Vibration Interference Decoupling Method for Acoustic Sensors Based on Triaxial Structure
By employing a decoupling method for triaxial acoustic sensors, signals in orthogonal directions are simultaneously acquired and processed. Cross-power spectral density and coherence function are calculated to extract pure acoustic signals. This solves the signal distortion problem caused by vibration interference in complex environments, achieving efficient signal separation and improved accuracy.
Patent Information
- Application Number
- CN202610437019.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-03
- Publication Date
- 2026-06-30
AI Technical Summary
Existing acoustic sensors suffer from signal distortion due to vibration interference in complex environments, which reduces detection accuracy and reliability. Existing methods also suffer from problems such as large size, high cost, high system complexity, or unstable compensation effect.
A triaxial acoustic sensor is used to synchronously acquire output signals in orthogonal directions. By calculating the cross power spectral density and coherence function, setting a weighting function, the frequency domain components of the pure acoustic signal are extracted, and an inverse Fourier transform is performed to obtain the decoupled acoustic signal.
It effectively separates sound waves and vibration signals, simplifies system structure, reduces costs, is suitable for scenarios with overlapping frequency bands, and improves detection accuracy and reliability.
Smart Images
Figure CN122306214A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of acoustic detection, and more particularly to a method for decoupling vibration interference from acoustic sensors based on a triaxial structure. Background Technology
[0002] In the field of acoustic detection, acoustic sensors often need to operate in complex environments such as vehicle platforms and sealed cabins of aerospace vehicles. These environments commonly suffer from mechanical vibration problems such as structural vibration, external impact, and mechanical operation. Vibration is transmitted through the sensor's mounting base to the acoustic-electric transducer sensing element, where it superimposes with the target acoustic wave signal, causing distortion of the sensor's output signal and severely reducing the accuracy and reliability of acoustic detection.
[0003] The existing methods for suppressing vibration interference are mainly divided into three categories, and all of them have obvious shortcomings. (1) Physical vibration isolation technology: Vibration transmission is attenuated by using vibration damping materials or designing vibration isolation structures. Although it is simple and direct, it is often bulky and costly, and it is difficult to completely isolate broadband vibration. (2) Single-axis signal filtering: Filtering or noise reduction is carried out using only the output signal of a single axis. When the vibration and sound wave signals overlap in the frequency band, it is difficult to effectively separate the two by relying solely on the difference in the spectrum. (3) Reference sensor method: Vibration sensors such as accelerometers are installed near the acoustic sensor. Compensation is carried out by measuring the vibration and establishing the transfer function. This method not only requires accurate transmission path modeling, but the additional sensors also increase the system complexity and cost. In practical applications, the transfer function may change with the environment, which leads to unstable compensation effect. Therefore, we propose a vibration interference decoupling method based on a triaxial acoustic sensor. Summary of the Invention
[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a vibration interference decoupling method for acoustic sensors based on a triaxial structure.
[0005] To achieve the above objectives, the present invention adopts the following technical solution: A vibration interference decoupling method based on a triaxial acoustic sensor is described below: Ⅰ: Collect output signals in different orthogonal directions, process the three-axis signals to obtain the corresponding frequency domain signals, and then calculate the cross power spectral density of the corresponding two axes; II: Normalize the calculated cross-power spectral density, and then generate the coherence functions between each pair of the three axes based on the processing results; III: Based on the coherence functions between each pair of the three axes, a weighting function is set, and then the frequency domain components of the pure acoustic signal are extracted according to the weighting function; IV: Perform inverse Fourier transform on the frequency domain components of the extracted pure acoustic signal to obtain the decoupled pure acoustic signal.
[0006] As a further aspect of the present invention, the specific steps for acquiring output signals in different orthogonal directions in step I are as follows: S1.1: Output signals in the three orthogonal directions (x, y, z) are simultaneously acquired using a triaxial acoustic sensor, which are the time-domain signals of the x, y, and z axes. For the triaxial time-domain signals acquired under vibration interference, mathematical expressions for the output signals in each axis are established based on the superposition characteristics of the sound pressure signal and the vibration coupling response. Each axial signal is the superposition of the target sound pressure signal and the vibration coupling response in that axis. The specific form of the mathematical expression for the output signal is as follows: In the formula, This indicates that the target sound pressure signal behaves consistently across all axes. , , These represent the coupled responses of the vibration on each axis; and due to the vector characteristics of the vibration, , , They typically have low statistical correlation and are associated with The phase relationship is random.
[0007] As a further aspect of the present invention, the specific steps for calculating the cross-power spectral density of the corresponding two axes in step I are as follows: S2.1: Retrieve the x, y, and z three-axis time domain signals and segment them into equal-length segments according to the preset time length. At the same time, set the inter-segment overlap rate to ensure that the segmented data completely covers the entire time range of the original three-axis time domain signal. Then, perform Fourier transform on each segmented three-axis time domain signal to convert the time domain signal into a frequency domain signal, and finally obtain the frequency domain signal corresponding to each segment of the time domain signal. S2.2: After processing all segmented time-domain signals, integrate the multiple frequency-domain signals of each axis to obtain the complete frequency-domain signals of the x, y, and z axes. , , Subsequently, to measure the correlation between pairs of axial frequency domain signals, the corresponding cross-power spectral density was calculated, and all calculated cross-power spectral densities were integrated to form three sets of cross-power spectral density results across the entire frequency range. The specific calculation formula for the cross-power spectral density is as follows: In the formula, It represents the expected value in mathematics, which is obtained by averaging multiple data segments in actual calculations.
[0008] As a further aspect of the present invention, the specific steps for generating the coherence functions between each pair of the three axes in step II are as follows: S3.1: Within the full frequency range, traverse the frequencies sequentially from low to high, and obtain the three sets of cross-power spectral density for each frequency point from the three sets of cross-power spectral density results. Then, perform a normalization operation on these three sets to obtain the three corresponding coherence functions at that frequency point. The specific calculation formula for the normalization operation is as follows: In the formula, express and The cross-power spectral density; and They represent and Self-power spectral density; The value range is [0, 1]. The closer the value is to 1, the stronger the linear correlation between the two signals at that frequency, that is, their amplitude and phase maintain a stable relationship; conversely, if it is close to 0, it means that the two signals are uncorrelated or have a complex relationship at that frequency. S3.2: Verify the range of values of the three sets of coherent functions calculated for all frequency points to confirm that all values are within the preset range. If a value exceeds the preset range, re-perform the normalization operation for the frequency point containing the value to correct the abnormal data until the values of the three sets of coherent functions at that frequency point are within the preset range. S3.3: Sort and integrate the three sets of coherent functions for all frequency points after verification in order of frequency from low to high to generate three complete sets of coherent function data: xy, xz, and yz.
[0009] As a further aspect of the present invention, the specific steps for extracting the frequency domain components of the pure acoustic signal in step III are as follows: S4.1: Retrieve the coherence function data between each pair of the three axes, and set the signal discrimination threshold of the coherence function according to the actual needs of the acoustic detection scenario. Then, traverse the entire frequency range by frequency point, and check whether each of the three sets of coherence functions corresponding to each frequency point exceeds the preset signal discrimination threshold. If all three values exceed the preset signal discrimination threshold, it is determined that the frequency component mainly comes from the acoustic signal; otherwise, it is determined that it is dominated by vibration interference. Finally, mark the discrimination results of each frequency point. S4.2: The minimum value of the three coherent functions at a certain frequency point is set as the weighting function. Then, the x, y, and z-axis frequency domain signals are retrieved, and three sets of frequency domain signal values are extracted for each frequency point according to the preset frequency traversal order. The corresponding average values are calculated, and then the average values of all frequency points are integrated to obtain the average spectrum of the three-axis signal across the entire frequency range. The specific form of the weighting function is as follows: ; S4.3: Using frequency points as units, multiply the triaxial average spectrum corresponding to each frequency point with the weighting function at that frequency point, then integrate the results of the calculation for each frequency point, sort them from low to high frequency, and finally obtain the frequency domain components of the pure acoustic signal. The specific representation of the frequency domain components of the pure acoustic signal is as follows: In the formula, , , These represent the spectra of the three-axis signals.
[0010] As a further aspect of the present invention, the specific steps for obtaining the decoupled pure acoustic signal in step IV are as follows: S5.1: Obtain and verify various parameters of the frequency domain components of the pure acoustic signal, and set the operation parameters of the inverse Fourier transform. Then, perform the inverse Fourier transform operation on the frequency domain components of the pure acoustic signal according to the set operation parameters to convert the frequency domain signal into a time domain signal. Then, obtain the original result of the time domain signal based on the operation to initially obtain the time domain data of the decoupled acoustic signal. S5.2: Remove time-domain signals that do not meet the preset standards from the transformed time-domain signal results, and calibrate the time axis of the remaining time-domain signals to make them completely aligned with the time axis of the original three-axis time-domain signals. Then, determine the post-processed time-domain signal results as the final decoupled pure acoustic signal.
[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention uses a triaxial acoustic sensor to simultaneously acquire output signals in three orthogonal directions (x, y, z) to obtain corresponding triaxial time-domain signals. Simultaneously, mathematical expressions are established for each axis of these signals, representing the superposition of the target sound pressure signal and the coupled response of axial vibration. Then, the triaxial time-domain signals are segmented into equal-length segments with preset durations and an inter-segment overlap rate is set. Fourier transforms are performed on each segmented time-domain signal, and the multiple frequency-domain signals are integrated to obtain a complete triaxial frequency-domain signal. , , Then, the three sets of cross-power spectral densities across the entire frequency range are calculated and integrated. These densities are then normalized frequency-wise to obtain the corresponding coherence functions. The coherence function values are verified and outliers are corrected. Three complete sets of coherence functions (xy, xz, and yz) are then integrated by frequency. A threshold for judging the coherence function signal is set, and the dominant signal components are verified and marked frequency-wise. The minimum value of the three sets of coherence functions at each frequency point is set as the weighting function. Simultaneously, the three-axis frequency domain signal is retrieved to calculate and integrate the average spectrum across the entire frequency range. The average spectrum is then multiplied frequency-wise by the weighting function and integrated to obtain the frequency domain of the pure acoustic signal. The components are analyzed, and the frequency domain component parameters are checked and the inverse Fourier transform parameters are set. After performing the transformation to obtain the original time domain result, non-compliant time domain signals are removed and the time axis is calibrated to align with the time axis of the initial three-axis time domain signal. Finally, the decoupled pure acoustic signal is determined, which has a clear physical mechanism and can independently distinguish each frequency component. It is suitable for scenarios where sound wave and vibration frequency bands overlap, effectively avoiding the problem that traditional time domain filtering methods cannot distinguish them. At the same time, no additional accelerometer or other reference sensors are required, which simplifies the system structure and reduces equipment costs and installation complexity. Attached Figure Description
[0012] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.
[0013] Figure 1 This is a flowchart of the vibration interference decoupling method for acoustic sensors based on a triaxial structure proposed in this invention. Figure 2 This is a flowchart of the vibration interference decoupling method for acoustic sensors based on a triaxial structure proposed in this invention. Figure 3 This is a diagram of the aliased signals acquired along the three axes of the acoustic sensor vibration interference decoupling method based on a triaxial structure proposed in this invention. Figure 4 The diagram shows the vibration interference decoupling results of the vibration interference decoupling method for acoustic sensors based on a triaxial structure proposed in this invention. Detailed Implementation
[0014] Example 1, referring to Figure 1 , Figure 2 and Figure 3 A vibration interference decoupling method based on a triaxial acoustic sensor is proposed, and the specific steps of the decoupling method are as follows: The output signals in different orthogonal directions are collected, and the three-axis signals are processed to obtain the corresponding frequency domain signals. Then, the cross power spectral density of the corresponding two axes is calculated.
[0015] Specifically, the output signals in the three orthogonal directions of x, y, and z are simultaneously acquired by a triaxial acoustic sensor, which are the time-domain signals of the x, y, and z axes. At the same time, for the triaxial time-domain signals acquired under the condition of vibration interference, mathematical expressions for the output signals of each axis are established based on the superposition characteristics of the sound pressure signal and the vibration coupling response. Each axial signal is the superposition of the target sound pressure signal and the vibration coupling response of that axis.
[0016] It should be further explained that the specific mathematical expression of the output signal is as follows: In the formula, This indicates that the target sound pressure signal behaves consistently across all axes. , , These represent the coupled responses of the vibration on each axis; due to the vector characteristics of the vibration, , , They typically have low statistical correlation and are associated with The phase relationship is random.
[0017] Specifically, the x, y, and z axis time-domain signals are retrieved and segmented into equal-length segments according to a preset time length. An overlap rate between segments is set to ensure that the segmented data completely covers the entire time range of the original three-axis time-domain signals. Then, a Fourier transform is performed on each segment of the three-axis time-domain signal to convert it into a frequency-domain signal. Finally, the frequency-domain signal corresponding to each segment is obtained. After processing all segmented time-domain signals, the multiple frequency-domain signals of each axis are integrated to obtain the complete frequency-domain signals for the x, y, and z axes. , , Subsequently, in order to measure the correlation between the two axial frequency domain signals, the corresponding cross power spectral density was calculated, and all the calculated cross power spectral densities were integrated to form three sets of cross power spectral density results across the entire frequency range.
[0018] It should be further explained that the specific formula for calculating the cross-power spectral density is as follows: In the formula, It represents the expected value in mathematics, which is obtained by averaging multiple data segments in actual calculations.
[0019] The calculated cross-power spectral density is normalized, and then the coherence functions between each pair of the three axes are generated based on the processing results.
[0020] Specifically, across the entire frequency range, the system iterates through the frequencies in ascending order, obtaining the three sets of cross-power spectral density for each frequency point from the three sets of cross-power spectral density results. These cross-power spectral density values are then normalized to obtain the three corresponding coherence functions for that frequency point. The range of values for the three sets of coherence functions calculated for all frequency points is verified to ensure all values are within a preset range. If a value exceeds the preset range, the normalization operation is re-performed for that frequency point to correct the abnormal data. This process continues until the values of the three sets of coherence functions for that frequency point are within the preset range. Finally, the three sets of coherence functions for all verified frequency points are sorted and integrated in ascending order to generate three complete sets of coherence function data: xy, xz, and yz.
[0021] It should be further explained that the specific calculation formula for normalization is as follows: In the formula, express and The cross-power spectral density; and They represent and Self-power spectral density; The value range is [0, 1]. The closer the value is to 1, the stronger the linear correlation between the two signals at that frequency, that is, their amplitude and phase maintain a stable relationship. Conversely, if the value is close to 0, it means that the two signals are uncorrelated or have a complex relationship at that frequency.
[0022] Example 2, refer to Figure 1 , Figure 2 and Figure 4 A vibration interference decoupling method based on a triaxial acoustic sensor is proposed, and the specific steps of the decoupling method are as follows: Based on the coherence functions between each pair of the three axes, a weighting function is set, and then the frequency domain components of the pure acoustic signal are extracted according to the weighting function.
[0023] Specifically, the coherence function data between each pair of the three axes is retrieved, and a signal discrimination threshold for the coherence function is set according to the actual needs of acoustic detection. Then, the frequency points are traversed sequentially across the entire frequency range. For each frequency point, the three sets of coherence functions are checked one by one to see if they all exceed the preset signal discrimination threshold. If all three values exceed the preset signal discrimination threshold, it is determined that the frequency component mainly originates from the acoustic signal; otherwise, it is determined that it is dominated by vibration interference. Finally, the discrimination results of each frequency point are marked, and the minimum value of the three coherence functions at a certain frequency point is set as the weight function. Then, the frequency domain signals of the x, y, and z axes are retrieved, and the three sets of frequency domain signal values at each frequency point are extracted according to the preset frequency traversal order. The corresponding average values are calculated, and then the average values of all frequency points are integrated to obtain the average spectrum of the three-axis signal across the entire frequency range. Taking the frequency point as the unit, the average spectrum of the three axes corresponding to each frequency point is multiplied by the weight function at the frequency point. The calculation results of each frequency point are then integrated and sorted from low to high frequency to finally obtain the frequency domain components of the pure acoustic signal.
[0024] It should be further explained that the specific form of the weighting function is as follows: ; The specific representation of the frequency domain components of a pure acoustic signal is as follows: In the formula, , , These represent the spectra of the three-axis signals.
[0025] The frequency domain components of the extracted pure acoustic signal are subjected to inverse Fourier transform to obtain the decoupled pure acoustic signal.
[0026] Specifically, the parameters of the frequency domain components of the pure acoustic signal are acquired and verified, and the operation parameters of the inverse Fourier transform are set. Then, the frequency domain components of the pure acoustic signal are subjected to inverse Fourier transform operation according to the set operation parameters to convert the frequency domain signal into a time domain signal. Based on the original result of the time domain signal obtained by the operation, the time domain data of the decoupled acoustic signal is initially obtained. Time domain signals that do not meet the preset standards in the transformed time domain signal result are removed. At the same time, the time axis of the remaining time domain signal is calibrated to make it completely aligned with the time axis of the initial three-axis time domain signal. Finally, the time domain signal result after the post-processing is determined as the final decoupled pure acoustic signal.
[0027] It should be further explained that the physical mechanism for achieving vibration interference decoupling described in this invention is as follows: (1) Sound waves are scalar pressure waves, and their propagation medium is air. The pressure acting on the acoustic-electric transducer unit can be expressed as: Under ideal plane wave conditions, when the wavelength of the sound wave is much larger than the sensor size, the sound pressure acting on the sensor in all directions is synchronous, in phase, and of equal amplitude. This means that the acoustic signal exhibits highly consistent pressure changes along the three orthogonal axes.
[0028] (2) Vibration is a vector field with a clear direction and polarity, and its mathematical description is given in the form of acceleration or displacement: in, These are the vibration acceleration components in three orthogonal directions. Due to the uncertainty of the vibration source and the complexity of the propagation path, these components often have low correlation or random phase relationships.
[0029] (3) As mentioned above, among the signals output by the sensor along the three axes, the acoustic signal, as a scalar field, has synchronous consistency across the three axes, while the vibration interference, as a vector field, exhibits anisotropic differences. By utilizing the synchronous consistency of the acoustic signal across the three axes and the anisotropic differences of the vibration signal, the target acoustic signal can be effectively extracted in the frequency domain through cross-spectral coherence analysis.
Claims
1. A vibration interference decoupling method for acoustic sensors based on a triaxial structure, characterized in that, The specific steps of this decoupling method are as follows: Ⅰ: Collect output signals in different orthogonal directions, process the three-axis signals to obtain the corresponding frequency domain signals, and then calculate the cross power spectral density of the corresponding two axes; II: Normalize the calculated cross-power spectral density, and then generate the coherence functions between each pair of the three axes based on the processing results; III: Based on the coherence functions between each pair of the three axes, a weighting function is set, and then the frequency domain components of the pure acoustic signal are extracted according to the weighting function; IV: Perform inverse Fourier transform on the frequency domain components of the extracted pure acoustic signal to obtain the decoupled pure acoustic signal.
2. The vibration interference decoupling method for acoustic sensors based on a triaxial structure according to claim 1, characterized in that, The specific steps for acquiring output signals in different orthogonal directions as described in step I are as follows: S1.1: Output signals in the three orthogonal directions (x, y, z) are simultaneously acquired using a triaxial acoustic sensor, which are the time-domain signals of the x, y, and z axes. For the triaxial time-domain signals acquired under vibration interference, mathematical expressions for the output signals in each axis are established based on the superposition characteristics of the sound pressure signal and the vibration coupling response. Each axial signal is the superposition of the target sound pressure signal and the vibration coupling response in that axis. The specific form of the mathematical expression for the output signal is as follows: In the formula, This indicates that the target sound pressure signal behaves consistently across all axes. , , These represent the coupled responses of the vibration on each axis; and due to the vector characteristics of the vibration, , , They typically have low statistical correlation and are associated with The phase relationship is random.
3. The vibration interference decoupling method for acoustic sensors based on a triaxial structure according to claim 2, characterized in that, The specific steps for calculating the cross-power spectral density of the corresponding two axes described in step I are as follows: S2.1: Retrieve the x, y, and z three-axis time domain signals and segment them into equal-length segments according to the preset time length. At the same time, set the inter-segment overlap rate to ensure that the segmented data completely covers the entire time range of the original three-axis time domain signal. Then, perform Fourier transform on each segmented three-axis time domain signal to convert the time domain signal into a frequency domain signal, and finally obtain the frequency domain signal corresponding to each segment of the time domain signal. S2.2: After processing all segmented time-domain signals, integrate the multiple frequency-domain signals of each axis to obtain the complete frequency-domain signals of the x, y, and z axes. , , Subsequently, to measure the correlation between pairs of axial frequency domain signals, the corresponding cross-power spectral density was calculated, and all calculated cross-power spectral densities were integrated to form three sets of cross-power spectral density results across the entire frequency range. The specific calculation formula for the cross-power spectral density is as follows: In the formula, It represents the expected value in mathematics, which is obtained by averaging multiple data segments in actual calculations.
4. The vibration interference decoupling method for acoustic sensors based on a triaxial structure according to claim 3, characterized in that, The specific steps for generating the coherence functions between each pair of the three axes in step II are as follows: S3.1: Within the full frequency range, traverse the frequencies sequentially from low to high, and obtain the three sets of cross-power spectral density for each frequency point from the three sets of cross-power spectral density results. Then, perform a normalization operation on these three sets to obtain the three corresponding coherence functions for that frequency point. The specific calculation formula for the normalization operation is as follows: In the formula, express and The cross-power spectral density; and They represent and Self-power spectral density; The value range is [0, 1]. The closer the value is to 1, the stronger the linear correlation between the two signals at that frequency, that is, their amplitude and phase maintain a stable relationship; conversely, if it is close to 0, it means that the two signals are uncorrelated or have a complex relationship at that frequency. S3.2: Verify the range of values of the three sets of coherent functions calculated for all frequency points to confirm that all values are within the preset range. If a value exceeds the preset range, re-perform the normalization operation for the frequency point containing the value to correct the abnormal data until the values of the three sets of coherent functions at that frequency point are within the preset range. S3.3: Sort and integrate the three sets of coherent functions for all frequency points after verification in order of frequency from low to high to generate three complete sets of coherent function data: xy, xz, and yz.
5. The vibration interference decoupling method for acoustic sensors based on a triaxial structure according to claim 4, characterized in that, The specific steps for extracting the frequency domain components of the pure acoustic signal in step III are as follows: S4.1: Retrieve the coherence function data between each pair of the three axes, and set the signal discrimination threshold of the coherence function according to the actual needs of the acoustic detection scenario. Then, in the full frequency range, traverse the frequency points in turn, and check whether the three sets of coherence functions corresponding to each frequency point exceed the preset signal discrimination threshold. If all three values exceed the preset signal discrimination threshold, it is determined that the frequency component mainly comes from the acoustic signal. Conversely, if the vibration interference is dominant, it is determined that the discrimination results at each frequency point are marked. S4.2: The minimum value of the three coherent functions at a certain frequency point is set as the weighting function. Then, the x, y, and z-axis frequency domain signals are retrieved, and three sets of frequency domain signal values are extracted for each frequency point according to the preset frequency traversal order. The corresponding average values are calculated, and then the average values of all frequency points are integrated to obtain the average spectrum of the three-axis signal across the entire frequency range. The specific form of the weighting function is as follows: ； S4.3: Using frequency points as units, multiply the triaxial average spectrum corresponding to each frequency point with the weighting function at that frequency point, then integrate the results of the calculation for each frequency point, sort them from low to high frequency, and finally obtain the frequency domain components of the pure acoustic signal. The specific representation of the frequency domain components of the pure acoustic signal is as follows: In the formula, , , These represent the spectra of the three-axis signals.
6. The vibration interference decoupling method for acoustic sensors based on a triaxial structure according to claim 5, characterized in that, The specific steps for obtaining the decoupled, clean acoustic signal in step IV are as follows: S5.1: Obtain and verify various parameters of the frequency domain components of the pure acoustic signal, and set the operation parameters of the inverse Fourier transform. Then, perform the inverse Fourier transform operation on the frequency domain components of the pure acoustic signal according to the set operation parameters to convert the frequency domain signal into a time domain signal. Then, obtain the original result of the time domain signal based on the operation to initially obtain the time domain data of the decoupled acoustic signal. S5.2: Remove time-domain signals that do not meet the preset standards from the transformed time-domain signal results, and calibrate the time axis of the remaining time-domain signals to make them completely aligned with the time axis of the original three-axis time-domain signals. Then, determine the post-processed time-domain signal results as the final decoupled pure acoustic signal.