Bridge state reliability evaluation method based on adaptive Gaussian process model

Abstract

The application discloses a bridge state reliability evaluation method based on an adaptive Gaussian process model, and is applied to the technical field of bridge state evaluation.The method comprises the following steps: acquiring bridge WIM data and bridge response monitoring data; extracting WIM peak values and response peak values; repairing historical data by using a GPM; training the GPM by using an adaptive moving window training strategy; repairing missing values of modeling data; storing probability modeling results of the response peak values; performing probability modeling on all steps of modeling data of a current sensor; performing probability modeling on modeling data of all sensors; and calculating reliability indexes of bridge components and structures.The method realizes self-repairing of missing values of bridge WIM peak values and response peak values by using the powerful nonlinear regression capability of the GPM, and proposes the adaptive moving window training strategy, so that the training efficiency is greatly improved under the premise that the accuracy is hardly reduced.

Description

Technical Field

[0001] This invention relates to the field of bridge condition assessment technology, and more specifically to a bridge condition reliability assessment method based on an adaptive Gaussian process model. Background Technology

[0002] Due to the influence of environmental climate, traffic loads, material degradation, fatigue damage, and extreme events, bridges inevitably suffer from defects, damage, and deformation. Therefore, regular bridge condition assessment is crucial for ensuring safe bridge operation. Existing bridge condition assessment methods primarily employ bridge reliability evaluation based on Structural Health Monitoring (SHM) data, which is considered an objective and reasonable method. The Gaussian Process Model (GPM), a nonparametric model based on a Bayesian framework, is widely used in model updating, uncertainty quantification, time series modeling, and bridge condition assessment due to its powerful nonlinear probabilistic modeling capabilities. However, traditional GPM-based bridge condition assessment methods face two challenges when dealing with long-term SHM data: firstly, bridge SHM data often has gaps, reducing the accuracy of bridge condition assessment; secondly, traditional GPM relies heavily on full-order or fixed-order training strategies, lacking adaptive modeling capabilities for large amounts of long-term SHM data, making it difficult to achieve an effective trade-off between accuracy and efficiency. Therefore, providing a bridge condition reliability assessment method based on an adaptive Gaussian Process Model is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0003] In view of this, the present invention provides a bridge state reliability evaluation method based on an adaptive Gaussian process model, constructs a bridge state reliability evaluation framework based on long-term SHM data, and proposes an adaptive moving window training strategy, which significantly improves computational efficiency with almost no decrease in accuracy.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A bridge state reliability evaluation method based on an adaptive Gaussian process model includes the following steps:

[0006] S1. Obtain bridge dynamic weighing and bridge response monitoring data from the bridge SHM system;

[0007] S2. Extract the peak value of bridge dynamic weighing and the peak value of bridge response caused by traffic load;

[0008] S3. Divide the data into historical data and modeling data, and use GPM to repair missing values ​​in the peak values ​​of the historical data.

[0009] S4. Use an adaptive moving window training strategy to train GPM;

[0010] S5. Repair missing values ​​in modeling data based on the GPM model;

[0011] S6. The predicted mean and predicted standard deviation of the peak value of the storage response are used as the probabilistic modeling results of the load effect in the current step.

[0012] S7. Repeat S4-S6 to perform probabilistic modeling on the modeling data of all steps of the current sensor.

[0013] S8. Repeat S2-S7 to perform probabilistic modeling on the modeling data of all sensors;

[0014] S9. Combining the probabilistic modeling results of peak response and the resistance model, the reliability index of bridge components is calculated using the first-order reliability method.

[0015] S10. Based on the reliability calculation results of bridge components, the reliability index of the bridge structure is calculated using a series model.

[0016] Optionally, S2 is as follows:

[0017] The low-frequency temperature-induced response of the bridge was eliminated by wavelet packet decomposition. The remaining high-frequency response was regarded as the bridge response caused by traffic load. The maximum values ​​of the bridge dynamic weighing data and the absolute value of the traffic load effect were calculated at the same time interval as the bridge dynamic weighing peak value and the bridge response peak value.

[0018] Optionally, S3 specifically refers to:

[0019] The bridge dynamic weighing peak value and the bridge response peak value are divided into historical data and modeling data at the same time point. The historical data is used as the initial training data for the prediction model. It is determined whether there are missing values ​​in the bridge dynamic weighing peak value. If there are, the known bridge dynamic weighing peak value is used to train the GPM autoregressive prediction to repair the missing values. It is then determined whether there are missing values ​​in the bridge response peak value. If there are, the repaired bridge dynamic weighing peak value and the known bridge response peak value are used to train the GPM regression prediction to repair the missing values.

[0020] Optionally, S4 specifically refers to:

[0021] Calculate the autocorrelation function of the bridge response peak:

[0022] ;

[0023] In the formula, For variables y The autocorrelation function, k The lag order is... For variables yThe autocovariance function; the cross-correlation function between the peak bridge response and the peak bridge dynamic weighing load:

[0024] ;

[0025] In the formula, For variables x and y The cross-correlation function between them j For mutual lag order, For variables x and y The cross-covariance function between them For variables x overall standard deviation For variables y The overall standard deviation;

[0026] Candidate moving window sizes for the autocorrelation and cross-correlation functions are selected using the Euclidean norm gradient, respectively.

[0027] ;

[0028] In the formula, To adjust the window size for the autocorrelation function, The gradient of the Euclidean norm of the autocorrelation function. For the number of continuous and stable gradients, For continuous and stable gradient thresholds;

[0029] ;

[0030] In the formula, To adjust the window size for the cross-correlation function, The gradient of the Euclidean norm of the cross-correlation function;

[0031] The final size of the adaptive moving window is taken from the maximum value of the moving window size of the correlation function and the moving window size of the cross-correlation function for the current training data:

[0032] ;

[0033] In the formula, To adapt to the moving window size, the original data is reduced in order using an adaptive moving window before training the GPM.

[0034] Optional, S5 specifically includes:

[0035] Determine if there are missing values ​​in the current step of the bridge dynamic weighing peak value. If so, establish an adaptive GPM for the bridge dynamic weighing peak value to predict and repair the missing values. Continue to determine if there are missing values ​​in the bridge response peak value. If so, combine the repaired bridge dynamic weighing peak value and the known bridge response peak value to establish an adaptive GPM to predict and repair the missing values.

[0036] Optional, S9 specifically includes:

[0037] Combining the probabilistic modeling results of peak response and the resistance model, the reliability index of bridge components is calculated using the first-order reliability method:

[0038] ;

[0039] In the formula, As a component reliability index, This is the mean of the resistance model. The standard deviation of the resistance model. This represents the mean value of the load effect. The standard deviation of the load effect, The sensor error coefficient is used; the component function is:

[0040] ;

[0041] In the formula, For component function, For resistance model, This is due to the load effect.

[0042] Optionally, S10 specifically refers to:

[0043] Based on the reliability calculation results of bridge components, a series model is used to calculate the reliability index of the bridge structure:

[0044] ;

[0045] In the formula, This is an indicator of bridge structural reliability. It is the inverse cumulative distribution function of the standard normal distribution. For the first i The failure probability of each component.

[0046] As can be seen from the above technical solutions, compared with the prior art, the present invention provides a bridge condition reliability evaluation method based on an adaptive Gaussian process model, which has the following beneficial effects: The present invention constructs a bridge condition reliability evaluation framework based on long-term SHM data, and utilizes the powerful nonlinear regression capability of GPM to achieve self-repair of missing values ​​of bridge WIM peak and response peak, solving the problems of existing bridge condition evaluation methods being unable to simultaneously consider the incompleteness of SHM data and the low evaluation efficiency when facing massive amounts of long-term SHM data; by proposing an adaptive moving window training strategy, as SHM data continues to accumulate, the size of the moving window is adaptively determined, significantly improving training efficiency while ensuring that the accuracy is almost not reduced, and the bridge condition reliability evaluation can be carried out dynamically and synchronously, successfully using long-term SHM data to serve bridge condition evaluation. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0048] Figure 1 This is a flowchart of the bridge condition reliability evaluation method of the present invention;

[0049] Figure 2 This is a comparison chart of the peak probability modeling of the response of the embodiments of the present invention and existing methods;

[0050] Figure 3 This is a comparison chart of the modeling accuracy and efficiency of the embodiments of the present invention and existing methods;

[0051] Figure 4 This is a schematic diagram of the bridge structural reliability evaluation results of the present invention. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] This invention discloses a bridge state reliability evaluation method based on an adaptive Gaussian process model, such as... Figure 1 As shown, it includes the following steps:

[0054] S1. Obtain bridge dynamic weighing (WIM) and bridge response monitoring data from the bridge SHM system; in this embodiment, bridge response data is taken as deflection.

[0055] S2. Extract the peak value of bridge dynamic weighing and the peak value of bridge response caused by traffic load;

[0056] S3. Divide the data into historical data and modeling data, and use GPM to repair missing values ​​in the peak values ​​of the historical data.

[0057] S4. Use an adaptive moving window training strategy to train GPM;

[0058] S5. Repair missing values ​​in modeling data based on the GPM model;

[0059] S6. The predicted mean and predicted standard deviation of the peak value of the storage response are used as the probabilistic modeling results of the load effect in the current step.

[0060] S7. Repeat S4-S6 to perform probabilistic modeling on the modeling data of all steps of the current sensor.

[0061] S8. Repeat S2-S7 to perform probabilistic modeling on the modeling data of all sensors;

[0062] S9. Combining the probabilistic modeling results of peak response and the resistance model, the reliability index of bridge components is calculated using the first-order reliability method.

[0063] S10. Based on the reliability calculation results of bridge components, the reliability index of the bridge structure is calculated using a series model.

[0064] Furthermore, S2 specifically refers to:

[0065] The low-frequency temperature-induced response of the bridge was eliminated by wavelet packet decomposition. The remaining high-frequency response was regarded as the bridge response caused by traffic load. The maximum values ​​of the bridge dynamic weighing data and the absolute value of the traffic load effect were calculated at the same time interval as the bridge dynamic weighing peak value and the bridge response peak value.

[0066] Furthermore, S3 specifically refers to:

[0067] The bridge dynamic weighing peak value and the bridge response peak value are divided into historical data and modeling data at the same time point. The historical data is used as the initial training data for the prediction model. It is determined whether there are missing values ​​in the bridge dynamic weighing peak value. If there are, the known bridge dynamic weighing peak value is used to train the GPM autoregressive prediction to repair the missing values. It is then determined whether there are missing values ​​in the bridge response peak value. If there are, the repaired bridge dynamic weighing peak value and the known bridge response peak value are used to train the GPM regression prediction to repair the missing values.

[0068] Furthermore, S4 specifically refers to:

[0069] Calculate the autocorrelation function of the bridge response peak:

[0070] ;

[0071] In the formula, For variables y The autocorrelation function, k The lag order is... For variables y The autocovariance function; the cross-correlation function between the peak bridge response and the peak bridge dynamic weighing load:

[0072] ;

[0073] In the formula, For variables x and y The cross-correlation function between them j For mutual lag order, For variables x and y The cross-covariance function between them For variables x overall standard deviation For variables y The overall standard deviation;

[0074] Candidate moving window sizes for the autocorrelation and cross-correlation functions are selected using the Euclidean norm gradient, respectively.

[0075] ;

[0076] In the formula, To adjust the window size for the autocorrelation function, The gradient of the Euclidean norm of the autocorrelation function. For the number of continuous and stable gradients, For continuous and stable gradient thresholds; in this example, Set to 3, Set to 0.0001;

[0077] ;

[0078] In the formula, To adjust the window size for the cross-correlation function, The gradient of the Euclidean norm of the cross-correlation function;

[0079] The final size of the adaptive moving window is taken from the maximum value of the moving window size of the correlation function and the moving window size of the cross-correlation function for the current training data:

[0080] ;

[0081] In the formula, To adapt to the moving window size, the WIM peak value is used as the independent variable in this embodiment of the invention. x With peak response as the dependent variable y Calculate the adaptive moving window size; reduce the order of the original data using the adaptive moving window and then train the GPM.

[0082] Furthermore, S5 specifically refers to:

[0083] Determine if there are missing values ​​in the current step of the bridge dynamic weighing peak value. If so, establish an adaptive GPM for the bridge dynamic weighing peak value to predict and repair the missing values. Continue to determine if there are missing values ​​in the bridge response peak value. If so, combine the repaired bridge dynamic weighing peak value and the known bridge response peak value to establish an adaptive GPM to predict and repair the missing values.

[0084] Furthermore, S9 specifically refers to:

[0085] Combining the probabilistic modeling results of peak response and the resistance model, the reliability index of bridge components is calculated using the first-order reliability method. Assuming the resistance model and load effects follow a normal distribution, and using one sensor to represent one component, the reliability index of a single component is:

[0086] ;

[0087] In the formula, As a component reliability index, This is the mean of the resistance model. The standard deviation of the resistance model. This represents the mean value of the load effect. The standard deviation of the load effect, The sensor error coefficient is used; the component function is:

[0088] ;

[0089] In the formula, For component function, For resistance model, This is due to the load effect.

[0090] Furthermore, S10 specifically refers to:

[0091] Based on the reliability calculation results of bridge components, a series model is used to calculate the reliability index of the bridge structure:

[0092] ;

[0093] In the formula, This is an indicator of bridge structural reliability. It is the inverse cumulative distribution function of the standard normal distribution. For the first i The failure probability of each component.

[0094] In one embodiment of the present invention, six months of SHM (Short-Length Modeling) data for a long-span cable-stayed bridge are obtained, with WIM (Warning-Length Modeling) data as the independent variable and deflection monitoring data as the dependent variable. The data from the first two months are used as historical data, and the data from the last four months are used as modeling data. The adaptive GPM (Gross-Mechanical Modeling) proposed in this embodiment is compared with the traditional GPM, which includes full-order GPM and fixed-order GPM. All three GPMs are optimized using the Adam algorithm.

[0095] The peak probability modeling results for adaptive GPM, full-order GPM, and fixed-order GPM are as follows: Figure 2 As shown, adaptive GPM and full-order GPM have almost identical predicted means and confidence intervals, indicating that their modeling effects are nearly identical. Furthermore, missing values ​​in the SHM data were automatically corrected. However, because the moving window size of fixed-order GPM is fixed, overfitting occurred in some parts.

[0096] The comparison results of modeling accuracy and efficiency of adaptive GPM, full-order GPM and fixed-order GPM are as follows: Figure 3 As shown, accuracy is quantified by root mean square error (RMSE) and mean absolute error (MAE). Comparing adaptive GPM and full-order GPM, their modeling accuracy is almost identical, with both RMSE and MAE errors within 1%. However, the adaptive GPM in this embodiment improves modeling efficiency by 49.1% compared to full-order GPM. Compared to full-order GPM, fixed-order GPM increases RMSE and MAE by 6.4% and 8.4% respectively, significantly reducing modeling accuracy. Therefore, compared to traditional methods, the adaptive GPM proposed in this embodiment can significantly improve training efficiency with almost no reduction in model accuracy, offering a significant advantage when processing continuously acquired long-term SHM data.

[0097] Bridge structural reliability evaluation results are as follows Figure 4 As shown, this embodiment can dynamically capture the changing trend of bridge reliability indicators, with the vast majority of observations falling within the 95% confidence interval. By comparing these values ​​with the bridge's design reliability indicators, the operational status of the bridge can be understood to a certain extent.

[0098] In summary, this embodiment can evaluate the reliability of bridge conditions based on long-term SHM data. This process considers both the potential incompleteness of SHM data and the low evaluation efficiency caused by long-term data accumulation. Based on continuously acquired SHM data, this embodiment can dynamically update the bridge structural reliability evaluation results. This embodiment can provide a certain degree of reference value for the safe operation and maintenance of bridges.

[0099] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0100] Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A bridge condition reliability evaluation method based on an adaptive Gaussian process model, characterized in that, Includes the following steps: S1. Obtain bridge dynamic weighing and bridge response monitoring data from the bridge SHM system; S2. Extract the peak value of bridge dynamic weighing and the peak value of bridge response caused by traffic load; S3. Divide the data into historical data and modeling data, and use the Gaussian process model (GPM) to repair missing values ​​in the peak values ​​of the historical data. S4. Train the Gaussian process model GPM using an adaptive moving window training strategy; S5. Repairing missing values ​​in modeling data based on the Gaussian process model (GPM); S6. The predicted mean and predicted standard deviation of the peak value of the storage response are used as the probabilistic modeling results of the load effect in the current step. S7. Repeat S4-S6 to perform probabilistic modeling on the modeling data of all steps of the current sensor. S8. Repeat S2-S7 to perform probabilistic modeling on the modeling data of all sensors; S9. Combining the probabilistic modeling results of peak response and the resistance model, the reliability index of bridge components is calculated using the first-order reliability method. S10. Based on the reliability calculation results of bridge components, the reliability index of the bridge structure is calculated using a series model. S4 specifically refers to: Calculate the autocorrelation function of the bridge response peak: ； In the formula, For variables y The autocorrelation function, k The lag order is... For variables y The autocovariance function; the cross-correlation function between the peak bridge response and the peak bridge dynamic weighing load: ； In the formula, For variables x and y The cross-correlation function between them j For mutual lag order, For variables x and y The cross-covariance function between them For variables x overall standard deviation For variables y The overall standard deviation; Candidate moving window sizes for the autocorrelation and cross-correlation functions are selected using the Euclidean norm gradient, respectively. ； In the formula, To adjust the window size for the autocorrelation function, The gradient of the Euclidean norm of the autocorrelation function. For the number of continuous and stable gradients, For continuous and stable gradient thresholds; ； In the formula, To adjust the window size for the cross-correlation function, The gradient of the Euclidean norm of the cross-correlation function; The final size of the adaptive moving window is taken from the maximum value of the moving window size of the correlation function and the moving window size of the cross-correlation function for the current training data: ； In the formula, To adapt to the moving window size, the original data is reduced in order using an adaptive moving window before training the GPM.

2. The bridge state reliability evaluation method based on an adaptive Gaussian process model according to claim 1, characterized in that, S2 specifically refers to: The low-frequency temperature-induced response of the bridge was eliminated by wavelet packet decomposition. The remaining high-frequency response was regarded as the bridge response caused by traffic load. The maximum values ​​of the bridge dynamic weighing data and the absolute value of the traffic load effect were calculated at the same time interval as the bridge dynamic weighing peak value and the bridge response peak value.

3. The bridge state reliability evaluation method based on an adaptive Gaussian process model according to claim 1, characterized in that, S3 specifically refers to: The bridge dynamic weighing peak value and the bridge response peak value are divided into historical data and modeling data at the same time point. The historical data is used as the initial training data for the prediction model. It is determined whether there are missing values ​​in the bridge dynamic weighing peak value. If there are, the known bridge dynamic weighing peak value is used to train the GPM autoregressive prediction to repair the missing values. It is then determined whether there are missing values ​​in the bridge response peak value. If there are, the repaired bridge dynamic weighing peak value and the known bridge response peak value are used to train the GPM regression prediction to repair the missing values.

4. The bridge state reliability evaluation method based on an adaptive Gaussian process model according to claim 1, characterized in that, S5 specifically refers to: Determine if there are missing values ​​in the current step of the bridge dynamic weighing peak value. If so, establish an adaptive GPM for the bridge dynamic weighing peak value to predict and repair the missing values. Continue to determine if there are missing values ​​in the bridge response peak value. If so, combine the repaired bridge dynamic weighing peak value and the known bridge response peak value to establish an adaptive GPM to predict and repair the missing values.

5. The bridge state reliability evaluation method based on an adaptive Gaussian process model according to claim 1, characterized in that, S9 specifically refers to: Combining the probabilistic modeling results of peak response and the resistance model, the reliability index of bridge components is calculated using the first-order reliability method: ； In the formula, As a component reliability index, This is the mean of the resistance model. The standard deviation of the resistance model. This represents the mean value of the load effect. The standard deviation of the load effect, The sensor error coefficient is used; the component function is: ； In the formula, For component function, For resistance model, This is due to the load effect.

6. The bridge state reliability evaluation method based on an adaptive Gaussian process model according to claim 1, characterized in that, S10 specifically refers to: Based on the reliability calculation results of bridge components, a series model is used to calculate the reliability index of the bridge structure: ； In the formula, This is an indicator of bridge structural reliability. It is the inverse cumulative distribution function of the standard normal distribution. For the first i The failure probability of each component.

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