Structure shock location method based on multiple wavelet decomposition and time reversal

Abstract

The application discloses a structure impact positioning method based on multiple wavelet decomposition and time reversal, which comprises receiving impact stress wave signals of each sensor on a monitoring area in a Cartesian coordinate system, selecting multiple different Morlet wavelet base functions according to the scale of the Morlet wavelet base function, decomposing the impact stress wave signals by the selected multiple different Morlet wavelet base functions, reconstructing the signals, performing normalization processing, assuming the similarity of all time reversal signal waveforms of the assumed impact source position by using a cosine similarity formula, and multiplying to obtain the pixel value of the assumed impact source position; calculating the pixel values of multiple assumed impact source positions in the monitoring area, and positioning the impact source position according to the pixel value. The method disclosed by the application adopts multiple Morlet wavelet base functions to decompose and reconstruct the impact stress wave signals, weakens the influence of interference signals such as boundary reflection and noise on impact positioning, and improves the positioning precision.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of structural health monitoring, and particularly relates to a structural impact positioning method. BACKGROUND

[0002] Composite stiffened panel structures are widely used in aerospace, rail transportation, marine engineering and other fields due to their excellent mechanical properties. However, the composite stiffened panel structures are inevitably threatened by external impacts during production, manufacturing, service and maintenance, causing visual invisible damages such as composite material indentation, delamination and fiber fracture, which leads to degradation of the mechanical bearing capacity of the structure and seriously affects its safety performance and service life. Structural health monitoring technology can monitor the state information of the structure in real time, and provide guidance for the health and safety maintenance of the structure. Therefore, impact monitoring of the composite stiffened panel structure is an important issue in the field of structural health monitoring.

[0003] Impact monitoring requires a reliable impact positioning method. The impact positioning method extracts feature information from the impact stress wave signals collected by sensors in the monitored structure and realizes impact positioning by combining specific algorithms. Existing impact positioning methods include time difference method, multiple signal classification algorithm, model-based optimization method and neural network-based impact positioning method. The time difference method obtains the geometric position relationship between multiple pairs of piezoelectric sensors and impact sources, and determines the impact position by extracting the arrival time difference of the impact stress wave between the sensors using signal processing technology. However, in complex stiffened structures, the impact stress wave has propagation forms such as boundary reflection and secondary scattering, making it difficult to accurately determine the arrival time. The multiple signal classification impact positioning algorithm estimates the impact position by performing eigenvalue decomposition on the covariance matrix of the sensor array output data, and utilizing the orthogonality of the signal subspace and the noise subspace. However, this method is too complex to calculate. The model-based optimization method converts the impact positioning problem into an optimal inverse problem to locate the impact source, but it is difficult to construct an optimization model for large-scale complex structures. In addition, the neural network-based impact positioning method requires a large number of impact tests on the monitored structure to construct a large sample data and corresponding label information library to train the network, which is not practical for large-scale aerospace structures and other types of structures. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of existing impact positioning methods and provide an improved structural impact positioning method.

[0005] To this end, some embodiments of the present application provide a structural impact location method based on multi-wavelet decomposition and time reversal, which comprises establishing a Cartesian coordinate system on a monitoring area of a monitored structure; marking the position coordinates of each sensor for receiving an impact stress wave signal on the Cartesian coordinate system; recording the received impact stress wave signal from each sensor and performing the following processing on each impact stress wave signal: selecting a plurality of different Morlet wavelet basis functions according to the scale of the Morlet wavelet basis function, and decomposing the impact stress wave signal with the plurality of Morlet wavelet basis functions; reconstructing the signals obtained by the plurality of Morlet wavelet basis functions into an impact stress wave signal, and then performing normalization processing to obtain a normalized reconstructed impact stress wave signal; and time-reversing the normalized reconstructed impact stress wave signal; calculating the waveform similarity of the time-reversed signal of each sensor relative to the compensation time delay of the assumed impact source position in the monitoring area by using the cosine similarity formula; multiplying all the waveform similarities of the time-reversed signals of the assumed impact source position to obtain the pixel value of the assumed impact source position; calculating the pixel values of a plurality of assumed impact source positions in the monitoring area; and locating the impact source position according to the pixel value.

[0006] In some embodiments, the position with the maximum pixel value and the highest color brightness is located as the impact source position

[0007] In some embodiments, calculating the waveform similarity of the time-reversed signal of each sensor relative to the compensation time delay of the assumed impact source position comprises dividing the monitoring area of the monitored structure into a plurality of grid points based on the Cartesian coordinate system, and setting any grid point as an assumed impact source position; calculating the relative time delay of the impact stress direct wave signal between each sensor according to the distance difference of each sensor to the grid point and the average speed of the impact stress wave propagating in the monitored structure; and calculating the waveform similarity of the time-reversed signal of different sensors after compensation time delay at the grid point by using the cosine similarity formula.

[0008] In some embodiments, the result obtained by multiplying the waveform similarities of the time-reversed signals between different sensors calculated at each grid point is taken as the pixel value at the grid point; and the pixel values of all grid points are calculated to realize virtual time-reversed focused imaging, wherein the position with the maximum pixel value and the highest color brightness in the image obtained by imaging represents the located impact source position.

[0009] The beneficial technical effects brought by the embodiments of the present application include: in some embodiments, the method proposed in the present application adopts multiple multi-Bessel wavelet basis functions to decompose and reconstruct the impact stress wave signal, enhances the amplitude of the direct wave signal of the impact stress wave, makes up for the attenuation of the impact stress wave signal by the stiffener, weakens the influence of interference signals such as boundary reflection and noise on impact positioning, and improves the positioning accuracy. In some embodiments, the method proposed in the present application multiplies the waveform similarity of the time reversal normalized reconstructed signal to realize impact imaging, which can further suppress the influence of noise on impact positioning and improve the imaging resolution. In some embodiments, the method proposed in the present application is based on the time reversal focusing theory, has the advantages of not needing prior knowledge of wave propagation medium and not needing complex modeling and strong practicability. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 A flowchart of a structure impact positioning method based on multiple wavelet decomposition and time reversal according to an embodiment of the present application;

[0011] Figure 2 A principle diagram of impact positioning in a method according to an embodiment of the present application;

[0012] Figure 3A 、 Figure 3B 、 Figure 3C 、 Figure 3D 、 Figure 3E 、 Figure 3F 、 Figure 3G 、 Figure 3H 、 Figure 3I 、 Figure 3J 、 Figure 3K 、 Figure 3L 、 Figure 3M 、 Figure 3N 、 Figure 3O Figures db1, db2, db3, db4, db5, db6, db7, db8, db9, db10, db11, db12, db13, db14, and db15 are respectively time domain signal diagrams of fifteen different scale multi-Bessel wavelet basis functions;

[0013] Figure 4 A composite material stiffened plate and a sensor arrangement diagram according to an embodiment of the present application;

[0014] Figure 5 A typical impact stress wave signal diagram according to an embodiment of the present application;

[0015] Figure 6A A signal diagram obtained by decomposing a db12 wavelet basis function according to an embodiment of the present application;

[0016] Figure 6BSignal graph obtained by db13 wavelet base function decomposition according to the embodiment of the application;

[0017] Figure 6C Signal graph obtained by db14 wavelet base function decomposition according to the embodiment of the application;

[0018] Figure 6D Signal graph obtained by db15 wavelet base function decomposition according to the embodiment of the application;

[0019] Figure 7A Signal graph obtained by normalized impact stress wave reconstruction according to the embodiment of the application;

[0020] Figure 7B Signal graph obtained by normalized impact stress wave reconstruction time reversal signal according to the embodiment of the application;

[0021] Figure 8 Impact source virtual time reversal focused imaging positioning result graph according to the embodiment of the application. DETAILED DESCRIPTION

[0022] The application will be further described in detail below in combination with the drawings and specific embodiments:

[0023] As shown in Figure 1 , a structural impact positioning method based on multiple wavelet reconstruction and time reversal signal similarity specifically comprises the following steps:

[0024] Step 1: Mark sensor position coordinates and record impact stress wave signals.

[0025] As shown in Figure 2 , a Cartesian coordinate system is established on the monitoring area of the monitored structure, taking the length direction of the structure as the positive direction of the x-axis and the width direction of the structure as the positive direction of the y-axis; the position coordinates of the sensors P i used for receiving impact stress wave signals excited by impact sources on the monitoring area are marked as (x i ,y i ), i = 1, 2,..., I, wherein I is the total number of sensors. The impact stress wave signals received by the sensors P i are recorded as S i (t).

[0026] Step 2: Multiple Daubechies wavelet base functions are used to decompose the impact stress wave signals S i (t).

[0027] Figure 3A 、 Figure 3B 、 Figure 3C 、 Figure 3D 、 Figure 3E、 Figure 3F 、 Figure 3G 、 Figure 3H 、 Figure 3I 、 Figure 3J 、 Figure 3K 、 Figure 3L 、 Figure 3M 、 Figure 3N 、 Figure 3O Fig. 1 shows the time domain signal graphs of fifteen different scale multi- Bessel wavelet basis functions db1, db2, db3, db4, db5, db6, db7, db8, db9, db10, db11, db12, db13, db14, and db15. According to the scale of the multi- Bessel wavelet basis function, a plurality of different multi-Bessel wavelet basis functions dbMare selected to decompose the impact stress wave signal S i (t) received by the sensor to obtain

[0028]

[0029] wherein the symbol dec represents the decomposition signal of the impact stress wave signal based on the Mth wavelet basis function dbM, and the selected multi-Bessel wavelet basis function set is Q.

[0030] Step 3: reconstructing and normalizing the impact stress wave signal.

[0031] The signals obtained by decomposing with a plurality of multi-Bessel wavelet basis functions The reconstructed impact stress wave signal is reconstructed to obtain the reconstructed impact stress wave signal

[0032]

[0033] wherein the symbol represents the signal obtained by decomposing the impact stress wave signal with the selected multi-Bessel wavelet basis function set Q The Hadamard product is calculated, and the symbol env represents taking the envelope value.

[0034] The reconstructed impact stress wave signal is normalized to obtain the normalized reconstructed impact stress wave signal

[0035]

[0036] wherein the frequency spectrum of the normalized reconstructed impact stress wave signal is

[0037]

[0038] where Imp(ω) is the frequency spectrum of the impact source excitation signal; H i (r,ω) is the transfer function of the structure; r is the distance from the impact source to the sensor; ω is the angular frequency.

[0039] Step 4: Time reversal of the normalized reconstructed impact stress wave signal.

[0040] The normalized reconstructed signal of each sensor is time reversed to obtain the time reversed signal

[0041]

[0042] where “*” denotes taking the complex conjugate of the signal.

[0043] If the time reversed signal is excited at all sensors, the response signal at the impact source location is C(ω):

[0044]

[0045] where H TR-i is the transfer function of the time reversed signal propagating from the i-th sensor to the impact source.

[0046] According to the principle of acoustic reciprocity: H TR-i = H i The time reversed signal can be written in matrix form H: Then the response signal at the impact source location C(ω) is:

[0047]

[0048] The inverse Fourier transform of C(ω) is:

[0049]

[0050] Therefore, if the time reversed signal of the impact stress wave signal received by the sensor is excited at the sensor, the signal will be focused at the impact source.

[0051] However, at a non-impact source location, because H TR-i ≠ H i , the signal cannot be focused.

[0052] Step 5: Calculate the similarity of the time reversed signal waveforms to achieve virtual time reversal focusing imaging and positioning of the impact source.

[0053] Since the impact source position is unknown, the time reversal signal excited by the sensor cannot be received at the real impact source position. The present application adopts a signal processing method to realize virtual time reversal focusing imaging. First, the monitoring area of the monitored structure is divided into a grid, and the grid point (x, y) is assumed to be the assumed impact source position. Then, the relative time delay of the direct wave of the impact stress signal between different sensors is calculated according to the distance difference between different sensors and the average velocity of the impact stress wave propagating in the monitored structure. Then, the waveform similarity of the time reversal signals between different sensors after compensation of the time delay is calculated by using the cosine similarity formula. Finally, the waveform similarity of the time reversal signals between different sensors at each grid point is multiplied to realize the time reversal focusing imaging positioning of the impact source, and the specific process is as follows: ij (τ ij (x,y)):

[0054] The distance from the assumed impact source position (x, y) to the i th sensor is L i (x,y):

[0055]

[0056] The distance difference from the assumed impact source position to different sensors is D ij (x,y):

[0057]

[0058] Where j represents the j th sensor.

[0059] For the assumed impact source position, the relative time delay τ of the impact stress wave signal received by different sensors is calculated ij (x,y):

[0060]

[0061] Where C is the average propagation velocity of the impact stress wave in the monitored structure.

[0062] According to the order of the impact stress wave received by the sensor, the time delay of the sensor is compensated, and the waveform similarity Sim of the normalized reconstructed time reversal signal containing the time length T of the direct wave of the impact stress wave after compensation of the time delay of the sensor is calculated by using the cosine similarity formula ij (τ ij (x,y)):

[0063]

[0064] Where:

[0065] wherein, L is the total sampling point number of the normalized reconstruction time reversal signal of the time length T, and l represents the lth sampling point;

[0066] wherein, T i is the ending time of the normalized reconstruction time reversal signal window of the impact stress wave signal received by the ith sensor.

[0067] The time reversal signal waveform similarity Sim ij (τ ij (x,y)) between different sensors calculated at each grid point is multiplied to obtain the result as the pixel value Image(x,y) at this place:

[0068]

[0069] The pixel values of all grid points are calculated to realize virtual time reversal focusing imaging, wherein the position with the maximum pixel value and the highest color brightness in the image obtained by imaging represents the predicted impact position.

[0070] Embodiment:

[0071] Figure 4 is the layout of the composite stiffened plate and the sensors thereon. As shown in Figure 4 , the size of the composite stiffened plate 10 is 2360mm×1260mm×2.24mm, containing a stiffener grid composed of transverse stiffeners 11 and longitudinal stiffeners 12, and 30 piezoelectric sensors 13 with a radius of 8mm are arranged on the back of the stiffened plate grid skin for receiving impact stress wave signals. According to step 1 in the above method, the lower left corner of the stiffened plate grid is taken as the origin to establish a Cartesian coordinate system, and the coordinates of each piezoelectric sensor and the impact source are recorded. An impact event is triggered at the position with coordinates (2005mm, 420mm) on the composite stiffened plate using a drop hammer device, and the impact stress wave signals received by the piezoelectric sensors are collected and recorded using a dynamic signal acquisition system with a sampling rate of 200kHz. Figure 5 is the impact stress wave signal received by one of the piezoelectric sensors. According to step 2 of the above method, the impact stress wave signal is decomposed using db12, db13, db14 and db15 wavelet basis functions, Figure 6A 、 Figure 6B 、 Figure 6C and Figure 6D , respectively. The signals obtained by decomposing the impact stress wave signal using db12, db13, db14 and db15 wavelet basis functions are shown in Figure 7AThe normalized reconstructed impact stress wave signal is shown. The time reversal of the normalized reconstructed impact stress wave signal is performed according to step 4 of the above method, and the result of the signal processing is shown in FIG. 6. Figure 7B Figure 8 The impact source virtual time reversal focused imaging positioning result obtained based on the time reversed signal according to step 5 of the above method is shown in FIG. 7. The brighter the position in the figure, the higher the possibility of the impact position. The intersection of the dashed lines is the actual impact position. Figure 7A 7B The imaging focus of the predicted impact position represented by the highest point in FIG. 8 is good, and the absolute positioning error with the actual impact position is only 5 mm. The experimental example shows that the method in the present application can be better applied to the impact position positioning of the complex composite stiffened plate structure.

[0072] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application, and are not a limitation of the present application. Those skilled in the art should understand that changes, modifications, additions or substitutions made within the essential technical scope of the present application also belong to the protection scope of the present application.​​

Claims

1. A structural impact location method based on multiple wavelet decomposition and time reversal, characterized by: The method includes the following steps: establishing a Cartesian coordinate system on the monitoring area of ​​the monitored structure; marking the position coordinates of each sensor for receiving the shock stress wave signal on the Cartesian coordinate system; recording the shock stress wave signal received from each of the sensors and performing the following processing on each shock stress wave signal: selecting a plurality of different Dobesi wavelet basis functions according to the scale of the Dobesi wavelet basis function to decompose the shock stress wave signal; reconstructing the shock stress wave signal of the signal obtained by decomposing the plurality of Dobesi wavelet basis functions, and then normalizing it to obtain a normalized reconstructed shock stress wave signal; and time-reversing the normalized reconstructed shock stress wave signal; calculating the time-reversed signal waveform similarity of each sensor after compensating for the time delay relative to the assumed shock source position in the monitoring area using the cosine similarity formula; and multiplying all the time-reversed signal waveform similarities of the assumed shock source position to obtain the pixel value of the assumed shock source position; Calculating pixel values ​​of multiple assumed impact source positions within the monitoring area; The impact source position is located according to the pixel value.

2. The structural impact location method based on multiple wavelet decomposition and time reversal according to claim 1, characterized in that: The position with the largest pixel value and the brightest color is located as the impact source position.

3. The structural impact location method based on multiple wavelet decomposition and time reversal according to claim 1, characterized in that: Calculating the waveform similarity of the time-reversed signal of each sensor after compensating for the time delay relative to the assumed impact source position using the cosine similarity formula includes: dividing the monitoring area of ​​the monitored structure into multiple grid points based on the Cartesian coordinate system, and setting any grid point as the assumed impact source position; calculating the relative time delay of the direct wave signal of the impact stress between each sensor based on the distance difference from each sensor to the grid point and the average speed of the impact stress wave propagating in the monitored structure; and calculating the waveform similarity of the time-reversed signal of different sensors after compensating for the time delay at the grid point using the cosine similarity formula.

4. The structural impact location method based on multiple wavelet decomposition and time reversal according to claim 3, characterized in that: Calculating the similarity of the time-reversed signal waveforms between different sensors at a certain grid point includes: calculating the distance difference between the grid point and different sensors , where i represents the i sensors, j represents the jth sensor, I is the total number of sensors, is the distance from the grid point to the i-th sensor, expressed as ; For this grid point, calculate the relative delay of the shock stress wave signal received by different sensors : , where C is the average propagation velocity of the impact stress wave in the monitored structure.

5. The structural impact location method based on multiple wavelet decomposition and time reversal according to claim 4, characterized in that: Calculating the waveform similarity of the time-reversed signals of different sensors after time delay compensation at the grid point using the cosine similarity formula includes: compensating the time delay of the sensor according to the order of the shock stress waves received by the sensor, and calculating the waveform similarity of the normalized reconstructed time-reversed signals of different sensors after time delay compensation with a duration of T including the direct wave of the shock stress wave using the cosine similarity formula: ;in: ; Wherein, L is the total number of sampling points with an inverse signal duration of T during normalized reconstruction, and l represents the lth sampling point.

6. The structural impact location method based on multiple wavelet decomposition and time reversal according to claim 1, characterized in that: The result of multiplying the time-reversed signal waveform similarities between different sensors calculated at each grid point is used as the pixel value at that grid point; and the pixel values ​​of all grid points are calculated to achieve virtual time-reversed focus imaging, wherein the position with the maximum pixel value and the brightest color in the image obtained by imaging represents the position of the located impact source.

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