Highway-railway dual-purpose bridge support displacement intelligent early warning method based on long-term monitoring data

Abstract

The invention discloses an intelligent early warning method for support displacement of a highway-railway dual-purpose bridge based on long-term monitoring data. The intelligent early warning method comprises the following steps: acquiring a temperature index and support displacement monitoring data; calculating longitudinal, vertical and transverse temperature differences of the steel truss girder structure; principal component analysis is carried out on the temperature indexes, and principal components influencing support displacement are extracted; establishing an optimal least square support vector machine prediction model; determining a support displacement early warning threshold value; calculating a displacement residual error of the test sample; and intelligent early warning is carried out on support displacement. The method can be used for accurately predicting the support displacement of the highway-railway dual-purpose bridge, and intelligent early warning of the support displacement under the influence of environmental factors is realized; the method can be implemented in a programmed manner, is simple and quick to operate and has wide engineering application value; the method is of great significance to guarantee driving safety of high-speed trains and overall performance of bridge structures.

Description

Technical Field

[0001] The present invention relates to the field of bridge structure health monitoring, and particularly to an intelligent early warning method for the displacement of bearings of a combined highway-railway bridge based on long-term monitoring data. Background Technique

[0002] At present, there are relatively few studies on applying monitoring technologies to combined highway-railway bridges for high-speed railways. In particular, there is no report on the monitoring of the displacement of bearings (longitudinal telescopic deformation) at the ends of steel truss girders of such bridges. However, currently, the displacement of bearings is usually measured by manual inspection. The obtained test data not only has large errors but also is discontinuous, and cannot reflect the change trend of the bearing displacement. In addition, the change in bearing displacement directly affects the working state of the rail expansion joint. If the deformation of the bearing appears abnormally, it will have a serious impact on the driving safety of high-speed trains and the comfort of passengers. Therefore, it is necessary to monitor the bearing displacement in real time and give early warnings about the bearing condition based on long-term monitoring data.

[0003] Therefore, based on long-term monitoring data, analyzing the variation law of bearing displacement under the action of temperature and establishing an intelligent early warning method for bearing displacement are of great significance for ensuring the driving safety of high-speed trains and the overall performance of bridge structures. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide an intelligent early warning method for the displacement of bearings of a combined highway-railway bridge.

[0005] Technical Solution: The present invention includes the following steps:

[0006] (1) Obtain temperature indicators and bearing displacement monitoring data;

[0007] (2) Calculate the longitudinal, vertical, and lateral temperature differences of the steel truss girder structure;

[0008] (3) Conduct principal component analysis on the temperature indicators to extract the principal components affecting the bearing displacement;

[0009] (4) Establish an optimal least squares support vector machine prediction model;

[0010] (5) Determine the early warning threshold for bearing displacement;

[0011] (6) Calculate the displacement residuals of the test samples;

[0012] (7) Conduct intelligent early warning on the bearing displacement.

[0013] Further, step (1) includes obtaining temperature indicators and bearing displacement monitoring data for two years. The sampling frequencies of the temperature indicators and the monitoring data are the same, both being collected once per hour. The temperature indicators include the ambient temperature and the temperature of the steel truss girder structure. Denote the ambient temperature at the i-th moment as T i, where \(i = 1, 2, \ldots, n\) and \(n\) is the total amount of ambient temperature data; the average temperature of the \(j\)-th section of the steel truss girder is denoted as where \(j = 1, 2, \ldots, m\) and \(m\) is the number of temperature measurement sections; the average temperatures at the top and bottom of the steel truss girder section are denoted as and the average temperatures at the upstream and downstream of the steel truss girder section are denoted as and

[0014] Furthermore, step (2) includes assuming that the longitudinal temperature difference of the steel truss girder at the \(i\)-th moment is \(LTG\) i , the vertical temperature difference is \(VTG\) i and the transverse temperature difference is \(TTG\) i , and the expressions are respectively:

[0015]

[0016] where \(i = 1, 2, \ldots, n\) and \(n\) is the total amount of ambient temperature data, and respectively represent the average temperatures at section \(k\) and section \(g\) at the \(i\)-th moment.

[0017] Furthermore, step (3) includes the following steps:

[0018] (3.1) Combine the temperature indicators, namely the ambient temperature \(T\) i , the longitudinal temperature difference \(LTG\) of the steel truss girder i , the vertical temperature difference \(VTG\) i and the transverse temperature difference \(TTG\) i to form the original data matrix \(X=(x\) ir ) n×t , where \(x\) ie is the observed value of the \(r\)-th temperature indicator at the \(i\)-th moment, \(i = 1, 2, \ldots, n\), \(r = 1, 2, \ldots, t\), and \(t\) is the number of temperature indicators;

[0019] (3.2) Standardize the original data matrix \(X=(x\) ir ) n×t to obtain a new set of indicators \(Y1, Y2, \ldots, Y\) t , and form the matrix \(Y=(y\) ir ) n×t , where \(y\) ir is the observed value of the \(i\)-th row and \(r\)-th column, and is expressed as:

[0020]

[0021] where,

[0022] (3.3) Calculate the covariance between each index in matrix Y to obtain the correlation coefficient matrix R = (r ir ) t×t , r ir is the value of the i-th row and r-th column of matrix R, reflecting the correlation degree between index Y i and Y r ;

[0023] (3.4) Solve for the t eigenvalues λ1 ≥ λ2 ≥ … λ t , and the corresponding normalized eigenvectors u1, u2, …, u t , where u r = (μ r1 , u r2 , …, u rt ) T , r = 1, 2, …, t, then the r-th principal component Z r is expressed as:

[0024] Z r = μ r1 Y1 + μ r2 Y2 + … + μ r Y t

[0025] (3.5) Calculate the variance contribution rate α r of the r-th principal component Z r , and the cumulative variance contribution rate γ of the first c principal components. The expressions are respectively:

[0026]

[0027] Usually, the first c (c ≤ t) principal components with a cumulative variance contribution rate λ ≥ 85% are selected to replace the original t indicators. These c principal components can comprehensively reflect the information of the original temperature indicators.

[0028] Further, step (4) includes inputting the principal components and the normalized bearing displacement, and training the least squares support vector machine prediction model, with the expression:

[0029]

[0030] where, x i is the input vector of the i-th sample; α i is the Lagrange multiplier; b is the bias; is the radial basis kernel function, and σ is the kernel function parameter;

[0031] Based on the principle of structural risk minimization, the above non-linear regression problem is solved through the following optimization problem:

[0032]

[0033] where γ is the penalty factor; e i is the error between the model prediction value and the actual value; the genetic algorithm is used to optimize the kernel function parameter σ and the penalty factor γ.

[0034] Furthermore, the steps of optimizing the parameters σ and γ by using the genetic algorithm include:

[0035] (4.1) Determine the maximum number of generations, population size, and the value ranges of the parameter σ and the kernel function parameter γ;

[0036] (4.2) Randomly generate W individuals G t , t = 1, 2,..., W, to form the initial population, and the individuals adopt the real number coding method;

[0037] (4.3) Decode the individuals into the actual values in the solution space and assign them to σ and γ, train the LSSVM model by using the extracted principal components and displacement samples, and calculate the fitness F t of each individual G t , and its expression is:

[0038]

[0039] where f(x i ) is the predicted value of the i-th training sample, and y i is the corresponding measured value;

[0040] (4.4) Through the genetic operations of selection, crossover, and mutation, eliminate the individuals with small fitness and inherit the individuals with large fitness to the next generation;

[0041] (4.5) If the maximum number of generations is reached, take the individual with the largest fitness as the output, and assign it to the penalty factor γ and the kernel function parameter σ to obtain the optimal least squares support vector machine prediction model.

[0042] Furthermore, the step (5) includes calculating the residual deformation ε i between the predicted value of the support seat displacement of the training sample and the measured result, i = 1, 2,..., N, and the expression is:

[0043] ε i = y i - f(x i )

[0044] where f(x i ) is the predicted value of the i-th training sample, and y i is the corresponding measured value;

[0045] Then, statistical analysis is carried out to obtain the mean value μ of the displacement residuals e and the standard deviation σ e . The confidence interval is used as the early warning threshold for the bearing displacement, and the expression is:

[0046] μ e -kσ e ≤ε i ≤μ e +kσ e

[0047] where ε i is the residual deformation of the i-th training sample, and k is a coefficient

[0048] Furthermore, step (6) includes inputting a new test sample and calculating the residual deformation ε of the test sample according to the optimal least squares support vector machine prediction model s . The expression is:

[0049] ε s =y s -f(x s )

[0050] where f(x s ) is the predicted value of the s-th test sample, and y s is the corresponding measured value

[0051] Furthermore, step (7) includes comparing the calculated residual deformation ε of the test sample s with the confidence interval [μ e -kσ e , μ e +kσ e to determine whether the change in the bearing displacement is normal

[0052] Furthermore, after the comparison, if ε s is within the confidence interval [μ e -kσ e , μ e +kσ e , it indicates that the change in the bearing displacement at time t s is normal

[0053] Furthermore, after the comparison, if ε s is outside the confidence interval [μ e -kσ e , μ e +kσ e , it indicates that an abnormal state different from the historical statistical information has occurred at the end of the structure at time t s , and thus an early warning is issued

[0054] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: The present invention can be used to accurately predict the displacement of the bearings of a combined highway-railway bridge, and realize the intelligent early warning of the bearing displacement under the influence of environmental factors; it can be realized programmatically, with simple and fast operation, and has wide engineering application value; it is of great significance for ensuring the driving safety of high-speed trains and the overall performance of the bridge structure. Description of the Drawings

[0055] Figure 1 is a flow chart of the present invention;

[0056] Figure 2 is an elevation view of the combined highway-railway bridge;

[0057] Figure 3 is a time history diagram of the environmental temperature;

[0058] Figure 4 is a temperature difference diagram of the steel truss girder structure; (a) is the longitudinal temperature difference; (b) is the vertical temperature difference; (c) is the transverse temperature difference.

[0059] Figure 5 is the contribution rate and cumulative contribution rate of each principal component;

[0060] Figure 6 Bearing displacement residual and probability density function diagram; (a) is the displacement residual; (b) is the probability density function diagram;

[0061] Figure 7 Bearing displacement early warning threshold diagram. Detailed Embodiment

[0062] The technical solution of the present invention will be further described below with reference to the drawings.

[0063] The present invention includes the following steps: (1) Obtain temperature indicators and bearing displacement monitoring data; (2) Calculate the longitudinal, vertical and transverse temperature differences of the steel truss girder structure; (3) Conduct principal component analysis on the temperature indicators to extract the principal components affecting the bearing displacement; (4) Establish an optimal least squares support vector machine prediction model; (5) Determine the bearing displacement early warning threshold; (6) Calculate the displacement residual of the test sample; (7) Conduct intelligent early warning on the bearing displacement.

[0064] Taking a certain combined highway-railway bridge as an example, the bridge is a five-span continuous steel truss girder cable-stayed bridge with a main span of 630m, and the span layout is (90 + 240 + 630 + 240 + 90)m. The bridge elevation is as Figure 2As shown in the figure. The bridge is arranged in two layers, with a six-lane expressway on the upper layer and an orthotropic steel bridge deck for the highway; a double-track railway special line on the lower layer and an orthotropic steel box structure for the railway bridge deck. The bridge adopts a three-main-truss and three-cable-plane structure type. The steel truss main girder is a plate-truss composite structure, adopting an N-shaped truss, with three main trusses arranged transversely across the bridge. The width of the main truss is 34.2m, the truss height is 15.5m, and the joint spacing is 15m. The bridge tower is a reinforced concrete structure, with 3×19 steel strand stay cables arranged on each side of each main tower, and a total of 228 stay cables are provided for the whole bridge.

[0065] Based on long-term monitoring data, clarify the intelligent early warning method for the displacement of the bearings of the combined highway-railway bridge, as Figure 1 shown. Select the monitoring data of the ambient temperature measuring point HT-1, the average temperature measuring points of the auxiliary pier section E-E and the mid-span section C-C of the steel truss girder, and the bearing displacement measuring point SD-1 in 2017 and 2018.

[0066] (1) Obtain the temperature index and the monitoring data of the bearing displacement;

[0067] The temperature index includes the ambient temperature and the temperature of the steel truss girder structure. Denote the ambient temperature in 2017 and 2018 as T i , i = 1, 2, …, n, where n is the total amount of ambient temperature data, and the ambient temperature time history is as Figure 3 shown; Denote the average temperature of the auxiliary pier section E-E of the steel truss girder as and the average temperature of the mid-span section C-C as Denote the average temperatures of the top and bottom of the mid-span section C-C of the steel truss girder as and Denote the average temperatures of the upstream and downstream of the mid-span section C-C of the steel truss girder as and

[0068] (2) Calculate the longitudinal, vertical and lateral temperature differences of the steel truss girder structure;

[0069] Include setting the longitudinal temperature difference of the steel truss girder at the i-th moment as LTG i , the vertical temperature difference as VTG i and the lateral temperature difference as TTG i , i = 1, 2, …, n, and their expressions are respectively:

[0070]

[0071] Among them, and respectively represent the average temperatures at the k-th section and the g-th section at the i-th moment. is the average temperature of the auxiliary pier section E-E of the steel truss girder is the average temperature of the mid-span section C-C The longitudinal, vertical and lateral temperature difference time histories of the steel truss girder structure are calculated as follows Figure 4 as shown

[0072] (3) Perform principal component analysis on the temperature indices to extract the principal components affecting the bearing displacement;

[0073] Let the ambient temperature be T i , the longitudinal temperature difference of the steel truss girder be LTG i , the vertical temperature difference be VTG i and the lateral temperature difference be TTG i to form the original data matrix X = (x ir ), n×t where x ir is the observed value of the r-th temperature index at the i-th moment, i = 1, 2,..., n, r = 1, 2,..., t, and t is the number of temperature indices;

[0074] Standardize the original data matrix X = (x ir ) n×t to obtain a new set of indices Y1, Y2,..., Y t , forming the matrix Y = (y ir ), n×t where y ir is the observed value of the i-th row and r-th column, and its expression is

[0075]

[0076] where

[0077] Calculate the covariance between the indices in matrix Y to obtain the correlation coefficient matrix R = (r ir ), t×t where r ir is the value of the i-th row and r-th column of matrix R, reflecting the correlation degree between indices Y i and Y r ;

[0078] Solve for the t eigenvalues λ1 ≥ λ2 ≥... λ t , and the corresponding standardized eigenvectors u1, u2,..., u t , where u r = (u r1 , u r2 ,..., u rt ), T r = 1, 2,..., t, then the r-th principal component Z r is expressed as:

[0079] Z r = μ r1 Y1 + μ r2 Y2 + L + μ rY t

[0080] Calculate the rth principal component Z r The variance contribution rate α r , and the cumulative variance contribution rate γ of the first c principal components are expressed as:

[0081]

[0082] Usually, the first c (c≤t) principal components that make the cumulative variance contribution rate λ≥85% are selected to replace the original t indicators. These c principal components can comprehensively reflect the information of the original temperature indicators.

[0083] Calculate the correlation coefficient matrix R between the temperature indicators, perform eigenvalue analysis on the matrix R, and obtain the variance contribution rate and cumulative contribution rate of each principal component, such as Figure 5 As shown, it can be seen that the variance contribution rate of the first principal component Z1 reaches 86.674%. According to the principal component selection standard, the original four temperature indicators can be replaced by principal component Z1.

[0084] (4) Establish the optimal least squares support vector machine prediction model;

[0085] First, the principal components and the standardized support shifts are input to train the least squares support vector machine prediction model, which is expressed as:

[0086]

[0087] Among them, x i is the input vector of i samples; α i is the Lagrange multiplier; b is the deviation; is the radial basis kernel function, where σ is the kernel function parameter;

[0088] Based on the principle of structural risk minimization, the above nonlinear regression problem is solved through the following optimization problem.

[0089]

[0090] In the formula, γ is the penalty factor; e i is the error between the model prediction and the actual value.

[0091] Secondly, the genetic algorithm is used to optimize the kernel function parameter σ and the penalty factor γ:

[0092] Determine the maximum evolutionary generations, population size, and the range of values of parameter σ and kernel function parameter γ;

[0093] Within the range of parameters σ and γ, W individuals G are randomly generated. t, where \(t = 1, 2, \cdots, W\), form the initial population, and the individuals adopt real - number coding;

[0094] Decode the individuals into the actual values in the solution space and assign them to \(\sigma\) and \(\gamma\). Train the LSSVM model using the extracted principal components and displacement samples, and calculate the fitness \(F\) of each individual \(G\) t of t , and its expression is:

[0095]

[0096] In the formula, \(f(x\) i ) is the predicted value of the \(i\) - th training sample, and \(y\) i is the corresponding measured value.

[0097] Through selection, crossover and mutation genetic operations, eliminate the individuals with small fitness and inherit the individuals with large fitness to the next generation;

[0098] If the maximum number of evolutionary generations is reached, take the individual with the largest fitness as the output, and assign it to the penalty factor \(\gamma\) and the kernel function parameter \(\sigma\) to obtain the optimal least - squares support vector machine prediction model.

[0099] In the case, when using the genetic algorithm to optimize the parameters of the least - squares support vector machine model with the monitoring data in 2017 as the training samples, the initial parameters are set as: the population size is 50, the maximum number of evolutionary generations is 200, the value range of the penalty factor \(\gamma\) is \([1, 1000]\), and the value range of the kernel function parameter \(\sigma\) is \([0.1, 100]\). After training, the optimal least - squares support vector machine prediction model is obtained.

[0100] (5) Determine the warning threshold of the bearing displacement;

[0101] Calculate according to the obtained optimal least - squares support vector machine prediction model, calculate the residual deformation \(\varepsilon\) between the predicted value of the bearing displacement of the training samples and the measured results i \(= y\) i \(- f(x\) i ), \(f(x\) i ) is the predicted value of the \(i\) - th training sample, \(y\) i is the corresponding measured value, \(i = 1, 2, \cdots, N\). Then conduct statistical analysis on the residual deformation to obtain the mean \(\mu\) e and the standard deviation \(\sigma\) e , and use the confidence interval with a certain assurance rate as the threshold level of the bearing displacement. Its expression is: \(\mu\) e \(- k\sigma\) e \(\leq\varepsilon\) i \(\leq\mu\) e \(+ k\sigma\) e , \(\varepsilon\) iis the residual deformation of the i-th training sample, and k is the coefficient.

[0102] In the case, the monitoring data (training samples) in 2017 were input into the optimal least squares support vector machine prediction model, and the residuals and their probability distributions between the measured seat displacement and the model prediction value were calculated, as Figure 6 shown. Through statistical analysis, the residual deformation approximately follows a normal distribution, with its mean μ e and standard deviation σ e being 0.00125 mm and 0.56 mm respectively. Taking the coefficient k as 3, corresponding to the 99.7% probability interval of the normal distribution, the threshold level of the seat displacement is [-1.678 mm, 1.682 mm].

[0103] (6) Calculate the displacement residuals of the test samples;

[0104] Input the new test samples, and calculate the residual deformation ε s of the test samples according to the optimal least squares support vector machine prediction model. Its expression is: ε s = y s - f(x s ), where f(x s ) is the predicted value of the s-th test sample, and y s is the corresponding measured value.

[0105] In the case, the monitoring data (test samples) in 2018 were input into the optimal least squares support vector machine prediction model, and the residuals ε s between the measured seat displacement and the model prediction value were calculated.

[0106] (7) Conduct intelligent early warning for the seat displacement.

[0107] Compare the calculated residual deformation ε s of the test samples with the confidence interval [μ e - kσ e , μ e + kσ e to determine whether the change in the seat displacement is normal. If ε s is within the confidence interval [μ e - kσ e , μ e + kσ e , it indicates that the change in the seat displacement at time t s is normal; if ε s is outside the confidence interval [μ e - kσ e , μ e + kσ e , it indicates that the change in the seat displacement at time t sAn abnormal state different from the historical statistical information occurred at the end of the time structure, thus triggering a warning.

[0108] In the case, the residual ε between the measured results of the bearing displacement and the model prediction values in 2018 s are all within the threshold level, as Figure 7 shown, indicating that the change in the bearing displacement is normal and no damage occurs.

Claims

1. An intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data, characterized in that: The method includes the following steps: (1) Obtain temperature indicators and bearing displacement monitoring data; (2) Calculate the longitudinal, vertical, and lateral temperature differences of the steel truss beam structure; (3) Conduct principal component analysis on the temperature indicators to extract the principal components affecting the bearing displacement; (4) Establish an optimal least squares support vector machine prediction model; (5) Determine the warning threshold for bearing displacement; (6) Calculate the displacement residuals of the test samples; (7) Conduct intelligent warning for the bearing displacement.

2. The intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data according to claim 1, characterized in that: The said step (1) includes obtaining the temperature indexes and the monitoring data of the bearing displacement for two years. The sampling frequencies of the temperature indexes and the monitoring data are the same, both being collected once per hour. The temperature indexes include the ambient temperature and the temperature of the steel truss girder structure. Denote the ambient temperature at the i-th moment as T i , where i = 1, 2, …, n, and n is the total amount of ambient temperature data; The average temperature of the j-th section of the steel truss girder is denoted as m is the number of temperature measurement sections; the average temperatures at the top and bottom of the steel truss girder section are denoted as and The average temperatures at the upstream and downstream of the steel truss girder section are denoted as and 3. The intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data according to claim 1, characterized in that: The step (2) includes assuming that the longitudinal temperature difference of the steel truss girder at the i-th moment is LTG i , the vertical temperature difference is VTG i and the transverse temperature difference is TTG i , and the expressions are respectively: where \(i = 1, 2, \ldots, n\), and \(n\) is the total amount of ambient temperature data, and respectively represent the average temperatures at the \(k\)-th cross-section and the \(g\)-th cross-section at the \(i\)-th moment.

4. The intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data according to claim 1, wherein: The step (3) includes the following steps: (3.1) The temperature index, i.e., the ambient temperature T i , the longitudinal temperature difference of the steel truss girder LTG i , the vertical temperature difference VTG i and the transverse temperature difference TTG i form the original data matrix X = (x ir ), n×t where x ie is the observed value of the r-th temperature index at the i-th moment, i = 1, 2,..., n, r = 1, 2,..., t, and t is the number of temperature indices; (3.2) Standardize the original data matrix X = (x ir ) n×t to obtain a new set of indicators Y1, Y2, ……, Y T , which form the matrix Y = (y ir ) n×t , where y ir is the observed value of the i-th row and r-th column, expressed as: Among them, (3.3) Calculate the covariance between each index in matrix Y to obtain the correlation coefficient matrix R = (r ir ) t×t , where r ir is the value at the i-th row and r-th column of matrix R, reflecting the correlation degree between index Y i and Y r . (3.4) Solve for the \(t\) eigenvalues \(\lambda_1\geq\lambda_2\geq\cdots\geq\lambda_t\) of matrix \(R\), t and the corresponding normalized eigenvectors \(u_1, u_2, \cdots, u_t\), t where \(u_r=(u_{r1}, u_{r2}, \cdots, u_{rp})\), \(r = 1, 2, \cdots, t\). Then the \(r\)th principal component \(Z_r\) r is expressed as: r1 r2 rt ) T r ​ Z r = μ r1 Y1 + μ r2 Y2 + … + μ r Y t (3.5) Calculate the variance contribution rate α of the r-th principal component Z r and the cumulative variance contribution rate γ of the first c principal components. The expressions are as follows: r ​ Usually, the first c (c ≤ t) principal components with the cumulative variance contribution rate λ ≥ 85% are selected to replace the original t indicators. These c principal components can comprehensively reflect the information of the original temperature indicators.

5. The intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data according to claim 1, characterized in that: The step (4) includes inputting the principal components and the standardized bearing displacement, and training the least squares support vector machine prediction model. The expression is: where x i is the input vector of the i-th sample; α i is the Lagrange multiplier; b is the bias; is the radial basis type kernel function, and σ is the kernel function parameter; Based on the principle of minimizing the structural risk, the above nonlinear regression problem is solved through the following optimization problem: Among them, γ is the penalty factor; e i is the error between the model prediction value and the actual value; the genetic algorithm is used to optimize the kernel function parameter σ and the penalty factor γ.

6. The intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data according to claim 5, characterized in that: The steps of optimizing the parameters σ and γ using the genetic algorithm include: (4.1) Determine the maximum number of evolutionary generations, population size, and the value ranges of the parameters σ and the kernel function parameter γ; (4.2) Randomly generate W individuals G within the value ranges of parameters σ and γ t , where t = 1, 2,..., W, to form an initial population, and the individuals adopt real number coding (4.3) Decode the individual into the actual value in the solution space and assign it to σ and γ. Use the extracted principal components and displacement samples to train the LSSVM model, and calculate the fitness F of each individual G t of t , and its expression is: where f(x i ) is the predicted value of the i-th training sample, and y i is the corresponding measured value; (4.4) Through genetic operations of selection, crossover, and mutation, eliminate the individuals with small fitness values and inherit the individuals with large fitness values to the next generation; (4.5) If the maximum number of evolutionary generations is reached, take the individual with the largest fitness value as the output, assign it to the penalty factor γ and the kernel function parameter σ, and obtain the optimal least squares support vector machine prediction model.

7. The intelligent early warning method for the displacement of the bearing of a railway-highway bridge based on long-term monitoring data according to claim 1, characterized in that: The step (5) includes calculating the residual deformation ε between the predicted value of the support displacement of the training sample and the measured result according to the obtained optimal least squares support vector machine prediction model i , where i = 1, 2,..., N, and the expression is: ε i = y i - f(x i ) where f(x i ) is the predicted value of the i-th training sample, and y i is the corresponding measured value; Then perform statistical analysis to obtain the mean μ of the displacement residuals e and the standard deviation σ e , and use the confidence interval as the early warning threshold for the bearing displacement. The expression is as follows: μ e -kσ e ≤ε i ≤μ e +kσ e where ε i is the residual deformation of the i-th training sample, and k is a coefficient.

8. The intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data according to claim 1, wherein: The step (6) includes inputting a new test sample and calculating the residual deformation ε of the test sample according to the optimal least squares support vector machine prediction model s , and the expression is: ε s = y s - f(x s ) where f(x s ) is the predicted value of the s-th test sample, and y s is the corresponding measured value.

9. The intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data according to claim 1, characterized in that: The step (7) includes the residual deformation ε of the calculated test sample s being compared with the confidence interval [μ e - kσ e , μ e + kσ e to determine whether the change in the bearing displacement is normal.

10. The intelligent early warning method for the displacement of the bearing of a combined road-rail bridge based on long-term monitoring data according to claim 9, wherein: After comparison, if ε s is within the confidence interval [μ e -kσ e , μ e +kσ e , it indicates that the change in the displacement of the support at time t s is normal; after comparison, if ε s is outside the confidence interval [μ e -kσ e , μ e +kσ e , it indicates that an abnormal state different from the historical statistical information has occurred at the end of the structure at time t s , thus giving an early warning.

Images