CN109916625B - Single-channel gear box multi-fault separation dual-core micro-processing system - Google Patents
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Abstract
The invention relates to a single-channel gearbox multi-fault separation dual-core micro-processing system, and belongs to the technical field of gearbox fault diagnosis and signal processing. The invention relates to a dual-core micro-processing system of a DSP and an ARM, wherein a DSP core comprises a phase space reconstruction parameter estimation module, a phase space reconstruction module, a reconstruction parameter adjustment module, a reconstruction signal separation module and a Fourier transform module, and the ARM core comprises a time-frequency domain spectrogram drawing module; the invention adopts the time delay reconstruction method for expansion, thereby avoiding the human intervention of the reconstructed signal by taking experience as the judgment standard; the influence of noise and redundancy in the gearbox on a reconstructed signal is reduced by adopting a principal component analysis method; and estimating a source signal probability density function by utilizing a finite support sample kernel function and FastICA fusion algorithm, further obtaining a nonlinear function according with the statistical characteristics of the source signal, and finally realizing effective separation of the signals. The method greatly reduces the influence of improper selection of the reconstruction parameters and the separation nonlinear function on the multi-fault separation of the gearbox.
Description
Technical Field
The invention relates to the technical field of gearbox fault diagnosis and signal processing analysis, in particular to a single-channel gearbox multi-fault separation dual-core micro-processing system.
Background
The gear box is an important mechanism for transmitting power of mechanical equipment, and is one of important research objects in mechanical failure diagnosis. Therefore, the research on the fault diagnosis technology of the gearbox is significant for guaranteeing the safe operation of mechanical equipment. The difficulty of fault detection is complex faults, and the estimation of the number of complex faults is the difficulty of complex fault diagnosis. In order to understand the operating state of the gearbox, the acceleration sensor typically picks up its vibration signal. However, the sensor can only be installed on the outer surface of the gear box, which causes the transmission path of the vibration signal collected by the sensor to be too long and the vibration signal to be a composite of a plurality of vibration signals, including redundant vibration of each component, and besides the influence of redundant vibration of the gear box, the influence of different interference sources of various electronic noises from the collection channel and large noise of the surrounding environment also exists, which causes the number of the actually collected sources of each channel to be often more than the number of the sensor, which increases the difficulty of diagnosis, so that a plurality of sensors are generally installed in a laboratory to collect signals. However, in practical engineering problems, due to cost problems and environmental problems, multiple sensors may not be installed, so that the single-channel blind source separation technical scheme for diagnosing the gearbox mixed fault becomes a research hotspot in recent years.
Most blind source signal separation methods are only suitable for positive or over-definite situations, so that aiming at the special underdetermined situation of a single channel, a virtual multi-channel idea is provided, the underdetermined situation is converted into the positive or over-definite situation by using a channel expansion technology, for example, patent documents with application publication number CN 109029973A and publication number 2018, 12 and 18 disclose a method for realizing mixed fault diagnosis of a single-channel gearbox, signals are mapped to a plurality of Inherent Modal Functions (IMF) by adopting Empirical Mode Decomposition (EMD), IMF components are selected by using a kurtosis criterion and a correlation coefficient criterion and then are reconstructed with source single-channel signals to form multi-channel signals, and the single channel is expanded to be multi-channel. However, EMD has poor anti-aliasing effects and it fails when the source signal is not a natural mode. In order to improve the method, a single-channel signal is decomposed by using Ensemble Empirical Mode Decomposition (EEMD), for example, patent documents with an authorization publication number of CN 107192553B and a publication date of 2018, 3, month and 2 disclose a gearbox composite fault diagnosis method based on blind source separation, white noise is added to a vibration signal after noise reduction to carry out EEMD signal decomposition, and the defect of poor saw resistance effect is overcome. However, the method for expanding the multichannel signal does not have a standard evaluation index, and still depends on human judgment, and needs to be based on prior information about the source signal. In gear fault detection, the C-C method of the phase space reconstruction technology can map a mixed signal source to a multi-dimensional space without human intervention. For example, patent documents with an authorization publication number of CN 106513879B and a publication date of 2019, 1 and 15 disclose a spark discharge state identification and detection method based on a chaos theory, and a reconstruction parameter is obtained by using a C-C method to reconstruct a phase space of a discharge state, so that expansion of a human intervention signal is avoided. Theoretically the reconstructed signal is equivalent to the source signal, but if the embedding dimensions and delay time are chosen correctly, an inappropriate choice of reconstruction parameters may lead to reconstruction errors.
In addition, signals of expansion reconstruction need to be separated, and FastICA is a fast algorithm of self-adaptive multi-channel blind source separation developed based on an independent analysis (ICA) algorithm and is widely applied to blind source separation. For example, patent document No. CN 103575523B, published as 2015, 12, 75523, and 9, discloses a rotating machine fault diagnosis method based on FastICA-spectral kurtosis-envelope spectrum analysis, and a FastICA method based on negative entropy maximization is adopted to decouple and separate measured multi-channel acceleration signals, so that the acquired mixed vibration signals are effectively separated. However, there is a wrong choice for the selection of the nonlinear function in the FastICA algorithm, which causes the FastICA algorithm to fall into a local extreme and thus deteriorates the separation performance, so that the selection of the nonlinear function is very important but difficult.
Therefore, the effect of improper selection of reconstruction parameters and the correct selection of the nonlinear function are effectively reduced, and the separation of multi-source faults in the gearbox is important.
Disclosure of Invention
In order to reduce the influence of improper signal reconstruction parameter selection on the reconstructed signal, and simultaneously avoid the influence of FastICA on the separation effect due to wrong selection of a nonlinear function. The invention provides a double-core micro-processing system for multi-fault separation of a single-channel gear box, which can analyze and process acceleration vibration signals of a single channel and effectively separate fault signals in mixed signals.
In order to achieve the technical purpose, the technical scheme of the invention is realized as follows:
a single-channel gearbox multi-fault separation dual-core micro-processing system is composed of a DSP and an ARM core, and comprises a phase space reconstruction parameter estimation module, a phase space reconstruction module, a reconstruction parameter adjustment module, a reconstruction signal separation module, a Fourier transform module and a time-frequency domain spectrogram drawing module.
The DSP and the ARM of the dual-core micro-processing system are clear in division of labor for data analysis and processing, and the division of labor is as follows:
the DSP core receives external input signal and determines the number of processesAccording to the object, let x ═ (1,2, … N) denote a time series of length N; firstly, a phase space reconstruction parameter estimation module solves the estimation value of the phase space reconstruction parameter, the estimation algorithm adopts a representative algorithm C-C method that the embedded dimension and the time delay are mutually dependent, and only a time window tau is ensuredwThe method comprises the steps of obtaining a single-channel signal, obtaining a multi-channel signal by using a finite support sample kernel function, obtaining a multi-channel signal by using a finite FasICA fusion algorithm, obtaining a multi-source time-frequency domain signal, obtaining a multi-channel signal by using a finite support sample kernel function, obtaining a multi-source time-frequency domain signal by using a finite support sample kernel function, obtaining a multi-channel signal by using a multi-channel signal, obtaining a multi-source time-frequency domain signal by using a multi-channel signal by using a time delay method, obtaining a group of matrix X (N- (m-1) tau-1) × m by using a phase space reconstruction module according to estimated phase space reconstruction parameters m and tau, adjusting the reconstruction parameter by using a principal component analysis method, reducing the influence of noise and redundancy in the expanded multi-channel signal by finding the principal component in X, and then mapping the signal to a new multi-.
And the ARM core draws the time frequency signal of the separated signal finally processed by the DSP and then is in butt joint with peripheral communication equipment.
For errors existing in the selection of parameters of the phase space reconstruction method, no phase space reconstruction parameter estimation algorithm can correctly estimate reconstruction parameters so far, so that the phase space reconstructed by the reconstruction parameters obtained according to the existing phase space reconstruction parameter estimation algorithm has reconstruction errors, and the most important reconstruction errors are that the reconstruction signals contain noise and redundant information. The principal component analysis method can take the reconstructed multi-dimensional signals as an original signal matrix, and map the reconstructed signals to a new multi-dimensional space by searching the principal components of the signals, so that noise and redundancy are reduced.
The specific processing process of the adjusting module of the phase space reconstruction parameter in the DSP kernel of the dual-core micro-processing system comprises the following steps:
s41: solving the covariance matrix cov (X) of the reconstructed signal and the covariance matrix cov (X) of the phase space matrix as shown in the following formula
In Cov (X), Cov (x) in the diagonalii) Is the variance of each dimension itself. Cov (x)ij) (i ≠ j) is the covariance of the i dimension and the j dimension. If τ is greater than its optimum value, noise is contained in the reconstructed phase space, i.e., Cov (x)ii) Will be smaller. If m is greater than its optimum, the reconstruction size is too large and Cov (x)ij) Will be larger. If Cov (x)ii) Large and Cov (x)ij) (i ≠ j) is less than the set value, the process is finished, if not, the process is switched to the next step
S42 calculating the eigenvalue lambda ∈ RmFeature vector P ∈ Rm×m
S43, removing the eigenvalue with the eigenvalue only accounting for 15 percent of the sum of the eigenvalues, namely removing the noise and redundant components, leaving the fault components of the gearbox, and finally changing the new eigenvector into P' ∈ Rm×e(e<m)
S44, retrieving a new reconstructed signal y (y ∈ R) according to the new eigenvalue and eigenvector((N-(m-1)τ-1)×e)) Thus, by eliminating the smallest eigenvalues and corresponding eigenvectors, the redundant dimension is reduced, enabling the characterization of a true real system to be revealed.
In order to separate a source signal from a mixed signal, an accurate probability density function G (y) needs to be known, a specific nonlinear function is used for replacing G (y) for FsatICA, however, under the condition that a source signal such as a gear box is unknown, the selection of the nonlinear function becomes the largest influence factor for separating the mixed signal, in order to solve the problem, a FastICA fusion algorithm based on a limited support sample kernel function is adopted by a reconstructed signal separation module, the probability density function of the reconstructed signal is estimated by the algorithm, the nonlinear function which accords with the statistical characteristic of the source signal is obtained, negative entropy is taken as a target function, and the advantages of the FastICA algorithm batch processing calculation method are combined, so that blind separation of the mixed signal is rapidly and accurately realized.
The specific processing process of the reconstruction signal separation module in the DSP kernel of the dual-core micro-processing system comprises the following steps:
s51: centering the reconstructed signal y to make the mean value of the reconstructed signal y become 0;
s52: whitening the signal to remove the correlation of the data;
s53: selecting the number m' of signals to be estimated, and setting iteration number p ← 1;
s54: selecting an initial weight vector (random) Wn；
S55: sorting the reconstructed signals in a non-decreasing order to obtain y ═ y { (y)1,y2,…yNIs obtained by
Estimating a probability density function of a kernel function of a finite support sample, wherein
For M finite support samples yi,yi+1,…yi+MAnd M denotes the length of the window, i.e. M denotes the length of the window
Deriving a lowest order kernel function by satisfying boundary conditions of limited support samples and basic conditions of a probability density function
In the formula, mui＝(yi+M-yi) (ii) obtaining G according to the conditions of the kernel functioni＝15μi -5And/16, finally obtaining the derivative of the probability density p (y) of random y:
thereby estimating a probability density function, solving a nonlinear function g, and solving the solutions of n optimization problems based on the principle of' separating one by one
The constraint conditions are as follows:
according to Kuhn Tucker conditions and | W | 1, may be passed through f (W) ═ E { zG (W)Tz) } + β W is 0, the optimal solution is solved, β is a constant, and a Newton iterative formula is adopted to solve the solution;
s56: order to
Wherein g' (. cndot.) represents the first derivative of g (-);
s57: reduction of Newton iterations to a reduced number of newton iterations through a series of reduction processes
Wn+1←Wn+1/‖Wn+1‖；
S58: if W isnIf not, returning to the step S56, otherwise, continuing;
s59: let n equal to n +1, if n ≦ m', return to step S54.
The method has the technical effects that the advantages of each core in the double-core are utilized on hardware, the DSP core is utilized to carry out phase space reconstruction parameter estimation, phase space reconstruction, reconstruction parameter adjustment, reconstruction signal separation and Fourier transformation, and the ARM core is utilized to carry out signal separation time-frequency domain spectrogram drawing. Aiming at the problems existing in the traditional single-channel blind source separation, the method for adjusting the parameters of the reconstructed signal by adopting a principal component analysis method is provided on software, so that the influence of noise and redundant signals in the reconstructed signal is reduced, finally, the source signal which is recovered due to the inaccuracy of a selected nonlinear function can be unsatisfactory when a traditional wider FastICA separation algorithm is used, and the FastICA fusion algorithm based on a limited support sample kernel function is adopted, so that the problem is solved, and finally, a high-speed and effective processing system can be provided for a diagnosis object with a complex environment and running condition, namely a gearbox.
Drawings
FIG. 1 is a block diagram of the system modules of the present invention;
FIG. 2 is a flow chart of a method of the present invention;
FIG. 3 is a flow chart of a reconstruction parameter adjustment module according to the present invention;
fig. 4 is a flow chart of the reconstructed signal separation module of the present invention.
Detailed Description
For a more clear description of the invention, reference is now made to the following detailed description and accompanying drawings.
Referring to fig. 1, the dual-core microprocessor system is composed of a DSP and an ARM core, and includes a phase space reconstruction parameter estimation module, a phase space reconstruction module, a reconstruction parameter adjustment module, a reconstruction signal separation module, and a time-frequency domain spectrogram drawing module. The phase space reconstruction parameter estimation module, the phase space reconstruction module, the reconstruction parameter adjustment module, the reconstruction signal separation module and the Fourier transform module belong to a DSP kernel operation module, and the time-frequency domain spectrogram drawing module belongs to an ARM module.
Referring to fig. 2, in the signal processing flow chart of the processing system, the DSP core receives an external input signal, establishes a processing data object, and sets x to (1,2, … N) to indicate that a time series with a length of N is a processing object. Firstly, a phase space reconstruction parameter estimation module in a DSP kernel obtains an estimation value of a phase space reconstruction parameter according to an acceleration vibration signal of a single-channel gear box, the estimation algorithm adopts a representative algorithm C-C method that an embedded dimension and time delay are interdependent, and only a time window tau is ensuredw(m-1) × τ is constant, where m is the embedding dimension and τ is the lag time; the phase space reconstruction module reconstructs the parameter m andtau, performing multichannel expansion on the single-channel signal by adopting a time delay method, and reconstructing a phase space to obtain a group of matrixes X (N- (m-1) × tau-1) × m;
referring to fig. 3, a flow chart of the reconstruction parameter adjusting module, the reconstruction parameter adjusting module adjusts the reconstruction parameters of the signals reconstructed according to the preliminarily estimated reconstruction parameters by using a principal component analysis method, and solves a covariance matrix cov (x) of the reconstructed signals, and a covariance matrix cov (x) of the phase space matrix is as shown in the following formula:
since if τ is greater than its optimal value, noise is contained in the reconstructed phase space, i.e., Cov (x)ii) Will be smaller. If m is greater than its optimum, the reconstruction size is too large and Cov (x)ij) Will be larger, so look at Cov (x)ii) And Cov (x)ij) (i ≠ j) size, Cov (x)ii) Large and Cov (x)ij) (i ≠ j) is less than the set value, the process is ended, if not, the process is switched to the next step, and then the characteristic value lambda ∈ R of the matrix is calculatedmFeature vector P ∈ Rm×mRemoving the characteristic value with the characteristic value only accounting for 15% of the total sum of the characteristic values, namely removing noise and redundant components, leaving the characteristic value of the suspected fault component of the gear box, and finally changing the new characteristic vector into P' ∈ Rm×e(e<m) recovering a new reconstructed signal y (y ∈ R) from the new eigenvalues and eigenvectors((N -(m-1)τ-1)×e)) Therefore, the redundant dimension is reduced by eliminating the minimum characteristic value and the corresponding characteristic vector, and the reconstruction parameter adjusting module completes the adjustment of the reconstruction parameter of the reconstruction phase space signal.
The above process completes the process of expanding from single channel to multiple channels and converting from under-determined condition to multi-source mixed signal of positive or over-determined condition, and then the operation is to carry out blind source separation on a multi-channel signal.
Referring to fig. 4, a detailed flowchart of the reconstructed signal separation module, the reconstructed signal separation module applies a FastICA fusion algorithm based on a finite support sample kernel to the adjusted new multi-dimensional phase space signal.
S51: centering the reconstructed signal y to make the mean value of the reconstructed signal y become 0;
s52: whitening the signal to remove the correlation of the data;
s53: selecting the number m' of signals to be estimated, and setting iteration number p ← 1;
s54: selecting an initial weight vector (random) WnProviding service for subsequent Newton iteration;
s55: sorting the pre-processing signals y in a non-decreasing order to obtain y ═ y1,y2,…yNIs obtained by
Estimating a probability density function of a kernel function of a finite support sample, wherein
For M finite support samples yi,yi+1,…yi+MAnd M denotes the length of the window, i.e. M denotes the length of the window
Deriving a lowest order kernel function by satisfying boundary conditions of limited support samples and basic conditions of a probability density function
In the formula, mui＝(yi+M-yi) (ii) obtaining G according to the conditions of the kernel functioni＝15μi -5And/16, finally obtaining the derivative of the probability density p (y) of random y:
thereby estimating the probability densityDegree function, calculating nonlinear function g, and solving the solutions of n optimization problems based on the principle of' separating one by one
The constraint condition is
According to the Kuhn-Tucker condition and | W | 1, can be passed through f (W) ═ E { zG (W)Tz) } + β W is 0, the optimal solution is solved, β is a constant, and a Newton iterative formula is adopted to solve the solution;
s56: order to
Wherein g' (. cndot.) represents the first derivative of g (-);
s57: reduction of Newton iterations to a reduced number of newton iterations through a series of reduction processes
Wn+1←Wn+1/‖Wn+1‖；
S58: judgment of WnConvergence of if WnIf the divergence is not the case, returning to the step S56, otherwise, continuing the next step;
s59: let n equal to n +1, if n ≦ m', return to step S54.
Finally, the fault source signal is separated, and N is { N ═ N1,N2…NLAnd L is the estimated number of fault sources }. And the Fourier transform module performs Fourier transform on the separated time domain signal to further obtain a corresponding frequency domain signal.
And the ARM core draws the time frequency signal of the separated signal finally processed by the DSP and then is in butt joint with peripheral communication equipment.
Claims (3)
1. A single-channel gearbox multi-fault separation dual-core micro-processing system is characterized in that the micro-processing system consists of a DSP and an ARM dual-core, and the dual-core micro-processing system comprises a phase space reconstruction parameter estimation module, a phase space reconstruction module, a reconstruction parameter adjustment module, a reconstruction signal separation module, a Fourier transform module and a time-frequency domain spectrogram drawing module;
a DSP core in the single-channel gearbox multi-fault separation dual-core microprocessing system completes signal input, phase space reconstruction parameter estimation, phase space reconstruction, reconstruction parameter adjustment, reconstruction signal separation and Fourier transformation, and an ARM core completes drawing of a time-frequency domain spectrogram and communication work of a peripheral interface;
the phase space reconstruction module reconstructs signals by a time delay method, a single-channel signal X ═ (1,2, … N) is set as a time sequence with the length of N, a group of matrixes X ═ (N- (m-1) × tau-1) × m are obtained after the phase space is reconstructed, wherein m is an embedding dimension, tau is lag time, and a C-C method is adopted for the reconstruction parameter estimation module, and a time window tau needs to be ensuredw(m-1) × τ is constant;
the reconstruction parameter adjusting module is mainly used for adjusting a reconstruction signal X by a principal component analysis method, reducing the influence of noise and redundancy in the expanded multi-channel signal by removing a characteristic value and a corresponding characteristic vector of which the characteristic value accounts for 15% of the total sum of the characteristic values in the X, and mapping the signal to a new multi-dimensional space y ∈ R according to the new characteristic value and the new characteristic vector((N -(m-1)τ-1)×e)Wherein e is<m；
The reconstruction signal separation module adopts a FastICA fusion algorithm based on the limited support sample kernel function, and estimates the probability density function of the limited support sample kernel function of the reconstruction signal from the reconstruction signal
Wherein phi (-) is the lowest order kernel function, the lowest order kernel function phi (y) satisfying the boundary condition of the finite support sample and the basic condition of the probability density function
In the formula, mui＝(yi+M-yi) (ii) obtaining G according to the conditions of the kernel functioni＝15μi -5Further, a derivative H (y) of the probability density of the reconstructed signal
Calculating a source signal probability density function to finally obtain a nonlinear function based on the statistical characteristics of the source signals;
the single-channel gearbox multi-fault separation dual-core micro-processing system comprises the following processing processes:
s1: vibration signals of the single-channel multi-fault-source gearbox are input into the single-channel gearbox multi-fault separation dual-core micro-processing system;
s2: estimating reconstruction parameters m and tau of the single-channel multi-fault gearbox vibration signal to be analyzed by a phase space reconstruction parameter estimation module based on a C-C algorithm;
s3: expanding the single-channel signal of the gear box to be analyzed into a multi-channel signal X (N- (m-1) × τ -1) × m by a phase space reconstruction module based on a time delay method according to the reconstruction parameters obtained in the step S2;
s4: a reconstruction parameter adjusting module based on the principal component analysis method maps the reconstruction signal to a new multidimensional space to adjust the reconstruction parameters and output the multidimensional signal again by searching the principal component of the reconstruction signal X obtained in the step S3;
s5: a reconstructed signal separation module based on a finite support sample kernel function algorithm and a FastICA fusion algorithm estimates a probability density function to obtain a nonlinear function based on statistical characteristics of a reconstructed signal, and the signal separation is realized on a newly obtained reconstructed signal S4 by taking negative entropy as a target function and combining with FastICA algorithm batch processing calculation;
s6: the Fourier transform module performs Fourier transform on the separated time domain signal so as to obtain a corresponding frequency spectrum;
and S7, the time-frequency spectrogram drawing module draws a time-frequency spectrogram of the time-frequency signal obtained in the S6, and further positions and quantifies the fault of the gearbox according to the time-frequency spectrogram.
2. The single-channel gearbox multi-fault separation dual-core micro-processing system according to claim 1, wherein the step S4 comprises:
s41: solving the covariance matrix Cov (X) of the reconstructed signal if Cov (x)ii) Large and Cov (x)ij) If (i is not equal to j) is less than the set value, ending, otherwise, switching to the next step;
s42 calculating the eigenvalue lambda ∈ RmFeature vector P ∈ Rm×m；
S43, removing the eigenvalue with the eigenvalue accounting for 15% of the sum of the eigenvalues, and changing the new eigenvalue into P' ∈ Rm×eWherein e is<m；
S44, recovering new reconstructed signal y, y ∈ R according to the new eigenvalue and eigenvector((N-(m-1)τ-1)×e)。
3. The single-channel gearbox multi-fault separation dual-core micro-processing system according to claim 1, wherein the step S5 comprises:
s51: centering the reconstructed signal y to make the mean value of the reconstructed signal y become 0;
s52: whitening the signal to remove the correlation of the data;
s53: selecting the number m' of signals to be estimated, and setting iteration number p ← 1;
s54: randomly selecting an initial weight vector Wn；
S55: estimating a probability density function by using a finite support sample kernel function algorithm, and solving a nonlinear function g;
s56: order to
Whereing' (. cndot.) represents the first derivative of g (-);
s57: according to
Wn+1←Wn+1/‖Wn+1‖；
S58: if W isnIf not, returning to S56, otherwise, continuing;
s59: let n equal to n +1, if n ≦ m', return to step S54.
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