High-rise building global response reconstruction method based on Kalman filtering

Abstract

The invention relates to the field of structural health monitoring and vibration analysis, in particular to a high-rise building global response reconstruction method based on Kalman filtering, which comprises the following steps: arranging a limited number of sensors at key positions of a high-rise building, acquiring key position response data of the high-rise building, and preprocessing the key position response data; establishing a state equation according to the mechanical model of the high-rise building, establishing an observation equation according to the sensor data, and establishing a dynamic state space model of the high-rise building based on the state equation and the observation equation; and a Kalman filtering algorithm is utilized to iteratively predict and update a state equation so as to realize the optimal estimation of the state of the power system and realize the reconstruction of the global response of the high-rise building. According to the method, blind area information can be effectively compensated under limited monitoring data, and accurate reconstruction of global response is realized.

Description

Technical Field

[0001] The present invention relates to the field of structural health monitoring and vibration analysis, and particularly to a method for reconstructing the global response of high-rise buildings based on Kalman filtering. Background Art

[0002] When high-rise buildings are subjected to extreme loads such as strong typhoons and earthquakes, they will generate violent vibrations and even suffer damage. Real-time monitoring of their dynamic responses is of great significance for the safety assessment and disaster warning of buildings. With the development of the Internet of Things and sensing technologies, more and more engineering structures are equipped with health monitoring systems, aiming to use sensor networks such as accelerometers, strain gauges, and displacement gauges to monitor the structural responses in real time, providing a basis for structural damage identification, safety assessment, and emergency decision-making. However, due to the large volume and complex internal structure of high-rise buildings, if we want to accurately capture the dynamic behavior of the structure, a large number of sensors usually need to be deployed to monitor the building structure in real time. However, this method has the following deficiencies: 1. High monitoring cost: To comprehensively monitor the responses of high-rise buildings, a large number of sensors need to be deployed, resulting in high equipment and maintenance costs. 2. Incomplete data: Due to the limited number of sensors, the entire building area cannot be covered, resulting in blind spots in the monitoring data. 3. Data noise interference: Environmental noise and equipment errors cause noise in the monitoring data, affecting the accuracy of response analysis. Therefore, there is an urgent need to propose a method for reconstructing the global response of high-rise building structures, which can achieve the optimal estimation of the responses at unmeasured positions based on the monitoring data of limited measurement points, so as to realize a complete structural safety assessment.

[0003] Kalman filtering is an efficient linear optimal estimation algorithm, which has the advantages of strong real-time performance and adaptive correction of noisy data. By fusing limited monitoring information with the structural system equation, the optimal state estimation can be achieved. Therefore, dynamically fusing the Kalman filtering algorithm with the state space equation of high-rise buildings can accurately reconstruct the global response of the structure based on a small amount of monitoring data, providing theoretical support for the overall structural safety assessment. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for reconstructing the global response of high-rise buildings based on Kalman filtering, aiming to solve the above problems.

[0005] The present invention provides a method for reconstructing the global response of high-rise buildings based on Kalman filtering, including:

[0006] Deploy a limited number of sensors at key positions of the high-rise building, collect the response data of the key positions of the high-rise building, and preprocess the response data of the key positions;

[0007] Establishing a state equation according to a mechanical model of the high-rise building, establishing an observation equation according to sensor data, and constructing a dynamic state space model of the high-rise building based on the state equation and the observation equation;

[0008] Using the Kalman filter algorithm, the state equation is iteratively predicted and updated to achieve the optimal estimation of the power system state and the reconstruction of the global response of the high-rise building;

[0009] The reconstructed global response of the high-rise building is compared with the response data of key locations, and the reconstructed global response data of the high-rise building is output based on the comparison results to conduct health assessment and safety warning of the high-rise building.

[0010] Preferably, the sensor includes an accelerometer, a displacement meter and an inclinometer.

[0011] Preferably, the preprocessing includes denoising and normalization.

[0012] Preferably, when establishing a state equation based on the structural characteristics and stress characteristics of a high-rise building, the state equation is expressed as:

[0013] X k+1 =ΦX k +Γu k ;

[0014] Among them, Xk represents the state vector at the kth moment, Φ represents the state transfer matrix, Γ represents the input transfer matrix, and uk represents the input vector at the kth moment.

[0015] Preferably, when establishing an observation equation based on sensor data, the expression of the observation equation is:

[0016] Y k =HX k +v k ;

[0017] Among them, Yk represents the observation vector at the kth moment, H represents the observation matrix, and vk represents the observation noise.

[0018] Preferably, when constructing a dynamic state space model of a high-rise building based on the state equation and the observation equation, the expression of the dynamic state space model is:

[0019]

[0020] Where wk represents process noise and vk represents observation noise.

[0021] Preferably, when constructing the dynamic state space model of a high-rise building, the parameters of the state equation and the observation equation are initialized according to the building material properties, structural characteristics and load conditions; wherein, the parameters include the mass matrix M, the stiffness matrix K, the damping matrix C, the observation matrix H and the noise covariance matrix, and the damping matrix C = αM + βK, where α and β represent damping coefficients and are obtained by modal test or finite element model calibration.

[0022] Preferably, using the Kalman filter algorithm, the prediction and update of the state equation are iteratively performed, including:

[0023] Using the dynamic state space model, the predicted state and the predicted covariance matrix are determined according to the historical state and the historical input vector;

[0024] Based on the predicted state and the local response data, the residual is determined, the Kalman gain is determined based on the predicted covariance matrix, and the updated state estimate and the updated covariance matrix are determined according to the residual and the Kalman gain.

[0025] Preferably, after using the Kalman filter algorithm to iteratively predict and update the state equation, it includes: adaptively adjusting the noise covariance matrix of the Kalman filter based on the residual covariance matching method to improve the accuracy of response reconstruction.

[0026] Preferably, comparing the reconstructed global response of the high-rise building with the response data at key positions includes: aligning and preprocessing the reconstructed data with the response data at key positions;

[0027] Calculating the error indexes between the reconstructed data and the response data at key positions, where the error indexes include root mean square error, correlation coefficient, mean absolute error and energy ratio, and obtaining the comparison result according to the error indexes.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0029] Aiming at the defects of monitoring blind areas, data noise interference and poor real-time performance existing in the prior art, the present invention proposes a global response reconstruction technology based on finite sensor data and the Kalman filter algorithm, which has the following remarkable advantages and effects:

[0030] 1. Reducing the monitoring cost: The prior art relies on a large number of sensors for full coverage layout, resulting in a high cost and complex maintenance of the monitoring system. The present invention can accurately reconstruct the global response of a high-rise building by arranging a limited number of sensors at key positions and combining the Kalman filter algorithm, significantly reducing the number of sensors and the layout cost.

[0031] 2. Filling data blind spots: Due to the limited number of sensors in traditional monitoring methods, there are monitoring blind spots. The present invention uses a kinetic model and a Kalman filtering algorithm to perform real-time calculation and compensation on the responses of unmonitored areas, realizing the response reconstruction of the entire structure of the building, and can effectively solve the problem of monitoring blind spots.

[0032] 3. Improving anti-noise performance: In the prior art, the data collected by sensors is easily affected by environmental noise and equipment errors, resulting in a decrease in analysis accuracy. The Kalman filtering algorithm adopted by the present invention has excellent noise suppression ability, can effectively filter out measurement noise and system disturbances, and improve data reliability and result accuracy.

[0033] 4. Enhancing real-time performance: The response reconstruction algorithm based on a model has problems such as slow processing speed and poor real-time performance. The Kalman filtering algorithm of the present invention has functions of real-time data fusion and dynamic update, can respond to the changes in the state of the building structure in real time, and meet the requirements of rapid early warning and real-time monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings according to the provided drawings without creative efforts.

[0035] Figure 1 It is a schematic flow chart of a method for reconstructing the global response of a high-rise building based on Kalman filtering of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] The following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0037] As Figure 1 shown, in some embodiments of the present application, the present invention provides a method for reconstructing the global response of a high-rise building based on Kalman filtering, including:

[0038] Deploy a limited number of sensors at key positions of the high-rise building, collect the response data of the key positions of the high-rise building, and preprocess the response data of the key positions;

[0039] Establishing a state equation according to a mechanical model of the high-rise building, establishing an observation equation according to sensor data, and constructing a dynamic state space model of the high-rise building based on the state equation and the observation equation;

[0040] Using the Kalman filter algorithm, the state equation is iteratively predicted and updated to achieve the optimal estimation of the power system state and the reconstruction of the global response of the high-rise building;

[0041] The reconstructed global response of the high-rise building is compared with the response data of key locations, and the reconstructed global response data of the high-rise building is output based on the comparison results to conduct health assessment and safety warning of the high-rise building.

[0042] As can be seen, this solution significantly improves data acquisition efficiency and accuracy, reduces the number of sensors used, and thus lowers monitoring costs. The application of the Kalman filter algorithm effectively integrates multi-source data, improving the accuracy of monitoring the structural health of high-rise buildings. Furthermore, this method exhibits excellent real-time performance and adaptability, adapting to monitoring needs in diverse environments and conditions, and providing a scientific basis for the maintenance and management of high-rise buildings.

[0043] In some embodiments of the present application, the sensor includes an accelerometer, a displacement meter, and an inclinometer.

[0044] It's understandable that by employing multiple sensor types, we can more comprehensively capture dynamic response information about high-rise buildings in different directions, thereby improving the accuracy and reliability of global response reconstruction. Furthermore, these sensors possess high precision and sensitivity, enabling them to promptly detect subtle changes in high-rise structures, providing more accurate data support for health assessments and safety warnings.

[0045] In some embodiments of the present application, the preprocessing includes denoising and normalization.

[0046] In this embodiment, preprocessing includes denoising and normalization. Denoising is intended to remove noise components in the data to improve data quality and ensure the accuracy of subsequent analysis. This usually involves the use of various filtering techniques, such as low-pass filtering, median filtering or wavelet transform, to reduce or eliminate random errors and irrelevant signals. Normalization is to scale the data so that it falls into a small specific interval, such as between 0 and 1 or -1 to 1. This process helps to eliminate the dimensional effects between different features, making the data numerically comparable, thereby improving the convergence speed and performance of the algorithm. Normalization methods include minimum-maximum normalization, z-score standardization, etc. Through these preprocessing steps, a solid foundation can be laid for subsequent data analysis and machine learning model training.

[0047] It is understandable that through the preprocessing steps, the accuracy and reliability of the data can be further improved. The denoising process can effectively remove the noise and interference in the sensor data to ensure the purity of the data; while the normalization process can unify the data collected by different sensors to the same magnitude, facilitating subsequent data analysis and processing. The implementation of these preprocessing steps provides a more accurate and reliable data basis for the global response reconstruction, further enhancing the accuracy of the high-rise building health assessment and safety warning.

[0048] In some embodiments of the present application, when establishing the state equation according to the mechanical model of the high-rise building, the expression of the state equation is:

[0049] X k+1 = ΦX k + Γu k ;

[0050] Wherein, Xk represents the state vector at the k-th moment, Φ represents the state transition matrix, Γ represents the input transition matrix, and uk represents the input vector at the k-th moment.

[0051] Specifically, the dynamic behavior of the high-rise building can be described by the following second-order differential equation:

[0052]

[0053] Where: M is the mass matrix, C is the damping matrix, K is the stiffness matrix, x(t) is the displacement vector, is the velocity vector, is the acceleration vector, and F(t) is the external excitation vector (such as wind load, seismic load, etc.).

[0054] To convert the second-order differential equation into a state-space model, the state vector X(t) is defined:

[0055]

[0056] Then the state equation can be written as a first-order differential equation:

[0057]

[0058] Where: A is the state matrix, in the form of:

[0059]

[0060] B is the input matrix, in the form of:

[0061]

[0062] u(t) is the input vector (external excitation F(t)).

[0063] For practical applications, the continuous-time state equation is usually discretized. Using a discrete time step Δt, the state equation can be expressed as:

[0064] X k+1 = ΦX k + Γu k ;

[0065] where Xk represents the state vector at the k-th moment, Φ represents the state transition matrix, Γ represents the input transition matrix, and uk represents the input vector at the k-th moment.

[0066] In some embodiments of the present application, when establishing the observation equation based on sensor data, the expression of the observation equation is:

[0067] Y k = HX k + v k ;

[0068] where Yk represents the observation vector at the k-th moment, H represents the observation matrix, and vk represents the observation noise.

[0069] In some embodiments of the present application, when constructing the dynamic state space model of a high-rise building based on the state equation and the observation equation, the expression of the dynamic state space model is:

[0070]

[0071] where wk represents the process noise and vk represents the observation noise.

[0072] It can be understood that by introducing the process noise wk and the observation noise vk, the dynamic response characteristics of a high-rise building under external excitation can be described more accurately. This model not only considers the deterministic part of the system but also fully considers the influence of random perturbations, thereby improving the accuracy and reliability of response reconstruction. In addition, using the Kalman filter algorithm to iteratively predict and update the state equation can achieve the optimal estimation of the dynamic system state, effectively cope with the dynamic changes of high-rise buildings under complex environmental conditions, and provide strong support for structural health monitoring and safety assessment.

[0073] In some embodiments of the present application, when constructing the dynamic state space model of a high-rise building, the parameters of the state equation and the observation equation are initialized according to the building material properties, structural characteristics, and load conditions; among them, the parameters include the mass matrix M, the stiffness matrix K, the damping matrix C, the observation matrix H, and the noise covariance matrix, and the damping matrix C = αM + βK, where α and β represent the damping coefficients and are obtained through modal tests or finite element model calibration.

[0074] It is understandable that by precisely initializing these parameters according to the specific attributes of the building, the accuracy and applicability of the model can be further improved. The mass matrix M reflects the mass distribution of the building structure, the stiffness matrix K describes the stiffness characteristics of the structure, and the damping matrix C synthesizes the energy dissipation characteristics of the structure during vibration. The observation matrix H defines the mapping relationship from the state vector to the observation vector, and the noise covariance matrix quantifies the statistical characteristics of the process noise wk and the observation noise vk. This meticulous parameter initialization process ensures that the dynamic state space model can accurately reflect the real dynamic behavior of high-rise buildings under external excitation, laying a solid foundation for subsequent state estimation and response reconstruction using the Kalman filter algorithm.

[0075] The parameter initialization based on physical characteristics in this application improves the model accuracy. The initial model highly matches the real structural dynamic behavior, reducing the convergence time of the Kalman filter; it provides a reliable benchmark for subsequent dynamic optimization (such as noise covariance adjustment).

[0076] The targeted design of the observation matrix effectively enhances the data fusion efficiency, reduces redundant calculations, and improves the efficiency in the update stage of the Kalman filter; it reduces the memory occupancy through sparse matrix design to adapt to the real-time computing requirements of embedded devices. And by comprehensively utilizing the advantages of different sensors (such as the high-frequency sensitivity of accelerometers and the low-frequency stability of inclinometers), it improves the frequency band coverage ability of the global response reconstruction. The reasonable initialization of the noise covariance matrix ensures the filtering stability, avoids filter divergence, and prevents state estimation deviation caused by the accumulation of model errors; it provides a reasonable starting point for subsequent dynamic adaptive adjustment (such as residual covariance matching).

[0077] In some embodiments of this application, the Kalman filter algorithm is used to iteratively predict and update the state equation, including: using the dynamic state space model to determine the predicted state and the predicted covariance matrix according to the historical state and the historical input vector; determining the residual based on the predicted state and the local response data, determining the Kalman gain based on the predicted covariance matrix, and determining the updated state estimate and the updated covariance matrix according to the residual and the Kalman gain.

[0078] Specifically, the prediction stage: Response prediction based on the dynamic state space model

[0079] In the prediction stage, the dynamic state space model, the historical state, and the historical input vector are used to make a prior estimate of the structural response at the next moment.

[0080] Input:

[0081] The state estimate at the previous moment (Displacement, velocity, etc.)

[0082] The covariance matrix P at the previous momentk∣k (Uncertainty in state estimation);

[0083] System input u k (such as discrete values of the external excitation F(t)).

[0084] Output:

[0085] Predicted state at the current moment

[0086] Predicted covariance matrix P k+1∣k .

[0087] The specific steps are as follows:

[0088] According to the state equation, use the state transition matrix Φ and the input matrix Γ to predict the state at the next moment:

[0089]

[0090] where Φ (state transition matrix, discretize the continuous model through matrix exponentiation);

[0091] Γ (input transition matrix).

[0092] Update the uncertainty (covariance matrix) of the state estimate:

[0093]

[0094] Q is the process noise covariance matrix, characterizing model errors (such as unmodeled dynamics, parameter uncertainties).

[0095] Update stage: fuse local response data to correct the prediction error

[0096] In the update stage, the measured data of the sensor is fused with the prediction result to correct the model deviation and obtain a more accurate posterior state estimate.

[0097] Input:

[0098] Predicted state and predicted covariance matrix P k+1∣k ;

[0099] Local response data Y k+1 (such as acceleration, displacement);

[0100] Observation noise covariance matrix R (sensor accuracy).

[0101] Output:

[0102] Corrected state estimate

[0103] Updated covariance matrix P k+1∣k+1。

[0104] Specific steps

[0105] Calculate the residual (Innovation): Compare the difference between the predicted observation value and the actual sensor data:

[0106]

[0107] H is the observation matrix that maps the state variables to the sensor measurements (such as extracting the displacement or acceleration of a specific floor).

[0108] Calculate the Kalman gain K k+1 : Determine the weight of the model prediction and the sensor data:

[0109] If the sensor accuracy is high (R is small), the gain K is large, and more trust is placed in the observed data; if the model accuracy is high (Q is small, the prediction covariance P k+1∣k is small), the gain K is small, and more reliance is placed on the model prediction.

[0110] Update the state estimate: Use the Kalman gain to correct the predicted value:

[0111]

[0112] Through residual feedback, correct the displacement and velocity estimates of all floors, even if the sensors are only deployed at local locations.

[0113] Update the covariance matrix: Correct the uncertainty of the state estimate:

[0114] P k+1|k+1 =(I - K k+1 H)P k+1|k ;

[0115] After fusing the sensor data, the uncertainty of the state estimate is reduced (the covariance matrix shrinks).

[0116] The sensor data directly reflects the deviation of the model prediction, and the Kalman gain dynamically balances the weights of the model and the data. Through the observation matrix H, the local sensor data is mapped to the global state (such as the displacement and velocity of all floors), realizing the inference from local to global.

[0117] It is understandable that by combining historical state information and local response data, the accurate prediction and real-time update of the global response of high-rise buildings are achieved. This method not only improves the accuracy of state estimation but also significantly enhances the robustness of the system, enabling it to maintain stable performance in the face of complex and changing external environments. In addition, the Kalman gain is used to dynamically adjust the update process, effectively balancing the weights between model prediction and observed data, and further optimizing the state estimation results. The application of this method provides strong technical support for the structural health monitoring and safety assessment of high-rise buildings, helps to detect potential safety hazards in a timely manner, and ensures the long-term stable operation of the building.

[0118] In some embodiments of the present application, using the Kalman filtering algorithm, iteratively predicting and updating the state equation, including: adaptively adjusting the noise covariance matrix of the Kalman filter based on the residual covariance matching method to improve the accuracy of response reconstruction.

[0119] It is understandable that by adaptively adjusting the noise covariance matrix, this method can more flexibly respond to the changes in the dynamic characteristics of high-rise building structures, further optimizing the accuracy of global response reconstruction. This adaptive adjustment mechanism enables the Kalman filtering algorithm to automatically adjust the filtering parameters in the face of different working conditions and external environment changes, thus maintaining the stability and accuracy of the prediction and update process. In addition, this adaptive adjustment strategy also helps to improve the convergence speed and computational efficiency of the algorithm, making the global response reconstruction process more efficient and reliable. The application of this innovative technology further enhances the intelligent level of high-rise building structural health monitoring and safety assessment, providing a more solid guarantee for the safe operation of the building.

[0120] In some embodiments of the present application, comparing the reconstructed global response of the high-rise building with the response data at key positions, including: aligning and preprocessing the reconstructed data with the response data at key positions; calculating the error metrics between the reconstructed data and the response data at key positions, where the error metrics include root mean square error, correlation coefficient, mean absolute error, and energy ratio, and obtaining the comparison result based on the error metrics.

[0121] It is understandable that the present application constructs a multi-dimensional error analysis framework by comprehensively adopting four types of indicators, namely, root mean square error (reflecting the overall deviation degree), correlation coefficient (evaluating trend consistency), mean absolute error (quantifying the average absolute difference), and energy ratio (characterizing the matching degree of signal energy distribution). This combined evaluation mechanism breaks through the limitations of single indicators, can not only capture the macroscopic accuracy of global response reconstruction but also identify the matching degree of local dynamic features, significantly improving the comprehensiveness and scientificity of the evaluation. By introducing a data alignment and preprocessing process, data heterogeneity problems such as time-domain offset, sampling rate difference, and noise interference are effectively solved, ensuring the benchmark consistency of comparative analysis. This technical path greatly reduces the misjudgment risk caused by data quality problems, making the credibility of the reconstructed model verification reach the engineering application level.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements do not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

[0123] For the system provided in the above embodiments, only the division of the above functional modules is used as an example for illustration. In actual applications, the above functions can be allocated to different functional modules according to needs, that is, the modules or steps in the embodiments of the present invention can be further decomposed or combined. For example, the modules in the above embodiments can be combined into one module, or further split into multiple sub-modules to complete all or part of the functions described above. The names of the modules and steps involved in the embodiments of the present invention are only used to distinguish each module or step and are not regarded as an improper limitation of the present invention.

[0124] Those skilled in the art should be able to realize that the modules and method steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. The programs corresponding to the software modules and method steps can be placed in a random access memory (RAM), memory, read-only memory (ROM), electrically erasable programmable ROM, register, hard disk, removable disk, CD-ROM, or any other form of storage medium well-known in the technical field. To clearly illustrate the interchangeability of electronic hardware and software, the composition and steps of each example have been generally described according to functions in the above description. Whether these functions are executed in the form of electronic 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 to exceed the scope of the present invention.

Claims

1. A method for reconstructing the global response of high-rise buildings based on Kalman filtering, characterized in that, Including: Deploy a limited number of sensors at key positions of a high-rise building, collect response data of the key positions of the high-rise building, and preprocess the response data of the key positions; Establish a state equation according to the mechanical model of the high-rise building, establish an observation equation according to the sensor data, and construct a dynamic state space model of the high-rise building based on the state equation and the observation equation; Use the Kalman filtering algorithm to iteratively predict and update the state equation to achieve the optimal estimation of the dynamic system state and the reconstruction of the global response of the high-rise building; Compare the reconstructed global response of the high-rise building with the response data of the key positions, and output the data of the reconstructed global response of the high-rise building according to the comparison result for the health assessment and safety warning of the high-rise building.

2. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 1, wherein, The sensors include accelerometers, displacement gauges and inclinometers.

3. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 1, wherein The preprocessing includes denoising processing and normalization processing.

4. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 1, characterized in that When establishing the state equation according to the mechanical model of the high-rise building, the expression of the state equation is: X k+1 = ΦX k + Γu k ; Where, Xk represents the state vector at the k-th moment, Φ represents the state transition matrix, Γ represents the input transition matrix, and uk represents the input vector at the k-th moment.

5. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 4, characterized in that, When establishing the observation equation according to the sensor data, the expression of the observation equation is: Y k = HX k + v k ; Where, Yk represents the observation vector at the k-th moment, H represents the observation matrix, and vk represents the observation noise.

6. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 5, wherein, When constructing the dynamic state space model of the high-rise building based on the state equation and the observation equation, the expression of the dynamic state space model is: Where, wk represents the process noise and vk represents the observation noise.

7. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 1, characterized in that, When constructing the dynamic state space model of the high-rise building, initialize the parameters of the state equation and the observation equation according to the building material properties, structural characteristics and load conditions; among them, the parameters include the mass matrix M, the stiffness matrix K, the damping matrix C, the observation matrix H and the noise covariance matrix, and the damping matrix C = αM + βK, where α and β represent the damping coefficients and are obtained by modal tests or finite element model calibration.

8. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 1, characterized in that, Using the Kalman filtering algorithm to iteratively predict and update the state equation includes: Using the dynamic state space model to determine the predicted state and the predicted covariance matrix according to the historical state and the historical input vector; Determine the residual based on the predicted state and the local response data, determine the Kalman gain based on the predicted covariance matrix, and determine the updated state estimate and the updated covariance matrix according to the residual and the Kalman gain.

9. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 8, wherein, After using the Kalman filtering algorithm to iteratively predict and update the state equation, it includes: adaptively adjusting the noise covariance matrix of the Kalman filter based on the residual covariance matching method to improve the accuracy of response reconstruction.

10. The method for reconstructing the global response of a high-rise building based on Kalman filtering according to claim 1, characterized in that, Comparing the reconstructed global response of the high-rise building with the response data of the key positions includes: Align and preprocess the reconstructed data and the response data of the key positions; Calculate the error indexes between the reconstructed data and the response data of the key positions. The error indexes include root mean square error, correlation coefficient, mean absolute error and energy ratio, and obtain the comparison result according to the error indexes.

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