A method and system for full-field vibration response detection based on under-sampled videos

Abstract

The application discloses a kind of vibration response full-field detection method and system based on undersampling video, belong to vibration measurement technical field.First, the measured structure is excited, and the natural frequency of structure is measured;With the natural frequency of structure as prior information, the common undersampling rate of each vibration band undersampling but not aliasing is calculated;Based on the common undersampling rate, the observation frequency spectrum after each natural frequency component is shifted is determined;The common undersampling rate obtained is set as the frame rate of camera acquisition, and the structure vibration video is acquired;The vibration signal of each pixel position of the acquired video image is extracted, and the structure vibration space-time signal matrix is obtained;Finally, according to the structure vibration space-time signal matrix and the observation frequency spectrum, the vibration response shape is identified, and the structure vibration response full-field detection is completed.The application does not need the aid of any external trigger device, liberates the constraint of pure sine or band-pass excitation of structure excitation, greatly improves the flexibility of undersampling video measurement system.

Description

Technical Field

[0001] This invention belongs to the field of vibration measurement technology, specifically relating to a method and system for full-field vibration response detection based on undersampled video. Background Technology

[0002] Vibration is widespread in precision manufacturing, civil engineering, and aerospace industries. Because it adversely affects product quality, structural health, and production safety, vibration monitoring and control have become perennial research topics in these sectors. However, with the rapid development of various industries, the requirements for vibration measurement are increasing, while traditional measurement methods have revealed more and more problems in long-term practice, gradually becoming unable to meet measurement needs. Contact sensors, in particular, suffer from limitations such as single-point measurement only, the potential for load effects, and time-consuming and labor-intensive installation and maintenance, exhibiting significant limitations in measuring vibrations of lightweight and large-area structures. Non-contact measurement methods, such as laser vibrometers, also suffer from single-point measurement, slow scanning speed, and high system costs. Therefore, video vibration measurement technology, which has emerged in recent years, offers advantages such as non-contact operation, high spatial resolution, good spatiotemporal synchronization, and simple system structure. It can compensate for many shortcomings of current vibration measurement technologies and serve as a powerful technological supplement in some special measurement scenarios.

[0003] However, video vibration measurement technology faces several thorny issues limiting its further development. As is well known, the sampling rate is the most crucial parameter in vibration measurement, determining whether vibration signals can be correctly acquired and recovered. Video measurement technology relies on high-speed cameras for signal acquisition, but compared to the sampling rates of tens to hundreds of thousands of hertz used by accelerometers and laser vibrometers, the sampling rate of high-speed cameras is much lower. This means they are ineffective in high-frequency vibration measurements. To address this problem, some studies have attempted to overcome the limitations of the sampling theorem on video measurement technology by designing camera triggering methods and structural excitation methods. However, this also brings problems such as high synchronization accuracy requirements, high system complexity, small single-measurement range, and time consumption. Summary of the Invention

[0004] The purpose of this invention is to address the problem that current video vibration measurement technology requires excessively high camera sampling rates, resulting in high data storage and transmission pressure, high computing power requirements, and high system costs. This invention provides a method and system for full-field vibration response detection based on undersampled video, which can use undersampled video to recover the spatial distribution of multi-frequency band vibration, fully leveraging the high spatial resolution advantage of video measurement technology to achieve full-field vibration response detection.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for full-field vibration response detection based on undersampled video includes the following steps:

[0007] Step 1: Excite the structure under test and measure its natural frequencies;

[0008] Step 2: Based on the structural natural frequencies obtained in Step 1 as prior information, calculate the common undersampling rate of each vibration frequency band that is undersampled but does not overlap.

[0009] Step 3: Determine the observed spectrum after shifting each inherent frequency component based on the common undersampling rate obtained in Step 2;

[0010] Step 4: Set the common undersampling rate obtained in Step 2 as the camera acquisition frame rate and acquire structural vibration video;

[0011] Step 5: Extract vibration signals from each pixel position of the video image acquired in Step 4 to obtain the spatiotemporal signal matrix of structural vibration;

[0012] Step 6: Identify the vibration response shape based on the spatiotemporal signal matrix and observed spectrum obtained in Steps 3 and 5, and complete the full-field detection of structural vibration response.

[0013] Furthermore, in step 1, a single-point measurement method is used to measure the natural frequency of the structure, including the use of accelerometers, laser vibrometers, etc.

[0014] Furthermore, step 2 specifically includes:

[0015] Step 2.1: Calculate the range of sub-Nyquist sampling rates for each frequency band component to be losslessly shifted according to the following formula;

[0016]

[0017] Among them, f L f represents the lower boundary of the signal frequency band. H f represents the upper boundary of the signal frequency band. s N represents the sampling rate, m represents the number of spectral compression shifts, and N represents the sampling rate. + Represents positive integers;

[0018] Step 2.2: Based on the above formula, ensure that the frequency bands do not overlap after being moved, and establish numerical constraints according to the formula:

[0019]

[0020] Among them, f Ho1 and f Lo1 These represent the observed frequencies at the upper and lower boundaries of the first frequency band, respectively; f Ho2 and f Lo2 represents the observed frequencies at the upper and lower boundaries of the second frequency band, respectively, calculated from the actual frequencies; ∨ represents an OR operation; m1 and m2 represent the number of shifts between the two frequency bands, respectively;

[0021] Step 2.3: Determine the common undersampling rate f based on the range and numerical constraints of the sub-Nyquist sampling rate for each frequency band. cs To satisfy:

[0022]

[0023] Where, m i Let ξ represent the number of compression shifts for the i-th frequency band, ∩ denotes the set intersection operation, and ξ denotes the number of frequency bands.

[0024] Furthermore, the observed spectrum f after the shifting of each inherent frequency component in step 3... o From the true frequency f r The number of frequency band compression and relocation operations, m, is determined as follows:

[0025]

[0026] Furthermore, the method for extracting the vibration signal in step 5 includes intensity optical flow, phase optical flow, and matching methods; specifically, the intensity optical flow method is as follows:

[0027] Continuous vibrations are sampled by a camera to form a discrete sequence of video frames; the intensity I(x,y,t) of the video frame image over time. n ) and the object's displacement s(x,y,t) n The relationship between them is:

[0028]

[0029] Where N represents the number of video frames, I0(x,y) represents the intensity of the reference image, and |▽I0| represents the scalar value of the intensity gradient of the reference image, calculated from the reference image.

[0030]

[0031] in, and These represent the partial derivatives in the row and column directions of the image, respectively, which are calculated using the Sobel operator gradient filter.

[0032] Furthermore, the vibration response identification methods in step 6 include the spectral imaginary part space method and the Hank matrix decomposition method, etc.; the spectral imaginary part space method specifically includes:

[0033] For structural vibration data acquired through video measurement, the vibration response is the displacement-time matrix s(x,y,t) composed of the displacements of each extracted pixel. n It is the sum of the product of the response shape and the time-domain signal at different frequencies:

[0034]

[0035] Where K represents the number of response components, φ k (x,y) represents the response shape corresponding to the k-th frequency component, s k (t n () represents the time-domain signal corresponding to the k-th frequency component;

[0036] Simultaneously perform Fourier transforms on both sides:

[0037]

[0038] The missing symbol f represents the vibration frequency at each pixel position.

[0039] As can be seen from the above formula, the response shape of the structure is uncoupled from the time domain signal. Therefore, even if the vibration signals of each frequency band are undersampled to the low frequency band, as long as destructive aliasing does not occur and the integrity of the vibration response information is maintained, the response shape can be fully recovered. This is the basis for full-field detection of vibration response under undersampling conditions.

[0040] Furthermore, in video measurement, pixel sensor arrays are natural spatial measurement points, and the shape of the vibration response can be determined by the peak value of the imaginary part of the frequency response function at each pixel location:

[0041]

[0042] Where Im[·] denotes the imaginary part operation, f ok This represents the observed frequency value corresponding to the k-th vibration response shape.

[0043] A computer device / apparatus / system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of a full-field vibration response detection method based on undersampled video.

[0044] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of a full-field vibration response detection method based on undersampled video.

[0045] The beneficial effects of this invention are as follows:

[0046] This invention proposes a full-field vibration response detection method based on undersampled video, which reduces the excessive demand on camera sampling frame rate in video vibration measurement technology, thereby reducing the data storage, transmission, computing power pressure, and system cost in high-frequency vibration measurement scenarios. Compared with existing technologies, this invention does not require any external triggering devices, freeing it from the constraints of pure sinusoidal or bandpass excitation of structural excitation. Even with a single full-band excitation using a hammer, it can accurately depict the response at each frequency, thus eliminating the limitation that the response at other frequencies outside the excitation band is zero, greatly improving the flexibility of the undersampled video measurement system. Attached Figure Description

[0047] Figure 1 This is a basic flowchart of a full-field vibration response detection method based on undersampled video according to the present invention;

[0048] Figure 2 Comparison of simulated vibration time-domain signals and spectra measured at different sampling rates;

[0049] Figure 3 The full-field detection results of the vibration response of the simulated vibration at different sampling rates;

[0050] Figure 4 Time-domain and frequency spectrum of cantilever beam vibration measured using a laser vibration meter;

[0051] Figure 5 Diagram of the experimental setup;

[0052] Figure 6 The time-domain and spectrum diagram of cantilever beam vibration extracted from undersampled video using the method of the present invention;

[0053] Figure 7 This is a diagram showing the multiple vibration modes of a cantilever beam. Detailed Implementation

[0054] The present invention will now be further described with reference to the accompanying drawings.

[0055] The accompanying drawings of the embodiments of the present invention clearly and completely describe the technical solutions of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0056] according to Figure 1 This invention proposes a full-field vibration response detection method based on undersampled video, such as... Figure 1 As shown, the main steps include:

[0057] Step 1: Excite the structure under test and measure its natural frequencies;

[0058] Step 2: Using the structure's natural frequency as prior information, calculate the common undersampling rate for each vibration frequency band that is undersampled but does not overlap.

[0059] Step 3: Determine the observed spectrum after the shifting of each inherent frequency component based on the common undersampling rate;

[0060] Step 4: Set the desired common undersampling rate to the camera's frame rate and acquire structural vibration video.

[0061] Step 5: Extract vibration signals from each pixel position of the acquired video image to obtain the spatiotemporal signal matrix of structural vibration;

[0062] Step 6: Identify the vibration response shape based on the structure's vibration spatiotemporal signal matrix and observed spectrum to complete the full-field detection of the structure's vibration response.

[0063] Example 1

[0064] In this embodiment, a simulated vibration is used to simulate the structural vibration in a real-world application. This simulated vibration mimics the damped vibration generated by a single full-band excitation of the structure under test, with the amplitude of the vibration signal decaying over time. The mixed-frequency vibration signal consists of three frequency band components: band 1 contains only a component with a frequency of 37 Hz; band 2 contains components with frequencies of 631 Hz, 633 Hz, and 635 Hz; and band 3 contains components with frequencies of 1493 Hz, 1498 Hz, and 1506 Hz. Each component corresponds to a vibration shape. To generate damped vibration, an attenuation factor is added to each frequency band signal, and the rate of attenuation is controlled by an attenuation exponent (the attenuation exponent refers to the exponential function e^(-1 / 2)). -λ In the equation (λ), a larger exponent indicates faster attenuation. Specifically, the attenuation exponent for band 1 is 1, for band 2 it is 3, and for band 3 it is 5. Simultaneously, Gaussian white noise is added to the simulated vibration to simulate system noise caused by factors such as ambient lighting and camera quantization imaging.

[0065] In step 1, f is used that conforms to the Nyquist sampling rate. s The simulated vibration was measured at 5000Hz, and the obtained vibration time domain and spectrum are as follows: Figure 2 As shown in Table 1, the natural frequency values ​​were obtained.

[0066] In step 2, the measured natural frequency is used as prior information, and the formula is applied... (m∈N + Calculate the range of sub-Nyquist sampling rates from which each frequency band component can be losslessly transferred;

[0067] Among them, f L f represents the lower boundary of the signal frequency band. H f represents the upper boundary of the signal frequency band.s N represents the sampling rate, m represents the number of spectral compression shifts, and N represents the sampling rate. + Represents a positive integer.

[0068] Within the defined range of sub-Nyquist sampling rates for lossless relocation of each frequency band component, ensure that the relocated frequency bands do not overlap, while also considering numerical constraints:

[0069]

[0070] Among them, f Ho1 and f Lo1 These represent the observed frequencies at the upper and lower boundaries of the first frequency band, respectively; f Ho2 and f Lo2 represents the observed frequencies of the upper and lower boundaries of the second frequency band, which can be calculated from the actual frequencies; ∨ represents the OR operation; m1 and m2 represent the number of shifts between the two frequency bands, respectively.

[0071] Determine the common undersampling rate f cs =570Hz, this sampling rate satisfies:

[0072]

[0073] Where, m i Let ξ represent the number of compression shifts for the i-th frequency band, ∩ denotes the set intersection operation, and ξ denotes the number of frequency bands.

[0074] In step 3, the observed spectrum after shifting each intrinsic frequency component is determined based on the common undersampling rate. The observed spectrum f after shifting each intrinsic frequency component is... o It can be determined by the actual frequency f r The number of frequency band compression and relocation operations, m, is determined as follows:

[0075]

[0076] When the common sampling rate f cs At 570Hz, the measured spectrum of the cantilever beam vibration is shown in Table 1.

[0077] In step 4, at a common sampling rate f cs =570Hz was used as the sampling rate to resample and measure the simulated vibration.

[0078] In step 5, the intensity optical flow method is used to extract vibration signals from each pixel location of the resampled simulated video image, resulting in a spatiotemporal signal matrix of structural vibration. This spatiotemporal signal matrix can be obtained from the intensity changes of the video image.

[0079]

[0080] Where N represents the number of video frames, I0(x,y) represents the intensity of the reference image, and |▽I0| represents the scalar value of the intensity gradient of the reference image, calculated from the reference image.

[0081]

[0082] in, and These represent the partial derivatives in the row and column directions of the image, respectively, and can be calculated using gradient filters such as the Sobel operator.

[0083] In this spatiotemporal signal matrix, with f s The time domain and spectrum of the vibration signal at the same pixel position in the sampled video at 5000Hz are as follows: Figure 2 As shown.

[0084] In step 6, the full-field vibration response of the simulated vibration is identified from the spatiotemporal signal matrix of the structural vibration using the spatial method of the imaginary part of the spectrum. Specifically, the shape of the vibration response can be determined by the peak value of the imaginary part of the frequency response function at each pixel location:

[0085]

[0086] Where Im[·] denotes the imaginary part operation, f ok This represents the observed frequency value corresponding to the k-th vibration response shape.

[0087] The results are as follows Figure 3 As shown. Among them Figure 3 (a) indicates the preset mode shape. Figure 3 (b) indicates f s The vibration mode measured at 5000Hz Figure 3 (c) indicates f s The vibration mode measured at 570Hz.

[0088] Table 1. Numerical values ​​of simulated vibration observation spectra measured at different sampling rates.

[0089]

[0090] Example 2

[0091] In this embodiment, the structure under test is a cantilever beam with one end fixed.

[0092] In step 1, a hammer is used to excite the cantilever beam, and a single-point laser vibration meter is used to measure it. The obtained vibration time domain and spectrum are as follows: Figure 4 As shown in Table 2, the natural frequency values ​​were obtained.

[0093] In step 2, the measured natural frequency is used as prior information, and the formula is applied... Calculate the range of sub-Nyquist sampling rates from which each frequency band component can be transferred without loss;

[0094] Among them, f L f represents the lower boundary of the signal frequency band. H f represents the upper boundary of the signal frequency band. s N represents the sampling rate, m represents the number of spectral compression shifts, and N represents the sampling rate. + Represents a positive integer.

[0095] Within the defined range of sub-Nyquist sampling rates for lossless relocation of each frequency band component, ensure that the relocated frequency bands do not overlap, while also considering numerical constraints:

[0096]

[0097] Among them, f Ho1 and f Lo1 These represent the observed frequencies at the upper and lower boundaries of the first frequency band, respectively; f Ho2 and f Lo2 represents the observed frequencies of the upper and lower boundaries of the second frequency band, which can be calculated from the actual frequencies; ∨ represents the OR operation; m1 and m2 represent the number of shifts between the two frequency bands, respectively.

[0098] Determine the common undersampling rate f cs =80Hz, this sampling rate satisfies:

[0099]

[0100] Where, m i Let ξ represent the number of compression shifts for the i-th frequency band, ∩ denotes the set intersection operation, and ξ denotes the number of frequency bands.

[0101] In step 3, the observed spectrum after shifting each intrinsic frequency component is determined based on the common undersampling rate. The observed spectrum f after shifting each intrinsic frequency component is... o It can be determined by the actual frequency f r The number of frequency band compression and relocation operations, m, is determined as follows:

[0102]

[0103] When the common sampling rate f cs At 80Hz, the measured spectrum of the cantilever beam vibration is shown in Table 2.

[0104] In step 4, at a common sampling rate f cs =80Hz was used as the camera's frame rate to capture video of the cantilever beam vibration. The experimental setup is as follows: Figure 5 As shown.

[0105] In step 5, the intensity optical flow method is used to extract vibration signals from each pixel location of the acquired video image, resulting in a spatiotemporal signal matrix of structural vibration. This spatiotemporal signal matrix can be obtained from the intensity changes of the video image.

[0106]

[0107] Where N represents the number of video frames, I0(x,y) represents the intensity of the reference image, and |▽I0| represents the scalar value of the intensity gradient of the reference image, calculated from the reference image.

[0108]

[0109] in, and These represent the partial derivatives in the row and column directions of the image, respectively, and can be calculated using gradient filters such as the Sobel operator. The time-domain and frequency spectrum of the vibration signal at one pixel location are shown below. Figure 6 As shown.

[0110] In step 6, the spatial method of the imaginary part of the spectrum is used to identify the cantilever beam as a full-field vibration response from the spatiotemporal signal matrix of structural vibration. Specifically, the shape of the vibration response can be determined by the peak value of the imaginary part of the frequency response function at each pixel location:

[0111]

[0112] Where Im[·] denotes the imaginary part operation, f ok This represents the observed frequency value corresponding to the k-th vibration response shape.

[0113] The results are as follows Figure 7 As shown, where Figure 7 (a) is the standard vibration mode of the cantilever beam. Figure 7 (b) shows the multi-mode vibration of the cantilever beam based on undersampled video recognition.

[0114] Table 2. Spectral values ​​measured by laser measuring instrument and video measurement method

[0115]

[0116] This invention proposes a full-field vibration response detection method based on undersampled video, which reduces the excessive demand on camera sampling frame rate in video vibration measurement technology, thereby reducing the data storage, transmission, computing power pressure, and system cost in high-frequency vibration measurement scenarios. Compared with existing technologies, this invention does not require any external triggering equipment, freeing it from the constraints of pure sinusoidal or bandpass excitation of structural excitation. Even with a single full-band excitation using a hammer, it can accurately depict the response at each frequency, thus eliminating the limitation that the response at other frequencies outside the excitation band is zero, greatly improving the flexibility of the undersampled video measurement system.

[0117] The implementation steps of the vibration response full-field detection method based on undersampled video proposed in this invention have been described in detail above. Specific examples have been used to illustrate the principle and implementation of this invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0118] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for full-field vibration response detection based on undersampled video, characterized in that: The method comprises the following steps: Step 1: excite the measured structure and measure the natural frequency of the structure; Step 2: calculate a common under-sampling rate for each vibration frequency band based on the natural frequency of the structure obtained in step 1 as prior information, wherein the common under-sampling rate is under-sampled but not aliasing with each other; Step 2.1: calculate the range of the sub-Nyquist sampling rate for each frequency band component to be moved without loss according to the following formula: where f L denotes the lower signal band edge, f H denotes the upper signal band edge, f s denotes the sampling rate, m denotes the number of spectral compression shifts, N + denotes a positive integer; Step 2.2: ensure that each frequency band is not crossed after being moved according to the above formula, and establish numerical constraints according to the formula: where f Ho1 and f Lo1 represent the observed frequencies of the lower and upper boundaries of the first frequency band, respectively; f Ho2 and f Lo2 represent the observed frequencies of the lower and upper boundaries of the second frequency band, respectively, calculated from the true frequencies; ∨ represents the OR operation; and m1 and m2 represent the number of shifts of the two frequency bands, respectively. Step 2.3: According to the range of values and numerical constraints of each sub-Nyquist sampling rate of the frequency band, determine the common under-sampling rate f cs such that: where m i denotes the number of compressed shifts of the ith frequency band, denotes the set intersection operation, and ξ denotes the number of frequency bands. Step 3: determine the observed frequency spectrum of each natural frequency component after being moved based on the common under-sampling rate obtained in step 2; Step 4: set the common under-sampling rate obtained in step 2 as the frame rate of the camera, and collect the vibration video of the structure; Step 5: extract the vibration signal of each pixel position of the video image collected in step 4 to obtain a structure vibration space-time signal matrix; Step 6: identify the vibration response shape according to the structure vibration space-time signal matrix and the observed frequency spectrum obtained in steps 3 and 5, and complete the full-field detection of the structure vibration response.

2. The method of claim 1, wherein: The natural frequency of the structure is measured by using a single-point measurement method in the step 1.

3. The method of claim 1, wherein: The observed frequency spectrum f in step 3 after shifting of each individual frequency component o is determined by the real frequency f r and the band compression shift number m: 。 4. The method of claim 1, wherein: The method for extracting the vibration signal in the step 5 includes an intensity optical flow method, a phase optical flow method and a matching method; the intensity optical flow method specifically includes: Continuous vibrations are sampled by a camera to form a discrete sequence of video frames; the intensity I(x,y,t) of the video frame image over time. n ) and the object displacement s(x,y,t) n The relationship between them is: where N represents the number of video frames, I0(x,y) represents the intensity of the reference image; represents the reference image intensity gradient scalar value, which is calculated from the reference image: wherein, and denote the partial derivatives in the image row, column direction, respectively, computed by Sobel operator gradient filters.

5. The method of claim 1, wherein: The identification method of the vibration response in the step 6 includes a spectral imaginary part space method and a Hankel matrix decomposition method; the spectral imaginary part space method specifically includes: For the structural vibration data collected by video measurement, the vibration response is the displacement-time matrix s(x, y, t n ) composed of the extracted displacement of each pixel, which is the sum of the response shape corresponding to different frequencies and the time domain signal product: where K denotes the number of response components, and k (x, y) denotes the response shape corresponding to the kth frequency component, and s k (t n ) denotes the time-domain signal corresponding to the kth frequency component. Meanwhile, Fourier transform is performed on both sides: where f represents the vibration frequency at each pixel position; The vibration response shape is determined by the imaginary part peak value of the frequency response function of each pixel position: where Im[·] denotes the imaginary part operation, f ok denotes the observed frequency value corresponding to the kth vibration response shape.

6. A computer apparatus / device / system comprising a memory, a processor, and a computer program stored on the memory, characterized in that: The processor executes the computer program to realize the steps of the method in any one of claims 1 to 5.

7. A computer readable storage medium having stored thereon computer programs / instructions, characterized in that: The computer program / instructions are executed by the processor to realize the steps of the method in any one of claims 1 to 5.

Images