A mechanical condition monitoring data repair method and system based on VMD and BiCS

Abstract

The present invention belongs to the field of mechanical condition monitoring data repair, and specifically relates to a mechanical condition monitoring data repair method and system based on VMD and BiCS. The method comprises: using a VMD model to decompose and reconstruct acquired monitoring data to obtain a reconstructed signal; using an improved BiCS method to repair the reconstructed signal to obtain repaired data; the improved BiCS method simplifies the reconstruction model in the method; the present invention firstly uses VMD to decompose and reduce the mechanical condition monitoring signal, which can effectively eliminate the influence of noise-related characteristics and retain signal characteristics, and at the same time uses Bi‑CS to establish a connection before and after the missing data, and mines the bearing fault information contained in the data under noise, so as to effectively restore the missing data.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical condition monitoring data repair, and in particular relates to a mechanical condition monitoring data repair method and system based on VMD and BiCS. Background Art

[0002] In order to grasp the operating status of mechanical equipment in real time, the use of wireless sensors to detect the status of mechanical vibration signals has become a hot issue in the field of prognostics and health management (PHM). However, in actual environments, mechanical signals are often affected by factors such as noise, bandwidth, and equipment short circuit, so that the received signals may not be complete. In the case of irreversible operation, resampling is impossible. At this time, if equipment status analysis is required, incomplete data must be used, and direct use of these data will affect the accuracy of fault detection or diagnosis results. If the noise interference in the actual collected data can be removed and the data lost during the collection process can be repaired, the accuracy of the equipment status analysis results will be improved. In response to the problem of noise reduction of mechanical signals, scholars have successively proposed methods such as Short-Time Fourier Transform (STFT), Kalman Filtering (KF), and Wavelet Transform (WT). Mechanical signals are generally non-stationary signals, but STFT cannot fully characterize the time-frequency transform characteristics of non-stationary signals, so this type of method has certain limitations. Although KF can process non-stationary signals, this type of method has large errors when processing missing signals or rapidly changing signals. WT has good local time-frequency characteristics, but because its basis function is difficult to adapt to signal changes, this type of method also has shortcomings. EMD has good adaptability and can reflect the local frequency characteristics of the signal very well, but there are problems such as endpoint effects and modal aliasing.

[0003] Most data recovery methods are based on historical monitoring data. Missing values ​​are restored through interpolation, regression, filling and other methods, so as to obtain more complete health detection data. After classifying the data, an improved cubic spline interpolation method based on priority allocation strategy is adopted. QU et al. used a multi-optimized adversarial neural network method to realize the recovery of missing value data of wind speed in wind farms. The above methods are all aimed at the recovery of missing value data with obvious trends and weak noise intensity, which cannot meet the requirements of recovering missing value data of mechanical monitoring vibration. Summary of the invention

[0004] In order to solve the problems existing in the above prior art, the present invention proposes a mechanical condition monitoring data repair method based on VMD and BiCS, the method comprising: acquiring monitoring data to be repaired, using a VMD model to decompose and reconstruct the acquired monitoring data to obtain a reconstructed signal; using an improved BiCS method to repair the reconstructed signal to obtain repaired data;

[0005] The process of repairing the reconstructed signal using the improved BiCS method includes:

[0006] S1: Perform an even extension on the observed missing signal x over period N, and obtain the even signal after extension as y∈R 2N×2N ;

[0007] S2: Perform DCT transformation on the even-extended signal to obtain a sparse dictionary matrix Ψ∈R 2N×2N ;

[0008] S3: Input the even signal y, sparse dictionary matrix Ψ and sparsity K into the improved reconstruction model to obtain a sparse representation

[0009] S4: Based on sparse representation The missing signal is repaired, and the repair formula is: Where y′ represents the repaired even signal, represents sparse representation, Ψ represents sparse dictionary matrix

[0010] S5: Perform inverse pair extension on y′ to obtain a repaired signal x′.

[0011] Preferably, the process of using the VMD model to decompose and reduce noise on the acquired monitoring data includes:

[0012] Step 1: Initialize VMD parameters [α, K]; where α represents the penalty function term and K represents the number of IMF components after signal separation.

[0013] Step 2: Decompose the acquired signal into K IMF components;

[0014] Step 3: Perform Hilbert-Huang transform on each IMF component to obtain the analytical signal of each component;

[0015] Step 4: Estimate the center frequency of each analytical signal and convert the spectrum of the analytical signal into a baseband signal;

[0016] Step 5: After obtaining the demodulated signal according to the baseband signal, calculate the Euclidean distance of the demodulated signal, and estimate the modal bandwidth of the signal according to the Euclidean distance; construct the target variation constraint function according to the modal bandwidth;

[0017] Step 6: Use the penalty function term α and the Lagrange multiplier operator to optimize the order variation constraint function;

[0018] Step 7: Calculate the optimal solution of the optimized order variation constraint function and obtain the optimal IMF component.

[0019] Furthermore, the expression of the analytical signal is:

[0020]

[0021] Where f(t) represents the analytical signal at time t, δ(t) represents the impulse signal, and u k (t) represents the IMF function.

[0022] Furthermore, the optimized target variation constraint function is:

[0023]

[0024] Among them, u k represents the decomposed IMF components, ω k represents the central frequency of IMF, λ represents the Lagrange multiplier, α represents the quadratic penalty function term, and u k (t) represents the IMF function, and λ(t) represents the Lagrange multiplier.

[0025] Preferably, the process of processing the input signal using the improved reconstruction model includes:

[0026] Step 1: Initialize parameters t, Λ0, and That is, let t=1,Λ0=1,2,3,···,N, Among them, t represents the current number of iterations, Λ0 represents the initial index set, represents the sparse representation obtained by the current iteration of the model, N represents the length of the sparse representation signal, Represents N×1 dimensional space;

[0027] Step 2: Obtain the sampling signal x, the sparse matrix ψ, and the sparsity K of the signal, where the length of the sampling signal x is N×1 and the size of the sparse matrix ψ is N×N; calculate the parameter Θ according to the sampling signal x and the sparse matrix ψ, and the calculation formula is: Θ=ψ -1 x; where Θ represents the sparse representation of the signal;

[0028] Step 3: Search for index λ based on the calculated parameter Θ i , so that

[0029] Step 4: Get the parameters based on the index Assign the value to the parameter Right now

[0030] Step 5: Parameter Λ i Update, the update formula is Λ i =Λ i-1 -{λ i}, t=t+1; if t≤K, return to step 3, otherwise stop the iteration and go to step 6;

[0031] Step 6: Based on the reconstruction results Get the value of Θ at index {Λ} and set the elements at other indexes to zero.

[0032] A mechanical condition monitoring data repair system based on VMD and BiCS, the system comprising: a data acquisition module, a VMD decomposition and reconstruction module, a BiCS reconstruction and repair module and an output module;

[0033] The data acquisition module is used to acquire the monitoring data of the machine to be repaired, and input the data into the VMD decomposition and reconstruction module;

[0034] The VMD decomposition and reconstruction module is used to decompose and denoise the monitoring data to be repaired, and reconstruct the decomposed and denoised data to obtain a reconstructed signal;

[0035] The BiCS reconstruction and repair module is used to repair the reconstructed signal to obtain repaired data;

[0036] The output module is used to output the repaired data.

[0037] To achieve the above objectives, the present invention further provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements any of the above-mentioned mechanical condition monitoring data repair methods based on VMD and BiCS.

[0038] To achieve the above-mentioned purpose, the present invention also provides a mechanical condition monitoring data repair device based on VMD and BiCS, comprising a processor and a memory; the memory is used to store a computer program; the processor is connected to the memory, and is used to execute the computer program stored in the memory, so that the mechanical condition monitoring data repair device based on VMD and BiCS performs any of the above-mentioned mechanical condition monitoring data repair methods based on VMD and BiCS.

[0039] Beneficial effects of the present invention:

[0040] The present invention firstly uses VMD to decompose and reduce the mechanical condition monitoring signal, which can effectively eliminate the influence of noise-related characteristics and retain the signal characteristics, simplify the reconstruction model, and improve the reconstruction efficiency. At the same time, Bi-CS is used to establish the connection before and after the missing data, and the bearing fault information contained in the data under noise is mined, so that the missing data can be effectively restored. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Attached Figure 1 It is an overall flow chart of an embodiment of the present invention;

[0042] Attached Figure 2 This is a simplified CS reconstruction model process in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] 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.

[0044] A mechanical condition monitoring data repair method based on VMD and Bi-CS. The specific implementation steps are as follows: Figure 1 As shown in the figure, VMD is used to reconstruct the missing signal, which effectively suppresses the noise characteristics in the vibration signal and retains the characteristics of the original signal. The data repaired by the Bi-CS method is used to establish the training before and after the data, which reduces the error of the repair result.

[0045] The process of decomposing and denoising the acquired monitoring data using the VMD model includes:

[0046] Step 1: Initialize VMD parameters [α, K]; where α represents the penalty function term and K represents the number of IMF components after signal separation.

[0047] Step 2: Decompose the acquired signal into K IMF components;

[0048] Step 3: Perform Hilbert-Huang transform on each IMF component to obtain the analytical signal of each component;

[0049]

[0050] Where f(t) represents the analytical signal at time t, δ(t) represents the impulse signal, and u k (t) represents the IMF function.

[0051] Step 4: Estimate the center frequency of each analytical signal and convert the spectrum of the analytical signal into a baseband signal;

[0052]

[0053] Step 5: After obtaining the demodulated signal according to the baseband signal, calculate the Euclidean distance of the demodulated signal, and estimate the modal bandwidth of the signal according to the Euclidean distance; construct the target variation constraint function according to the modal bandwidth;

[0054]

[0055] Step 6: Use the penalty function term α and the Lagrange multiplier operator to optimize the order variation constraint function;

[0056]

[0057] Among them, u k represents the decomposed IMF components, ω k represents the central frequency of IMF, λ represents the Lagrange multiplier, α represents the quadratic penalty function term, and u k (t) represents the IMF function, and λ(t) represents the Lagrange multiplier.

[0058] Step 7: Calculate the optimal solution of the optimized order variation constraint function and obtain the optimal IMF component.

[0059] When the VMD algorithm performs modal decomposition on the signal, the random noise in the bearing vibration signal will be separated into higher modes. By removing the higher frequency modal components, the noise in the signal can be suppressed. On the other hand, this paper also uses the principle of non-correlated modal removal, which can not only suppress the interference of noise, but also eliminate the non-correlated unintentional interference signals mixed in the bearing vibration signal.

[0060] Compressed Sensing (CS) theory projects the original collected data into a sparse space with only a small number of measurement values, and obtains the complete signal by adopting an appropriate reconstruction algorithm. The reconstruction process is as follows: Figure 2 shown.

[0061] Assume that the complete original signal can be represented as x∈R N , the collected lossy signal is x′∈R N. Set in the acquisition program: If there is no data input at the current moment, the corresponding data value at that moment is set to zero (in fact, during the operation of the equipment, the output value of the vibration sensor is generally not equal to zero when it works normally. Even if it is zero, it can be considered a random situation, so this setting will not affect the recovery algorithm). Assuming that x′ contains M non-zero elements, the number of zero-value elements is N–M. Let the set of corresponding position indices of all zero-value elements be Z, that is, Z={i|x′=0}(i=1,2,…,N), remove the NM zero values ​​in x′, and keep the order and size of other element values ​​unchanged, and the observed signal y∈R M . Let I N ∈R N×N As the identity matrix, I N The jth row (j∈Z) in is deleted, and the order and size of other rows remain unchanged, and the matrix Φ∈R is obtained. M×N This matrix Φ is equivalent to the measurement matrix in CS theory.

[0062] According to the above definition,

[0063] y=Φx (2.1)

[0064] Assume that the original vibration signal x can be obtained through the dictionary matrix Ψ∈R N×N To perform sparse

[0065] Θ=Ψ·x (2.2)

[0066] Where Θ is the sparse representation coefficient vector. From the above formula, we can see that:

[0067] x=Ψ -1 ·Θ (2.3)

[0068] Substitute (2.3) into (2.1) and let A = ΦΨ -1 , then

[0069] y=ΦΨ -1 Θ=AΘ (2.4)

[0070] Now we know the observation value y and the measurement matrix A, and need to reconstruct Θ, which is sparse, and this becomes a signal reconstruction process under the CS framework. The reconstruction needs to meet the conditions: A must satisfy the restricted isometry property (RIP).

[0071] If A satisfies RIP, or the matrices Φ and Ψ are unrelated, then the estimated value of the sparse vector Θ can be reconstructed In getting After that, we can further calculate the estimated x value of the complete signal x, that is,

[0072]

[0073] The process of repairing the reconstructed signal using the BiCS method includes:

[0074] (1) Perform an even extension on the observed missing signal x over period N, and obtain the even signal after extension as y∈R 2N×2N ; The even extension is: using f(-x)=f(x) to expand the domain of the function f(x) defined on [0,a] to [-a,a];

[0075] (2) Perform DCT transformation on the even-extended input signal to obtain the sparse dictionary matrix Ψ∈R 2N×2N ;

[0076] (3) The even signal y, the sparse dictionary matrix Ψ, and the sparsity K are passed as input into the simplified reconstruction model to obtain the sparse representation

[0077] (4) Based on sparse representation The missing signal is repaired, and the repair formula is: Where y′ represents the repaired even signal, represents sparse representation, Ψ represents sparse dictionary matrix;

[0078] (5) Perform inverse even extension on y′ to obtain the repaired signal x′. Inverse even extension is the inverse process of even extension, and the repaired signal is obtained by weighted average of the function values ​​in the symmetric interval.

[0079] The process of processing the input signal using the improved reconstruction model includes:

[0080] S31: Initialize parameters t, Λ0 and That is, let t=1,Λ0=1,2,3,···,N, Among them, t represents the current number of iterations, Λ0 represents the initial index set, represents the sparse representation obtained by the current iteration of the model, N represents the length of the sparse representation signal, Represents N×1 dimensional space;

[0081] S32: Obtain a sampled signal x, a sparse matrix ψ, and a sparsity K of the signal, wherein the length of the sampled signal x is N×1, and the size of the sparse matrix ψ is N×N; calculate a parameter Θ according to the sampled signal x and the sparse matrix ψ, and the calculation formula is: Θ=ψ -1 x; where Θ represents the sparse representation of the sampled signal;

[0082] S33: Search index λ according to calculated parameter Θ i , so that

[0083] S34: Parameters obtained according to the index Assign the value to the parameter Right now

[0084] S35: For parameter Λ i Update, the update formula is Λ i =Λ i-1 -{λ i}, t=t+1; if t≤K, return to step 3, otherwise stop the iteration and go to step 6;

[0085] S36: Based on the reconstruction Get the value of Θ at index {Λ} and set the elements at other indexes to zero.

[0086] To verify the improvement effect of the proposed method on data recovery, the deep groove ball bearing data of Western Reserve University was selected to verify the proposed method. Under the same experimental environment and experimental parameters, six reconstruction algorithms including OMP (Orthogonal Matching Pursuit, OMP), ROMP (Regularized Orthogonal Matching Pursuit, ROMP), CoSaMP (Compressive Sampling MP, CoSaMP), SP, StOMP (Stage wise OMP, StOMP), and SWOMP (Stagewise Weak OMP, SWOMP) were selected from the compressed sensing algorithm, and the CS, VMD-CS, and VMD-BiCS methods were used for recovery respectively. The recovery results were evaluated using RMSE, as shown in Table 1. The data recorded in the table are the mean RMSE of the five data segments. It can be seen from the table analysis that the addition of VMD reduces the reconstruction error of the traditional CS algorithm. This is because VMD retains and highlights the characteristics of the original signal while denoising, so that the subsequent recovery algorithm can better recover the fault characteristics of the missing parts. Continuing the analysis, it can be seen that the RMSE of the recovered data by the VMD-BiCS method is smaller than that of CS and VMD-CS. Analysis of the reasons shows that the introduction of bidirectional recovery enables the recovery algorithm to link the missing data before and after, mine the fault feature information of the data, reduce the volatility of the recovery results, and thus effectively recover the missing values.

[0087] A mechanical condition monitoring data repair system based on VMD and BiCS, the system comprising: a data acquisition module, a VMD decomposition and reconstruction module, a BiCS reconstruction and repair module and an output module;

[0088] The data acquisition module is used to acquire the monitoring data of the machine to be repaired, and input the data into the VMD decomposition and reconstruction module;

[0089] The VMD decomposition and reconstruction module is used to decompose and denoise the monitoring data to be repaired, and reconstruct the decomposed and denoised data to obtain a reconstructed signal;

[0090] The BiCS reconstruction and repair module is used to repair the reconstructed signal to obtain repaired data;

[0091] The output module is used to output the repaired data.

[0092] The specific implementation of the system of the present invention is the same as the specific implementation of the method.

[0093] In one embodiment of the present invention, the present invention further includes a computer-readable storage medium having a computer program stored thereon, and when the program is executed by a processor, the program implements any of the above-mentioned mechanical condition monitoring data repair methods based on VMD and BiCS.

[0094] Those skilled in the art can understand that all or part of the steps of implementing the above-mentioned method embodiments can be completed by hardware related to the computer program. The aforementioned computer program can be stored in a computer-readable storage medium. When the program is executed, the steps of the above-mentioned method embodiments are executed; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other media that can store program codes.

[0095] A machine condition monitoring data repair device based on VMD and BiCS comprises a processor and a memory; the memory is used to store a computer program; the processor is connected to the memory and is used to execute the computer program stored in the memory, so that the machine condition monitoring data repair device based on VMD and BiCS performs any of the above-mentioned machine condition monitoring data repair methods based on VMD and BiCS.

[0096] Specifically, the memory includes: ROM, RAM, magnetic disk, USB flash drive, memory card or optical disk, etc., which can store program codes.

[0097] Preferably, the processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components.

[0098] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for repairing mechanical condition monitoring data based on VMD and BiCS, characterized in that: include: Acquire the monitoring data to be repaired, and use the VMD model to decompose and reconstruct the acquired monitoring data to obtain a reconstructed signal; The improved BiCS method is used to repair the reconstructed signal and obtain the repaired data; The process of repairing the reconstructed signal using the improved BiCS method includes: S1: Perform an even extension on the observed missing signal x over period N, and obtain the even signal after extension as y∈R 2N×2N ; S2: Perform DCT transformation on the even-extended signal to obtain a sparse dictionary matrix Ψ∈R 2N×2N ; S3: Input the even signal y, sparse dictionary matrix Ψ and sparsity K into the improved reconstruction model to obtain a sparse representation Specifically include: S31: Initialize parameters t, Λ0 and That is, let t=1,Λ0=1,2,3,···,N, Among them, t represents the current number of iterations, Λ0 represents the initial index set, represents the sparse representation obtained by the current iteration of the model, N represents the length of the sparse representation signal, Represents N×1 dimensional space; S32: Obtain a sampled signal x, a sparse matrix ψ, and a sparsity K of the signal, wherein the length of the sampled signal x is N×1, and the size of the sparse matrix ψ is N×N; calculate a parameter Θ according to the sampled signal x and the sparse matrix ψ, and the calculation formula is: Θ=ψ -1 x; where Θ represents the sparse representation of the sampled signal; S33: Search index λ according to calculated parameter Θ i , so that S34: Parameters obtained according to the index Assign the value to the parameter Right now S35: For parameter Λ i Update, the update formula is Λ i =Λ i-1 -{λ i }, t=t+1; if t≤K, return to step 3, otherwise stop the iteration and go to step 6; S36: Based on the reconstruction Get the value of Θ at index {Λ} and set the elements at other indexes to zero; S4: Based on sparse representation The missing signal is repaired, and the repair formula is: Where y′ represents the repaired even signal, represents sparse representation, Ψ represents sparse dictionary matrix; S5: Perform inverse pair extension on y′ to obtain a repaired signal x′.

2. The method for repairing mechanical condition monitoring data based on VMD and BiCS according to claim 1, characterized in that: The process of decomposing and denoising the acquired monitoring data using the VMD model includes: Step 1: Initialize VMD parameters [α, K]; where α represents the penalty function term and K represents the number of IMF components after signal separation. Step 2: Decompose the acquired signal into K IMF components; Step 3: Perform Hilbert-Huang transform on each IMF component to obtain the analytical signal of each component; Step 4: Estimate the center frequency of each analytical signal and convert the spectrum of the analytical signal into a baseband signal; Step 5: After obtaining the demodulated signal according to the baseband signal, calculate the Euclidean distance of the demodulated signal, and estimate the modal bandwidth of the signal according to the Euclidean distance; construct the target variation constraint function according to the modal bandwidth; Step 6: Use the penalty function term α and the Lagrange multiplier operator to optimize the order variation constraint function; Step 7: Calculate the optimal solution of the optimized order variation constraint function and obtain the optimal IMF component.

3. The method for repairing mechanical condition monitoring data based on VMD and BiCS according to claim 2, characterized in that: The expression of the analytical signal is: Where f(t) represents the analytical signal at time t, δ(t) represents the impulse signal, and u k (t) represents the IMF function.

4. The method for repairing mechanical condition monitoring data based on VMD and BiCS according to claim 2, characterized in that: The optimized target variation constraint function is: Among them, u k represents the decomposed IMF components, ω k represents the central frequency of IMF, λ represents the Lagrange multiplier, α represents the quadratic penalty function term, and u k (t) represents the IMF function, and λ(t) represents the Lagrange multiplier.

5. A machine condition monitoring data repair system based on VMD and BiCS, the system being used to execute any one of the machine condition monitoring data repair methods based on VMD and BiCS in claims 1 to 4, characterized in that: The system includes: a data acquisition module, a VMD decomposition and reconstruction module, a BiCS reconstruction and repair module, and an output module; The data acquisition module is used to acquire the monitoring data of the machine to be repaired, and input the data into the VMD decomposition and reconstruction module; The VMD decomposition and reconstruction module is used to decompose and denoise the monitoring data to be repaired, and reconstruct the decomposed and denoised data to obtain a reconstructed signal; The BiCS reconstruction and repair module is used to repair the reconstructed signal to obtain repaired data; The output module is used to output the repaired data.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program is executed by a processor to implement the machine condition monitoring data repair method based on VMD and BiCS as claimed in any one of claims 1 to 4.

7. A mechanical condition monitoring data repair device based on VMD and BiCS, characterized in that: It comprises a processor and a memory; the memory is used to store a computer program; the processor is connected to the memory and is used to execute the computer program stored in the memory, so that the mechanical condition monitoring data repair device based on VMD and BiCS executes any one of the mechanical condition monitoring data repair methods based on VMD and BiCS in claims 1 to 4.

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