Denoising Method for Dual-Frequency Comb Interference Fringe Signal Based on Improved VMD-GWO Algorithm

Abstract

The present invention discloses a denoising method for dual optical comb interference fringe signals based on an improved VMD-GWO algorithm. Step 1: Obtain the dual optical comb interference fringe signals to get the original dual optical comb interference fringe signal f(t). Step 2: Take the original dual optical comb interference fringe signal f(t) as the input signal and perform iterative optimization and decomposition processing of the VMD-GWO algorithm to obtain the optimal solution (k, α) that converges to the fitness function. Step 3: Use the optimal solution (k, α) as the VMD decomposition parameters with the optimal signal-to-noise ratio and envelope symmetry. Step 4: Screen each modal component and select several modal components that contain the dual optical comb interference fringes. Step 5: Discard the high- and low-frequency noise signals. Step 6: Reconstruct the dual optical comb interference fringe signals. Compared with the prior art, the present invention improves the signal-to-noise ratio of the dual optical comb interference fringe signals and the accuracy of peak position extraction, and optimizes the time-domain shape characteristics of the dual optical comb interference fringes.

Description

Technical Field

[0001] The present invention belongs to the technical field of dual-comb measurement, and particularly relates to a method for denoising dual-comb ranging signals based on an improved variational mode decomposition algorithm. Background Technique

[0002] An optical frequency comb appears as a series of ultrafast pulsed lasers with stable time intervals in the time domain, having extremely high time resolution and extremely narrow pulse widths; in the frequency domain, it appears as frequency comb teeth with intervals equal to the repetition frequency, and the intervals of each comb tooth have extremely high stability, and its spectrum is like an accurate frequency ruler. A dual-comb consists of a pair of optical frequency combs with a small repetition frequency difference, and their repetition frequencies are f r1 and f r2 , where f r2 = f r1 +Δf. As shown in Figure 1 , it is a schematic diagram of the time-domain characteristics of a dual-comb. Based on the principle of optical asynchronous sampling, the dual-comb can achieve automatic scanning without a mechanical scanning device, obtain a cross-correlation interference signal, and meet the bandwidth range of the photodetector. Compared with a single optical frequency comb, the dual-comb measurement technology has better comprehensive performance in terms of optical measurement indicators such as measurement accuracy, measurement rate, and unambiguous range.

[0003] In a dual-comb ranging system, the time-of-flight method is usually used to achieve absolute distance measurement. When the time-domain pulse signal of the dual-comb does not contain a large chirp and its shape is close to Gaussian, the distance result can be calculated by calculating the time delay between the peaks of the reference interference signal and the measurement interference signal. In the case of low signal-to-noise ratio, since noise will distort the shape of the dual-comb interference signal, it is difficult to obtain the accurate signal peak position, resulting in difficulties in improving both the resolution accuracy and detection range of the dual-comb. Therefore, seeking an effective denoising method is a key measure to overcome the limitations of dual-comb ranging. Summary of the Invention

[0004] Aiming at the influence of noise on the calculation of the distance result in dual-comb ranging signals, the present invention proposes a method for denoising dual-comb interference fringe signals based on an improved VMD-GWO algorithm. Based on the time-frequency characteristics of dual-comb interference fringe signals, the GWO algorithm is used to optimize the VMD parameters to obtain the optimal decomposition method, realizing a method for denoising dual-comb interference fringe signals based on VMD signal decomposition and GWO parameter optimization.

[0005] The present invention is realized by the following technical solutions:

[0006] A method for denoising dual-comb interference fringe signals based on an improved VMD-GWO algorithm, the method comprising the following steps:

[0007] Step 1: Obtain the dual-comb interference fringe signal containing the target distance information to get the original dual-comb interference fringe signal f(t).

[0008] Step 2: Take the original dual-comb interference fringe signal f(t) as the input signal, perform iterative VMD-GWO algorithm optimization and decomposition processing. Decompose the original dual-comb interference fringe signal f(t) according to the optimal parameters of VMD, and use GWO for global search and iteration to obtain the optimal solution (k, α) that converges to the fitness function. Here, k is the number of modes, and α is the quadratic penalty factor.

[0009] Step 3: Take the optimal solution (k, α) as the VMD decomposition parameters that achieve the optimal signal-to-noise ratio and envelope symmetry, including k modal components f1(t), f2(t), …, f k (t);

[0010] Step 4: Screen each modal component and select several modal components that contain the dual-comb interference fringes.

[0011] Step 5: Discard the high- and low-frequency noise signals.

[0012] Step 6: Add the screened modal components to obtain the reconstructed signal of the dual-comb interference fringes.

[0013] The reconstructed signal of the dual-comb interference fringe signal has a quasi-Gaussian envelope characteristic that retains the pulse energy amplitude.

[0014] In Step 2, the iterative VMD-GWO algorithm decomposition and optimization process specifically includes the following steps:

[0015] Calculate the individual fitness of each gray wolf individual. If the current gray wolf individual meets the fitness condition, update the individual fitness. The specific operation process is as follows: Calculate the signal-to-noise ratio according to the characteristics of the dual-comb interference fringe signal, specifically including the ratio of the peak power to the noise power of the input signal. Use the Hilbert transform algorithm for the signal-to-noise ratio signal to obtain the envelope symmetry. Select the signal-to-noise ratio signal and the envelope symmetry for weighted ratio, and use the weight coefficient to balance the relationship between the signal-to-noise ratio and the envelope symmetry. Finally, take the maximum value of the ratio result as the required gray wolf individual fitness condition.

[0016] When the fitness update of each group of gray wolf individuals is completed, let the iteration number l = l + 1, further update the position of each gray wolf individual, and continue with the VMD decomposition; Use the GWO algorithm to continuously perform global search and iteration according to the set fitness function to update the position of the gray wolf individual; Finally, when the iteration number reaches the set maximum iteration number l maxWhen the fitness of the gray wolf individuals converges to the optimal solution, the position of the gray wolf individual corresponding to the maximum value of the current fitness function is output, that is, the VMD decomposition parameters (k, α) that satisfy the optimal signal-to-noise ratio and envelope symmetry, and the entire GWO iterative optimization process is completed.

[0017] The iterative VMD-GWO algorithm decomposition and optimization process also includes pre-initializing the relevant parameters of the VMD-GWO algorithm, including setting the gray wolf population size N = 30, the maximum number of iterations l max = 100, the data range of the number of modes k is [2, 15], and the data range of the quadratic penalty factor α is [100, 5000]; after initialization, the original dual-comb interference fringe signal f(t) is decomposed by VMD according to the decomposition parameters (k, α) to obtain the VMD decomposition signal.

[0018] This method is applicable to at least dual-comb ranging signals, spectral analysis signals, and three-dimensional surface shape signals.

[0019] This method is applicable to dual-comb optical systems.

[0020] Compared with the prior art, a dual-comb interference fringe signal denoising method based on an improved VMD-GWO algorithm of the present invention can achieve the following beneficial technical effects:

[0021] 1) By screening the modal components and signal reconstruction, the signal-to-noise ratio of the dual-comb interference fringe signal and the accuracy of peak position extraction are improved;

[0022] 2) The removal of the noise part in the dual-comb interference fringe signal is realized, and the time-domain shape characteristics of the dual-comb interference fringe are optimized;

[0023] 3) The reconstructed signal has a high signal-to-noise ratio. While retaining the pulse energy amplitude, the interference fringe shape is optimized, and it has significant quasi-Gaussian envelope characteristics, which are the characteristics and advantages that clearly distinguish this method from other denoising algorithms and other applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a time-domain characteristic diagram of the dual-comb interference fringe signal;

[0025] Figure 2 It is a schematic flow diagram of a dual-comb interference fringe signal denoising method based on an improved VMD-GWO algorithm of the present invention;

[0026] Figure 3 It is a schematic flow diagram of the VMD-GWO algorithm processing;

[0027] Figure 4 It is a schematic diagram of the original dual-comb interference fringe signal and each modal component after VMD decomposition;

[0028] Figure 5 Schematic diagram of the reconstructed signal of the dual-comb interference fringe signal;

[0029] Figure 6 Waveform comparison diagram of the interference pattern before and after denoising by the method of the present invention. Detailed implementation manners

[0030] The present invention will be further described in detail below in conjunction with the drawings and embodiments.

[0031] Based on Variational Mode Decomposition (VMD), the present invention decomposes the original dual-comb interference fringe signal into multiple modal components. Based on the physical characteristics of the dual-comb interference fringe signal, the Grey Wolf Optimization (GWO) algorithm is used to iteratively optimize two parameters, namely the number of modes k and the quadratic penalty factor α of VMD, and the optimal solution that satisfies the fitness function of the dual-comb interference fringe signal and the corresponding modal components are selected.

[0032] As Figure 2 shown, a method for denoising dual-comb interference fringe signals based on the VMD-GWO algorithm of the present invention includes the following steps:

[0033] Step 1: Build a dual-comb ranging system, obtain the dual-comb interference fringe signal containing target distance information, and obtain the original dual-comb interference fringe signal f(t) through a photodetector and related data acquisition devices;

[0034] Step 2: Take the original dual-comb interference fringe signal f(t) as the input signal, and perform optimized and decomposed processing by the improved iterative VMD-GWO (Variational Mode Decomposition algorithm and Grey Wolf Optimization algorithm); decompose the original dual-comb interference fringe signal f(t) according to the optimal parameters of VMD, and use GWO for global search and iteration to obtain the optimal solution (k, α) that converges to the fitness function;

[0035] Step 3: Take the optimal solution (k, α) as the VMD decomposition parameters with the optimal signal-to-noise ratio and envelope symmetry of the obtained signal, including k modal components f1(t), f2(t), …, f k (t);

[0036] Step 4: Screen each modal component, and select several modal components that contain dual-comb interference fringes;

[0037] Step 5: Discard high- and low-frequency noise signals;

[0038] Step 6: Add the selected modal components to reconstruct the dual-comb interference fringe signal; this step effectively removes the base noise part in the original signal, and the reconstructed signal has a high signal-to-noise ratio. At the same time, it can better extract and restore the interference fringes submerged in the noise.

[0039] As Figure 3 shown, it is a schematic diagram of the optimization and decomposition process of the VMD-GWO algorithm, which specifically includes the following steps:

[0040] Step 21: Initialize the relevant parameters of the VMD-GWO algorithm, including setting the number of gray wolf populations N = 30, the maximum number of iterations l max = 100, the data range of the number of modes k is [2, 15], and the data range of the quadratic penalty factor α is [100, 5000]; for example, in the present invention, the value of the optimal decomposition parameters (k, α) obtained by the GWO algorithm iteration is (14, 3045);

[0041] Step 22: After completion of the initialization, perform VMD decomposition on the original dual-comb interference signal f(t) according to the decomposition parameters (k, α) to obtain the VMD decomposition signal; the specific algorithm description is as follows:

[0042] Collect the interference fringe signal of the dual-comb ranging system and perform VMD decomposition on it, decompose the signal into a set of modal components with limited bandwidth, so that each modal component has a different estimated bandwidth, thereby constructing the corresponding VMD constrained variational model. The VMD constrained variational model is expressed as:

[0043]

[0044] In the formula, f represents the original dual-comb interference fringe signal, u k (t) represents the k-th modal component, ω k (t) represents the center frequency of the modal component, t represents time, δ(t) represents the unit impulse function, represents the gradient at time t, * represents convolution, j represents the imaginary unit, and ||·||2 represents the L2 norm.

[0045] To solve the VMD constrained variational problem, introduce the Lagrange operator λ and λ(t) to transform the VMD constrained variational model into an unconstrained variational problem. The transformed VMD unconstrained variational model is expressed as:

[0046]

[0047] In the formula, k is the number of modes, α is the quadratic penalty factor, λ is the Lagrange operator, λ(t) is the Lagrange operator at time t, L({u k},{ω k}, λ) represents the Lagrangian equation of the unconstrained variational problem;

[0048] By setting the VMD parameters (k, α), the mode decomposition of the original dual-comb interference fringe signal f is performed to obtain k mode components under different bandwidths;

[0049] Step 23: Therefore, take the VMD parameters (k, α) as the gray wolf individuals in the GWO algorithm, and calculate the individual fitness of each gray wolf individual;

[0050] Step 24: Determine whether the individual fitness of the current gray wolf individual meets the pre-set fitness condition;

[0051] Step 25: If the current gray wolf individual meets the fitness condition, update the individual fitness. The specific operation process is as follows: Calculate the signal-to-noise ratio according to the characteristics of the dual-comb interference fringe signal, specifically including the ratio of the peak power to the noise power of the input signal. Use the Hilbert transform algorithm for the signal-to-noise ratio signal to obtain the envelope symmetry. Select the signal-to-noise ratio signal and the envelope symmetry for weighted matching, and use different weight coefficients to balance the relationship between the signal-to-noise ratio and the envelope symmetry. Finally, take the maximum value of the matching result as the required fitness condition of the gray wolf individual, which can be specifically expressed as:

[0052] fitness = max(w1·SNR + w2·Sym) (3)

[0053] In the formula, SNR represents the signal-to-noise ratio of the input signal, Sym represents the envelope symmetry of the input signal, w1 and w2 represent the weight coefficients of the corresponding parts, max represents taking the maximum value, and fitness represents the fitness condition of the gray wolf individual.

[0054] On the contrary, if the current gray wolf individual does not meet the fitness condition, retain the current gray wolf individual fitness;

[0055] Step 26: Determine whether the current iteration number is less than the maximum iteration number, that is, l < l max ;

[0056] Step 27: If not, the iteration process ends, and the optimal parameter solution is output;

[0057] Step 28: If so, continue the iteration, accumulate the iteration number, and let l = l + 1;

[0058] Step 29: Update the position of the gray wolf individual, and repeat the above process, that is, steps 22 to 28;

[0059] In summary, the optimization and decomposition process of the VMD-GWO algorithm includes that after the fitness of each group of gray wolf individuals is updated, the iteration number l = l + 1, and at the same time, the positions of each gray wolf individual are further updated, and the VMD decomposition continues; the GWO algorithm continuously performs global search and iteration according to the set fitness function to update the positions of gray wolf individuals; finally, when the iteration number reaches the set maximum iteration number l max the fitness of the gray wolf individuals converges to the optimal solution. Output the position of the gray wolf individual corresponding to the maximum value of the current fitness function, that is, the VMD decomposition parameters (k, α) that satisfy the optimal signal-to-noise ratio and envelope symmetry, and complete the entire GWO iterative optimization process.

[0060] The algorithm of the present invention is a denoising method for the physical characteristics of dual-comb interference fringe signals, which is applicable to dual-comb ranging signals, spectral analysis signals, three-dimensional surface shape signals, etc., and especially applicable to any dual-comb optical system, such as a dual-comb system based on two independent mode-locked lasers, a single-cavity dual-comb system, a microcavity dual-comb system, etc.

[0061] As Figure 4 shown, it is a schematic diagram of the original dual-comb interference fringe signal and each modal component after VMD decomposition. Each group of modal component signals represents the original signal components in different bandwidth ranges. From the attached Figure 4 it can be seen that modes 10 - 12 contain the dual-comb interference fringe signal, that is, the modal components 1 - 9, 13, and 14 containing noise are discarded.

[0062] As Figure 5 shown, it is a schematic diagram of the reconstructed signal of the dual-comb interference fringe. (5a) is the original dual-comb interference fringe signal; (5b) is the reconstructed dual-comb interference fringe signal.

[0063] As Figure 6 shown, it is a comparison diagram of the interference pattern waveforms before and after denoising by this method. The interference pattern waveforms before and after denoising by the present invention are compared, and it is found that the present invention simultaneously optimizes the envelope shape and has a good quasi-Gaussian envelope characteristic, which is very beneficial to the subsequent Hilbert transform processing and peak-finding accuracy, and thus can effectively improve the measurement range and accuracy of dual-comb ranging.

[0064] The dual-comb interference fringe signal denoising method proposed by the present invention combines the advantages of the VMD and GWO algorithms, overcomes the influence of noise on the dual-comb interference signal, optimizes the signal-to-noise ratio of the dual-comb interference fringe signal, improves the shape of the dual-comb fringes, and enhances the accuracy of extracting the peak position of the dual-comb. The present invention can achieve the denoising process of the dual-comb interference fringe signal, improves the environmental adaptability of the dual-comb ranging system, and expands the application scenarios of the dual-comb in the field of precision measurement. Since the present denoising algorithm is a denoising method for the physical characteristics of the dual-comb signal, it can be extended to be applicable to dual-comb ranging signals, spectral analysis signals, three-dimensional surface shape signals, etc., and is especially applicable to any dual-comb optical system, such as dual-femtosecond laser dual-comb, single-cavity dual-comb system, etc.

Claims

1. A denoising method for dual-comb interference fringe signals based on an improved VMD-GWO algorithm, characterized in that, The method includes the following steps: Step 1: Obtain a dual-comb interference fringe signal containing target distance information to get the original dual-comb interference fringe signal f(t); Step 2: Take the original dual-comb interference fringe signal f(t) as the input signal, perform iterative VMD-GWO algorithm optimization and decomposition processing, decompose the original dual-comb interference fringe signal f(t) according to the optimal parameters of VMD, and use GWO for global search and iteration to obtain the optimal solution (k,α) that converges to the fitness function, where k is the number of modes and α is the quadratic penalty factor; Step 3: Take the optimal solution (k, α) as the VMD decomposition parameters that achieve the optimal signal-to-noise ratio and envelope symmetry, including k modal components f1(t), f2(t), …, f k (t); Step 4: Screen each modal component and select several modal components that contain dual-comb interference fringes; Step 5: Discard high- and low-frequency noise signals; Step 6: Add the selected modal components to obtain the reconstructed signal of the dual-comb interference fringe.

2. A denoising method for dual optical comb interference fringe signals based on an improved VMD-GWO algorithm according to claim 1, characterized in that, The reconstructed signal of the dual-comb interference fringe signal has a Gaussian-like envelope feature that retains the pulse energy amplitude.

3. A denoising method for dual optical comb interference fringe signals based on an improved VMD-GWO algorithm as described in claim 1, characterized in that, In Step 2, the specific process of the iterative VMD-GWO algorithm decomposition and optimization processing includes the following flow: Take the VMD parameters (k,α) as the gray wolf individuals in the GWO algorithm, calculate the individual fitness of each gray wolf individual. If the current gray wolf individual meets the fitness condition, update the individual fitness. The specific operation process is as follows: Calculate the signal-to-noise ratio according to the characteristics of the dual-comb interference fringe signal, specifically including the ratio of the peak power to the noise power of the input signal. Use the Hilbert transform algorithm to obtain the envelope symmetry of the signal-to-noise ratio signal. Select the signal-to-noise ratio signal and the envelope symmetry for weighted matching, and use the weight coefficient to balance the relationship between the signal-to-noise ratio and the envelope symmetry. Finally, take the maximum value of the matching result as the required gray wolf individual fitness condition; After the fitness of each group of gray wolf individuals is updated, let the iteration number \(l = l + 1\), further update the position of each gray wolf individual, and continue with the VMD decomposition; use the GWO algorithm to continuously perform global search and iteration according to the set fitness function, and update the position of the gray wolf individuals; finally, when the iteration number reaches the set maximum iteration number \(l\) max the fitness of the gray wolf individuals converges to the optimal solution; output the position of the gray wolf individual corresponding to the maximum value of the current fitness function, that is, the VMD decomposition parameters \((k,α)\) that satisfy the optimal signal-to-noise ratio and envelope symmetry, and complete the entire GWO iterative optimization process.

4. A denoising method for dual optical comb interference fringe signals based on an improved VMD-GWO algorithm as claimed in claim 3, wherein, The iterative VMD-GWO algorithm decomposition and optimization process also includes pre-initializing the relevant parameters of the improved VMD-GWO algorithm, including setting the number of gray wolf populations N = 30, the maximum number of iterations l max = 100, the data range of the number of modes k is [2, 15], and the data range of the quadratic penalty factor α is [100, 5000]; after initialization, the original dual-comb interference fringe signal f(t) is decomposed by VMD according to the decomposition parameters (k, α) to obtain the VMD decomposition signal.

5. A denoising method for dual optical comb interference fringe signals based on an improved VMD-GWO algorithm as claimed in claim 1, characterized in that, This method is at least applicable to dual-comb ranging signals, spectral analysis signals, and three-dimensional surface shape signals.

6. A method for denoising double optical comb interference fringe signals based on an improved VMD-GWO algorithm according to claim 1, characterized in that This method is applicable to dual-comb optical systems.

7. A denoising method for dual optical comb interference fringe signals based on an improved VMD-GWO algorithm according to claim 1, characterized in that, Finally, take the maximum value of the matching result as the required gray wolf individual fitness condition, specifically expressed as: fitness=max(w1·SNR+w2·Sym) In the formula, SNR represents the signal-to-noise ratio of the input signal, Sym represents the envelope symmetry of the input signal, w1 and w2 represent the weight coefficients of the corresponding parts, max represents taking the maximum value, and fitness represents the fitness condition of the gray wolf individual.

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