A fractional fourier transform domain adaptive signal decomposition method, storage medium and computer

Abstract

The application discloses a fractional Fourier transform domain adaptive signal decomposition method, a storage medium and a computer, and relates to the field of signal processing. k The application introduces the concept of convolution under fractional Fourier transform, and decomposes the signal to be decomposed into K (K>1) eigenmode components m k The center fractional frequency of each eigenmode component under the transform angle alpha is u k The constraint condition is that the mode component sum is equal to the input signal, the application changes the decomposition process into an optimal solution problem of solving the constraint variation problem, effectively decomposes the signal with non-energy-aggregated frequency domain, and improves the signal decomposition efficiency. The application is applied to the field of adaptive decomposition of non-stationary signals.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of signal processing, and particularly relates to a fractional Fourier transform domain adaptive signal decomposition method. BACKGROUND

[0002] Signal decomposition is a basic problem in signal processing discipline, which directly affects the method and result of subsequent signal analysis and processing. At present, signal decomposition is usually to model the signal as a linear superposition of a set of simple single-component signals. The definition of single-component signal in the signal model determines the signal decomposition method and result to a great extent. In the existing signal decomposition methods, adaptive signal decomposition method is concerned due to its adaptability and complete data-driven characteristics, and has been widely applied in the fields of communication, radar, aviation, power and the like.

[0003] In the existing adaptive signal decomposition methods, variational mode decomposition is favored, which can decompose a complex multi-component signal into simple signal components modeled by amplitude-frequency modulation signals, and has robustness to noise. According to the frequency domain narrowband characteristics of the amplitude-frequency modulation signal, the variational mode decomposition solves the amplitude-frequency modulation signal model parameters through frequency domain bandwidth minimization, so as to obtain each component of the signal. Compared with other adaptive signal decomposition methods, the variational mode decomposition has a rigorous mathematical theoretical basis support, and has stability to noise.

[0004] The variational mode decomposition decomposes a signal f(t) into a series of amplitude-frequency modulation signal components with limited bandwidth, which is usually referred to as an intrinsic mode function. It is assumed that the energy of each intrinsic mode function m k (t) is mainly concentrated in the center frequency ω k in the frequency domain, that is, it has frequency energy aggregation. The energy aggregation of each intrinsic mode function can be described by its baseband bandwidth, that is, the smaller the bandwidth, the more concentrated the energy. For each intrinsic mode function m k (t) with a center frequency ω k , in order to calculate its baseband bandwidth, first, the analytic signal corresponding to it is constructed by Hilbert transform, so as to obtain the one-sided spectrum of non-negative frequency. Then, the frequency spectrum of the constructed analytic signal is shifted to the baseband with a center frequency of zero by the frequency shift operator . Finally, according to the time-frequency analysis theory, the baseband bandwidth is obtained by calculating the square of the two-norm of the frequency operator , and the corresponding baseband bandwidth of each intrinsic mode component is calculated, and the final calculation result is as follows

[0005]

[0006] In the formula, f(t) is a signal to be decomposed, {m k} = {m1...m K} are eigenmode functions, {ω k} = {ω1...ω K} represent the center frequency of each eigenmode function, K is the initialized mode number, represents a frequency operator, which is defined as represents a frequency shift operator, which is defined as represents the Hilbert transform of the eigenmode component, that is, In the formula, the symbol * represents convolution operation. After simplification, there is

[0007]

[0008] It can be seen that the premise assumption of the variational mode decomposition is that the signal to be decomposed is energy-aggregated in the frequency domain. However, for the signal with non-energy-aggregated frequency domain, the processing result is not optimal. The signal with non-energy-aggregated frequency domain is widely used in the fields of communication, radar, sonar and the like. At present, there is a lack of a decomposition method to solve the decomposition problem of the signal with non-energy-aggregated frequency domain. SUMMARY

[0009] The application solves the decomposition problem of the signal with non-energy-aggregated frequency domain.

[0010] The technical scheme of the application is specifically as follows:

[0011] The adaptive signal decomposition method in the fractional Fourier transform domain provided by the application comprises the following steps:

[0012] Step 1: initializing parameters and performing fractional Fourier transform on the signal f(t) to be decomposed to obtain F α (u), wherein the initialized parameters include an outer loop count parameter c, an inner loop cycle number n, a mode component marker parameter k, a fractional Fourier transform of an eigenmode component, a fractional Fourier transform of a Lagrange multiplier and a center fractional frequency;

[0013] Step 2: updating the outer loop count parameter c and updating the angle α of the signal f(t) to be decomposed according to the calculation of the information entropy;

[0014] Step 3: updating the inner loop cycle number n according to the number of the updated angle α;

[0015] Step 4: sequentially updating the mode component marker parameter k, the fractional Fourier transform of the eigenmode component and the center fractional frequency according to the updated inner loop cycle number n;

[0016] Step five: compare the updated modal component marker parameter k and c+1, when the updated modal component marker parameter k is less than c+1, jump to step four, repeat the above operation; otherwise, proceed to the next step;

[0017] Step six: update the fractional order Fourier transform of the Lagrange multiplier;

[0018] Step seven: repeat steps three to six until the stop condition is met, update the modal component marker parameter k=0, and calculate the angle of energy concentration at this time according to the updated fractional Fourier transform of the eigenmodal component

[0019] Step eight: compare and τ, if , then n=0, and return to step three, otherwise proceed to the next step;

[0020] Step nine: inverse transform the updated fractional Fourier transform of the eigenmodal component to output m K-c (t) at this time, if c>1, update F α (u), jump to step two, repeat the above operation; otherwise, output m K (t) to complete the decomposition.

[0021] Further, a preferred mode is provided, which updates the outer loop count parameter and updates the angle α of the signal f(t) to be decomposed according to the calculation of information entropy, specifically:

[0022] The updated outer loop count parameter is:

[0023] c=c-1,

[0024] The angle α of the signal f(t) to be decomposed is updated according to the calculation of information entropy, specifically:

[0025]

[0026] Where F α (u) represents the fractional order Fourier transform of the signal f(t) to be decomposed, and u is the variable of the fractional order Fourier transform domain.

[0027] Further, a preferred mode is provided, which updates the inner loop period according to the number of updated angles α in step three, specifically:

[0028] n=n+1.

[0029] Further, a preferred mode is provided, which sequentially updates the modal component marker parameter, the fractional Fourier transform of the eigenmodal component, and the central fractional frequency in step four, specifically:

[0030] The updated modal component marker parameter is:

[0031] k = k + 1,

[0032] The updated fractional Fourier transform of the eigenmodal component is:

[0033]

[0034] wherein, is the fractional Fourier transform of the eigenmodal component of the n+1th iteration, is the fractional Fourier transform of the eigenmodal component of the nth iteration, is the central fractional order frequency of the nth iteration, and η is the weight of the penalty term in the augmented Lagrangian function;

[0035] The updated central fractional order frequency is:

[0036]

[0037] wherein, is the central fractional order frequency of the n+1th iteration.

[0038] Further, a preferred mode is provided, wherein the fractional Fourier transform of the updated Lagrange multiplier in step six is:

[0039]

[0040] wherein, is the fractional Fourier transform of the Lagrange multiplier of the n+1th iteration, is the fractional Fourier transform of the Lagrange multiplier of the n+1th iteration.

[0041] Further, a preferred mode is provided, wherein the stopping condition in step seven is:

[0042] or n≥N,

[0043] wherein N is the cycle number stopping condition.

[0044] Further, a preferred mode is provided, wherein the updating F α (u) is:

[0045]

[0046] Further, a preferred mode is provided, wherein the outer loop count parameter c is the total number of modal components K.

[0047] Based on the same inventive concept, the application further provides a computer readable storage medium for storing a computer program, wherein the computer program performs the adaptive signal decomposition method in the fractional Fourier transform domain according to any one of the above.

[0048] Based on the same inventive concept, the application further provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor performs the adaptive signal decomposition method in the fractional Fourier transform domain according to any one of the above.

[0049] The application has the advantages that:

[0050] The application solves the problem of non-aggregated signal decomposition in the frequency domain.

[0051] The adaptive signal decomposition method in the fractional Fourier transform domain provided by the application introduces the concept of convolution under fractional Fourier transform, decomposes the signal to be decomposed into K (K>1) eigenmode components m k (t) with a limited bandwidth in the fractional domain, and the center fractional frequency of each eigenmode component under the transform angle a is u k The constraint condition is that the sum of the mode components is equal to the input signal, the application changes the decomposition process into an optimal solution problem of solving the constrained variation problem, effectively decomposes the signal with non-aggregated energy in the frequency domain, and improves the signal decomposition efficiency.

[0052] The application is applied to the field of adaptive decomposition of non-stationary signals, and in actual scenes, the application can be applied to the fields of communication, radar, sonar and the like. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 The adaptive signal decomposition method in the fractional Fourier transform domain according to the first embodiment is a flowchart;

[0054] Figure 2 The time domain waveform of the original signal f(t) according to the eleventh embodiment;

[0055] Figure 3 The time domain waveform of the original eigenmode component f1(t) according to the eleventh embodiment;

[0056] Figure 4 The time domain waveform of the original eigenmode component f2(t) according to the eleventh embodiment;

[0057] Figure 5 The time domain waveform of the original eigenmode component f3(t) according to the eleventh embodiment;

[0058] Figure 6The original signal f(t) spectrum described in embodiment eleven, wherein the abscissa represents frequency / Hz, and the ordinate represents the amplitude of the spectrum;

[0059] Figure 7 The fractional Fourier transform spectrum of the original signal f(t) at angle a = 3.1345 described in embodiment eleven, wherein the abscissa represents fractional frequency, and the ordinate represents the amplitude of the spectrum;

[0060] Figure 8 The comparison chart of the decomposed output eigenmode component m1(t) and the original eigenmode component f1(t) described in embodiment eleven, wherein the abscissa represents time t / s, and the ordinate represents amplitude;

[0061] Figure 9 The comparison chart of the decomposed output eigenmode component m2(t) and the original eigenmode component f2(t) described in embodiment eleven, wherein the abscissa represents time t / s, and the ordinate represents amplitude;

[0062] Figure 10 The comparison chart of the decomposed output eigenmode component m3(t) and the original eigenmode component f3(t) described in embodiment eleven, wherein the abscissa represents time t / s, and the ordinate represents amplitude. DETAILED DESCRIPTION

[0063] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application.

[0064] Embodiment one, see Figure 1 This embodiment describes a fractional Fourier transform domain adaptive signal decomposition method, which comprises the following steps:

[0065] Step one: initialize parameters and perform fractional Fourier transform on the signal to be decomposed f(t) to obtain F α (u), wherein the initialized parameters include outer loop count parameter c, inner loop period number n, mode component marker parameter k, fractional Fourier transform of eigenmode component, fractional Fourier transform of Lagrange multiplier and central fractional frequency;

[0066] Step two: update the outer loop count parameter, and update the angle a at which the signal to be decomposed f(t) is aggregated according to the calculation of information entropy;

[0067] Step three: update the inner loop period number according to the number of updated angle a;

[0068] Step four: update the modal component marker parameter, the fractional Fourier transform of the eigenmodal component and the central fractional frequency according to the updated inner loop cycle number;

[0069] Step five: compare the updated modal component marker parameter k and c+1, when the updated modal component marker parameter k is less than c+1, jump to step four and repeat the above operation; otherwise, proceed to the next step;

[0070] Step six: update the fractional order Fourier transform of the Lagrange multiplier;

[0071] Step seven: repeat steps three to six until the stop condition is met, update the modal component marker parameter k=0, and calculate the angle of energy concentration at this time according to the updated fractional Fourier transform of the eigenmodal component

[0072] Step eight: compare and τ, if , then n=0 and return to step three, otherwise proceed to the next step;

[0073] Step nine: inverse transform the updated fractional Fourier transform of the eigenmodal component to output m K-c (t), at this time, if c>1, update F α (u) and jump to step two to repeat the above operation; otherwise, output m K (t) to complete the decomposition.

[0074] The adaptive signal decomposition method in the fractional Fourier transform domain according to the embodiment introduces the concept of convolution under fractional Fourier transform, decomposes the signal to be decomposed into K (K>1) eigenmodal components m k (t) with a limited bandwidth in the fractional domain, and the central fractional frequency of each eigenmodal component under the transform angle α is u k , and the constraint condition is that the modal component sum is equal to the input signal. The present application changes the decomposition process into a problem of solving the optimal solution of the constrained variational problem, effectively decomposes the signal with non-concentrated energy in the frequency domain, and improves the signal decomposition efficiency.

[0075] Specifically, the principle of the fractional Fourier transform according to the embodiment is as follows:

[0076] First, the definition of fractional Fourier transform is introduced. The fractional Fourier transform of an arbitrary energy-limited signal f(t)∈L 2 (R) is defined as

[0077]

[0078] wherein denotes the fractional Fourier transform operator, and the kernel function is given by

[0079]

[0080] wherein k∈Z, and α denotes the angle of the fractional Fourier transform, and the variable u is usually called the fractional frequency, and the coordinate axis on which it lies is usually called the fractional Fourier transform domain (for short, the fractional domain). Correspondingly, the formula of the inverse transform of the fractional Fourier transform is

[0081]

[0082] wherein the superscript * denotes the conjugate operation. In particular, when α=π / 2, the fractional Fourier transform degenerates into the traditional Fourier transform. Therefore, the frequency domain determined by the traditional Fourier transform can be regarded as a special case of the fractional domain at the angle α=π / 2. In addition, in order to simplify the analysis, the concept of fractional convolution under the fractional Fourier transform is also introduced. The fractional convolution of any two energy-limited signals f(t) and g(t) is defined as

[0083]

[0084] Under the fractional Fourier transform, the fractional convolution satisfies

[0085]

[0086] wherein G(ucscα) denotes the Fourier transform of the signal g(t) (the transform element is stretched by a scale cscα).

[0087] Based on this, the principle of the decomposition method described in the embodiment is as follows:

[0088] 1) First, according to the calculation of the information entropy, the angle α at which the energy of the signal f(t) is best concentrated is determined, i.e., the following formula

[0089]

[0090] wherein F α (u) denotes the fractional Fourier transform of the signal f(t).

[0091] 2) According to the fractional Fourier transform theory, the fractional analytic signal z k (t) corresponding to the intrinsic mode component m k (t) is calculated by using the fractional Hilbert transform, i.e. wherein is called the fractional Hilbert transform of the intrinsic mode component m k (t), and its definition is Therefore, the intrinsic mode components m can be obtained. k The one-sided fractional spectrum of the non-negative fractional frequency of (t), i.e.

[0092]

[0093] In the formula, Z k,α (u) and M k,α (u) represents z respectively k (t) and m k The fractional Fourier transform of (t). Further, equation (9) can be rewritten as...

[0094] Z k,α (u)=(1+sgn[u])M k,α (u) (10)

[0095] In the formula, sgn[u] represents the sign function, which is specifically defined as follows:

[0096]

[0097] 3) Through the fractional frequency shift operator The fractional analytic signal z k Fractional-order spectral shift u of (t) k Moved to baseband, i.e.

[0098]

[0099] 4) Based on time-frequency analysis theory, using fractional-order frequency operators... The baseband bandwidth is calculated by taking the square of the L2 norm, and the baseband bandwidth of each eigenmode component is also calculated. The final calculation results are as follows.

[0100]

[0101] In the formula, the fractional frequency operator The definition of f(t) is the signal to be decomposed, {m k}={m1......m K} represents the intrinsic mode functions, {u k}={u1......u K Let} represent the center fractional frequency of each eigenmode function, and K be the number of initialized modes. Further simplification yields...

[0102]

[0103] According to the above steps, the adaptive signal decomposition process based on the fractional Fourier transform domain is converted into the optimal solution of a variational problem in the embodiment. In order to find the optimal solution of the constrained variational problem, a Lagrange multiplier λ(t) is introduced, and a penalty factor η is added to convert the constrained variational problem into an unconstrained variational problem, and at the same time, the objective function to be minimized needs to be converted into an augmented Lagrangian function, that is,

[0104]

[0105] In the formula, <·,·> represents the inner product operation. Based on the foregoing analysis, using the Parseval theorem of the fractional Fourier transform, formula (15) can be further rewritten in the form of the fractional Fourier transform domain, that is,

[0106]

[0107] In the formula, M k,α (u), F α (u) and Λ α (t) respectively represent the fractional Fourier transform of the eigenmodal component m k (t), the signal to be decomposed f(t) and the Lagrange multiplier λ(t).

[0108] Solving the minimization problem equivalent to formula (13), the optimal solution is used to update the fractional Fourier transform M k,α (u) of each eigenmodal component, that is,

[0109]

[0110] In the fractional Fourier transform domain, the solution of formula (17) is

[0111]

[0112] Similarly, solving the minimization problem equivalent to formula (13), the optimal solution is used to update the central fractional frequency of each eigenmodal component, that is,

[0113]

[0114] The central fractional frequency of the eigenmodal component is obtained as

[0115]

[0116] Based on the foregoing analysis, using the alternating direction multiplier method, the adaptive signal decomposition in the fractional Fourier transform domain is performed:

[0117] Step 1: Initialize parameters, and perform fractional Fourier transform on the signal to be decomposed f(t) to obtain F α(u), wherein the initialization parameters include an outer loop count parameter c, an inner loop cycle number n, a modal component index parameter k, a fractional Fourier transform of an intrinsic modal component, a fractional order Fourier transform of a Lagrange multiplier, and a central fractional order frequency;

[0118] Step two: updating the outer loop count parameter c and the angle α of energy concentration of the signal f(t) to be decomposed according to the calculation of information entropy;

[0119] Step three: updating the inner loop cycle number n according to the order of the updated angle α;

[0120] Step four: sequentially updating the modal component index parameter k, the fractional Fourier transform of the intrinsic modal component, and the central fractional order frequency according to the updated inner loop cycle number n;

[0121] Step five: comparing the updated modal component index parameter k with c+1, if the updated modal component index parameter k is smaller than c+1, jumping to step four and repeating the above operations; otherwise, proceeding to the next step;

[0122] Step six: updating the fractional order Fourier transform of the Lagrange multiplier;

[0123] Step seven: repeating steps three to six until a stop condition is met, updating the modal component index parameter k=0, and calculating the angle α of energy concentration according to the updated fractional Fourier transform of the intrinsic modal component;

[0124] Step eight: comparing with τ, if , then n=0, and returning to step three; otherwise, proceeding to the next step;

[0125] Step nine: inversely transforming the updated fractional Fourier transform of the intrinsic modal component into m K-c (t), at this time, if c>1, updating F α (u) and jumping to step two to repeat the above operations; otherwise, outputting m K (t) to complete the decomposition.

[0126] Embodiment two, the embodiment is a further limitation of the adaptive signal decomposition method in the fractional Fourier transform domain according to the signal decomposition method in the fractional Fourier transform domain in embodiment one, the updating of the outer loop count parameter c and the angle α of energy concentration of the signal f(t) to be decomposed according to the calculation of information entropy is specifically:

[0127] The updating of the outer loop count parameter c is:

[0128] c=c-1,

[0129] The angle a of the signal f(t) to be decomposed is updated according to the information entropy, specifically:

[0130]

[0131] Wherein, F α (u) represents the fractional Fourier transform of the signal f(t) to be decomposed, and u is the variable of the fractional Fourier transform domain.

[0132] The outer loop counting method of the embodiment is sequentially decreased.

[0133] Embodiment three, the embodiment is a further limitation of the fractional Fourier transform domain adaptive signal decomposition method of embodiment one, step three updates the inner loop period number according to the updated angle a, specifically:

[0134] n=n+1.

[0135] In the embodiment, the inner loop period number is updated sequentially by 1.

[0136] Embodiment four, the embodiment is a further limitation of the fractional Fourier transform domain adaptive signal decomposition method of embodiment one, step four sequentially updates the modal component marker parameter, the fractional Fourier transform of the eigenmodal component and the central fractional order frequency, specifically:

[0137] The updated modal component marker parameter is:

[0138] k=k+1,

[0139] The updated fractional Fourier transform of the eigenmodal component is:

[0140]

[0141] Wherein, is the fractional Fourier transform of the eigenmodal component of the n+1th iteration, is the fractional Fourier transform of the eigenmodal component of the nth iteration, is the central fractional order frequency of the nth iteration, and η is the weight of the penalty term in the augmented Lagrange function;

[0142] The updated central fractional order frequency is:

[0143]

[0144] Wherein, is the central fractional order frequency of the n+1th iteration.

[0145] This implementation method updates the modal component labeling parameters by incrementing one by one, and also provides a specific method for the fractional Fourier transform of intrinsic modal components.

[0146] Implementation Method 5: This implementation method further defines the adaptive signal decomposition method in the fractional Fourier transform domain described in Implementation Method 1. Specifically, the fractional Fourier transform for updating the Lagrange multipliers in step six is ​​as follows:

[0147]

[0148] in, For the fractional Fourier transform of the Lagrange multipliers in the (n+1)th iteration, Let f(x) be the fractional Fourier transform of the Lagrange multipliers in the (n+1)th iteration.

[0149] This implementation provides a fractional Fourier transform update method for Lagrange multipliers.

[0150] Implementation Method Six: This implementation method further defines the adaptive signal decomposition method in the fractional Fourier transform domain described in Implementation Method One. The cutoff condition in step seven is:

[0151] Or n≥N,

[0152] Where N represents the loop count cutoff condition.

[0153] In practical applications, when the following conditions are met If n≥N, proceed to the next step; otherwise, repeat steps three through six until the cutoff condition is met.

[0154] Implementation Method Seven: This implementation method further defines the adaptive signal decomposition method in the fractional Fourier transform domain described in Implementation Method One. Step Nine, updating F... α (u) is:

[0155]

[0156] This implementation provides an updated fractional Fourier transform F... α (u) method.

[0157] Implementation Method Eight: This implementation method further defines the adaptive signal decomposition method in the fractional Fourier transform domain described in Implementation Method One, wherein the outer loop counting parameter c is 3.

[0158] This implementation provides a specific example.

[0159] Embodiment nine, a computer readable storage medium according to the embodiment, the computer readable storage medium is used for storing a computer program, the computer program executes the adaptive signal decomposition method in the fractional Fourier transform domain according to any one of the embodiments one to eight.

[0160] Embodiment ten, a computer device according to the embodiment, comprising a memory and a processor, the memory has stored a computer program, when the processor runs the computer program stored in the memory, the processor executes the adaptive signal decomposition method in the fractional Fourier transform domain according to any one of the above.

[0161] Embodiment eleven, see Figures 2 to 10 The embodiment is described. The embodiment is a specific embodiment of the adaptive signal decomposition method in the fractional Fourier transform domain according to the embodiment one, and is also used for explaining the embodiments two to eight, specifically:

[0162] The embodiment selects an experimental signal as a non-stationary signal f(t) = f1(t) + f2(t) + f3(t) composed of three different components, wherein each intrinsic modal component is in the form of f1(t) = cos(37πt + 50t 3 ), f2(t) = cos(71πt + 70t 2 ), f3(t) = 0.5cos(576πt), the signal duration is [0, 1], the unit is second s. The original signal, that is, the signal to be decomposed, is shown in Figure 2 , and the time domain waveforms of the three intrinsic modal components are shown in Figure 3 , Figure 4 and Figure 5 .

[0163] Figure 6 The frequency spectrum of the original signal is Figure 7 , and the fractional order Fourier transform spectrum of the original signal f(t) at an angle α = 3.1345 is shown in Figure 6 and Figure 7 It can be seen that the three intrinsic modal component support intervals of the original signal in the frequency domain overlap with each other and cannot be clearly distinguished, however, the original signal contains three support intervals at the angle α = 3.1345 in the fractional order Fourier transform domain, which correspond to the three intrinsic modal components, and each intrinsic modal component can be extracted in turn based on the method proposed in the embodiment. The specific implementation steps are as follows:

[0164] Step one, performing fractional order Fourier transform on the signal to be decomposed f(t) to obtain F α (u), initializing the parameter modal number K = 3, the angle α = 0.0001 of the fractional order Fourier transform, and The penalty term weight η = 2000, and the fractional Fourier transform of the intrinsic mode components. Center fractional frequency Fractional Fourier Transform of Lagrange Multipliers The counting parameter c = K, the update step size ρ = 0.5, the loop count cutoff condition N = 500, and the error cutoff condition ε = 10. -8 and τ = 10 -8 The final output is the intrinsic mode function sequence {m k (t)}={m1(t),m2(t),…m K (t)};

[0165] Step 2: Update the outer loop counter parameter c = c-1, the period counter parameter n,k = 0, and update the value of α according to equation (8), and assign α to

[0166] Step 3: Update the number of inner loop cycles n = n + 1;

[0167] Step 4: Update k = k + 1;

[0168] Step 5: Update

[0169] Step Six: Update

[0170] Step 7: Compare the values ​​of k and c+1. ​​If k is less than c+1, it means that the decomposition of all modes has not been completed. In this case, go to step 4. Otherwise, proceed to the next step.

[0171] Step 8: Update

[0172] Step 9: Repeat steps 4 through 8 until the cutoff condition is met.

[0173] Or n≥N;

[0174] Step 10: Update k = 0;

[0175] Step 11, according to the formula Determine the angle of its energy concentration

[0176] Step 12: Comparison With τ, if At that time, then If n = 0, return to step three; otherwise, proceed to the next step.

[0177] Step 13, Fractional Fourier inverse transform The output is mK-c (t), at this time if c>1 update the signal as is input into step two. Otherwise update fractional inverse Fourier transform of output is m K (t), the decomposition is completed. The time-domain waveform comparison chart of the decomposition obtained eigenmode component and the original eigenmode component is shown in Figure 8 , Figure 9 and Figure 10 , wherein Figure 8 is the comparison chart of the decomposition output eigenmode component m1(t) and the original eigenmode component f1(t), Figure 9 is the comparison chart of the decomposition output eigenmode component m2(t) and the original eigenmode component f2(t), Figure 10 is the comparison chart of the decomposition output eigenmode component m3(t) and the original eigenmode component f3(t).

[0178] The technical solutions of the present application provided in the above description in combination with the drawings are further described in detail in order to highlight the advantages and benefits, and are not used as the limitation of the present application. Any modification, combination, improvement and equivalent replacement of the present application based on the principle of the present application should be included in the protection scope of the present application.

Claims

1. A method of adaptive signal decomposition in the fractional Fourier transform domain, characterized by, The decomposition method comprises: Step one: initialize parameters, and decompose the signal to be decomposed Step two: perform fractional Fourier transform to obtain , wherein the initialized parameters include an outer loop count parameter c , an inner loop period number n , a modal component marker parameter k , a fractional Fourier transform of an eigenmodal component, a fractional Fourier transform of a Lagrange multiplier, and a central fractional frequency; the signal to be decomposed is a radar signal; Step two: update the outer loop count parameter and update the signal to be decomposed according to the calculation of information entropy Angle of convergence ; Step three: update the number of inner loop cycles according to the updated angle times. Step four: according to the updated inner cycle number, sequentially update the modal component marker parameter, fractional Fourier transform of the eigenmodal component and central fractional frequency; Step five: compare the updated modal component signature parameters k and , when the updated modal component signature parameters k are smaller than , jump to step four, repeat the above operation; otherwise, proceed to the next step; Step six: update the fractional order Fourier transform of the Lagrange multiplier; Step seven: repeat steps three to six until a stopping condition is met, updating the modal component marker parameters and compute the angle of energy concentration at this time according to the fractional Fourier transform of the updated eigenmodal components ; Step eight: compare with if then update , and go back to step three, otherwise proceed to the next step; step nine: inverse transform the updated fractional Fourier transform of the proper mode component to at this time, if update and jump to step two to repeat the above operations; otherwise output , completing the decomposition.

2. A method of adaptive signal decomposition in the fractional Fourier transform domain according to claim 1, characterized in that, The update outer loop count parameter, and update the signal to be decomposed according to the calculation of information entropy Angle of convergence Specifically: The updated outer cycle count parameter is: ， The calculating updating of the signal to be decomposed according to information entropy Angle of convergence Specifically, ， wherein denotes the fractional Fourier transform of the signal to be decomposed is a variable in the fractional Fourier transform domain.​ 3. The method of claim 1, wherein the method is characterized by: the updated angle according to step three the number of inner loop cycles is updated, in particular as follows: 。 4. The method of claim 1, wherein, The sequentially updating the modal component marker parameter, fractional Fourier transform of the eigenmodal component and central fractional frequency in step four is specifically: The updated modal component marker parameter is: ， The updated fractional Fourier transform of the eigenmodal component is: ， wherein, is the n fractional Fourier transform of the eigenmodal component of the is the n fractional Fourier transform of the eigenmodal component of the is the n center fractional frequency of the is the weight of the penalty term in the augmented Lagrangian function; The updated central fractional frequency is: ， wherein, is the center fractional frequency of the n+1 iteration.

5. The method of claim 1, wherein the method is characterized by: The updating the fractional order Fourier transform of the Lagrange multiplier in step six is specifically: ， wherein is the n Fractional Fourier transform of the Lagrange multiplier of the is the n Fractional Fourier transform of the Lagrange multiplier of the 6. The method of claim 1, wherein, The stop condition in step seven is: or , wherein is the number of cycles cutoff condition.

7. The method of claim 1, wherein, the update of step nine is: 。 8. The method of claim 1, wherein, The outer loop count parameter c is the total number of eigenmode components K .

9. A computer-readable storage medium, characterized in that, The computer readable storage medium is used to store a computer program, and the computer program executes the adaptive signal decomposition method in the fractional Fourier transform domain according to any one of claims 1-8.

10. A computer device, comprising: The computer readable storage medium comprises a memory and a processor, and the memory stores a computer program; when the processor runs the computer program stored in the memory, the processor executes the adaptive signal decomposition method in the fractional Fourier transform domain according to any one of claims 1-8.

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