Phi-OTDR signal noise reduction method based on adaptive VMD and improved threshold wavelet transform

Abstract

The invention discloses a noise reduction method for a phi-OTDR (Phase Sensitive Optical Time Domain Reflectometer) system. According to the method, adaptive variational mode decomposition (VMD) and an improved threshold wavelet transform technology are fused. The method comprises the following steps of: firstly, dynamically determining an optimal decomposition layer number by adopting a self-adaptive VMD algorithm based on a minimum Bhattacharyya distance criterion, and decomposing an original phi-OTDR signal into a plurality of intrinsic mode functions (IMF) with different frequency characteristics; then, calculating a correlation coefficient between each IMF component and the original signal, and carrying out improved threshold wavelet transform processing on the IMF components of which the correlation coefficients are lower than a preset threshold to suppress high-frequency noise components; and meanwhile, the IMF component with a relatively high correlation coefficient is reserved, so that effective information of an original signal is reserved to the greatest extent. And finally, reconstructing the processed IMF component to obtain a phi-OTDR (Optical Time Domain Reflectometer) signal with a high signal-to-noise ratio. According to the invention, the noise interference in the phi-OTDR system can be effectively reduced, the sensitivity and reliability of the system are improved, and powerful support is provided for high signal-to-noise ratio optical fiber sensing application.

Description

(I) Technical field

[0001] The present invention relates to the field of optical fiber sensing technology, and in particular to a method for The method combines signal processing and digital filtering techniques to improve The performance of the system in complex environments. (II) Background technology

[0002] As a highly sensitive distributed fiber optic sensing technology, it has been widely used in perimeter security, structural health monitoring, pipeline leakage detection and other fields. Its basic principle is based on the Rayleigh scattering effect in the optical fiber, and the environmental disturbance along the optical fiber is sensed by analyzing the backscattered light signal. However, due to the complexity of the system itself and environmental factors, Various noises will inevitably be introduced into the signal, such as thermal noise, shot noise, environmental vibration, etc. These noises will seriously affect the system signal-to-noise ratio and reduce the sensing accuracy and reliability.

[0003] Traditional noise reduction methods, such as low-pass filtering, while suppressing high-frequency noise, are prone to cause the loss of high-frequency components of the signal, resulting in signal distortion, especially when monitoring fast-changing dynamic disturbances. For example, time domain averaging reduces random noise by collecting signals multiple times and taking the average value, but this method is not sufficiently responsive to non-stationary noise and time domain changes of signals, and has poor real-time performance.

[0004] Some modern signal processing methods, such as wavelet transform and variational mode decomposition (VMD), are Signal denoising provides a new idea. As a multi-resolution analysis tool, wavelet transform can effectively extract the time-frequency characteristics of the signal, but its denoising effect depends largely on the choice of threshold. The traditional fixed threshold method is difficult to adapt to the complex and changeable noise environment. Too high a threshold will cause signal loss, and too low a threshold will not effectively suppress noise. VMD, as an emerging signal decomposition technology, can decompose complex nonlinear and non-stationary signals into multiple intrinsic mode functions (IMFs), but the setting of the decomposition layer K value has a great influence on the decomposition result. The traditional fixed K value method is difficult to achieve the optimal decomposition effect.

[0005] The present invention proposes a method based on adaptive VMD and improved threshold wavelet transform The signal denoising method aims to overcome the limitations of traditional denoising techniques. The core advantages of this method are: first, using the adaptive VMD algorithm to automatically determine the optimal number of decomposition layers according to the intrinsic characteristics of the signal, and to achieve complex non-stationary The precise decomposition of the signal effectively avoids the problem of over-decomposition or under-decomposition of modes in the traditional fixed-parameter VMD method, reduces the modal aliasing phenomenon, and lays the foundation for subsequent noise reduction. Secondly, for the low-correlation modal components obtained by decomposition, the improved adaptive threshold wavelet transform is used for refined noise reduction. The threshold function can dynamically adjust the threshold according to the distribution of wavelet coefficients, while effectively suppressing noise, retaining signal details to the maximum extent, avoiding signal distortion and high-frequency information loss that may be caused by the traditional fixed threshold method, especially when monitoring dynamic disturbances. It can maintain the transient characteristics of the signal. Through the adaptive decomposition of VMD and the adaptive threshold processing of the improved wavelet transform, a staged and complementary noise reduction strategy is implemented, which effectively improves the signal-to-noise ratio of the system and significantly improves the fidelity of the signal. This method can effectively handle complex and changeable noise environments and enhance The system's ability to perceive environmental disturbances provides a more reliable signal processing foundation for applications such as perimeter security and structural health monitoring, and has significant application value. (III) Summary of the invention

[0006] The present invention aims to solve the existing In order to solve the shortcomings of the system noise reduction technology, a noise reduction method based on adaptive VMD and improved threshold wavelet transform is proposed. The core of this method is to realize the adaptive optimization of the number of VMD decomposition layers, and use the correlation coefficient to accurately select the IMF components of the signal to be denoised. Subsequently, the improved adaptive threshold wavelet transform is applied to the selected IMF components to effectively suppress the noise and retain the effective information of the original signal to the maximum extent. Finally, the effective IMF components after noise reduction are reconstructed to obtain a noise reduction signal with a high signal-to-noise ratio. The present invention significantly improves the noise reduction performance through adaptive decomposition and refined noise reduction processing. The system's signal-to-noise ratio and sensitivity provide reliable technical support for achieving high-precision distributed fiber optic sensing.

[0007] To achieve the above purpose, the technical solution adopted by the present invention includes the following key links:

[0008] This application is a method based on adaptive VMD and improved threshold wavelet transform. The system noise reduction method comprises the following steps:

[0009] S1: Locate the vibration event according to the phase difference algorithm, and extract the phase signal at the location point as the signal to be denoised x(t). The phase information is a time domain signal.

[0010] S2: Use the minimum Bhattacharyya distance criterion to adaptively obtain the optimal decomposition level K of VMD.

[0011] S3: According to the optimal decomposition layer number K, the denoised signal x(t) is decomposed by VMD to obtain K IMF components, which are recorded as (IMF1, IMF2, ..., IMF K ).

[0012] S4: Calculate the Pearson correlation coefficient R between each IMF component and the information to be denoised i , where i is the index of the IMF component. If the correlation coefficient R i If it is lower than the preset threshold of 0.3, then go to step 5 to perform improved threshold wavelet denoising. Otherwise, the IMF is directly retained. i Quantity.

[0013] S5: Correlation coefficient R i IMF below the preset threshold of 0.3 i The components are denoised by improved threshold wavelet and reconstructed to obtain the denoised IMF i ’ Quantity.

[0014] S6: Calculate the IMF after noise reduction i ’ The Pearson correlation coefficient R between the component and the signal to be denoised x(t) i ’ , if the correlation coefficient R i ’ If it is lower than the preset threshold of 0.3, the IMF will be eliminated. i ’ Component, otherwise the IMF is retained directly i ’ Quantity.

[0015] S7: All retained IMF i Components and IMF i ’ The components are superimposed and reconstructed to obtain the final noise reduction signal x ’ (t).

[0016] Variational mode decomposition (VMD) is an adaptive signal decomposition algorithm, whose goal is to decompose the input signal into a set of IMFs with local bandwidth characteristics. The core mechanism of VMD is to solve the variational problem iteratively and use the center frequency constraint to make the center frequency of each IMF converge to the optimal value, thereby achieving signal decomposition. The present invention uses the minimum Bhattacharyya distance as the evaluation index and dynamically selects the optimal decomposition level K, avoiding errors caused by human settings.

[0017] Preferably, the step S2 includes the following sub-steps:

[0018] S2.1 uses Bhattacharyya distance to measure the similarity of adjacent IMF components after VMD decomposition.

[0019] S2.2 automatically searches for the optimal VMD decomposition level K so that frequency mixing does not occur between the IMF components.

[0020] Preferably, the step S4 includes the following sub-steps:

[0021] S4.1 calculates the Pearson correlation coefficient between each IMF component and the original signal.

[0022] The IMF components with lower S4.2 correlation coefficients (less than 0.3) usually contain more noise and require the next step of wavelet denoising.

[0023] The IMF components with higher correlation coefficients are directly retained.

[0024] Preferably, the step S5 includes the following sub-steps:

[0025] S5.1 performs wavelet decomposition on the screened noise IMF components.

[0026] S5.2 uses an adaptive threshold method to dynamically adjust the threshold value according to the scale of wavelet decomposition. This method can better adapt to the noise characteristics of different scales.

[0027] S5.3 uses soft threshold processing to suppress noise in high-frequency coefficients.

[0028] S5.4 Finally, the processed high-frequency coefficients and low-frequency coefficients are reconstructed by wavelet to obtain the IMF components after noise reduction.

[0029] Preferably, the step S6 includes the following sub-steps:

[0030] S6.1 calculates the Pearson correlation coefficient between the denoised IMF component and the original signal.

[0031] S6.2 If the correlation of the denoised IMF component is still low (less than 0.3), it is discarded because it may still contain too much noise.

[0032] S6.3 Otherwise, the denoised IMF component is retained.

[0033] The beneficial effects of the present invention are:

[0034] The number of VMD decomposition layers is adaptively determined based on the minimum Bhattacharyya distance criterion, which avoids the errors caused by human settings and improves the robustness and applicability of the algorithm.

[0035] The improved threshold wavelet transform is used to effectively suppress noise at multiple scales, thereby improving the noise reduction accuracy and signal-to-noise ratio.

[0036] The correlation coefficient is used to screen the IMF components, and only the IMF components that are strongly correlated with the original signal are reconstructed, thereby retaining the effective information of the signal to the maximum extent. (IV) Description of the drawings

[0037] Figure 1 The invention is an adaptive VMD and improved threshold wavelet transform Overall flow chart of the signal noise reduction method.

[0038] Figure 2 It is based on frequency division multiplexing System diagram.

[0039] Figure 3 It is a phase waterfall diagram. This diagram can be used to locate vibration events.

[0040] Figure 4 It is a restored waveform diagram for vibration events.

[0041] Figure 5 It is the optimal K IMF component time domain map.

[0042] Figure 6 It is the restored waveform of the vibration event obtained after the final noise reduction. (V) Specific implementation methods

[0043] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain the present invention, but cannot be understood as limiting the present invention.

[0044] This application is a method based on adaptive variational mode decomposition (VMD) and improved threshold wavelet transform. The signal noise reduction method comprises the following steps:

[0045] S1: Locate the vibration event according to the phase difference algorithm, and extract the phase signal at the location point as the signal to be denoised x(t). The phase information is a time domain signal.

[0046] S2: Use the Bhattacharyya distance method to adaptively obtain the optimal decomposition layer parameter K of VMD.

[0047] S3: According to the optimal decomposition layer number K, the denoised signal x(t) is decomposed by VMD to obtain K IMF components, which are recorded as (IMF1, IMF2, ..., IMF K ).

[0048] S4: Calculate the Pearson correlation coefficient R between each IMF component and the information to be denoised i, where i is the index of the IMF component. If the correlation coefficient R i If it is lower than 0.3, go to step 5 to perform improved threshold wavelet denoising. Otherwise, keep the IMF directly. i Quantity.

[0049] S5: Correlation coefficient R i IMF below 0.3 i The components are denoised by improved threshold wavelet and reconstructed to obtain the denoised IMF i ’ Quantity.

[0050] S6: Calculate the IMF after noise reduction i ’ The Pearson correlation coefficient R between the component and the signal to be denoised x(t) i ’ , if the correlation coefficient R i ’ If it is lower than 0.3, the IMF will be eliminated. i ’ Component, otherwise the IMF is retained directly i ’ Quantity.

[0051] S7: All retained IMF i Components and IMF i ’ The components are superimposed and reconstructed to obtain the final noise reduction signal x ’ (t).

[0052] Preferably, Bhattacharyya distance is an indicator used to measure the similarity of two probability distributions, and its mathematical definition is as follows:

[0053]

[0054] Where p and q represent the discrete probability distributions of the two IMF components. The smaller the BD value, the more similar the two distributions are.

[0055] The step S2 includes the following sub-steps:

[0056] S2.1: Set the search range of VMD decomposition parameter K to [K min ,K max ], where K min and K max The minimum and maximum number of layers for the preset.

[0057] S2.2: Within the search range, from K min Start traversing each K value, perform VMD decomposition on the signal to be denoised x(t), and obtain K IMF components.

[0058] S2.3: For each IMF component obtained by the decomposition level K, calculate the Bhattacharyya distances of all adjacent IMF components and take the smallest Bhattacharyya distance DB min .

[0059] S2.4: Determine the minimum Bhattacharyya distance DB min The relationship between DB min If it is less than 0.005, the traversal ends and the K value is taken as the optimal decomposition layer parameter; otherwise, the traversal continues.

[0060] Different IMF components have different correlations with the original signal, and noise is usually concentrated in components with lower correlation. The present invention uses the Pearson correlation coefficient to measure the correlation between the IMF component and the original signal.

[0061] In step S4, the calculation formula of the Pearson correlation coefficient is as follows:

[0062]

[0063] Among them, Cov[x(t),IMF i ] represents the signal to be denoised x(t) and IMF i The covariance of the components, Var[x(t)] and Var[IMF i ] represent the signal to be denoised x(t) and IMF respectively i The standard deviation of the component, which is used to assess the linear correlation between two variables.

[0064] Wavelet transform is a multi-scale analysis method that achieves noise reduction by decomposing the signal into different frequency components. The present invention adopts an improved threshold method to adaptively adjust the threshold value according to the wavelet decomposition scale to better adapt to the noise characteristics of different scales.

[0065] The present invention proposes an adaptive threshold calculation formula, which can dynamically adjust the threshold according to the number of decomposition layers:

[0066]

[0067] In the formula, λ j is the adaptive improved threshold of the j-th layer of wavelet decomposition, σ j It represents the noise standard deviation estimate of the high-frequency coefficients of the jth layer, N represents the length of the IMF signal, and b is an adjustable parameter that controls the trend of the threshold changing with the number of decomposition layers.

[0068] In step S5, the soft threshold processing is specifically as follows:

[0069]

[0070] Where ω represents the high-frequency coefficient after wavelet decomposition, η(ω) represents the high-frequency coefficient after threshold processing, and sign(x) is the sign function.

[0071] Preferably, the step of improving the threshold wavelet transform in step S5 is:

[0072] S5.1 performs multi-scale wavelet decomposition on the selected IMF components to obtain high-frequency coefficients and low-frequency coefficients.

[0073] S5.2 uses the above-mentioned adaptive improved threshold to perform soft threshold processing on the high-frequency coefficients to effectively suppress noise.

[0074] S5.3 uses the processed high-frequency coefficients and low-frequency coefficients to perform wavelet reconstruction to obtain the IMF component after noise reduction.

[0075] IMF component reconstruction and noise removal. In order to further improve the noise reduction effect, the Pearson correlation coefficient between the noise-reduced IMF component and the original signal is calculated again. If the correlation coefficient is less than 0.3, the IMF component is removed, otherwise it is retained. All retained or noise-reduced IMF components are reconstructed to obtain the final noise-reduced φ-OTDR signal.

[0076] Example:

[0077] For the vibration event signal detected in the φ-OTDR system based on frequency division multiplexing, the signal processing is performed by the φ-OTDR system noise reduction method based on adaptive VMD and improved threshold wavelet transform. The algorithm flow chart of the signal processing is shown in Figure 1 shown.

[0078] The present invention proposes a φ-OTDR system based on frequency division multiplexing for realizing high-sensitivity distributed vibration sensing. The system structure is as follows Figure 2 As shown, the core uses a quad-frequency modulation module to generate four frequency band chirped pulses with timing. The frequency ranges of these pulses are: 90-110MHz, 190-210MHz, 290-310MHz and 390-410MHz. The system pulse repetition frequency is 5kHz, the bandwidth of a single frequency pulse signal is 20kHz, and the pulse width is 10μs. The total length of the sensing fiber is 18km, the system sampling rate is 1.25GS / s, and the sampling time is 20ms.

[0079] In order to verify the performance of the system, a piezoelectric ceramic (PZT) is placed as a vibration source 17km away from the starting end of the optical fiber. The PZT is driven by a sinusoidal signal with a frequency of 900Hz and a peak-to-peak value of 400mVpp. The PZT is used to simulate actual vibration events. The sensor signals of the four frequency components collected are first preprocessed to form four matrix signals, and then matched filtering is performed. Subsequently, the phase information is extracted through IQ demodulation. The four extracted phase signals are combined in time sequence and differentially processed to generate a phase waterfall diagram. The phase waterfall diagram within the range of 16-18km is shown in the figure. Figure 3 As shown. Figure 3 It can be seen that the vibration event can be accurately located at 17 km.

[0080] In order to deeply analyze the characteristics of vibration events, the phase signal at 17 km is selected as the signal to be de-noised, such as Figure 4 As shown. The signal is affected by noise, and the waveform presents an irregular sawtooth shape. The present invention proposes a φ-OTDR signal denoising method based on adaptive VMD and improved threshold wavelet transform. First, an adaptive algorithm is used to determine the optimal decomposition layer number of VMD, and K=10 is obtained. Then, the signal to be denoised is decomposed by VMD using the optimal decomposition layer number, and 10 IMF components are obtained, as shown in FIG. Figure 5 As shown. Next, based on the correlation coefficient method, the 10 IMF components obtained by decomposition are divided into noise IMF components with low correlation and effective IMF components with high correlation. Subsequently, the noise IMF components with low correlation are subjected to wavelet denoising using the improved wavelet threshold function, and correlation analysis is performed again to remove the residual IMF components with low correlation. Finally, the effective IMF components remaining after processing are retained and reconstructed by superposition to obtain the final denoised phase signal, as shown in Figure 6 shown.

Claims

1. A wavelet transform based on adaptive VMD and improved threshold The signal noise reduction method is characterized by: The following steps are involved: S1: Locate the vibration event according to the phase difference algorithm, and extract the phase signal at the location point as the signal to be denoised x(t). The phase information is a time domain signal. S2: Use the minimum Bhattacharyya distance criterion to adaptively obtain the optimal decomposition level K of VMD. S3: According to the optimal decomposition layer number K, the denoised signal x(t) is decomposed by VMD to obtain K IMF components, which are recorded as (IMF1, IMF2, ..., IMF K ). S4: Calculate the Pearson correlation coefficient R between each IMF component and the information to be denoised i , where i is the index of the IMF component. If the correlation coefficient R i If it is lower than the preset threshold value of 0.3, then go to step S5 to perform improved threshold wavelet denoising; otherwise, directly retain the IMF i Quantity. S5: Correlation coefficient R i IMF below the preset threshold of 0.3 i The components are denoised by improved threshold wavelet and reconstructed to obtain the denoised IMF i ’ Quantity. S6: Calculate the IMF after noise reduction i ’ The Pearson correlation coefficient R between the component and the signal to be denoised x(t) i ’ , if the correlation coefficient R i ’ If it is still below the preset threshold of 0.3, the IMF will be eliminated. i ’ Component, otherwise keep the IMF i ’ Quantity. S7: All retained IMF i Components and IMF i ’ The components are superimposed and reconstructed to obtain the final noise reduction signal x ’ (t).

2. The method according to claim 1, characterized in that In S2, the IMF component is discrete sample data, and the calculation formula of Bhattacharyya distance is as follows: Among them, p(x) and q(x) represent the discrete probability distributions of the two IMF components, which are used to measure the similarity of the two distributions.

3. The method according to claim 1, characterized in that The step S2 includes the following sub-steps: S2.1: Set the search range of VMD decomposition parameter K to [K min ,K max ], where K min and K max The minimum and maximum number of layers for the preset. S2.2: Within the search range, from K min Start traversing each K value, perform VMD decomposition on the signal to be denoised x(t), and obtain K IMF components. S2.3: For each IMF component obtained by the decomposition level K, calculate the Bhattacharyya distances of all adjacent IMF components and take the smallest Bhattacharyya distance DB min . S2.4: Determine the minimum Bhattacharyya distance DB min The relationship between DB min If it is less than 0.005, the traversal ends and the K value is taken as the optimal decomposition layer parameter; otherwise, the traversal continues.

4. The method according to claim 1, characterized in that: In step S4, the calculation formula of the Pearson correlation coefficient is as follows: Among them, Cov[x(t),IMF i ] represents the signal to be denoised x(t) and IMF i The covariance of the components, Var[x(t)] and Var[IMF i ] represent the noise reduction signal x(t) and IMF respectively i The standard deviation of the component, which is used to assess the linear correlation between two variables.

5. The method according to claim 1, characterized in that In step S5, the adaptive improved threshold calculation formula is as follows: Among them, λ j is the adaptive improved threshold of the j-th layer of wavelet decomposition, σ j It represents the noise standard deviation estimate of the high-frequency coefficients of the jth layer, N represents the length of the IMF signal, and b is an adjustable parameter that controls the trend of the threshold changing with the number of decomposition layers.

6. The method according to claim 1, characterized in that In step S5, the soft threshold processing is specifically as follows: Among them, ω represents the high-frequency coefficient after wavelet decomposition, η(ω) represents the high-frequency coefficient after threshold processing, and sign(·) is the sign function.

Images