Method for measuring inter-story displacement of building under seismic excitation based on exposure integral correction

Abstract

This invention relates to the field of seismic response measurement of building structures, specifically to a method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction. This method acquires building image signals and obtains the pixel displacement matrix using optical flow; constructs an exposure integral imaging model to correct amplitude and phase deviations, and achieves subspace robustness through weighted low-rank decomposition; extracts a virtual baseline to calculate the initial scaling factor and dynamically updates it through Kalman filtering; finally, it calculates the physical inter-story displacement and evaluates the uncertainty, and designs additional row-level compensation for rolling shutter cameras.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of building structure seismic response measurement, more particularly, it relates to a building inter-story displacement measurement method under seismic excitation based on exposure integral correction. BACKGROUND

[0002] Building inter-story displacement is a core index for evaluating structural damage degree and determining seismic safety under seismic action, and its measurement accuracy directly affects the judgment of building seismic performance, and is a key basis for building seismic design and post-disaster evaluation. At present, non-contact visual measurement gradually replaces traditional contact sensors (such as displacement meters and strain gauges) due to its convenient operation and the ability to realize intensive monitoring of measuring points, and becomes an important technical direction for building inter-story displacement measurement.

[0003] However, the existing visual measurement technology has the following significant defects under seismic excitation: first, the camera exposure integration process will cause amplitude attenuation and phase delay of the displacement signal, especially in high-frequency seismic response, which will greatly reduce the measurement accuracy, and there is a lack of targeted correction scheme; second, the line-level readout delay of the rolling shutter camera is easy to cause image tilt blur, the feature point matching in weak texture areas is easy to be disturbed by noise, and the scale factor is usually a fixed value, which is easy to cause scale drift due to vibration and environmental changes, further amplifying the measurement error; third, the existing methods are not optimized for the dynamic characteristics of the seismic scene, and it is difficult to balance measurement accuracy and robustness, which cannot meet the demand for data reliability in structural safety evaluation.

[0004] In view of the above problems, the present application provides a building inter-story displacement measurement method under seismic excitation based on exposure integral correction, which effectively solves the key technical problems of exposure integral deviation and rolling shutter interference through multi-link innovative design. SUMMARY

[0005] In view of the deficiencies of the prior art, the purpose of the present application is to provide a building inter-story displacement measurement method under seismic excitation based on exposure integral correction.

[0006] To achieve the above purpose, the present application provides the following technical scheme:

[0007] The building inter-story displacement measurement method under seismic excitation based on exposure integral correction specifically comprises the following steps:

[0008] Step 1, image acquisition: acquire image sequences of the building, and take dark field images of the building with a preset number of frames;

[0009] Step 2, pixel displacement time history estimation: for the image sequences in step 1, multiple feature points in the strong texture area of the target area are selected, and optical flow matching is performed on each frame of image based on the initial frame, and the pixel displacement matrix is integrated;

[0010] Step 3, Exposure Integration Correction: Construct an exposure integration imaging model, perform joint amplitude and phase correction, and perform inverse Fourier transform on the corrected frequency domain signal to obtain the displacement time history after exposure integration compensation.

[0011] Step 4, Subspace Robustness: The displacement after exposure integral compensation is optimized using a data-driven shape subspace constraint method, and a weighted low-rank decomposition model is used to construct the subspace; under the subspace constraint, the obtained subspace basis vectors are normalized and orthogonalized, and the robust displacement time history is output.

[0012] Step 5, Scale Factor Calibration: Extract the virtual baseline and calculate the initial scale factor; model the scale factor as a random walk process and use Kalman filtering to obtain the real-time scale factor;

[0013] Step Six: Calculation and Uncertainty Assessment of Inter-story Displacement: Representative zones for the upper and lower stories are selected from the robustned displacement time history. The average displacement of the upper story is calculated separately. Average displacement of the lower layer Through formula Calculate physical inter-story displacement ,in, For the first The frame scaling factor state; measurement uncertainty is estimated using the Cramér-Rao lower bound;

[0014] Step 7, Rolling shutter compensation: When using a rolling shutter camera, first perform row-level timestamp modeling and row-level resampling, and then execute steps 3 to 6.

[0015] Furthermore, the construction of the exposure integral imaging model is as follows: ;

[0016] in, Indicates the camera exposure time; This represents the actual displacement signal of the building structure in the time domain; express Fourier transform; Represents the frequency domain transfer function; Represents the actual displacement Fourier transform; Indicates the frequency of the displacement signal;

[0017] The displacement measurement deviation caused by exposure integration is described by the frequency domain transfer function, which is as follows: ;

[0018] in, The frequency of the displacement signal; The exposure time is obtained by reading camera metadata and then optimizing it using multi-frequency least squares fitting; sinc(x) is the sigma function. The imaginary unit, Describe the phase delay caused by exposure integration.

[0019] Furthermore, the aforementioned amplitude and phase joint correction is specifically as follows:

[0020] Within a defined frequency band, the pixel displacement matrix frequency domain signal The correction is performed using the following formula: ;

[0021] For each frequency point f, if , To establish an amplitude threshold, a Wiener-type deconvolution is used for stabilization, as detailed below: ;

[0022] in, express The conjugate of complex numbers; These are regularization parameters, determined using a data-driven approach.

[0023] Furthermore, the subspace construction is as follows:

[0024] Displacement time history matrix after exposure integral compensation Construct the spatiotemporal matrix M using a weighted low-rank decomposition model: in, Represents the element-wise weight matrix; For Hadamard's element-wise product; It is a spatiotemporal matrix, with each row corresponding to the displacement time history of one feature point and each column corresponding to the displacement of all feature points in one frame; The time basis matrix has a dimension of NT×r; NT is the spatial basis matrix with dimensions Nex×r; NT represents the number of frames in the image sequence, Nex represents the feature points selected in step two, and r is the subspace dimension. Norm; For regularization parameters.

[0025] Furthermore, the subspace dimension is determined as follows:

[0026] The singular value cumulative energy threshold is used to determine the singular value sequence by performing singular value decomposition on the spatiotemporal matrix M. Calculate the cumulative energy percentage: ;

[0027] in, The energy accumulation threshold, This indicates the length of the singular value sequence.

[0028] Furthermore, the scaling factor calibration is as follows:

[0029] S51. Virtual baseline extraction: Locating building columns through edge detection, linear Hough transform, and RANSAC fitting.

[0030] S52. Initial scaling factor calculation: The scaling factor s is the ratio of the physical length to the pixel length, with an initial value of... for: ;

[0031] in, The pixel length of the virtual baseline; This refers to the actual physical length of the column;

[0032] S53, Kalman Filter Online Update: Construct state equations and observation equations, model s as a random walk process, and update online using virtual baseline observations.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. Eliminate exposure integral bias and improve signal accuracy: By constructing an exposure integral imaging model containing a frequency domain transfer function, the amplitude and phase of the displacement signal are jointly corrected. Combined with Wiener-type deconvolution stabilization processing, the displacement signal attenuation and phase delay caused by exposure time are effectively offset, solving the high-frequency response bias problem in traditional visual measurement.

[0035] 2. Enhance measurement robustness and avoid scale drift: A weighted low-rank decomposition is used to construct the subspace, and weights are assigned according to the strength of the feature point texture to suppress noise interference in weak texture areas; the scale factor is modeled as a random walk process and dynamically updated online through Kalman filtering to solve the problem of easy drift of fixed scale factors and ensure the long-term accuracy of pixel-physical displacement conversion. Attached Figure Description

[0036] Figure 1 This is a flowchart of a method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction;

[0037] Figure 2 This is a flowchart of the scaling factor calibration for the present invention. Detailed Implementation

[0038] Example 1, refer to Figure 1 This embodiment of the method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction takes a seismic simulation shaking table test of a three-story reinforced concrete frame structure as the application scenario to achieve high-precision measurement of inter-story displacement. Specifically, it includes the following steps:

[0039] Step 1: Image Acquisition.

[0040] An industrial camera was selected, with a resolution of 2592×1944 pixels and a standard frame rate of [missing information]. To meet the time resolution requirements of seismic wave excitation in the experiment; the lens focal length is 8mm, the installation height is 5m above the ground, the lens optical axis is perpendicular to the building facade, and it covers the target area of ​​adjacent floors 1-2 of the building, including geometric features such as columns and curtain wall vertical seams.

[0041] Exposure time was read from camera metadata before the experiment. The initial value is 30ms in this embodiment; 30 frames of dark field images are captured for subsequent noise power spectrum calculation; the acceleration signal output by the vibration table (sampling rate 1000Hz) is acquired simultaneously as a benchmark for displacement measurement results.

[0042] El Centro seismic waves were applied to the shaking table, and the peak ground acceleration was... The duration is Ts, during which image sequences are continuously acquired, resulting in a total of NT frames (Ts × 10 ... ), denoted as image sequence , This is the frame number.

[0043] In this embodiment, the standard frame rate Exposure time Peak acceleration Duration T=20, NT=500;

[0044] Step 2: Pixel displacement time history estimation.

[0045] The pixel displacement time history of the target region is estimated using the pyramid Lucas–Kanade (LK) optical flow method. The specific parameters and operations are as follows:

[0046] Shi-Tomasi corner detection was used in the target area (1st and 2nd floor facades). Based on the test scenario, the corner response threshold was set to 200 and the maximum number of feature points was set to 800. Feature points in areas with strong texture (such as column edges and curtain wall vertical seams) were selected and recorded as Nex feature points.

[0047] The specific settings for the pyramid LK optical flow parameters include: top layer resolution 1 / 8 of the original size, bottom layer original size, and 3 pyramid layers; balancing accuracy and computational efficiency, the search window size is set to 15×15 pixels; to remove weak texture feature points with gradients less than 5 and avoid mismatches, the gradient threshold is set to 5; to improve the robustness of displacement estimation, the number of multi-scale iterations is set to 3; all of the above parameters are the optimal parameters determined through multiple experiments in real-world scenarios.

[0048] Optical flow matching is performed on each frame of the image and the initial frame (t=1) to obtain the time history of the pixel displacement in the x-direction for each feature point, which is then integrated into a pixel displacement matrix. Where NT=500, corresponding to the number of time frames. The i-th row and j-th column represents the pixel displacement of the i-th feature point in the j-th frame; the x-direction is consistent with the seismic excitation direction;

[0049] Step 3: Exposure integration correction.

[0050] By establishing an exposure integral imaging model, Amplitude and phase joint correction is performed to eliminate motion blur and amplitude underestimation. The specific process is as follows:

[0051] S31. Construction of Exposure Integration Imaging Model: ;

[0052] in, Indicates the camera exposure time; This represents the actual displacement signal of the building structure in the time domain; express Fourier transform; Represents the frequency domain transfer function; Represents the actual displacement Fourier transform; The frequency of the displacement signal;

[0053] The displacement measurement deviation caused by exposure integration is described by the frequency domain transfer function, which is as follows: ;

[0054] in, The value range is 0-12.5Hz (according to the Nyquist sampling theorem, a frame rate of 25fps corresponds to a maximum frequency of 12.5Hz). The initial value is 30ms, read from camera metadata, and then optimized using multi-frequency least squares fitting: 5 feature frequency points are selected. , , , , Based on the true displacement obtained by integrating the acceleration signal from the shaking table, a fitting was performed. The optimized value is 29.5ms; sinc(x) is the Singer function, defined as... , This describes the attenuation effect of exposure integral on signal amplitude. The imaginary unit, Describe the phase delay caused by exposure integration (delay time is...) );

[0055] S32, Combined Amplitude and Phase Correction: Within a defined frequency band (0-12.5Hz), for... frequency domain signal The correction is performed using the following formula: ;

[0056] For each frequency point f, calculate ,like , As an amplitude threshold, this embodiment aims to avoid excessive amplification of noise in the low-frequency band. The stabilization process is performed using Wiener-type deconvolution, as detailed below: ;

[0057] in, express The conjugate of complex numbers; for The Fourier transform result; To determine the canonical parameters related to the noise power spectrum, a data-driven approach is used to test different... The quality of signal recovery and the effectiveness of noise suppression are determined in this embodiment. ;

[0058] right Perform an inverse Fourier transform to obtain the displacement time history after exposure integral compensation. .

[0059] Step 4: Subspace robustness.

[0060] A shape subspace is constructed by weighted low-rank decomposition, and time regularization is combined to suppress noise, drift, and weak texture interference. The specific process is as follows:

[0061] S41. Weighted low-rank decomposition to construct subspace: The displacement-time history matrix after exposure integral compensation... Construct the spatiotemporal matrix M using a weighted low-rank decomposition model: ;

[0062] in, This represents the element-wise weight matrix. In this embodiment, the weight of weak texture regions (such as feature points on wall stains) is set to 0.3, and the weight of strong texture regions (pillar edges, vertical seams) is set to 1.0. The weight is adaptively allocated based on the gradient magnitude of the feature points (e.g., gradient magnitude < 10 is set to 0.3, and gradient magnitude ≥ 10 is set to 1.0). For Hadamard's element-wise product; It is a spatiotemporal matrix, with each row corresponding to the displacement time history of one feature point and each column corresponding to the displacement of all feature points in one frame; Let r be the time basis matrix (dimension NT×r), where r is the dimension of the subspace; Let be the spatial basis matrix (dimension Nex×r); It is the Frobenius norm; This is a regularization parameter, used in this embodiment to suppress overfitting. ; r represents the dimension of the subspace, determined using the singular value cumulative energy threshold: singular value decomposition is performed on M to obtain the singular value sequence. Calculate the cumulative energy percentage: ;

[0063] in, The energy accumulation threshold is determined based on prior knowledge of the domain. S42. Subspace Constraints: The obtained subspace basis vectors are normalized and orthogonalized to output the robust displacement time history. , used for constrained displacement field estimation;

[0064] Step 5: Scale factor calibration.

[0065] Based on the geometric invariants of building columns (virtual baseline), online self-calibration and updating are achieved without the need for external rulers, such as... Figure 2 As shown, the specific process is as follows:

[0066] S51. Virtual baseline extraction: Locate building columns (geometric invariants) through line detection and fitting, as follows (the parameters in steps S511~S513 can be adjusted according to the actual scene and target object):

[0067] S511, Edge Detection: The first frame image is processed using the Canny operator, with a low threshold set to 50 and a high threshold set to 150, to extract the edges of the pillars;

[0068] S512, Linear Hough Transform: Angle step 1°, distance step 1 pixel, detects vertical lines (pillar edge).

[0069] S513, RANSAC fitting: 100 iterations, interior point threshold of 2 pixels, fitting the left and right edges of the pillar to obtain the pixel length of the virtual baseline. Pixels (actual physical length of the column is) (This refers to the standard column height in the architectural design drawings).

[0070] S52. Initial scaling factor calculation: The scaling factor s (unit: m / pixel) is the ratio of the physical length to the pixel length. The initial value is: ;

[0071] S53. Kalman Filter Online Update: Modeling s as a random walk process, updating it online using virtual baseline observations to suppress scale drift, the process is as follows:

[0072] S531, State Equations: ; Indicates the first Frame scaling factor status; Represents process noise, obeying , The standard deviation of scale drift during the experiment was set.

[0073] S532, Observation Equation: ; Indicates the first The virtual baseline observations of the frame are obtained by fitting the column edges of the current frame. , ; Represents observation noise, obeying , From multiple fittings Standard deviation calculation;

[0074] S533, Filtering Update: Update using a sliding window (window size 10 frames in this embodiment), calculated once every 10 frames. To achieve dynamic correction;

[0075] Step 6: Calculation of inter-story displacement and assessment of uncertainty.

[0076] S61. Selection of upper and lower representative zones: In the robust displacement time history The upper and lower representative bands were selected, and after filtering by Shi-Tomasi corner detection, the following results were obtained: and For example, the feature points in rows 50-60 at the top of layer 1 and rows 180-190 at the bottom of layer 2, after being filtered by Shi-Tomasi corner detection, have 85 and 92 feature points at the top of layer 1 and the bottom of layer 2, respectively.

[0077] S62. Spatial Mean and Difference: Using Formulas Calculate the average displacement of the upper layer using the formula Calculate the average displacement of the lower layer using the formula Calculate the physical inter-story displacement, unit: m;

[0078] S63. Uncertainty Assessment: The Cramér-Rao lower bound (CRLB) is used for estimation, as shown in the following formula: ;

[0079] in, The signal-to-noise ratio (SNR) of a displacement signal is calculated as the ratio of the signal standard deviation to the noise standard deviation.

[0080] Step 7: Roll shutter compensation.

[0081] If a rolling shutter camera is used, such as the rolling shutter camera in this embodiment (corresponding to a global shutter camera that does not require step seven), row-level timestamp modeling and resampling need to be added:

[0082] S71, Row-level timestamp modeling: Total number of rows in the camera is 1944, row readout time... , No. The timestamp of the row is ( (frame trigger time);

[0083] S72, Row-level resampling: Linear interpolation is used to resample the displacement time histories of different rows to a unified frame timestamp. To eliminate the tilt blur caused by line readout delay, perform exposure integral correction in step three.

[0084] Through the detailed description of the above embodiments, the seismic-excited inter-story displacement measurement method based on exposure integral correction of the present invention achieves high-precision measurement of inter-story displacement under seismic excitation through the synergistic integration of multiple technological innovations. Its core logic lies in addressing the key error sources of visual measurement one by one: exposure integral correction solves signal amplitude and phase deviations; subspace robustness improves data anti-interference capabilities; Kalman filtering dynamically updates the scaling factor to avoid scale drift; and rolling shutter compensation adapts to more camera types. Each step forms a complete technology chain, optimizing the entire process from data acquisition and signal processing to result calculation. This effectively overcomes the problems of insufficient accuracy and poor robustness of existing visual measurements in seismic scenarios, providing reliable and high-precision inter-story displacement data for building structure seismic response assessment, and assisting in structural safety determination and seismic performance optimization.

[0085] The above formulas are all dimensionless calculations, and the preset parameters in the formulas should be set by those skilled in the art according to the actual situation.

[0086] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0087] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0088] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0089] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0090] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0091] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0092] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction, characterized in that, The method flow is as follows: Step 1: Image Acquisition: Obtain an image sequence of the building and capture a preset number of building images; Step 2, Pixel displacement time history estimation: Select strong texture feature points in the target region of the image sequence, perform optical flow matching based on the initial frame, and integrate them into a pixel displacement matrix; Step 3, Exposure Integration Correction: Construct an exposure integration imaging model, perform joint amplitude and phase correction, and perform inverse Fourier transform on the corrected frequency domain signal to obtain the displacement time history after exposure integration compensation. Step 4, Subspace Robustness: A data-driven shape subspace constraint method is adopted, and a subspace is constructed through a weighted low-rank decomposition model; under the constraints of this subspace, the basis vectors are normalized and orthogonalized, and the robust displacement time history is output. Step 5: Scale factor calibration: Extract the virtual baseline and calculate the initial scale factor; The scaling factor is modeled as a random walk process, and Kalman filtering is used to obtain the real-time scaling factor. Step 6: Calculation of inter-story displacement and assessment of uncertainty: Select representative zones of the upper and lower floors of the building in the robust displacement time history, calculate the corresponding average displacement, and calculate the physical inter-story displacement in combination with the scaling factor state. Step 7, Rolling shutter compensation: When using a rolling shutter camera, first perform row-level timestamp modeling and row-level resampling, and then execute steps 3 to 6.

2. The method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction according to claim 1, characterized in that, The construction of the exposure integral imaging model is as follows: ; in, Indicates the camera exposure time; This represents the actual displacement signal of the building structure in the time domain; express Fourier transform; Represents the frequency domain transfer function; Represents the actual displacement Fourier transform; The frequency of the displacement signal; The displacement measurement deviation caused by exposure integration is described by the frequency domain transfer function, which is as follows: ; Where sinc(x) is the Singer function; The imaginary unit, Describe the phase delay caused by exposure integration.

3. The method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction according to claim 1, characterized in that, The aforementioned amplitude and phase joint correction is as follows: Within a defined frequency band, the pixel displacement matrix frequency domain signal The correction is performed using the following formula: ; For each frequency point f, if , To establish an amplitude threshold, a Wiener-type deconvolution is used for stabilization, as detailed below: ; in, express The conjugate of complex numbers; These are regularization parameters, determined using a data-driven approach.

4. The method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction according to claim 1, characterized in that, The subspace construction is as follows: Displacement time history matrix after exposure integral compensation Construct the spatiotemporal matrix M using a weighted low-rank decomposition model: ; in, Represents the element-wise weight matrix; For Hadamard's element-wise product; It is a spatiotemporal matrix, with each row corresponding to the displacement time history of one feature point and each column corresponding to the displacement of all feature points in one frame; The time basis matrix has a dimension of NT×r; NT is the spatial basis matrix with dimensions Nex×r; NT represents the number of frames in the image sequence, Nex represents the feature points selected in step two, and r is the subspace dimension. for Norm; For regularization parameters.

5. The method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction according to claim 4, characterized in that, The subspace dimension is determined as follows: The singular value cumulative energy threshold is used to determine the singular value sequence by performing singular value decomposition on the spatiotemporal matrix M. Calculate the cumulative energy percentage: ; in, The energy accumulation threshold, This indicates the length of the singular value sequence.

6. The method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction according to claim 1, characterized in that, The scaling factor calibration is as follows: S51. Virtual baseline extraction: Locating building columns through edge detection, linear Hough transform, and RANSAC fitting. S52. Initial scaling factor calculation: The scaling factor s is the ratio of the physical length to the pixel length, with an initial value of... for: ; in, The pixel length of the virtual baseline; This refers to the actual physical length of the column; S53, Kalman Filter Online Update: Construct state equations and observation equations, model s as a random walk process, and update online using virtual baseline observations.

7. The method for measuring inter-story displacement of buildings under seismic excitation based on exposure integral correction according to claim 6, characterized in that, The online update of the Kalman filter is as follows: S531. Constructing the state equation ; Indicates the first Frame scaling factor status; Indicates process noise; S532, Constructing the observation equation ; Indicates the first The virtual baseline observations of the frame are obtained by fitting the column edges of the current frame. , ; Indicates observation noise; Indicates the actual physical length of the column; Indicates the first The pixel length of the frame virtual baseline; S533: Uses a sliding window update, calculating once every fixed number of frames within the window. .

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