Finite element model updating and safety assessment method for complex engineering structures

Abstract

The application discloses a finite element model correction and safety state evaluation method suitable for complex engineering structures and belongs to the technical field of civil engineering structure safety state evaluation, and comprises the following steps: establishing an initial nonlinear finite element model and obtaining multi-source response data under strong load; performing global parameter sensitivity analysis on all physical parameters and screening out key correction parameters; setting initial system parameters of a UKF algorithm and dividing time windows; sequentially performing single UKF iteration in each time window, recursively updating parameters between windows, and stopping until a convergence condition is met; constructing a mapping relationship between the key correction parameters and structure failure probability by using a Kriging model, and completing proxy model training; and in online evaluation, updating parameters by using an improved UKF algorithm, inputting the updated parameters into the Kriging model, and obtaining the structure failure probability. The application realizes rapid updating of high-dimensional parameters of complex engineering structures and real-time evaluation of safety states by using the above method.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural safety status assessment technology, and in particular to a finite element model modification and safety status assessment method applicable to complex engineering structures. Background Technology

[0002] Civil engineering structures (such as bridges, high-rise buildings, and spatial steel structures) gradually accumulate damage during long-term operation due to material aging, environmental erosion, fatigue loads, and extreme disasters (strong winds, earthquakes, etc.). This leads to a decrease in structural stiffness and load-bearing capacity, and in severe cases, may cause safety accidents. In recent years, structural health monitoring systems have been widely used in major projects, providing a large amount of measured data for structural condition assessment. Finite element model correction technology based on monitoring data, by combining measured responses with numerical simulations, can effectively improve the fidelity of structural digital models, thereby achieving more reliable safety condition assessments.

[0003] Existing finite element model correction methods are mainly divided into two categories: one is linear model correction methods based on frequency domain characteristics (such as natural frequency and mode shape), and the other is nonlinear model correction methods based on time domain response (such as acceleration and displacement). For engineering structures under heavy loads, their mechanical behavior often exhibits significant nonlinear characteristics (such as material hysteresis, large geometric deformation, boundary slip, etc.), making it difficult for linear methods to accurately describe the true response of the structure. Therefore, nonlinear finite element model correction has become a current research hotspot.

[0004] In the field of nonlinear model correction, the Unscented Kalman Filter (UKF) algorithm has attracted widespread attention due to its advantages such as being able to handle strongly nonlinear systems and not requiring the computation of the Jacobian matrix. However, the traditional UKF algorithm has the following technical drawbacks when applied to complex engineering structures: First, the traditional UKF algorithm adopts a time-step iterative strategy, requiring multiple nonlinear dynamic analyses of the finite element model at each iteration. When the structural model parameters have high dimensionality and long response time series, the computational cost increases dramatically, making it difficult to achieve efficient online model updates. Second, the traditional UKF algorithm only uses the observation data at the current moment for state estimation, lacking a feedback mechanism for historical estimation biases, resulting in a slow parameter convergence rate. Third, existing model correction methods mostly stop at parameter identification itself, failing to effectively connect the corrected model parameters with the structural failure probability. To assess the safety margin of the structure under extreme loads, it is usually necessary to perform a large number of nonlinear time history analyses again, resulting in extremely high computational costs.

[0005] Therefore, there is a need for an online evaluation method that can balance computational efficiency and convergence accuracy, and can quickly correlate the model correction results with the probability of structural failure. Summary of the Invention

[0006] The purpose of this invention is to provide a finite element model correction and safety status assessment method applicable to complex engineering structures, and to solve the problems of high computational cost and slow convergence speed of the UKF algorithm due to the high parameter dimensionality in existing nonlinear finite element model correction methods, as well as the disconnect between model correction and safety assessment.

[0007] To achieve the above objectives, this invention provides a finite element model modification and safety status assessment method applicable to complex engineering structures, comprising the following steps: S1. Based on the design data and material test results, establish the initial nonlinear finite element model of the engineering structure and determine all physical parameters of the initial nonlinear finite element model; acquire multi-source response data of the engineering structure under strong load through a health monitoring system installed on the engineering structure, record the external excitation load, and preprocess the multi-source response data. S2. Perform global parameter sensitivity analysis on all physical parameters, screen out key correction parameters with high sensitivity to structural response, form a set of key correction parameters after dimensionality reduction from the key correction parameters, and pre-set the value range of the key correction parameters. S3. Initialize the initial system parameters of the Unscented Kalman Filter (UKF) algorithm. The initial system parameters include the mean, covariance, process noise matrix, and observation noise matrix of the key correction parameters. Segment the multi-source response data by setting a time window, and set the maximum number of iterations and convergence accuracy threshold of the UKF algorithm. S4. Integrate the multi-source monitoring data within each time window, and then, based on the UKF initial system parameters set in step S3, perform a single UKF iteration within the first time window, and output the update results of the key correction parameters and their covariance. S5. Using the updated results of the key correction parameters and their covariance output in step S4 as the UKF initial system parameters for the next time window, perform UKF iteration in the next time window and output the updated results of the key correction parameters and their covariance in a new round. S6. Repeat steps S4 and S5. When the output update result meets the maximum number of iterations or the convergence accuracy threshold set in step S3, stop the parameter update and output the final key correction parameter update result. S7. Using the initial nonlinear finite element model, the range of key correction parameters preset in step S2, and the preset extreme loads and failure thresholds, calculate the structural failure probability through numerical simulation, generate training samples, and use the Kriging model to construct the mapping relationship between the key correction parameters and the structural failure probability, thus completing the training of the Kriging model. S8. During the operation of the engineering structure, when the health monitoring system acquires multi-source response data when the structure encounters strong loads, it executes steps S4 to S6 to quickly complete the iterative update of key correction parameters, uses the updated key correction parameters as input to the trained Kriging model, outputs the structural failure probability, and completes a rapid assessment of the safety status of the engineering structure.

[0008] Preferably, in step S1, the multi-source response data is the dynamic response data of the structure under strong loads, collected by sensors, including acceleration, displacement, strain, and tilt angle; the strong loads include strong winds or earthquakes; preprocessing includes outlier removal, low-pass filtering, signal smoothing, and data normalization, wherein high-frequency noise in the data is removed by low-pass filtering, and the observed data is mapped to [data source missing] by data normalization. Intervals are used to eliminate the influence of dimensions.

[0009] Preferably, in step S2, the global parameter sensitivity analysis adopts a variance-based method, which quantifies the influence of parameter changes on the structural response by randomly selecting different parameter combinations within the feasible range of all physical parameters, and considers the interaction between parameters.

[0010] Preferably, in step S3, setting the time window includes: setting the window length. ,in The multi-source response data is then divided into several time windows in chronological order. , ,in The first time series One window, This indicates the total number of windows in the partition.

[0011] Preferably, in step S4, integrating the multi-source monitoring data within each time window includes: integrating the multi-source response data within each time window into a single vector, which serves as the measured value vector.

[0012] Preferably, in step S4, performing a single UKF iteration within the first time window specifically involves: based on the set initial UKF system parameters, performing an unscented transformation within the time window to generate... There are Sigma points, among which Indicates the dimension of the key correction parameters; runs using the initial nonlinear finite element model. Sub-nonlinear dynamic analysis is performed to obtain the vector corresponding to the measured values. The predicted value vector is generated; by performing a single UKF iteration, the updated mean, covariance, measurement covariance matrix, and process covariance matrix of the key correction parameters are obtained; among them, the updated mean of the key correction parameters is the updated result of the key correction parameters, and the updated covariance, measurement covariance matrix, and process covariance matrix constitute the updated result of the covariance.

[0013] Preferably, in step S6, stopping parameter updates and outputting the final key correction parameter update results specifically includes: sequentially updating the parameters in each time window. The UKF iteration is performed. When the absolute value of the difference between the key correction parameter obtained in the current iteration and the key correction parameter obtained in the previous iteration is less than the convergence accuracy threshold, or when the number of iterations reaches the maximum number of iterations, the iteration stops and the last parameter update result is output as the nonlinear model correction result.

[0014] Preferably, completing the training of the Kriging model and outputting the structural failure probability includes the following steps: S81. Take the extreme loads of the area where the engineering structure is located as structural inputs, and consider the randomness of the loads to generate a random load sequence. S82. Based on the initial nonlinear finite element model, generate random samples within the preset range of key correction parameters, and calculate the structural failure probability under different parameter combinations according to the subset simulation algorithm. S83. Train the Kriging model using key correction parameters and their corresponding structural failure probabilities as training samples. S84. After training is complete, input the key correction parameters updated by UKF iterations into the trained Kriging model and output the structural failure probability. S85. For each engineering structure, provided that no major repairs or reinforcements or changes in its function are carried out, only one Kriging model training is required throughout the entire process.

[0015] Therefore, the present invention employs the aforementioned finite element model correction and safety status assessment method applicable to complex engineering structures, and has the following beneficial effects: (1) To address the challenge of high-dimensional parameter correction in nonlinear finite element models of complex engineering structures, this invention employs a variance-based global sensitivity method to calculate the sensitivity of parameter changes to the structural response. Since this method calculates parameter sensitivity from a global parameter perspective, it not only quantifies the sensitivity of a single parameter to changes in the structural response but also considers the interactive effects between parameter combinations, significantly improving the reliability of selecting high-sensitivity parameters for the model.

[0016] (2) This invention addresses the challenge of correcting nonlinear finite element models for complex engineering structures by proposing a nonlinear model correction algorithm based on an improved UKF. This algorithm adds a feedback loop to the iteration process, using the mean, covariance, process noise, and observation noise matrix of the parameters within the current window as the initial values ​​for the next window's UKF iteration. By dynamically adjusting the initial iteration values, it effectively reduces the approximation error of the sigma point and the estimation bias caused by observation noise, making the corrected parameters closer to the actual parameters of the structure and significantly improving the matching degree between the nonlinear finite element model and the dynamic characteristics of the actual structure.

[0017] (3) The improved UKF algorithm proposed in this invention avoids invalid iterations while ensuring correction accuracy by reasonably setting the threshold for the number of iterations and the threshold for convergence accuracy. Compared with the ordinary UKF algorithm, the improved UKF algorithm can achieve high-precision correction without multiple iterations, further improving the correction efficiency. It can meet the needs of rapid correction of nonlinear finite element models in engineering practice and provide timely and reliable theoretical support for the safety assessment of structures.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of an embodiment of the finite element model correction and safety status assessment method applicable to complex engineering structures according to the present invention. Figure 2 This is a material model diagram of an embodiment of the finite element model correction and safety status assessment method applicable to complex engineering structures of the present invention; Figure 3 This is a bar chart of the total Sobol index of structural model parameters in an embodiment of the finite element model correction and safety status assessment method applicable to complex engineering structures of the present invention; Figure 4 This is a comparison chart of the parameter convergence results of the improved UKF algorithm under different time window lengths in an embodiment of the finite element model correction and safety status assessment method applicable to complex engineering structures of the present invention. Figure 5 This is a schematic diagram of the adaptive subset region for calculating the structural failure probability using the subset simulation algorithm in an embodiment of the finite element model correction and safety status assessment method applicable to complex engineering structures of the present invention. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0022] Example 1 like Figure 1 As shown, the finite element model modification and safety status assessment method applicable to complex engineering structures includes the following steps: Step 1: Establish an initial nonlinear finite element model and obtain multi-source response data Based on engineering design drawings, material test reports, and experience from similar projects, an initial nonlinear finite element model of the engineering structure is established in finite element software (such as OpenSees, ABAQUS, etc.). A material constitutive model capable of simulating the hysteretic characteristics of the structure under strong loads is selected; for example, the Giuffre-Menegotto-Pinto constitutive model can be used for steel structures, and a damage-plastic model can be used for concrete structures. Simultaneously, the nonlinear behavior of boundary conditions (such as support slippage, gap closure, etc.) and damping models (such as Rayleigh damping) are defined.

[0023] All physical parameters that may affect the structural response in the initial nonlinear finite element model are included in the complete set of physical parameters, denoted as . , This represents the total number of parameters. These parameters include, but are not limited to, the material's elastic modulus, yield strength, hardening modulus, damping coefficient, and boundary spring stiffness.

[0024] A health monitoring system is installed on the structure to collect multi-source response data of the structure during operation using sensors (accelerometers, displacement gauges, strain gauges, inclinometers, etc.). The focus is on collecting dynamic response data of structures when subjected to strong loads (such as strong winds and earthquakes). These represent the obtained structural response sequences, including acceleration, displacement, strain, and tilt angle. This indicates the length of the acquired structural response time series. External excitation loads are also recorded. (such as wind speed time history, earthquake acceleration time history).

[0025] The acquired multi-source response data undergoes preprocessing, including outlier removal, low-pass filtering (to remove high-frequency noise), signal smoothing, and data normalization. Normalization maps the data to... The interval is used to eliminate the influence of units and improve the convergence speed of subsequent algorithms. The preprocessed data is stored in the database for later use.

[0026] Step 2: Global parameter sensitivity analysis and selection of key correction parameters A variance-based global parameter sensitivity analysis method (Sobol index method) is used to analyze all physical parameters. Perform sensitivity analysis. The specific steps are as follows: (1) Determine the feasible range of each physical parameter, for example .

[0027] (2) Generate two independent sequences using Sobol sequences Sampling matrix and ,in The sample size (e.g., 8000). This represents the total number of parameters. Then, based on... and generate interference matrix It is used to separate the contribution of individual parameters and parameter interactions to the output.

[0028] (3) Transform the matrix , and Substitute each set of parameters into the initial nonlinear finite element model, calculate the corresponding structural response, and obtain the response matrix. , and .

[0029] (4) Calculate the total Sobol index of each parameter according to the following formula. : ; ; ; in, Indicates the parameter index. Represents the structural response matrix. This represents the total variance. express The Middle The response value of each sample. express The Middle The response value of each sample. express The Middle The response value of each sample. for The mean, for The mean, Indicates the first All physical parameters, Indicates the first The first-order Sobol exponent of each physical parameter is used to quantify the contribution of that parameter alone to the total variance of the structural response. The variance of the conditional expectation can be expressed by matrices A, B, and The output response is approximated, i.e. .

[0030] (5) Based on the preset sensitivity threshold (e.g., 0.05), select parameters whose total Sobol exponent is greater than the threshold as key correction parameters to form the set of key correction parameters after dimensionality reduction.

[0031] Step 3: Initialize UKF algorithm parameters and segment the time window Initialize the initial system parameters for the UKF algorithm, including the mean, covariance matrix, and process noise covariance matrix of the key correction parameters. Q Covariance matrix of observation noise R The mean value can be set according to the design value or the initial nonlinear finite element model value, and the covariance matrix is ​​usually set as a diagonal matrix (e.g., with an element of 0.1). and It can be set based on experience or model error estimation.

[0032] Set time window length ( ), the preprocessed multi-source response data Divided chronologically into a time window ( ),in ( (Total time steps), with the remaining data placed in the last window. Set the maximum number of iterations and the convergence accuracy threshold for the UKF algorithm (e.g., convergence is considered to occur when the number of iterations does not exceed 100 and the relative change in parameters is less than 0.01).

[0033] Step 4: Perform a single UKF iteration within the first time window. The multi-source response data within each time window are integrated, and the response data from all time steps within the window are concatenated into a single measured value vector. .

[0034] Based on the UKF initial system parameters set in step 3, in the first time window Perform an unscented transformation internally to generate There are Sigma points, among which This represents the dimension of the key correction parameters. Each Sigma point is substituted into the initial nonlinear finite element model, and nonlinear dynamic analysis is run to obtain the vector corresponding to the measured values. A set of predicted value vectors. The Kalman gain is calculated through a single UKF iteration, the state is updated, and the updated results of key correction parameters are output. and the update results of its covariance (The measurement covariance matrix and the process covariance matrix are obtained simultaneously and used as internal parameters for subsequent iterations.)

[0035] Step 5: Inter-window recursive iteration Update the results using the key correction parameters output in step 4. Covariance Update Results As the next time window The initial UKF value, in Perform the same UKF iteration as step 4, and output the results of the new round of key correction parameter updates. and its covariance .

[0036] Step 6: Convergence Judgment and Final Output Repeat steps 4 and 5 to process each time window in turn. After each iteration, the absolute value of the difference between the key correction parameters obtained in the current iteration and those obtained in the previous iteration is calculated. If the difference of all key correction parameters is less than the preset convergence accuracy threshold, or if the number of iterations (i.e., the number of time windows processed) reaches the preset maximum number of iterations, then parameter updates are stopped. The final key correction parameter update result is output. This completes the correction of the nonlinear finite element model.

[0037] Step 7: Construction and Training of the Kriging Proxy Model A mapping relationship between key correction parameters and structural failure probabilities is constructed using a Kriging model. The specific steps are as follows: (1) The feasible range of each key correction parameter determined in step 2 (e.g.) ,in Within the range of actual or reference values ​​of the parameters, generated using Latin hypercube or random sampling methods. Group parameter samples.

[0038] (2) Take the extreme loads (such as rare earthquakes and once-in-a-century strong winds) in the area where the engineering structure is located as structural inputs, and consider the randomness of the loads (such as the earthquake amplitude following a certain probability distribution) to generate a random load sequence.

[0039] (3) Based on the initial nonlinear finite element model, for each set of parameter samples, the subset simulation algorithm is used to calculate the failure probability of the structure under extreme loads. Failure indices are defined (such as the inter-story drift angle exceeding the standard limit of 1 / 50). The subset simulation efficiently calculates the small failure probability by adaptively constructing an intermediate subset region.

[0040] (4) Train the Kriging model with the key correction parameters as input and the corresponding failure probabilities as output. Optimize the hyperparameters of the Kriging model (such as correlation function parameters, regression coefficients, etc.) by maximizing the likelihood function or cross-validation.

[0041] (5) After training, a Kriging surrogate model that can quickly predict the failure probability is obtained. For each engineering structure, under the premise that no major repairs or reinforcements or changes in function occur, only one Kriging model training is required throughout the entire process.

[0042] Step 8: Quick Online Security Status Assessment During the operation of the engineering structure, after the health monitoring system acquires multi-source response data when the structure encounters strong loads, steps 4 to 6 above are executed to quickly complete the iterative update of key correction parameters. The updated key correction parameters are then input into the trained Kriging model, which immediately outputs the failure probability of the structure under extreme loads. Engineers use this failure probability to determine the safety status of the structure and decide whether reinforcement or maintenance measures are necessary.

[0043] Example 2 To verify the effectiveness and advancement of the method proposed in this invention, this embodiment uses a seven-story spatial steel frame structure under seismic load as the numerical simulation object, such as... Figure 2 As shown, an initial nonlinear finite element model was established based on the OpenSees open-source platform, and the nonlinear model was corrected and the safety status was assessed according to the steps of Example 1.

[0044] 1. Structural Model and Parameter Settings This seven-story spatial steel frame structure has a floor height of 3.0m and a planar layout span and depth of 6.0m. 24a I-beams are used for beam elements, and 30b I-beams for column elements, both simulated using spatial three-dimensional beam elements. The material constitutive model uses the Giuffre-Menegotto-Pinto model (simulating the hysteretic properties of steel), which includes three main parameters: yield strength... Elastic modulus and hardening modulus Each floor's frame columns and beams are defined using three parameters, for a total of seven floors, resulting in 42 nonlinear material parameters. Structural damping is set as Rayleigh damping with two damping coefficients. and This is also part of all the physical parameters to be corrected. Geometric dimensions can be accurately obtained through on-site measurements and are not included in the correction parameters. The preset reference values ​​(i.e., the actual physical values ​​of the structure) for each parameter are: Beam element: , , ; Column unit: , , ; Damping coefficient: =0.05, =0.0036; in, , indicating the floor number. The initial mean values ​​of the key correction parameters in the initial nonlinear finite element model are randomly combined at 0.85 to 1.25 times the preset reference values ​​to simulate the initial modeling error.

[0045] 2. Load and monitoring data simulation The external excitation used was the El Centro seismic wave, with a sampling frequency of 50 Hz and a duration of 30 s. The acceleration responses of the first and top layers, as well as the displacement response of the top layer, were selected as multi-source response data. 5% random white noise was added to the numerical simulation results to simulate actual measurement noise. The above data were preprocessed, including low-pass filtering, detrending, and normalization, before use.

[0046] 3. Selection of key correction parameters A variance-based global parameter sensitivity analysis method (Sobol exponent method) is employed, setting the feasible intervals for all physical parameters as... ( (Preset reference values ​​for each parameter), generate two sampling matrices A and B (8000×44 dimensions) containing 8000 parameter combinations, and further generate 44 interference matrices. Substitute each set of parameters into the initial nonlinear finite element model to calculate the structural response, and calculate the total Sobol exponent of each parameter according to the formula in Example 1. Set the sensitivity threshold to 0.05, and select 14 parameters with a total Sobol exponent greater than 0.05 as key correction parameters (see Example 1). Figure 3 ). Figure 3 This is a bar chart showing the total Sobol index for each physical parameter. The horizontal axis represents the parameter number, the vertical axis represents the total Sobol index, and the horizontal dashed line represents the 0.05 threshold line. (Example:) Figure 3It can be seen that when the sensitivity index is set to 0.05, 14 parameters are selected as the key parameters of the nonlinear model. For complex nonlinear finite element models, the selected parameter vector still has a high dimensionality.

[0047] 4. Improved UKF parameter correction Set the time window length =15, dividing the total time steps (1501 steps) into 100 time windows (the remaining 1 step is placed in the last window). UKF initial system parameters: the initial mean of the key correction parameters is taken as 0.85 to 1.25 times the preset reference value (see the original text for specific vectors), the initial covariance diagonal element is set to 0.1, and the process noise matrix... The diagonal element is set to 1.0·10. -6 The variance of acceleration measurements in the observation noise matrix is ​​set to 5.10. -3 m / s 2 The displacement measurement variance was set to 1.1 mm. The maximum number of iterations was set to 100, and the convergence accuracy threshold was set to 0.01 (i.e., convergence occurs when the relative change in parameters is less than 1%).

[0048] UKF iterations were performed sequentially for each time window. Within each window, multi-source response data were integrated into a single vector, Sigma points were generated, and the initial nonlinear finite element model was invoked for nonlinear dynamic analysis. Key correction parameters and their covariances were updated recursively between windows. To compare the impact of time window length, a [missing information - likely a parameter or setting] was also set. =30. Figure 4 Convergence curves for the key correction parameters under different time window lengths are presented. The results show that when... When the value is 15, all key correction parameters converge to near the preset reference value, with a maximum correction error of only 3.35%; while when... The convergence accuracy decreases when the time window is 30. This invention improves the UKF algorithm (time window). =15), the runtime of the nonlinear finite element model correction was reduced from 3.5 hours in the traditional UKF to 0.41 hours, and the computational efficiency was greatly improved.

[0049] 5. Kriging Model Training and Failure Probability Prediction A Kriging model is constructed using 14 selected key correction parameters as input and structural failure probability as output. The feasible intervals for the key correction parameters are set as follows: ( (As a preset reference value), the extreme load still adopts the El Centro wave, and the randomness of the load is considered: the peak ground acceleration of the earthquake follows a Gaussian normal distribution with a mean of 0.5g and a standard deviation of 0.1g. According to the Chinese "Code for Seismic Design of Buildings", the inter-story drift angle limit for multi-story and high-rise steel structures under rare earthquakes is 1 / 50, so the failure threshold is set to 0.02.

[0050] A subset simulation algorithm was used to calculate the structural failure probability under different combinations of key correction parameters. A total of 800 sets of random parameter samples were generated, and the calculations were performed using MATLAB-OpenSees interactive simulation. Figure 5 A schematic diagram of the subset region constructed for adaptive simulation of the subset: Two intermediate subsets are constructed, with corresponding displacement angle thresholds of 0.0177 and 0.0211, respectively.

[0051] The failure probability calculated by subset simulation is 0.0249, while the result calculated by traditional Monte Carlo method (100,000 simulations) is 0.0247, with a relative error of only 0.81%, proving that subset simulation has good accuracy and efficiency.

[0052] Eighty hundred samples were divided into a training set (720 samples) and a test set (80 samples) at a ratio of 9:1 to train the Kriging model. The trained model was then used to predict the failure probability under 10 sets of random key correction parameter combinations, and the results are shown in Table 1. The maximum prediction error was only 2.12%, indicating that the Kriging model can accurately map the relationship between key correction parameters and structural failure probability.

[0053] Table 1 Prediction Results

[0054] 6. Online assessment application The trained Kriging model is then applied to online structural safety assessment. When a new set of seismic loads is applied, the health monitoring system collects multi-source response data in real time. Key correction parameters are rapidly updated through steps 4 to 6, and then input into the Kriging model. Within seconds, the failure probability of the structure under extreme earthquake conditions in its current state can be obtained, providing a theoretical basis for post-disaster safety assessment and reinforcement decisions for engineering structures.

[0055] This embodiment verifies the effectiveness of the method of the present invention in complex engineering structures (seven-story spatial steel frame): the improved UKF algorithm reduces the computation time from 3.5 hours to 0.41 hours, and the correction error of key correction parameters is less than 3.35%; the maximum error of the Kriging model in predicting the probability of structural failure is only 2.12%. This method significantly improves the efficiency and accuracy of nonlinear model correction and realizes an integrated and rapid response from key correction parameter identification to safety assessment.

[0056] Therefore, this invention adopts the finite element model correction and safety status assessment method applicable to the above-mentioned complex engineering structures. By using time window batch processing, the number of UKF iterations is reduced from the number of time steps to the number of windows, which greatly improves the computational efficiency. The correction accuracy is improved by parameter recursion between windows and convergence discrimination. Combined with the Kriging proxy model, the correction parameters are quickly mapped to the structural failure probability, which meets the needs of rapid post-disaster assessment.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for finite element model modification and safety status assessment applicable to complex engineering structures, characterized in that, Includes the following steps: S1. Based on the design data and material test results, establish the initial nonlinear finite element model of the engineering structure and determine all physical parameters of the initial nonlinear finite element model; acquire multi-source response data of the engineering structure under strong load through a health monitoring system installed on the engineering structure, record the external excitation load, and preprocess the multi-source response data. S2. Perform global parameter sensitivity analysis on all physical parameters, screen out key correction parameters with high sensitivity to structural response, form a set of key correction parameters after dimensionality reduction from the key correction parameters, and pre-set the value range of the key correction parameters. S3. Set the initial system parameters for the unscented Kalman filter algorithm. The initial system parameters include the mean, covariance, process noise matrix, and observation noise matrix of the key correction parameters. Segment the multi-source response data by setting a time window, and set the maximum number of iterations and the convergence accuracy threshold for the unscented Kalman filter algorithm. S4. Integrate the multi-source monitoring data within each time window, and then, based on the initial system parameters of the unscented Kalman filter set in step S3, perform a single unscented Kalman filter iteration within the first time window, and output the update results of the key correction parameters and their covariance. S5. Using the updated results of the key correction parameters and their covariance output in step S4 as the initial system parameters for the unscented Kalman filter in the next time window, perform unscented Kalman filter iteration in the next time window and output the updated results of the key correction parameters and their covariance in a new round. S6. Repeat steps S4 and S5. When the output update result meets the maximum number of iterations or the convergence accuracy threshold set in step S3, stop the parameter update and output the final key correction parameter update result. S7. Using the initial nonlinear finite element model, the range of key correction parameters preset in step S2, and the preset extreme loads and failure thresholds, calculate the structural failure probability through numerical simulation, generate training samples, and use the Kriging model to construct the mapping relationship between the key correction parameters and the structural failure probability, thus completing the training of the Kriging model. S8. During the operation of the engineering structure, when the health monitoring system acquires multi-source response data when the structure encounters strong loads, it executes steps S4 to S6 to quickly complete the iterative update of key correction parameters, uses the updated key correction parameters as input to the trained Kriging model, outputs the structural failure probability, and completes a rapid assessment of the safety status of the engineering structure.

2. The finite element model correction and safety status assessment method applicable to complex engineering structures according to claim 1, characterized in that, In step S1, the multi-source response data consists of the dynamic response data of the structure under strong loads, collected by sensors, including acceleration, displacement, strain, and tilt angle; strong loads include strong winds or earthquakes; preprocessing includes outlier removal, low-pass filtering, signal smoothing, and data normalization. Specifically, low-pass filtering removes high-frequency noise from the data, and data normalization maps the observed data to... Intervals are used to eliminate the influence of dimensions.

3. The finite element model correction and safety status assessment method applicable to complex engineering structures according to claim 1, characterized in that, In step S2, the global parameter sensitivity analysis adopts a variance-based method. By randomly selecting different parameter combinations within the feasible range of all physical parameters, the influence of parameter changes on the structural response is quantified, and the interaction between parameters is considered.

4. The finite element model correction and safety status assessment method applicable to complex engineering structures according to claim 1, characterized in that, In step S3, setting the time window includes: setting the window length. ,in The multi-source response data is then divided into several time windows in chronological order. , ,in The first time series One window, This indicates the total number of windows in the partition.

5. The finite element model correction and safety status assessment method applicable to complex engineering structures according to claim 1, characterized in that, In step S4, the integration of multi-source monitoring data within each time window includes: integrating the multi-source response data within each time window into a single vector, which serves as the measured value vector.

6. The finite element model correction and safety status assessment method applicable to complex engineering structures according to claim 5, characterized in that, In step S4, performing a single unscented Kalman filter iteration within the first time window specifically involves: based on the set initial system parameters for the unscented Kalman filter, performing an unscented transform within the time window to generate... There are Sigma points, among which Indicates the dimension of the key correction parameters; runs using the initial nonlinear finite element model. Sub-nonlinear dynamic analysis is performed to obtain the vector corresponding to the measured values. The predicted value vector is generated; by performing a single unscented Kalman filter iteration, the updated mean, covariance, measurement covariance matrix, and process covariance matrix of the key correction parameters are obtained; among them, the updated mean of the key correction parameters is the updated result of the key correction parameters, and the updated covariance, measurement covariance matrix, and process covariance matrix constitute the updated result of the covariance.

7. The finite element model correction and safety status assessment method applicable to complex engineering structures according to claim 1, characterized in that, In step S6, stopping parameter updates and outputting the final key correction parameter update results specifically includes: sequentially updating the parameters in each time window. The unscented Kalman filter iteration is performed. When the absolute value of the difference between the key correction parameters obtained in the current iteration and the key correction parameters obtained in the previous iteration is less than the convergence accuracy threshold, or when the number of iterations reaches the maximum number of iterations, the iteration stops and the last parameter update result is output as the nonlinear model correction result.

8. The finite element model correction and safety status assessment method applicable to complex engineering structures according to claim 1, characterized in that, The steps to complete the training of the Kriging model and output the structural failure probability are as follows: S81. Take the extreme loads of the area where the engineering structure is located as structural inputs, and consider the randomness of the loads to generate a random load sequence. S82. Based on the initial nonlinear finite element model, generate random samples within the preset range of key correction parameters, and calculate the structural failure probability under different parameter combinations according to the subset simulation algorithm. S83. Train the Kriging model using key correction parameters and their corresponding structural failure probabilities as training samples. S84. After training is completed, the key correction parameters of the unscented Kalman filter iterative update are input into the trained Kriging model, and the structural failure probability is output. S85. For each engineering structure, provided that no major repairs or reinforcements or changes in its function are carried out, only one Kriging model training is required throughout the entire process.

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