Gravitational wave signal noise reduction processing method

Abstract

The invention belongs to the technical field of gravitational wave signal detection, and particularly relates to a gravitational wave signal noise reduction processing method, which is used for better analyzing and processing a space gravitational wave signal, and comprises the following steps: firstly, optimizing two main parameters of variational mode decomposition (VMD) through a parrot algorithm (PO), namely a decomposition layer number K and a penalty factor alpha; the method comprises the following steps: firstly, decomposing a mode of a gravitational wave signal, dividing the decomposed mode into a reserved mode component and a noise mode component, carrying out further noise reduction processing on the noise mode component by adopting an improved wavelet threshold algorithm (IWT), and finally, reconstructing the reserved signal mode and the processed noise signal mode to obtain the final noise-reduced gravitational wave signal. The method has the capability of separating gravitational wave signals from noise, global search and local optimum are well balanced during parameter selection, and a new technical means is provided for noise reduction and analysis of the gravitational wave signals.

Description

Technical Field

[0001] The present invention relates to the technical field of gravitational wave signal detection, and in particular to a gravitational wave signal noise reduction processing method. Background Art

[0002] Detecting gravitational waves in space is a highly challenging field in modern astronomy, aiming to capture and analyze one of the faintest signals in the universe. During the detection process, gravitational wave signals are processed by components such as four-quadrant photodetectors, transimpedance amplifiers, anti-aliasing filters, and digital-to-analog converters. This adds significant noise to the signal, making it even more difficult to discern. Therefore, separating the noise from the gravitational wave signal remains a major technical challenge.

[0003] To address this issue, in addition to hardware optimization and improvements, algorithmic processing of gravitational wave signals is also crucial. The variational mode decomposition (VMD) algorithm excels in processing nonstationary signals and is widely used in fields such as signal noise reduction, image processing, and biomedicine. It decomposes signals into distinct central frequencies. However, the selection of VMD parameters is crucial and impacts the effectiveness of the decomposition. Therefore, to address this difficulty in VMD parameter selection, the Parrot algorithm (PO) was introduced to obtain optimal parameters, removing noise while retaining the useful signal components. This effectively extracts gravitational wave signals from the noise, providing reliable technical support for subsequent gravitational wave research and analysis. Summary of the Invention

[0004] (1) Technical problems solved

[0005] In response to the shortcomings of the existing technology, the present invention provides a method for noise reduction of gravitational wave signals, which solves the problems raised in the above background technology.

[0006] (2) Technical solution

[0007] In order to achieve the above-mentioned purpose, the present invention specifically adopts the following technical solutions:

[0008] A method for noise reduction of gravitational wave signals comprises the following steps:

[0009] S1. The gravitational wave signal obtained by the detector is used as the input signal to initialize the parameters and the parrot population;

[0010] S2, optimization of variational mode decomposition VMD parameters according to the four processes of Parrot algorithm PO;

[0011] S3. Obtain the optimal parameters of VMD, the number of decomposition layers K and the penalty factor α;

[0012] S4. Perform modal decomposition of the gravitational waves according to the optimal parameters and divide them into retained modal components and noise modal components;

[0013] S5, denoising the noise modal component by improving the wavelet threshold IWT;

[0014] S6. Signal reconstruction.

[0015] Furthermore, in S1, the gravitational wave signal is expressed as the input signal:

[0016] f(t)=u(t)+n(t)

[0017] Where u(t) represents the gravitational wave signal and n(t) represents the noise;

[0018] Initialize the parameters of the PO and VMD algorithms and initialize the parrot population:

[0019]

[0020] Where rand(0,1) represents a random number within the range, represents the initial position of the i-th parrot.

[0021] Furthermore, in S2, PO is divided into four processes: foraging, staying, communicating, and fear of strangers. The formula for each process iteration is:

[0022] This is the process of foraging behavior;

[0023]

[0024] Where, Indicates the updated position, X best Indicates the best position of the current search, Levy distribution describes the parrot's flight process, Indicates the average position within the current population;

[0025] This is the process of staying behavior;

[0026]

[0027] In the formula, ones(1,dim) represents the all-one vector of dimension dim, the second part represents the process of flying to the host, and the third part represents the random position of the host.

[0028] This is the process of communicative behavior;

[0029]

[0030] Where, Indicates the behavior of individual parrots joining a group, It indicates the process of individuals flying out of the group after communicating;

[0031] It’s a process of moving away from strangers;

[0032]

[0033] Where, Redirects the act of flying towards the owner. Indicates the behavior of staying away from strangers, and performs iterative parameter optimization based on the above four parrot behaviors.

[0034] Furthermore, in S3, the VMD parameters are further optimized, and the gravitational wave signal is decomposed using the optimal decomposition level K and penalty factor α; the modal component is expressed as:

[0035] u k (t) = A k (t)cos[φ k (t)];

[0036] Where A k (t) represents the modal component amplitude, φ k (t) represents the instantaneous frequency of the modal component;

[0037] The construction and solution of the variational problem are expressed as follows:

[0038]

[0039] In the formula, {u k (t)} is a set of K modal components, ω k represents the set of center frequencies of K modal components;

[0040]

[0041] Where λ is the Lagrange multiplier and α is the penalty factor;

[0042] The iterative update of the variational problem is as follows:

[0043]

[0044] Where, They represent the values ​​after iterative update.

[0045] Furthermore, in S4, the modal component is divided into a retained modal component and a noise modal component according to the sample entropy fitness function.

[0046] Furthermore, in S5, for the noise modal function, the noise is further reduced by improving the wavelet threshold algorithm IWT:

[0047]

[0048] Where sgn(ω) is the sign function, λ is the threshold, are the coefficients after improved wavelet decomposition.

[0049] Furthermore, in S6, the retained modal component and the noise modal component after IWT denoising are reconstructed to obtain the final denoised gravitational wave signal.

[0050] (3) Beneficial effects

[0051] Compared with the prior art, the present invention provides a method for noise reduction of gravitational wave signals, which has the following features:

[0052] Beneficial effects:

[0053] The present invention can optimize two key parameters of the VMD algorithm, namely the decomposition layer number K and the penalty factor α, through the PO algorithm, achieve a good balance between global search and local optimization, and avoid the difficulty of parameter selection.

[0054] The present invention effectively separates gravitational wave signals from noise, improves the signal-to-noise ratio of gravitational wave signals, and reduces the root mean square error, providing a new technical means in data processing algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a schematic diagram of the algorithm flow structure of the present invention;

[0056] Figure 2 This is a schematic diagram of the signal segment GW150914[22001-27000] of the present invention;

[0057] Figure 3 This is the VMD decomposition diagram of the GW150914[22001-27000] segment signal of the present invention;

[0058] Figure 4 This is a schematic diagram of the noise reduction results of the GW150914 [22001-27000] segment signal of the present invention. DETAILED DESCRIPTION

[0059] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0060] Example

[0061] like Figure 1-4 As shown, a method for denoising a gravitational wave signal according to an embodiment of the present invention includes:

[0062] S1. The gravitational wave signal obtained by the detector is used as the input signal to initialize the parameters and the parrot population; the input signal is expressed as:

[0063] f(t)=u(t)+n(t)

[0064] Where t is time, u(t) represents the pure gravitational wave signal, and n(t) represents various noises, including photon shot noise, light intensity coupling noise, dark current noise, resistor thermal noise, and crosstalk noise.

[0065] Initialize the parrot population and parameters:

[0066]

[0067] Where rand(0,1) represents a random number within the range, represents the initial position of the i-th parrot.

[0068] S2. Optimize the variational mode decomposition (VMD) parameters based on the four processes of the parrot algorithm (PO). Based on the characteristics of domesticated parrots, the PO algorithm can be divided into four behavioral processes, namely foraging behavior, staying behavior, communication behavior, and fear of strangers, and the parameters are iteratively updated.

[0069] Foraging behavior process:

[0070]

[0071] Where, Indicates the updated position, X best Indicates the best position of the current search, Levy distribution describes the parrot's flight process, Indicates the average position within the current population;

[0072] Stay behavior process:

[0073]

[0074] In the formula, ones(1,dim) represents the all-one vector of dimension dim, the second part represents the process of flying to the host, and the third part represents the random position of the host.

[0075] Communication behavior process:

[0076]

[0077] Where, Indicates the behavior of individual parrots joining a group, It indicates the process of individuals flying out of the group after communicating;

[0078] Stay away from strangers behavior process:

[0079]

[0080] Where, Redirects the act of flying towards the owner. It means staying away from strangers.

[0081] The minimum envelope entropy was selected as the fitness function, and the parameters were iteratively optimized according to the four parrot behavior processes.

[0082] S3. Get the optimal parameters of VMD, the number of decomposition layers K and the penalty factor α; further optimize the VMD parameters to obtain the optimal decomposition parameters of VMD, such as Figure 1 As shown in the left part of the flow chart;

[0083] The modal components are expressed as:

[0084] u k (t) = A k (t)cos[φ k (t)];

[0085] Where A k (t) represents the modal component amplitude, φ k (t) represents the instantaneous frequency of the modal component;

[0086] The construction and solution of the variational problem are expressed as follows:

[0087]

[0088] In the formula, {u k (t)} is a set of K modal components, ω k represents the set of center frequencies of K modal components;

[0089]

[0090] Where λ is the Lagrange multiplier and α is the penalty factor;

[0091] The iterative update of the variational problem is as follows:

[0092]

[0093] Where, They represent the values ​​after iterative update.

[0094] Through the PO optimization VMD process, the optimal parameters of the variational modal decomposition of the gravitational wave signal, the number of modes K and the penalty factor α are obtained to decompose the gravitational wave signal.

[0095] S4. Perform modal decomposition of gravitational waves based on optimal parameters and divide them into retained modal components and noise modal components. Introduce sample entropy and variance contribution rate mechanisms to distinguish modal components. Based on the fitness function, divide the modal components into retained modal components and noise modal components. Retained modal components are modal components that contain more gravitational wave signals and are temporarily retained. Noise modal components are components that contain more noise and require further processing.

[0096] S5. The noise modal component is subjected to denoising by improving the wavelet threshold IWT. For the noise modal component, which contains more noise, the noise is further reduced by improving the wavelet threshold algorithm IWT, such as Figure 1 The right part of the flow chart is shown.

[0097]

[0098] Where sgn(ω) is the sign function, λ is the threshold, It is the coefficient after improved wavelet decomposition. This part further reduces noise by improving wavelet decomposition.

[0099] S6. Signal reconstruction: reconstruct the retained modal components and the noise modal components after IWT denoising, that is, add the retained modal components and the noise modal components after IWT processing to obtain the final denoised gravitational wave signal.

[0100] Figure 2 This is the data segment [22001-27000] of the original signal of gravitational wave GW150914. It can be seen that there is a lot of noise in the signal. Figure 3 The VMD decomposition of the gravitational wave GW150914 [22001-27000] segment signal is shown in Figure 1. The optimal number of mode decompositions is five. Figure 4 This is the result of reconstructing the gravitational wave GW150914 [22001-27000] segment signal after algorithm processing. It can be seen intuitively that the noise and gravitational wave signal are effectively separated, and the waveform characteristics of the gravitational wave signal are retained.

[0101] By introducing PO to optimize VMD, the problem of difficult parameter selection is solved, the accuracy of decomposition and the real-time performance of the algorithm are improved, and the computational efficiency is improved. This process achieves the purpose of gravitational wave signal noise reduction and improves the accuracy and quality of gravitational wave signals.

[0102] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for denoising gravitational wave signals, characterized by: The following steps are included: S1. The gravitational wave signal obtained by the detector is used as the input signal to initialize the parameters and the parrot population; S2, optimize the variational mode decomposition VMD parameters according to the four processes of the Parrot algorithm PO; S3. Obtain the optimal parameters of VMD, the number of decomposition layers K and the penalty factor α; S4. Perform modal decomposition of the gravitational waves according to the optimal parameters and divide them into retained modal components and noise modal components; S5, denoising the noise modal component by improving the wavelet threshold IWT; S6. Signal reconstruction.

2. The method for denoising a gravitational wave signal according to claim 1, wherein: In S1, the gravitational wave signal is expressed as the input signal: f(t)=u(t)+n(t) Where u(t) represents the gravitational wave signal and n(t) represents the noise; Initialize the parameters of the PO and VMD algorithms and initialize the parrot population: Where rand(0,1) represents a random number within the range, represents the initial position of the i-th parrot.

3. The method for denoising gravitational wave signals according to claim 1, wherein: In S2, PO is divided into four processes: foraging, staying, communicating, and fear of strangers. The formula for each process iteration is: This is the process of foraging behavior; Where, Indicates the updated position, X best Indicates the best position of the current search, Levy distribution describes the parrot's flight process, Indicates the average position within the current population; This is the process of staying behavior; In the formula, ones(1,dim) represents the all-one vector of dimension dim, the second part represents the process of flying to the host, and the third part represents the random position of the host. This is the process of communicative behavior; Where, Indicates the behavior of individual parrots joining a group, It indicates the process of individuals flying out of the group after communicating; It’s a process of moving away from strangers; Where, Redirects the act of flying towards the owner. Indicates the behavior of staying away from strangers, and performs iterative parameter optimization based on the above four parrot behaviors.

4. The method for denoising a gravitational wave signal according to claim 1, wherein: In S3, the VMD parameters are further optimized, and the gravitational wave signal is decomposed using the optimal decomposition level K and penalty factor α; the modal component is expressed as: u k (t)=A k (t)cos[φ k (t)]; Where A k (t) represents the modal component amplitude, φ k (t) represents the instantaneous frequency of the modal component; The construction and solution of the variational problem are expressed as follows: In the formula, {u k (t)} is a set of K modal components, ω k represents the set of center frequencies of K modal components; Where λ is the Lagrange multiplier and α is the penalty factor; The iterative update of the variational problem is as follows: Where, They represent the values ​​after iterative update.

5. The method for denoising gravitational wave signals according to claim 1, wherein: In S4, the modal component is divided into a retained modal component and a noise modal component according to the sample entropy fitness function.

6. The method for denoising gravitational wave signals according to claim 1, wherein: In S5, for the noise modal function, the noise is further reduced by improving the wavelet threshold algorithm IWT: Where sgn(ω) is the sign function, λ is the threshold, are the coefficients after improved wavelet decomposition.

7. The method for denoising a gravitational wave signal according to claim 1, wherein: The S6 reconstructs the retained modal components and the noise modal components after IWT denoising to obtain the final denoised gravitational wave signal.

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