CN115661332A - Structural modal identification method based on digital image correlation method and motion amplification technology - Google Patents

Structural modal identification method based on digital image correlation method and motion amplification technology Download PDF

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CN115661332A
CN115661332A CN202211046686.9A CN202211046686A CN115661332A CN 115661332 A CN115661332 A CN 115661332A CN 202211046686 A CN202211046686 A CN 202211046686A CN 115661332 A CN115661332 A CN 115661332A
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vibration
initial
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amplification
detected
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晏班夫
罗磊
田华
牛孜飏
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Hunan University
China Construction Fifth Engineering Bureau Co Ltd
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Hunan University
China Construction Fifth Engineering Bureau Co Ltd
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Abstract

The application relates to a structural modal identification method, a structural modal identification device, a structural modal identification computer device, a structural modal storage medium and a structural modal computer program product based on a digital image correlation method and a motion amplification technology. The method comprises the following steps: decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, and decomposing each spectrogram into a plurality of frequency domain sub-bands; performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected; respectively performing motion amplification processing on target phase data based on the optimal amplification coefficient corresponding to each order of vibration of the structure to be detected to obtain vibration amplification results of each order of the structure to be detected; obtaining a displacement time-course curve corresponding to each measuring point on the structure to be measured when each order vibrates according to each vibration amplification result; and extracting the vibration mode of the structure to be detected corresponding to each order of mode based on each displacement time-course curve. By adopting the method, the modal identification precision can be improved.

Description

Structural modal identification method based on digital image correlation method and motion amplification technology
Technical Field
The present application relates to the field of structural vibration modal identification technologies, and in particular, to a structural modal identification method and apparatus, a computer device, a storage medium, and a computer program product based on a digital image correlation method and a motion amplification technology.
Background
The mode is the inherent vibration characteristic of the structure, and the calculation or experimental analysis process for obtaining the mode parameters is called mode analysis, and the mode analysis provides a reliable means for the design and performance evaluation of the structure. The traditional structural modal identification mainly comprises the steps of analyzing and calculating original data (generally acceleration time-course information) of structural vibration, wherein data acquisition is the most critical step, however, for some special and complex structures (such as a large-span suspension bridge, an ultra-long cable and the like), the aspects of arrangement, installation and the like of traditional sensors are greatly limited, and the traditional data acquisition method cannot meet the measurement requirements, so that a non-contact measurement method of structural vibration is needed.
Meanwhile, in the existing non-contact measurement modal identification patents, indoor tests are mostly adopted for verification and explanation, excitation equipment is required to be applied to apply excitation on a structure to serve as an input signal, and finally, a frequency response function is used for estimating modal parameters, so that the application in practical engineering is difficult.
Disclosure of Invention
In view of the foregoing, it is desirable to provide a structural modality identification method, apparatus, computer device, computer readable storage medium and computer program product based on digital image correlation and motion amplification techniques, which can improve the accuracy of modality analysis.
In a first aspect, the present application provides a structural modality identification method based on a digital image correlation method and a motion amplification technology. The method comprises the following steps:
acquiring an initial structure vibration video;
decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, and decomposing each spectrogram into a plurality of frequency domain sub-bands;
performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected;
respectively performing motion amplification processing on the target phase data based on the optimal amplification coefficient corresponding to each order of vibration of the structure to be detected to obtain vibration amplification results of each order of the structure to be detected;
obtaining a displacement time-course curve corresponding to each measuring point on the structure to be measured when the measuring point vibrates in each order according to each vibration amplification result;
and extracting the vibration mode of the structure to be detected corresponding to each order mode based on each displacement time course curve.
In one embodiment, after the obtaining the initial structure vibration video, before decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, the method further includes:
performing framing processing on the initial structure vibration video, and decomposing the initial structure vibration video into initial structure vibration image sequences;
and performing two-dimensional discrete Fourier transform processing on each initial structure vibration image sequence to obtain a spectrogram corresponding to each frame of initial structure vibration image.
In one embodiment, the decomposing the spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video to decompose each spectrogram into a plurality of frequency domain subbands includes:
based on a preset downsampling proportion, downsampling each frame of initial structure vibration image of the initial structure vibration video to obtain subimages of multiple scales;
and decomposing each frequency spectrogram into a plurality of frequency domain sub-bands according to the amplitude information and the phase information contained in each pixel point in each frequency spectrogram.
In one embodiment, the performing band-pass filtering processing on the phase data corresponding to each frequency domain subband to obtain target phase data corresponding to each frequency domain subband of the structure to be measured includes:
and performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band based on a time domain band-pass filter to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected, wherein the time domain band-pass filter is provided with band-pass filtering parameters of each order.
In one embodiment, the band-pass filter parameters include a center frequency, an upper limit frequency, and a lower limit frequency, and the determination manner of the band-pass filter parameters includes:
acquiring a measuring point displacement time-course curve of any measuring point on the structure to be measured in the initial structure vibration video; carrying out Fourier transform processing on the measuring point displacement time-course curve to obtain the natural vibration frequency information of each order of the structure to be measured; taking each self-oscillation frequency information as the central frequency of the time domain band-pass filter; and determining the upper limit frequency and the lower limit frequency according to each central frequency and by combining bandwidth setting.
In one embodiment, the method further comprises:
when determining the optimal amplification coefficient corresponding to each step of vibration of the structure to be detected, executing the following steps:
acquiring a plurality of initial amplification factors, wherein each initial amplification factor is determined based on an arithmetic progression rule;
based on each initial amplification factor, respectively carrying out motion amplification processing on the target phase data to obtain amplified and synthesized vibration videos of each amplification synthesis structure;
evaluating each amplified composite structure video by taking a modal confidence criterion as an evaluation standard to obtain a modal confidence curve, wherein the modal confidence curve is a fitting curve of each initial amplification factor and a modal confidence value;
and when the modal confidence value meets the preset modal confidence value condition, selecting the corresponding initial amplification factor as the amplification factor.
In one embodiment, the extracting, based on each of the displacement time-course curves, a mode shape corresponding to each order mode of the structure to be tested includes:
selecting a plurality of identification points on the structure to be tested, and selecting one point from the identification points as a research point;
according to each displacement time-course curve, acquiring a research point time displacement curve of the research point in the test time;
screening out each extreme point from the research point time displacement curve based on the research point time displacement curve, and obtaining each extreme point time based on the time corresponding to each extreme point;
determining a corresponding extreme point moment vibration pattern diagram according to each extreme point moment, wherein the extreme point moment vibration pattern diagram is determined by the displacement of each identification point at the extreme point moment;
averaging the moment mode patterns of the extreme points to obtain average mode patterns;
and performing sine function fitting and normalization on each mean value vibration mode diagram, and extracting the vibration mode of the structure to be detected corresponding to each order of mode.
In a second aspect, the present application further provides a structural modality recognition apparatus based on digital image correlation and motion amplification technology, the apparatus including:
the data acquisition module is used for acquiring a vibration video of the initial structure;
the data processing module is used for decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video and decomposing each spectrogram into a plurality of frequency domain sub-bands;
the filtering module is used for carrying out band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected;
the motion amplification module is used for respectively performing motion amplification processing on the target phase data based on the optimal amplification coefficient corresponding to each order of vibration of the structure to be detected to obtain vibration amplification results of each order of the structure to be detected;
the curve acquisition module is used for acquiring displacement time-course curves corresponding to the measuring points on the structure to be measured during vibration of each order according to the vibration amplification results;
and the vibration mode extraction module is used for extracting the vibration mode of the structure to be detected corresponding to each order of mode based on each displacement time course curve.
In a third aspect, the present application also provides a computer device. The computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the structural modal identification method based on the digital image correlation method and the motion amplification technology when executing the computer program.
In a fourth aspect, the present application further provides a computer-readable storage medium. The computer-readable storage medium has stored thereon a computer program, which when executed by a processor, implements the steps of the above-mentioned structural modality identification method based on the digital image correlation method and the motion amplification technology.
In a fifth aspect, the present application further provides a computer program product. The computer program product comprises a computer program, which when executed by a processor implements the steps of the above-mentioned structural modality recognition method based on the digital image correlation method and the motion amplification technique.
The structural modal identification method, the structural modal identification device, the computer equipment, the storage medium and the computer program product based on the digital image correlation method and the motion amplification technology are characterized in that an initial structural vibration video is obtained; decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, and decomposing each spectrogram into a plurality of frequency domain sub-bands; performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected, so that the phase data of other structures except the structure to be detected in the initial structure vibration video can be filtered, only the phase data of the structure to be detected is reserved, and further, performing motion amplification processing on each target phase data to obtain vibration amplification results of each order of the structure to be detected; obtaining a displacement time-course curve corresponding to each measuring point on the structure to be measured when each order vibrates according to each vibration amplification result; based on each displacement time-course curve, the vibration mode of the structure to be detected corresponding to each order mode is extracted, the extracted curve of the structure to be detected in each order mode can be clear and visual, frequency response function calculation is not needed, the identification vibration mode of the structure to be detected in each order can be extracted, and the identification precision of the structure mode can be effectively improved through the method.
Drawings
FIG. 1 is a diagram of an embodiment of an application environment of a structural modality recognition method based on a digital image correlation method and a motion amplification technology;
FIG. 2 is a flow chart illustrating a method for identifying a structural modality based on a digital image correlation method and a motion amplification technique according to an embodiment;
FIG. 3 is a graph illustrating a time course of displacement of a region point according to a structural modal recognition method based on a digital image correlation method and a motion amplification technique according to an embodiment;
FIG. 4 is a frequency spectrum diagram of a structural modality recognition method based on a digital image correlation method and a motion amplification technology in another embodiment;
FIG. 5 is a diagram illustrating the modal confidence criterion values of the structural modal recognition method based on the digital image correlation method and the motion amplification technique according to an embodiment;
FIG. 6 is a schematic diagram illustrating a modal confidence curve of a structural modal recognition method based on a digital image correlation method and a motion amplification technique according to an embodiment;
FIG. 7 is a flow chart illustrating the vibration pattern obtaining process of the structural modal identification method based on the digital image correlation method and the motion amplification technique according to an embodiment;
FIG. 8 is a flow diagram of a method for structural modality recognition based on digital image correlation and motion amplification techniques in one embodiment;
FIG. 9 is a block diagram of the structure of the structural mode recognition apparatus in one embodiment;
fig. 10 is an internal structural diagram of a computer device in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of and not restrictive on the broad application.
The structural modality identification method based on the digital image correlation method and the motion amplification technology provided by the embodiment of the application can be applied to the application environment shown in fig. 1. The application environment shown in fig. 1 includes a data acquisition device 102, a structure 104 to be measured, and an electronic device 106, where the data acquisition device 102 may be a DIC (digital image correlation) measurement device (such as a high-speed camera), specifically, the high-speed camera may acquire a free damping vibration video of the structure 104 to be measured, and then transmit the video to the electronic device 106, and the electronic device 106 processes the damping vibration video through the structure mode identification method based on the digital image correlation method and the motion amplification technology of the present application, so as to obtain a mode parameter of the structure to be measured.
Wherein the data collection device 102 communicates with the electronic device 106 via a network. The electronic device 102 may be, but not limited to, various personal computers, notebook computers, smart phones, tablet computers, internet of things devices, and portable wearable devices, and the internet of things devices may be smart speakers, smart televisions, smart air conditioners, smart car-mounted devices, and the like. The portable wearable device can be a smart watch, a smart bracelet, a head-mounted device, and the like. The electronic device 106 may also be a server, and the server may be implemented by a stand-alone server or a server cluster composed of a plurality of servers.
Specifically, the electronic device 106 acquires an initial structure vibration video; decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, and decomposing each spectrogram into a plurality of frequency domain sub-bands; performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected; respectively performing motion amplification processing on the target phase data based on the optimal amplification coefficient corresponding to each order of vibration of the structure to be detected to obtain vibration amplification results of each order of the structure to be detected; obtaining a displacement time-course curve corresponding to each measuring point on the structure to be measured during each order of vibration according to each vibration amplification result; and extracting the corresponding vibration mode of the structure to be detected in each order of mode based on each displacement time-course curve.
In one embodiment, as shown in fig. 2, a structural modality recognition method based on a digital image correlation method and a motion amplification technology is provided, which is described by taking the method as an example applied to the electronic device 106 in fig. 1, and includes the following steps:
step S202, acquiring an initial structure vibration video.
The initial structure vibration video may be a video acquired by acquiring a structure free damping vibration video through a DIC (digital image correlation) measurement device (such as a high-speed camera), wherein in the initial structure vibration video, in addition to vibration information of a structure to be detected (such as a pylon of a bridge), vibration information of other structures (such as a running automobile, a railing of the bridge, and the like) may also exist, and vibration information of a pedestrian passing by may also exist.
In one embodiment, when the DIC measuring equipment is used for collecting the initial structure vibration video, the imaging plane of the camera is parallel to the surface of the structure to be measured, and calibration of the camera is performed simultaneously.
In one embodiment, when the initial structure vibration video is processed, speckle processing can be performed on the surface of the structure to be measured, so that the DIC can conveniently perform target point displacement tracking, and the speckle processing can be omitted if the structure surface has obvious textures.
Step S204, performing decomposition processing on a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, and decomposing each spectrogram into a plurality of frequency domain sub-bands.
The initial structure vibration video is composed of frames of initial structure vibration images, fast Fourier transform processing is conducted on the frames of initial structure vibration images respectively, a spectrogram of each frame of initial structure vibration image can be obtained, decomposition processing refers to decomposing the spectrogram into frequency domain sub-bands according to the tangential direction and the radial direction, image information (such as amplitude, phase and the like) of the same frequency domain sub-band is similar, the spectrogram is decomposed into a plurality of frequency domain sub-bands, and therefore when time domain band-pass filtering is conducted subsequently, the frequency domain sub-bands with similar image information of the same frequency domain sub-band often have the characteristic of a similar motion state in a time domain, and therefore the time domain band-pass filtering effect can be effectively improved.
In one embodiment, after the obtaining of the initial structure vibration video, decomposing a spectrogram corresponding to each frame of the initial structure vibration image of the initial structure vibration video, and before the decomposing, further includes:
performing framing processing on the initial structure vibration video, and decomposing the initial structure vibration video into initial structure vibration image sequences;
and performing two-dimensional discrete Fourier transform processing on each initial structure vibration image sequence to obtain a spectrogram corresponding to each frame of initial structure vibration image.
The initial structure vibration image sequence refers to continuous series of images with different time and different directions obtained after framing processing is performed on an initial structure vibration video, the framing processing can refer to dividing the initial structure vibration video according to time to obtain each initial structure vibration image sequence, then two-dimensional discrete Fourier transform processing is performed on each initial structure vibration image sequence, and a space domain can be converted into a frequency domain to obtain a spectrogram corresponding to each frame of initial structure vibration image.
Step S206, performing band-pass filtering processing on the phase data corresponding to each frequency domain subband to obtain target phase data corresponding to each frequency domain subband of the structure to be measured.
The phase data refers to phase change time domain data distributed along time and corresponding to frequency domain sub-bands obtained after fast Fourier inverse transformation is carried out on each frequency domain sub-band, the band-pass filtering processing refers to that a time domain band-pass filter with filtering parameters is adopted to carry out band-pass filtering processing on the phase data, only the phase data of the structure to be detected can be reserved, the phase data of other structures except the structure to be detected is filtered, and finally the reserved phase data is used as target phase data corresponding to the frequency domain sub-bands of the structure to be detected.
In one embodiment, after obtaining each frequency domain sub-band, the following operations may be performed on any frequency domain sub-band, and first, the frequency domain sub-band is inverse fast fourier transformed and converted into the spatial domain, i.e., phase data is formed. And for each frame of initial structure vibration image, corresponding phase data of the frequency domain sub-band is obtained, and the phase data is subtracted from the phase data of the first frame of image, so that phase change time domain data changing along time can be obtained.
And S208, respectively performing motion amplification treatment on the target phase data based on the optimal amplification coefficient corresponding to each order of vibration of the structure to be detected, and obtaining vibration amplification results of each order of the structure to be detected.
The optimal amplification factor refers to an optimal amplification factor for each order of vibration, and the motion amplification processing may refer to performing linear amplification on the target phase data by a certain factor, that is, performing phase operation processing. The target phase data comprises phase data of each order of the structure to be detected, so that vibration amplification results of the structure to be detected in each order can be obtained after the target phase data is amplified.
And step S210, obtaining a displacement time-course curve corresponding to each measuring point on the structure to be measured during each vibration step according to each vibration amplification result.
The measuring points on the structure to be measured can refer to any one pixel point forming the structure to be measured, the displacement time course curve refers to a curve synthesized by the relevant information of a plurality of measuring points of the structure to be measured, the abscissa of the displacement time course curve can be the testing duration, the ordinate can refer to the attribute (such as the length of a cable tower) of the structure to be measured, the ordinate can be the displacement of each marking point at each time point, the displacement time course curve can be obtained according to the vibration amplification result, and the vibration amplification result of each step corresponds to the corresponding displacement time course curve.
Step S212, extracting the corresponding vibration mode of the structure to be detected in each order mode based on each displacement time course curve.
The vibration mode refers to a fitting curve containing vibration information of the structure to be detected, the vibration mode can be used for extracting modal parameters, correspondingly, a plurality of vibration modes exist for the structure to be detected with the multi-order mode, and after the vibration mode is obtained, the structural modal information of the structure to be detected at each order can be directly extracted from each vibration mode.
In the structural modal identification method based on the digital image correlation method and the motion amplification technology, an initial structure vibration video is obtained; decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, and decomposing each spectrogram into a plurality of frequency domain sub-bands; performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected, so that vibration signals of other structures in the initial structure vibration video can be filtered, only the vibration signals of the structure to be detected are reserved, and further, performing motion amplification processing on each target phase data to obtain vibration amplification results of each order of the structure to be detected; obtaining a displacement time-course curve corresponding to each measuring point on the structure to be measured when each order vibrates according to each vibration amplification result; based on each displacement time-course curve, extracting the vibration mode corresponding to each order mode of the structure to be detected, enabling the extracted mode of the structure to be detected to be clear and intuitive to the curve in each order mode, thereby not needing to carry out frequency response function calculation, also extracting the identification vibration mode of the structure to be detected in each order, and finally determining the structure mode information of the structure to be detected in each order through each identification vibration mode. The method can effectively improve the structural modal identification precision.
In one embodiment, the decomposing the spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video to decompose each spectrogram into a plurality of frequency domain subbands includes:
based on a preset downsampling proportion, downsampling each frame of initial structure vibration image of the initial structure vibration video to obtain sub-images of multiple scales;
and decomposing each frequency spectrogram into a plurality of frequency domain sub-bands according to amplitude information and phase information contained in each pixel point in each frequency spectrogram.
The prediction down-sampling proportion refers to a set proportion for down-sampling each frame of initial structure vibration image, the preset down-sampling proportion can be set adaptively according to actual requirements and the like, wherein when the initial structure vibration image is down-sampled, a complex operable pyramid (complex operable pyramid) can be used for decomposing the frequency domain structure vibration image according to scale, size, position and the like to obtain amplitude information and phase information after local wavelet transformation, and a plurality of frequency domain sub-bands are determined according to the amplitude information and the phase information, so that a better filtering effect is achieved.
In one embodiment, the performing band-pass filtering processing on the phase data corresponding to each frequency domain subband to obtain target phase data corresponding to each frequency domain subband of the structure to be measured includes:
and performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band based on a time domain band-pass filter to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected, wherein the time domain band-pass filter is provided with band-pass filtering parameters of each order.
The time domain band-pass filter is provided with band-pass filtering parameters of each order, and the band-pass filtering parameters can comprise central frequency, frequency band values and the like. The target phase data can be obtained by filtering the phase data by using a time domain band-pass filter.
In one embodiment, the manner of taking the band-pass filtering parameter includes: acquiring a measuring point displacement time-course curve of any measuring point on the structure to be measured in the initial structure vibration video; carrying out Fourier transform processing on the measuring point displacement time curve data to obtain the self-oscillation frequency information of each order of the structure to be measured; respectively taking the self-vibration frequency information as the central frequency of a time domain band-pass filter; and determining the upper limit frequency and the lower limit frequency of each order of the time domain band-pass filter according to each central frequency and by combining bandwidth setting, wherein the band-pass filtering parameters comprise the upper limit frequency and the lower limit frequency.
The measuring point is any pixel point in an initial structure vibration image of the structure to be measured, a measuring point displacement time-course curve of displacement of the measuring point along with time change can be obtained through fitting of any measuring point, then, for the measuring point displacement time-course curve, fourier transform processing can be carried out on data of the measuring point displacement time-course curve, a spectrogram corresponding to the measuring point displacement time-course curve is obtained, and self-vibration frequency information of each order of the structure to be measured can be determined from the spectrogram, so that the self-vibration frequency information of each order is used as the central frequency of the time domain band-pass filter, and the upper limit frequency and the lower limit frequency of the time domain band-pass filter are determined according to the central frequency and in combination with bandwidth setting.
In one embodiment, after the initial structure vibration video is subjected to framing processing, an initial structure vibration image of each frame can be represented as an image sequence (x, t), where x represents a position, and t represents a time, any pixel point in an area where a structure to be measured belongs can be obtained from the image sequence and used as a measurement point, after the measurement point is determined, the measurement point is selected as a displacement tracking calculation point at a video information processing end, and a measurement point displacement time course curve is obtained by combining with a high-speed camera calibration parameter, as shown in fig. 3, the measurement point displacement time course curve of any measurement point, where the abscissa of fig. 3 is Times (time) in seconds, the ordinate is Displacemen (displacement) in millimeters, and vibration amplitudes in intervals 2 and 3 are about 1 mm.
In one embodiment, the self-oscillation frequency of each order is a frequency corresponding to an extreme point of an amplitude in each order of oscillation information of the structure to be measured, as shown in fig. 4, the frequency is obtained after fourier transform is performed on a measurement point displacement time course curve, an abscissa of fig. 4 is a frequency, a unit is hz, and an ordinate is an amplitude, the fig. 4 includes 4 extreme points together, that is, the structure to be measured has 4 orders of oscillation, the 4 extreme points are 7.559, 11.60, 15.53, and 19.34, respectively, then the frequencies corresponding to the 4 extreme points can be used as the self-oscillation frequency of the first order, the self-oscillation frequency of the second order, the self-oscillation frequency of the third order, and the self-oscillation frequency of the fourth order of the structure to be measured, and finally the self-oscillation frequencies of the respective orders are used as the center frequency of the band-pass filter.
In one embodiment, the method further comprises:
when determining the optimal amplification coefficient corresponding to each step of vibration of the structure to be detected, executing the following steps:
acquiring a plurality of initial amplification coefficients, wherein each initial amplification coefficient is determined based on an arithmetic progression rule;
based on each initial amplification factor, respectively carrying out motion amplification treatment on the target phase data to obtain amplified and synthesized vibration videos of each amplified and synthesized structure;
evaluating each amplified composite structure video by taking a modal confidence criterion as an evaluation standard to obtain a modal confidence curve, wherein the modal confidence curve is a fitting curve of each initial amplification factor and a modal confidence value;
and when the modal confidence value meets the preset modal confidence value condition, selecting the corresponding initial amplification factor as the amplification factor.
The initial amplification factor refers to a factor that can linearly amplify target phase data to a certain extent and increase the amplitude of the target phase data, and the arithmetic progression rule refers to a rule that makes the difference between the initial amplification factors the same, for example, when the initial amplification factor is selected, the initial amplification factor can be determined according to a preset arithmetic progression rule, and the initial amplification factor is set with 10 times as a first class and 100 times as a maximum initial amplification factor, so the initial amplification factor can be 10, 20, 30, 40. Therefore, different initial amplification factors are selected for each order of vibration of the structure to be detected to carry out a comparison test, evaluation is carried out according to the amplification effect, and the most suitable amplification factor of each order is determined.
The preset modal confidence value condition may refer to whether the modal confidence value is in a stable state, and when the preset modal confidence value condition is in the stable state, the preset modal confidence value condition is determined to be satisfied, and after the vibration video of each amplified synthetic structure is obtained, the modal confidence criterion may be used as an evaluation criterion to evaluate each amplified synthetic structure video to obtain a modal confidence curve, where the modal confidence curve is a fitting curve of each initial amplification coefficient and the modal confidence value, and a maximum initial amplification coefficient corresponding to the modal confidence value when the preset modal confidence value condition is in the stable state is used as an optimal amplification coefficient.
As can be seen from equation (1), different motion in an image can be represented by a series of signals with different amplitudes and phases:
Figure BDA0003822650100000121
wherein A is ω Represents the amplitude, phi ω The phase is represented, ω represents angular frequency, x represents a certain pixel point in any frame image, and f (x) can represent signal representation of a certain frame image.
As can be seen from equation (1), the image I (x) at the x position and the t time can be obtained by replacing variables with the above equation, so as to uniformly convert equation (1) from a sine function and a cosine function to an exponential function, as shown in equation (2), so as to facilitate subsequent calculation:
Figure BDA0003822650100000122
the image difference between two moments can be represented by a phase difference, and then the motion amplification of the structure is performed by using the phase difference amplification to obtain an amplified image, wherein α is the amplification factor:
Figure BDA0003822650100000123
the mode confidence curve is a curve formed by fitting each initial amplification factor and an MAC (mode confidence criterion) value, and can be used for expressing the change condition of the MAC value along with each initial amplification factor, wherein the value range of the MAC value is [0 ], the larger the value is, the closer the test mode is to the theoretical mode, as shown in fig. 5, the more detailed MAC description diagram corresponding to each point on the two curves is shown in fig. 6, the confidence curve diagram obtained after amplification of the first-order mode of the structure to be measured is based on the phase (amplification factor) and the riches transformation, the change of the MAC value is not large when the value is 0-60 times, and the MAC value is sharply reduced after the amplification factor exceeds 60 times, that is, when the amplification factor of the structure to be measured is 60 times, the MAC value and the video amplification effect reach a relatively perfect state. And similarly, simulating the vibration of other orders, and testing the change of the MAC value by adopting the increment of a 10-time amplification factor so as to obtain the optimal amplification factor of the vibration of each order.
In one embodiment, after amplifying each target phase data, video synthesis processing may be performed by combining the high-pass residual, the low-pass residual, and each vibration amplification result to obtain a plurality of target structure vibration videos, where in the target structure vibration video, the vibration portion of the structure to be detected is amplified, and finally, according to each target structure vibration video, a displacement time-course curve corresponding to each order of vibration of the structure to be detected is obtained.
In one embodiment, when a displacement time-course curve corresponding to each order of vibration of a structure to be tested is obtained according to a target structure vibration video, displacement tracking processing can be performed on the target structure vibration video to obtain the displacement time-course curve of the structure to be tested on each order, specifically, a sub-pixel matching algorithm can be adopted during processing, the sub-pixel matching algorithm is the essence of DIC deformation testing, and based on an iteration initial value provided by an integer pixel initial value search algorithm, the sub-pixel matching algorithm can converge the integer pixel initial value to a sub-pixel-level local optimal solution, namely, sub-pixel-level deformation testing is realized, so that the precision of the structure displacement time-course curve is improved.
In one embodiment, the extracting, based on each of the displacement time-course curves, a mode shape corresponding to each order mode of the structure to be tested includes:
selecting a plurality of identification points on the structure to be tested, and selecting one point from the identification points as a research point;
according to each displacement time course curve, acquiring a research point time displacement curve of the research point in a test time;
screening out each extreme point from the research point time displacement curve based on the research point time displacement curve, and obtaining each extreme point time based on the time corresponding to each extreme point;
determining a corresponding extreme point moment vibration pattern diagram according to the extreme point moments, wherein the extreme point moment vibration pattern diagram is determined by the displacement of the test points at the extreme point moments;
averaging the moment vibration pattern maps of the extreme points to obtain average vibration pattern maps;
and performing sine function fitting and normalization on each mean value vibration mode graph, and extracting the vibration mode of the structure to be detected corresponding to each order of mode.
The method comprises the steps of selecting any one identification point from all test points on a structure to be tested as a research point, extracting a research point time displacement curve of the research point from the displacement time curve according to an obtained displacement time curve, aiming at the research point time displacement curve, determining the corresponding moment of each extreme point, and obtaining the moment of each extreme point.
After the extreme point moment is determined, the displacement of all the test points at the extreme point moment can be extracted from the displacement time-course curve, and therefore the extreme point moment vibration pattern diagram is formed.
Theoretically, the vibration conditions of all points on a structure should be the same, but at the time of measurement, the vibration conditions of the points may be different, and therefore, by selecting a plurality of identification points, the variance is reduced. And averaging the vibration mode maps at all extreme points to obtain all average value vibration mode maps, and finally performing normalized fitting processing on all average value vibration modes to determine the identification vibration mode of the structure to be detected at each order, so as to improve the accuracy of the identification vibration mode.
In one embodiment, as shown in fig. 7, a block diagram of a process for obtaining the mode shape identification in a specific embodiment is shown:
after the motion amplification processing is performed on the initial structure vibration video, the vibration conditions of each order of the amplified structure are directly obtained, as shown in fig. 7, the specific identification process is as follows: firstly, 7 (a) is a structure displacement time-course curve, one point can be selected from all identification points in the structure displacement time-course curve to serve as a research point, then a research point time displacement curve of the research point in a test time is made based on the structure displacement time-course curve, and each extreme point and the time when each extreme point occurs in the research point time displacement curve are screened out; then, the displacements of all the identification points at each extreme point time are obtained, a preliminary mode shape diagram (as shown in fig. 7 (b)) is obtained, the mode shape diagram can be processed and averaged (as shown in fig. 7 (c)), wherein the solid line is obtained according to the positive value points, and the dotted line is obtained according to the negative value points; the sine function fitting and normalization are performed on fig. 7 (c), and the result is shown in fig. 7 (d), wherein fig. 7 (d) is the final recognized mode shape.
In one embodiment, as shown in fig. 8, a flow chart of a structural modality recognition method based on a digital image correlation method and a motion amplification technology in an embodiment is shown:
firstly, obtaining an original video acquired by DIC measurement and identification, wherein the original structural vibration video may be a video acquired by DIC (digital image correlation) measurement equipment (such as a high-speed camera) performing structural free damping vibration video, and in the original video, in addition to vibration information of a structure to be measured (such as a pylon of a bridge), vibration information of other structures (such as a running automobile, a railing of the bridge and the like) may exist, and vibration information of a passing pedestrian may also exist.
When the DIC measuring equipment is used for collecting original videos, an imaging plane of a camera is parallel to the surface of a structure to be measured, meanwhile, the camera is calibrated, specifically, a projection matrix is used for converting the surface of the structure to be measured to the imaging plane of the camera, the camera calibration is combined, so that the corresponding relation between actual coordinates and camera coordinates is determined, the surface of the structure to be measured is parallel to the imaging plane of the camera as much as possible, the matrix can be conveniently obtained, and calculation errors are reduced.
Then processing the original video, specifically, performing framing processing on the original video, and decomposing the original video into vibration images of original structures; fourier transformation processing is carried out on each original vibration image to obtain each frequency domain structure vibration image corresponding to each original structure vibration image, then a complex steerable pyramid (complex steerable pyramid) is adopted to decompose the video according to the space scale (pixel), direction and position to obtain the amplitude and phase information after local wavelet transformation, and finally the phase change time domain data corresponding to each frequency domain sub-band is determined.
Furthermore, according to the values of the filtering parameters, the time domain bandpass filtering processing is respectively carried out on the phase change time domain data corresponding to each frequency domain sub-band, and as the values of the filtering parameters are determined according to the vibration information of the structure to be detected, only the phase change data of the frequency band of the structure to be detected can be reserved through the time domain bandpass filtering, the phase change data of other structures except the structure to be detected is filtered, and finally the reserved phase change data is used as the target phase data corresponding to the structure to be detected.
After the time domain band-pass filtering, noise reduction and amplification can be performed, specifically, when motion amplification calculation is performed by using each order of natural frequency as a center frequency, different amplification coefficients are selected for a comparison test, evaluation is performed according to an amplification effect, and the most suitable amplification factor of each order of frequency is determined, so that a better amplification effect is achieved.
After amplifying each target phase data, combining the high-pass residual error, the low-pass residual error and each structure mode amplification result, and then performing video synthesis processing to obtain a plurality of target structure vibration videos, wherein in the target vibration videos, the vibration part of the structure to be detected is amplified, and finally, according to each target structure vibration video, a structure displacement time-course curve of the structure to be detected in each order is obtained.
It should be understood that, although the steps in the flowcharts related to the embodiments as described above are sequentially displayed as indicated by arrows, the steps are not necessarily performed sequentially as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a part of the steps in the flowcharts related to the embodiments described above may include multiple steps or multiple stages, which are not necessarily performed at the same time, but may be performed at different times, and the execution order of the steps or stages is not necessarily sequential, but may be rotated or alternated with other steps or at least a part of the steps or stages in other steps.
Based on the same inventive concept, the embodiment of the present application further provides a structural modality recognition apparatus for implementing the structural modality recognition method based on the digital image correlation method and the motion amplification technology. The implementation scheme for solving the problem provided by the apparatus is similar to the implementation scheme described in the above method, so specific limitations in one or more embodiments of the structural modality recognition apparatus provided below can be referred to the limitations of the structural modality recognition method based on the digital image correlation method and the motion amplification technology, and are not described herein again.
In one embodiment, as shown in fig. 9, there is provided a structural modality recognition apparatus including: data acquisition module, data processing module, filtering module, motion amplification module, curve acquisition module and mode of vibration draw the module, wherein:
and the data acquisition module 902 is used for acquiring the initial structure vibration video.
A data processing module 904, configured to perform decomposition processing on a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, and decompose each spectrogram into a plurality of frequency domain subbands.
A filtering module 906, configured to perform band-pass filtering on the phase data corresponding to each frequency domain subband, to obtain target phase data corresponding to each frequency domain subband of the structure to be detected.
And a motion amplification module 908, configured to perform motion amplification processing on the target phase data respectively based on an optimal amplification coefficient corresponding to each order of vibration of the structure to be detected, so as to obtain a vibration amplification result of each order of the structure to be detected.
A curve obtaining module 910, configured to obtain, according to each vibration amplification result, a displacement time-course curve corresponding to each measurement point on the structure to be measured during each order of vibration.
A vibration mode extracting module 912, configured to extract, based on each of the displacement time-course curves, a vibration mode corresponding to each order mode of the structure to be tested.
In one embodiment, the apparatus further comprises: a framing processing module;
the framing processing module is used for framing the initial structure vibration video and decomposing the initial structure vibration video into initial structure vibration image sequences; and performing two-dimensional discrete Fourier transform processing on each initial structure vibration image sequence to obtain a spectrogram corresponding to each frame of initial structure vibration image.
In one embodiment, the data processing module is further configured to perform downsampling processing on each frame of initial structure vibration image of the initial structure vibration video based on a preset downsampling ratio to obtain sub-images of multiple scales; and decomposing each frequency spectrogram into a plurality of frequency domain sub-bands according to amplitude information and phase information contained in each pixel point in each frequency spectrogram.
In one embodiment, the filtering module is configured to perform band-pass filtering processing on the phase data corresponding to each frequency domain subband based on a time domain band-pass filter, so as to obtain target phase data corresponding to each frequency domain subband of the structure to be detected, where the time domain band-pass filter is provided with band-pass filtering parameters of each order.
In one embodiment, the filtering module is configured to determine a natural frequency of each order of the structure to be tested according to each order of vibration information of the structure to be tested; and taking each self-oscillation frequency as the central frequency of time domain band-pass filtering, wherein the filtering parameter value comprises a central frequency value.
In one embodiment, the band-pass filtering parameters include a center frequency, an upper limit frequency and a lower limit frequency, and the filtering module is configured to obtain a measuring point displacement time-course curve of any measuring point on a structure to be measured in the initial structure vibration video; carrying out Fourier transform processing on the measuring point displacement time course curve to obtain the self-oscillation frequency information of each order of the structure to be measured; taking the self-oscillation frequency information as the central frequency of the time domain band-pass filter; and determining the upper limit frequency and the lower limit frequency according to each central frequency and by combining bandwidth setting.
In one embodiment, the apparatus further comprises: an optimal amplification factor determining module;
the optimal amplification factor determining module is used for acquiring a plurality of initial amplification factors, and each initial amplification factor is determined based on an arithmetic progression rule; based on each initial amplification factor, respectively carrying out motion amplification treatment on the target phase data to obtain amplified and synthesized vibration videos of each amplified and synthesized structure; evaluating each amplified composite structure video by taking a modal confidence criterion as an evaluation standard to obtain a modal confidence curve, wherein the modal confidence curve is a fitting curve of each initial amplification factor and a modal confidence value; and when the modal confidence value meets the preset modal confidence value condition, selecting the corresponding maximum initial amplification factor as the optimal amplification factor.
In one embodiment, the vibration mode extraction module is configured to select a plurality of identification points on the structure to be tested, and select one of the identification points as a research point; according to each displacement time course curve, acquiring a research point time displacement curve of the research point in a test time; screening out each extreme point from the research point time displacement curve based on the research point time displacement curve, and obtaining each extreme point time based on the time corresponding to each extreme point; determining a corresponding extreme point moment vibration pattern diagram according to each extreme point moment, wherein the extreme point moment vibration pattern diagram is determined by the displacement of each identification point at the extreme point moment; averaging the moment mode patterns of the extreme points to obtain average mode patterns; and performing sine function fitting and normalization on each mean value vibration mode diagram, and extracting the vibration mode of the structure to be detected corresponding to each order of mode.
The modules in the structural mode recognition device can be wholly or partially implemented by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as shown in fig. 10. The computer device includes a processor, a memory, a communication interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The communication interface of the computer device is used for communicating with an external terminal in a wired or wireless manner, and the wireless manner can be realized through WIFI, a mobile cellular network, NFC (near field communication) or other technologies. The computer program is executed by a processor to implement a structural modality recognition method based on a digital image correlation method and a motion amplification technique. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on the shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.
Those skilled in the art will appreciate that the architecture shown in fig. 10 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In one embodiment, a computer device is provided, which includes a memory and a processor, the memory stores a computer program, and the processor implements the steps of the structural modality recognition method based on the digital image correlation method and the motion amplification technology when executing the computer program.
In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the above-mentioned structural modality recognition method based on a digital image correlation method and a motion amplification technique.
In one embodiment, a computer program product is provided, which comprises a computer program, which when executed by a processor, performs the steps of the above-described structural modality recognition method based on the digital image correlation method and the motion amplification technique.
It should be noted that the data (including but not limited to data for analysis, stored data, presented data, etc.) referred to in the present application are information and data authorized by the user or sufficiently authorized by each party.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, databases, or other media used in the embodiments provided herein can include at least one of non-volatile and volatile memory. The nonvolatile Memory may include a Read-Only Memory (ROM), a magnetic tape, a floppy disk, a flash Memory, an optical Memory, a high-density embedded nonvolatile Memory, a resistive Random Access Memory (ReRAM), a Magnetic Random Access Memory (MRAM), a Ferroelectric Random Access Memory (FRAM), a Phase Change Memory (PCM), a graphene Memory, and the like. Volatile Memory can include Random Access Memory (RAM), external cache Memory, and the like. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM), among others. The databases referred to in various embodiments provided herein may include at least one of relational and non-relational databases. The non-relational database may include, but is not limited to, a block chain based distributed database, and the like. The processors referred to in the embodiments provided herein may be general purpose processors, central processing units, graphics processors, digital signal processors, programmable logic devices, quantum computing based data processing logic devices, etc., without limitation.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.

Claims (10)

1. A structural modal identification method based on a digital image correlation method and a motion amplification technology is characterized by comprising the following steps:
acquiring an initial structure vibration video;
decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video, and decomposing each spectrogram into a plurality of frequency domain sub-bands;
performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected;
respectively performing motion amplification processing on the target phase data based on the optimal amplification coefficient corresponding to each order of vibration of the structure to be detected to obtain vibration amplification results of each order of the structure to be detected;
obtaining a displacement time-course curve corresponding to each measuring point on the structure to be measured when the measuring point vibrates in each order according to each vibration amplification result;
and extracting the vibration mode of the structure to be detected corresponding to each order mode based on each displacement time course curve.
2. The method according to claim 1, wherein after the obtaining of the initial structure vibration video, before the decomposing the spectrogram corresponding to each frame of the initial structure vibration image of the initial structure vibration video, further comprises:
performing framing processing on the initial structure vibration video, and decomposing the initial structure vibration video into initial structure vibration image sequences;
and performing two-dimensional discrete Fourier transform processing on each initial structure vibration image sequence to obtain a spectrogram corresponding to each frame of initial structure vibration image.
3. The method according to claim 1, wherein the decomposing the spectrogram corresponding to each frame of the initial structural vibration image of the initial structural vibration video to decompose each spectrogram into a plurality of frequency-domain subbands comprises:
based on a preset downsampling proportion, downsampling each frame of initial structure vibration image of the initial structure vibration video to obtain subimages of multiple scales;
and decomposing each frequency spectrogram into a plurality of frequency domain sub-bands according to amplitude information and phase information contained in each pixel point in each frequency spectrogram.
4. The method according to claim 1, wherein the performing band-pass filtering processing on the phase data corresponding to each of the frequency domain sub-bands to obtain target phase data corresponding to each of the frequency domain sub-bands of the structure to be measured includes:
and based on a time domain band-pass filter, performing band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected, wherein the time domain band-pass filter is provided with band-pass filtering parameters of each order.
5. The method according to claim 4, wherein the band-pass filter parameters include a center frequency, an upper limit frequency and a lower limit frequency, and the determination of the band-pass filter parameters includes:
acquiring a measuring point displacement time-course curve of any measuring point on the structure to be measured in the initial structure vibration video;
carrying out Fourier transform processing on the measuring point displacement time course curve to obtain the self-oscillation frequency information of each order of the structure to be measured;
taking each self-oscillation frequency information as the central frequency of the time domain band-pass filter;
and determining the upper limit frequency and the lower limit frequency according to each central frequency and by combining bandwidth setting.
6. The method of claim 1, further comprising:
when determining the optimal amplification coefficient corresponding to each step of vibration of the structure to be detected, executing the following steps:
acquiring a plurality of initial amplification coefficients, wherein each initial amplification coefficient is determined based on an arithmetic progression rule;
based on each initial amplification factor, respectively carrying out motion amplification treatment on the target phase data to obtain amplified and synthesized vibration videos of each amplified and synthesized structure;
evaluating each amplified composite structure video by taking a modal confidence criterion as an evaluation standard to obtain a modal confidence curve, wherein the modal confidence curve is a fitting curve of each initial amplification factor and a modal confidence value;
and when the modal confidence value meets the preset modal confidence value condition, selecting the corresponding maximum initial amplification factor as the optimal amplification factor.
7. The method according to claim 1, wherein the extracting, based on each of the displacement time-course curves, a mode shape corresponding to each order mode shape of the structure to be tested comprises:
selecting a plurality of identification points on the structure to be tested, and selecting one point from the identification points as a research point;
according to each displacement time course curve, acquiring a research point time displacement curve of the research point in a test time;
screening out each extreme point from the research point time displacement curve based on the research point time displacement curve, and obtaining each extreme point time based on the time corresponding to each extreme point;
determining a corresponding extreme point moment mode pattern diagram according to each extreme point moment, wherein the extreme point moment mode pattern diagram is determined by the displacement of each identification point at the extreme point moment;
averaging the moment mode patterns of the extreme points to obtain average mode patterns;
and performing sine function fitting and normalization on each mean value vibration mode diagram, and extracting the vibration mode of the structure to be detected corresponding to each order of mode.
8. A structural modality recognition apparatus based on digital image correlation and motion amplification techniques, the apparatus comprising:
the data acquisition module is used for acquiring a vibration video of the initial structure;
the data processing module is used for decomposing a spectrogram corresponding to each frame of initial structure vibration image of the initial structure vibration video and decomposing each spectrogram into a plurality of frequency domain sub-bands;
the filtering module is used for carrying out band-pass filtering processing on the phase data corresponding to each frequency domain sub-band to obtain target phase data corresponding to each frequency domain sub-band of the structure to be detected;
the motion amplification module is used for respectively performing motion amplification processing on the target phase data based on the optimal amplification coefficient corresponding to each order of vibration of the structure to be detected to obtain vibration amplification results of each order of the structure to be detected;
the curve acquisition module is used for acquiring displacement time-course curves corresponding to the measuring points on the structure to be measured during vibration of each order according to the vibration amplification results;
and the vibration mode extraction module is used for extracting the vibration mode of the structure to be detected corresponding to each order of mode based on each displacement time-course curve.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the method of any of claims 1 to 7.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 7.
CN202211046686.9A 2022-08-30 2022-08-30 Structural modal identification method based on digital image correlation method and motion amplification technology Pending CN115661332A (en)

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