FDM-DAS multi-carrier separation method and system

Abstract

The application belongs to the technical field of optical fiber acoustic wave sensing, and particularly relates to an FDM-DAS multi-carrier frequency separation method and system, which comprises the following steps: generating K detection light pulses with different optical frequencies, injecting the detection light pulses into a sensing optical fiber, carrying out coherent mixing of backscattered light of the sensing optical fiber and local light of continuous light, outputting a mixed electrical signal containing K carrier frequency beat components through a photoelectric detector, extracting the amplitude and phase of each carrier frequency beat component by using an orthogonal recursive least square algorithm, averaging the amplitudes in a time window at the same spatial position to obtain the amplitude at the spatial position, phase unwrapping to obtain a continuous phase, weighting and fusing the amplitudes of the carrier frequency beat components to obtain a robust phase estimation resistant to coherent fading, and carrying out spatial differentiation and phase unwrapping on the robust phase estimation to obtain a strain or acoustic signal distributed along the optical fiber, so that demodulation is not required for each carrier frequency, and the calculation efficiency is improved.

Description

Technical Field

[0001] This application belongs to the field of fiber optic acoustic wave sensing technology, specifically an FDM-DAS multi-carrier frequency separation method and system. Background Technology

[0002] Distributed acoustic sensing (DAS) technology is based on the principle of phase-sensitive optical time-domain reflectometry (Φ-OTDR). It obtains vibration or acoustic information distributed along the sensing fiber by detecting the phase change of the backscattered Rayleigh light along the fiber. Due to its unique advantages such as long distance, fully distributed, and real-time monitoring, DAS technology has been widely used in fields such as oil and gas pipeline monitoring, earthquake detection, perimeter security, and traffic monitoring.

[0003] In traditional single-frequency DAS systems, continuous light emitted from a narrow-linewidth laser is modulated into optical pulses by an acousto-optic modulator (AOM). The resulting backscattered Rayleigh light beats with the local oscillator light after being injected into the sensing fiber, and optical phase information is extracted through I / Q demodulation. However, since Rayleigh backscattering is a coherent superposition of scatterers randomly distributed along the fiber, its amplitude and phase are random. At certain spatial locations, the contributions of the scatterers may cause destructive interference, leading to extreme attenuation of the scattered light amplitude, a phenomenon known as coherence fading. At the coherence fading point, due to the extremely low signal amplitude, the signal-to-noise ratio of phase estimation drops sharply, causing phase measurement failure and severely affecting the spatial continuity and measurement reliability of the DAS system.

[0004] To address the coherent fading problem, researchers proposed a Frequency Division Multiplexing (FDM) DAS (FDM-DAS) scheme: multiple AOMs with different frequency shifts are used to generate multiple probe light pulses with different optical frequencies. Since Rayleigh scattering corresponding to different optical frequencies has different random interference patterns, coherent fading is unlikely to occur simultaneously on all frequency channels at the same spatial location. By selecting the frequency channel with the highest signal-to-noise ratio or fusing the results of multiple channels, coherent fading can be effectively suppressed.

[0005] In an FDM-DAS system, the electrical signal received by the photodetector contains beat frequency components of K different carrier frequencies. The traditional method is to perform I / Q demodulation on each carrier frequency separately (i.e., the 4N superposition method), requiring K independent demodulation processes. The computational complexity increases linearly with the number of carrier frequencies. Furthermore, the traditional 4N superposition method uses a square wave reference signal for mixing, which has limited frequency selectivity. When multiple carrier frequencies exist simultaneously, crosstalk may occur between channels, affecting the accuracy of frequency separation.

[0006] Currently, there is a lack of a demodulation method that can efficiently separate multiple carrier frequency components in a single processing cycle while ensuring high orthogonal isolation between channels. Summary of the Invention

[0007] This application provides a method and system for multi-carrier separation in FDM-DAS, which solves the technical problems of existing FDM-DAS, such as the need to demodulate each carrier frequency separately, high computational complexity, and insufficient inter-channel crosstalk suppression.

[0008] The first aspect of this application provides an FDM-DAS multi-carrier separation method, including: By applying different frequency shifts to the continuous light output from the narrow linewidth laser using K acousto-optic modulators, K probe light pulses with different optical frequencies are generated and injected into the sensing fiber. The backscattered light from the sensing fiber coherently mixes with the local oscillator light of the continuous light. Coherent mixing is acquired through a photodetector, and a mixed electrical signal containing K carrier frequency beat frequency components is output. For mixed electrical signals, the orthogonal recursive least squares algorithm is used, with K known normalized carrier frequencies as normalized angular frequencies. At the same time, the amplitude and phase of the beat frequency component of each carrier frequency are extracted. The amplitude at the same spatial location is obtained by averaging the amplitude within a time window. The phase is de-wrapped to obtain the continuous phase. Based on the amplitude and continuous phase at the spatial location, the amplitudes of each carrier frequency beat frequency component are weighted and fused to obtain a robust phase estimate that resists coherent fading. Spatial difference and phase unwrapping are performed on the robust phase estimate to obtain the strain or acoustic signal distributed along the optical fiber.

[0009] Furthermore, the continuous light output from the narrow-linewidth laser is split into K paths by an optical splitter. The k-th path undergoes a frequency shift applied by the k-th acousto-optic modulator, resulting in a modulated optical pulse whose optical frequency is the superposition of the optical frequency output from the narrow-linewidth laser and the frequency shift. Path modulation optical pulse.

[0010] Furthermore, the aforementioned The modulated optical pulses are combined by an optical combiner and injected into the sensing fiber. Each pulse is emitted sequentially in time, with the time interval between adjacent pulses being... satisfy: , in, For the refractive index of the sensing fiber, The length of the sensing fiber. It is the speed of light in a vacuum.

[0011] Furthermore, the mixed electrical signal output by the photodetector is represented as: , in, For the first The spatial location of each carrier frequency Rayleigh backscattering amplitude at that location For the first The normalized angular frequency of each carrier frequency, For frequency shift, Sampling frequency, For the first The spatial location of each carrier frequency The optical phase information carried at the location Additive noise, This represents the total number of carrier frequencies.

[0012] Furthermore, the orthogonal recursive least squares algorithm includes: For each normalized angular frequency, construct a sine reference signal and a cosine reference signal; Initialize the weight vectors, autocorrelation inverse matrix, and adaptive magnitude estimate for the sine and cosine channels; For each normalized angular frequency, recursive least squares updates are performed on both the sine and cosine channels. The outputs of the sine and cosine channels at the same frequency are added together to obtain the complete estimated components of the normalized angular frequency. Summing all the complete estimated components of the normalized angular frequencies yields a combined estimated signal containing all the normalized angular frequency components; Using the combined estimated signal as the target signal, adaptive amplitude estimation is performed on each normalized angular frequency to obtain the sine amplitude and cosine amplitude of each normalized angular frequency. Based on the updated sine and cosine amplitudes of each normalized angular frequency, the amplitude and phase of each carrier frequency beat frequency component are calculated. The amplitude at the same spatial location is obtained by averaging the amplitudes within a time window, and the phase is de-wound to obtain the continuous phase.

[0013] Furthermore, the amplitudes of the beat frequency components of each carrier frequency are weighted and fused, including: For each spatial location, the amplitude squared value of each preset carrier frequency beat frequency component is calculated; the ratio of the amplitude squared value of each carrier frequency beat frequency component to the sum of the amplitude squared values ​​of all carrier frequency beat frequency components is used as the weighting coefficient of the carrier frequency beat frequency component; the weighting coefficient of each carrier frequency beat frequency component is multiplied by the continuous phase value of the corresponding carrier frequency beat frequency component and then summed to obtain the robust phase estimate of the spatial location.

[0014] Furthermore, the robust phase estimate is spatially differentially analyzed and phase unwrapped to obtain the strain or acoustic signal distributed along the fiber, including: Along the spatial dimension of the optical fiber, the robust phase estimates at adjacent positions are differentially analyzed to obtain a spatial phase difference sequence. One-dimensional unwinding is performed on the spatial phase difference sequence to eliminate the 2π phase jump and obtain a continuous spatial phase difference distribution; The unwound continuous spatial phase difference is converted into strain distribution or acoustic signal along the optical fiber according to a preset calibration relationship.

[0015] A second aspect of this application provides an FDM-DAS multi-carrier separation system, comprising: Narrow linewidth lasers are used to emit continuous laser light. An optical splitter is used to split a continuous laser beam into two paths: a local oscillator beam and a signal beam. A multi-channel radio frequency driver is used to generate multiple drive signals of different frequencies; The parallel multi-carrier modulation branch includes K parallel acousto-optic modulators, and the driving terminals of each acousto-optic modulator are respectively connected to different frequency output channels of the multi-channel RF driver; the signal light input terminal of the parallel multi-carrier modulation branch is connected to the signal light output terminal of the optical splitter, and is used to modulate the signal light into probe light pulses with different frequency shifts. An optical combiner includes multiple input terminals that are respectively connected to the output terminals of each acousto-optic modulator, used to combine multiple probe light pulses with different carrier frequencies into one. Erbium-doped fiber amplifiers are used to amplify the power of multi-frequency probe light pulses after beam combining. The optical circulator is connected to the output of the erbium-doped fiber amplifier through the first port, connected to the sensing fiber through the second port, and outputs backscattered light carrying phase information through the third port. Sensing optical fiber is used to transmit probe light pulses and generate backscattered Rayleigh scattering; A mixer fiber coupler is connected to the local oscillator output of the optical splitter via a first input terminal and to the third port of the optical circulator via a second input terminal, for coherent mixing of the local oscillator light and the backscattered light. A photodetector, connected to the output of the mixer fiber coupler, is used to convert the mixed optical signal into a mixed electrical signal containing K carrier frequency beat frequency components. The data acquisition module is used to perform analog-to-digital conversion on the hybrid electrical signal and output a multi-carrier frequency digital signal; The data demodulation module is used to perform single-synchronous demodulation and separation of the multi-carrier digital signal using the orthogonal recursive least squares method, and after weighted fusion with amplitude information, it performs spatial differential and phase unwinding to obtain strain or acoustic signals distributed along the optical fiber.

[0016] Furthermore, the orthogonal recursive least squares algorithm includes: For each normalized angular frequency, construct a sine reference signal and a cosine reference signal; Initialize the weight vectors, autocorrelation inverse matrix, and adaptive magnitude estimate for the sine and cosine channels; For each normalized angular frequency, recursive least squares updates are performed on both the sine and cosine channels. The outputs of the sine and cosine channels at the same frequency are added together to obtain the complete estimated components of the normalized angular frequency. Summing all the complete estimated components of the normalized angular frequencies yields a combined estimated signal containing all the normalized angular frequency components; Using the combined estimated signal as the target signal, adaptive amplitude estimation is performed on each normalized angular frequency to obtain the sine amplitude and cosine amplitude of each normalized angular frequency. Based on the updated sine and cosine amplitudes of each normalized angular frequency, the amplitude and phase of each carrier frequency beat frequency component are calculated. The amplitude at the same spatial location is obtained by averaging the amplitudes within a time window, and the phase is de-wound to obtain the continuous phase.

[0017] Compared with the prior art, the advantages of this application are as follows: This application utilizes the multi-frequency orthogonal separation characteristics of orthogonal recursive least squares to simultaneously extract the amplitude and phase of all carrier frequency beat frequency components in a single process, eliminating the need for demodulation of each carrier frequency separately and improving computational efficiency. Orthogonal recursive least squares separates the beat frequency components based on their orthogonality, offering superior frequency selectivity compared to traditional square wave mixing methods and effectively avoiding crosstalk between frequency channels. Orthogonal recursive least squares naturally obtains amplitude information while extracting the phase of each frequency channel, allowing for direct weighted fusion using this amplitude information without additional amplitude detection steps. Furthermore, the normalized angular frequency of orthogonal recursive least squares is precisely determined by the AOM driving frequency, eliminating frequency uncertainty. Parameters such as the forgetting factor can be adjusted according to signal characteristics to adapt to different application scenarios. Attached Figure Description

[0018] Figure 1 A flowchart illustrating an FDM-DAS multi-carrier separation method provided in this application embodiment; Figure 2 A schematic diagram of the structure of an FDM-DAS multi-carrier separation system provided in this application embodiment; Figure 3 (a) a time-domain plot and (b) a power spectral density plot of the hybrid beat frequency electrical signal provided in the embodiments of this application; Figure 4 The following diagrams show the separation results of the amplitude and phase of the multi-carrier signal provided in the embodiments of this application: (a) is the amplitude diagram, and (b) is the phase diagram. Figure 5The demodulation results of the piezoelectric transducer signal provided by the FDM-DAS multi-carrier frequency separation method in the embodiments of this application are shown in the figure. (a) is the vibration waveform of the driving signal with a driving voltage of 2V and a frequency of 10Hz, and (b) is the vibration waveform of the driving signal with a driving voltage of 2V and a frequency of 30Hz. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0020] like Figure 1 As shown, this application proposes an FDM-DAS multi-carrier separation system. Figure 1 The solid line with an arrow indicates the transmission direction of the optical path or circuit. It includes: a narrow-linewidth laser 1, an optical splitter 2, an acousto-optic modulator 1 3, an acousto-optic modulator 2 4, an optical combiner 5, an erbium-doped fiber amplifier 6, an optical circulator 7, a sensing fiber 1 8, a piezoelectric transducer 9, a sensing fiber 2 10, a mixer fiber coupler 11, a photodetector 12, a data acquisition module 13, a data demodulation module 14, and a multi-channel RF driver 15. The narrow-linewidth laser 1 emits continuous laser light; the optical splitter 2 splits the continuous laser light into a local oscillator beam and a signal beam; the multi-channel RF driver 15 generates multiple drive signals of different frequencies; the parallel multi-carrier modulation branch contains K parallel acousto-optic modulators, each with its drive terminal connected to a different frequency output channel of the multi-channel RF driver; the signal light input terminal of the parallel multi-carrier modulation branch is connected to the signal light output terminal of the optical splitter 2, used to modulate the signal light into probe light pulses with different frequency shifts. The optical combiner 5 includes multiple input terminals that are respectively connected to the output terminals of each acousto-optic modulator, and is used to combine multiple probe light pulses with different carrier frequencies into one. Erbium-doped fiber amplifier 6 is used to amplify the power of the combined multi-frequency probe light pulses; The optical circulator 7 is connected to the output of the erbium-doped fiber amplifier 6 through the first port, connected to the sensing fiber through the second port, and outputs backscattered light carrying phase information through the third port. Sensing optical fiber is used to transmit probe light pulses and generate backscattered Rayleigh scattering; The mixer fiber coupler 11 is connected to the local oscillator output of the optical splitter 2 through the first input terminal and the third port of the optical circulator 7 through the second input terminal, and is used to coherently mix the local oscillator light with the backscattered light. The photodetector 12 is connected to the output end of the mixer fiber coupler 11 and is used to convert the mixed optical signal into a mixed electrical signal containing K carrier frequency beat frequency components. Data acquisition module 13 is used to perform analog-to-digital conversion on the hybrid electrical signal and output a multi-carrier digital signal; The data demodulation module 14 is used to perform single-synchronous demodulation and separation of the multi-carrier digital signal using the orthogonal recursive least squares method, and after weighted fusion with amplitude information, perform spatial differential and phase unwinding to obtain strain or acoustic signals distributed along the optical fiber.

[0021] In the system architecture, the continuous laser emitted by the narrow-linewidth laser 1 is first split into two parts by the optical splitter 2: one part (20%) serves as the local oscillator light, which is directly connected to the mixer fiber coupler 11; the other part (80%) serves as the signal light, which enters the parallel multi-carrier frequency modulation branch. The multi-channel RF driver 15 provides different driving frequencies for the parallel acousto-optic modulators, which in this embodiment are 80MHz and 200MHz respectively. The signal light is modulated into probe light pulses with different frequency shifts by acousto-optic modulators 3 to 4 (the dashed line between acousto-optic modulators 3 and 4 indicates that it can be expanded to K parallel frequency channels). These light pulses with different carrier frequencies are combined by the optical combiner 5 and then amplified by the erbium-doped fiber amplifier 6. The amplified multi-frequency probe light pulses are injected into the sensing link composed of sensing fiber 8, piezoelectric transducer 9, and sensing fiber 10 through the optical circulator 7, wherein the piezoelectric transducer 9 is connected in series between the two fiber segments to simulate the excited acoustic vibration signal. When the probe light pulse propagates in the sensing fiber, it undergoes backscattering Rayleigh. The backscattered light, carrying external acoustic wave phase information, returns along its original path and enters the mixer fiber coupler 11 through the output port of the optical circulator 7. At the mixer fiber coupler 11, the backscattered light carrying multi-carrier frequency signals coherently mixes with the local oscillator light. The mixed optical signal is received by the photodetector 12 and converted into a mixed electrical signal containing K beat frequency components. This mixed electrical signal finally enters the data acquisition module 13 for high-speed analog-to-digital conversion and is then sent to the data demodulation module 14. In the data demodulation module 14, the mixed multi-carrier frequency digital signal is demodulated and separated synchronously in a single operation using the orthogonal recursive least squares method, and weighted fusion is performed in conjunction with amplitude information to achieve high-fidelity acoustic signal demodulation resistant to coherent fading.

[0022] See Figure 2 This application provides an FDM-DAS multi-carrier separation method, including: S101 uses K acousto-optic modulators to apply different frequency shifts to the continuous light output from the narrow linewidth laser, generating K probe light pulses of different optical frequencies, which are then injected into the sensing fiber. S102, the backscattered light from the sensing fiber coherently mixes with the local oscillator light of the continuous light. S103, coherent mixing is acquired by photodetector 12 and a mixed electrical signal containing K carrier frequency beat frequency components is output; S104, for the mixed electrical signal, the orthogonal recursive least squares algorithm is used, with K known normalized carrier frequencies as normalized angular frequencies, and the amplitude and phase of each carrier frequency beat frequency component are extracted at the same time. The amplitude at the same spatial location is obtained by averaging the amplitude within a time window, and the phase is de-wrapped to obtain the continuous phase. S105, based on the amplitude and continuous phase at the spatial location, weighted fusion of the amplitudes of each carrier frequency beat frequency component is performed to obtain a robust phase estimate against coherent fading; S106 performs spatial difference and phase unwrapping on the robust phase estimate to obtain the strain or acoustic signal distributed along the optical fiber.

[0023] In step S101, the continuous light output from the narrow-linewidth laser 1 is split into K paths by the optical splitter 2. The k-th path is frequency-shifted by the k-th acousto-optic modulator, and the optical frequency of the generated modulated optical pulse is the superposition of the optical frequency output from the narrow-linewidth laser 1 and the frequency shift, thus obtaining... Path modulation optical pulse.

[0024] The optical frequency of the generated modulated light pulse is: , in, The optical frequency output by the narrow linewidth laser 1. The frequency shift refers to the driving frequency of the k-th narrow-linewidth laser 1; the K modulated optical pulses are combined by the optical combiner 5 and injected into the sensing fiber. When each pulse is emitted sequentially in time, the time interval between adjacent pulses is... satisfy: , in, The refractive index of the optical fiber. The length of the sensing fiber. It is the speed of light in a vacuum; it ensures that all backscattered light from the previous pulse returns before the next pulse is emitted, thus avoiding spatial aliasing.

[0025] In step S102, the multi-carrier probe light pulses after being bundled by the optical combiner 5 are sequentially amplified by the erbium-doped fiber amplifier 6 and input to the first port and output to the second port of the optical circulator 7, and then injected into the sensing fiber link composed of sensing fiber 1 8, piezoelectric transducer 9 and sensing fiber 2 10.

[0026] When a probe light pulse propagates in a sensing fiber, backscattering occurs due to the microscopic inhomogeneities of the fiber's refractive index. This backscattered light returns along the original path of the fiber, carrying the phase information accumulated along the probe light pulse's propagation path. When external sound waves or vibrations act on the sensing fiber, the fiber length and refractive index are slightly perturbed, causing a change in the phase of the backscattered light. This phase change is linearly related to the intensity of the external perturbation.

[0027] The backscattered light re-enters the second port of the optical circulator 7 and is output from its third port to enter the subsequent mixing stage.

[0028] The other continuous light stream split from optical splitter 2 serves as the local oscillator, maintaining continuous output without undergoing acousto-optic modulation or pulse modulation. This local oscillator is directly connected to the first input of the mixer fiber coupler 11. The local oscillator retains all the coherent characteristics of the original optical frequency of the narrow-linewidth laser 1, and its continuous output ensures stable coherence efficiency when coherently mixed with backscattered light.

[0029] The backscattered light output from the third port of the optical circulator 7 and the local oscillator light output from the optical splitter 2 simultaneously enter the mixer fiber coupler 11. This fiber coupler 11 is typically a 2×2 fiber coupler or a 3dB fiber coupler, achieving power matching and spatial superposition of the two optical signals.

[0030] In step S103, coherent mixing is acquired by photodetector 12, and a mixed electrical signal containing K carrier frequency beat frequency components is output. The optical signal, after coherent mixing by mixing fiber coupler 11, contains K beat frequency components of different carrier frequencies. This mixed optical signal is transmitted to the optical input end of photodetector 12 via optical fiber. To ensure detection efficiency, the output port of mixing fiber coupler 11 and the photosensitive surface of photodetector 12 are directly connected by low-loss optical fiber or by spatial optical coupling.

[0031] The mixed electrical signal output by photodetector 12 is represented as follows: , in, For the first The spatial location of each carrier frequency Rayleigh backscattering amplitude at that location For the first The normalized angular frequency of each carrier frequency, For frequency shift, Sampling frequency, For the first The spatial location of each carrier frequency The optical phase information carried at the location Additive noise, The total number of carrier frequencies, It is a mixed electrical signal. These are the sampling points.

[0032] In step S104, the mixed electrical signal contains K carrier frequency beat frequency components with known center frequencies. Each center frequency is equal to the driving frequency of each acousto-optic modulator at the front end of the system, and these frequencies are known prior to the signal. The demodulation task is to simultaneously extract the amplitude and phase of each carrier frequency beat frequency component from the mixed electrical signal, thereby recovering the external sound wave information corresponding to each sensing channel.

[0033] The orthogonal recursive least squares algorithm used includes: For each normalized angular frequency, construct a sine reference signal and a cosine reference signal, and represent each normalized angular frequency as... Construct a sinusoidal reference signal Sum and cosine reference signal : , ; in, For sampling points; Initialize the weight vectors, autocorrelation inverse matrix, and adaptive amplitude estimate for the sine and cosine channels. For the sine channel, the weight vector of the sine channel... (length is) The inverse autocorrelation matrix of the sinusoidal channel ,in Let the filter order be . For regularization parameters, for An identity matrix of order 1; For the cosine channel, initialize the weight vector of the cosine channel. The inverse autocorrelation matrix of the cosine channel The form and weight vector of the sine channel The inverse autocorrelation matrix of the sinusoidal channel same; Adaptive amplitude estimation for initializing the sinusoidal channel Adaptive amplitude estimation of cosine channel ; For each normalized angular frequency, recursive least squares updates are performed on both the sine and cosine channels. The outputs of the sine and cosine channels at the same frequency are added together to obtain the complete estimated components of the normalized angular frequency. Summing all the complete estimated components of the normalized angular frequencies yields a combined estimated signal containing all normalized angular frequency components; where, for each sampling point... Perform the following recursive update: Sine Channel Update: Constructing input vectors , express The sinusoidal reference signal at the sampling point express The sinusoidal reference signal at the sampling point; Calculate the estimated signal , For input vectors transpose; Calculate the estimation error , It is a mixed electrical signal; Calculate the gain vector ; Update the weight vector of the sine channel. , To estimate the error conjugate, Gain vector transpose; Update the inverse autocorrelation matrix of the sine channel. ; in, Forgetting factor; Cosine channel update: The process is completely symmetrical with the sine channel, using Construct the input vector and update the weight vector of the cosine channel. Autocorrelation inverse matrix of the cosine channel ; Using the combined estimated signal as the target signal, adaptive amplitude estimation is performed on each normalized angular frequency to obtain the sine amplitude and cosine amplitude of each normalized angular frequency. Adaptive amplitude estimation updates are performed for each normalized angular frequency, including: Calculate the sinusoidal channel fitting signal ; for The sine amplitude of the sine channel at the sampling point; Calculate the fitting error ; Update the sine amplitude of the sine channel: ; The iteration step size, for The sine amplitude of the sampling point; Similarly, the cosine channel's cosine amplitude is updated. .

[0034] Based on the updated sine and cosine amplitudes of each normalized angular frequency, the amplitude and phase of each carrier frequency beat frequency component are calculated, and the phase is unwound to obtain a continuous phase. The formula is as follows: , , in, The amplitude of the carrier frequency beat frequency component. For the phase of the carrier frequency beat frequency component, Phase unwrapping is performed to obtain continuous phase. ,right The amplitude at a spatial location is obtained by averaging the amplitudes over a time window at the same spatial location. .

[0035] In step S105, the amplitudes of each carrier frequency beat frequency component are weighted and fused based on the amplitude and continuous phase at the spatial location to obtain a robust phase estimate against coherent fading, including: For each spatial location, the squared amplitude value of each preset frequency channel is calculated; the ratio of the squared amplitude of each carrier frequency beat component at its spatial location to the sum of the squared amplitudes of all carrier frequency beat components at their spatial locations is used as the weighting coefficient of the carrier frequency beat component; the weighting coefficients of each carrier frequency beat component are multiplied by the continuous phase values ​​of the corresponding carrier frequency beat components and then summed to obtain the robust phase estimate of the spatial location. The formula is expressed as: , Using the square of the amplitude as a weight can more effectively suppress the noise contribution of low signal-to-noise ratio channels.

[0036] Unlike traditional methods, this embodiment does not employ frequency-by-frequency filtering, down-conversion, or frequency sweeping. Instead, it utilizes an orthogonal recursive least squares algorithm to treat all K known normalized carrier frequencies as parallel normalized angular frequencies, and synchronously extracts the parameters of each carrier frequency beat frequency component within a unified recursive framework.

[0037] For the k-th normalized angular frequency, the orthogonal recursive least squares algorithm internally generates a pair of mutually orthogonal reference signals: a sine reference signal and a cosine reference signal. The frequencies of both reference signals are equal to the known normalized carrier frequency of that frequency channel. The sine reference signal is used to extract the in-phase component from the carrier frequency beat frequency component, and the cosine reference signal is used to extract the quadrature component.

[0038] For each normalized angular frequency, the orthogonal recursive least squares algorithm maintains two independent recursive least squares filter channels: a sine channel and a cosine channel. Each filter channel internally maintains a set of weight vectors and an inverse autocorrelation matrix. The length of the weight vectors is equal to the filter order, which determines the orthogonal recursive least squares algorithm's ability to track the time-varying characteristics of the signal; the inverse autocorrelation matrix is ​​used to recursively estimate the autocorrelation characteristics of the input signal and is the core of achieving fast convergence.

[0039] At each new sampling point, the orthogonal recursive least squares algorithm performs the following operations simultaneously on all K normalized angular frequencies: For the sine channel with the k-th normalized angular frequency, the orthogonal recursive least squares algorithm takes the sine reference values ​​from the current time and several past times as the input vector, and performs an inner product operation with the current sine channel weight vector to obtain the instantaneous estimated output of the normalized angular frequency. Similarly, the cosine channel uses cosine reference values ​​to obtain its estimated output. The sine channel output and the cosine channel output of the same frequency are added together to form the complete estimated component of the normalized angular frequency at the current sampling point.

[0040] Subsequently, the complete estimated components of all K normalized angular frequencies are summed to obtain the combined estimate of the hybrid electrical signal at the current moment. The difference between this combined estimate and the actual acquired value of the hybrid electrical signal is the estimation error at the current moment. This error is simultaneously used to drive the weight update of all carrier frequency beat frequency components.

[0041] During the weight update process, each normalized angular frequency first calculates a gain vector based on the current autocorrelation inverse matrix, the input vector, and a pre-defined forgetting factor. The gain vector determines the proportion by which the current estimation error corrects the weight vector. Subsequently, the weight vector is updated according to the product of the gain vector and the estimation error. Finally, the autocorrelation inverse matrix is ​​recursively updated based on the forgetting factor, the gain vector, and the input vector, preparing for the gain calculation at the next time step.

[0042] The above recursive least squares update process enables the weight vectors of each normalized angular frequency to converge quickly to the optimal value, thereby making the combined estimate approximate the original hybrid electrical signal with the minimum mean square error.

[0043] The output of the recursive least squares filter, i.e., the combined estimated signal, is further used as the target signal for adaptive amplitude estimation updates. The purpose of adaptive amplitude estimation updates is to decompose the sine and cosine amplitudes of each normalized angular frequency from the combined estimated signal, i.e., the sine and cosine amplitudes of each carrier frequency beat frequency component.

[0044] For each normalized angular frequency, the current sinusoidal amplitude is first multiplied by the sinusoidal reference signal to obtain the sinusoidal fitted signal for that normalized angular frequency. The sinusoidal fitted signals for all normalized angular frequencies are summed to obtain the total fitted signal. The difference between the combined estimated signal and the total fitted signal is the fitting error.

[0045] Subsequently, the sinusoidal amplitude of each normalized angular frequency is updated by multiplying the fitting error by the sinusoidal reference signal and then by a preset iteration step size. The cosine amplitude is updated in a completely symmetrical manner, using a cosine reference signal instead of a sinusoidal reference signal.

[0046] This update process is based on the least mean square criterion, and has a simple structure and low computational cost. Since the input signal updated by the adaptive amplitude estimation has already undergone noise suppression and signal enhancement by the recursive least squares filter of the previous stage, the adaptive amplitude estimation can quickly converge to the true value with low computational cost.

[0047] In step S106, the robust phase estimate is spatially differentially analyzed and phase unwrapped to obtain the strain or acoustic signal distributed along the optical fiber, including: Along the spatial dimension of the optical fiber, a spatial phase difference sequence is obtained by performing differential operations on the robust phase estimates of adjacent positions; that is, the spatial phase difference between adjacent positions is obtained by subtracting the phase value of the previous adjacent position from the phase value of the next position. Repeating this operation for all adjacent positions on the fiber yields a complete spatial phase difference sequence. When external sound waves or vibrations act on a segment of the optical fiber, the phase change of that segment differs significantly from that of adjacent undisturbed segments; spatial differential operations directly extract this difference. Simultaneously, common-mode noise such as laser phase drift and light source frequency jitter exhibits strong correlation between adjacent positions. Therefore, spatial differential operations can significantly improve the signal-to-noise ratio, making weak local strain signals stand out from strong common-mode noise.

[0048] One-dimensional unwrapping is performed on the spatial phase difference sequence to eliminate 2π phase jumps and obtain a continuous spatial phase difference distribution. The phase unwrapping process is as follows: traversing the spatial phase difference sequence point by point along the spatial dimension of the optical fiber, starting from the starting point. During the traversal, the difference between the current point and the previous point is monitored in real time. When the absolute value of this difference exceeds a preset threshold (usually set to π), a phase jump is determined to have occurred. At this time, the phase values ​​of the current point and all subsequent points are added to or subtracted from an integer multiple of 2π to smoothly eliminate the jump. This judgment and correction operation is repeated until the entire spatial phase difference sequence has been processed.

[0049] The unwound continuous spatial phase difference is converted into strain distribution or acoustic signal along the optical fiber according to a preset calibration relationship. This conversion is the final output link of the entire signal processing chain. The principle of strain mapping is based on the strain-phase response characteristics of optical fiber. When an optical fiber is stretched or compressed, its length and refractive index change, causing a corresponding change in the phase of the light wave propagating within it. This change has a definite linear relationship with the strain, and the proportionality coefficient is determined by parameters such as the photoelastic coefficient of the optical fiber, the wavelength of the light wave, and the refractive index of the fiber core. This proportionality coefficient can be obtained through theoretical calculation or experimental calibration. In actual processing, multiplying the unwound spatial phase difference by the preset calibration coefficient yields the strain value at the corresponding location. Arranging the strain values ​​at all locations in spatial order yields the strain curve distributed along the optical fiber.

[0050] Acoustic signal mapping is an important application of strain mapping. When external sound waves act on an optical fiber, they generate dynamic compression and stretching within the fiber, resulting in a rapidly changing strain signal over time. The waveform of this dynamic strain signal directly corresponds to the sound pressure waveform of the sound wave. Therefore, for each spatial location, the sequence of strain values ​​changing over time can be directly output to obtain the sound wave signal detected at that location. By organizing the time-varying sound wave signals from all locations in spatial order, the complete sound field information distributed along the optical fiber can be reconstructed.

[0051] In one example, Frequency shifts are applied using acousto-optic modulator 3 and acousto-optic modulator 4, respectively. and frequency shift The system is configured as follows: Narrow linewidth laser 1 outputs optical frequency... The continuous light is split into two paths by optical splitter 2. The first path is frequency-shifted by acousto-optic modulator 3. The second path applies a frequency shift via the acousto-optic modulator 24. Two modulated optical pulses are sequentially injected into sensing fiber 1 8, piezoelectric transducer 9, and sensing fiber 2 10 under timing control.

[0052] The time-domain representation of the hybrid beat frequency electrical signal output by photodetector 12 is as follows: Figure 3 As shown in (a), the time-domain signal has a stable amplitude over a long time scale, and the beat frequency process is continuous and smooth. Its power spectral density (PSD) is as follows: Figure 3 As shown in (b), the frequency domain has only two clean dominant frequency components, namely and The system exhibits low stray noise and excellent coherent beat frequency quality. The independent coexistence of the two sets of beat frequencies indicates that the beam incident on the photodetector 12 contains two sets of interferometric wavelength pairs.

[0053] The data demodulation module 14 processes the mixed electrical signal using an orthogonal recursive least squares algorithm, taking K known normalized carrier frequencies as normalized angular frequencies, and simultaneously extracting the amplitude and phase of each carrier frequency beat frequency component. For each spatial location, it performs weighted fusion based on the amplitude of each carrier frequency beat frequency component to obtain a robust phase estimate resistant to coherent fading. The robust phase estimate is then subjected to spatial difference and phase unwrapping to obtain the strain or acoustic signal distributed along the optical fiber.

[0054] In one example, the parameters of the orthogonal recursive least squares algorithm are set as follows: forgetting factor. Regularization parameters filter order iteration step size Due to the sampling rate of data acquisition module 13 , , .by and As two normalized angular frequencies and For two different frequency shifts, It is 80MHz. For a frequency range of 200MHz, an orthogonal recursive least squares algorithm is performed on the mixed electrical signal at each spatial location to simultaneously obtain the amplitude of both frequency channels. , and phase , See Figure 4 The separation results of amplitude and phase of multi-carrier signals are shown in the figure. Figure 4 In diagram (a), the amplitude diagram shows that CH1 is the true amplitude at 80 MHz, and the extracted amplitude of CH1 is the extracted amplitude at 80 MHz. CH2 is the true amplitude at 200 MHz, and the extracted amplitude of CH2 is the extracted amplitude at 200 MHz. The amplitudes corresponding to the two frequency shifts after separation match the true values, and there is a certain amplitude difference between the two frequency shifts. Figure 4 (b) is the phase diagram. CH1 is the true phase at 80MHz, and CH1 extraction is the extracted phase at 80MHz. CH2 is the true phase at 200MHz, and CH2 extraction is the extracted phase at 200MHz. It can be seen that the amplitudes corresponding to the two frequency shifts after separation are consistent with the true values. The two carrier frequencies have independent phase dynamic changes without crosstalk or phase confusion.

[0055] For each spatial location Calculate the weighted phase: , At the coherent fading point, the amplitude of the fading channel When the value approaches zero, its weight automatically decreases, thus preventing phase estimation failure. This is a robust phase estimation.

[0056] Robust phase estimation Spatial differential scanning calorimetry is used to eliminate common-mode laser phase noise, followed by phase unwrapping along the slow time axis. This yields strain or acoustic signals distributed along the optical fiber, which here correspond to the vibration waveforms of sinusoidal signals with a driving voltage of 2V and a frequency of 10Hz and a driving voltage of 2V and a frequency of 30Hz, respectively, driven by piezoelectric transducer 9. Figure 5 The diagram shown illustrates the demodulation results of the signal from piezoelectric transducer 9. Figure 5 (a) in the figure shows the vibration waveform of the drive signal with a drive voltage of 2V and a frequency of 10Hz. Figure 5 (b) shows the vibration waveform of the drive signal with a drive voltage of 2V and a frequency of 30Hz. It can be seen that the phase oscillation frequency of the demodulated output corresponds one-to-one with the drive voltage frequency of the piezoelectric transducer 9, and can accurately reproduce the two forced vibration cycles of 10Hz and 30Hz.

[0057] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A multi-carrier separation method for FDM-DAS, characterized in that, include: By applying different frequency shifts to the continuous light output from a narrow-linewidth laser using K acousto-optic modulators, K probe light pulses with different optical frequencies are generated and injected into the sensing fiber. The backscattered light from the sensing fiber coherently mixes with the local oscillator light of the continuous light. Coherent mixing is acquired through a photodetector, and a mixed electrical signal containing K carrier frequency beat frequency components is output. For mixed electrical signals, the orthogonal recursive least squares algorithm is used, with K known normalized carrier frequencies as normalized angular frequencies. At the same time, the amplitude and phase of the beat frequency component of each carrier frequency are extracted. The amplitude at the same spatial location is obtained by averaging the amplitude within a time window. The phase is de-wrapped to obtain the continuous phase. Based on the amplitude and continuous phase at the spatial location, the amplitudes of each carrier frequency beat frequency component are weighted and fused to obtain a robust phase estimate that resists coherent fading. Spatial difference and phase unwrapping are performed on the robust phase estimate to obtain the strain or acoustic signal distributed along the optical fiber.

2. The FDM-DAS multi-carrier separation method according to claim 1, characterized in that, The continuous light output from the narrow-linewidth laser is split into K paths by an optical splitter. The k-th path undergoes a frequency shift applied by the k-th acousto-optic modulator. The optical frequency of the resulting modulated optical pulse is the superposition of the optical frequency output from the narrow-linewidth laser and the frequency shift. Path modulation optical pulse.

3. The FDM-DAS multi-carrier separation method according to claim 2, characterized in that, The The modulated optical pulses are combined by an optical combiner and injected into the sensing fiber. Each pulse is emitted sequentially in time, with the time interval between adjacent pulses being... satisfy: , in, For the refractive index of the sensing fiber, The length of the sensing fiber. It is the speed of light in a vacuum.

4. The FDM-DAS multi-carrier separation method according to claim 1, characterized in that, The mixed electrical signal output by the photodetector is represented as follows: ， in, For the first The spatial location of each carrier frequency Rayleigh backscattering amplitude at that location For the first The normalized angular frequency of each carrier frequency, For frequency shift, Sampling frequency, For the first The spatial location of each carrier frequency The optical phase information carried at the location Additive noise, This represents the total number of carrier frequencies.

5. The FDM-DAS multi-carrier separation method according to claim 1, characterized in that, Orthogonal recursive least squares algorithms include: For each normalized angular frequency, construct a sine reference signal and a cosine reference signal; Initialize the weight vectors, autocorrelation inverse matrix, and adaptive magnitude estimate for the sine and cosine channels; For each normalized angular frequency, recursive least squares updates are performed on both the sine and cosine channels. The outputs of the sine and cosine channels at the same frequency are added together to obtain the complete estimated components of the normalized angular frequency. The complete estimated components of all normalized angular frequencies are summed to obtain a combined estimated signal containing all normalized angular frequency components. Using the combined estimated signal as the target signal, adaptive amplitude estimation is performed on each normalized angular frequency to obtain the sine amplitude and cosine amplitude of each normalized angular frequency. Based on the updated sine and cosine amplitudes of each normalized angular frequency, the amplitude and phase of each carrier frequency beat frequency component are calculated. The amplitude at the same spatial location is obtained by averaging the amplitudes within a time window, and the phase is de-wound to obtain the continuous phase.

6. The FDM-DAS multi-carrier separation method according to claim 1, characterized in that, The amplitudes of the beat frequency components of each carrier frequency are weighted and fused, including: For each spatial location, the amplitude squared value of each preset carrier frequency beat frequency component is calculated; the ratio of the amplitude squared value of each carrier frequency beat frequency component to the sum of the amplitude squared values ​​of all carrier frequency beat frequency components is used as the weighting coefficient of the carrier frequency beat frequency component; the weighting coefficient of each carrier frequency beat frequency component is multiplied by the continuous phase value of the corresponding carrier frequency beat frequency component and then summed to obtain the robust phase estimate of the spatial location.

7. The FDM-DAS multi-carrier separation method according to claim 1, characterized in that, Spatial difference and phase unwrapping are performed on the robust phase estimate to obtain strain or acoustic signals distributed along the optical fiber, including: Along the spatial dimension of the optical fiber, the robust phase estimates at adjacent positions are differentially analyzed to obtain a spatial phase difference sequence. One-dimensional unwinding is performed on the spatial phase difference sequence to eliminate the 2π phase jump and obtain a continuous spatial phase difference distribution; The unwound continuous spatial phase difference is converted into strain distribution or acoustic signal along the optical fiber according to a preset calibration relationship.

8. An FDM-DAS multi-carrier separation system, characterized in that, include: Narrow linewidth lasers are used to emit continuous laser light. An optical splitter is used to split a continuous laser beam into two paths: a local oscillator beam and a signal beam. A multi-channel radio frequency driver is used to generate multiple drive signals of different frequencies; The parallel multi-carrier modulation branch includes K parallel acousto-optic modulators, and the driving terminals of each acousto-optic modulator are respectively connected to different frequency output channels of the multi-channel RF driver; the signal light input terminal of the parallel multi-carrier modulation branch is connected to the signal light output terminal of the optical splitter, and is used to modulate the signal light into probe light pulses with different frequency shifts. An optical combiner includes multiple input terminals that are respectively connected to the output terminals of each acousto-optic modulator, used to combine multiple probe light pulses with different carrier frequencies into one. Erbium-doped fiber amplifiers are used to amplify the power of multi-frequency probe light pulses after beam combining. The optical circulator is connected to the output of the erbium-doped fiber amplifier through the first port, connected to the sensing fiber through the second port, and outputs backscattered light carrying phase information through the third port. Sensing optical fiber is used to transmit probe light pulses and generate backscattered Rayleigh scattering; A mixer fiber coupler is connected to the local oscillator output of the optical splitter via a first input terminal and to the third port of the optical circulator via a second input terminal, for coherent mixing of the local oscillator light and the backscattered light. A photodetector, connected to the output of the mixer fiber coupler, is used to convert the mixed optical signal into a mixed electrical signal containing K carrier frequency beat frequency components. The data acquisition module is used to perform analog-to-digital conversion on the hybrid electrical signal and output a multi-carrier frequency digital signal; The data demodulation module is used to perform single-synchronous demodulation and separation of the multi-carrier digital signal using the orthogonal recursive least squares method, and after weighted fusion with amplitude information, it performs spatial differential and phase unwinding to obtain strain or acoustic signals distributed along the optical fiber.

9. An FDM-DAS multi-carrier separation system according to claim 8, characterized in that, Orthogonal recursive least squares algorithms include: For each normalized angular frequency, construct a sine reference signal and a cosine reference signal; Initialize the weight vectors, autocorrelation inverse matrix, and adaptive magnitude estimate for the sine and cosine channels; For each normalized angular frequency, recursive least squares updates are performed on both the sine and cosine channels. The outputs of the sine and cosine channels at the same frequency are added together to obtain the complete estimated components of the normalized angular frequency. Summing all the complete estimated components of the normalized angular frequencies yields a combined estimated signal containing all the normalized angular frequency components; Using the combined estimated signal as the target signal, adaptive amplitude estimation is performed on each normalized angular frequency to obtain the sine amplitude and cosine amplitude of each normalized angular frequency. Based on the updated sine and cosine amplitudes of each normalized angular frequency, the amplitude and phase of each carrier frequency beat frequency component are calculated. The amplitude at the same spatial location is obtained by averaging the amplitudes within a time window, and the phase is de-wound to obtain the continuous phase.

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