An early warning method for extreme stress of steel aqueduct structures based on a sliding window Gaussian process model

Abstract

The present invention discloses a method for early warning of extreme stress of steel aqueduct structures based on a sliding window Gaussian process model. This method utilizes the advantages of the Gaussian process regression model in predicting non-linear time series to predict the stress state of steel aqueduct structures under the action of temperature and water flow loads, and realizes real-time early warning of the safety performance of cross-sections. The method of the present invention uses a window function that is updated synchronously with the prediction process to select training data. Since the window length does not increase with the increase of the time series, when the amount of monitoring data increases significantly, it can significantly enhance the prediction and early warning efficiency of structural strain extremes, and has important theoretical significance and engineering application value for the long-term health monitoring and structural safety assessment of large steel aqueduct structures.

Description

Technical Field

[0001] The present invention relates to the field of structural health monitoring, and particularly to an extreme stress warning method for steel aqueduct structures based on a sliding window Gaussian process model. Background Art

[0002] As a key hub of water diversion projects, aqueduct structures have been widely used in large-scale water conservancy projects in China such as the South-to-North Water Diversion Project and the Yangtze River to Huaihe River Water Diversion Project. However, under long-term service conditions, due to harsh environmental factors and water flow loads, aqueduct structures usually suffer from varying degrees of defects and diseases, which have a significant impact on the safe operation of aqueduct structures. Since aqueduct structures are often located in areas with many rivers and complex geographical environments, the cost of manual inspection is relatively high. Therefore, long-term monitoring of the safety performance of aqueduct structures based on a health monitoring system is one of the important means to ensure the safe operation of such structures.

[0003] Structural health monitoring technology has evolved from diagnosis based on monitoring to prediction of future states based on monitoring. The great advantage of measured strain data is that it can be directly used to indicate the safety reserve of structures and structural components, and can also provide information related to the load-bearing capacity of the entire structure. Therefore, more and more structural state diagnoses and predictions choose to use the structural stress response values obtained from measured strain data as the basis. Accurately predicting the structural stress response is a necessary step for reliable diagnosis and prediction of structural conditions. The autoregressive model (AR) is currently widely studied for use in structural health detection systems. The autoregressive model defines a linear parameter structure to reflect the relationship between the current output and the previous output, and the parameters of the autoregressive model are obtained through least squares estimation. However, for large and complex structures subjected to multi-source effects such as live loads and environmental loads, their stress evolution is a typical non-linear dynamic process rather than a simple linear dynamic process. In addition, the online monitoring-derived stress data extracted from the structural health monitoring system is extremely large. This urgently requires the development of a structural stress response prediction method with high computational efficiency and high accuracy. Summary of the Invention

[0004] Aiming at the problems in the above background art, the purpose of the present invention is to provide an extreme stress warning method for steel aqueduct structures based on a sliding window Gaussian process model, which is used for predicting the stress state of key sections of large steel aqueduct structures and further applied to the safety warning of this type of structure. This method overcomes the low efficiency problem of traditional Gaussian process models in non-linear time series prediction. It can not only effectively control the length of training data, but also use continuously updated monitoring data for predicting unknown structural responses. While ensuring prediction accuracy, it can effectively reduce the prediction efficiency of the Gaussian process model. Furthermore, it can significantly enhance the warning efficiency of steel aqueduct structures, and has important theoretical significance and engineering application value for the long-term health monitoring and structural safety assessment of large steel aqueduct structures.

[0005] To achieve the above object, the specific technical solution of the present invention is as follows:

[0006] An extreme stress warning method for steel aqueduct structures based on a sliding window Gaussian process model is carried out according to the following steps:

[0007] Step 1: Use the strain sensors set at the key sections of the steel aqueduct structure to record the strain data of the structure under long-term service conditions, and use the obtained strain monitoring data as the initial training data of the Gaussian process model. The training data can be expressed as where, represents the strain monitoring data with a length of n, is the corresponding time series.

[0008] Step 2: Use the training data described in Step 1 to train the Gaussian process model, obtain the trained Gaussian process model, and predict the strain data y n+1 at time t n+1 .

[0009] Step 3: Export the strain prediction value at time t n+1 obtained in Step 2, convert it into the stress value of the cross-section, compare the predicted stress value with the allowable stress value of the key section of the steel aqueduct structure, and use this as the basis for setting the warning conditions of the steel aqueduct structure.

[0010] Step 4: Set the sliding window length. When the strain value at time t n+1 is obtained, put it into the training data. At this time, in order to predict the strain response at the next moment, the window is updated one step forward at the same time to ensure that the dimension of the training data remains n.

[0011] Step 5: Repeat Steps 1 to 4 to perform real-time warning on the safety performance of the key section of the steel aqueduct structure.

[0012] Furthermore, when training the Gaussian process model in Step 2 to optimize the hyperparameters of the Gaussian process prediction model, the process can be expressed as: combining the Bayesian inference method and the initial training data described in Step 1, constructing the likelihood function under the known conditions, which is simplified as shown in Equation (1), and the partial derivative calculation result of its hyperparameters of the Gaussian process model is shown in Equation (2):

[0013]

[0014]

[0015] In the above equations, are hyperparameters to be determined for the Gaussian process model; R is an n×n covariance matrix that can be determined by Equation (3).

[0016]

[0017] In Equation (3), R ij = C(y i , y j ), where C(.,.) is the kernel function of the Gaussian process model and can be further expressed as:

[0018]

[0019] where η 2 is the variance of the time series; l k is the characteristic length scale; d is the input dimension;

[0020] The conjugate gradient optimization algorithm is used to optimize the likelihood function L(Θ) described in Step 3, and the optimal solution of the hyperparameters is derived as shown in Equation (5):

[0021]

[0022] Furthermore, predict the strain data y n+1 at time t n+1 , and substitute the data number at time t n+1 into the trained Gaussian process model to obtain the expectation and variance of the strain prediction value at time t n+1 as shown in Equations (6) to (7):

[0023]

[0024]

[0025] where C * , can be further expressed as C * = (t n+1 , X) and

[0026] Furthermore, convert the mean value of the strain prediction at time t n+1 into the stress value of the cross-section, which is the product of the obtained strain value and the elastic modulus of its corresponding component, and can be specifically expressed as:

[0027]

[0028] where E s is the elastic modulus of the steel component, and δ n+1 is the stress value of the critical cross-section at time t n+1 .

[0029] Furthermore, for the allowable stress value of the key section of the steel aqueduct structure described in step 3, this stress allowable value is the ultimate tensile / compressive stress of the steel member minus the stress value caused by the self-weight effect of the structure.

[0030] Furthermore, for the warning condition setting of the steel aqueduct structure described in step 3, its characteristics are as described in equation (9):

[0031]

[0032] where δ u is the ultimate tensile / compressive strength of the steel member, and δ static represents the stress value of the key section under the condition of the self-weight of the structure; using is to ensure that the warning result of this method has 99.7% effectiveness.

[0033] Furthermore, the selection principle of the sliding window length described in step 4 is characterized by small model prediction error, high calculation accuracy, etc. The window moves forward as the monitoring data is updated, and always maintains a fixed length.

[0034] The present invention proposes to use the Gaussian process model prediction method to perform real-time prediction on the stress state of the key section of the steel aqueduct structure. The Gaussian process prediction model, as a non-parametric probability model, combined with the Bayesian inference method, can effectively realize the derivation of the posterior probability distribution of the unknown response of the structure through prior information. Although the Gaussian process model has been successfully applied to the prediction problem of complex non-linear time series. Although the Gaussian process prediction model is very effective for characterizing the dynamic non-linearity of the structural stress response, due to the gradual accumulation of the structural response data collected by the monitoring system, when using the Gaussian process model for structural response forecasting, it will cause too high a response prediction cost. Therefore, the present invention proposes a sliding window-based Gaussian process prediction model for structural response prediction. This method can not only effectively control the length of the training data, but also use the continuously updated monitoring data for the prediction of the unknown structural response. While ensuring the prediction accuracy, it can effectively reduce the prediction efficiency of the Gaussian process model. Furthermore, it can significantly enhance the warning efficiency of the steel aqueduct structure, and has important theoretical significance and engineering application value for the long-term health monitoring and structural safety assessment of large steel aqueduct structures.

[0035] Compared with the existing technology, the beneficial effects of the present invention are reflected in:

[0036] 1. The present invention overcomes the problem of low efficiency of traditional Gaussian process models in nonlinear time series prediction. By adding a moving window of fixed length to the time series of structural dynamic responses to select the training data for the Gaussian process model, this method can not only effectively control the length of the training data, but also use the continuously updated monitoring data for predicting unknown structural responses. While ensuring the prediction accuracy, it can effectively reduce the prediction efficiency of the Gaussian process model.

[0037] 2. The stress monitoring data of key sections can intuitively reflect the operation state of the steel aqueduct structure under the coupling action of external loads such as environment and water body. Compared with monitoring data such as acceleration and displacement, the stress monitoring data is more likely to judge the safety performance of the structure from the aspect of structural strength. Therefore, the present invention uses the stress state at the key section of the steel aqueduct structure as an early warning index, enabling the management and maintenance personnel to timely master the operation state of the steel aqueduct structure.

[0038] 3. When setting the early warning index, the stress prediction value at the key section is calculated using μ±3σ to ensure that the stress prediction value has a reliability of 99.7%. Then, the ultimate tensile / compressive strength of the steel member minus the stress value caused by the self-weight of the structure is used as the setting reference value of the early warning index, and 50%, 70%, and 80% of the reference value are used as the boundary values of the three-level early warning index respectively, which can effectively achieve the hierarchical early warning of the safety performance of the steel aqueduct structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is the flowchart of the stress extreme value early warning of the steel aqueduct structure based on the sliding window Gaussian process model.

[0040] Figure 2 is the schematic diagram of the on-site layout of the aqueduct in the specific embodiment;

[0041] Figure 3 is the overall layout diagram of the strain measurement points of the aqueduct in the specific embodiment (1 / 2 bridge span);

[0042] Figure 4 is Figure 3 the schematic diagram of the strain monitoring curve of measurement points 3 - 10 in

[0043] Figure 5 is the setting of the moving window of the Gaussian process prediction model in the specific embodiment Figure 1 ;

[0044] Figure 6 is the setting of the moving window of the Gaussian process prediction model in the specific embodiment Figure 2 ; (a) is the training data, (b) is the stress prediction result;

[0045] Figure 7 is the real-time safety early warning diagram of the aqueduct structure in the specific embodiment. Specific implementation mode

[0046] See Figure 1 , in this embodiment, a method for warning the extreme stress of a steel aqueduct structure based on a sliding window Gaussian process model is carried out according to the following steps:

[0047] Step 1. In the health monitoring system of the steel aqueduct structure, take the strain monitoring data of the stress measurement points at the key sections of the steel aqueduct structure under the service state as the object, where the measured strain data is Y = {y1, y2,... y n-1 , y n , corresponding time series is X = {t1, t2,... t n-1 , t n}. The measured time-strain data D = {X, Y} is used as the initial training data of the stochastic Gaussian process model.

[0048] In the embodiment, the time series vector X is numbered according to the order of data acquisition. Among them, the obtained key section monitoring data is the strain data of the steel aqueduct structure under the coupled action of environmental and water body loads. Taking the time series as the input and the strain data as the output, the training data of the Gaussian process model is constructed. The input-output relationship of the Gaussian process model can be expressed as:

[0049] Input: Initial training data D = {X, Y}, where

[0050] Output: Use the expectation μ and variance σ 2 to predict the response y n+1,…N of the strain sensor at point A at time t n+1,…N .

[0051] Step 2. Define the initial parameters of the Gaussian process model: where the expected value μ0 is 0 and the covariance is

[0052] Step 3. Combine the Bayesian inference method and the initial training data described in Step 1 to construct a likelihood function under the known conditions. After simplification, it is shown in Equation (1), and the calculation result of the partial derivative of the Gaussian process model hyperparameters is shown in Equation (2):

[0053]

[0054]

[0055] In the above equations, is the hyperparameter to be determined by the Gaussian process model; R is an n×n covariance matrix, which can be determined by Equation (3)

[0056]

[0057] In Equation (3), I is an n×n identity matrix, and R ij = C(t i , t j ), where C(.,.) is the kernel function of the Gaussian process model. In the prediction of structural vibration response, the kernel function usually adopts the squared exponential form, as shown in Equation (4):

[0058]

[0059] where η 2 is the variance of the time series; k is the fixed-length parameter; d is the input dimension.

[0060] Step 4: Use the conjugate gradient optimization algorithm to optimize the likelihood function L(Θ) in Step 3, and derive the optimal solution of the hyperparameters, as shown in Equation (5):

[0061]

[0062] Step 5: Substitute the optimized hyperparameters in Step 4 into the Gaussian process model to obtain the expectation and variance of the strain prediction values at the n+1 step, as shown in Equations (6) to (7):

[0063]

[0064]

[0065] where C * , can be further expressed as C * = (t n+1 , X) and

[0066] Step 6: Convert the strain prediction mean value at time t n+1 into the stress value of the cross-section, which is characterized by multiplying the obtained strain value by the elastic modulus of its corresponding component, and can be specifically expressed as:

[0067]

[0068] Step 7: Export the strain prediction values at the n+1 step obtained in Step 5, calculate the stress value and perform hierarchical early warning on the safety performance of the key cross-section of the steel aqueduct structure at the n+1 step through Equation (9):

[0069]

[0070] In Equation (9), δ uis the ultimate tensile / compressive strength of the steel member, δ static represents the stress value of the key section under the condition of the self-weight of the structure; Using is to ensure that the early warning results of this method have 99.7% effectiveness.

[0071] Step 8, when the true monitoring data of the key section t n+1 is obtained, the true monitoring data is automatically put into the historical training data, and a moving window with a length of n is used to identify the training data. The process is as follows:

[0072] Use the moving window to select new training data D -1 ={X -1 , Y -1}, where X -1 ←[t2,t3,…,t n+1 , and the corresponding strain training data is Y -1 ←[y2,y3,…,y n+1 , X -1 is the input data that does not include the time t1. Similarly, Y -1 is the monitoring data sequence of the strain value that does not include the time t1.

[0073] Step 9, repeat steps 2-6 to realize the safety early warning of the steel aqueduct structure. Specific embodiments

[0075] Experimental verification: The steel aqueduct described in the engineering background adopts a three-span truss beam-arch composite system, and the span layout is (68 + 110 + 68) m. The designed longitudinal slope of the aqueduct is 1 / 15000. The steel aqueduct adopts a three-span truss beam-arch composite system, and the span layout is (68 + 110 + 68) m. Horizontally, it is arranged in divided widths. The width of a single water tank is 24 m, the clear distance between two water tanks is 10 m, and the total width is 58.0 m. The on-site layout of the aqueduct is as Figure 2 shown.

[0076] In order to test whether the bearing capacity of the aqueduct structure meets the requirements under the water filling test state, the aqueduct structure is monitored in real time during the water filling test. The types of monitoring data include: strain, support displacement, environmental data, etc. In order to verify the applicability of the method proposed by the present invention, the stress extreme value early warning is carried out by selecting the strain measurement point data at the arch foot.

[0077] The layout of the strain measurement points of the aqueduct is as Figure 3 shown, and the strain monitoring curves of measurement points 3-10 are as Figure 4 shown. Among them, the elastic modulus of the steel member is taken as 2.06×10 5MPa, the yield strength of the material is 345 MPa. Based on the finite element model analysis, under the condition of self-weight, the stress at the calculation measurement point 3-10 is 48.2 MPa. Therefore, the allowable tensile / compressive stress value at this measurement point is 296.8 MPa. According to the process proposed by the present invention, as Figures 5 to 7 shown, it can effectively realize the real-time safety warning of the key sections of the aqueduct structure.

Claims

1. An extreme stress warning method for steel aqueduct structures based on a sliding window Gaussian process model, characterized in that, Proceed as follows: Step 1: Use the strain sensors set at the key sections of the steel aqueduct structure to record the strain data of the structure under long-term service conditions, and use the obtained strain monitoring data as the initial training data of the Gaussian process model. The training data can be expressed as where represents the strain monitoring data with a length of n, is the corresponding time series; Step 2: Use the training data in step 1 to train the Gaussian process model to obtain the trained Gaussian process model and predict the critical section of the steel aqueduct at t n+1 The strain data y n+1 ; Step 3. Export the strain prediction value at the moment t obtained in Step 2, convert it into the stress value of the cross-section, compare the predicted stress value with the allowable stress value of the key cross-section of the steel aqueduct structure, and use this as the basis for setting the warning conditions for the steel aqueduct structure; n+1 Export the predicted strain value at the moment n+1 , convert it into the stress value of the cross-section, compare the predicted stress value with the allowable stress value of the key cross-section of the steel aqueduct structure, and use this as the basis for setting the warning conditions for the steel aqueduct structure; Step 4. Set the sliding window length. When the strain value at time t n+1 is obtained, put it into the training data. At this time, in order to predict the strain response at the next moment, the window is updated one step forward simultaneously to ensure that the dimension of the training data remains n; Step 5: Repeat Steps 1 to 4 to conduct real-time early warning on the safety performance of the key sections of the steel aqueduct structure; In step 2, the Gaussian process model is trained to optimize the hyperparameters of the Gaussian process prediction model. The process can be described as follows: Combining the Bayesian inference method and the initial training data described in step 1, a likelihood function under the known conditions is constructed. After simplification, it is shown in equation (1), and the calculation result of the partial derivative of the likelihood function with respect to the hyperparameters of the Gaussian process model is shown in equation (2): In the above equation, are hyperparameters to be determined by the Gaussian process model; R is an n×n covariance matrix that can be determined by Equation (3); In equation (3), R ij = C(y i , y j ), where C(.,.) is the kernel function of the Gaussian process model and can be further expressed as: where η 2 is the variance of the time series; l k is the characteristic length scale; d is the input dimension; Use the conjugate gradient optimization algorithm to optimize the likelihood function L(Θ), and derive the optimal solution of the hyperparameters, as shown in Equation (5): 。 2. The extreme stress warning method for steel aqueduct structures based on a sliding window Gaussian process model according to claim 1, characterized in that Predict the strain data y of the key section of the steel aqueduct at t n+1 . Substitute the data number at time t n+1 into the trained Gaussian process model to obtain the expectation and variance of the strain prediction value at time t n+1 . As shown in equations (6) - (7): n+1 ​ Among them, C * , can be further expressed as C * =(t n+1 , X) and X is a time series vector.

3. The extreme stress warning method for steel aqueduct structures based on a sliding window Gaussian process model according to claim 1, characterized in that Convert the mean value of strain prediction at time t n+1 into the stress value of the cross-section by multiplying the obtained strain value by the elastic modulus of its corresponding component, which can be specifically expressed as: Among them, E s is the elastic modulus of the steel member, and δ n+1 is the stress value of the key section at time t n+1 .

4. The extreme stress warning method for steel aqueduct structures based on a sliding window Gaussian process model according to claim 1, characterized in that The allowable stress value of the key section of the steel aqueduct structure described in Step 3, which is the ultimate tensile / compressive stress of the steel member minus the stress value caused by the self-weight effect of the structure.

5. The extreme stress warning method for steel aqueduct structures based on a sliding window Gaussian process model according to claim 1, characterized in that The early warning condition setting of the steel aqueduct structure described in Step 3, as described in Equation (9): Among them, δ u is the ultimate tensile / compressive strength of the steel member, and δ static represents the stress value of the key section under the condition of the self-weight of the structure; Using is to ensure that the warning result of this method has 99.7% effectiveness.

6. The extreme stress warning method for steel aqueduct structures based on the sliding window Gaussian process model according to claim 1, characterized in that, The selection principle of the sliding window length in Step 4 is that the model prediction error is small and the calculation accuracy is high. The window moves forward as the monitoring data is updated, always keeping the length fixed.

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