Method for predicting static behavior of bridge based on dynamic load

Abstract

The present invention discloses a method for predicting the static behavior of a bridge based on dynamic loading, comprising the following steps: establishing a full-bridge structural analysis model according to the design data of the existing bridge; conducting dynamic loading tests on the existing bridge to obtain the bridge dynamic response values; performing sensitivity analysis on each design parameter in the initial structural analysis model to obtain and determine the key design parameters to be corrected that affect the bridge structure; based on the uniform design sampling method, using machine learning intelligent algorithms, constructing training samples of the key design parameters to be corrected and establishing a surrogate prediction model; correcting the initial structural analysis model using the prediction results of machine learning and intelligent algorithms; predicting the static behavior of the bridge based on the corrected structural analysis model; introducing an error analysis method to evaluate the prediction results of the bridge static force. The beneficial effects of the present invention are: reducing the cost of the bridge static load test, reducing the damage to the bridge's own structure, and having high prediction result accuracy.

Description

Technical Field

[0001] The present invention relates to the technical fields of civil engineering, structural engineering, bridge detection and health monitoring, and particularly relates to a method for predicting the static behavior of bridges based on dynamic loads. Background Art

[0002] With the rapid development of global transportation construction, the total number of bridges has increased sharply globally since this century. According to statistics in 2019, there are 878,300 highway bridges in China alone. Facing the huge number of bridges, it is particularly important to quickly evaluate the performance of existing bridge structures, identify damage, conduct intelligent analysis, and control their safety performance.

[0003] Currently, the effective method for evaluating the technical state of bridge structures is through load tests. However, bridge load tests have the problems of high test costs, long test processes, large workloads, certain damage to bridge structures, and the need to close roads, which seriously affect normal traffic. Facing the huge number of bridges that urgently need to be quickly evaluated for their technical conditions, how to improve the efficiency of bridge detection, reduce the cost of bridge detection, avoid the impact on traffic caused by closing roads, ensure the accuracy and reliability of test results, and achieve intelligent identification, rapid detection, and intelligent analysis and evaluation decisions for bridge structures has become a problem that needs to be solved in current research. Although the dynamic load test of bridges can only identify the dynamic performance of the overall bridge structure, compared with static load tests, its cost is relatively low, the test time is relatively short, the test process is relatively simple, and the impact on traffic is relatively small.

[0004] Therefore, researchers in this field are committed to proposing a method for predicting the static behavior of bridges based on dynamic loads, using the dynamic load test results with lower costs, higher efficiency, and less traffic impact to accurately predict the static load results of bridges. Summary of the Invention

[0005] In view of the deficiencies and defects existing in the current health monitoring, damage identification, intelligent analysis, and performance evaluation of existing bridges, the problem to be solved by the present invention is to achieve the goal of quickly predicting the static behavior of bridges based on relatively simple, low-cost, convenient, and efficient dynamic load test results, combined with machine learning intelligent algorithms and model correction techniques.

[0006] To achieve the above object, the present invention proposes a method for predicting the static behavior of bridges based on dynamic loads, which is characterized by including the following steps:

[0007] Step 1: According to the design data of the existing bridge, establish a structural analysis model of the whole bridge; and use the structural analysis model as the initial structural analysis model for subsequent model correction;

[0008] Step 2: Conduct a dynamic load test on the existing bridge to obtain the bridge dynamic response value;

[0009] Step 3: Conduct a sensitivity analysis on each design parameter in the initial structural analysis model to obtain and determine the key design parameters to be corrected that affect the bridge structure;

[0010] Step 4: Based on the uniform design sampling method, use machine learning intelligent algorithms to construct training samples of the key design parameters to be corrected and establish a surrogate prediction model;

[0011] Step 5: Use the prediction results of machine learning and intelligent algorithms to correct the initial structural analysis model to obtain a corrected structural analysis model;

[0012] Step 6: Predict the static behavior of the bridge based on the corrected structural analysis model;

[0013] Step 7: Introduce an error analysis method to evaluate the prediction results of the bridge static force; among them, the root mean square error (RMSE) analysis method is used for error analysis, and the calculation formula of the root mean square error is as follows:

[0014]

[0015] where, are the experimental response values and the predicted response values of the intelligent prediction model corresponding to the i-th group of samples respectively, is the average value of the experimental response values.

[0016] Furthermore, the structural analysis model in Step 1 is usually modeled by numerical methods, and the numerical methods are modeling methods such as finite element, boundary element, discrete element, and / or infinite element.

[0017] Furthermore, when measuring the dynamic load of the bridge in Step 2, contact or non-contact, direct or indirect measurement methods (such as machine vision measurement methods) are used to measure the bridge to obtain the dynamic characteristic parameters of the bridge; among them, the parameters of the dynamic characteristics include the frequency, vibration mode, damping, impact coefficient, dynamic deflection, and dynamic strain of the bridge, etc.

[0018] Furthermore, in Step 3, a sensitivity analysis method is used to conduct a sensitivity analysis on each design parameter of the initial structural analysis model of the bridge in Step 1, analyze the sensitivity weight indexes of different design parameters, and determine the key design parameters to be corrected of the bridge. Among them, the sensitivity analysis method can also use the grey correlation degree method to achieve the weight analysis of the key parameters to be corrected.

[0019] Furthermore, in Step 4, the uniform design sampling method is used to construct training samples of the key design parameters to be corrected that are evenly distributed in space, and a prediction model is established in combination with intelligent algorithms; among them, the intelligent algorithms include prediction methods such as Bayesian theory, Gaussian process method, Kriging model, and various surrogate models.

[0020] Furthermore, based on the prediction model constructed in step 4, step 5 calls the bridge dynamic load test results obtained in step 2 to predict each key design parameter to be corrected, and substitutes the prediction results of each key design parameter to be corrected into the initial structural analysis model of the bridge constructed in step 1 to achieve the correction of the initial structural analysis model.

[0021] Furthermore, based on the corrected structural analysis model, step 6 applies the load conditions in the corrected structural analysis model according to the static load test plan of the bridge to achieve the prediction of the bridge's static force results. Among them, the static load prediction results can be the deformation, internal force, stress, etc. of the whole bridge or part of it respectively.

[0022] Step 7 introduces an error analysis method to evaluate the prediction results of the bridge's static load. Among them, the error analysis usually adopts the root mean square error (RMSE) analysis method.

[0023] Based on the dynamic load test results of existing bridges, combined with the structural analysis model correction method and intelligent algorithm technology, the present invention realizes the accurate prediction of the static force behavior of existing bridges and achieves the following technical effects:

[0024] (1) Predicting the static force behavior of bridges based on the dynamic load test results of existing bridges greatly reduces the cost of bridge static force tests, improves the detection efficiency, avoids the problem of closed traffic caused by static load tests, and reduces the damage to the structure itself during the bridge loading process;

[0025] (2) Using intelligent algorithms and combining the model correction method to predict the static force behavior of existing bridges, the obtained prediction results have high accuracy and are more in line with the actual bridge health conditions.

[0026] (3) The proposed method can achieve rapid static force behavior analysis for a large number of bridges, and can conduct a comprehensive safety assessment of the overall structure of the bridges, providing a new method for bridge health monitoring and operation and maintenance. Description of the Drawings

[0027] Figure 1a is the flowchart of the present invention.

[0028] Figure 1b is the flowchart of the method for predicting the static force behavior of bridges based on dynamic load in the present invention;

[0029] Figure 2 is the graph of the bridge dynamic load test results of an embodiment of the present invention (the abscissa is the sampling time and the ordinate is the amplitude);

[0030] Figure 3Parameter sensitivity analysis result graph in an embodiment of the present invention;

[0031] Figure 4 It is a flowchart combining the analysis model correction and intelligent algorithm of the present invention;

[0032] Figure 5 It is a comparison graph of the static load test results predicted for a bridge and the actual on-site static load test results in an embodiment of the present invention. Detailed implementation manners

[0033] The following will describe in detail the specific implementation manners of the embodiments of the present invention with reference to the accompanying drawings. It should be understood that the specific implementation manners described herein are only used to illustrate and explain the embodiments of the present invention, and are not used to limit the embodiments of the present invention.

[0034] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0035] The present invention will be described in detail below with reference to the accompanying drawings and in combination with exemplary embodiments.

[0036] Step 1: Establish an initial structural analysis model of the bridge according to the existing bridge design data;

[0037] According to the existing bridge design data, clarify the geometric shapes, specific dimensions, material property values of each component of the bridge, and the form of boundary conditions, and use structural analysis software to establish an initial analysis model of the bridge structure. This analysis model serves as the reference model for subsequent model correction. Among them, this analysis model is usually a numerical model, such as a finite element model, a boundary element model, a discrete element model, an infinite element model, etc. Commonly used analysis software includes ANSYS, ABAQUS, Midas, etc.

[0038] Step 2: Conduct dynamic load tests on the existing bridge to obtain the bridge dynamic response values;

[0039] To obtain the bridge dynamic response values, in a specific embodiment, the ambient excitation method in the direct measurement method is used to conduct on-site dynamic load tests on an existing bridge. During the test, vibration pickups are arranged at the typical sections of L / 8, L / 4, and L / 2 of the bridge to obtain the vibration response of the bridge under ground pulsation. Figure 2 It is the result of the dynamic load test on a bridge in the embodiment, where the abscissa is the test time and the ordinate is the amplitude. Performing Fourier transform on this time-domain result can obtain the frequency-domain result reflecting the frequency characteristics of the bridge.

[0040] The Fourier transform formula is:

[0041] where: j is the imaginary unit, j^2 = -1, dimensionless; T is the period, in seconds; X is the primitive function of x; t is the time, in seconds; ω is the frequency, and x(t) is a continuous-time signal.

[0042] Step 3: Conduct a sensitivity analysis on each design parameter in the initial structural analysis model to obtain and determine the key design parameters to be corrected that affect the bridge structure:

[0043] Based on the initial bridge structure model established in Step 1, select the design parameters to be corrected. Use the global sensitivity analysis method to conduct a sensitivity analysis on different design parameters. By the method of controlling variables, each time change the variation threshold of one design parameter by 10%, keep other design parameters unchanged, and calculate the influence degree of the corresponding first two-order frequency response results f1 and f2 of the bridge structure when different design parameters change, so as to determine the sensitivity weight index of different design parameters.

[0044] The key parameters include design parameters such as structural geometric dimensions, elastic modulus of concrete materials, and unit weight of concrete. Using the sensitivity analysis method, change the structural design parameters one by one, calculate the corresponding structural response values, construct a sensitivity analysis model for key parameters, quantify the specific influence effects of different parameters on the bridge structure, and determine the key design parameters to be corrected. Figure 3 It is the result of parameter sensitivity analysis in an embodiment. It should be noted that the parameters in this embodiment are K1, K2, K3, r1, r2, r3 respectively, and the corresponding structural response results are the first 2-order frequencies f1 and f2.

[0045] Step 4: Based on the uniform design sampling method, use the machine learning intelligent algorithm to construct training samples of the key design parameters to be corrected and establish a surrogate prediction model:

[0046] According to the key design parameters to be corrected determined in Step 3, set variable thresholds for each parameter respectively, write them into a macro file, use the structural analysis software to read the macro file of parameter thresholds, and calculate the corresponding structural response values within the thresholds for each group of parameters in turn. This response value can be the frequencies of each order of the bridge or the deflection value of a certain measuring point of the bridge, etc. Generate training samples through a finite number of calculations, and use this training sample to establish a prediction model. Figure 4 This is the flowchart of the combination of the structural analysis model correction and the intelligent algorithm of the present invention.

[0047] Specifically, Step 4 is based on the uniform design sampling method, uses the intelligent algorithm to establish training samples of design parameters and response results, and establishes a Kriging prediction model:

[0048] According to the key design parameters to be corrected determined by the sensitivity analysis in step 3, in this embodiment, K1, K2, K3, r1, r2, and r3 are the parameters to be corrected. The uniform design sampling method is adopted, and through the uniform design table U n (m r ), where U represents the uniform design table, n represents the required number of uniform tests, m represents the number of factor levels that can be accommodated, and r represents the maximum number of factors that can be arranged.

[0049] In this embodiment, a uniform design table of U 30 (30 6 ) is established, that is, 30 tests, 30 levels, and 6 parameters. The training samples of the intelligent algorithm are composed of the corresponding structural response frequency results f1 and f2. The specific training samples are shown in Table 1.

[0050] Based on this training sample, substitute it into the Kriging theory model:

[0051] y(x) = f(x) T β + Z(x) (3);

[0052] In the formula: y(x) is the Kriging model function, T represents the meaning of transpose; f(x) is the polynomial model, and β is the regression coefficient. Z(x) is a random process, which is called the variogram or correlation model, and then the Kriging surrogate prediction model is established.

[0053] Step 5: Use the prediction results of machine learning and intelligent algorithms to correct the initial structural analysis model to obtain the corrected structural analysis model;

[0054] According to the training samples established in step 4, input the result data obtained from the dynamic load test in step 2, and predict a set of optimal values of the parameters to be corrected through the machine learning intelligent algorithm. Substitute this set of predicted values into the initial structural analysis model to realize the correction of the structural analysis model.

[0055] The machine learning intelligent algorithm includes the Kriging model algorithm, Gaussian process algorithm, Bayesian algorithm, random forest algorithm, cloud theory algorithm, and various surrogate models, etc.

[0056] In this embodiment, the Kriging model algorithm is adopted. First, the Kriging model includes two parts: polynomial and random distribution, that is, y(x) = f(x) T β + Z(x), where:

[0057] f(x) T β = [f 1 (x), f 2 (x),..., f p (x)]β = f 1(x)β 1 + f 2 (x)β 2 +... + f p (x)β p (4);

[0058] f(x) is a polynomial model, p is the number of polynomials, and β is the regression coefficient.

[0059] Z(x) is a random process, called the variogram or correlation model. The covariance matrix of Z(x) is:

[0060]

[0061] Where: Cov() is the covariance; σ is the standard deviation; θ is the hyperparameter. x i and x j are sample points; is the spatial correlation function between any two sample points x i and x j in the sample points, and its functional form is:

[0062]

[0063] In the prediction process of the Kriging regression function model, the problem is transformed into a minimum optimization problem, that is By solving the minimum optimization problem of the formula, the parameter θ is obtained, and then the optimal Kriging prediction model can be constructed, where θ is the hyperparameter, m is a natural number, m = 1, 2, 3,... m, and σ is the standard deviation.

[0064] Step 6, perform bridge static behavior prediction based on the modified structural analysis model;

[0065] Based on the structural analysis model modified in step 5, the numerical model has been in line with the performance of the actual bridge. Simulate the loading in the modified numerical model according to the loading positions of the actual bridge static load test, and calculate the displacement, stress and other results of typical sections such as the mid-span and supports of the bridge through the structural analysis software. In this embodiment, the longitudinal deflections W1 - W18 of a 3-span continuous beam bridge under the action of a mid-span concentrated load are predicted and compared with the measured results for verification.

[0066] Step 7, introduce an error analysis method to evaluate the prediction results of bridge static force; among them, the root mean square error RMSE analysis method is used for error analysis;

[0067] The present invention proposes the root mean square error RMSE (Root Mean Squared Error) as the evaluation index of the prediction results.

[0068] The root mean square error calculation formula is as follows:

[0069]

[0070] in, are the experimental response value and the predicted response value of the intelligent prediction model for the i-th group of samples, is the average value of the experimental response. RMSE is used to evaluate the accuracy of the intelligent prediction model. The closer this value is to 0, the smaller the error between the experimental response value and the predicted value of the intelligent prediction model.

[0071] Table 1U 30 (30 6 ) Design Matrix

[0072]

[0073] Table 2 Initial value, measured value and predicted value of each deflection measuring point (mm)

[0074]

[0075] Table 3 Deflection error analysis

[0076]

[0077] In the description of the present invention, it is to be understood that the terms “center”, “longitudinal”, “lateral”, “length”, “width”, “thickness”, “up”, “down”, “front”, “back”, “left”, “right”, “vertical”, “horizontal”, “top”, “bottom”, “inside”, “outside”, “clockwise”, “counterclockwise”, “axial”, “radial”, “circumferential”, etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as limiting the present invention.

[0078] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0079] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral one; it can be a mechanical connection, an electrical connection, or communication with each other; it can be a direct connection, or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0080] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may mean that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, a first feature being "above", "above" or "above" a second feature may mean that the first feature is directly above or obliquely above the second feature, or simply means that the first feature is higher in level than the second feature. A first feature being "below", "below" or "below" a second feature may mean that the first feature is directly below or obliquely below the second feature, or simply means that the first feature is lower in level than the second feature.

[0081] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0082] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. Method for predicting static behavior of bridge based on dynamic load, characterized in that, it includes the following steps: Step 1: According to the design data of the existing bridge, establish a structural analysis model of the whole bridge; and use the structural analysis model as the initial structural analysis model for subsequent model correction; Step 2: Conduct dynamic load test on the existing bridge to obtain the bridge dynamic response value; Step 3: Conduct sensitivity analysis on each design parameter in the initial structural analysis model to obtain and determine the key design parameters to be corrected that affect the bridge structure; Step 4: Based on the uniform design sampling method, use machine learning intelligent algorithm to construct a training sample of the key design parameters to be corrected and establish a surrogate prediction model; Step 5: Use the prediction results of machine learning and intelligent algorithm to correct the initial structural analysis model to obtain the corrected structural analysis model; Step 6: Predict the static behavior of the bridge based on the corrected structural analysis model; Step 7: Introduce an error analysis method to evaluate the prediction results of the bridge static force; among them, the root mean square error RMSE analysis method is used for error analysis; the root mean square error calculation formula is as follows: wherein, are the test response value and the predicted response value of the intelligent prediction model corresponding to the i-th group of samples respectively, is the average value of the experimental response values.

2. The method for predicting static behavior of bridge based on dynamic load according to claim 1, characterized in that: The structural analysis model in Step 1 is modeled by numerical methods, and the numerical methods are finite element, boundary element, discrete element and / or infinite element modeling methods.

3. The method for predicting static behavior of bridge based on dynamic load according to claim 2, characterized in that: When conducting the dynamic load test on the bridge in Step 2, the dynamic performance of the bridge is measured by contact or non-contact, direct or indirect methods; among them, the parameters of the dynamic performance include the frequency, vibration mode, damping, impact coefficient, dynamic deflection and dynamic strain of the bridge.

4. The method for predicting static behavior of bridge based on dynamic load according to claim 3, characterized in that: In Step 2, the ambient excitation method in the direct measurement method is used to conduct on-site dynamic load test on an existing bridge; during the test, vibration pickups are arranged at typical sections of L / 8, L / 4, L / 2 of the bridge to obtain the vibration response of the bridge under ground pulsation, and the Fourier transform is performed on the obtained time domain results to obtain the frequency domain results reflecting the frequency characteristics of the bridge; The Fourier transform formula is as follows: In the formula: j is the imaginary unit, j^2=-1, dimensionless; T is the period, unit is second; X is the original function of x; t is the time, unit is second; ω is the frequency, x(t) is the continuous time signal.

5. The method for predicting static behavior of bridge based on dynamic load according to claim 3, characterized in that: In Step 3, the sensitivity analysis method is used to conduct sensitivity analysis on each design parameter of the initial structural analysis model of the bridge in Step 1, analyze the sensitivity weight index of different design parameters, and determine the key design parameters to be corrected of the bridge.

6. The method for predicting static behavior of bridge based on dynamic load according to claim 5, characterized in that: Step 4 adopts the uniform design sampling method to construct a training sample of the key design parameters to be corrected with uniform spatial distribution, and combines intelligent algorithms to establish a prediction model; among them, the intelligent algorithms include Bayesian theory, Gaussian process method and / or Kriging model.

7. The method for predicting the static behavior of a bridge based on dynamic loads as described in claim 6, characterized in that: The intelligent algorithm adopted in step 4 is the Kriging model algorithm; Among them, the Kriging model consists of two parts, a polynomial and a random distribution, that is, y(x) = f(x) T β + Z(x), where: f(x) T β = [f 1 (x), f 2 (x),..., f p (x)]β = f 1 (x)β 1 + f 2 (x)β 2 +... + f p (x)β p (4); f(x) is a polynomial vector, p is the number of polynomials, and β is the regression coefficient; Z(x) is a random process, called the variogram or correlation model, and the covariance matrix of Z(x) is: Where: Cov() is the covariance; σ is the standard deviation; θ is the hyperparameter; x i and x j are sample points; is the spatial correlation function of any two sample points x i and x j and its functional form is: In the process of predicting with the Kriging regression function model, the problem is transformed into a minimum optimization problem, that is By solving the minimum optimization problem of the formula, the parameter θ can be obtained, and then the optimal Kriging prediction model can be constructed, where θ is a hyperparameter, m is a natural number, m = 1, 2, 3, … m, and σ is the standard deviation.

8. The method for predicting the static behavior of a bridge based on dynamic loads as described in claim 7, characterized in that: Based on the prediction model constructed in step 4, call the bridge dynamic load test results obtained in step 2, predict each key design parameter to be corrected, and substitute the prediction results of each key design parameter to be corrected into the initial structural analysis model of the bridge constructed in step 1 to realize the correction of the initial structural analysis model.

9. The method for predicting the static behavior of a bridge based on dynamic loads as described in claim 6, characterized in that: Based on the corrected structural analysis model, according to the static load test scheme of the bridge, apply the load conditions in the corrected structural analysis model to realize the prediction of the bridge static results.

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