An adaptive multivariate time-varying signal decomposition method and system

Abstract

The application provides a kind of adaptive multivariate time-varying signal decomposition method and system, belong to mechanical operation process signal decomposition field, including: using hilbert transform to multivariate time-varying signal is analyzed and is expressed, obtains multivariate signal analytic formula;Suppose there is a common frequency component in all channels, simplify multivariate signal analytic formula;Through demodulation technology obtains demodulated multivariate frequency modulation mode and is multiplied with frequency shift operator, after the frequency spectrum of demodulated multivariate frequency modulation mode is moved to baseband, using the real signal of multivariate time-varying signal replaces multivariate time-varying signal, obtains multivariate input signal;Using recursive extraction framework, establishes objective function and is discretized;Based on the objective function after discretization, update demodulation signal and extract target signal mode, and based on the demodulation signal in multivariate input signal updates common instantaneous frequency, realizes the decomposition of multivariate time-varying signal.The application solves the problem that prior knowledge of multivariate signal mode is needed in existing multivariate signal decomposition method.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of signal decomposition in mechanical operation process, and more particularly, relates to an adaptive multivariate time-varying signal decomposition method and system. BACKGROUND

[0002] Signals in nature, such as signals generated by mechanical vibration, biomedical signals and speech signals, etc., all show nonlinear and non-stationary characteristics. Such signals are also called non-stationary nonlinear frequency modulation signals, which are usually composed of multiple components (i.e. multiple signal modes) and noise, and have complex frequency and amplitude content. Usually, these components contain key information reflecting the essence of things. Therefore, in order to better understand the essence of the signal, the signal mode should be extracted and the potential information in the signal should be revealed.

[0003] With the advancement of sensors and technology, multivariate data types often appear in modern engineering and disciplines. Therefore, multivariate data processing methods have attracted the interest of many researchers, and researchers have developed many multivariate extensions of existing univariate signal processing methods, such as: multivariate empirical mode decomposition (MEMD), complex variational mode decomposition (CVMD), two-dimensional variational mode decomposition (2D-VMD), multivariate variational mode decomposition (MVMD), multivariate nonlinear chirp decomposition (MNCMD) and successive multivariate variational mode decomposition (SMVMD), etc. However, most of the existing multivariate signal decomposition methods have the following problems: (1) requiring prior knowledge of multivariate signal modes; (2) limited to narrowband signal analysis; (3) mode mixing. SUMMARY

[0004] In view of the defects of the prior art, the purpose of the present application is to provide an adaptive multivariate time-varying signal decomposition method (AMCMD) and system, which aims to solve the problem that the existing signal decomposition method can only realize the decomposition of non-stationary nonlinear multivariate signals under the condition of requiring prior knowledge of multivariate signal modes.

[0005] To achieve the above object, in one aspect, the application provides a self-adaptive multi-element time-varying signal decomposition method, comprising the following steps:

[0006] S1: establishing a multi-element time-varying signal of multiple channels, using Hilbert transform to analytically express the multi-element time-varying signal, defining a set of unique regular amplitude and phase functions, and obtaining an analytical expression of the multi-element signal;

[0007] S2: assuming that there is a common frequency component in all channels, simplifying the analytical expression of the multi-element signal;

[0008] S3: multiplying the demodulated multi-element frequency modulation mode with a frequency shift operator, moving the spectrum of the demodulated multi-element frequency modulation mode to the baseband, using the real signal of the multi-element time-varying signal to replace the multi-element time-varying signal, and obtaining a multi-element input signal;

[0009] S4: using a recursive extraction framework, based on the multi-element input signal, establishing a target function with the condition of minimizing the residual energy of two demodulated signals, and discretizing the target function;

[0010] S5: updating the demodulated signal and extracting the target signal mode based on the discretized target function, and updating the common instantaneous frequency based on the demodulated signal in the multi-element input signal, to realize the decomposition of the multi-element time-varying signal; wherein the target signal mode is the vector product of the kernel function and the demodulated signal; the common instantaneous frequency of each mode component of all channels is estimated as the power-weighted average.

[0011] Further preferably, S1 specifically comprises the following steps:

[0012] S1.1: establishing a multi-element time-varying signal X(t) of C channels, whose expression is:

[0013]

[0014] wherein a c (t), f c (t) and respectively represent the instantaneous amplitude, the instantaneous frequency and the initial phase of the cth channel;

[0015] S1.2: analytically expressing the multi-element time-varying signal by Hilbert transform, defining a unique regular amplitude and phase function, and obtaining an analytical expression of the multi-element signal;

[0016]

[0017] wherein, represents the Hilbert transform operator; X a (t) is the analytical expression of the multi-element time-varying signal.

[0018] Further preferably, the simplified polyphase signal analysis expression is:

[0019]

[0020] wherein a(t) = [a1(t),...,a C (t)] T .

[0021] Further preferably, S3 specifically comprises the following steps:

[0022] S3.1: using a demodulation technique, representing the demodulated polyphase frequency modulation pattern as a product of the simplified polyphase signal analysis expression and a demodulation operator; specifically:

[0023]

[0024] wherein, denotes a frequency function of the demodulation operator; f c denotes a carrier frequency;

[0025] S3.2: shifting the spectrum of the demodulated polyphase frequency modulation pattern to baseband by multiplying the demodulated polyphase frequency modulation pattern with a frequency shift operator, and obtaining a baseband signal:

[0026]

[0027] wherein f(t) denotes a common instantaneous frequency of the polyphase frequency modulation signal; the common instantaneous frequency of the polyphase frequency modulation pattern is estimated by finding the smoothing frequency function for which the obtained baseband signal has the narrowest frequency band;

[0028] S3.3: based on the baseband signal, using a real signal of a polyphase time-varying signal to replace the polyphase time-varying signal;

[0029]

[0030] wherein, is a real part extraction operator; is an imaginary part extraction operator; p(t) and q(t) are demodulation signals;

[0031] S3.4: obtaining a polyphase input signal;

[0032]

[0033] wherein p k (t) = [p 1,k (t), p 2,k (t),..., p C,k (t)] T , qk (t) = [q 1,k (t), q 2,k (t),... q C,k (t)] T , denotes white Gaussian noise; K is the number of modes; C is the number of channels; k denotes the kth mode; p c,k (t) and q c,k (t) are two demodulation signals of the kth mode and the cth channel.

[0034] Further preferably, S4 specifically comprises the following steps:

[0035] S4.1: assigning the multivariate input signal to the residual signal, presetting the common instantaneous frequency of the first mode number, and constructing the initial kernel function using the initial common instantaneous frequency; starting from the first mode, performing step S4.2;

[0036] S4.2: establishing the target function corresponding to the kth mode and the cth channel under the condition of minimizing the two demodulation signals of the kth mode and the cth channel in the multivariate input signal and minimizing the residual function;

[0037] S4.3: time-discretizing the target function to construct the discretized target function corresponding to the kth mode and the cth channel.

[0038] Further preferably, S5 specifically comprises the following steps:

[0039] S5.1: calculating the vector of the corresponding demodulation signal according to the discretized target function corresponding to the kth mode and the cth channel;

[0040] S5.2: calculating the product of the kernel function and the vector of the demodulation signal in S5.1, and extracting the target signal mode corresponding to the kth mode and the cth channel;

[0041] S5.3: repeating steps S5.1-S5.2 until all channels corresponding to the discretized target function are executed S5.1-S5.2, and then going to S5.4;

[0042] S5.4: calculating the increment of the corresponding common instantaneous frequency using the arctangent operation of the ratio of the two demodulation signals of the kth mode and the cth channel;

[0043] S5.5: combining the common instantaneous frequency increment in S5.4, and solving the smooth instantaneous frequency increment of the kth mode and the cth channel using the smoothness prior method;

[0044] S5.6: summing the common instantaneous frequency of the kth mode and the cth channel and the corresponding smooth instantaneous frequency increment to update the common instantaneous frequency vector of the kth mode and the cth channel.

[0045] S5.7: Power-weighted average the common instantaneous frequency vector in the current mode in all channels, calculate the common instantaneous frequency in the current mode in all channels, and update the kernel function;

[0046] S5.8: Determine whether the internal loop condition is greater than the internal stop threshold, if greater than the internal stop threshold, go to S5.1, otherwise go to S5.9;

[0047] S5.9: Update the residual signal using the difference between the multi-element input signal and the target signal mode in all channels, and convert the signal mode to the next mode;

[0048] S5.10: Determine whether the external loop condition is greater than the external stop threshold, if greater, go to S4.2; otherwise, output all target signal modes and common instantaneous frequencies.

[0049] Further preferably, the objective function is:

[0050]

[0051]

[0052] where β>0 is a penalty parameter; p c,k (t) and q c,k (t) are two demodulation signals; represents the residual energy; g c is the target signal mode in the cth channel;

[0053] The discretized objective function is:

[0054]

[0055] where, p c,k = [p c,k (t0)…p c,k (t N-1 )], q c,k = [q c,k (t0)…q c,k (t N-1 )], g c = [g c (t0)…g c (t N-1 )] T ; D k is related to the demodulation frequency , and is represented as D k = [C k S k ], C k= diag [cos (φ k (t0),…,cos (φ k (t N-1 ))], S k = diag [sin (φ k (t0),…,sin (φ k (t N-1 ))], Λ = diag [Θ, Θ], Θ is a second-order difference operator with dimension (N-2) × N, which is expressed as:

[0056]

[0057] The vector of demodulated signals is:

[0058]

[0059] The common instantaneous frequency in the current mode is:

[0060]

[0061] wherein, is the instantaneous amplitude of mode k in channel c; is the common instantaneous frequency in the kth mode of the cth channel.

[0062] On the other hand, the application provides an adaptive multi-element time-varying signal decomposition system, comprising:

[0063] A Hilbert transform module is configured to use Hilbert transform to analytically represent the multi-element time-varying signal, define a set of unique regular amplitude and phase functions, and obtain the analytical expression of the multi-element signal;

[0064] An analytical expression simplification module is configured to simplify the analytical expression of the multi-element signal by assuming that there is a common frequency component in all channels;

[0065] A spectrum conversion module is configured to move the spectrum of the demodulated multi-element frequency modulation mode to the baseband by multiplying the demodulated multi-element frequency modulation mode with a frequency shift operator;

[0066] A multi-element input signal acquisition module is configured to combine the baseband signal, use the real signal of the multi-element time-varying signal to replace the multi-element time-varying signal, and acquire the multi-element input signal;

[0067] A discrete target function establishment module is configured to use a recursive extraction framework, based on the multi-element input signal, to establish a target function with the condition of minimizing the residual energy of the two demodulated signals, and to discretize the target function;

[0068] The decomposition module of the multivariate time-varying signal updates the demodulation signal and extracts the target signal mode based on the discretized target function, and calculates the common instantaneous frequency based on the demodulation signal in the multivariate input signal, so as to realize the decomposition of the multivariate time-varying signal; wherein the target signal mode is the vector product of the kernel function and the demodulation signal; the common instantaneous frequency of each mode component of all channels is estimated as the power weighted average.

[0069] Further preferably, the multivariate time-varying signal is:

[0070]

[0071] Wherein X(t) is a multivariate time-varying signal; a c (t), f c (t) and respectively represent the instantaneous amplitude, the instantaneous frequency and the initial phase of the cth channel;

[0072] The analytical expression of the multivariate signal is:

[0073]

[0074] Wherein, represents the Hilbert transform operator; X a (t) is the analytical expression of the multivariate time-varying signal;

[0075] The simplified analytical expression of the multivariate signal is:

[0076]

[0077] Wherein a(t) = [a1(t), …, a C (t)] T ;

[0078] Multivariate input signal;

[0079]

[0080] Wherein p k (t) = [p 1,k (t), p 2,k (t), … p C,k (t)] T , q k (t) = [q 1,k (t), q 2,k (t), … q C,k (t)] T , represents white Gaussian noise; K is the mode number; C is the channel number; k represents the kth mode; p c,k (t) and q c,k(t) is the two demodulation signals of the kth mode cth channel.

[0081] Further preferably, the establishing module of the discretization target function comprises:

[0082] An initialization setting unit is configured to assign the multivariate input signal to the residual signal, preset the common instantaneous frequency of the first mode number, and construct an initial kernel function using the initial common instantaneous frequency;

[0083] A target function construction unit is configured to establish the target function corresponding to the kth mode cth channel under the condition of minimizing the two demodulation signals of the kth mode cth channel in the multivariate input signal and minimizing the residual function;

[0084] A target function discretization unit is configured to time-discretize the demodulation signal target function, and construct the discretized target function corresponding to the kth mode cth channel.

[0085] Further preferably, the decomposition module of the multivariate time-varying signal comprises:

[0086] A vector calculation unit of the demodulation signal is configured to calculate the vector of the corresponding demodulation signal according to the discretized target function corresponding to the kth mode cth channel;

[0087] A target signal mode extraction unit is configured to calculate the product of the kernel function and the vector of the demodulation signal, and extract the target signal mode corresponding to the kth mode cth channel;

[0088] An increment calculation unit of the common instantaneous frequency is configured to calculate the increment of the common instantaneous frequency using the arctangent operation of the ratio of the two demodulation signals of the kth mode cth channel;

[0089] A calculation unit of the smoothed instantaneous frequency increment is configured to combine the common instantaneous frequency increment and solve the smoothed instantaneous frequency increment of the kth mode cth channel using a smoothing degree prior method;

[0090] A calculation unit of the common instantaneous frequency vector is configured to sum the common instantaneous frequency of the kth mode cth channel and the corresponding smoothed instantaneous increment, and update the common instantaneous frequency vector of the kth mode cth channel;

[0091] A calculation unit of the common instantaneous frequency is configured to calculate the common instantaneous frequency of the current mode in all channels by power-weighted averaging the common instantaneous frequency vectors of the current mode in all channels, and update the kernel function;

[0092] A first discriminator is configured to determine whether the internal loop condition is greater than the internal stop threshold value, and if it is greater than the internal stop threshold value, drive the vector calculation unit of the demodulation signal to run, otherwise drive the residual signal update unit.

[0093] a residual signal updating unit for updating the residual signal by using the difference between the multi-input signal and the target signal pattern in all channels;

[0094] a second discriminator for judging whether the outer loop condition is greater than the outer stop threshold, if yes, driving the target function construction unit to run, otherwise, outputting all target signal patterns and the common instantaneous frequency.

[0095] Further preferably, the multi-input time-varying signal X(t) is:

[0096]

[0097] wherein a c (t), f c (t) and respectively represent the instantaneous amplitude, the instantaneous frequency and the initial phase of the cth channel;

[0098] The multi-input signal analysis expression is:

[0099]

[0100] wherein, represents the Hilbert transform operator; X a (t) is the multi-input signal analysis expression;

[0101] The deformed multi-input signal analysis expression is:

[0102]

[0103] wherein a(t) = [a1(t), …, a C (t)] T ;

[0104] The multi-input signal;

[0105]

[0106] wherein p k (t) = [p 1,k (t), p 2,k (t), … p C,k (t)] T , q k (t) = [q 1,k (t), q 2,k (t), … q C,k (t)] T , represents white Gaussian noise; K is the mode number; C is the channel number; k represents the kth mode; p c,k (t) and q c,k(t) are two demodulated signals for the cth channel, the kth mode.

[0107] Further preferably, the objective function is:

[0108]

[0109]

[0110] where β > 0 is a penalty parameter; p c,k (t) and q c,k (t) are two demodulated signals; denotes the residual energy; g c is the target signal mode in the cth channel;

[0111] The discretized objective function is:

[0112]

[0113] where, p c,k = [p c,k (t0)... p c,k (t N-1 )], q c,k = [q c,k (t0)... q c,k (t N-1 )], g c = [g c (t0)... g c (t N-1 )] T ; D k is related to the demodulation frequency and is denoted as D k = [C k S k ], C k = diag [cos(φ k (t0),..., cos(φ k (t N-1 ))], S k = diag [sin(φ k (t0),..., sin(φ k (t N-1 ))], Λ = diag [Θ, Θ], Θ is a second-order difference operator of dimension (N-2) x N and is denoted as:

[0114]

[0115] The vector of demodulated signals is:

[0116]

[0117] The common instantaneous frequency in the current mode is:

[0118]

[0119] wherein, is the instantaneous amplitude of mode k in channel c; is the common instantaneous frequency in the kth mode of the cth channel.

[0120] Overall, compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects:

[0121] The present application adopts the method of recursive extraction framework, does not need the prior knowledge of the mode number of the multivariate time-varying signal, overcomes the difficulty of the multivariate signal processing method of the joint extraction framework needing the prior knowledge of the mode number, establishes a discretization objective function for each mode, extracts the target signal mode while calculating the common instantaneous frequency vector. The present application solves the problem that the existing signal decomposition method can only realize the decomposition of the non-stationary nonlinear multivariate signal under the condition of needing the prior knowledge of the multivariate signal mode.

[0122] The present application provides a target function based on a multivariate input signal, minimizes the residual energy while minimizing two demodulation signals, and discretizes the target function demodulation signal in time, and constructs the discretized target function corresponding to the kth mode and the cth channel. The calculation complexity of the recursive extraction framework method can be effectively reduced, the calculation cost is lower, the calculation efficiency is higher, and the method can also be used for processing complex wideband noise signals. BRIEF DESCRIPTION OF DRAWINGS

[0123] Figure 1 is the flowchart of the adaptive multivariate frequency modulation signal decomposition method provided by the embodiment of the present application;

[0124] Fig. 2(a) is a simulation signal decomposition effect diagram of the amplitude-frequency variation obtained by using the AMCMD method provided by the embodiment of the present application;

[0125] Fig. 2(b) is a simulation signal decomposition effect diagram of the amplitude-frequency variation obtained by using the MNCMD method provided by the embodiment of the present application;

[0126] Fig. 2(c) is a simulation signal decomposition effect diagram of the amplitude-frequency variation obtained by using the MVMD method provided by the embodiment of the present application;

[0127] Fig. 3(a) is an effect diagram of decomposing the vibration data at three bearings on a water turbine rotor-bearing system by using the AMCMD method provided by the embodiment of the present application;

[0128] Figure 3(b) is an effect diagram of decomposing vibration data at three bearings on a water turbine rotor-bearing system by using the MNCMD method according to an embodiment of the present application;

[0129] Figure 3(c) is an effect diagram of decomposing vibration data at three bearings on a water turbine rotor-bearing system by using the MVMD method according to an embodiment of the present application;

[0130] Figure 4(a) is a spectrum diagram of signals and components after decomposition by using the AMCMD method according to an embodiment of the present application;

[0131] Figure 4(b) is a spectrum diagram of signals and components after decomposition by using the MNCMD method according to an embodiment of the present application;

[0132] Figure 4(c) is a spectrum diagram of signals and components after decomposition by using the MVMD method according to an embodiment of the present application. DETAILED DESCRIPTION

[0133] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application.

[0134] EMBODIMENT

[0135] The adaptive multi-variate time-varying signal decomposition method provided by the present application will be described in detail below with reference to the accompanying drawings, simulation examples and water turbine vibration data:

[0136] Step (1): establishing a multi-channel amplitude modulation-frequency modulation (AM-FM) signal; first, a group of C multi-variate time-varying signals X(t) of channels are expressed as:

[0137]

[0138] wherein, a c (t), f c (t) and respectively represent the instantaneous amplitude, the instantaneous frequency and the initial phase of the cth channel; by using the Hilbert transform, the analytic expression of the multi-variate time-varying signal is defined to have a unique regular amplitude and phase function, and the analytic expression of the multi-variate signal is established; the analytic expression of the multi-variate signal is expressed as the multi-variate time-varying signal itself and the Hilbert transform of the multi-variate time-varying signal, i.e.:

[0139]

[0140] wherein, Hilbert transform operator; the mathematical description of the above formula considers C channels isolated from each other; in the present application, assuming that there is a common frequency component in all data channels, the analytic expression of the multivariate signal is simplified as:

[0141]

[0142] wherein a(t)=[a1(t),…,a C (t)] T ;

[0143] The wideband multivariate time-varying signal is converted into a narrowband multivariate frequency-modulated signal G(t) by using demodulation technology; the demodulated multivariate frequency-modulated mode The product of X a (t) and the demodulation operator Ω - is calculated to obtain:

[0144]

[0145] wherein, denotes the frequency function of the demodulation operator; f c denotes the carrier frequency; the spectrum of the demodulated multivariate frequency-modulated mode is moved to the baseband by multiplying the demodulated multivariate frequency-modulated mode with the frequency shift operator exp(-j2πf c t) to estimate the signal bandwidth; through the above description, the multivariate baseband signal is expressed as:

[0146]

[0147] The baseband signal expression can be obtained:

[0148]

[0149] wherein f(t) denotes the common instantaneous frequency of the multivariate time-varying signal X(t); the common instantaneous frequency of the multivariate frequency-modulated mode is estimated by finding the smooth frequency function of the obtained baseband signal having the narrowest frequency band; when , the demodulated signal will become a pure amplitude modulation signal centered on the carrier frequency, in which case the demodulated signal will have the smallest bandwidth.

[0150] In the present application, the real signal is used instead of the multivariate time-varying signal, i.e.:

[0151]

[0152] wherein,

[0153] is the real part extraction operator; Imaginary part extraction operator;

[0154] Assuming the mode number and channel number are K and C respectively, the multivariate input signal G = [g1, g2, … gK] is expressed as: C ] and the expression is:

[0155]

[0156] where p k (t) = [p 1,k (t), p 2,k (t), … p C,k (t)] T , q k (t) = [q 1,k (t), q 2,k (t), … q C,k (t)] T , white Gaussian noise;

[0157] Step (2): initialize the parameters required by the method; initialize the multichannel input data G, the penalty parameter β and the regularization parameter α; set the external and internal stop thresholds υ and e; and set the maximum number of iterations count_n;

[0158] Step (3): let r represent the residual signal, assign the multivariate input signal G to the initial residual signal, i.e. r k = G, at this time k = 1; obtain the initial common instantaneous frequency and construct the initial kernel function with the initial instantaneous frequency

[0159] Step (4): use the greedy algorithm to establish the objective function; since AMCMD adopts a recursive extraction framework, it captures modes one by one, reduces the computational cost and does not require prior knowledge about the number of modes; specifically:

[0160] In order to extract the kth MCM from the multivariate input signal, the objective function solved by AMCMD is as follows:

[0161]

[0162]

[0163] where the first two terms are the smoothness constraints imposed by the two demodulation signals; the third term represents the residual signal energy in the cth channel; β > 0 is a penalty parameter; and the objective function represents a function established under the condition of minimizing the residual energy while minimizing the two demodulation signals;

[0164] Step (5): Discretize the objective function; to make the objective function more stable and save computing resources, the objective function is discretized; assuming that the signal is observed in the discrete time t = t0,..., t N-1 , the discretized expression of the objective function is:

[0165]

[0166] where, p c,k = [p c,k (t0)... p c,k (t N-1 )], q c,k = [q c,k (t0)... q c,k (t N-1 )] ; g c = [g c (t0)... g c (t N-1 )] T ; D k is related to the demodulation frequency , denoted as D k = [C k S k ], C k = diag [cos (φ k (t0),..., cos (φ k (t N-1 ))], S k = diag [sin (φ k (t0),..., sin (φ k (t N-1 ))], where, Λ = diag [Θ, Θ], where Θ is a second-order difference operator with dimension (N-2) × N, denoted as:

[0167]

[0168] Step (6): Update the vector of demodulated signals; for the nth iteration, the vector of demodulated signals is updated as:

[0169]

[0170] The extracted target signal pattern can be written as:

[0171]

[0172] The target signal pattern is the product of the kernel function and the updated vector of demodulated signals;

[0173] The operations in steps (4)-(6) are performed on the signals in all C channels;

[0174] Step (7): updating the common instantaneous frequency; from the vector of demodulated signals, it can be seen that the common instantaneous frequency is not explicitly represented, that is, the objective function is nonlinearly related to the instantaneous frequency; by applying an arctangent operation to the ratio of two demodulated signals, the increment of the common instantaneous frequency is obtained;

[0175]

[0176] Since the instantaneous frequency under the nonlinear frequency modulation mode is a smooth function, it is assumed that the common instantaneous frequency increment also satisfies the band-limited function property, and the smoothness prior method is used to solve the common instantaneous frequency increment:

[0177]

[0178] wherein, α>0 is a regularization parameter; according to the above formula, the smooth instantaneous frequency increment is calculated as:

[0179]

[0180] wherein, I is an identity matrix, the term is a weighted moving average (low-pass filter); then, the common instantaneous frequency vector is updated as:

[0181]

[0182] It is worth noting that the result of the solution is the instantaneous frequency of the kth mode in the channel c; while the joint evolution of the multivariate signal G(t) near the time t needs to evolve at a certain common instantaneous frequency; therefore, the common instantaneous frequency information of the multivariate signal is represented as the power-weighted average of the common instantaneous frequency of the kth mode component , that is:

[0183]

[0184] wherein, is the instantaneous amplitude of the mode k in the channel c; the kernel function D k is updated using the updated common instantaneous frequency information;

[0185] Step (8): using to determine whether the internal loop condition is greater than the internal stop threshold; if the determination condition is greater than the internal stop threshold, steps (6) and (7) are performed; if the determination condition is less than the stop threshold, jump to step (9);

[0186] Step (9): using r k = G-g c update the residual signal, where g c is the target signal pattern in the cth channel; set k = k + 1;

[0187] Step (10): using determine whether the outer loop condition is greater than the outer stop threshold; if the outer loop condition is greater than the outer stop threshold, execute steps (3) to (9); if the outer loop condition is less than the outer stop threshold, exit the loop;

[0188] Step (11): output the target signal pattern {g c,k}, where c = 1, 2, … C, k = 1, 2, … K.

[0189] In order to compare the effectiveness of the adaptive multivariate time-varying signal decomposition method provided by the present application, in the experiment, MVMD, MNCMD and the method of the present application are respectively used to decompose multivariate simulation signals and multivariate real signals, and the decomposition performance, noise robustness and pattern alignment properties of each method are compared; the synthesized signal is composed of two-channel signals with varying amplitudes and frequencies, and noise with a mean of 0 and a standard deviation of 0.5 is added to each channel, and the synthesized signal is as follows:

[0190]

[0191] Figures 2(a) to (c) show the decomposition results of the three methods, from which it can be seen that the method provided by the present application and MNCMD can align all the patterns according to the common frequency components and accurately extract the real patterns; the execution times of the decomposition algorithms of the two are 0.036 seconds and 0.558 seconds respectively; since the method provided by the present application uses a recursive extraction framework, it extracts signal patterns one by one from the original multivariate signal, so the decomposition efficiency of the method of the present application is higher; in contrast, MVMD cannot correctly extract the patterns and appears to have mode aliasing linearly. At the same time, this embodiment also shows that the method provided by the present application has strong noise robustness.

[0192] The adaptive multi-component time-varying signal decomposition method provided by the application is applied to vibration data at three bearings of a rotor-bearing system of a hydroelectric generating set in a certain pumped storage power station; the data is collected from displacement sensors at upper guide bearings, lower guide bearings and water guide bearings (i.e. three channels) of the hydroelectric generating set, wherein the pumped storage unit is operated in a relatively stable stage; the rated speed of the pumped storage unit is 375 rpm, the rated power is 400 MW, the sampling time is 1.28 s, and the sampling point number is 1024; the first four modes of the three-channel signals are extracted by using the method; FIGS. 3(a)-(c) show the original waveforms of the three-channel vibration signals and the decomposition results of the three methods; as can be seen from FIGS. 3(a)-(c), the MVMD cannot correctly extract the modes, and the modes u3 and u4 become noise; FIGS. 4(a)-(c) plot the frequency spectrum of the signal and the corresponding frequency spectrum of the extracted mode; as can be seen from FIGS. 4(a)-(c), the method provided by the application and the MNCMD accurately extract the modes, while the modes u3 and u4 in the MVMD are not correctly extracted (FIG. 4(c)), and mode aliasing occurs, which shows that the method cannot well process time-varying signals; in contrast, the AMCMD and the MNCMD can correctly capture the modes and have the mode alignment property, so the AMCMD and the MNCMD have better decomposition performance when processing time-varying signals, but the AMCMD does not need to give the number of prior modes, and the MNCMD needs to give the number of modes of the multi-component time-varying signal in advance due to the use of the joint extraction framework.

[0193] In summary, compared with the prior art, the application has the following advantages:

[0194] The method of the application adopts the recursive extraction framework, does not need the prior knowledge of the number of modes of the multi-component time-varying signal, overcomes the lack of the multi-component signal processing method of the joint extraction framework, establishes a discretization objective function for each mode, extracts the target signal mode and calculates the common instantaneous frequency vector at the same time, and solves the problem that the existing signal decomposition method can only realize the decomposition of the non-stationary nonlinear multi-component signal when the prior knowledge of the multi-component signal mode is needed.

[0195] The method provided by the application establishes an objective function based on the multi-component input signal, minimizes the residual energy while minimizing two demodulation signals, and performs time discretization on the demodulation signal of the objective function to construct a discretized objective function corresponding to the kth mode and the cth channel. The method can effectively reduce the computational complexity of the recursive extraction framework, so that the calculation cost is lower and the calculation efficiency is higher, and the method can also be used for processing complex wideband noise signals.

[0196] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of adaptive multivariate time-varying signal decomposition, characterized by, The method comprises the following steps: S1: establishing a multi-channel multivariate time-varying signal, using Hilbert transform to analytically express the multivariate time-varying signal, defining a set of unique regular amplitude and phase functions, and obtaining an analytical expression of the multivariate signal; S2: assuming that there is a common frequency component in all channels, simplifying the analytical expression of the multivariate signal; S3: multiplying the demodulated multivariate frequency modulation mode by a frequency shift operator, moving the frequency spectrum of the demodulated multivariate frequency modulation mode to the baseband, using the real signal of the multivariate time-varying signal to replace the multivariate time-varying signal, and obtaining a multivariate input signal; S4: using a recursive extraction framework, based on the multivariate input signal, establishing a target function with the condition of minimizing two demodulation signals and minimizing the residual energy, and discretizing the target function; S5: based on the discretized target function, updating the demodulation signal and extracting the target signal mode, and updating the common instantaneous frequency based on the demodulation signal in the multivariate input signal, to realize the decomposition of the multivariate time-varying signal; wherein the target signal mode is the vector product of the kernel function and the demodulation signal; the common instantaneous frequency of each mode component of all channels is estimated as a power-weighted average.

2. The adaptive polyadic time-varying signal decomposition method of claim 1, wherein, S1 specifically comprises the following steps: S1.1: establishing a multivariate time-varying signal X(t) of C channels, and its expression is: where a c (t), f c (t) and respectively denote the instantaneous amplitude, the instantaneous frequency and the initial phase of the c-th channel. S1.2: using Hilbert transform to analytically express the multivariate time-varying signal, defining a unique regular amplitude and phase function, and obtaining an analytical expression of the multivariate signal; wherein denotes the Hilbert transform operator; X a (t) is a multivariate time-varying signal analytical expression.

3. The adaptive polyadic time-varying signal decomposition method of claim 2, wherein, The simplified analytical expression of the multivariate signal is: where a(t) = [a1(t),...,a C (t)] T .

4. The adaptive polyadic time-varying signal decomposition method of claim 3, wherein, S3 specifically comprises the following steps: S3.1: using demodulation technology, using the product of the simplified analytical expression of the multivariate signal and the demodulation operator to represent the demodulated multivariate frequency modulation mode; specifically: wherein denotes a frequency function of the demodulation operator; f c denotes the carrier frequency; S3.2: multiplying the demodulated multivariate frequency modulation mode by a frequency shift operator, moving the frequency spectrum of the demodulated multivariate frequency modulation mode to the baseband, and obtaining a baseband signal: Wherein f(t) represents the common instantaneous frequency of the multivariate frequency modulation signal; the common instantaneous frequency of the multivariate frequency modulation mode is estimated by finding the smooth frequency function when the obtained baseband signal has the narrowest frequency band; S3.3: based on the baseband signal, using the real signal of the multivariate time-varying signal to replace the multivariate time-varying signal; wherein is a real part extraction operator; is an imaginary part extraction operator; p(t) and q(t) are demodulated signals; S3.4: obtaining a multivariate input signal; where p k (t) = [p 1,k (t), p 2,k (t),... p C,k (t)] T and q k (t) = [q 1,k (t), q 2,k (t),... q C,k (t)] T , denotes a white Gaussian noise; K is the number of modes; C is the number of channels; k denotes the kth mode; p c,k (t) and q c,k (t) are the two demodulated signals of the kth mode in the cth channel.

5. The adaptive polyadic time-varying signal decomposition method of claim 4, wherein, S4 specifically comprises the following steps: S4.1: assigning the multivariate input signal to the residual signal, presetting the common instantaneous frequency of the first mode number, and constructing an initial kernel function using the initial common instantaneous frequency; starting from the first mode, step S4.2 is executed; S4.2: establishing a target function corresponding to the kth mode and the cth channel based on the condition of minimizing two demodulation signals of the kth mode and the cth channel in the multivariate input signal and minimizing the residual function; S4.3: time-discretizing the target function to construct a discretized target function corresponding to the kth mode and the cth channel.

6. The adaptive polyadic time-varying signal decomposition method of claim 5, wherein, S5 specifically comprises the following steps: S5.1: calculating the vector of the corresponding demodulation signal according to the discretized target function corresponding to the kth mode and the cth channel; S5.2: calculating the vector product of the kernel function and the demodulation signal in S5.1 to extract the target signal mode corresponding to the kth mode and the cth channel; S5.3: Repeat steps S5.1-S5.2 until all channel corresponding discretization target function is executed S5.1-S5.2, go to S5.4; S5.4: The ratio of the two demodulation signals of the kth mode cth channel is calculated by using the inverse tangent operation, and the increment of the corresponding common instantaneous frequency is calculated; S5.5: Combine the common instantaneous frequency increment in S5.4, and solve the smoothing instantaneous frequency increment of the kth mode cth channel using the smoothing degree prior method; S5.6: The common instantaneous frequency of the kth mode cth channel is summed with the corresponding smoothing instantaneous frequency increment, and the common instantaneous frequency vector of the kth mode cth channel is updated; S5.7: The common instantaneous frequency vector in the current mode of all channels is power weighted and averaged to calculate the common instantaneous frequency of all channels in the current mode, and the kernel function is updated; S5.8: Determine whether the internal loop condition is greater than the internal stop threshold, if greater than the internal stop threshold, go to S5.1, otherwise go to S5.9; S5.9: Update the residual signal using the difference between the multi-input signal and the target signal mode in all channels, and switch the mode to the next mode; S5.10: Determine whether the external loop condition is greater than the external stop threshold, if greater than, go to S4.2; otherwise, output all target signal modes and common instantaneous frequencies.

7. The adaptive polyadic time-varying signal decomposition method of claim 6, wherein, The target function is: where β > 0 is a penalty parameter; p c,k (t) and q c,k (t) are two demodulated signals; denotes the residual energy; g c is the target signal pattern in the cth channel; The discretized target function is: wherein p c,k = [p c,k (t0)... p c,k (t N-1 )], q c,k = [q c,k (t0)... q c,k (t N-1 )], g c = [g c (t0)... g c (t N-1 )] T ; D k is related to the demodulation frequency and is expressed as D k = [C k S k ], C k = diag [cos(φ k (t0),..., cos(φ k (t N-1 ))], S k = diag [sin(φ k (t0),..., sin(φ k (t N-1 ))], Λ = diag [Θ, Θ], Θ is a second-order difference operator of dimension (N-2) x N and is expressed as: The vector of demodulation signals is: The common instantaneous frequency in the current mode is: wherein, is the instantaneous amplitude of mode k in channel c; is the common instantaneous frequency for the kth mode in the cth channel.

8. An adaptive polyphase time-varying signal decomposition system, characterized by, It includes: The Hilbert transform module is used to analyze the multi-time-varying signal by using Hilbert transform, define a set of unique regular amplitude and phase functions, and obtain the analytical expression of the multi-input signal; The analytical expression simplification module is used to simplify the analytical expression of the multi-input signal by assuming that there is a common frequency component in all channels; The spectrum conversion module is used to move the frequency spectrum of the demodulated multi-frequency mode to the baseband by multiplying the demodulated multi-frequency mode with the frequency shift operator; The multi-input signal acquisition module is used to obtain the multi-input signal by using the real signal of the multi-time-varying signal to replace the multi-time-varying signal in combination with the baseband signal; The discretized target function establishment module is used to establish a target function based on the multi-input signal using a recursive extraction framework, and to minimize the residual energy of the two demodulation signals, and to discretize the target function; The multi-time-varying signal decomposition module updates the demodulation signal and extracts the target signal mode based on the discretized target function, and calculates the common instantaneous frequency based on the demodulation signal in the multi-input signal, to realize the decomposition of the multi-time-varying signal; wherein the target signal mode is the product of the kernel function and the vector of demodulation signals; the common instantaneous frequency of each mode component of all channels is estimated as a power weighted average.

9. The adaptive polyadic time-varying signal decomposition system of claim 8, wherein, The multi-time-varying signal is: where X(t) is a multivariate time-varying signal; a c (t), f c (t) and denote the instantaneous amplitude, the instantaneous frequency and the initial phase of the c-th channel, respectively. The analytical expression of the multi-input signal is: wherein denotes the Hilbert transform operator; X a (t) is a multivariate time-varying signal analytical expression; The simplified analytical expression of the multi-input signal is: where a(t) = [a1(t),...,aM(t)]T C (t)] T ; The multi-input signal; where p k (t) = [p 1,k (t), p 2,k (t),... p C,k (t)] T and q k (t) = [q 1,k (t), q 2,k (t),... q C,k (t)] T , denotes a white Gaussian noise; K is the number of modes; C is the number of channels; k denotes the kth mode, respectively; p c,k (t) and q c,k (t) are the two demodulated signals of the kth mode in the cth channel.

10. The adaptive polyadic time-varying signal decomposition system of claim 8, wherein, The discretized target function establishment module includes: The initialization setting unit is configured to assign the multivariate input signal to the residual signal, preset a common instantaneous frequency of a first mode number, and construct an initial kernel function using the initial common instantaneous frequency; The target function construction unit is configured to establish a target function corresponding to the kth mode and the cth channel based on the condition of minimizing two demodulation signals of the kth mode and the cth channel in the multivariate input signal and minimizing a residual function; The target function discretization unit is configured to perform time discretization on the target function to construct a discretized target function corresponding to the kth mode and the cth channel; The decomposition module of the multivariate time-varying signal comprises: The vector calculation unit of the demodulation signal is configured to calculate a vector of the corresponding demodulation signal according to the discretized target function corresponding to the kth mode and the cth channel; The target signal mode extraction unit is configured to calculate a product of the kernel function and the vector of the demodulation signal, and extract a target signal mode corresponding to the kth mode and the cth channel; The common instantaneous frequency increment calculation unit is configured to calculate a common instantaneous frequency increment by using an inverse tangent operation of a ratio of the two demodulation signals of the kth mode and the cth channel; The smooth instantaneous frequency increment calculation unit is configured to combine the common instantaneous frequency increment and solve a smooth instantaneous frequency increment of the kth mode and the cth channel by using a smoothness prior method; The common instantaneous frequency vector calculation unit is configured to sum the common instantaneous frequency of the kth mode and the cth channel and the corresponding smooth instantaneous increment to update a common instantaneous frequency vector of the kth mode and the cth channel; The common instantaneous frequency calculation unit is configured to calculate a common instantaneous frequency of a current mode in all channels by performing power-weighted averaging on the common instantaneous frequency vectors of the current mode in all channels, and update the kernel function; The first discriminator is configured to determine whether an internal loop condition is greater than an internal stop threshold, and if the internal loop condition is greater than the internal stop threshold, drive the vector calculation unit of the demodulation signal to run, otherwise drive the residual signal update unit; The residual signal update unit is configured to update the residual signal by using a difference between the multivariate input signal and the target signal mode in all channels; The second discriminator is configured to determine whether an external loop condition is greater than an external stop threshold, and if the external loop condition is greater than the external stop threshold, drive the target function construction unit to run, otherwise output all target signal modes and common instantaneous frequencies.

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