Isotropic material plate impact positioning method constructed based on wavenumber domain response function

Abstract

The invention provides an isotropic material plate impact positioning method constructed based on a wavenumber domain response function, belongs to the technical field of aircrafts, solves the problem that an existing impact positioning method is low in positioning precision and robustness, and comprises the steps that a frequency dispersion curve of guided waves is calculated according to material attributes and geometric dimensions of a detected piece; selecting a preset frequency interval, constructing a wavenumber-angle relation function, and combining the wavenumber-angle relation function 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; drawing a pattern presented by the spatial domain response distribution function into an electrode of a piezoelectric crystal to obtain a directivity sensor capable of screening frequency components according to directions; the method comprises the following steps: rigidly connecting a plurality of directional sensors to a detected piece, outputting-1dB bandwidth of a response signal, constructing a fan-shaped region of each directional sensor, and taking an intersection region of all fan-shaped regions as a positioning result of an 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 aerospace technology, especially the rapid development of special spacecraft technologies 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 also been enhanced. However, the density of space debris in Earth orbit has also increased year by year, increasing the risk of collision with in-orbit spacecraft, posing a huge challenge to the operational safety of in-service spacecraft. Timely and effective monitoring and locating of space debris impact events on spacecraft is conducive to the assessment, diagnosis and repair of spacecraft structural damage caused by impact events, thereby ensuring the in-orbit service life of spacecraft.

[0003] Therefore, people try to improve the above technical solutions. Li Xiaolu et al. disclosed in the invention patent CN101776441A "a real-time online spacecraft shell impact degree and impact location measurement system". The method is to lay a distributed fiber Bragg grating sensor system in the spacecraft shell. When the spacecraft shell is subjected to external impact and stress and strain occur, the deformation around the impact point causes the central wavelength of the monitoring light wave of the fiber Bragg grating sensor to change. The optical signal demodulation system converts the central wavelength change value of the monitoring light wave into the stress and strain of three sensor positions (or more) around the impact point, and inputs it into the spacecraft shell impact degree and impact location calculation system to determine the spacecraft shell impact degree and impact location.

[0004] In the technical solution of Li Xiaolu et al., the positioning accuracy and area of ​​the impact are limited by the density and range of the fiber optic sensor arrangement. Zhou Hao et al. disclosed in the invention patent CN113218875A a "positioning system and positioning method for a spacecraft impacted by space debris". This method uses the in-plane shear wave SH0 wave and the four-point geometric positioning method to locate the impact of space debris, mark the peak time difference of the pulse signal generated by the impact, determine the radius of the circle with three sensors at a long distance as the center, determine the common tangent circle of the three circles, and use the center of the circle as the result of the impact positioning.

[0005] In the technical solution of Zhou Hao et al., the large-range 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 accuracy of peak time difference extraction. The positioning accuracy of this method is not robust. Summary of the invention

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

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

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

[0009] 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;

[0010] Step 4: Plot the pattern presented by the spatial domain response distribution function into an electrode of a piezoelectric crystal to obtain a directional sensor having a frequency component that is screened according to a direction;

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

[0012] Preferably, in step 2, constructing a wave number-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 step of constructing a wave number domain response function in step 3, and performing Fourier transform on the wave number domain response function to obtain a spatial domain response distribution function comprises:

[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)) direction of receiving mechanical vibration signal;

[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 scaling 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, thereby obtaining a directional sensor with the ability to filter frequency components 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.

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

[0027] Step 5.1: When the isotropic elastic plate is hit, the shock wave spreads out 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 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 ] is in the 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 positioning 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 according to the frequency, and quickly locates the impact event occurring on the plate-like structure through the intersection area of ​​the receiving directions of multiple sensors, and is suitable for various occasions requiring structural health monitoring.

[0031] 2. The present invention has strong anti-interference capability: the system 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.

[0032] 3. The present invention can adapt to complex environments and large-scale monitoring: guided waves can propagate over long distances in the material plate and carry key information of the impact point. By rationally arranging a small number of sensors, a large-scale coverage of the spacecraft structure can be achieved, reducing system cost and weight, and adapting to the complex space environment of the spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0034] Figure 2A schematic diagram of a 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 diagram 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 fan-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 result provided by the present invention. DETAILED DESCRIPTION

[0039] Combination 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 waveguide 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 L and c T are the longitudinal and transverse 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 guided wave propagation, the frequency-wave number response function is The system response at different frequencies and wave numbers is described:

[0047]

[0048] When satisfied When 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 wave number 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 tested object;

[0051] S2: Select a preset frequency interval, construct a wave number-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), is the vector coordinate obtained by discretizing the wave number-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 exhibits the characteristic 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)) direction of receiving mechanical vibration signal;

[0061] This implementation method 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: Plotting the pattern presented by the spatial domain response distribution function into the electrode of the piezoelectric crystal to obtain a directional sensor with the ability to filter frequency components according to direction;

[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, thereby obtaining a directional sensor with the ability to filter frequency components 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.

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

[0065] S501: When the isotropic elastic plate is impacted, the shock wave spreads around 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 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 ] is in the 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 positioning result of the impact point;

[0067] This implementation can adapt to complex environments and large-scale monitoring. The guided waves can propagate over long distances in the material plate and carry key information about the impact point. By properly arranging a small number of sensors, a large-scale coverage of the spacecraft structure can be achieved, reducing system cost and weight, and adapting to the complex space environment of the spacecraft.

[0068] Example

[0069] Combination Figure 2-6 This embodiment is described as follows. Figure 2 As shown, Figure 2 The frequency-wavenumber dispersion curve of a 6060 aluminum alloy plate with a thickness of 1 mm. 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 wave number interval through formula (4), and the wave number 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, in this embodiment, according to formula (5) Projection into 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 frequency components filtered according to 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 regarded as the positive and negative electrode area of ​​the piezoelectric sensor; the area with an absolute value lower than the threshold is regarded 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 waveguide 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 spectral components, 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 in the fan-shaped area obtained by this positioning method.

[0073] like Figure 6 As shown, when the waveguide 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 is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. An isotropic material plate impact positioning method based on a wave number domain response function is characterized in that: The steps of the isotropic material plate impact positioning method constructed based on the wave number domain response function include: Step 1: Calculate the dispersion curve of the guided wave according to the material properties and geometric dimensions of the test piece; Step 2: Select a preset frequency interval, construct a wave number-angle relationship function, and combine it with the frequency curve to obtain a frequency-angle function; 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; Step 4: Plot the pattern presented by the spatial domain response distribution function into an electrode of a piezoelectric crystal to obtain a directional sensor having a frequency component that is screened according to a direction; Step 5: Rigidly connect several directional sensors to the detected object, output the -1dB bandwidth of the response signal, and construct the fan-shaped area of ​​each directional sensor. The intersection area of ​​all the fan-shaped areas is used as the positioning result of the impact point.

2. The isotropic material plate impact positioning method based on wave number domain response function construction according to claim 1 is characterized in that: Step 2 specifically includes: 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); Wavenumber-angle relationship function The expression is: In formula (1), is the vector coordinate obtained by discretizing the wave number-angle relationship function, and are mutually orthogonal unit vectors.

3. The isotropic material plate impact positioning method based on wave number domain response function construction according to claim 1 is characterized in that: The steps of constructing a wave number domain response function in step 3 and performing Fourier transform on the wave number domain response function to obtain a 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 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)) direction of receiving mechanical vibration signal; Wavenumber domain response function The expression is: 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 scaling constant of continuity, j is an imaginary number, J0(0)=1.

4. The isotropic material plate impact positioning method based on wave number domain response function construction according to claim 1 is characterized in that: The directional sensor having the function of filtering frequency components according to directions 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, so as to obtain a directional sensor with the ability to filter frequency components 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.

5. According to the isotropic material plate impact positioning method based on wave number domain response function construction according to claim 1, the step of obtaining the positioning result of the impact point in step 5 comprises: Step 5.1: When the isotropic elastic plate is hit, the shock wave spreads out 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 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 ] is in the 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]; Step 5.2: Calculate the fan-shaped areas of all directional sensors, and use the intersection of the fan-shaped areas as the positioning result of the impact point.

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