Cable reflection coefficient spectrum noise reduction method based on GMM (Gaussian Mixture Model) and related device

Abstract

The invention provides a GMM (Gaussian Mixture Model)-based cable reflection coefficient spectrum noise reduction method and a related device. The method comprises the following steps: converting a reflection coefficient spectrum X of a detected power cable collected by a reflection coefficient spectrometer into a parameter model s (n); respectively extracting a real part and an imaginary part of the parameter model s (n), constructing a two-dimensional matrix xn, processing observation data based on the two-dimensional matrix xn by using a Gaussian probability density function, and solving a log-likelihood function for the Gaussian probability density function; updating parameters in the iterative log-likelihood function by adopting an EM algorithm until convergence; and eliminating interference data in the observation data, and outputting a noise reduction result. According to the method, the noise level in the cable reflection coefficient spectrum can be remarkably reduced, the signal-to-noise ratio of signals is improved, fault features are more prominent, and a more accurate data basis is provided for subsequent fault diagnosis.

Description

Technical Field

[0001] The present invention relates to the technical field of cable defect positioning, and in particular to a GMM-based cable reflection coefficient spectrum denoising method and a related device. Background Art

[0002] The method of locating cable defects based on cable characteristic impedance is to use a network analyzer to collect the refraction and reflection signals generated when the incident signal encounters impedance mismatch points such as defects in the transmission line, obtain the cable characteristic impedance information, and locate the cable defects.

[0003] However, this method also has many hardware and technical problems to be solved. In the frequency domain reflection method, the noise influence of the cable reflection coefficient spectrum is an issue that cannot be ignored. The presence of noise will reduce the signal-to-noise ratio of the reflection coefficient spectrum, making the effective signal submerged by the noise, making it difficult to accurately extract the fault characteristics, and the interference may cause waveform distortion and peak shift, thereby reducing the positioning accuracy. Summary of the invention

[0004] The present invention provides a GMM-based cable reflection coefficient spectrum denoising method and related devices. The GMM method is used to process the reflection coefficient spectrum, which can significantly reduce the noise level in the cable reflection coefficient spectrum, make the fault characteristics more prominent, improve the signal-to-noise ratio, and enhance the accuracy and reliability of signal processing.

[0005] A cable reflection coefficient spectrum denoising method based on GMM, comprising:

[0006] Convert the reflection coefficient spectrum X of the tested power cable collected by the reflection coefficient spectrometer into a parameter model s(n);

[0007] Extract the real and imaginary parts of the parameter model s(n) respectively and construct a two-dimensional matrix x n , using Gaussian probability density function to process the two-dimensional matrix x n , obtaining a log-likelihood function for the Gaussian probability density function;

[0008] The EM algorithm is used to update the parameters in the iterative log-likelihood function until convergence;

[0009] Eliminate interference data in the observed data and output the noise reduction result.

[0010] Furthermore, the parameter model s(n) is:

[0011]

[0012] Where q is the number of reflected waves, A i is the amplitude of the i-th reflected wave, is the frequency of the reflected wave, and w(n) is the sampling noise.

[0013] Furthermore, the two-dimensional matrix x n for:

[0014]

[0015] Two-dimensional matrix x n Translates to:

[0016] x n =S rai +W rai (3).

[0017] Furthermore, the Gaussian probability density function is used to process the two-dimensional matrix x n Observation data, and obtaining the log-likelihood function for the Gaussian probability density function, specifically including:

[0018] The D-dimensional Gaussian probability density function is:

[0019]

[0020] Where μ is the data center point, Σ is a symmetric semi-finite matrix, and D is the data dimension; if the observation data X = {x 1 , x 2 , …, x n , …, x N}, then the joint probability function based on GMM is expressed as:

[0021]

[0022] where K, α = {α 1 , α 2 , ..., α k},μ={μ 1 , μ 2 , ..., μ k} and Σ={Σ 1 ,Σ 2 , ..., Σ k} respectively represent the number of models, weights, number of data center points and number of covariance matrices;

[0023] Take the log-likelihood function for P(X|α,μ,Σ), that is

[0024]

[0025] Furthermore, the method of updating the parameters in the iterative log-likelihood function using the EM algorithm until convergence specifically includes:

[0026] Step E:

[0027] According to the Bayesian formula, find the nth group of samples x generated by the kth Gaussian mixture model GMM n The posterior probability γ nk for:

[0028]

[0029] According to formula (7), we can get:

[0030]

[0031] According to the principle of Jensen inequality, we get the following function:

[0032]

[0033] By adjusting the lower bound function of formula (9), the maximum value of the lower bound function is obtained, so that formula (9) gradually approaches the optimal solution or obtains a local optimal solution, and substitute formula (3) into formula (9) to obtain:

[0034]

[0035] M-step:

[0036] Applying formula (10) to μ k Find the partial derivative, that is

[0037]

[0038] Let (11) be equal to 0, we get

[0039]

[0040] Substituting equation (10) for Σ k Find the partial derivative, that is

[0041]

[0042] Let (13) be equal to 0, we get

[0043]

[0044] make

[0045]

[0046] Apply formula (15) to α k Find the partial derivative

[0047]

[0048] Let (16) be equal to 0, and we get:

[0049]

[0050] The parameters μ are respectively calculated by equations (12), (14) and (17). k ,Σ k , α k Iterative update, and then repeat the E step and M step until convergence.

[0051] Furthermore, the removing of interference data from the observed data and outputting a noise reduction result specifically includes:

[0052] The smallest weight α k The corresponding data are treated as noise and removed, and the rest are superimposed to reconstruct the cable reflection coefficient spectrum.

[0053] A cable reflection coefficient spectrum noise reduction device based on GMM, comprising:

[0054] A data processing module, used for converting the reflection coefficient spectrum X of the tested power cable collected by the reflection coefficient spectrometer into a parameter model s(n);

[0055] The log-likelihood function acquisition module is used to extract the real and imaginary parts of the parameter model s(n) and construct a two-dimensional matrix x n , using Gaussian probability density function to process the two-dimensional matrix x n , obtaining a log-likelihood function for the Gaussian probability density function;

[0056] A parameter updating and iterating module is used to update the parameters in the iterative log-likelihood function using the EM algorithm until convergence;

[0057] The noise removal module is used to remove interference data from the observed data and output the noise reduction result.

[0058] Furthermore, the parameter model s(n) is:

[0059]

[0060] Where q is the number of reflected waves, A i is the amplitude of the i-th reflected wave, is the frequency of the reflected wave, and w(n) is the sampling noise.

[0061] Furthermore, the two-dimensional matrix x n for:

[0062]

[0063] Two-dimensional matrix x n Translates to:

[0064] x n =S rai +Wrai (3).

[0065] Furthermore, the log-likelihood function acquisition module uses a Gaussian probability density function to process the two-dimensional matrix x n Observation data, and obtaining the log-likelihood function for the Gaussian probability density function, specifically including:

[0066] The D-dimensional Gaussian probability density function is:

[0067]

[0068] Where μ is the data center point, Σ is a symmetric semi-finite matrix, and D is the data dimension; if the observation data X = {x 1 , x 2 , …, x n , …, x N}, then the joint probability function based on GMM is expressed as:

[0069]

[0070] where K, α = {α 1 , α 2 , ..., α k},μ={μ 1 , μ 2 , ..., μ k} and Σ={Σ 1 ,Σ 2 , ..., Σ k} respectively represent the number of models, weights, number of data center points and number of covariance matrices;

[0071] Take the log-likelihood function for P(X|α,μ,Σ), that is

[0072]

[0073] Furthermore, the parameter updating and iterating module uses the EM algorithm to update the parameters in the iterative log-likelihood function until convergence, specifically including:

[0074] Step E:

[0075] According to the Bayesian formula, find the nth group of samples x generated by the kth Gaussian mixture model GMM n The posterior probability γ nk for:

[0076]

[0077] According to formula (7), we can get:

[0078]

[0079] According to the principle of Jensen inequality, we get the following function:

[0080]

[0081] By adjusting the lower bound function of formula (9), the maximum value of the lower bound function is obtained, so that formula (9) gradually approaches the optimal solution or obtains a local optimal solution, and substitute formula (3) into formula (9) to obtain:

[0082]

[0083] M-step:

[0084] Applying formula (10) to μ k Find the partial derivative, that is

[0085]

[0086] Let (11) be equal to 0, we get

[0087]

[0088] Substituting equation (10) for Σ k Find the partial derivative, that is

[0089]

[0090] Let (13) be equal to 0, we get

[0091]

[0092] make

[0093]

[0094] Apply formula (15) to α k Find the partial derivative

[0095]

[0096] Let (16) be equal to 0, and we get:

[0097]

[0098] The parameters μ are respectively calculated by equations (12), (14) and (17). k ,Σ k , α k Iterative update, and then repeat the E step and M step until convergence.

[0099] Furthermore, the noise removal module is specifically used for:

[0100] The smallest weight α kThe corresponding data are treated as noise and removed, and the rest are superimposed to reconstruct the cable reflection coefficient spectrum.

[0101] A cable reflection coefficient spectrum noise reduction system based on GMM, comprising: a computer-readable storage medium and a processor;

[0102] The computer-readable storage medium is used to store executable instructions;

[0103] The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the GMM-based cable reflection coefficient spectrum denoising method.

[0104] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the GMM-based cable reflection coefficient spectrum denoising method.

[0105] The beneficial effects of the present invention compared with the prior art are:

[0106] The present invention can significantly reduce the noise level in the cable reflection coefficient spectrum, improve the signal-to-noise ratio, make the fault characteristics more prominent, and provide a more accurate data basis for subsequent fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 It is a flow chart of the cable reflection coefficient spectrum noise reduction method based on GMM of the present invention.

[0108] Figure 2 is the reflectance spectrum without defects;

[0109] Figure 3 is the reflection coefficient spectrum with defect. DETAILED DESCRIPTION

[0110] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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 creative work are within the scope of protection of the present invention.

[0111] See also Figure 1 The embodiment of the present invention provides a cable reflection coefficient spectrum denoising method based on GMM, comprising the following steps:

[0112] Step 1: Convert the reflection coefficient spectrum X of the tested power cable collected by the reflection coefficient spectrometer into a parameter model s(n):

[0113]

[0114] Where q is the number of reflected waves, A i is the amplitude of the i-th reflected wave, is the frequency of the reflected wave, w(n) is the sampling noise;

[0115] Step 2: Extract the real and imaginary parts of the parameter model s(n) respectively and construct a two-dimensional matrix x n :

[0116]

[0117] The two-dimensional matrix x n can be transformed into:

[0118] x n =S rai +W rai (3)

[0119] Gaussian Mixture Model (GMM) is an effective method to solve engineering problems and is favored by many researchers. The D-dimensional Gaussian probability density function is:

[0120]

[0121] Where μ is the data center point, Σ is a symmetric semi-finite matrix, and D is the data dimension. If the observation data X = {x 1 , x 2 , …, x n , …, x N}, then the joint probability function based on GMM can be expressed as:

[0122]

[0123] where K, α = {α 1 , α 2 , ..., α k},μ={μ 1 , μ 2 , ..., μ k} and Σ={Σ 1 ,Σ 2 , ..., Σ k} respectively represent the number of models, weights, number of data center points and number of covariance matrices.

[0124] For ease of calculation, first take the log-likelihood function of P(X|α,μ,Σ), that is

[0125]

[0126] Obviously, it is difficult to directly obtain the values ​​of each parameter from formula (6). Since the EM algorithm has stable estimation performance for GMM, the EM algorithm is used to estimate the parameters.

[0127] Step 3: Use the EM algorithm to update the parameters in the iterative log-likelihood function until convergence.

[0128] The EM algorithm is the expectation maximum algorithm, which is an iterative algorithm used for maximum likelihood estimation or maximum a posteriori probability estimation of probability parameter models containing hidden variables. The algorithm steps of EM are divided into:

[0129] Step E: Calculate the expected value of the log-likelihood function of the complete data;

[0130] M step: Get the new parameter value by maximizing the value of the intermediate quantity.

[0131] The following will be described in detail:

[0132] Step E:

[0133] According to the Bayesian formula, we can find the nth group of samples x generated by the kth Gaussian mixture model GMM n The posterior probability γ nk for:

[0134]

[0135] According to formula (7), it is obvious that:

[0136]

[0137] Then, according to the principle of Jensen inequality, we get the following function:

[0138]

[0139] By adjusting the lower bound function of formula (9), the maximum value of the lower bound function can be obtained, so that the above formula can gradually approach the optimal solution or obtain a local optimal solution, and substitute formula (3) into formula (9) to obtain:

[0140]

[0141] M-step:

[0142] Applying formula (10) to μ k Find the partial derivative, that is

[0143]

[0144] Let (11) be equal to 0, we can get

[0145]

[0146] Substituting equation (10) for Σ k Find the partial derivative, that is

[0147]

[0148] Let (13) be equal to 0, we can get

[0149]

[0150] make

[0151]

[0152] Apply formula (15) to α k Taking partial derivatives we get

[0153]

[0154] Let (16) be equal to 0, and we get:

[0155]

[0156] The parameters μ are calculated by equations (12), (14), and (17). k ,Σ k , α k Iterative update, and then repeat the E step and M step until convergence.

[0157] Step 4: Eliminate interference data in the observed data and output the noise reduction result:

[0158] Finally, the α with the smallest weight k The corresponding data is regarded as noise, which is removed, and the rest is superimposed to reconstruct the cable reflection coefficient spectrum and improve the signal-to-noise ratio.

[0159] Defect-free cable simulation:

[0160] The reflection coefficient spectrum of a 500m long 10kV cable is simulated. The simulation scanning frequency bandwidth is 0.15~100MHz, the step size is 0.01MHz, and Gaussian white noise with a signal-to-noise ratio of 50dB is added to the reflection coefficient spectrum. The GMM algorithm is then used to process the noisy reflection coefficient spectrum. The simulation and processing results are shown in Figure 2. Figure 2 The results show that the GMM algorithm of the present invention can effectively eliminate noise and reconstruct the reflection coefficient spectrum, effectively fit the effective data and improve the signal-to-noise ratio.

[0161] Simulation of a cable with defects:

[0162] Compared with defect-free cables, defective cables will produce equivalent frequencies in the spectrum, making the data more complex and difficult to fit. In order to verify the applicability of the GMM method, the reflection coefficient spectrum of a 500m long 10kV cable with a 0.5m defect at 200m was simulated. The simulation scanning frequency bandwidth was 0.15~100MHz, the step size was 0.01MHz, and Gaussian white noise with a signal-to-noise ratio of 50dB was added to the reflection coefficient spectrum. The GMM algorithm was then used to process the noisy reflection coefficient spectrum. The simulation and processing results are shown in Figure 2. Figure 3 The results show that the GMM algorithm effectively eliminates noise while retaining the equivalent frequency caused by defects, accurately reconstructs the reflection coefficient spectrum, fits the data according to the trend brought by the equivalent frequency, and improves the signal-to-noise ratio.

[0163] The embodiment of the present invention further provides a cable reflection coefficient spectrum noise reduction device based on GMM, comprising:

[0164] A data processing module, used for converting the reflection coefficient spectrum X of the tested power cable collected by the reflection coefficient spectrometer into a parameter model s(n);

[0165] The log-likelihood function acquisition module is used to extract the real and imaginary parts of the parameter model s(n) and construct a two-dimensional matrix x n , using Gaussian probability density function to process the two-dimensional matrix x n , obtaining a log-likelihood function for the Gaussian probability density function;

[0166] A parameter updating and iterating module is used to update the parameters in the iterative log-likelihood function using the EM algorithm until convergence;

[0167] The noise removal module is used to remove interference data from the observed data and output the noise reduction result.

[0168] Another embodiment of the present invention provides a GMM-based cable reflection coefficient spectrum noise reduction system, comprising: a computer-readable storage medium and a processor;

[0169] The computer-readable storage medium is used to store executable instructions;

[0170] The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the GMM-based cable reflection coefficient spectrum denoising method.

[0171] Another embodiment of the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the GMM-based cable reflection coefficient spectrum denoising method is implemented.

[0172] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0173] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0174] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0175] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A cable reflection coefficient spectrum denoising method based on GMM, characterized by: The steps include: Convert the reflection coefficient spectrum X of the tested power cable collected by the reflection coefficient spectrometer into a parameter model s(n); Extract the real and imaginary parts of the parameter model s(n) respectively and construct a two-dimensional matrix x n , using Gaussian probability density function to process the two-dimensional matrix x n , obtaining a log-likelihood function for the Gaussian probability density function; The EM algorithm is used to update the parameters in the iterative log-likelihood function until convergence; Eliminate interference data in the observed data and output the noise reduction result.

2. The cable reflection coefficient spectrum denoising method based on GMM as claimed in claim 1, characterized in that: The parameter model s(n) is: Where q is the number of reflected waves, A i is the amplitude of the i-th reflected wave, is the frequency of the reflected wave, and w(n) is the sampling noise.

3. The cable reflection coefficient spectrum denoising method based on GMM as claimed in claim 2, characterized in that: The two-dimensional matrix x n for: Two-dimensional matrix x n Translates to: x n =S rai +W rai (3)。 4. The cable reflection coefficient spectrum denoising method based on GMM as claimed in claim 3, characterized in that: The Gaussian probability density function is used to process the two-dimensional matrix x n Observation data, and obtaining the log-likelihood function for the Gaussian probability density function, specifically including: The D-dimensional Gaussian probability density function is: Where μ is the data center point, Σ is a symmetric semi-finite matrix, and D is the data dimension; if the observation data X = {x1, x2, ..., x n , …, x N }, then the joint probability function based on GMM is expressed as: Among them, K, α = {α1, α2,..., α k },μ={μ1,μ2,...,μ k } and Σ={Σ1, Σ2,...,Σ k } respectively represent the number of models, weights, number of data center points and number of covariance matrices; Take the log-likelihood function for P(X|α,μ,Σ), that is 5. The cable reflection coefficient spectrum denoising method based on GMM as claimed in claim 4, characterized in that: The method of updating the parameters in the iterative log-likelihood function using the EM algorithm until convergence specifically includes: Step E: According to the Bayesian formula, find the nth group of samples x generated by the kth Gaussian mixture model GMM n The posterior probability γ nk for: According to formula (7), we can get: According to the principle of Jensen inequality, we get the following function: By adjusting the lower bound function of formula (9), the maximum value of the lower bound function is obtained, so that formula (9) gradually approaches the optimal solution or obtains a local optimal solution, and substitute formula (3) into formula (9) to obtain: M-step: Applying formula (10) to μ k Find the partial derivative, that is Let (11) be equal to 0, we get Substituting equation (10) for Σ k Find the partial derivative, that is Let (13) be equal to 0, we get make Apply formula (15) to α k Find the partial derivative Let (16) be equal to 0, and we get: The parameters μ are respectively calculated by equations (12), (14) and (17). k ,Σ k , α k Iterative update, and then repeat the E step and M step until convergence.

6. The cable reflection coefficient spectrum denoising method based on GMM as claimed in claim 5, characterized in that: The removing of interference data from the observed data and outputting the noise reduction result specifically includes: The smallest weight α k The corresponding data are treated as noise and removed, and the rest are superimposed to reconstruct the cable reflection coefficient spectrum.

7. A cable reflection coefficient spectrum noise reduction device based on GMM, characterized in that: include: A data processing module, used for converting the reflection coefficient spectrum X of the tested power cable collected by the reflection coefficient spectrometer into a parameter model s(n); The log-likelihood function acquisition module is used to extract the real and imaginary parts of the parameter model s(n) and construct a two-dimensional matrix x n , using Gaussian probability density function to process the two-dimensional matrix x n , obtaining a log-likelihood function for the Gaussian probability density function; A parameter updating and iterating module is used to update the parameters in the iterative log-likelihood function using the EM algorithm until convergence; The noise removal module is used to remove interference data from the observed data and output the noise reduction result.

8. The cable reflection coefficient spectrum noise reduction device based on GMM as claimed in claim 7, characterized in that: The parameter model s(n) is: Where q is the number of reflected waves, A i is the amplitude of the i-th reflected wave, is the frequency of the reflected wave, and w(n) is the sampling noise.

9. The cable reflection coefficient spectrum noise reduction device based on GMM as claimed in claim 8, characterized in that: The two-dimensional matrix x n for: Two-dimensional matrix x n Translates to: x n =S rai +W rai (3)。 10. The cable reflection coefficient spectrum noise reduction device based on GMM as claimed in claim 9, characterized in that: The log-likelihood function acquisition module uses a Gaussian probability density function to process the two-dimensional matrix x n Observation data, and obtaining the log-likelihood function for the Gaussian probability density function, specifically including: The D-dimensional Gaussian probability density function is: Where μ is the data center point, Σ is a symmetric semi-finite matrix, and D is the data dimension; if the observation data X = {x1, x2, ..., x n , …, x N }, then the joint probability function based on GMM is expressed as: Among them, K, α = {α1, α2,..., α k },μ={μ1,μ2,...,μ k } and Σ={Σ1, Σ2,...,Σ k } respectively represent the number of models, weights, number of data center points and number of covariance matrices; Take the log-likelihood function for P(X|α,μ,Σ), that is 11. The cable reflection coefficient spectrum noise reduction device based on GMM as claimed in claim 10, characterized in that: The parameter updating and iterating module uses the EM algorithm to update the parameters in the iterative log-likelihood function until convergence, specifically including: Step E: According to the Bayesian formula, find the nth group of samples x generated by the kth Gaussian mixture model GMM n The posterior probability γ nk for: According to formula (7), we can get: According to the principle of Jensen inequality, we get the following function: By adjusting the lower bound function of formula (9), the maximum value of the lower bound function is obtained, so that formula (9) gradually approaches the optimal solution or obtains a local optimal solution, and substitute formula (3) into formula (9) to obtain: M-step: Substituting equation (10) for μ k Find the partial derivative, that is Let (11) be equal to 0, we get Substituting equation (10) for Σ k Find the partial derivative, that is Let (13) be equal to 0, we get make Apply formula (15) to α k Find the partial derivative Let equation (16) equal to 0, and we get: The parameters μ are respectively calculated by equations (12), (14) and (17). k ,Σ k , α k Iterative update, and then repeat the E step and M step until convergence.

12. The cable reflection coefficient spectrum noise reduction device based on GMM according to claim 11, characterized in that: The noise removal module is specifically used for: The smallest weight α k The corresponding data are treated as noise and removed, and the rest are superimposed to reconstruct the cable reflection coefficient spectrum.

13. A cable reflection coefficient spectrum noise reduction system based on GMM, comprising: A computer readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the GMM-based cable reflection coefficient spectrum denoising method according to any one of claims 1 to 6.

14. A non-transitory computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the cable reflection coefficient spectrum denoising method based on GMM according to any one of claims 1 to 6 is implemented.

Images