Vibration response full-field detection method and system based on undersampled video

Abstract

The invention discloses a vibration response full-field detection method and system based on an undersampled video, and belongs to the technical field of vibration measurement. Firstly, a measured structure is excited, and the inherent frequency of the structure is measured; with the inherent frequency of the structure as prior information, calculating an undersampling but non-aliasing common undersampling rate of each vibration frequency band; determining an observation spectrum after each inherent frequency component is moved based on the common under-sampling rate; setting the common under-sampling rate as a camera acquisition frame rate, and acquiring a structure vibration video; performing vibration signal extraction on each pixel position of the acquired video image to obtain a structural vibration space-time signal matrix; and finally, recognizing a vibration response shape according to the structural vibration space-time signal matrix and the observation spectrum, and completing structural vibration response full-field detection. According to the method, the assistance of any external triggering equipment is not needed, the constraint of pure chord or band-pass excitation of structural excitation is liberated, and the flexibility of an undersampling video measurement system is greatly improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration measurement, and in particular relates to a full-field detection method and system for vibration response based on under-sampling video. Background Art

[0002] Vibration is widely present in precision manufacturing, civil engineering, aerospace and other fields. Since it will have an adverse effect on product quality, structural health and production safety, monitoring and controlling vibration has become an eternal research topic in these industries. However, with the rapid development of various industries, the requirements for vibration measurement are increasing day by day, and traditional measurement methods have exposed more and more problems in long-term practice, and it is gradually difficult to meet the measurement needs. Among them, contact sensors have problems such as only single-point measurement, load effect, and time-consuming and labor-intensive installation and maintenance. There are obvious limitations in the vibration measurement of lightweight structures and large-area structures. Non-contact measurement methods such as laser vibrometers also have problems such as single-point measurement, slow scanning speed, and expensive system prices. Therefore, the video vibration measurement technology that has emerged in recent years can make up for many shortcomings of current vibration measurement technology due to its advantages such as non-contact, high spatial resolution, good spatiotemporal synchronization and simple system structure, and can become a powerful technical supplement in some special measurement scenarios.

[0003] However, video vibrometer technology has thorny problems that limit its further development. As we all know, sampling rate is the most important parameter for vibration measurement, which determines whether the vibration signal can be correctly collected and restored. Video measurement technology relies on high-speed cameras for signal acquisition. Compared with the sampling rates of tens of thousands of hertz to hundreds of thousands of hertz of equipment such as accelerometers and laser vibrometers, the sampling rate of high-speed cameras is much lower, which means that it will be helpless in high-frequency vibration measurement. In order to solve this problem, some studies have designed camera triggering methods and structural excitation methods to break through the limitations of sampling theorem on video measurement technology, but 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 the present invention is to provide a full-field detection method and system for vibration response based on under-sampled video, in order to address the problem that the current video vibration measurement technology has too high requirements on the camera sampling rate, which causes high pressure on data storage and transmission, high computing power requirements and high system costs. The under-sampled video can be used to restore the spatial distribution of multi-band vibrations, give full play to the high spatial resolution advantage of video measurement technology, and realize full-field detection of vibration response.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A method for full-field detection of vibration response based on under-sampling video comprises the following steps:

[0007] Step 1: Excite the structure under test and measure the natural frequency of the structure;

[0008] Step 2: Based on the structural natural frequency obtained in step 1 as prior information, calculate the common undersampling rate of each vibration frequency band that is undersampled but not overlapped with each other;

[0009] Step 3: Determine the observed spectrum after each natural frequency component is moved 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 collect the structural vibration video;

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

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

[0013] Furthermore, in step 1, the natural frequency of the structure is measured using a single-point measurement method, including using an accelerometer, a laser vibrometer, etc.

[0014] Furthermore, the step 2 is specifically as follows:

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

[0016]

[0017] Among them, f L represents the lower boundary of the signal frequency band, f H represents the upper boundary of the signal frequency band, f s represents the sampling rate, m represents the number of spectrum compression and shifting times, N + represents a positive integer;

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

[0019]

[0020] Among them, f Ho1 and f Lo1 Respectively represent the observation frequencies of the upper and lower boundaries of the first frequency band; f Ho2 and f Lo2 Respectively represent the observed frequencies of the upper and lower boundaries of the second frequency band, which are calculated from the true frequency; ∨ represents the OR operation; m 1 and m 2 Respectively represent the number of shifts of the two frequency bands;

[0021] Step 2.3: Determine the common undersampling rate f according to the sub-Nyquist sampling rate range and numerical constraints of each frequency band cs , so that it satisfies:

[0022]

[0023] Among them, m i represents the number of compression and shifting of the ith frequency band, ∩ represents the set intersection operation, and ξ represents the number of frequency bands.

[0024] Furthermore, the observed spectrum f after each natural frequency component is moved in step 3 o From the real frequency f r And the number of band compression shifts m is determined:

[0025]

[0026] Furthermore, the method for extracting the vibration signal in step 5 includes an intensity optical flow method, a phase optical flow method, a matching method, etc.; the intensity optical flow method is specifically:

[0027] The continuous vibration is sampled by the camera to form a discrete video frame sequence; the intensity of the video frame image in time I(x, y, t n ) and the object displacement s(x,y,t n ) is:

[0028]

[0029] Where N represents the number of video frames, I 0 (x, y) represents the intensity of the reference image; |▽I 0 | represents the reference image intensity gradient scalar value, which is calculated from the reference image:

[0030]

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

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

[0033] For the structural vibration data collected by video measurement, the vibration response is the displacement-time matrix s(x, y, t n ), which is the sum of the products of the response shapes and the time domain signal at different frequencies:

[0034]

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

[0036] Take the Fourier transform of both sides at the same time:

[0037]

[0038] Among them, the missing symbols are explained as follows: f represents the vibration frequency of each pixel position;

[0039] It can be seen from the above formula that the response shape of the structure is uncoupled from the time domain signal. Therefore, even if the vibration signals in each frequency band are undersampled to a 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 completely restored. This is the basis for full-field detection of vibration response under undersampling conditions.

[0040] Furthermore, in video measurement, the pixel sensor array is a natural spatial measurement point, and the vibration response shape can be determined by the peak value of the imaginary part of the frequency response function at each pixel position:

[0041]

[0042] Among them, Im[·] represents the operation of taking the imaginary part, f ok Represents the observed frequency value corresponding to the kth vibration response shape.

[0043] A computer device / equipment / system comprises 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 vibration response full-field detection method based on under-sampled video.

[0044] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of a vibration response full-field detection method based on under-sampled video.

[0045] The beneficial effects of the present invention are:

[0046] The present invention proposes a full-field detection method for vibration response based on under-sampled video, which is used to reduce the excessive demand for camera sampling frame rate of video vibration measurement technology, thereby reducing data storage, transmission, computing pressure and system cost in high-frequency vibration measurement scenarios. Compared with the prior art, the present invention does not require the assistance of any external trigger device, freeing the constraints of pure sine or bandpass excitation of structural excitation. Even if a hammer is used for a single full-band excitation, each frequency response can be correctly depicted, thereby eliminating the limitation that other frequency responses outside the excitation band are all zero, greatly improving the flexibility of the under-sampled video measurement system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a basic flow chart of a vibration response full-field detection method based on under-sampled video of 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 to the simulated vibration at different sampling rates;

[0050] Figure 4 The vibration time domain and spectrum of the cantilever beam measured using a laser vibrometer;

[0051] Figure 5 This is a diagram of the experimental setup;

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

[0053] Figure 7 This is the multi-order vibration mode diagram of the cantilever beam. DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with the accompanying drawings.

[0055] The drawings in the embodiments of the present invention clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] according to Figure 1 ,The present invention proposes a full-field detection method for vibration response based on under-sampled video, such as Figure 1 As shown, it mainly includes the following steps:

[0057] Step 1: Excite the structure under test and measure the natural frequency of the structure;

[0058] Step 2, using the structural natural frequency as prior information, calculate the common undersampling rate of each vibration frequency band that is undersampled but not overlapped;

[0059] Step 3, determining the observed spectrum after each inherent frequency component is moved based on the common undersampling rate;

[0060] Step 4: Set the required common undersampling rate as the camera acquisition frame rate, and collect the structural vibration video;

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

[0062] Step 6: Identify the vibration response shape based on the structural vibration space-time signal matrix and the observed spectrum to complete the full-field detection of the structural vibration response.

[0063] Example 1

[0064] In this embodiment, a simulated vibration is used to simulate the structural vibration in actual applications. The simulated vibration simulates the damped vibration generated by a single full-band excitation of the structure to be tested, and the amplitude of the vibration signal decays over time. The mixed vibration signal consists of three frequency band components, frequency band 1 only contains components with a frequency value of 37 Hz, frequency band 2 contains components with frequency values ​​of 631 Hz, 633 Hz and 635 Hz, and frequency band 3 contains components with frequency values ​​of 1493 Hz, 1498 Hz and 1506 Hz, and each component corresponds to a vibration shape. In order to form damped vibration, an attenuation factor is added to each frequency band signal, and the attenuation speed is controlled by the attenuation exponent (the attenuation exponent refers to the exponential function e -λ The larger the exponent, the faster the decay. The attenuation exponent of band 1 is 1, the attenuation exponent of band 2 is 3, and the attenuation exponent of band 3 is 5. At the same time, Gaussian white noise is added to the simulated vibration to simulate the system noise caused by factors such as scene illumination and camera quantitative imaging.

[0065] In step 1, use a Nyquist sampling rate f s =5000Hz to measure the simulated vibration, and the obtained vibration time domain and spectrum are as follows Figure 2 The obtained natural frequency values ​​are shown in Table 1.

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

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

[0068] Within the determined sub-Nyquist sampling rate range for lossless transfer of each frequency band component, ensure that each frequency band does not cross after being transferred, while considering the numerical constraints:

[0069]

[0070] Among them, f Ho1 and f Lo1 Respectively represent the observation frequencies of the upper and lower boundaries of the first frequency band; f Ho2 and f Lo2 Respectively represent the observed frequencies of the upper and lower boundaries of the second frequency band, which can be calculated from the true frequency; ∨ represents the OR operation; m 1 and m 2 Respectively represent the number of shifts of the two frequency bands.

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

[0072]

[0073] Among them, m i represents the number of compression and shifting of the ith frequency band, ∩ represents the set intersection operation, and ξ represents the number of frequency bands.

[0074] In step 3, the observed spectrum after each natural frequency component is moved is determined based on the common undersampling rate. The observed spectrum after each natural frequency component is moved is f o The real frequency f r And the number of band compression shifts m is determined:

[0075]

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

[0077] In step 4, with a common sampling rate f cs =570Hz as the sampling rate, and resample the simulated vibration for measurement.

[0078] In step 5, the intensity optical flow method is used to extract the vibration signal at each pixel position of the resampled simulated video image to obtain the structural vibration spatiotemporal signal matrix. The vibration spatiotemporal signal matrix can be obtained from the intensity change of the video image:

[0079]

[0080] Where N represents the number of video frames, I 0 (x, y) represents the intensity of the reference image; |▽I 0 | represents the reference image intensity gradient scalar value, which is calculated from the reference image:

[0081]

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

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

[0084] In step 6, the spectrum imaginary space method is used to identify the full-field vibration response of the simulated vibration from the structural vibration space-time signal matrix. Specifically, the vibration response shape can be determined by the imaginary peak of the frequency response function at each pixel position:

[0085]

[0086] Among them, Im[·] represents the operation of taking the imaginary part, f ok Represents the observed frequency value corresponding to the kth vibration response shape.

[0087] The results are as follows Figure 3 As shown. Figure 3 (a) represents the preset vibration mode, 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 Simulated vibration observation spectrum values ​​measured at different sampling rates

[0089]

[0090] Example 2

[0091] In this embodiment, the structure to be measured is a cantilever beam with one end fixed.

[0092] In step 1, the cantilever beam is excited by a force hammer and measured by a single-point laser vibrometer. The obtained vibration time domain and spectrum are as follows: Figure 4 The obtained natural frequency values ​​are shown in Table 2.

[0093] In step 2, the measured natural frequency is used as prior information and the formula Calculate the range of sub-Nyquist sampling rates within which each frequency band component can be moved losslessly;

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

[0095] Within the determined sub-Nyquist sampling rate range for lossless transfer of each frequency band component, ensure that each frequency band does not cross after being transferred, while considering the numerical constraints:

[0096]

[0097] Among them, f Ho1 and f Lo1 Respectively represent the observation frequencies of the upper and lower boundaries of the first frequency band; f Ho2 and f Lo2 Respectively represent the observed frequencies of the upper and lower boundaries of the second frequency band, which can be calculated from the true frequency; ∨ represents the OR operation; m 1 and m 2 Respectively represent the number of shifts of the two frequency bands.

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

[0099]

[0100] Among them, m i represents the number of compression and shifting of the ith frequency band, ∩ represents the set intersection operation, and ξ represents the number of frequency bands.

[0101] In step 3, the observed spectrum after each natural frequency component is moved is determined based on the common undersampling rate. The observed spectrum after each natural frequency component is moved is f o The real frequency f r And the number of band compression shifts m is determined:

[0102]

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

[0104] In step 4, with a common sampling rate f cs = 80 Hz as the camera acquisition frame rate, and the cantilever beam vibration is captured by video. The experimental setup is as follows Figure 5shown.

[0105] In step 5, the intensity optical flow method is used to extract the vibration signal at each pixel position of the collected video image to obtain the structural vibration spatiotemporal signal matrix. The vibration spatiotemporal signal matrix can be obtained from the intensity change of the video image:

[0106]

[0107] Where N represents the number of video frames, I 0 (x, y) represents the intensity of the reference image; |▽I 0 | represents the reference image intensity gradient scalar value, which is calculated from the reference image:

[0108]

[0109] in, and Represent the partial derivatives of the image row and column directions, which can be calculated by gradient filters such as the Sobel operator. The time domain and spectrum of the vibration signal at one pixel position are as follows: Figure 6 shown.

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

[0111]

[0112] Among them, Im[·] represents the operation of taking the imaginary part, f ok Represents the observed frequency value corresponding to the kth vibration response shape.

[0113] The results are as follows Figure 7 As shown, Figure 7 (a) is the standard vibration mode of the cantilever beam. Figure 7 (b) Multi-order vibration modes of the cantilever beam identified based on undersampled video.

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

[0115]

[0116] The present invention proposes a full-field detection method for vibration response based on under-sampled video, which can reduce the excessive demand of video vibration measurement technology on camera sampling frame rate, thereby reducing data storage, transmission, computing pressure and system cost in high-frequency vibration measurement scenarios. Compared with the prior art, the present invention does not require the assistance of any external trigger device, freeing the constraints of pure sine or bandpass excitation of structural excitation. Even if a hammer is used for a single full-band excitation, each frequency response can be correctly depicted, thereby eliminating the limitation that other frequency responses outside the excitation band are all zero, greatly improving the flexibility of the under-sampled video measurement system.

[0117] The above is a detailed introduction to the implementation steps of a full-field detection method for vibration response based on under-sampling video proposed in the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for general technical personnel in this field, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0118] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A full-field detection method for vibration response based on under-sampled video, characterized in that: The following steps are involved: Step 1: Excite the structure under test and measure the natural frequency of the structure; Step 2: Based on the structural natural frequency obtained in step 1 as prior information, calculate the common undersampling rate of each vibration frequency band that is undersampled but not overlapped with each other; Step 3: Determine the observed spectrum after each natural frequency component is moved based on the common undersampling rate obtained in step 2; Step 4: Set the common undersampling rate obtained in step 2 as the camera acquisition frame rate, and collect the structural vibration video; Step 5: Extract vibration signals from each pixel position of the video image collected in step 4 to obtain a structural vibration spatiotemporal signal matrix; Step 6: Identify the vibration response shape based on the structural vibration space-time signal matrix and observation spectrum obtained in steps 3 and 5, and complete the full-field detection of the structural vibration response.

2. The method for full-field detection of vibration response based on under-sampling video according to claim 1, characterized in that: In step 1, the natural frequency of the structure is measured using a single-point measurement method.

3. The method for full-field detection of vibration response based on under-sampling video according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1: Calculate the range of sub-Nyquist sampling rates for lossless transfer of each frequency band component according to the following formula; Among them, f L represents the lower boundary of the signal frequency band, f H represents the upper boundary of the signal frequency band, f s represents the sampling rate, m represents the number of spectrum compression and shifting times, N + represents a positive integer; Step 2.2: According to the above formula, ensure that the frequency bands do not cross after being moved, and establish numerical constraints according to the formula: Among them, f Ho1 and f Lo1 Respectively represent the observation frequencies of the upper and lower boundaries of the first frequency band; f Ho2 and f Lo2 They represent the observed frequencies of the upper and lower boundaries of the second frequency band, respectively, which are calculated from the true frequency; ∨ represents the OR operation; m1 and m2 represent the number of shifts of the two frequency bands, respectively; Step 2.3: Determine the common undersampling rate f according to the sub-Nyquist sampling rate range and numerical constraints of each frequency band cs , so that it satisfies: Among them, m i represents the number of compression and shifting of the ith frequency band, ∩ represents the set intersection operation, and ξ represents the number of frequency bands.

4. The method for full-field detection of vibration response based on under-sampling video according to claim 1, characterized in that: The observed spectrum f after each natural frequency component is moved in step 3 o From the real frequency f r And the number of band compression shifts m is determined:

5. The method for full-field detection of vibration response based on under-sampling video according to claim 1, characterized in that: The method for extracting vibration signals in step 5 includes intensity optical flow method, phase optical flow method and matching method; the intensity optical flow method is specifically: The continuous vibration is sampled by the camera to form a discrete video frame sequence; the intensity of the video frame image in time I(x, y, t n ) and the object displacement s(x,y,t n ) is: Where N is the number of video frames, I0(x,y) is the intensity of the reference image, and |▽I0| is the scalar value of the reference image intensity gradient, which is calculated from the reference image: in, and They represent the partial derivatives of the image in row and column directions, respectively, and are calculated using the Sobel operator gradient filter.

6. The method for full-field detection of vibration response based on under-sampling video according to claim 1, characterized in that: The vibration response identification method in step 6 includes a spectrum imaginary part space method and a Hank matrix decomposition method; the spectrum imaginary part space method is specifically: For the structural vibration data collected by video measurement, the vibration response is the displacement-time matrix s(x, y, t n ), which is the sum of the products of the response shapes and the time domain signal at different frequencies: Among them, K represents the number of response components, φ k (x,y) represents the response shape corresponding to the kth frequency component, s k (t n ) represents the time domain signal corresponding to the kth frequency component; Take the Fourier transform of both sides at the same time: Among them, the missing symbols are explained as follows: f represents the vibration frequency of each pixel position; The vibration response shape is determined by the peak of the imaginary part of the frequency response function at each pixel location: Among them, Im[·] represents the operation of taking the imaginary part, f ok Represents the observed frequency value corresponding to the kth vibration response shape.

7. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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