Underground space optical cable high-fidelity sound restoration method based on DAS system
By establishing a spatial distribution mapping relationship for optical cables in the DAS system and using a safety helmet to enhance vibration response, high-fidelity acoustic signal restoration of optical cables in underground spaces was achieved, solving the problem of poor acoustic coupling of optical cables. This method is suitable for long-distance, large-scale monitoring and rescue applications.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV
- Filing Date
- 2023-09-06
- Publication Date
- 2026-06-23
AI Technical Summary
Existing DAS systems suffer from poor acoustic coupling of optical cables in underground spaces, making it difficult to detect low-energy human voice signals and thus unable to reproduce high-fidelity audio signals.
By establishing a spatial distribution mapping relationship for optical cables in a quiet environment, signal superposition is achieved using the high correlation of multiple sensor nodes to filter out background noise, and the optical cables are raised using a safety helmet to enhance vibration response, thus realizing high-fidelity reproduction of sound signals.
It achieves high-fidelity audio signal restoration of optical cables in underground spaces, and is suitable for long-distance and wide-area monitoring scenarios, especially for rapid rescue in mining accidents and geological disasters.
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Figure CN117167088B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of signal processing technology, and specifically relates to a high-fidelity sound restoration method for underground optical cables based on a DAS system. Background Technology
[0002] Distributed optical fiber acoustic sensing systems (DAS systems) can monitor the sound field distribution along the sensing fiber at one end, offering advantages such as high sensitivity, wide response bandwidth, electromagnetic interference resistance, long distance, large range, and fully distributed monitoring. In underground spaces, DAS systems can not only monitor for disasters in real time but also transmit critical information easily and promptly. Their electromagnetic interference resistance ensures high reliability in harsh environments, sufficient to meet the information transmission needs of sudden disasters. However, the existing optical cables deployed in underground spaces that DAS systems utilize often have multi-layered composite sheathing materials, resulting in poor direct acoustic coupling between the internal fibers and the external environment. They are often only sensitive to high-energy impact signals and not very sensitive to low-energy human voice signals. Therefore, to achieve integrated applications of disaster alarm, trapped personnel location, and sound signal transmission, a high-fidelity sound restoration technology based on DAS systems for underground optical cables is urgently needed. Summary of the Invention
[0003] Technical problem solved: This invention discloses a high-fidelity sound restoration method for underground optical cables based on a DAS system. It can achieve rapid positioning based on the spatial distribution mapping relationship of optical cables. At the same time, after filtering out background noise from the collected signals, the signals are linearly superimposed by utilizing the high correlation of signals from multiple spatial sensing nodes near the positioning location to suppress additive random noise and achieve high-fidelity restoration of the sound signal.
[0004] Technical solution:
[0005] A method for high-fidelity sound restoration of optical cables in underground spaces based on a DAS system, comprising the following steps:
[0006] S1, connect the optical cable to the distributed optical fiber sound field sensing system at one end. The optical cable serves as a distributed optical fiber microphone sensor, and the distributed optical fiber sound field sensing system serves as a data acquisition and demodulation device for the distributed optical fiber microphone sensor.
[0007] S2, continuously collect data in a quiet environment and statistically analyze the energy distribution of background noise;
[0008] S3, collect data on the optical cable, mark the spatial position of the optical cable by manually tapping it, and establish the spatial distribution mapping relationship of the optical cable;
[0009] S4, demodulate the real-time signal collected by the optical cable, identify whether it contains energy impact signals generated by the impact of the raised optical cable, and if so, locate the abnormal energy distribution location in the energy impact signal and obtain the location point.
[0010] S5. Continuously analyze the time domain signal of the positioning point, filter out low frequency interference signals, and perform waveform similarity evaluation analysis on multiple adjacent points of the positioning point to identify whether there are phase abnormal signals. If there are, remove the phase abnormal signals and proceed to step S6; otherwise, proceed directly to step S6.
[0011] S6, the acoustic signals of multiple equivalent sensing nodes adjacent to the positioning point are superimposed and averaged to suppress additive noise, and then the acoustic signals are restored.
[0012] Furthermore, in step S3, the distance between two adjacent calibration points is greater than a spatial resolution.
[0013] Furthermore, in step S4, the elevated optical cable is subjected to vibration from the vibration source. Forced vibration is generated under the excitation of [something]. A string vibration model under one-end excitation is constructed, and the vibration solution of the string is obtained. Represented as:
[0014]
[0015]
[0016] in, The amplitude of the vibration source is represented. It is the angular frequency of the vibration source. It is the location where the vibration is applied. It is an inherent coefficient determined by the tension and linear density of the string. It is the natural frequency of the free vibration of the string. Take a positive integer. Represents the position of string vibration. Represents the moment of string vibration;
[0017] In the string vibration model, the steady-state frequency of forced vibration is equal to the excitation source frequency, and the dominant frequency of the response is... coefficient With endpoints near And increase, Near the point, the amplitude of the string vibration response is the largest.
[0018] Furthermore, in step S4, an object with a cavity structure is used to elevate the optical cable.
[0019] Furthermore, in step S4, a safety helmet is used to elevate the optical cable.
[0020] Furthermore, the sound pressure experienced by the safety helmet in the sound field For the incident wave sound field Scattered wave sound field External radiated sound field and internal radiated sound field The sum:
[0021]
[0022] Sound pressure Substituting this into the formula for the work done by an external force, we get:
[0023]
[0024] in, This represents the work done by sound pressure on the helmet. Represents the spherical amplitude distribution function. Represents the surface area of a sphere. It is the angle between the position vector of a point on the sphere in spherical coordinates and the z-axis, also known as the polar angle. This indicates the maximum score, determined by the shape of the helmet.
[0025] Furthermore, in step S6, the process of superimposing and averaging the acoustic signals of multiple equivalent sensing nodes adjacent to the positioning point to suppress additive noise, and then restoring the acoustic signals, includes the following steps:
[0026] The sound signal generated by any vibration source in space can be equivalently represented as a signal composed of m frequency components superimposed. The sound signal generated by the vibration source at time t... Represented as:
[0027]
[0028] in Let be the amplitude of the i-th frequency component. Let be the angular frequency of the i-th frequency component. Let i be the phase of the i-th frequency component. The acoustic signal propagating to the nth optical fiber equivalent sensing node Represented as:
[0029]
[0030] in It is an amplitude attenuation factor that takes into account both the loss during the propagation of the acoustic signal and the loss during the coupling process of the optical fiber, and its value is between 0 and 1. The propagation time from the sound source to the nth equivalent sensing node is expressed as:
[0031]
[0032] in It is the average propagation time from the sound source to the optical fiber sensing section. It is the time delay of the nth equivalent sensing node;
[0033] In actual acoustic wave detection, the data collected by the nth equivalent sensing node It is a sound wave signal With random noise signals Superposition:
[0034] ;
[0035] Time-shifting the data collected by the nth equivalent sensor node yields:
[0036] ;
[0037] For the time-shifted corrected signal After directly superimposing the values and taking the average, we get:
[0038]
[0039] in Represents the equivalent sound wave signal. Represents the equivalent noise signal. That is, the signal obtained by superimposing and averaging.
[0040] Furthermore, the improvement in signal-to-noise ratio for:
[0041]
[0042] in yes Amplitude attenuation factor of each equivalent sensing node The average value, The signal after space gain The signal-to-noise ratio, It is the signal-to-noise ratio of the signal collected by the nth equivalent sensing node.
[0043] Beneficial effects:
[0044] First, the high-fidelity sound restoration method for underground optical cables based on a DAS system of the present invention directly connects a distributed fiber optic acoustic sensing system to the underground optical cable. Before system installation, the optical cable's spatial location is calibrated using methods such as tapping, establishing a spatial distribution mapping relationship and statistically analyzing the background noise energy distribution. During system operation, on-site personnel use safety helmets to suspend the sensing optical cable in mid-air. After continuous tapping of the cable, audio disturbances are applied. The DAS system at the terminal continuously collects and processes the data, identifying the impact signal of the tapping energy and achieving rapid positioning based on the spatial distribution mapping relationship of the optical cable. After filtering out background noise from the collected signals, the signals are linearly superimposed using the high correlation of signals from multiple spatial sensing nodes near the positioning location to suppress additive random noise, achieving high-fidelity restoration of the sound signal.
[0045] Secondly, the high-fidelity sound restoration method for underground optical cables based on the DAS system of the present invention is applicable to long-distance, large-scale, and multi-point monitoring application scenarios, and is especially suitable for rapid rescue work when mining accidents, geological disasters, and underground space construction accidents occur. Attached Figure Description
[0046] Figure 1 This is a flowchart of the high-fidelity sound restoration method for underground optical cables based on a DAS system, according to an embodiment of the present invention.
[0047] Figure 2 This is a schematic diagram of a high-fidelity sound restoration method for underground optical cables based on a DAS system, according to an embodiment of the present invention.
[0048] Figure 3 This is a schematic diagram of optical cable sensitization according to an embodiment of the present invention, which describes a high-fidelity sound restoration method for underground optical cables based on a DAS system.
[0049] Figure 4 This is a schematic diagram of the time-domain signal linear superposition effect of a high-fidelity sound restoration method for underground optical cables based on a DAS system, according to an embodiment of the present invention.
[0050] Figure 5 This is a schematic diagram illustrating the signal-to-noise ratio improvement result of a high-fidelity sound restoration method for underground optical cables based on a DAS system according to an embodiment of the present invention.
[0051] Figure 6 This is a schematic diagram illustrating the sound restoration effect of helmet-mounted optical cable sensitization enhancement in a high-fidelity sound restoration method for underground optical cables based on a DAS system, according to an embodiment of the present invention. Detailed Implementation
[0052] The following embodiments are provided to enable those skilled in the art to more fully understand the present invention, but do not limit the invention in any way.
[0053] This invention discloses a high-fidelity sound restoration method for underground optical cables based on a DAS system. The high-fidelity sound restoration method for underground optical cables includes the following steps:
[0054] S1, connect the optical cable to the distributed optical fiber sound field sensing system at one end. The optical cable serves as a distributed optical fiber microphone sensor, and the distributed optical fiber sound field sensing system serves as a data acquisition and demodulation device for the distributed optical fiber microphone sensor.
[0055] S2, continuously collect data in a quiet environment and statistically analyze the energy distribution of background noise;
[0056] S3, collect data on the optical cable, mark the spatial position of the optical cable by manually tapping it, and establish the spatial distribution mapping relationship of the optical cable;
[0057] S4, demodulate the real-time signal collected by the optical cable, identify whether it contains energy impact signals generated by the impact of the raised optical cable, and if so, locate the abnormal energy distribution location in the energy impact signal and obtain the location point.
[0058] S5. Continuously analyze the time domain signal of the positioning point, filter out low frequency interference signals, and perform waveform similarity evaluation analysis on multiple adjacent points of the positioning point to identify whether there are phase abnormal signals. If there are, remove the phase abnormal signals and proceed to step S6; otherwise, proceed directly to step S6.
[0059] S6, the acoustic signals of multiple equivalent sensing nodes adjacent to the positioning point are superimposed and averaged to suppress additive noise, and then the acoustic signals are restored.
[0060] See Figure 1 The high-fidelity sound restoration method for underground optical cables specifically includes:
[0061] S1, during the system setup phase, existing optical cables in the underground space are connected to the DAS system at one end. These optical cables act as distributed fiber optic microphone sensors throughout the underground space, while the DAS system functions as the data acquisition and demodulation device for these distributed fiber optic microphones, operating in a data acquisition and demodulation room above ground. The DAS system, installed in the data acquisition room, is unaffected by external disturbances. The optical cables used in this invention can be ordinary communication optical cables, achieving high-sensitivity detection of acoustic signals without the need for sensitization treatment.
[0062] S2, during the system setup phase, continuously collect data from the optical cable in a quiet environment, demodulate the collected signals to obtain background noise, analyze the spectral information of the background noise, and statistically analyze its noise distribution.
[0063] S3. Using spatial resolution as the interval, the entire optical cable is tapped segment by segment, and the actual tapping positions are recorded. The DAS system collects signals throughout the process, locates the tapping signals, and establishes a one-to-one spatial distribution mapping relationship between the actual tapping positions and the vibration signal points calibrated by the DAS system. Preferably, when calibrating the spatial positions, there should be as many calibration points as possible, and the distance between two adjacent calibration points should be as small as possible, provided it is greater than one spatial resolution.
[0064] S4. During the accident, trapped personnel in the underground space elevate the optical cable using their safety helmets to form a sensing element, continuously striking the elevated position for a period of time. The optical cable, suspended and taut under the helmet's elevation, can be considered a string, suitable for a string vibration model under one-end excitation. The vibration amplitude of the optical cable is greatest near the helmet's elevation point. On one hand, the amplitude of the forced vibration of the optical cable is increased; on the other hand, when the suspended optical cable is long, the selectable spatial gain area is also larger.
[0065] In practice, trapped personnel can select the longest possible section of fiber optic cable in the trapped area, stretch it taut against the ground, and secure both ends. Then, insert a safety helmet into the gap between the cable and the ground. This creates two effects on the cable: the lateral shear force of the helmet causes longitudinal tension, effectively "tautling" the cable and generating longitudinal stress; and the cable, positioned on top of the helmet and separated from the ground, creates a suspended section. After this simple procedure, the cable's mechanical properties can be simplified to a string model. Compared to being placed on the ground, the damping of forced vibration is significantly reduced, thus significantly improving its sensitivity to vibration.
[0066] Specifically, by elevating the optical cable, leaving the two sides of the elevation point suspended, the optical cable, when disturbed, undergoes forced vibration under the excitation of the vibration source. This can be simplified as a string vibration model under one-end excitation: the endpoint of the string... The incentive for the position Ignoring other external forces and initial vibration, the vibration solution of the string is... It can be represented as:
[0067] .
[0068]
[0069] in, The amplitude of the vibration source is represented. It is the angular frequency of the vibration source. It is the location where the vibration is applied. It is an inherent coefficient determined by the tension and linear density of the string. It is the natural frequency of the free vibration of the string. Take natural numbers, Represents the position of string vibration. Represents the moment of string vibration.
[0070] In the string vibration model, the steady-state frequency of forced vibration is equal to the excitation source frequency, and the dominant frequency of the response is... The coefficient is With endpoints near The increase indicates that... Near the point, the amplitude of the string vibration response is the largest, that is, the forced vibration amplitude of the optical cable is the largest and the phase change is the most obvious near the raised position.
[0071] When safety is ensured, items with hollow structures, such as helmets, should be preferred for elevating optical cables. The helmet receives sound wave energy in the sound field, generating forced vibrations at the same frequency as the sound field. This vibration then acts as the excitation source for elevating the optical cable, transmitting the vibrations to it. A safety helmet can be approximated as a spherical shell in the sound field, and the sound pressure it experiences is the incident wave sound field. Scattered wave sound field External radiated sound field Internal radiated sound field The sum, that is:
[0072] .
[0073] Substituting sound pressure as an external force into the formula for the work done by an external force, we get:
[0074]
[0075] in, This represents the work done by sound pressure on the helmet. Represents the spherical amplitude distribution function. Represents the surface area of a sphere. It is the angle between the position vector of a point on the sphere in spherical coordinates and the z-axis, also known as the polar angle. This indicates the maximum score, determined by the shape of the helmet.
[0076] The helmet's surface is hemispherical. Due to its larger surface area exposed to the sound field, the hemispherical surface receives significantly more sound wave energy than the optical cable itself of the same size. Therefore, it has a larger response amplitude to the sound field, resulting in greater vibrational excitation of the optical cable by the helmet. intensity The larger size increases the disturbance energy acting on the optical cable, further improving the system's sensitivity.
[0077] S5. After continuously striking the elevated fiber optic cable for a period of time, the trapped personnel shouted to the elevated cable and helmet. The helmet's hemispherical surface, with its larger exposed surface area in the sound field, receives significantly more sound wave energy than the fiber optic cable itself over the same length, resulting in a larger response amplitude to sound wave excitation. After being excited by the sound waves, the helmet, upon reaching a near-steady state, generates a vibration response with the same frequency as the sound waves, acting as a new excitation source and transmitting the vibration to the fiber optic cable. Because the helmet's vibration amplitude is much greater than the fiber optic cable's vibration response amplitude under sound wave excitation, the helmet is the primary vibration source for the fiber optic cable. Compared to the situation without a helmet, the helmet's excitation of the fiber optic cable... With larger amplitude Therefore, the vibration response amplitude of optical cables is larger and the sensitivity is higher. When shouting, people should try to get as close to the helmet as possible to maximize the sound wave energy received by the helmet.
[0078] S6 demodulates the signals collected by the equipment. By analyzing the energy distribution of the demodulated signal, if a significantly higher energy signal appears compared with the energy distribution of the quiet environment, it is determined that an accident or disaster has occurred and an alarm is issued. By identifying the energy impact signal generated by the impact, the location of the trapped personnel is quickly located by using the spatial distribution mapping relationship of the optical cable.
[0079] S7 continuously analyzes the time-domain signals of the positioning point and its nearby sensor nodes. After filtering out low-frequency interference signals, it performs waveform similarity evaluation analysis on the time-domain signals of multiple adjacent points of the positioning point to determine whether there are any phase abnormal signals.
[0080] S8. If a phase anomaly signal exists, it is discarded. Data points with normal phase are retained for subsequent stacking and averaging, while phase anomaly points are not included in the stacking and averaging process. Figure 4 Figure (a) shows ten sinusoidal time-domain signals from a given location point and nine adjacent points. After removing outliers, these signals are directly linearly superimposed. The resulting sinusoidal signal is obtained by... Figure 4 Figure (b) shows that by increasing the number of superimposed signals, the signal-to-noise ratio of the superimposed signal can be improved.
[0081] S9, after removing phase abnormal signals, performs superposition and average suppression of additive noise on multiple adjacent points at the positioning point to improve the signal-to-noise ratio, thereby achieving high-fidelity restoration of the sound signal.
[0082] The signal-to-noise ratio is improved by superimposing and averaging signals from multiple adjacent points at the positioning point to suppress additive noise. ,in yes Amplitude attenuation factor of each equivalent sensing node The average value. The number of equivalent sensing nodes participating in the superimposed average. The larger the value, the greater the improvement in signal-to-noise ratio after spatial gain processing. The specific principle is as follows:
[0083] The acoustic signal generated by a vibration source in space can actually be equivalent to a signal composed of multiple frequency components superimposed on each other. Therefore, the acoustic signal generated by the vibration source at time t can be expressed as follows:
[0084]
[0085] in The amplitude of each frequency component, Angular frequency, If the phase is given, then the acoustic signal propagating to the equivalent sensing node of the optical cable can be represented as:
[0086]
[0087] in It is an amplitude attenuation factor that takes into account both the loss during the propagation of the acoustic signal and the loss during the coupling process of the optical fiber, and its value is between 0 and 1. It is the propagation time from the sound source to the nth equivalent sensing node, which can be further expressed as:
[0088]
[0089] in It is the average propagation time from the sound source to the optical fiber sensing section. This is the time delay of the nth equivalent sensing node. Generally, when the sensing area is within a sufficiently small spatial range, the time delay between equivalent sensing nodes is... It can be ignored.
[0090] In actual acoustic wave detection, the data collected by the nth equivalent sensing node It is a sound wave signal With random noise signals Superposition:
[0091]
[0092] According to the corresponding Time-shifting the above signal, we get:
[0093]
[0094] For the time-shifted corrected signal After direct superposition, take the average:
[0095]
[0096] in Represents the equivalent sound wave signal. Represents the equivalent noise signal. That is, the signal obtained after superposition and averaging. The superposition process described above is the spatial gain process.
[0097] The signal-to-noise ratio (SNR) is typically defined as the ratio of signal strength variance to noise strength variance. Therefore, before spatial gain, the SNR of the signals acquired by each equivalent sensing node is:
[0098]
[0099] in It is the variance of the sound wave signal from the sound source. It is the variance of the random noise signal of the nth equivalent sensing node. It is generally considered that the random noise signals of different equivalent sensing nodes... They are independent of each other. Therefore, the signal after spatial gain... The signal-to-noise ratio can be expressed as:
[0100]
[0101]
[0102]
[0103] Assuming that the noise signals have the same noise energy, i.e. , Then, the signal-to-noise ratio is improved after spatial gain:
[0104]
[0105] Superimposing multiple signals The improvement in signal-to-noise ratio ,in yes Amplitude attenuation factor of each equivalent sensing node The average value. From the above formula, it can be seen that the equivalent sensing node... The larger the value, the greater the improvement in signal-to-noise ratio after spatial gain processing. Therefore, in subsequent signal processing, averaging the signals from N adjacent sensing nodes after removing phase anomalous signals can suppress additive noise and improve the signal-to-noise ratio. Figure 5 This demonstrates that as the number of superimposed signals increases, the signal-to-noise ratio of the superimposed signal gradually increases.
[0106] After the optical cable forms an acoustic enhancement structure with the safety helmet, according to the model of excited string vibration described above, the vibration response of the optical cable near the helmet is the greatest, and this section of the optical cable experiences the most significant acoustic enhancement effect. The effect of raising the optical cable in the helmet to achieve acoustic enhancement is as follows: Figure 6As shown, during actual testing, the speaker loudly shouted the numbers 1-10 and "There's someone here" over the fiber optic cable. The spectrogram of the reconstructed audio shows that the speaker's voice was more clearly reproduced over the cable with the helmet raised. Furthermore, because the current DAS system uses a sliding phase detection algorithm for signal demodulation in space, the signals from the sensor nodes within this section of the fiber optic cable are highly correlated. Therefore, averaging the demodulated signals from the sensor nodes within this section of the cable can suppress additive random noise. The signal-to-noise ratio improvement of the reconstructed sound signal obtained using this spatial gain algorithm is limited by the number of signals in the linearly superimposed average. Therefore, the longer the fiber optic cable with the gain range, and the more sensor nodes within this range for a given spatial resolution, the higher the upper limit of the spatial gain effect.
[0107] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.
Claims
1. A method for high-fidelity sound restoration of optical cables in underground spaces based on a DAS system, characterized in that, The method for high-fidelity sound restoration of optical cables in underground spaces includes the following steps: S1, connect the optical cable to the distributed optical fiber sound field sensing system at one end. The optical cable serves as a distributed optical fiber microphone sensor, and the distributed optical fiber sound field sensing system serves as a data acquisition and demodulation device for the distributed optical fiber microphone sensor. S2, continuously collect data in a quiet environment and statistically analyze the energy distribution of background noise; S3, collect data on the optical cable, mark the spatial position of the optical cable by manually tapping it, and establish the spatial distribution mapping relationship of the optical cable; S4, demodulate the real-time signal collected by the optical cable, use an object with a cavity structure to elevate the optical cable, identify whether it contains an energy impact signal generated by the impact of the elevated optical cable being struck, if it does, locate the abnormal energy distribution location in the energy impact signal and obtain the location point. S5. Continuously analyze the time domain signal of the positioning point, filter out low frequency interference signals, and perform waveform similarity evaluation analysis on multiple adjacent points of the positioning point to identify whether there are phase abnormal signals. If there are, remove the phase abnormal signals and proceed to step S6; otherwise, proceed directly to step S6. S6, the acoustic signals of multiple equivalent sensing nodes adjacent to the positioning point are superimposed and averaged to suppress additive noise, and then the acoustic signals are restored. In step S3, the distance between two adjacent calibration points is greater than one spatial resolution. In step S4, the elevated optical cable is subjected to vibration from the vibration source. Forced vibration is generated under the excitation of [something]. A string vibration model under one-end excitation is constructed, and the vibration solution of the string is obtained. Represented as: ; ; in, The amplitude of the vibration source is represented. It is the angular frequency of the vibration source. It is the location where the vibration is applied. It is an inherent coefficient determined by the tension and linear density of the string. It is the natural frequency of the free vibration of the string. Take a positive integer. Represents the position of string vibration. Represents the moment of string vibration; In the string vibration model, the steady-state frequency of forced vibration is equal to the excitation source frequency, and the dominant frequency of the response is... coefficient With endpoints near And increase, Near the point, the amplitude of the string vibration response is the largest.
2. The method for high-fidelity sound restoration of underground optical cables based on a DAS system according to claim 1, characterized in that, In step S4, a safety helmet is used to elevate the optical cable.
3. The method for high-fidelity sound restoration of underground optical cables based on a DAS system according to claim 2, characterized in that, Sound pressure on a safety helmet in a sound field For the incident wave sound field Scattered wave sound field External radiated sound field and internal radiated sound field The sum: ; Sound pressure Substituting this into the formula for the work done by an external force, we get: ; in, This represents the work done by sound pressure on the helmet. Represents the spherical amplitude distribution function. Represents the surface area of a sphere. It is the angle between the position vector of a point on the sphere in spherical coordinates and the z-axis, also known as the polar angle. This indicates the maximum score, determined by the shape of the helmet.
4. The method for high-fidelity sound restoration of underground optical cables based on a DAS system according to claim 1, characterized in that, Step S6, which involves superimposing and averaging the acoustic signals of multiple equivalent sensing nodes adjacent to the positioning point to suppress additive noise, and then restoring the acoustic signals, includes the following steps: The sound signal generated by any vibration source in space can be equivalently represented as a signal composed of m frequency components superimposed. The sound signal generated by the vibration source at time t... Represented as: ; in Let be the amplitude of the i-th frequency component. Let be the angular frequency of the i-th frequency component. Let i be the phase of the i-th frequency component. The acoustic signal propagating to the nth optical fiber equivalent sensing node Represented as: ; in It is an amplitude attenuation factor that takes into account both the loss during the propagation of the acoustic signal and the loss during the coupling process of the optical fiber, and its value is between 0 and 1. It is the propagation time from the sound source to the nth equivalent sensing node, expressed as: ; in It is the average propagation time from the sound source to the optical fiber sensing section. It is the time delay of the nth equivalent sensing node; In actual acoustic wave detection, the data collected by the nth equivalent sensing node It is a sound wave signal With random noise signals Superposition: ; Time-shifting the data collected by the nth equivalent sensor node yields: ; For the time-shifted corrected signal After directly superimposing the values and taking the average, we get: ; in, Represents equivalent sound wave signal , Represents the equivalent noise signal. , That is, the signal obtained by superimposing and averaging.
5. The method for high-fidelity sound restoration of underground optical cables based on a DAS system according to claim 4, characterized in that, Improvement in signal-to-noise ratio for: ; in ,yes Amplitude attenuation factor of each equivalent sensing node The average value, The signal after space gain signal-to-noise ratio, It is the signal-to-noise ratio of the signal collected by the nth equivalent sensing node.