A method for quantifying uncertainty based on seismic interferometry

Abstract

The present invention relates to the technical field of structural health monitoring, and more specifically, to an uncertainty quantification method based on seismic interferometry. This method comprises determining a measurement configuration based on the measurement conditions of the structure to be measured, constructing a time-domain seismic interferometry model based on the measurement configuration and soil-structure interaction effect data, and identifying modal parameters based on the seismic interferometry model. Furthermore, the method calculates the minimum variance lower bound of the modal parameters using a Cramer-Rao lower bound, and obtains the uncertainty and spatial resolution of the mode shape using an uncertainty propagation formula. This method overcomes the lack of parameter uncertainty quantification in seismic interferometry.

Description

Technical Field

[0001] The present invention relates to the technical field of structural health monitoring, and in particular to an uncertainty quantification method based on seismic interferometry. Background Art

[0002] Structural modal identification, a key aspect of structural health monitoring, aims to accurately extract key parameters such as natural frequency, damping ratio, and mode shape from dynamic response data. Compared to classical modal analysis methods with known inputs, operational modal analysis (OMA) based on ambient excitation has gained widespread application in civil engineering due to its lack of artificial excitation sources. However, the lack of input information from ambient excitation significantly increases the uncertainty of parameter estimation. This fundamental difference makes uncertainty quantification a key approach to enhancing the credibility of modal identification.

[0003] Operational modal analysis mainly relies on the white noise assumption of excitation. Existing operational modal analysis methods under environmental excitation cannot decouple non-stationary excitation sources (such as earthquakes and rail transit) from soil-structure interaction effects, resulting in significant deviations in modal parameter identification results.

[0004] Although modal parameter identification methods based on seismic interferometry decouple non-stationary excitation sources and soil-structure interaction effects, existing parameter estimation algorithms based on seismic interferometry lack a systematic uncertainty quantification framework and are unable to determine the lower limit of parameter estimation accuracy. This results in an inability to assess the impact of factors such as sensor configuration, data length, and signal-to-noise ratio on the identification results. Therefore, the shortcomings of existing technologies can be summarized as follows: (1) the inability to quantify the reliability of measurement results; and (2) the inability to quantify factors that affect uncertainty.

[0005] Therefore, an uncertainty quantification method based on seismic interferometry is urgently needed to solve the above problems. Summary of the Invention

[0006] The purpose of the present invention is to provide an uncertainty quantification method based on seismic interferometry: compared with existing uncertainty quantification methods, it does not need to rely on a specific algorithm, but directly uses the Clemero lower bound system to give an analytical minimum variance lower bound, thereby achieving theoretically true minimum uncertainty quantification.

[0007] The purpose of the present invention can be achieved through the following technical solutions:

[0008] A method for quantifying uncertainty based on seismic interferometry, comprising:

[0009] Determining a measurement configuration based on measurement conditions of the structure to be measured, wherein the measurement configuration includes the number of measurement points, measurement duration, and signal-to-noise ratio;

[0010] A time-domain seismic interferometry model is constructed based on the measurement configuration and soil-structure interaction effect data, and modal parameters are identified based on the seismic interferometry model.

[0011] The minimum variance lower bound of the modal parameters is calculated using the Cramer-Rao lower bound, and the uncertainty and spatial resolution of the vibration mode are obtained using the uncertainty transfer formula.

[0012] Furthermore, the number of measuring points M is uniformly distributed within the height region, and the measurement duration includes at least several natural cycles of vibration of the structure to be measured. The estimation of the signal-to-noise ratio includes: using a finite element analysis method, predicting the vibration response of the structure to be measured under different working conditions, obtaining an expected intensity range of the vibration signal, and adjusting the target signal-to-noise ratio based on the expected intensity range of the vibration signal.

[0013] Furthermore, a time-domain seismic interferometry model is constructed based on the measurement configuration and soil-structure interaction effects. Modal parameter identification based on the seismic interferometry model and soil-structure interaction effect data specifically includes the following steps:

[0014] According to the residue theorem, the seismic interferometry model in the time domain is determined as the superposition of orthogonal modal fields:

[0015] in, For the earthquake interference model, namely the impulse response function, the soil-structure interaction effect data include: is the sensor position, is the reference sensor position, For time, is the height of the object being measured, is the shear wave velocity, where is the damping ratio, is the modal order, For the The frequency of the order, where the damping ratio and quality factor exist relationship;

[0016] The damping ratio is calculated based on the seismic interferometry model. and the first-order frequency , the damping ratio and the first-order frequency are recorded as modal parameters.

[0017] Furthermore, the calculation of the minimum variance lower bound of the modal parameters using the Cramer-Rao lower bound specifically includes the following process:

[0018] When the number of measuring points is single, the damping ratio and the first-order frequency Taking the partial derivatives we get: ;

[0019] ;

[0020] Where C is a constant,

[0021] According to the Fisher information matrix, when the sampling rate is zero and the observation time is infinite, each sensor will produce an impulse response function by deconvolution with the reference sensor. Then the closed-form solution of its Fisher information matrix is: ;

[0022] ;

[0023] and are the Fisher information matrices of fundamental frequency and damping ratio, respectively, is the sampling frequency corresponding to the sth acquisition moment, is the variance of the noise;

[0024] According to the definition of Cramer-Rao lower bound, the normalized first-order frequency and damping ratio The minimum lower bound of the variance is: ;

[0025] ;

[0026] in, and is the Cramer-Rao lower bound for the fundamental frequency and damping ratio, is the mean of the fundamental frequency, is the mean value of the damping ratio, is the first-order frequency The minimum lower bound of the variance, is the damping ratio The smallest lower bound on variance.

[0027] Furthermore, the calculation of the minimum variance lower bound of the modal parameters using the Cramer-Rao lower bound also includes the following process:

[0028] When the number of measurement points is M, the overall Fisher information matrix obtained based on all measurement points is: ;in, is the reference height;

[0029] By using the transformation from discrete summation to integral and the integral formula, the asymptotic law of the Fisher information matrix is ​​obtained;

[0030] According to the definition of Cramer-Rao lower bound, the normalized first-order frequency and damping ratio The minimum lower bound of the variance is: ;

[0031] ;

[0032] in, and is the Cramer-Rao lower bound for the fundamental frequency and damping ratio, is the mean of the fundamental frequency, is the mean value of the damping ratio, is the first-order frequency Under the minimum variance of is the damping ratio The smallest lower bound on variance.

[0033] Furthermore, the uncertainty and spatial resolution of the mode shape are obtained through the uncertainty transfer formula, which specifically includes the following process:

[0034] Using the uncertainty transfer formula:

[0035] ;

[0036] in, 、 and They are vibration mode functions Preset parameters 、 , the standard deviation corresponding to z, is the vibration mode function obtained after uncertainty propagation The standard deviation of the standard deviation is recorded as the uncertainty of the vibration mode and the law of spatial resolution is calculated. .

[0037] Compared with the existing solutions, the present invention achieves the following beneficial effects:

[0038] The present invention determines the measurement configuration according to the measurement conditions of the structure to be measured, constructs a time-domain seismic interferometry model based on the measurement configuration and soil-structure interaction effect data, and identifies modal parameters based on the seismic interferometry model; calculates the minimum variance lower bound of the modal parameters through the Cramer-Rao lower bound, and obtains the uncertainty and spatial resolution of the vibration mode through the uncertainty transfer formula, thereby overcoming the problem of lack of parameter uncertainty quantification based on seismic interferometry.

[0039] Compared with existing uncertainty quantification methods, it does not need to rely on specific algorithms, but directly uses the Clemero lower bound system to give an analytical minimum variance lower bound to achieve the theoretical true minimum uncertainty.

[0040] Compared with the existing operational mode identification methods, the present invention decouples the excitation non-stationarity and soil-structure interaction effects in actual working conditions through seismic interferometry. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments described in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0042] Figure 1 1 is a flow chart of an uncertainty quantification method based on seismic interferometry according to an embodiment of the present invention;

[0043] Figure 2 Schematic diagram of the asymptotic lower bounds of fundamental frequency and damping ratio with different numbers of sampling points in an embodiment of the present invention;

[0044] Figure 3 Schematic diagram of the theoretical lower bound of the variance of the vibration mode under different numbers of measurement points and noise levels according to an embodiment of the present invention;

[0045] Figure 4 3 is an effect diagram of the uncertainty bounds of the fundamental frequency and the damping ratio under different signal-to-noise ratios according to an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0047] In addition, the described features, structures or characteristics can be combined in any suitable manner in one or more example embodiments. In the following description, many specific details are provided to provide a full understanding of the example embodiments of the present disclosure. However, those skilled in the art will appreciate that the technical solutions of the present disclosure can be practiced while omitting one or more of the specific details, or other methods, components, steps, etc. can be adopted. In other cases, well-known structures, methods, implementations or operations are not shown or described in detail to avoid obscuring various aspects of the present disclosure.

[0048] Figure 1 FIG. 1 is a flow chart of an uncertainty quantification method based on seismic interferometry according to an embodiment of the present invention. Figure 1As shown, first, the measurement configuration is determined based on the measurement conditions of the structure to be measured (such as the number of sensors, measurable time, and sensor quality). The measurement configuration includes the number of measurement points, measurement time, and signal-to-noise ratio:

[0049] Number of measuring points

[0050] Purpose: The number of measurement points determines the richness of the structural vibration information obtained. More measurement points can more comprehensively capture the vibration response of the structure at different locations, helping to more accurately identify modal parameters. For example, for a simple beam structure, setting only a single measurement point at one end of the beam will only capture vibration information at that point and may not accurately identify all the beam's modes, especially high-order modes. However, if multiple measurement points are evenly distributed across the beam, a more comprehensive understanding of the beam's vibration behavior at different locations can be achieved, improving the accuracy of modal parameter identification.

[0051] Determination method: The structure's geometry, complexity, and the desired modal order need to be comprehensively considered. Generally speaking, for complex structures, more measurement points are required to fully capture their vibration characteristics. A preliminary dynamic analysis of the structure, such as through finite element analysis, can be performed. Based on the results, the approximate location and number of measurement points can be preliminarily determined, and then appropriate adjustments can be made during actual measurements.

[0052] Measurement duration

[0053] Effect: Measurement duration affects the integrity of vibration data. Longer measurement durations can record the vibration of the structure over different time periods, including any random vibration components that may occur, thereby improving the reliability of modal parameter identification. For example, when measuring the vibration of a bridge, if the measurement duration is too short, it may only capture the vibration response of the bridge under specific traffic loads, but not the vibration response of the bridge under other environmental factors such as wind loads and earthquakes, resulting in deviations in the modal parameter identification results.

[0054] Determination method: The structure's natural period and the duration of various external factors that may affect structural vibration must be considered. Generally speaking, the measurement duration should cover at least several natural periods of the structure to ensure accurate identification of the modal parameters. Furthermore, the cost and feasibility of the actual measurement must be considered. While ensuring measurement accuracy, the measurement duration should be minimized.

[0055] Signal-to-noise ratio

[0056] Function: The signal-to-noise ratio reflects the relative strength of the useful signal and the noise signal in the measurement signal. A higher signal-to-noise ratio means the measurement signal contains more useful information, which can improve the accuracy of modal parameter identification. For example, when measuring a small vibration signal, if the ambient noise is high, resulting in a low signal-to-noise ratio, the noise component in the measurement signal will mask the useful signal, resulting in large errors in the modal parameter identification results.

[0057] Determination method: The measurement environment can be evaluated to understand the possible noise sources and their strength. Then, based on the expected strength of the structural vibration signal, the required signal-to-noise ratio can be estimated. In actual measurements, the signal-to-noise ratio can be improved by using appropriate sensors, filtering techniques, and other means.

[0058] Subsequently, the seismic interferometry method was used to decouple the effects of excitation nonstationarity and soil-structure interaction, identifying the wave velocity and quality factor parameters. Next, the Cramer-Rao lower bound was used to identify the minimum variance lower bounds for the frequency and damping ratio. Finally, the uncertainty transfer theory formula was used to calculate the uncertainty of the modal parameters (mode shapes). Most importantly, the laws that influence the uncertainty were clarified.

[0059] In summary, the present invention determines the measurement configuration according to the measurement conditions of the structure to be measured, constructs a time-domain seismic interferometry model based on the measurement configuration and soil-structure interaction effect data, and identifies modal parameters based on the seismic interferometry model; calculates the minimum variance lower bound of the modal parameters through the Cramer-Rao lower bound, and obtains the uncertainty and spatial resolution of the vibration mode through the uncertainty transfer formula, thereby overcoming the problem of lack of parameter uncertainty quantification based on seismic interferometry.

[0060] Compared with existing uncertainty quantification methods, it does not need to rely on specific algorithms, but directly uses the Clemero lower bound system to give an analytical minimum variance lower bound to achieve the theoretical true minimum uncertainty.

[0061] Compared with the existing operational mode identification methods, the present invention decouples the excitation non-stationarity and soil-structure interaction effects in actual working conditions through seismic interferometry.

[0062] In some embodiments, the number M of measurement points is evenly distributed within the height region.

[0063] In some embodiments, a time-domain seismic interferometry model is constructed based on the measurement configuration and the soil-structure interaction effect, and modal parameters are identified based on the seismic interferometry model and the soil-structure interaction effect data, specifically comprising the following process:

[0064] According to the residue theorem, the seismic interferometry model in the time domain is determined as the superposition of orthogonal modal fields:

[0065] in, For the earthquake interference model, namely the impulse response function, the soil-structure interaction effect data include: is the sensor position, is the reference sensor position, For time, is the height of the object being measured, is the shear wave velocity, where is the damping ratio, is the modal order, For the The frequency of the order, where the damping ratio and quality factor exist relationship;

[0066] The damping ratio is calculated based on the seismic interferometry model. and the first-order frequency , the damping ratio and the first-order frequency are recorded as modal parameters.

[0067] In some embodiments, calculating the minimum variance lower bound of the modal parameters using the Clamey-Rao lower bound specifically includes the following process:

[0068] When the number of measuring points is single, the damping ratio and the first-order frequency Taking the partial derivatives we get: ;

[0069] ;

[0070] Where C is a constant,

[0071] According to the Fisher information matrix, when the sampling rate is zero and the observation time is infinite, each sensor will produce an impulse response function by deconvolution with the reference sensor. Then the closed-form solution of its Fisher information matrix is: ;

[0072] ;

[0073] and are the Fisher information matrices of fundamental frequency and damping ratio, respectively, is the sampling frequency corresponding to the sth acquisition moment, is the variance of the noise;

[0074] According to the definition of Cramer-Rao lower bound, the normalized first-order frequency and damping ratio The minimum lower bound of the variance is: ;

[0075] ;

[0076] in, and is the Cramer-Rao lower bound for the fundamental frequency and damping ratio, is the mean of the fundamental frequency, is the mean value of the damping ratio, is the first-order frequency The minimum lower bound of the variance, is the damping ratio The smallest lower bound on variance.

[0077] In some embodiments, calculating the minimum variance lower bound of the modal parameters using the Clamey-Rao lower bound further includes the following process:

[0078] The calculation of the minimum variance lower bound of the modal parameters using the Cramer-Rao lower bound also includes the following steps:

[0079] When the number of measurement points is M, the overall Fisher information matrix obtained based on all measurement points is: ;in, is the reference height;

[0080] By using the transformation from discrete summation to integral and the integral formula, the asymptotic law of the Fisher information matrix is ​​obtained;

[0081] According to the definition of Cramer-Rao lower bound, the normalized first-order frequency and damping ratio The minimum lower bound of the variance is: ;

[0082] ;

[0083] in, and is the Cramer-Rao lower bound for the fundamental frequency and damping ratio, is the mean of the fundamental frequency, is the mean value of the damping ratio, is the first-order frequency The minimum lower bound of the variance, is the damping ratio The smallest lower bound on variance.

[0084] In some embodiments, obtaining the uncertainty and spatial resolution of the mode shape using the uncertainty propagation formula specifically includes the following process:

[0085] The uncertainty and spatial resolution of the vibration mode are obtained through the uncertainty transfer formula, which specifically includes the following process:

[0086] Using the uncertainty transfer formula:

[0087] ;

[0088] in, 、 and They are vibration mode functions Preset parameters 、 , the standard deviation corresponding to z, is the vibration mode function obtained after uncertainty propagation The standard deviation of the standard deviation is recorded as the uncertainty of the vibration mode and the law of spatial resolution is calculated. .

[0089] The following uses the vibration measurement of a cantilever beam structure as an example to illustrate the implementation steps of the uncertainty quantification method based on seismic interferometry proposed in this invention. First, the measurement conditions are introduced. Assume that the measurement object is a cantilever beam structure, the excitation method is white noise excitation, and the excitation signal is a broadband signal.

[0090] Step 1: Measurement system layout

[0091] Assume the building to be measured is 15 meters tall, the reference floor is located at the lower level (i.e., the modal parameters are measured with the lower level as the fixed end), and the sensors are evenly distributed throughout the building. The wave velocity c and quality factor Q are parameters that need to be estimated, and their true values ​​are assumed to be 312.63 m / s and 50 / 3, respectively.

[0092] Step 2: Identify modal parameters based on seismic interferometry

[0093] First, vibration data is obtained using the measurement system layout. The impulse response function is calculated through deconvolution. Then, Monte Carlo simulations (200 independent experiments) are performed to calculate the mean square error (MSE) of the modal parameter estimates based on a specific algorithm (such as the least squares method).

[0094] Step 3: Determine the uncertainty of modal parameters and their influencing factors

[0095] A variance lower bound model for seismic interferometry parameter estimation is established. By substituting the parameters (measurement point location, measurement data length, signal-to-noise ratio), the theoretical lower bound is obtained based on the formula. The influence of the number of samples on the theoretical lower bound is analyzed based on the numerically calculated lower bound. Figure 2 Schematic diagram of the asymptotic lower bounds of fundamental frequency and damping ratio with different numbers of sampling points in an embodiment of the present invention. Figure 2 As shown, it can be seen that the numerical lower bound can be very close to the theoretical formula. Afterwards, the theoretical lower bound is calculated based on the formula and compared with the numerical lower bound. Figure 3It is a schematic diagram of the lower bound of the theoretical variance of the vibration mode in the embodiments of the present invention under different numbers of measurement points and noise levels. As Figure 3 shown, the influence of the reduction in the number of measurement points on the parameter error can be obtained, and the number of measurement points conforms to the 1 / M theory. Finally, the tightness of the Cramer-Rao bound under different signal-to-noise ratios needs to be discussed. Figure 4 It is an effect diagram of the uncertainty bounds of the fundamental frequency and damping ratio under different signal-to-noise ratios in the embodiments of the present invention. As Figure 4 shown, an effective region (SNR > 10 dB), a relaxation region (-15 dB < SNR < 1 dB), and an invalid region (SNR < -15 dB) are obtained. When using this theory, it is necessary to determine the region where it is located.

[0096] As described above, only one embodiment of the present invention is provided, and it does not impose any limitation on the technical scope of the present invention. Therefore, any minor modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention all fall within the scope of the technical solution of the present invention.

[0097] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination. When implemented using software, the above embodiments can be implemented in whole or in part in the form of 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, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. 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 by wire (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that the computer can access or a data storage device such as a server or data center that includes one or more collections of available media. The available medium can be a magnetic medium (such as a floppy disk, hard disk, magnetic tape), an optical medium (such as a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0098] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or by a combination of computer software and electronic hardware. Whether these functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans can use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of the present application.

[0099] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0100] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is merely a division of some logical functions. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0101] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0102] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A method for quantifying uncertainty based on seismic interferometry, characterized in that: Methods include: Determining a measurement configuration based on measurement conditions of the structure to be measured, wherein the measurement configuration includes the number of measurement points, measurement time, and signal-to-noise ratio; A time-domain seismic interferometry model is constructed based on the measurement configuration and soil-structure interaction effect data, and modal parameters are identified based on the seismic interferometry model. The minimum variance lower bound of the modal parameters is calculated using the Cramer-Rao lower bound, and the uncertainty and spatial resolution of the vibration mode are obtained using the uncertainty transfer formula. The calculation of the minimum variance lower bound of the modal parameters using the Cramer-Rao lower bound specifically includes the following process: When the number of measuring points is single, the damping ratio and the first-order frequency Taking the partial derivatives we get: ； ； Where C is a constant, According to the Fisher information matrix, when the sampling rate is zero and the observation time is infinite, each sensor will produce an impulse response function by deconvolution with the reference sensor. Then the closed-form solution of its Fisher information matrix is: ； ； and are the Fisher information matrices of fundamental frequency and damping ratio, respectively, is the sampling frequency corresponding to the sth acquisition moment, is the variance of the noise; According to the definition of Cramer-Rao lower bound, the normalized first-order frequency and damping ratio The minimum lower bound of the variance is: ； ； in, and is the Cramer-Rao lower bound for the fundamental frequency and damping ratio, is the mean of the fundamental frequency, is the mean value of the damping ratio, is the first-order frequency The minimum lower bound of the variance, is the damping ratio The smallest lower bound of variance; The calculation of the minimum variance lower bound of the modal parameters using the Cramer-Rao lower bound also includes the following steps: When the number of measurement points is M, the overall Fisher information matrix obtained based on all measurement points is: ;in, is the reference height; By using the transformation from discrete summation to integral and the integral formula, the asymptotic law of the Fisher information matrix is ​​obtained; According to the definition of Cramer-Rao lower bound, the normalized first-order frequency and damping ratio The minimum lower bound of the variance is: ； ； in, and is the Cramer-Rao lower bound for the fundamental frequency and damping ratio, is the mean of the fundamental frequency, is the mean value of the damping ratio, is the first-order frequency Under the minimum variance of is the damping ratio The smallest lower bound of variance; The uncertainty and spatial resolution of the vibration mode are obtained through the uncertainty transfer formula, which specifically includes the following process: Using the uncertainty transfer formula: ； in, 、 and They are vibration mode functions Preset parameters 、 , the standard deviation corresponding to z, is the vibration mode function obtained after uncertainty propagation The standard deviation of the standard deviation is recorded as the uncertainty of the vibration mode and the law of spatial resolution is calculated. .

2. The uncertainty quantification method based on seismic interferometry according to claim 1, characterized in that: The number of measuring points M is uniformly distributed within the height region, and the measurement duration includes at least several natural cycles of vibration of the structure to be measured. The estimation of the signal-to-noise ratio includes: using a finite element analysis method to predict the vibration response of the structure to be measured under different working conditions, obtaining an expected intensity range of the vibration signal, and adjusting the target signal-to-noise ratio based on the expected intensity range of the vibration signal.

3. The uncertainty quantification method based on seismic interferometry according to claim 1, characterized in that: A time-domain seismic interferometry model is constructed based on the measurement configuration and soil-structure interaction effects. Modal parameter identification based on the seismic interferometry model and soil-structure interaction effect data includes the following steps: According to the residue theorem, the seismic interferometry model in the time domain is determined as the superposition of orthogonal modal fields: in, For the earthquake interference model, namely the impulse response function, the soil-structure interaction effect data include: is the sensor position, is the reference sensor position, For time, is the height of the object being measured, is the shear wave velocity, where is the damping ratio, is the modal order, For the The frequency of the order, where the damping ratio and quality factor exist relationship; The damping ratio is calculated based on the seismic interferometry model. and the first-order frequency , the damping ratio and the first-order frequency are recorded as modal parameters.

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