CN110261052A - Using power hammer excitation and photogrammetric Modal Analysis of Structures system and method - Google Patents
Using power hammer excitation and photogrammetric Modal Analysis of Structures system and method Download PDFInfo
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Abstract
The present invention relates to a kind of using power hammer excitation and photogrammetric Modal Analysis of Structures system and method, using power hammer excitation and the photogrammetric test of contactless Produced by Modal and analysis system, it is characterized in that, overcome the previous analysis being only capable of mostly based on photogrammetric modal analysis system to structure progress OMA, the synchronous acquisition that the present invention passes through power hammer and video, it can reach the measurement of whole audience displacement synchronous, it can accurately estimate the structural frequency response Jacobian matrix hammered into shape by power and video determines, give full play to the advantage of EMA, improve the precision and reliability of Modal Parameter Identification.Realize the Non-contact modal test and analysis to the quick high accuracy of structure.
Description
Technical Field
The invention belongs to the field of structural vibration modal testing, and relates to a structural vibration modal analysis system and method adopting force hammer excitation and photogrammetry.
Background
The experimental modal analysis is a basic means for acquiring the inherent characteristics of the engineering structure such as vibration frequency, damping, modal shape and the like. In practical engineering application, according to the difference of data acquisition, methods commonly used for structural vibration mode analysis are mainly classified into two types: the method comprises the following steps that firstly, traditional modal analysis based on input and output, namely Experimental Modal Analysis (EMA); the second is modal analysis based on output only, i.e. working modal analysis (OMA). In the last 20 years, working mode analysis has become an increasingly research focus, and all output-based mode identification methods are developed under the assumption that the working mode analysis is based on output response only, i.e. the input is assumed to be white noise. The input encountered in engineering practice probably does not satisfy the assumption, so that the recognition work generally encounters some troubles, such as difficult modal order determination, too many false modes, recognition errors and the like. The use of a force hammer to acquire the input signal effectively solves this problem.
Commonly used to obtain output are acceleration sensors, laser vibrometers and high-speed cameras. The acceleration sensor is the most common and widely used modal testing tool, and has the advantages of direct measurement, high measurement precision and the like. However, the use of acceleration sensor measurements introduces additional mass, and contact measurement tools are not suitable for some special test conditions. Compared with an acceleration sensor, the laser vibration meter is a non-contact measuring instrument, the measuring precision is high, and the measuring frequency band is wide. The disadvantage is that it takes a long time to acquire the measurement data of the scanning area, which is time-consuming and labor-consuming. The use of a high-speed camera overcomes the disadvantages of the two measurement tools mentioned above, and this measurement method is also known as photogrammetry.
Most of the existing mode analysis systems based on photogrammetry can only analyze videos or images independently, can only perform OMA on structures, cannot analyze input signals of the videos and force hammers simultaneously, and cannot exert the advantages of EMA. The invention discloses a structural vibration modal analysis system adopting force hammer excitation and photogrammetry for overcoming the existing defects, which can simultaneously analyze the input of a force hammer and the output of a high-speed camera and provide a reliable non-contact experimental modal analysis technology for an actual engineering structure.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a structural vibration mode analysis system and a structural vibration mode analysis method adopting force hammer excitation and photogrammetry.
Technical scheme
A structural vibration mode analysis system adopting force hammer excitation and photogrammetry is characterized by comprising a force hammer, an IEPE signal conditioner, a data acquisition unit, a trigger circuit and a high-speed camera; an IEPE type pressure sensor is arranged in the force hammer; the output end of the force hammer signal is connected with an IEPE signal conditioner, one path of signal is led out from the output end of the IEPE signal conditioner to the input end of the trigger circuit, and the other path of signal is connected with a data processing PC unit through a data acquisition unit; the output end of the trigger circuit is connected with a trigger circuit of the high-speed camera, and the output of the high-speed camera is connected with the data processing PC unit; when the force hammer applies an exciting force to a measured structure, the IEPE type pressure sensor converts a force signal into an electric signal to be output, and the output electric signal is input to the data processing PC unit through the IEPE signal conditioner and the data acquisition unit; meanwhile, the output of the IEPE signal conditioner starts a high-speed camera through a trigger circuit, and the high-speed camera captures image data in real time when the force hammer applies exciting force to the measured structure and transmits the image data to a data processing PC unit; and the data processing PC unit processes the two signals to carry out structural vibration mode analysis on the measured structure.
And a primary amplifier is connected between the IEPE signal conditioner and the data acquisition unit.
A method for obtaining vibration displacement by adopting the structural vibration mode analysis system adopting force hammer excitation and photogrammetry is characterized by comprising the following steps:
step 1, measuring relative resolution mu coefficient of a field of view: taking a round mark point of a measured object as a measurement view field by a high-speed camera, acquiring a data image containing the round mark by the high-speed camera, and calculating a round outline position and a diameter pixel p by a round detection algorithm, wherein the relative resolution coefficient at the measurement point isdrP is the diameter of the circle mark, the diameter of the circle obtained by the circle detection algorithm, and the unit is pixel;
step 2: setting the sampling rate of the force hammer excitation to 3200hz and the sampling time to be 4 s; setting the acquisition frame rate of the high-speed camera to be 3200fps, and setting the number of the triggered acquisition frames to be 12800; the force hammer strikes the round mark point to be measured, the force hammer is excited to obtain a force signal, and a high-speed camera acquisition module is triggered to obtain a video data image;
step 3, detecting the characteristic points of the video data image: taking the first frame image as a reference frame, taking mark points in the reference frame image as regions of Interest (regions of Interest, ROI), and detecting the ROI regions by adopting a Harris corner detection algorithm to obtain position coordinates of a plurality of pixel points; taking the position coordinates of the pixel points as a starting point of tracking;
step 4, carrying out target tracking on the feature points: the target tracking adopts a Kanade-Lucas-Tomasi algorithm, and the sequence of the collected images is S ═ (I) from the time tt,It+1,...,It+k) U denotes the position coordinates of the u point on the image at time t, and is denoted as It(x,y)
The motion offset d ═ d (d) occurs from t to t +1x,dy) If u is located at the t +1 th point on the image, the position is recorded as It+1(x+dx,y+dy) (ii) a Within a neighborhood w centered on point u, there is a difference function:
ε(d)＝ε(dx,dy)＝∫w(It(x,y)-It+1(x+dx,y+dy))2dw
the aim is to calculate the motion offset d so that the value of epsilon (d) is minimal; in the process, a Newton iteration method is adopted to enable the value of epsilon (d) to be converged, and if the value exceeds the iteration set times and is not converged, the tracking of the position point is considered to be invalid;
step 5, screening target tracking tracks: image ItStarting from u point as initial image of final track, tracking is forward tracking until image It+kThen the motion trajectory is (u)t,ut+1,...,ut+k) Is marked asIt+k→ItIs recorded as backward tracingBut the initial tracking point isEnd point ut；
Order toThe tracking track errors in both forward and reverse directions are:
the threshold was set at δ 0.001, unit: a pixel;
when in useIf so, the tracked track is considered to be effective, otherwise, the tracking is considered to be invalid;
step 6, measuring the vibration displacement of the points: according to the relative resolution coefficient mu at the measuring point in the step 1, the heel meeting the precision requirement is obtained in the step 4Trace track TkThen the vibration displacement at the measurement point is: x is mu.Tk。
In the step 3, a SURF and minimum feature detection algorithm is adopted to replace a Harris corner detection algorithm, so as to obtain position coordinates of a plurality of pixel points.
In the step 4, a Newton iteration method is adopted to set the number of iterations for convergence of the value of epsilon (d) to be 30-50.
A structural vibration modal analysis system adopting force hammer excitation and photogrammetry and a method for carrying out modal analysis by using the obtained vibration displacement are characterized by comprising the following steps:
step (1), frequency response function calculation: n measuring points are arranged on the measured structure, the n measuring points are fixed at the o measuring point (o is less than or equal to n), the vibration is excited for k times, and the exciting force of each time is recorded as fi(i ═ 1,2,. k); the vibration displacement of all the measuring points of the structure is measured as follows after each vibration excitation: x ═ X1,x2,...xnAfter exciting for k times, the vibration displacement of each measuring point is as follows: xi(i＝1,...2k)；
A frequency response function ofWherein,represents XiAnd fiThe cross-power spectrum of (a) is estimated,denotes fiEstimating the self-power spectrum of the signal;
the frequency response function matrix is
Are respectively pairedCorrecting the phase shift of the whole phase to obtain a new frequency response function
Step (2), modal parameter identification: to the obtained k-order frequency response function matrixTaking the average, i.e.
H is to beoIs written intoWherein N iso(omega) is a numerator polynomial, and D (omega) is a denominator polynomial;
thenWherein N is of polynomial order, Zj(ω) is a basis function, matrix coefficient AjAnd BojIs the last parameter to be estimated;
determine denominator coefficient matrix α (α ═ { a ═ a)1,A2,...An}T) Solving α for eigenvalues λ of the adjoint matrixrAnd a eigenvector V whose poles are eigenvalues λrModal engagement vector LrThe last row of the V matrix; natural frequency ω of the r-th orderrAnd damping ratio ζrCalculated from the following formula:
mode shape phi of the r-th orderrCalculated from the following formula:
wherein [ LR ] is a lower residual term and [ UR ] is an upper residual term.
Advantageous effects
The structural vibration modal analysis system and method adopting force hammer excitation and photogrammetry provided by the invention are characterized in that the non-contact structural vibration modal test and analysis system adopting force hammer excitation and photogrammetry is characterized in that the problem that most of the traditional modal analysis systems based on photogrammetry can only analyze the structure is solved. And the rapid and high-precision non-contact modal test and analysis of the structure are realized.
Drawings
FIG. 1 is a hardware system design.
Fig. 2 is a schematic diagram of modal testing of a cantilever beam.
Fig. 3 is a test chart of relative resolution.
Fig. 4 is a flowchart of the vibration displacement calculation.
Fig. 5 is an error calculation process of the target tracking algorithm.
Fig. 6 is a modal analysis flow diagram.
FIG. 7 is a steady state diagram calculation of the vibrational modes of a cantilever beam structure
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
hardware design:
1. the force hammer excitation module: the device comprises a force hammer, an IEPE signal conditioner, a charge amplifier, data acquisition equipment and data acquisition software. The function of the force hammer excitation system is to apply an excitation force to a measured structure and collect an excitation force signal. The working principle of the force hammer used by the system is that an IEPE type pressure sensor is integrated in the force hammer, the hammer head of the force hammer strikes a tested structure, the pressure sensor can be triggered to work, a force signal is converted into an electric signal to be output, the output electric signal is collected by data collection equipment into an experimental computer, and the force signal is converted into the force signal by dividing the sensitivity of the force hammer. It should be noted that IEPE type sensors generally cannot be directly connected to a data acquisition device and require a constant current source, i.e., an IEPE signal conditioner. Therefore, in the system, the output end of the force hammer signal is firstly connected into the IEPE signal conditioner, and then the output end of the force hammer signal is led out from the IEPE signal conditioner to the computer. When the model with lower sensitivity is selected, the conversion rate of the force signal to the electric signal is low, and the amplitude of the generated electric signal is lower. In this case, a charge amplifier is required for the subsequent force signal analysis.
2. And the trigger camera acquisition module comprises an IEPE signal conditioner, a trigger circuit, a camera external trigger line, a high-speed video camera and high-speed video acquisition software. The trigger camera acquisition system has the function of ensuring that the modal analysis system can acquire an excitation signal and a response signal simultaneously, namely, the high-speed camera is triggered to acquire synchronously when the force hammer strikes the structure to be detected. In the force hammer excitation system, a signal of a force hammer passes through an IEPE signal conditioner, a path of signal is led out from the output end of the IEPE signal conditioner to the input end of a trigger circuit, a voltage comparator and a charge amplifier are integrated in the trigger circuit and are compared with a reference voltage set by the voltage comparator, and when the voltage of the input end is greater than the reference voltage, a voltage comparator module starts to work and outputs a TTL level; otherwise, the voltage comparator module does not operate. The voltage comparator module adopts a TLV3501 chip, the delay time can reach 4.5ns, and the trigger delay can be avoided within the sampling frequency of 1 MHz. The amplitude of the output voltage is equal to the power supply voltage of the trigger circuit, and the power supply voltage is 3.5-5V generally. And connecting the output end of the trigger circuit to an external trigger circuit of the camera, connecting the other end of the trigger circuit to an external trigger port of the high-speed camera, and when the trigger port receives a TTL level, starting to acquire a video by the high-speed camera.
The method comprises the following steps:
1. and (3) calculating vibration displacement:
(1) relative resolution calculation of the measurement field of view the relative resolution α of the measurement field of view is expressed as:in order to avoid the image distortion caused by the lens as much as possible, the resolution is calculated first only in the field at the measurement point. The method comprises the following specific steps: placing a circular mark in the same plane as the point to be measured in the vicinity of the point, the diameter of the circular mark being known as drWhen the circle detection algorithm is used to find the circle contour position and the diameter pixel p of 15mm, the relative resolution coefficient at the measuring point can be expressed as
(2) Detecting characteristic points: after a high-speed video source is collected, a first frame image of the video is extracted as a reference frame. Taking a certain mark point in the reference frame image as an example, a mark point region (ROI region) is manually selected, and the ROI region is detected by using a Harris corner detection algorithm to obtain the position coordinates of a plurality of pixel points. In addition to the Harris corner detection algorithm, SURF and minimum feature detection algorithms may be used. And taking the position coordinates of the pixel points as the starting point of tracking.
(3) And (3) tracking the characteristic points by adopting a Kanade-Lucas-Tomasi (KLT) algorithm, wherein the position of a reference point is assumed to be (X, y), the position of a second frame is assumed to be (X + ξ, y + η) if the motion offset d is generated to be (ξ), and the KLT algorithm assumes that the brightness at two points is consistent, namely I (X, y,0) is I (X + ξ, y + η, t), J (X) is I (X, y,0), I (X + d) is I (X + ξ, y + η, t), and the target tracking is carried out on the characteristic points by adopting a Kanade-Lucas-Tomasi (KLT) algorithm
J(X)＝I(X+d)+n(X) (1)
Where n (X) is noise. The difference value of the luminance at two points can be expressed as:
ε＝∫w[I(X+d)-J(X)]2wdX (2)
wherein, w is the size of the set solving area window; ε is noted as the residual, which is a function of the square of the motion deviation d.
First, a first order Taylor expansion of I (X + d) is performed to obtain:
I(X+d)＝I(X)+g·d (3)
whereinCan be substituted by the formula (2):
ε＝∫w[I(X)+g·d-J(X)]2wdX＝∫w(h+g·d)2wdX (4)
wherein h ═ i (x) -j (x). The residual is minimized, and the first derivative of the last term of equation (4) to d is zero, i.e.:
∫w(h+g·d)gwdA＝0 (5)
because (g.d) g ═ g (gg)T) d, and d is considered continuous within w, then:
(∫wggTwdA)d＝-∫whdgwdA (6)
can be simplified as G.d ═ e, where G ═ jek-wggTwdA，e＝∫w(J-I) gwdA, e is the calculated residual, and Newton's iteration is used to solve for d. Through experimental testsThe number of iterations was set to 30. When the result converges, the obtained solution is considered as an accurate solution; if not, the tracking of the position point is considered to be invalid.
(4) Screening target tracking tracks: when the feature point detection is performed on each measured point region, a plurality of texture feature points are obtained. However, the tracking accuracy of each feature point is not high, and even when some feature points are tracked, the position information of the pixel points is lost. Therefore, the tracking tracks of these feature points need to be filtered to assume that the image sequence is S ═ (I)t,It+1,...,It+k) Wherein u ═ x1,y1) Representing the position at the image point at time t. Image ItStarting from point u as the starting image of the final trajectory, tracking is started until image It+kThen the motion trajectory is (u)t,ut+1,...,ut+k). This process is called forward trace and is notedAlso, It+k→ItIs recorded as backward tracingBut the initial tracking point isEnd point ut. Order toThe tracking track errors in both forward and reverse directions are:the threshold is set to be 0.001 (unit: pixel) when δ is setWhen the track is valid, the track is considered to be valid, otherwise, the track is considered to be invalid.
(5) Estimating a measurement pointObtaining a relative resolution coefficient α at the measuring point in the step (1), and obtaining a tracking track T meeting the precision requirement in the step (4)kThen the vibration displacement at that measurement point can be expressed as x- α · Tk。
2. Experimental Modal Analysis (EMA). The experimental modal analysis is mainly divided into two steps: the method comprises the steps of integrating the input of a force hammer and the output of a camera to calculate a frequency response function of a structure; secondly, the modal parameters of the structure, namely frequency, damping and mode shape, are estimated by the frequency response function.
(1) Calculating a frequency response function: if n measuring points are arranged on the measured structure and fixed at the o-th measuring point (o is less than or equal to n), exciting for k times, and recording the exciting force of each time as fi(i ═ 1,2.. k). The vibration displacement of all the measuring points of the structure is measured as follows after each vibration excitation: x ═ X1,x2,...xnAfter exciting for k times, the vibration displacement of each measuring point is as follows: xi(i ═ 1,2.. k). The frequency response function can be defined by XiFourier transform ratio of F, i.e.In experimental modal analysis, H is estimatedi(f) The method of (1) generally employs H1By estimation methods, i.e.Wherein,represents XiAnd fiThe cross-power spectrum of (a) is estimated,denotes fiSelf-power spectrum estimation. Then the complete column of the frequency response function matrix can be represented asTo be provided withFor reference, respectively toCorrecting the phase shift of the whole phase to obtain a new frequency response function
(2) Modal parameter identification: to the obtained k-order frequency response function matrixTaking the average, i.e.H is to beoIs written intoWherein N isoAnd (omega) is a numerator polynomial, and D (omega) is a denominator polynomial. N is a radical ofo(ω) and D (ω) may be represented asWherein N is of polynomial order, Zj(ω) is a basis function, matrix coefficient AjAnd BojIs the last parameter to be estimated, a denominator coefficient matrix α is determined (α ═ { a })1,A2,...An}T) By solving for the eigenvalues λ of the adjoint matrix of αrAnd a eigenvector V whose poles are eigenvalues λrModal engagement vector LrThe last row of the V matrix.
Natural frequency ω of the r-th orderrAnd damping ratio ζrThe mode shape phi of the r-th order obtained from the formula (7)rThe following equation (8) can be obtained:
wherein [ LR ] is a lower residual term and [ UR ] is an upper residual term.
The free-free mode test of the cantilever beam is taken as an example.
Structural vibration mode test analysis system using force hammer excitation and photogrammetry, including hardware system design (fig. 1) and software system analysis. A free-free mode test schematic of the cantilever is shown in fig. 2. Wherein: cantilever beam 1, power hammer 2, signal conditioner 3, trigger circuit 4, data acquisition equipment 5, high-speed camera 6, light filling system 7, structural vibration mode analysis computer 8.
The specific experimental steps are as follows:
1. and (4) setting an experiment. The two ends of the cantilever beam are suspended by spring ropes to simulate a free-free test state. The mark points are adhered on the surface of the testing side to be used as measuring points, and the position of the camera is adjusted to enable the measuring view field to be concentrated on one side of the mark points of the cantilever beam, as shown in figure 1. The acquisition frame rate of the camera is 3200fps, and the acquisition time is 4 s;
2. the relative resolution of the measurement field of view is calculated. Above the cantilever beam, a special circular mark is placed, which is known to have a diameter of 15 mm. An image is captured with a high speed camera as shown in fig. 3. And obtaining the pixel number occupied by the circular mark in the image by adopting a circle detection algorithm, and calculating to obtain the relative resolution. To reduce the effect of image distortion during measurement, this operation is performed at each measurement point, resulting in a relative resolution at each measurement point.
3. And synchronously acquiring a force hammer signal and a video signal. The device comprises a hardware hammer, a high-speed video camera, a camera external trigger wire, data acquisition equipment, an IEPE signal conditioner, a trigger circuit and an experimental computer which are required to be used for synchronous acquisition. In order to ensure the consistency of the acquired data, the sampling rate of the force hammer excitation system is 3200hz, the sampling time is 4s, the acquisition frame rate of the trigger camera acquisition system is 3200fps, and the acquisition frame number after triggering is 12800. When the force hammer strikes the third measuring point, the force hammer excitation module obtains a force signal, and the camera acquisition module is triggered to obtain a video source.
4. And calculating vibration displacement. And (4) inputting the video source obtained in the step (3) into a vibration displacement calculation system to obtain a time-dependent change curve of the coordinate positions of all the measurement points. The specific flow chart of the video algorithm processing system is shown in fig. 4. The calculation process of the target tracking error is shown in fig. 5.
And calculating modal parameters. And synthesizing the force signal and the vibration displacement signal after the multiple times of excitation, and obtaining the modal parameters of the structure by an experimental modal analysis system. The modal analysis flow is shown in fig. 6. Fig. 7 is a steady state diagram of the vibration modes of the cantilever structure, and table 1 shows the frequency results of the acceleration sensor and the high speed camera. Table 2 is the MAC values measured by the acceleration sensor and the high speed camera.
TABLE 1 frequency identification results of acceleration sensor and high-speed camera
| Order of the order | Acceleration sensor | High-speed camera |
| 1 | 60.834 | 60.875 |
| 2 | 330.344 | 330.524 |
| 3 | 544.699 | 545.965 |
| 4 | 812.488 | 814.126 |
| 5 | 1134.711 | 1138.104 |
| 7 | 1511.746 | 1514.374 |
TABLE 2 calculation of MAC values for acceleration sensors and high-speed cameras
| Order of the order | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | 98.07 | 1.52 | 2.26 | 1.67 | 0.55 | 1.72 |
| 2 | 3.99 | 97.96 | 1.72 | 2.63 | 2.11 | 2.84 |
| 3 | 2.41 | 2.06 | 97.54 | 1.57 | 2.93 | 2.41 |
| 4 | 1.79 | 1.74 | 2.93 | 93.82 | 2.64 | 0.91 |
| 5 | 0.37 | 1.32 | 3.04 | 2.43 | 90.08 | 3.02 |
| 6 | 1.98 | 1.32 | 1.86 | 1.78 | 3.48 | 86.52 |
Claims (6)
1. A structural vibration mode analysis system adopting force hammer excitation and photogrammetry is characterized by comprising a force hammer, an IEPE signal conditioner, a data acquisition unit, a trigger circuit and a high-speed camera; an IEPE type pressure sensor is arranged in the force hammer; the output end of the force hammer signal is connected with an IEPE signal conditioner, one path of signal is led out from the output end of the IEPE signal conditioner to the input end of the trigger circuit, and the other path of signal is connected with a data processing PC unit through a data acquisition unit; the output end of the trigger circuit is connected with a trigger circuit of the high-speed camera, and the output of the high-speed camera is connected with the data processing PC unit; when the force hammer applies an exciting force to a measured structure, the IEPE type pressure sensor converts a force signal into an electric signal to be output, and the output electric signal is input to the data processing PC unit through the IEPE signal conditioner and the data acquisition unit; meanwhile, the output of the IEPE signal conditioner starts a high-speed camera through a trigger circuit, and the high-speed camera captures image data in real time when the force hammer applies exciting force to the measured structure and transmits the image data to a data processing PC unit; and the data processing PC unit processes the two signals to carry out structural vibration mode analysis on the measured structure.
2. A structural vibration mode analysis system using force hammer excitation and photogrammetry according to claim 1, wherein: and a primary amplifier is connected between the IEPE signal conditioner and the data acquisition unit.
3. A method of obtaining vibrational displacements using a structural vibrational mode analysis system using force hammer excitation and photogrammetry as claimed in claim 1 or 2, characterized by the steps of:
step 1, measuring relative resolution mu coefficient of a field of view: taking a round mark point of a measured object as a measurement view field by a high-speed camera, acquiring a data image containing the round mark by the high-speed camera, and calculating a round outline position and a diameter pixel p by a round detection algorithm, wherein the relative resolution coefficient at the measurement point isdrP is the diameter of the circle mark, the diameter of the circle obtained by the circle detection algorithm, and the unit is pixel;
step 2: setting the sampling rate of the force hammer excitation to 3200hz and the sampling time to be 4 s; setting the acquisition frame rate of the high-speed camera to be 3200fps, and setting the number of the triggered acquisition frames to be 12800; the force hammer strikes the round mark point to be measured, the force hammer is excited to obtain a force signal, and a high-speed camera acquisition module is triggered to obtain a video data image;
step 3, detecting the characteristic points of the video data image: taking the first frame image as a reference frame, taking mark points in the reference frame image as regions of Interest (regions of Interest, ROI), and detecting the ROI regions by adopting a Harris corner detection algorithm to obtain position coordinates of a plurality of pixel points; taking the position coordinates of the pixel points as a starting point of tracking;
step 4, carrying out target tracking on the feature points: the target tracking adopts a Kanade-Lucas-Tomasi algorithm, and the sequence of the collected images is S ═ (I) from the time tt,It+1,...,It+k) U denotes the position coordinates of the u point on the image at time t, and is denoted as It(x,y)
The motion offset d ═ d (d) occurs from t to t +1x,dy) If u is located at the t +1 th point on the image, the position is recorded as It+1(x+dx,y+dy) (ii) a Within a neighborhood w centered on point u, there is a difference function:
ε(d)＝ε(dx,dy)＝∫w(It(x,y)-It+1(x+dx,y+dy))2dw
the aim is to calculate the motion offset d so that the value of epsilon (d) is minimal; in the process, a Newton iteration method is adopted to enable the value of epsilon (d) to be converged, and if the value exceeds the iteration set times and is not converged, the tracking of the position point is considered to be invalid;
step 5, screening target tracking tracks: image ItStarting from u point as initial image of final track, tracking is forward tracking until image It+kThen the motion trajectory is (u)t,ut+1,...,ut+k) Is marked asIt+k→ItIs recorded as backward tracingBut the initial tracking point isEnd point ut；
Order toThe tracking track errors in both forward and reverse directions are:
the threshold was set at δ 0.001, unit: a pixel;
when in useIf so, the tracked track is considered to be effective, otherwise, the tracking is considered to be invalid;
step 6, measuring the vibration displacement of the points: according to the relative resolution coefficient mu at the measuring point in the step 1, the tracking track T meeting the precision requirement is obtained in the step 4kThen the vibration displacement at the measurement point is: x is mu.Tk。
4. The method of claim 3, wherein: in the step 3, a SURF and minimum feature detection algorithm is adopted to replace a Harris corner detection algorithm, so as to obtain position coordinates of a plurality of pixel points.
5. The method of claim 3, wherein: in the step 4, a Newton iteration method is adopted to set the number of iterations for convergence of the value of epsilon (d) to be 30-50.
6. A method of modal analysis of structural vibration using force hammer excitation and photogrammetry as claimed in claim 1 or 2, and vibration displacements obtained as claimed in claim 3 or 4, characterised by the steps of:
step (1), frequency response function calculation: n measuring points are arranged on the measured structure and fixed at the o-th measuring point (o is less than or equal to n),exciting k times, and the exciting force of each time is recorded as fi(i ═ 1,2,. k); the vibration displacement of all the measuring points of the structure is measured as follows after each vibration excitation: x ═ X1,x2,...xnAfter exciting for k times, the vibration displacement of each measuring point is as follows: xi(i＝1,2...k)；
A frequency response function ofWherein,represents XiAnd fiThe cross-power spectrum of (a) is estimated,denotes fiEstimating the self-power spectrum of the signal;
the frequency response function matrix is
Are respectively pairedCorrecting the phase shift of the whole phase to obtain a new frequency response function
Step (2), modal parameter identification: to the obtained k-order frequency response function matrixTaking the average, i.e.
Write Ho toWherein No (omega) is a numerator polynomial and D (omega) is a denominator polynomial;
thenWherein N is of polynomial order, Zj(ω) is a basis function, matrix coefficient AjAnd BojIs the last parameter to be estimated;
determine denominator coefficient matrix α (α ═ { a ═ a)1,A2,...An}T) Solving α for eigenvalues λ of the adjoint matrixrAnd a eigenvector V whose poles are eigenvalues λrModal engagement vector LrThe last row of the V matrix; natural frequency ω of the r-th orderrAnd damping ratio ζrCalculated from the following formula:
mode shape phi of the r-th orderrCalculated from the following formula:
wherein [ LR ] is a lower residual term and [ UR ] is an upper residual term.
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