Isotropic material plate impact location method based on wavenumber domain response function

Abstract

The present invention proposes an isotropic material plate impact positioning method based on a wavenumber domain response function, which belongs to the field of aircraft technology and solves the problems of low positioning accuracy and robustness of existing impact positioning methods. The steps include: calculating the dispersion curve of the guided wave according to the material properties and geometric dimensions of the detected part; selecting a preset frequency range, constructing a wavenumber-angle relationship function, and combining it with the frequency curve to obtain a frequency-angle function; constructing a wavenumber domain response function, and performing Fourier transform on the wavenumber domain response function to obtain a spatial domain response distribution function; mapping the pattern presented by the spatial domain response distribution function into an electrode of a piezoelectric crystal to obtain a directional sensor with a frequency component filtered according to direction; rigidly connecting several directional sensors to the detected part, outputting the 1dB bandwidth of the response signal, and constructing a fan-shaped area for each directional sensor, and using the intersection area of ​​all fan-shaped areas as the positioning result of the impact point.

Description

Technical Field

[0001] The invention relates to an isotropic material plate impact positioning method constructed based on a wave number domain response function, and belongs to the technical field of aircraft. Background Art

[0002] With the continuous advancement of space technology, especially the rapid development of specialized spacecraft such as long-life near-Earth space stations, manned spacecraft, and deep-space probes, the service life of new-generation spacecraft has been extended and their ability to adapt to harsh environments has been enhanced. However, the density of space debris in Earth orbit has also increased year by year, increasing the risk of collisions with in-orbit spacecraft and posing a significant challenge to the operational safety of in-orbit spacecraft. Timely and effective monitoring and location of space debris impacts on spacecraft facilitates the assessment, diagnosis, and repair of structural damage caused by impacts, thereby ensuring the in-orbit service life of spacecraft.

[0003] Therefore, attempts have been made to improve upon the aforementioned technical solution. In their invention patent CN101776441A, Li Xiaolu et al. disclosed a "real-time online spacecraft shell impact severity and impact location measurement system." This method involves installing a distributed fiber Bragg grating (FBG) sensor system within the spacecraft shell. When the spacecraft shell is subjected to an external impact and generates stress and strain, the deformation around the impact point causes a change in the central wavelength of the fiber Bragg grating sensor's monitoring lightwave. An optical signal demodulation system then converts the central wavelength change of the monitoring lightwave into stress and strain at three (or more) sensor locations around the impact point. These values ​​are then input into a spacecraft shell impact severity and impact location calculation system to determine the spacecraft shell impact severity and impact location.

[0004] In the technical solution proposed by Li Xiaolu et al., the accuracy and area of ​​impact positioning are limited by the density and range of the fiber optic sensor layout. Zhou Hao et al., in their invention patent CN113218875A, disclosed a "system and method for locating spacecraft impacted by space debris." This method uses in-plane shear waves (SH0) and a four-point geometric positioning method to locate impact debris. The method marks the peak time difference of the pulse signal generated by the impact, determines the radius of a circle centered on three distant sensors, and then determines the common tangent circle of the three circles, using the center of the circle as the impact location result.

[0005] In the technical solution proposed by Zhou Hao and others, the large-scale propagation characteristics of guided waves can be used to achieve large-scale impact positioning with a relatively small number of sensors. However, the time difference extraction accuracy of the positioning signal is an important factor affecting the positioning accuracy. In actual application scenarios, complex environmental noise, sound wave dispersion and attenuation and other factors have a significant impact on the peak time difference extraction accuracy. The positioning accuracy of this method is not very robust. Summary of the Invention

[0006] In order to solve the problems of low positioning accuracy and robustness of existing impact positioning methods, the present invention proposes an isotropic material plate impact positioning method based on a wavenumber domain response function. The specific steps include:

[0007] Step 1: Calculate the dispersion curve of the guided wave based on the material properties and geometric dimensions of the test piece;

[0008] Step 2: Select a preset frequency range, construct a wavenumber-angle relationship function, and combine it with the frequency curve to obtain the frequency-angle function;

[0009] Step 3: Construct the wavenumber domain response function and perform Fourier transform on the wavenumber domain response function to obtain the spatial domain response distribution function;

[0010] Step 4: Plot the pattern presented by the spatial domain response distribution function onto the electrodes of the piezoelectric crystal to obtain a directional sensor capable of filtering frequency components according to direction;

[0011] Step 5: Rigidly connect several directional sensors to the test object, output the -1dB bandwidth of the response signal, and construct a fan-shaped area for each directional sensor. The intersection of all fan-shaped areas is used as the location result of the impact point.

[0012] Preferably, in step 2, constructing a wavenumber-angle relationship function and combining it with the frequency curve to obtain a frequency-angle function specifically includes:

[0013] Select the frequency interval [f m ,f M ], in [f m ,f M ]Calculate the A0 mode wave number interval within the frequency interval [k m ,k M ] and establish the wave number interval and angle interval [θ m ,θ M ], and the wave number-angle relationship function is obtained. According to the wave number-frequency relationship function k of the A0 mode of the guided wave dispersion curve A0 (f), according to the wave number-frequency relationship function k A0 (f) and wave number-angle relationship function Construct the frequency-angle function θ n (f);

[0014] Wavenumber-angle relationship function The expression is:

[0015]

[0016] In formula (1), is the vector coordinate obtained by discretizing the wave number-angle relationship function, and are mutually orthogonal unit vectors.

[0017] Preferably, the steps of constructing a wavenumber domain response function in step 3 and performing Fourier transform on the wavenumber domain response function to obtain a spatial domain response distribution function include:

[0018] Step 3.1: Using the Bessel function of the first kind, according to The wave number-angle relationship function Projection into the wave number space of an isotropic elastic plate The wave number domain response function is obtained from

[0019]

[0020] Step 3.2: Convert the wavenumber domain response function Perform inverse Fourier transform to obtain the spatial domain response distribution function Ω(θ n (f)), the waveguide passes through the region Ω(θ n (f)) After that, the A0 mode in the obtained mechanical vibration signal satisfies And according to the frequency-angle function θ n (f) Analyze the frequency components and determine the region Ω(θ n (f) The direction of receiving mechanical vibration signals;

[0021] Wavenumber domain response function The expression is:

[0022]

[0023] In formula (2), is the coordinate (k x ,k y ) is the wave number space, N is the wave number-angle relationship function The number of discretized coordinate points, a is the adjustment The scale constant of continuity, j is an imaginary number, J0(0)=1.

[0024] Preferably, obtaining the directional sensor capable of filtering frequency components according to directions in step 4 specifically includes:

[0025] The pattern presented by the spatial domain response distribution function is drawn into the electrode of the piezoelectric crystal, and the mechanical vibration signal is linearly converted into an electrical signal through the inverse piezoelectric effect of the piezoelectric crystal, resulting in a directional sensor with the ability to filter frequency components according to direction. The waveguide receiving direction of the directional sensor and the main frequency of the response signal satisfy the frequency-angle function.

[0026] Preferably, the step of obtaining the location result of the impact point in step 5 includes:

[0027] Step 5.1: When the isotropic elastic plate is hit, the shock wave spreads outward in the form of guided waves with the impact point as the center. When the guided waves pass through the directional sensor rigidly connected to the plate, the sensor responds with a peak frequency of f max The electrical signal with peak frequency -1dB bandwidth is [f lower ,f upper ], using the frequency-angle function θ n (f) Calculate the peak frequency-1dB bandwidth [f lower ,f upper ] direction interval [θ1,θ2], that is, the impact point detected by the current directional sensor is located in the fan-shaped area of ​​[θ1,θ2];

[0028] Step 5.2: Calculate the fan-shaped areas of all directional sensors and use the intersection of the fan-shaped areas as the location result of the impact point.

[0029] The beneficial effects of the present invention are:

[0030] 1. The present invention utilizes a sensor that can determine the receiving direction of guided waves based on frequency. It can quickly locate impact events occurring on plate-like structures through the intersection of multiple sensor receiving directions. It is suitable for various occasions requiring structural health monitoring.

[0031] 2. The present invention has strong anti-interference capability: the system performs fine analysis on the frequency components, reduces the influence of environmental noise and signal attenuation on the detection results, and improves the robustness of the system.

[0032] 3. This invention is adaptable to complex environments and large-scale monitoring: guided waves can propagate over long distances within a material plate, carrying critical information about the impact point. By rationally deploying a small number of sensors, it can achieve wide coverage of a spacecraft structure, reducing system cost and weight and adapting to the complex space environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A schematic flow chart of the isotropic material plate impact positioning method based on the wavenumber domain response function provided by the present invention;

[0034] Figure 2Schematic diagram of the frequency-wavenumber dispersion curve of a 6060 aluminum alloy plate with a thickness of 1 mm provided by the present invention;

[0035] Figure 3 A flow chart of obtaining an angle-frequency curve provided by the present invention;

[0036] Figure 4 The spatial domain response area Ω(θ n (f) Schematic diagram of the normalization results;

[0037] Figure 5 A flow chart for obtaining a sector-shaped area of ​​an impact point of a single directional sensor provided by the present invention;

[0038] Figure 6 This is a schematic diagram of the impact positioning results provided by the present invention. DETAILED DESCRIPTION

[0039] Combine Figure 1 This embodiment is described. First, the principle of using the waveguide dispersion curve to design the wavenumber domain response distribution of the isotropic elastic plate and then controlling the propagation direction of the guided wave is described.

[0040] The relationship between the frequency and wave number k(f) of a guided wave propagating on an isotropic elastic plate can be characterized by the following dispersion equation:

[0041]

[0042] In formula (1), f is the waveguide frequency, h is the half thickness of the plate, k is the wave number, and c is the waveguide frequency. L and c T are the longitudinal and shear wave velocities, respectively.

[0043] For guided waves in an isotropic elastic plate, the wave number k is a scalar along the wave propagation direction. Assuming that the wave propagates along a certain angle θ, the wave number vector It can be expressed as:

[0044]

[0045] In formula (2), and are mutually orthogonal unit vectors.

[0046] In the propagation of guided waves, the frequency-wavenumber response function The system response at different frequencies and wave numbers is described:

[0047]

[0048] When satisfied When , the response function This means that the guided wave with frequency f is conductive in the θ direction;

[0049] Secondly, if Figure 1 As shown, the steps of the isotropic material plate impact positioning method constructed based on the wavenumber domain response function described in this embodiment include:

[0050] S1: Calculate the dispersion curve of the guided wave according to the material properties and geometric dimensions of the test piece;

[0051] S2: Select a preset frequency range, construct a wavenumber-angle relationship function, and combine it with the frequency curve to obtain a frequency-angle function;

[0052] Select the frequency interval [f m ,f M ], calculate the A0 mode wave number interval [k m ,k M ] and establish the wave number interval and angle interval [θ m ,θ M ], and the wave number-angle relationship function is obtained. According to the wave number-frequency relationship function k of the A0 mode of the guided wave dispersion curve A0 (f), according to the wave number-frequency relationship function k A0 (f) and wave number-angle relationship function Construct the frequency-angle function θ n (f), wave number-angle relationship function as follows:

[0053]

[0054] In formula (4), are the vector coordinates obtained by discretizing the wavenumber-angle relationship function.

[0055] S3: Construct the wave number domain response function and perform Fourier transform on the wave number domain response function to obtain the spatial domain response distribution function;

[0056] S301: The first kind of Bessel function has J0(0)=1, and shows the characteristics of attenuated oscillation as x increases. Therefore, the first kind of Bessel function can be used according to The wave number-angle relationship function Projection into the wave number space of an isotropic elastic plate The wavenumber domain response function obtained by projection is as follows:

[0057]

[0058] In formula (5), is the coordinate (k x ,k y ) is the wave number space, N is the wave number-angle relationship function The number of discretized coordinate points, a is the adjustment The scaling constant of continuity, j is an imaginary number.

[0059] S302: Wave number domain response function Perform inverse Fourier transform to obtain the spatial domain response distribution with the same directivity as the wave number domain response distribution. When the guided wave propagating on the isotropic elastic plate passes through the region Ω(θ n (f)) After that, the A0 mode in the obtained mechanical vibration signal satisfies

[0060] S303: Given the material properties and geometric dimensions of the isotropic material plate, according to the frequency-angle function θ n (f) Analyze the frequency components and determine the region Ω(θ n (f) The direction of receiving mechanical vibration signals;

[0061] This embodiment performs a fine analysis of the frequency components, reduces the influence of environmental noise and signal attenuation on the detection results, and improves the robustness of the system.

[0062] S4: The pattern presented by the spatial domain response distribution function is mapped onto the electrodes of the piezoelectric crystal to obtain a directional sensor with a direction-based frequency component screening capability.

[0063] The pattern presented by the spatial domain response distribution function is drawn into the electrode of the piezoelectric crystal, and the mechanical vibration signal is linearly converted into an electrical signal through the inverse piezoelectric effect of the piezoelectric crystal, resulting in a directional sensor with the ability to filter frequency components according to direction. The waveguide receiving direction of the directional sensor and the main frequency of the response signal satisfy the frequency-angle function.

[0064] S5: Rigidly connect several directional sensors to the detected object, output the -1dB bandwidth of the response signal, and construct a fan-shaped area for each directional sensor. The intersection of all the fan-shaped areas is used as the positioning result of the impact point.

[0065] S501: When the isotropic elastic plate is hit, the shock wave spreads outward in the form of guided waves with the impact point as the center. When the guided waves pass through the directional sensor rigidly connected to the plate, the sensor responds with a peak frequency of f max The electrical signal with peak frequency -1dB bandwidth is [f lower ,f upper ], using the frequency-angle function θ n (f) Calculate the peak frequency-1dB bandwidth [flower ,f upper ] direction interval [θ1,θ2], that is, the impact point detected by the current directional sensor is located in the fan-shaped area of ​​[θ1,θ2];

[0066] S502: Calculate the fan-shaped areas of all directional sensors, and use the intersection of the fan-shaped areas as the location result of the impact point;

[0067] This implementation is adaptable to complex environments and large-scale monitoring. Guided waves can propagate across long distances within the material sheet, carrying critical information about the impact point. By strategically deploying a small number of sensors, wide-area coverage of the spacecraft structure can be achieved, reducing system cost and weight and adapting to the complex space environment.

[0068] Example

[0069] Combine Figure 2-6 This embodiment is described as follows. Figure 2 As shown, Figure 2 The frequency-wavenumber dispersion curve of 6060 aluminum alloy plate with a thickness of 1mm. In the range of [200,350]kHz, the A mode only contains the A0 mode, which is used to construct the wavenumber domain response function. The frequency range is calculated and the wave number range is [530,1510]rad / m.

[0070] like Figure 3 As shown, in this embodiment, the [0,180]°rad angle interval is mapped to the [530,1510]rad / m wavenumber interval through formula (4), and the wavenumber vector is obtained. use and Figure 2 The dispersion curve of [200,350]kHz gives the angle-frequency relationship θ n (f).

[0071] like Figure 4 As shown, this embodiment uses formula (5) to convert Projection to wavenumber space The wave number domain response function is obtained Will Perform inverse Fourier transform to obtain n (f) Spatial domain response area Ω(θ n (f)), Ω(θ n (f)) is normalized and drawn as an electrode on a piezoelectric crystal to obtain a directional sensor with a frequency component that is filtered according to the direction. 0.4max(Ω(θ n(f))) is used as the threshold and normalized. The area with an absolute value higher than the threshold is defined as the positive and negative electrode area of ​​the piezoelectric sensor; the area with an absolute value lower than the threshold is defined as the ground electrode area.

[0072] like Figure 5 As shown, this embodiment uses simulation software to simulate the effect of the sensor sensing the direction of the impact point. The impact signal is applied in the 70° direction of the directional sensor. The difference between the positive and negative signals of the sensor is the result of the guided wave generated by the impact passing through the spatial domain response area Ω (θ n (f)) response signal, the response signal is Fourier transformed to analyze the spectrum component, the -1dB bandwidth is [165,185]kHz, according to θ n (f) The curve determines that the angle interval is [61,72]°, and the impact point is located within the fan-shaped area obtained by this positioning method.

[0073] like Figure 6 As shown, when the guided wave generated by the impact passes through the directional sensors at other positions on the board, this embodiment calculates the fan-shaped areas of the respective angle intervals based on the -1dB bandwidth of the electrical signal responded by the sensor, limits the impact point to the intersection area of ​​these fan-shaped areas, and uses the intersection area as the impact positioning result.

[0074] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. An isotropic material plate impact positioning method based on a wavenumber domain response function is characterized in that: The steps of the isotropic material plate impact positioning method constructed based on the wavenumber domain response function include: Step 1: Calculate the dispersion curve of the guided wave based on the material properties and geometric dimensions of the test piece; Step 2: Select a preset frequency range, construct a wavenumber-angle relationship function, and combine it with the dispersion curve to obtain the frequency-angle function; Step 2 specifically includes: Select the frequency interval that contains only A0 mode in the A mode of the guided wave dispersion curve ,exist Calculate the A0 modal wave number interval within the frequency interval And establish wave number interval and angle interval The corresponding relationship between wave number and angle is obtained. , according to the wave number-frequency relationship function of the A0 mode of the guided wave dispersion curve , according to the wave number-frequency relationship function and the wavenumber-angle relationship function Constructing a frequency-angle function ; Wavenumber-angle relationship function The expression is: （1）； In formula (1), is the vector coordinate obtained by discretizing the wave number-angle relationship function, and are mutually orthogonal unit vectors; Step 3: Construct the wave number domain response function and perform Fourier transform on the wave number domain response function to obtain the spatial domain response distribution function; The steps of constructing the wavenumber domain response function in step 3 and performing Fourier transform on the wavenumber domain response function to obtain the spatial domain response distribution function include: Step 3.1: Using the Bessel function of the first kind, according to The wave number-angle relationship function Projection into the wave number space of an isotropic elastic plate The wave number domain response function is obtained from ; Step 3.2: Convert the wavenumber domain response function Perform inverse Fourier transform to obtain the spatial domain response distribution function with the same directivity as the wavenumber domain response distribution , the waveguide passes through the area of ​​spatial domain response distribution Afterwards, the A0 mode in the obtained mechanical vibration signal satisfies , and according to the frequency-angle function Analyze frequency components and determine the area The direction of receiving mechanical vibration signals; Wavenumber domain response function The expression is: （2）； In formula (2), For coordinates The wave number space formed by is the wave number-angle relationship function The number of discretized coordinate points, To adjust The scale constant of continuity, is an imaginary number, ; Step 4: Plot the pattern presented by the spatial domain response distribution function onto the electrodes of the piezoelectric crystal to obtain a directional sensor capable of filtering frequency components according to direction; Step 5: Rigidly connect several directional sensors to the test object, output the -1dB bandwidth of the response signal, and construct a fan-shaped area for each directional sensor. The intersection of all fan-shaped areas is used as the location result of the impact point.

2. The isotropic material plate impact positioning method based on wavenumber domain response function according to claim 1 is characterized in that: The directional sensor having the ability to filter frequency components according to direction obtained in step 4 specifically includes: The pattern presented by the spatial domain response distribution function is drawn into the electrode of a piezoelectric crystal, and the mechanical vibration signal is linearly converted into an electrical signal through the inverse piezoelectric effect of the piezoelectric crystal, thereby obtaining a directional sensor with a frequency component filtered according to direction, and the waveguide receiving direction of the directional sensor and the main frequency of the response signal satisfy the frequency-angle function.

3. According to the isotropic material plate impact location method based on wavenumber domain response function construction in claim 1, the step of obtaining the location result of the impact point in step 5 comprises: Step 5.1: When the isotropic elastic plate is hit, the shock wave spreads outward in the form of guided waves with the impact point as the center. When the guided waves pass through the directional sensor rigidly connected to the plate, the sensor responds with a peak frequency of The electrical signal has a peak frequency and a -1dB bandwidth of , using the frequency-angle function Calculate peak frequency-1dB bandwidth Direction range , that is, the impact point detected by the current directional sensor is located at within the sector area; Step 5.2: Calculate the fan-shaped areas of all directional sensors and use the intersection of the fan-shaped areas as the location result of the impact point.

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