Buffered guided wave imaging monitoring method for a vehicle thermal protection system impact event

Abstract

The application discloses a buffer guided wave imaging monitoring method for impact events of a thermal protection system of a carrier, and relates to the field of aerospace structure health monitoring, and specifically comprises the following steps: S1: arranging piezoelectric sheets in a safe area on the cold end side of the thermal protection system; S2: when an impact occurs, guided waves are generated in the structure and are buffered to propagate to each piezoelectric sheet; S3: synchronously collecting the buffered guided wave signals received by each piezoelectric sheet; S4: preliminarily determining the wave arrival time of the direct wave in each buffered guided wave signal; S5: pre-aligning the starting points of the buffered guided wave signals; S6: sequentially time-shifting each buffered guided wave signal by different time steps to the right; S7: performing imaging processing by using the buffered guided wave signals time-shifted by different steps to the right; S8: repeating steps S6-S7 to obtain imaging results of time-shifting by different time steps to the right; and S9: taking the imaging with the highest maximum pixel value as the buffered guided wave monitoring result. The application solves the problem of high-reliability online sensing and monitoring of impact events of the thermal protection system under severe high-temperature working conditions.

Description

Technical Field

[0001] This invention relates to the field of aerospace structural health monitoring, and in particular to a buffer guided wave imaging monitoring method for impact events in a launch vehicle thermal protection system. Background Technology

[0002] The world's space program has entered a new phase of large-scale space travel, creating an urgent need for launch vehicle development. To cope with the extreme high temperatures generated by aerodynamic heating during high-speed atmospheric reentry, launch vehicles must be equipped with thermal protection systems. These systems are the most critical core systems for developing and ensuring the safe operation of launch vehicles under extreme conditions. The safety and integrity of their structure directly determine the success or failure of launch vehicle development and the operational capability of next-generation space transportation systems. In actual service, launch vehicle thermal protection systems not only experience extremely harsh high-temperature and aerodynamic environments but are also likely to be subjected to external impacts. Typical impact events on thermal protection systems include lightning strikes during ground and launch, impacts from detached components during launch, and impacts from space debris during space operations. These impact events severely reduce the safety and reliability of the thermal protection system structure and can easily lead to catastrophic accidents. Therefore, research on online monitoring of thermal protection system impact events has become increasingly important. However, thermal protection systems operate under harsh high-temperature conditions, which can make it difficult for sensors placed in the structure under test to function properly or even survive. This seriously hinders the application of impact event monitoring technology, which relies on the safe and reliable operation of sensors, in thermal protection systems.

[0003] Currently, representative thermal protection systems widely used on launch vehicles include reinforced carbon / carbon materials, ultra-high temperature ceramic materials, integral toughened and oxidation-resistant composite materials, metal thermal protection systems, and ceramic matrix composite cover-type thermal protection systems. These are typically installed on key thermal protection areas on the windward surfaces of the launch vehicle, such as the nose cone, wing leading edge, and fuselage. To facilitate disassembly, inspection, and maintenance for reusable applications, most of these thermal protection systems on launch vehicles utilize mechanical connections, including bolted and adhesive joints. Monitoring impact events for these mechanically connected thermal protection systems has become a critical and urgent challenge.

[0004] Therefore, it is necessary to provide a buffer guided wave imaging monitoring method for impact events in the thermal protection system of a launch vehicle to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a buffered guided wave imaging monitoring method for impact events in a vehicle's thermal protection system. Utilizing the advantage of the long-distance buffered propagation of guided wave responses generated by structural impacts, a piezoelectric sensor is placed in the cold structure on the cold side of the thermal protection system. When the hot panel of the thermal protection system is impacted, a guided wave response is generated at the impact point and propagates buffered from the hot panel structure to the piezoelectric sensor in the cold structure via a mechanical connection mechanism. This enables buffered guided wave piezoelectric sensing of impact events in the thermal protection system. Based on this, iterative imaging processing is performed on the buffered guided wave signals acquired by the piezoelectric sensor to ultimately achieve imaging monitoring of impact events in the thermal protection system.

[0006] To achieve the above objectives, the present invention provides a method for monitoring shock events in a launch vehicle's thermal protection system using buffer guided wave imaging, comprising the following steps:

[0007] S1: Q piezoelectric elements are arranged in the safety area on the cold end side of the thermal protection system, where Q is not less than 3;

[0008] S2: When an impact event occurs, a guided wave response is generated in the thermal structure of the thermal protection system and propagates along the connecting mechanism to the piezoelectric elements P arranged on the cold end side. i Place;

[0009] S3: Synchronously acquire data from each piezoelectric element P i Received buffered guided wave signal I i (t), where t is a time variable, i = 1, 2, ..., Q;

[0010] S4: Preliminary determination of each buffered waveguide signal I i (t) time of arrival of the direct wave pt i And select pt i minimum value pt min ;

[0011] S5: Transfer each buffered waveguide signal I i (t) shifts left by pt min Obtain the buffered guided wave signal v with pre-aligned starting point. i (t)=I i (t+pt min );

[0012] S6: Transfer each buffered waveguide signal v i (t) Shift the time step to the right by Δt to obtain v i (t-Δt);

[0013] S7: Utilize all v i (t-Δt) is used for high-resolution imaging processing;

[0014] S8: Repeat steps S6-S7 above to obtain the result for v. i (t) Imaging results after shifting to the right by different time steps nΔt, and the maximum pixel value M in each imaging result is extracted. n Where n is the number of time steps to the right, n = 1, 2, ..., N, and N is the maximum number of time steps to the right;

[0015] S9: With maximum M n The corresponding high-resolution imaging results serve as the final buffer guided wave imaging monitoring results for impact events in the thermal protection system.

[0016] Preferably, step S7 specifically includes the following steps:

[0017] S71: For each v i (t-Δt) is subjected to dispersion compensation processing to obtain a buffered guided wave signal v1 with enhanced resolution. i (t);

[0018] S72: Construct any two piezoelectric elements P i and P j Buffered guided wave signals between: v ij (t)=v1 i (t)*v1 j (t)*v a (t), where j = 1, 2, ..., Q, i ≠ j, * denotes convolution operation, v a (t) represents the selected center frequency ω c Narrowband waveform, ω c The selected center angular frequency;

[0019] S73: Find v ij The envelope s of (t) ij (t);

[0020] S74: Calculate the pixel values ​​at all locations within the monitoring area of ​​the thermal protection system.

[0021] Where (x,y) are the coordinates of any location within the monitoring area of ​​the thermal protection system, s ij [t ij [x,y)] is the envelope s corresponding to the pixel at (x,y). ij (t) represents the amplitude of the acquired signal, t ij (x,y) is v ij The waveguide mode corresponding to (t) propagates from the monitoring area (x, y) through buffers to the piezoelectric element P. i and P j The sum of the corresponding buffer propagation time and reference time;

[0022] S75: Calculate the pixel values ​​at all locations within the monitoring area of ​​the thermal protection system to obtain high-resolution imaging results.

[0023] Preferably, in step S2, the impact events include lightning strikes to the launch vehicle's thermal protection system on the ground and during launch, impacts from tools or detached parts, and impacts from space debris during space operations.

[0024] Preferably, step S71 specifically includes the following steps:

[0025] S711: Obtain the linearized wavenumber curve: K1(ω)=K0(ω) c )+1 / c g ·(ω-ω c ), where K1(ω) is the linearized wavenumber curve, K0(ω) is the absolute or relative wavenumber curve of the original dispersion of the guided mode corresponding to the buffered guided signal, ω is the angular frequency, and c g For the corresponding guided wave mode at ω c Group velocity of downward propagation;

[0026] S712: Calculate the frequency domain interpolation mapping sequence: Where Ω1(ω) is the calculated frequency domain interpolation mapping sequence. It is the inverse function of K0(ω);

[0027] S713: For v i (t-Δt) is subjected to frequency domain interpolation: V1 i (ω)=V i [Ω1(ω)], where V1 i (ω) represents the result of frequency domain interpolation, V i (ω) is v i Fourier transform result of (t-Δt);

[0028] S714: For V1 i (ω) is used to perform an inverse Fourier transform to obtain v1 i (t);

[0029] S715: Only retain v1 versions i In (t), the part corresponding to the direct wave is set to zero, and the subsequent signal part is set to zero.

[0030] Therefore, the present invention employs the above-mentioned buffer guided wave imaging monitoring method for impact events in a launch vehicle thermal protection system, which has the following beneficial effects:

[0031] (1) The present invention uses a piezoelectric sheet arranged in the safe area on the cold end side of the thermal protection system to realize safe and reliable buffer wave online sensing of the thermal protection system under harsh high temperature conditions.

[0032] (2) This invention solves the problems of unknown pre-acquisition time of impact buffered waveguide response signal and difficulty in directly implementing impact imaging monitoring by iterative imaging of buffered waveguide signals with different delays.

[0033] (3) In the iterative imaging of buffered guided waves in the present invention, the dispersion compensation processing of buffered guided waves is considered, which improves the imaging resolution and enhances the reliability of impact imaging monitoring of thermal protection systems with complex structures.

[0034] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0035] Figure 1 This is a flowchart of a buffer guided wave imaging monitoring method for impact events in a launch vehicle thermal protection system according to the present invention;

[0036] Figure 2 This is a structural diagram of the thermal protection system in this invention;

[0037] Figure 3 This is a top view of the thermal protection system of the present invention facing the thermal panel;

[0038] Figure 4 This is a bottom view of the thermal protection system of the present invention facing the cold panel;

[0039] Figure 5 This is the buffered propagation path of the guided wave in the thermal protection system of the present invention, which propagates from the impact point of the hot panel through the support buffer to the piezoelectric sheet P3 on the lower surface of the cold panel.

[0040] Figure 6 It is the buffered guided wave signal I1(t) synchronously acquired by the piezoelectric element P1 in this invention;

[0041] Figure 7 It is the buffered guided wave signal I2(t) synchronously acquired by the piezoelectric element P2 in this invention;

[0042] Figure 8 It is the buffered guided wave signal I3(t) synchronously acquired by the piezoelectric element P3 in this invention;

[0043] Figure 9 It is the buffered guided wave signal I4(t) synchronously acquired by the piezoelectric element P4 in this invention;

[0044] Figure 10 It is the buffered guided wave signal v1(t) with the starting point pre-aligned in this invention;

[0045] Figure 11 It is the buffered guided wave signal v2(t) with the starting point pre-aligned in this invention;

[0046] Figure 12 It is the buffered guided wave signal v1(t-Δt) shifted to the right by one time step Δt in this invention;

[0047] Figure 13 It is the buffered guided wave signal v2(t-Δt) that is shifted to the right by one time step Δt in this invention;

[0048] Figure 14 It is the dispersion compensation result v11(t) of the buffered guided wave signal v1(t-Δt) in this invention;

[0049] Figure 15 It is the dispersion compensation result v12(t) of the buffered guided wave signal v2(t-Δt) in this invention;

[0050] Figure 16 The narrowband waveform v in this invention a (t);

[0051] Figure 17 The buffered guided wave signal v between the piezoelectric elements P1 and P2 constructed in this invention is 12 (t) and its envelope s 12 (t);

[0052] Figure 18 This is the imaging result of shifting the time step Δt to the right in this invention;

[0053] Figure 19 It is the maximum pixel value of the imaging result of the time-shifted non-synchronous length number in this invention;

[0054] Figure 20 This is the imaging result shifted 10 time steps to the right in this invention. Detailed Implementation

[0055] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0057] The terms "comprising" or "including" as used in this invention mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements. Terms such as "inner," "outer," "upper," and "lower" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this invention, unless otherwise explicitly specified and limited, the term "attached" and similar terms should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0058] like Figure 1 As shown, the present invention provides a buffer guided wave imaging monitoring method for impact events in the thermal protection system of a launch vehicle, comprising the following steps:

[0059] S1: Q piezoelectric elements are arranged in the safety area on the cold end side of the thermal protection system, where Q is not less than 3;

[0060] S2: When an impact event occurs, a guided wave response is generated in the thermal structure of the thermal protection system and propagates along the connecting mechanism to the piezoelectric elements P arranged on the cold end side. i In step S2, the impact events include lightning strikes to the launch vehicle's thermal protection system on the ground and during launch, impacts from tools or detached parts, and impacts from space debris during space operations.

[0061] S3: Synchronously acquire data from each piezoelectric element P i Received buffered guided wave signal I i (t), where t is a time variable, i = 1, 2, ..., Q;

[0062] S4: Preliminary determination of each buffered waveguide signal I i (t) time of arrival of the direct wave pt i And select pt i minimum value pt min ;

[0063] S5: Transfer each buffered waveguide signal I i (t) shifts left by pt min Obtain the buffered guided wave signal v with pre-aligned starting point. i (t)=I i (t+ptmin );

[0064] S6: Transfer each buffered waveguide signal v i (t) Shift the time step to the right by Δt to obtain v i (t-Δt);

[0065] S7: Utilize all v i (t-Δt) is used for high-resolution imaging processing; step S7 specifically includes the following steps:

[0066] S71: For each v i (t-Δt) is subjected to dispersion compensation processing to obtain a buffered guided wave signal v1 with enhanced resolution. i (t);

[0067] Step S71 specifically includes the following steps:

[0068] S711: Obtain the linearized wavenumber curve: K1(ω)=K0(ω) c )+1 / c g ·(ω-ω c ), where K1(ω) is the linearized wavenumber curve, K0(ω) is the absolute or relative wavenumber curve of the original dispersion of the guided mode corresponding to the buffered guided signal, ω is the angular frequency, and c g For the corresponding guided wave mode at ω c Group velocity of downward propagation;

[0069] S712: Calculate the frequency domain interpolation mapping sequence: Where Ω1(ω) is the calculated frequency domain interpolation mapping sequence. It is the inverse function of K0(ω);

[0070] S713: For v i (t-Δt) is subjected to frequency domain interpolation: V1 i (ω)=V i [Ω1(ω)], where V1 i (ω) represents the result of frequency domain interpolation, V i (ω) is v i Fourier transform result of (t-Δt);

[0071] S714: For V1 i (ω) is used to perform an inverse Fourier transform to obtain v1 i (t);

[0072] S715: Only retain v1 versions i In (t), the part corresponding to the direct wave is set to zero, and the subsequent signal part is set to zero.

[0073] S72: Construct any two piezoelectric elements Pi and P j Buffered guided wave signals between: v ij (t)=v1 i (t)*v1 j (t)*v a (t), where j = 1, 2, ..., Q, i ≠ j, * denotes convolution operation, v a (t) represents the selected center frequency ω c Narrowband waveform, ω c The selected center angular frequency;

[0074] S73: Find v ij The envelope s of (t) ij (t);

[0075] S74: Calculate the pixel values ​​at all locations within the monitoring area of ​​the thermal protection system. Where (x,y) are the coordinates of any location within the monitoring area of ​​the thermal protection system, s ij [t ij [x,y)] is the envelope s corresponding to the pixel at (x,y). ij (t) represents the amplitude of the acquired signal, t ij (x,y) is v ij The waveguide mode corresponding to (t) propagates from the monitoring area (x, y) through buffers to the piezoelectric element P. i and P j The sum of the corresponding buffer propagation time and reference time;

[0076] S75: Calculate the pixel values ​​at all locations within the monitoring area of ​​the thermal protection system to obtain high-resolution imaging results.

[0077] S8: Repeat steps S6-S7 above to obtain the result for v. i (t) Imaging results after shifting to the right by different time steps nΔt, and the maximum pixel value M in each imaging result is extracted. n Where n is the number of time steps to the right, n = 1, 2, ..., N, and N is the maximum number of time steps to the right;

[0078] S9: With maximum M n The corresponding high-resolution imaging results serve as the final buffer guided wave imaging monitoring results for impact events in the thermal protection system.

[0079] Example

[0080] Thermal protection system structure as follows Figure 2As shown, the hot panel and support are made of TC4 titanium alloy. The hot panel is designed as a trapezoid with a thickness of 3mm, and the two bases and heights are 120mm, 160mm, and 300mm respectively. The cold panel is a rectangular 2024 aluminum alloy, measuring 170mm × 304mm × 3mm. The distance between the hot and cold panels is 27mm, and they are mechanically connected by the support. BB pellets are fired at the upper surface of the hot panel using a toy gun to simulate external impact. The impact monitoring range of the hot panel is 300mm × 120mm. Figure 3 The impact point and monitoring range of the hot panel are given. In the experiment, the hot panel was heated to 280°C using a heating plate, while the structural temperature of the piezoelectric element attachment on the cold panel was only 80°C. Therefore, the bracket in the thermal protection system acts as a high-temperature buffer waveguide, effectively isolating the cold and hot panels from their high-temperature operating conditions. It can also serve as a medium for wave propagation.

[0081] Specifically, the following steps are included:

[0082] (1) The safe area on the cold end side of the thermal protection system, i.e. Figure 4 Four piezoelectric elements P1 to P4 are arranged near the four bracket connection points of the intercooler panel.

[0083] (2) When the hot panel is subjected to impact, a guided wave response is generated in the hot panel of the thermal protection system, and it propagates along the connecting bracket to the four piezoelectric plates P1 to P4 arranged on the lower surface of the cold panel, such as... Figure 5 As shown.

[0084] (3) The buffered guided wave signals I1(t) to I2(t) received by each piezoelectric element P1 to P4 are synchronously acquired at a sampling rate of 10MHz, such as Figures 6-9 As shown.

[0085] (4) Initially determine the arrival times pt1 to pt4 of the direct waves in each buffered guided wave signal I1(t) to I4(t), and select the minimum value pt1 to pt4. min It is 170.1 μs;

[0086] (5) Shift each buffered waveguide signal I1(t) to the left by pt. min The pre-aligned buffered guided wave signals v1(t)~v4(t) are obtained from the starting point. Figure 10 and Figure 11 v1(t) and v2(t) for pre-aligned starting points are given respectively;

[0087] (6) Determine a sufficiently small time step as Δt = 3μs, and shift each buffered guided wave signal v1(t) to v4(t) to the right by Δt to obtain v i (t-Δt), where i = 1, 2, 3, 4. Figure 12 and Figure 13 v1(t-Δt) and v2(t-Δt) are given respectively;

[0088] (7) Utilize all v i (t-Δt) is processed for high-resolution imaging, which includes the following steps:

[0089] For each v i (t-Δt) is subjected to dispersion compensation processing to obtain a buffered guided wave signal v1 with enhanced resolution. i (t), Figure 14 and Figure 15 v11(t) and v12(t) are given respectively.

[0090] Construct any two piezoelectric elements P i and P j Buffered guided wave signals between: v ij (t)=v1 i (t)*v1 j (t)*v a (t), where j = 1, 2, 3, 4, i ≠ j, * denotes convolution operation, v a (t) represents the selected narrowband waveform with a center frequency of 90kHz, such as Figure 16 As shown. Figure 17 The buffered guided signal v between P1 and P2 is given. 12 (t).

[0091] Using the Hilbert transform, obtain each v ij The envelope s of (t) ij (t), such as Figure 17 As shown.

[0092] Calculate the pixel values ​​at all locations within the monitoring area of ​​the thermal protection system:

[0093]

[0094] Calculate the pixel values ​​at all locations within the monitoring area of ​​the thermal protection system to obtain high-resolution imaging results, such as... Figure 18 As shown;

[0095] (8) Repeat steps (6) to (7) above to obtain the result for v. i (t) Imaging results after shifting to the right by different time steps nΔt, and the maximum pixel value M in each imaging result is extracted. n ,like Figure 19 As shown;

[0096] (9) With the maximum M 10 The corresponding high-resolution imaging results serve as the final buffer guided wave imaging monitoring results for impact events in the thermal protection system, such as... Figure 20 As shown, "X" represents the actual impact location. It can be seen that the imaging results match the actual impact location, which proves the accuracy of the buffer waveguide imaging monitoring results.

[0097] Therefore, this invention employs the aforementioned buffer guided wave imaging monitoring method for impact events in a launch vehicle's thermal protection system. By using piezoelectric elements arranged in the safe area on the cold end side of the thermal protection system, reliable online sensing of buffer guided waves can be achieved for impact events in the thermal protection system under harsh high-temperature conditions. Simultaneously, iterative imaging of buffer guided wave signals with different delays solves the problems of unknown pre-acquisition time of the impact buffer guided wave response signal and the difficulty in directly implementing impact imaging monitoring.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for monitoring impact events in a launch vehicle's thermal protection system using buffered guided wave imaging, characterized in that: Includes the following steps: S1: Arranged in the safe area on the cold end side of the thermal protection system. A piezoelectric element, Not less than 3; S2: When an impact event occurs, a guided wave response is generated in the thermal structure of the thermal protection system and propagates along the connecting mechanism to the piezoelectric elements arranged on the cold end side. Place; S3: Synchronously acquire data from each piezoelectric element Received buffered waveguide signal ,in, For time variables, ; S4: Preliminary determination of each buffer waveguide signal Time of arrival of direct waves and select minimum value ; S5: Transfer each buffered waveguide signal Shift to the left Obtain the buffered guided wave signal with pre-aligned starting point. ; S6: Transfer each buffered waveguide signal Shift time step to the right ,get ; S7: Utilize all Perform high-resolution imaging processing; S71: For each Dispersion compensation processing is performed to obtain a buffered waveguide signal with enhanced resolution. ; S72: Construct any two piezoelectric elements and Buffered guided wave signals between: ,in, , , This represents the convolution operation. The selected center frequency is Narrowband waveform, The selected center angular frequency; S73: Seeking envelope ; S74: Calculate the pixel values ​​at all locations within the monitoring area of ​​the thermal protection system. ,in, These are the coordinates of any location within the monitoring area of ​​the thermal protection system. for The pixel at that location corresponds to the envelope. The acquired signal amplitude, for The corresponding guided wave mode from the monitoring area Starting from the location, the propagation is buffered and transmitted to the piezoelectric element. and The sum of the corresponding buffer propagation time and reference time; S75: Calculate the pixel values ​​at all locations within the monitoring area of ​​the thermal protection system to obtain high-resolution imaging results; S8: Repeat steps S6-S7 above to obtain the desired result. Shift to the right by different time steps The maximum pixel value is extracted from each of the subsequent imaging results. ,in, This represents the number of time steps shifted to the right. , The maximum number of time steps for a rightward time shift; S9: at the maximum The corresponding high-resolution imaging results serve as the final buffer guided wave imaging monitoring results for impact events in the thermal protection system.

2. The buffer guided wave imaging monitoring method for impact events in a launch vehicle thermal protection system according to claim 1, characterized in that: In step S2, impact events include lightning strikes to the launch vehicle's thermal protection system on the ground and during launch, impacts from tools or detached parts, and impacts from space debris during space operations.

3. The buffer guided wave imaging monitoring method for impact events in a launch vehicle thermal protection system according to claim 1, characterized in that: Step S71 specifically includes the following steps: S711: Obtaining the linearized wavenumber curve: ,in, For linearized wavenumber curves, The absolute or relative wavenumber curve of the original dispersion of the guided wave mode corresponding to the buffered guided wave signal. Angular frequency, For the corresponding guided wave mode in Group velocity of downward propagation; S712: Calculate the frequency domain interpolation mapping sequence: ,in, The calculated frequency domain interpolation mapping sequence, for The inverse function; S713: Yes Perform frequency domain interpolation: ,in, This is the result of frequency domain interpolation. for The Fourier transform result; S714: Yes Performing the inverse Fourier transform yields ; S715: Only retain each The part corresponding to the direct wave is set to zero, and the subsequent signal part is set to zero.

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