3-binary tree filter bank can be used to decompose the signal. At the same decomposition level, the signal is decomposed into a series of narrowbands with the same bandwidth but different center frequencies; as the number of decomposition levels increases, the bandwidth of the narrowband signal becomes narrower. At the k-th decomposition level (k = 1, ..., K, where K is the maximum number of decomposition levels), the signal is decomposed into B... k A narrowband signal. Let c k,l (t n ) represents the l-th (l=1,…,B) layer k. k If there are ) narrowband signals, then the bandwidth BW of the narrowband signal is... k and center frequency FC k,l BW k =Fs / 2 / B k and FC k,l =BW k ·(l-1 / 2).

[0051] S2. Calculate the squared envelope spectrum of each narrowband signal, and construct a time-frequency information matrix using the squared envelope spectra of all narrowband signals.

[0052] For any narrowband signal c k,l (t n Its square envelope spectrum SES k,l The calculation is as follows:

[0053]

[0054] Where Δf is the frequency interval, which is generally determined by a numerical calculation algorithm. When SES is calculated using Fast Fourier Transform... k,l hour, Where floor is the floor function, with parameters m = 1, ..., M, and j is the imaginary unit. For narrowband signal c k,l (t n The envelope of ). It is important to note that when SES is required... k,l When information of at least frequency band [0, Ys] is included, M = floor(Ys / Δf) + 1; the upper limit of bandwidth Ys can be selected as needed, but cannot exceed Fs / 2.

[0055] In this embodiment, the narrowband signal c is solved. k,l (t n envelope The method is not fixed. The envelope spectrum of a narrowband signal can be solved using the Hilbert Transform or the Teager-Kaiser energy operator, but it is not limited to these two methods.

[0056] S3. Identify candidate fault frequencies based on the local features of the squared envelope spectrum of the narrowband signal. In this embodiment, the following steps are included:

[0057] S31. Construct an indicator vector based on the squared envelope spectrum of the narrowband signal:

[0058] According to narrowband envelope spectrum SES k,l Construct the indicator vector Id k,l =[Id k,l (1),Id k,l (2),...,Id k,l (M)] T ID k,l Only 0 or 1 is used to indicate local maxima information in the envelope spectrum of narrowband signals, as follows:

[0059]

[0060] In the formula, the parameter P takes a positive integer and controls the vector Id. k,l The sparsity of zero elements in non-zero regions.

[0061] S32. Calculate the number η(m) of narrowband envelope spectra that take a local maximum at frequency m·Δf based on the constructed indicator vector.

[0062] The number of narrowband envelope spectra that take a local maximum at frequency m·Δf is counted and denoted as η(m). The indicator vector Id obtained from S32... k,l It can be seen that η(m) can be expressed as:

[0063]

[0064] Next, η(m) is arranged in descending order, m = 1, ..., M, to obtain the vector.

[0065] S33. Calculate the frequencies of the top D candidate faults based on the vectors arranged in descending order in S32.

[0066] According to the vector Calculate the frequencies of the top D candidate faults. The formula is as follows:

[0067]

[0068] The characteristics of the candidate fault frequencies obtained after calculation are as follows: Figure 3 As shown.

[0069] S4. Construct the optimization objective function based on the candidate frequencies and solve the blind deconvolution filter;

[0070] S41. Construct a blind deconvolution filter h = [h0,...,h...] S-1 ] T Where S is the filter length, and the filtered signal y of the blind deconvolution filter is as follows: Figure 2 As shown, it is represented as:

[0071]

[0072] S42. Calculate the cyclic stability index based on the candidate fault frequency according to the filtered signal.

[0073] The calculation formula is as follows:

[0074]

[0075] Where: |y| 2 =[|y(t S-1 )| 2 ,...,|y(t N-1 )| 2 ] T E = [e1,...,e D ], E * and E T These are the conjugate matrix and transpose matrix of matrix E, respectively. Substituting equation (5) into equation (6), we can obtain the cyclic stability index. It can be represented in the following form:

[0076]

[0077] Among them, R XWX=X T WX, R XX =X T X, W=((N-S+1))diag(γ[y]) / (y T y), diag(γ[y]) represents the vector γ[y] = E * E T |y| 2 The generated diagonal matrix consists of / (N-S+1). By maximizing Solve for filter h.

[0078] S43, By maximizing the cyclic stability index Solve for the filter.

[0079] In this embodiment, by maximizing The method for solving the filter h is not fixed. h can be solved by finding the eigenvalues: From formula (7), it can be seen that... The filter h that takes the maximum value is R. XWX h = R XX The eigenvector corresponding to the largest eigenvalue of hλ. Therefore, h can be solved using the following iterative strategy:

[0080] Step 1: Initialize filter h;

[0081] Step 2: Calculate matrix W using the given X and h;

[0082] Step 3: Solve for R XWX h = R XX The eigenvector h corresponding to the largest eigenvalue of hλ;

[0083] Step 4: Return to Step 2 until filter h converges.

[0084] The above method is only a typical approach to solving for filter h, but it is not limited to this method alone. Other methods, such as particle swarm optimization, can also be used to solve for the filter. The obtained optimal filter response is as follows: Figure 4 As shown.

[0085] S5. Calculate the blind deconvolution filter signal and extract the fault characteristics of rotating machinery.

[0086] Substituting the calculated filter h into formula (5) yields the deconvolution filtered signal y, such as... Figure 5 As shown.

[0087] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0088] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0089] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0090] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0091] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A blind deconvolution method based on candidate fault frequencies, characterized in that, Includes the following steps: S1. Collect the vibration acceleration signal of rotating machinery and decompose the vibration acceleration signal into narrowband signals with different center frequencies and bandwidths; S2. Calculate the squared envelope spectrum of each narrowband signal, and construct a time-frequency information matrix using the squared envelope spectra of all narrowband signals. The squared envelope spectrum of the narrowband signal is calculated as follows: in, For frequency intervals, , j The imaginary unit, Narrowband signal The envelope. S3. Identify candidate fault frequencies based on the local features of the square envelope spectrum of the narrowband signal; S4. Construct the optimization objective function based on the candidate frequencies and solve the blind deconvolution filter, which includes the following steps: S41. Construct a blind deconvolution filter ,in S The length of the filter is the filtered signal of the blind deconvolution filter. y Represented as: in, The original signal, , S is the sampling time, S is the filter length, and N is the signal length; S42. Calculate the cyclic stability index based on the candidate fault frequency according to the filtered signal. The calculation method is as follows: in, and They are matrices The conjugate and transpose of the matrix are given by matrix E as follows: S43, By maximizing the cyclic stability index Solve for the filter; S5. Calculate the blind deconvolution filter signal and extract the fault characteristics of rotating machinery.

2. The blind deconvolution method based on candidate fault frequency according to claim 1, characterized in that, S3 specifically includes the following steps: S31. Construct an indicator vector based on the squared envelope spectrum of the narrowband signal: in, The first step in the acceleration signal decomposition process k One decomposition layer, Indicates the first k The first layer l A narrowband signal M is the number of indicator vectors; S32. Calculate the frequency based on the constructed indicator vector. Number of narrowband envelope spectra that take local maxima , is represented as: For the first step in the acceleration signal decomposition process k The number of narrowband signals in each decomposition layer, where K is the number of decomposition layers; Will Arrange them in descending order to form a vector, resulting in a vector. ; S33. Calculate the frequencies of the top D candidate faults based on the vectors arranged in descending order in S32.

3. The blind deconvolution method based on candidate fault frequency according to claim 2, characterized in that, In S31, the indicator vector indicates the local maximum information value in the narrowband signal envelope spectrum. in, It is a positive integer. For the first One indicator vector.

4. The blind deconvolution method based on candidate fault frequency according to claim 2, characterized in that, The calculation method for the first D candidate fault frequencies in S33 is as follows: in, For the first Fault frequency.

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