CN112367063B - Self-adaptive center frequency mode decomposition method and system - Google Patents
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Abstract
The invention relates to a self-adaptive center frequency mode decomposition method and a self-adaptive center frequency mode decomposition system, which comprise the following steps: establishing a data-driven self-adaptive center frequency rapid positioning strategy; establishing a primary decomposition strategy meeting signal reconstruction; and realizing the self-adaptive decomposition of the non-stationary signal by combining the data-driven self-adaptive center frequency quick positioning strategy and the primary decomposition strategy meeting the signal reconstruction. The method effectively avoids the problems of mode aliasing and the like caused by unreasonable parameter setting, and has good accuracy and high efficiency.
Description
Technical Field
The present invention relates to the technical field of signal decomposition and detection, and in particular, to a method and a system for decomposing a self-adaptive center frequency mode.
Background
The signal decomposition method is very key to the detection and analysis of industrial signals. Many adaptive signal analysis methods are currently developed, such as empirical mode decomposition, local mean decomposition, local feature decomposition, adaptive local iterative filter decomposition, empirical wavelet decomposition, and nonlinear mode decomposition. These methods have respective limitations, for example, there are problems of requiring preset parameters, mode aliasing, end-point effect, etc., which results in that the application range of the existing adaptive signal decomposition method is limited. In particular, the variational mode decomposition method proposed an adaptive signal decomposition technique in 2014, which can decompose a non-stationary signal with multiple components into multiple mode components with certain meaning. Compared with the traditional self-adaptive decomposition method, the variational mode decomposition method has more obvious advantages, such as noise suppression, non-recursive screening, clear physical significance and the like, and has been applied in many fields. However, these methods focus on how to determine suitable decomposition parameters, and it is difficult to balance the relationship between the calculation efficiency and accuracy and lack some adaptivity. Therefore, it is necessary to provide a new signal analysis method to better apply the detection and analysis of industrial signals by breaking through the limitation of the variational mode decomposition method.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the problems of complicated optimization process, poor accuracy and low efficiency of the decomposition parameters such as the bandwidth parameters, the number of mode components and the like in the prior art, thereby providing the self-adaptive center frequency mode decomposition method and the self-adaptive center frequency mode decomposition system which avoid the complicated optimization process of the decomposition parameters such as the bandwidth parameters, the number of mode components and the like, and have good accuracy and high efficiency.
In order to solve the above technical problem, a method for decomposing a self-adaptive center frequency mode according to the present invention includes: establishing a data-driven self-adaptive center frequency rapid positioning strategy; establishing a primary decomposition strategy meeting signal reconstruction; and realizing the self-adaptive decomposition of the non-stationary signal by combining the data-driven self-adaptive center frequency quick positioning strategy and the primary decomposition strategy meeting the signal reconstruction.
In one embodiment of the present invention, a method for establishing a data-driven adaptive center frequency fast positioning strategy includes: establishing an optimization solving model for identifying the single components; constructing a relation between the center frequency of iteration 1 time and the initial estimation frequency; and establishing a convergence tendency discriminant function.
In one embodiment of the present invention, the method for establishing the optimal solution model for identifying the single component includes: optimization solution model Lone(ur(t),ωr) Is composed of
Wherein u isr(t) is a single component, ωrIs ur(t) a center frequency, x (t) is the non-stationary signal to be decomposed, η represents a bandwidth parameter,
represents the partial derivative with respect to time t, δ (t) is the dirichlet distribution function, denotes the convolution operator,
the representation takes a 2 norm.
In one embodiment of the invention, the optimization solution model Lone(ur(t),ωr) Is solved by the following two iterative computations
And
wherein X (ω) is the frequency spectrum of the non-stationary signal X (t) to be decomposed;
for the nth iteration, the value of u is obtainedr(t) an optimized spectrum;
for the nth iteration, the value of u is obtainedr(t) a center frequency; f. ofsFor the sampling frequency of the non-stationary signal x (t) to be decomposed, and two iterative computations given ur(t) center frequency ωrInitial estimated value of
In one embodiment of the invention, the center frequency is constructed by iterating 1 time through two iteration calculation formulas
And the initial estimated frequency
The relation of (1):
in one embodiment of the present invention, the method for establishing the convergence trend discriminant function is as follows:
wherein
Given the jth initial center frequency, j is 1,2, …, N is the number of frequency points within the analysis band,
is composed of
Iterating the center frequency of 1 time, the sign of T (j) appears once from positive to negative, that is, T (j) is greater than 0 and T (j +1) < 0, then the number of components in the non-stationary signal to be decomposed is added with 1, the k time of the sign of T (j) is changed from positive to negative, then the true center frequency omega of the k time componentkApproximately satisfies the following relationship:
therefore, the number of all the intrinsic components of the to-be-decomposed non-stationary signal in the analysis frequency band and the approximate central frequency value { omega } of the number can be obtained based on the convergence tendency discriminant function1,ω2,…,ωk,…}。
In one embodiment of the present invention, a method for establishing a primary decomposition strategy satisfying signal reconstruction includes: establishing a multi-component decomposition model, and if a given group of initial center frequencies are close to the real center frequency of each component, not needing iterative computation; and all components contained in the non-stationary signal to be decomposed are obtained through the established inverse Fourier transform.
In one embodiment of the invention, when building a multi-component decomposition model: establishing a multicomponent u1(t),…ul(t),…uK(t) decomposition model Ltwo{u1(t),…ul(t),…uK(t) }, and
where K is the number of mode components contained in the non-stationary signal to be decomposed, model Ltwo{u1(t),…ul(t),…uK(t) } solving is performed by two iterative computations
And
by providing a given set of initial center frequencies
Is close to u1(t),…ul(t),…uK(t) the true center frequency of each component,
directly reconstructing to obtain U through one-time decomposition without iterative calculationm(ω), and
then by inverse Fourier transform { u }1(t),u2(t),…,uK(t)}＝IFFT(Um(ω))m∈{1,2,…,K}Obtaining all components u contained in the non-stationary signal to be decomposed1(t),…ul(t),…uK(t) in which IFFT (U)m(ω)) represents the pair Um(ω) performing an inverse Fourier transform.
In an embodiment of the present invention, a method for combining the data-driven adaptive center frequency fast positioning strategy and the primary decomposition strategy satisfying signal reconstruction includes: analyzing the to-be-decomposed non-stationary signals by using a data-driven self-adaptive center frequency rapid positioning strategy to obtain approximate center frequency of the implicit components; and taking the approximate center frequency obtained by analysis as the initial center frequency in a primary decomposition strategy meeting signal reconstruction, and obtaining all components contained in the non-stationary signal to be decomposed by utilizing the primary decomposition strategy meeting the signal reconstruction.
The invention also provides a self-adaptive center frequency mode decomposition system, which comprises: the first establishing module is used for establishing a data-driven self-adaptive center frequency rapid positioning strategy; the second establishing module is used for establishing a primary decomposition strategy meeting the signal reconstruction; and the combination module is used for combining the data-driven self-adaptive center frequency rapid positioning strategy and the primary decomposition strategy meeting the signal reconstruction to realize the self-adaptive decomposition of the non-stationary signal.
Compared with the prior art, the technical scheme of the invention has the following advantages:
according to the self-adaptive center frequency mode decomposition method and system, a data-driven self-adaptive center frequency rapid positioning strategy is established, the number of components contained in a non-stationary signal and the approximate center frequency of the components can be determined in a self-adaptive manner, particularly, a convergence trend discrimination function is established by utilizing a first iteration center frequency, the calculation efficiency of the method can be obviously improved, and the parameter selection problem of the traditional variational mode decomposition algorithm is effectively avoided; establishing a one-time decomposition strategy meeting signal reconstruction, wherein the reconstruction can be realized by the decomposition result of the to-be-decomposed non-stationary signal under the strategy, and the strategy can be analyzed only by iterating once after an approximate value of the central frequency and the real central frequency is given, so that the efficiency of the algorithm is obviously improved, the dependence of the traditional decomposition method on preset parameters is overcome, and the problems of mode aliasing and the like caused by unreasonable parameter setting are effectively avoided; the data-driven adaptive center frequency rapid positioning strategy and the one-time decomposition strategy meeting the signal reconstruction are combined to realize the adaptive decomposition of the non-stationary signal, so that the complicated optimization process of the traditional variational mode decomposition method on the decomposition parameters such as bandwidth parameters, the number of mode components and the like is avoided, and the accuracy and the efficiency are good.
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In order that the present disclosure may be more readily and clearly understood, reference is now made to the following detailed description of the embodiments of the present disclosure taken in conjunction with the accompanying drawings, in which
FIG. 1 is a flow chart of an adaptive center frequency pattern decomposition method of the present invention;
FIG. 2 is a set of non-stationary signals in an embodiment of the present invention
FIG. 3 shows the result of the discriminant function of convergence trend obtained by the data-driven adaptive center frequency fast positioning strategy analysis of the non-stationary signal with the bandwidth parameter η of 2500 in the embodiment of the present invention;
fig. 4 shows that the center frequency input identified in this embodiment satisfies the first decomposition strategy of signal reconstruction to obtain two components contained in the non-stationary signal;
FIG. 5 shows two components obtained by using the prior art variational mode decomposition method in this embodiment;
fig. 6 shows two components obtained by the bandwidth fourier decomposition method in this embodiment.
Detailed Description
Example one
As shown in fig. 1, the present embodiment provides an adaptive center frequency mode decomposition method, which includes the following steps: step S1: establishing a data-driven self-adaptive center frequency rapid positioning strategy; step S2: establishing a primary decomposition strategy meeting signal reconstruction; step S3: and realizing the self-adaptive decomposition of the non-stationary signal by combining the data-driven self-adaptive center frequency quick positioning strategy and the primary decomposition strategy meeting the signal reconstruction.
In the adaptive center frequency mode decomposition method according to this embodiment, in step S1, a data-driven adaptive center frequency fast positioning strategy is established, so that the number of components and their approximate center frequencies contained in a non-stationary signal can be adaptively determined, and particularly, a convergence trend discrimination function is established by using a first iteration center frequency, so that the calculation efficiency of the method can be significantly improved, and the problem of parameter selection of a conventional variational mode decomposition algorithm is effectively avoided; in the step S2, a one-time decomposition strategy satisfying signal reconstruction is established, under which the decomposition result of the to-be-decomposed non-stationary signal can be reconstructed, and after an approximate value of the central frequency and the true central frequency is given, the strategy can be analyzed by only iterating once, so that the efficiency of the algorithm is significantly improved, the dependence of the traditional decomposition method on preset parameters is overcome, and the problems of mode aliasing and the like caused by unreasonable parameter setting are effectively avoided; in the step S3, the data-driven adaptive center frequency fast positioning strategy and the one-time decomposition strategy satisfying the signal reconstruction are combined to realize adaptive decomposition of the non-stationary signal, so as to avoid a cumbersome optimization process of the traditional variational mode decomposition method on the decomposition parameters such as bandwidth parameters and the number of mode components, and the method has good accuracy and high efficiency.
In step S1, the method for establishing the data-driven adaptive center frequency fast positioning policy includes: establishing an optimization solving model for identifying the single components; constructing a relation between the center frequency of iteration 1 time and the initial estimation frequency; and establishing a convergence tendency discriminant function.
Establishing an optimized solution model L for identifying the single componentsone(ur(t),ωr) Is composed of
Wherein u isr(t) is a single component, ωrIs ur(t) a center frequency, x (t) is the non-stationary signal to be decomposed, η represents a bandwidth parameter,
represents the partial derivative with respect to time t, δ (t) is the dirichlet distribution function, denotes the convolution operator,
the representation takes a 2 norm.
The optimization solution model Lone(ur(t),ωr) Is solved by the following two iterative computations (2) and (3)
Wherein X (omega) is the nonstationary signal to be decomposedSpectrum of number x (t);
for the nth iteration, the value of u is obtainedr(t) an optimized spectrum;
for the nth iteration, the value of u is obtainedr(t) a center frequency; f. ofsFor the sampling frequency of the non-stationary signal x (t) to be decomposed, and for the two iterative computations (2) and (3) u is givenr(t) center frequency ωrInitial estimated value of
Constructing 1-time iteration center frequency by two iteration calculation formulas (2) and (3)
And the initial estimated frequency
The relation of (1):
at a given initial center frequency
Under the condition, the frequency of the frequency tends to be the real center frequency in the iterative optimization process. Thus, if given an initial center frequency
Less than the true center frequency, the iterative optimization process will gradually increase; otherwise, the optimization process is gradually reduced along with the iteration. For this purpose, iteration 1 of the center frequency, which can be obtained using equation (4), is used
With a given initial center frequency
To determine a given initial center frequency
Whether smaller or larger than the true center frequency. Considering that the non-stationary signal to be decomposed tends to be a multi-component signal, there is a given initial center frequency around each component
The magnitude of the center frequency is different from the real center frequency, so that an iterative optimization process is brought about
Either increasing or decreasing.
Based on the above properties, further disclosure is made regarding analyzing all initial center frequencies within the frequency band by constructing equation (5)
And the magnitude of the frequency in the true of each component in the non-stationary signal to be decomposed.
Wherein,
for a given jth initial center frequency, j is 1,2, …, and N is the number of frequency points in the analysis band
Is composed of
Center frequency of 1 iteration.
The method for establishing the convergence tendency discriminant function comprises the following steps:
the convergence tendency discriminant function is utilized to obtain that the symbol of T (j) appears once in the process of changing from positive sign to negative sign, namely T (j) is greater than 0 and T (j +1) is less than 0, and the number of components in the to-be-decomposed non-stationary signal is added with 1. The k-th transition of the sign of T (j) from positive to negative, the true center frequency ω of the k-th componentkApproximately satisfies the following relationship:
therefore, the number of all the intrinsic components of the to-be-decomposed non-stationary signal in the analysis frequency band and the approximate central frequency value { omega } of the number can be obtained based on the convergence tendency discriminant function1,ω2,…,ωk,…}。
In step S2, the method for establishing the primary decomposition strategy that satisfies the signal reconstruction includes: establishing a multi-component decomposition model, and if a given group of initial center frequencies are close to the real center frequency of each component, not needing iterative computation; and all components contained in the non-stationary signal to be decomposed are obtained through the established inverse Fourier transform.
When a multi-component decomposition model is established: establishing a multicomponent u1(t),…ul(t),…uK(t) decomposition model is Ltwo{u1(t),…ul(t),…uK(t)}
Where K is the number of mode components contained in the non-stationary signal to be decomposed, model Ltwo{u1(t),…ul(t),…uKThe solution of (t) is achieved by the following two iterative computations (9) and (10).
If given a set of initial center frequencies
Is close to u1(t),…ul(t),…uK(t) the true center frequency of each component,
does not need iterative computation, namely, directly reconstructs the U by one-time decompositionm(ω), i.e., equation (9) does not require iterative computation, and U can be obtained directlym(ω) m ∈ {1,2, …, K }, as follows:
all components u contained in the non-stationary signal to be decomposed are obtained by inverse Fourier transform as shown in equation (12)1(t),…ul(t),…uK(t)。
{u1(t),u2(t),…,uK(t)}＝IFFT(Um(ω))m∈{1,2,…,K}(12) In which IFFT (U)m(ω)) represents the pair Um(ω) performing an inverse Fourier transform.
In step S3, the method for combining the data-driven adaptive center frequency fast positioning strategy and the first decomposition strategy satisfying signal reconstruction includes: analyzing the to-be-decomposed non-stationary signals by using a data-driven self-adaptive center frequency rapid positioning strategy to obtain approximate center frequency of the implicit components; and taking the approximate center frequency obtained by analysis as the initial center frequency in a primary decomposition strategy meeting signal reconstruction, and obtaining all components contained in the non-stationary signal to be decomposed by utilizing the primary decomposition strategy meeting the signal reconstruction.
Specifically, the data-driven adaptive center frequency fast positioning strategy analyzes the nonstationary signal to be decomposed to obtain the approximate center frequency { omega ] of the embedded component in the nonstationary signal1,ω2,…,ωk… }; approximate center frequency [ omega ] obtained by analysis1,ω2,…,ωk… as initial center frequency in a one-time decomposition strategy to satisfy signal reconstruction
And then all components u contained in the to-be-decomposed non-stationary signal are obtained by utilizing a one-time decomposition strategy satisfying signal reconstruction1(t),…ul(t),…uK(t)。
The processing effect of the present invention is illustrated by a set of non-stationary signals.
FIG. 2 is a set of non-stationary signals x (t):
x(t)＝A1cos(2πω1t)+A2cos(2πω2t) (13)
the concrete parameters are as follows: harmonic amplitude A1＝1，A20.8, frequency ω1＝10Hz，ω2100Hz, signal sampling frequency fs＝2000Hz。
The use of the data-driven adaptive center frequency fast positioning strategy can determine that two center frequencies are contained in the non-stationary signal, as shown in fig. 3. The center frequency input identified in step S1 satisfies the primary decomposition strategy of signal reconstruction, resulting in the decomposition result shown in fig. 4. The decomposition result is very consistent with the real component, and the effect is better. Fig. 5 and 6 are results of a conventional variational mode decomposition method and a bandwidth fourier decomposition method, respectively, and it can be seen that the analysis results of the two methods are different from the real components.
Example two
Based on the same inventive concept, the present embodiment provides an adaptive center frequency pattern decomposition system, which solves the problems in the same manner as the adaptive center frequency pattern decomposition method, and the repeated parts are not repeated.
The present embodiment provides an adaptive center frequency mode decomposition system, including:
the first establishing module is used for establishing a data-driven self-adaptive center frequency rapid positioning strategy;
the second establishing module is used for establishing a primary decomposition strategy meeting the signal reconstruction;
and the combination module is used for combining the data-driven self-adaptive center frequency rapid positioning strategy and the primary decomposition strategy meeting the signal reconstruction to realize the self-adaptive decomposition of the non-stationary signal.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications therefrom are within the scope of the invention.
Claims (2)
1. An adaptive center frequency mode decomposition method, characterized by comprising the following steps:
step S1: the method for establishing the data-driven self-adaptive center frequency quick positioning strategy comprises the following steps: establishing an optimization solving model for identifying the single components; constructing a relation between the center frequency of iteration 1 time and the initial estimation frequency; the method for establishing the convergence tendency discriminant function and the optimal solution model for identifying the single component comprises the following steps: optimization solution model Lone(ur(t),ωr) Is composed of
Wherein u isr(t) is a single component, ωrIs ur(t) a center frequency, x (t) is the non-stationary signal to be decomposed, η represents a bandwidth parameter,
represents the partial derivative with respect to time t, δ (t) is the dirichlet distribution function, denotes the convolution operator,
the expression is taken as 2 norms, and the optimization solution model Lone(ur(t),ωr) Is solved by the following two iterative computations
And
wherein X (ω) is the frequency spectrum of the non-stationary signal X (t) to be decomposed;
for the nth iteration, the value of u is obtainedr(t) an optimized spectrum;
for the nth iteration, the value of u is obtainedr(t) a center frequency; f. ofsFor the sampling frequency of the non-stationary signal x (t) to be decomposed, and two iterative computations given ur(t) center frequency ωrInitial estimated value of
Construction of iterative 1-time center frequency by two iterative calculation formulas
And the initial estimated frequency
The relation of (1):
method for establishing convergence trend discriminant functionComprises the following steps:
wherein
Given the jth initial center frequency, j is 1,2, …, N is the number of frequency points within the analysis band,
is composed of
Iterating the center frequency of 1 time, the sign of T (j) appears once from positive to negative, that is, T (j) is greater than 0 and T (j +1) < 0, then the number of components in the non-stationary signal to be decomposed is added with 1, the k time of the sign of T (j) is changed from positive to negative, then the true center frequency omega of the k time componentkApproximately satisfies the following relationship:
therefore, the number of all the intrinsic components of the to-be-decomposed non-stationary signal in the analysis frequency band and the approximate central frequency value { omega } of the number can be obtained based on the convergence tendency discriminant function1,ω2,…,ωk,…}；
Step S2: the method for establishing the primary decomposition strategy meeting the signal reconstruction comprises the following steps: establishing a multi-component decomposition model, and if a given group of initial center frequencies are close to the real center frequency of each component, not needing iterative computation; all components contained in the non-stationary signal to be decomposed are obtained through the established inverse Fourier transform, and when a multi-component decomposition model is established: establishing a multicomponent u1(t),…ul(t),…uK(t) decomposition model Ltwo{u1(t),…ul(t),…uK(t)Are multiplied by
Where K is the number of mode components contained in the non-stationary signal to be decomposed, model Ltwo{u1(t),…ul(t),…uK(t) } solving is performed by two iterative computations
And
by providing a given set of initial center frequencies
Is close to u1(t),…ul(t),…uK(t) the true center frequency of each component,
directly reconstructing to obtain U through one-time decomposition without iterative calculationm(ω), and
then by inverse Fourier transform { u }1(t),u2(t),…,uK(t)}＝IFFT(Um(ω))m∈{1,2,…,K}Obtaining all components u contained in the non-stationary signal to be decomposed1(t),…ul(t),…uK(t) in which IFFT (U)m(ω)) represents the pair Um(ω) performing an inverse fourier transform;
step S3: the data-driven self-adaptive center frequency fast positioning strategy and the primary decomposition strategy meeting the signal reconstruction are combined to realize the self-adaptive decomposition of the non-stationary signal, and the method combining the data-driven self-adaptive center frequency fast positioning strategy and the primary decomposition strategy meeting the signal reconstruction is as follows: analyzing the to-be-decomposed non-stationary signals by using a data-driven self-adaptive center frequency rapid positioning strategy to obtain approximate center frequency of the implicit components; and taking the approximate center frequency obtained by analysis as the initial center frequency in a primary decomposition strategy meeting signal reconstruction, and obtaining all components contained in the non-stationary signal to be decomposed by utilizing the primary decomposition strategy meeting the signal reconstruction.
2. An adaptive center frequency mode decomposition system, comprising:
the first establishing module is used for establishing a data-driven self-adaptive center frequency rapid positioning strategy, and the establishing of the data-driven self-adaptive center frequency rapid positioning strategy comprises the following steps: establishing an optimization solving model for identifying the single components; constructing a relation between the center frequency of iteration 1 time and the initial estimation frequency; establishing a convergence trend discrimination function, and establishing an optimization solving model for identifying the single component as follows: optimization solution model Lone(ur(t),ωr) Is composed of
Wherein u isr(t) is a single component, ωrIs ur(t) a center frequency, x (t) is the non-stationary signal to be decomposed, η represents a bandwidth parameter,
represents the partial derivative with respect to time t, δ (t) is the dirichlet distribution function, denotes the convolution operator,
the expression is taken as 2 norms, and the optimization solution model Lone(ur(t),ωr) Is solved by the following two iterative computations
And
is completed, wherein X (omega) is the non-stationary signal to be decomposedThe spectrum of x (t);
for the nth iteration, the value of u is obtainedr(t) an optimized spectrum;
for the nth iteration, the value of u is obtainedr(t) a center frequency; f. ofsFor the sampling frequency of the non-stationary signal x (t) to be decomposed, and two iterative computations given ur(t) center frequency ωrInitial estimated value of
Construction of iterative 1-time center frequency by two iterative calculation formulas
And the initial estimated frequency
The relation of (1):
establishing a convergence trend discriminant function as follows:
wherein
Given the jth initial center frequency, j is 1,2, …, N is the number of frequency points within the analysis band,
is composed of
Iterating the center frequency of 1 time, the sign of T (j) appears once from positive to negative, that is, T (j) is greater than 0 and T (j +1) < 0, then the number of components in the non-stationary signal to be decomposed is added with 1, the k time of the sign of T (j) is changed from positive to negative, then the true center frequency omega of the k time componentkApproximately satisfies the following relationship:
therefore, the number of all the intrinsic components of the to-be-decomposed non-stationary signal in the analysis frequency band and the approximate central frequency value { omega } of the number can be obtained based on the convergence tendency discriminant function1,ω2,…,ωk,…}；
The second establishing module is used for establishing a primary decomposition strategy meeting the signal reconstruction, and the establishing of the primary decomposition strategy meeting the signal reconstruction is as follows: establishing a multi-component decomposition model, and if a given group of initial center frequencies are close to the real center frequency of each component, not needing iterative computation; all components contained in the non-stationary signal to be decomposed are obtained through the established inverse Fourier transform, and when a multi-component decomposition model is established: establishing a multicomponent u1(t),…ul(t),…uK(t) decomposition model Ltwo{u1(t),…ul(t),…uK(t) }, and
where K is the number of mode components contained in the non-stationary signal to be decomposed, model Ltwo{u1(t),…ul(t),…uK(t) } solving is performed by two iterative computations
And
by providing a given set of initial center frequencies
Is close to u1(t),…ul(t),…uK(t) the true center frequency of each component,
directly reconstructing to obtain U through one-time decomposition without iterative calculationm(ω), and
then by inverse Fourier transform { u }1(t),u2(t),…,uK(t)}＝IFFT(Um(ω))m∈{1,2,…,K}Obtaining all components u contained in the non-stationary signal to be decomposed1(t),…ul(t),…uK(t) in which IFFT (U)m(ω)) represents the pair Um(ω) performing an inverse fourier transform;
a combination module, configured to combine the data-driven adaptive center frequency fast positioning policy and the primary decomposition policy satisfying signal reconstruction to implement adaptive decomposition of a non-stationary signal, where the combination of the data-driven adaptive center frequency fast positioning policy and the primary decomposition policy satisfying signal reconstruction is as follows: analyzing the to-be-decomposed non-stationary signals by using a data-driven self-adaptive center frequency rapid positioning strategy to obtain approximate center frequency of the implicit components; and taking the approximate center frequency obtained by analysis as the initial center frequency in a primary decomposition strategy meeting signal reconstruction, and obtaining all components contained in the non-stationary signal to be decomposed by utilizing the primary decomposition strategy meeting the signal reconstruction.
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