Physical and data hybrid driven suspension bridge dynamic response prediction method under main shock and aftershock

Abstract

The invention discloses a physical and data hybrid driven suspension bridge dynamic response prediction method under main and aftershocks, and relates to the technical field of suspension bridge earthquake response prediction. Determining an acceleration time program sequence of main and aftershock vibration; aiming at the ground anchor type steel truss suspension bridge, considering the uncertainty of key parameters, and establishing a finite element model; collecting bridge output parameters, establishing a data set and dividing the data set into a training set and a verification set; carrying out normalization processing on the data; establishing a physical constraint equation, and solving a main beam midspan longitudinal displacement wave under physical constraint; constructing a machine learning model by using the training set based on ANN and LSTM; establishing a machine learning model loss function; verifying the machine learning model; and a machine learning model is utilized to predict main beam midspan longitudinal displacement waves. According to the method, the displacement time history considering the uncertainty of the key parameters and under the action of main and aftershock seismic actions can be calculated, and the adverse effect caused by the fact that the uncertainty of the key parameters and the aftershock stage cannot be considered in a traditional prediction method is made up.

Description

Technical Field

[0001] The invention relates to the technical field of earthquake response prediction of suspension bridges, in particular to a method for predicting dynamic response of suspension bridges under main and aftershocks driven by a hybrid of physics and data. Background Art

[0002] In the field of bridge seismic research, the application of deep learning is still in the exploratory stage, especially in the prediction of bridge seismic response, where there is still a large gap in research. However, more and more scholars have realized the importance of machine learning technology in the field of bridge seismic resistance. For example, after studying the seismic analysis methods of small and medium-span bridges, Wang Kehai and others pointed out that bridge seismic analysis based on artificial intelligence will become the future development direction. Jia Junfeng, Guo Wei and other scholars further believe that machine learning and emerging technologies such as artificial intelligence combined with efficient algorithms are expected to provide more efficient and scientific solutions for reasonable seismic parameter identification, seismic input selection, bridge earthquake damage prediction, earthquake damage identification, and rapid post-earthquake assessment.

[0003] As one of the most widely used and effective algorithms in the current field of machine learning, deep learning has important significance in the research and application of bridge seismic resistance. However, the current research on bridge seismic response prediction is mainly focused on beam bridges, and there is still a blank in the response time history prediction of suspension bridges, especially ground-anchored steel truss suspension bridges. At the same time, the introduction of physical constraint methods in machine learning can greatly improve the accuracy of the model. In addition, in the actual bridge construction process, bridge parameters often differ from the design drawings due to construction errors, and the uncertainty of such parameters also has a certain impact on the prediction of seismic response. Therefore, when predicting the seismic response of bridges, it is very necessary to incorporate the uncertainty of actual parameters into the analysis. Taking the above aspects into consideration, the present invention proposes a method for predicting the dynamic response of suspension bridges under main and aftershocks driven by a hybrid of physics and data. Summary of the invention

[0004] In order to address the shortcomings of the background technology, the present invention provides a method for predicting the dynamic response of a suspension bridge under mainshocks and aftershocks driven by a hybrid of physics and data. It is aimed at predicting the time history of seismic response of a ground-anchored steel truss suspension bridge, and can calculate the displacement time history considering the uncertainty of key parameters and the action of mainshock and aftershock earthquakes, thereby compensating for the adverse effects of traditional prediction methods that cannot consider the uncertainty of key parameters and the aftershock stage.

[0005] To achieve the above object, the present invention adopts the following technical scheme: a method for predicting the dynamic response of a suspension bridge under main and aftershocks driven by a hybrid of physics and data, comprising the following steps:

[0006] Step 1: Determine the main and aftershock ground motions

[0007] The summarized mainshock-aftershock ground motion consists of three stages, including the mainshock stage, the gap stage and the aftershock stage;

[0008] (1) Determination of the main shock stage after induction: Select n main shock ground motions, whose peak acceleration should conform to the normal distribution. The peak acceleration of the main shock stage after induction is recorded as PGA mso ;

[0009] (2) The duration of the gap phase after induction is set to 30 s;

[0010] (3) Determination of the aftershock stage after induction: Calculate the peak acceleration of the aftershock ground motion corresponding to each main shock ground motion, which should conform to the normal distribution. The peak acceleration of the aftershock stage after induction is recorded as PGA zoo ;

[0011] According to the calculated PGA mso and PGA zoo Determine the acceleration time history of the main aftershock ground motion and record the acceleration time history of the main shock stage as The gap stage is recorded as The acceleration time history of the aftershock stage is recorded as Then the analytical expression of the acceleration time series of the main aftershock ground motion is:

[0012]

[0013] Step 2: Create a finite element model

[0014] For the ground-anchored steel truss suspension bridge, eight key design parameters are determined, including the main beam span l span , the initial strain of the main cable ε0, the diameter of the main cable d d1 , boom diameter d d2 , bridge tower height h tower , concrete strength E c , Suspension steel strength E sd and the main beam steel strength E sz ;

[0015] Taking into account the uncertainty of key parameters in actual situations, an error value is added or subtracted for each key parameter according to the requirements to form the corresponding allowable range of the key parameters, and the allowable range of the key parameters is divided into m equal parts. M sampling points are randomly selected from each partition of the allowable range of the key parameters, and then the sampling matrix X is obtained by combining them as follows:

[0016]

[0017] Sampling is performed in the sampling matrix X, one point is randomly sampled in each row, and a corresponding acceleration time sequence of the main shock and aftershock ground motion is selected to form m groups of sample pairs, and the sample set A of the main shock and aftershock ground motion-anchored steel truss suspension bridge structure is constructed. η It is expressed as follows:

[0018]

[0019] Finite element model was established using finite element software. Sample set A η A finite element model is established for each pair of samples in a row, and a total of m finite element models are established;

[0020] Step 3: Collect bridge output parameters

[0021] Output the longitudinal displacement wave Δδ1,...,Δδ of the main beam corresponding to each finite element model in the finite element software j , establish the data set T corresponding to the input and output of each finite element model o It is expressed as follows:

[0022]

[0023] The dataset T o Divide into training set T according to 7:3 o1 and validation set T o2 , which is expressed as follows:

[0024]

[0025] Step 4: Process the dataset

[0026] For the data set T o The data in are normalized to be in the range of 0 to 1, and the normalized training set and validation set are obtained;

[0027] Step 5: Establish physical constraint equations

[0028] Using physical constraint equations to construct the acceleration time sequence of mainshock and aftershock ground motions The longitudinal displacement wave Δδ of the main beam at mid-span under physical constraints p =Δδ p,1 ,...,Δδ p,j The relationship between them is expressed as follows:

[0029]

[0030] In the formula, M represents the mass matrix of the structure, C represents the damping matrix, and K represents the stiffness matrix;

[0031] Under the initial condition Δδ p =0, In the case of , the gradient recursive method is used to solve the longitudinal displacement wave Δδ of the main beam mid-span under the physical constraints of each finite element model in the training set. p , which is expressed as follows:

[0032]

[0033] In the formula, Δδ p,t Denotes Δδ p The displacement of the node at time t, t = 1, ..., j, ζ represents the damping ratio, ω represents the fundamental frequency of the structure, f t represents the system mass recovery force, Δt represents the time interval;

[0034] Step 6: Build a machine learning model

[0035] Input any row in the normalized training set as parameter Denoted as y η , the corresponding output parameters Δδ1,...,Δδ j Denoted as c η =c1,...,c j , the transfer function s is determined by ANN artificial neural network modeling, which is expressed as follows:

[0036] c η =s(y η W i +b i )

[0037]

[0038] Where W i and b i Represent the weight and bias term of nonlinear mapping respectively;

[0039] The LSTM long short-term memory model is modeled as a machine learning model, which consists of an input gate, a forget gate, and an output gate, expressed as:

[0040] Input gate: r η =s(W t y η +U t y η-1 +b t )

[0041] Forget gate: h η =s(W h y η +U h y η-1 +b h )

[0042] f η =tanh(Wf y η +U f y η-1 +b f )

[0043] o η =s(W o y η +U o y η-1 +b o )

[0044]

[0045] Output gate: c η =h η *c η-1 +r η *f η

[0046] h η =o η *tanh(c η )

[0047] Where W t , W h , W f , W o represents the corresponding weight, U t , U h , U f , U o represents the corresponding hidden weight, b t 、b h 、b f 、b o represents the corresponding bias term;

[0048] Step 7: Establish a machine learning model loss function

[0049] The longitudinal displacement wave of the main beam at mid-span predicted by the machine learning model is denoted as χ η =χ1,...,χ j , use the loss function to quantify the error between the predicted value and the true value, and the loss function of the physical constraint is recorded as L p , the data-constrained loss function is recorded as L d , using mean square error as the objective function, the total function of the constraint is recorded as L, which is expressed as follows:

[0050]

[0051] L=αL p +βL d

[0052] α+β=1

[0053] In the formula, λ p and λ d Represent the overfitting adjustment value introduced by the loss function of physical constraints and data constraints, ω p and ω d Represent the optimization parameters of the loss functions for physical constraints and data constraints respectively;

[0054] Step 8: Validate the machine learning model

[0055] The normalized validation set is imported into the machine learning model for validation. The prediction accuracy of the machine learning model is evaluated by the evaluation index. If the prediction value meets the required accuracy, it is used as the final machine learning model. If not, return to step 6 to retrain the machine learning model until it meets the requirements.

[0056] Step 9: Use machine learning models to make predictions

[0057] By inputting the selected new acceleration time sequence of mainshock and aftershock earthquake motions into the final machine learning model, the predicted longitudinal displacement wave of the main beam mid-span can be output.

[0058] Furthermore, in step 1, the selection rule of the main earthquake ground motion is:

[0059] ① The magnitude of the main earthquake is greater than 6.5;

[0060] ②The peak acceleration of each main shock ground motion record is greater than 0.2g;

[0061] ③The peak velocity of each main shock ground motion record is greater than 15 cm / s;

[0062] ④ The focal mechanism of the earthquake is a thrust fault or a strike-slip layer;

[0063] ⑤ The epicenter distance of the main earthquake is not less than 10 km;

[0064] ⑥ The effective period of the seismic wave of the main earthquake is not less than 4s.

[0065] Furthermore, in step 2, m sampling points are randomly selected from the allowable range of key parameters and the error values ​​corresponding to each key parameter are expressed as follows:

[0066] L span =(l span,1 ,...,l span,m ) T ,l span -2m≤l span,1 ,...,l span,m ≤l span +2m

[0067] E0=(ε 0,1 ,...,ε 0,m ) T ,ε0-0.0001≤ε 0,1 ,...,ε 0,m ≤ε0+0.0001

[0068] D d1 =(d d1,1 ,...,d d1,m ) T ,d d1 -5mm≤d d1,1 ,...,d d1,m ≤d d1 +5mm

[0069] D d2 =(d d2,1 ,...,d d2,m ) T ,d d2 -2mm≤d d2,1 ,...,d d2,m ≤d d2 +2mm

[0070] H tower =(h tower，1 ,...,h tower，m ) T ,h tower -1m≤h tower，1 ,...,h tower，m ≤h tower +1m

[0071]

[0072] Where, L span , E0, D d1 , D d2 , H tower , They respectively represent the vectors of sampling point combinations extracted from the allowed range of the corresponding key parameters.

[0073] Furthermore, in step 6, the AM attention mechanism is used to improve the accuracy of the machine learning model, as shown below:

[0074] e η =vtanh(W e h η +b e )

[0075]

[0076] In the formula, eη represents the attention score function, v represents the weight vector of the attention score function, W e represents the weight matrix of the attention score function, b e represents the bias term of the attention score function, γ η Attention weight, s η Represents the output layer of the attention mechanism.

[0077] Furthermore, in step eight, the root mean square error RMSE, mean absolute error MAE or R 2 Evaluation indicators.

[0078] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention significantly improves the accuracy and reliability of earthquake response prediction by introducing physical constraint equations and uncertainty modeling of key parameters. At the same time, the method can take into account the complex influence of key parameter uncertainty and mainshock and aftershock earthquake motions on the response of ground-anchored steel truss suspension bridges, overcoming the shortcomings of traditional prediction methods in dealing with key parameter uncertainty and aftershock stages. It not only realizes the accurate calculation of the displacement time history of the ground-anchored steel truss suspension bridge under the mainshock and aftershock earthquake motions, but also effectively improves the generalization ability and applicability of the prediction results, providing more scientific and efficient technical support for the seismic performance evaluation and optimization design of suspension bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 is a flow chart of the method of the present invention;

[0080] Figure 2 It is an acceleration time sequence diagram of a main shock and aftershock earthquake motion listed in the embodiment. DETAILED DESCRIPTION

[0081] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0082] like Figure 1 As shown in FIG. 1 , the method for predicting the dynamic response of a suspension bridge under main and aftershock shocks driven by a hybrid of physics and data includes the following steps:

[0083] Step 1: Determine the main and aftershock ground motions

[0084] The summarized mainshock-aftershock ground motion consists of three stages, including the mainshock stage, the gap stage and the aftershock stage.

[0085] (1) The method for determining the main shock stage after induction is as follows:

[0086] Select n main earthquake ground motions that meet the site conditions, n ≥ 200, and the selection rules are:

[0087] ① The magnitude of the main earthquake is greater than 6.5;

[0088] ②The peak acceleration of each main shock ground motion record is greater than 0.2g;

[0089] ③The peak velocity of each main shock ground motion record is greater than 15 cm / s;

[0090] ④ The focal mechanism of the earthquake is a thrust fault or a strike-slip layer;

[0091] ⑤ The epicenter distance of the main earthquake is not less than 10 km;

[0092] ⑥ The effective period of the seismic wave of the main earthquake is not less than 4s;

[0093] The peak acceleration of the selected n main shock ground motions is recorded as PGA ms , which should conform to the normal distribution, for the n PGA ms The peak acceleration of the main shock phase after induction is recorded as PGA mso , determined by the following formula:

[0094]

[0095] Where σ1 is PGA ms The standard deviation of PGA ms , a1 is the acceleration of the main shock ground motion;

[0096] (2) The duration of the gap phase after induction is set to 30 s;

[0097] (3) The method for determining the aftershock stage after induction is as follows:

[0098] The peak acceleration of each selected aftershock ground motion corresponding to the main shock ground motion is recorded as PGA zo , determined by the following formula:

[0099]

[0100] In the formula, m s is the magnitude of the main shock, δ M is the ratio of the magnitude of the aftershock to the magnitude of the main shock, v0 is the reference shear wave velocity, which is 760 m / s, and v s-30 is the average shear wave velocity of the selected main shock ground motion at a depth of 30 m, d sis the distance to the main shock fault, β1~β4 are the regression coefficients after fitting, obtained by fitting the main shock and aftershock ground motion sequences from the PEER database, β1=0.250, β2=3.986, β3=0.206, β4=0.012;

[0101] Calculated PGA zo Should conform to the normal distribution, for the n PGA zo The peak acceleration of the aftershock phase after induction is recorded as PGA zoo , determined by the following formula:

[0102]

[0103] Where σ2 is PGA zo The standard deviation of PGA zo a2 is the acceleration of aftershock ground motion.

[0104] According to the calculated PGA mso and PGA zoo Determine the acceleration time history of the main aftershock ground motion and record the acceleration time history of the main shock stage as The gap stage is recorded as The acceleration time history of the aftershock stage is recorded as Then the analytical expression of the acceleration time series of the main aftershock ground motion is:

[0105]

[0106] Step 2: Create a finite element model

[0107] For the ground-anchored steel truss suspension bridge, eight key design parameters are determined, including the main beam span l span , the initial strain of the main cable ε0, the diameter of the main cable d d1 , boom diameter d d2 , bridge tower height h tower , concrete strength E c , Suspension steel strength E sd , Main beam steel strength E sz .

[0108] Taking into account the uncertainty of key parameters in actual situations, an error value is added or subtracted for each key parameter according to the requirements to form the corresponding key parameter allowable range, and the key parameter allowable range is divided into m equal parts. The probability interval of each partition is 1 / m, so that the eight-dimensional space is divided into m 8 Partitions, randomly select a sampling point from each partition in the allowed range of each key parameter, that is, m sampling points are selected from each key parameter allowed range, and a total of 8m sampling points are selected, which are expressed as follows:

[0109] L span =(l span,1 ,...,l span,m ) T ,l span -2m≤l span,1 ,...,l span,m ≤l span +2m

[0110] E0=(ε 0,1 ,...,ε 0,m ) T ,ε0-0.0001≤ε 0,1 ,...,ε 0,m ≤ε0+0.0001

[0111] D d1 =(d d1,1 ,...,d d1,m ) T ,d d1 -5mm≤d d1,1 ,...,d d1,m ≤d d1 +5mm

[0112] D d2 =(d d2,1 ,...,d d2,m ) T ,d d2 -2mm≤d d2,1 ,...,d d2,m ≤d d2 +2mm

[0113] H tower =(h tower，1 ,...,h tower，m ) T ,h tower -1m≤h tower，1 ,...,h tower，m ≤h tower +1m

[0114]

[0115] Where, L span , E0, D d1 , D d2 , H tower , They respectively represent the vectors of sampling point combinations extracted from the allowed range of the corresponding key parameters.

[0116] The vectors of the sampling point combinations extracted from the allowed range of the eight key parameters are combined to obtain the sampling matrix X, which is expressed as follows:

[0117]

[0118] Sampling is performed in the sampling matrix X, one point is randomly sampled in each row, and a corresponding acceleration time sequence of the main shock and aftershock ground motion is selected to form m groups of sample pairs, and the sample set A of the main shock and aftershock ground motion-anchored steel truss suspension bridge structure is constructed. η It is expressed as follows:

[0119]

[0120] Finite element model was established using finite element software. Sample set A η A finite element model is established for each pair of samples in a row, and a total of m finite element models are established;

[0121] Step 3: Collect bridge output parameters

[0122] Output the longitudinal displacement wave Δδ1,...,Δδ of the main beam corresponding to each finite element model in the finite element software j , establish the data set T corresponding to the input and output of each finite element model o It is expressed as follows:

[0123]

[0124] The dataset T o Divide into training set T in proportion o1 and validation set T o2 , preferably divided according to 7:3, as shown below:

[0125]

[0126] Step 4: Process the dataset

[0127] For the data set T o The data in is normalized to be in the range of 0 to 1, and the normalized training set and validation set are obtained. The normalization is expressed as follows:

[0128]

[0129] In the formula, x represents the data in the data set, x min and x max Respectively represent the minimum and maximum values ​​of each parameter, x n Represents the processed data;

[0130] Step 5: Establish physical constraint equations

[0131] Using physical constraint equations to construct the acceleration time sequence of mainshock and aftershock ground motions The longitudinal displacement wave Δδ of the main beam at mid-span under physical constraints p =Δδ p,1 ,...,Δδ p,j The relationship between them is expressed as follows:

[0132]

[0133] Where M represents the mass matrix of the structure, C represents the damping matrix, and K represents the stiffness matrix.

[0134] Under the initial condition Δδ p =0, In the case of , the equilibrium condition can be written in the form of a state space vector, and the gradient recursion method is used to solve the longitudinal displacement wave Δδ of the main beam mid-span under the physical constraints of each finite element model in the training set. p , which is expressed as follows:

[0135]

[0136] In the formula, Δδ p,t Denotes Δδ p The displacement of the node at time t, t = 1, ..., j, ζ represents the damping ratio, ω represents the fundamental frequency of the structure, f t represents the system mass recovery force, Δt represents the time interval;

[0137] Step 6: Build a machine learning model

[0138] ANN-LSTM is used for machine learning, where ANN artificial neural network is used to extract the o The LSTM long short-term memory model is used to learn the long-term changes in the relationship between input and output.

[0139] Input any row in the normalized training set as parameter Denoted as y η , the corresponding output parameters Δδ1,...,Δδ j Denoted as c η =c1,...,c j , the transfer function s is determined by ANN artificial neural network modeling, which is expressed as follows:

[0140] c η =s(y η W i +b i )

[0141]

[0142] Where W i and b iThey represent the weight and bias of nonlinear mapping respectively.

[0143] The LSTM long short-term memory model is modeled as a machine learning model, which consists of an input gate, a forget gate, and an output gate, expressed as:

[0144] Input gate: r η =s(W t y η +U t y η-1 +b t )

[0145] Forget gate: h η =s(W h y η +U h y η-1 +b h )

[0146] f η =tanh(W f y η +U f y η-1 +b f )

[0147] o η =s(W o y η +U o y η-1 +b o )

[0148]

[0149] Output gate: c η =h η *c η-1 +r η *f η

[0150] h η =o η *tanh(c η )

[0151] Where W t , W h , W f , W o represents the corresponding weight, U t , U h , U f , U o represents the corresponding hidden weight, b t , b h , b f , b orepresents the corresponding bias term.

[0152] The AM attention mechanism is used to improve the accuracy of the machine learning model, as shown below:

[0153] e η =vtanh(W e h η +b e )

[0154]

[0155] In the formula, e η represents the attention score function, v represents the weight vector of the attention score function, W e represents the weight matrix of the attention score function, b e represents the bias term of the attention score function, γ η Attention weight, s η Represents the output layer of the attention mechanism;

[0156] Step 7: Establish a machine learning model loss function

[0157] The longitudinal displacement wave of the main beam at mid-span predicted by the machine learning model is denoted as χ η =χ1,...,χ j , use the loss function to quantify the error between the predicted value and the true value, and the loss function of the physical constraint is recorded as L p , the data-constrained loss function is recorded as L d , using mean square error as the objective function, the total function of the constraint is recorded as L, which is expressed as follows:

[0158]

[0159] L=αL p +βL d

[0160] α+β=1

[0161] In the formula, λ p and λ d Represent the overfitting adjustment value introduced by the loss function of physical constraints and data constraints, ω p and ω d Represent the optimization parameters of the loss functions for physical constraints and data constraints respectively;

[0162] Step 8: Validate the machine learning model

[0163] The normalized validation set is imported into the machine learning model for validation, and the root mean square error (RMSE), mean absolute error (MAE), or R 2The prediction accuracy of the machine learning model is evaluated by the evaluation index. If the prediction value meets the required accuracy, it is used as the final machine learning model. If not, return to step 6 to retrain the machine learning model until it meets the requirements.

[0164] Step 9: Use machine learning models to make predictions

[0165] By inputting the selected new acceleration time sequence of mainshock and aftershock earthquake motions into the final machine learning model, the predicted longitudinal displacement wave of the main beam mid-span can be output.

[0166] Example

[0167] Taking Dalian Xinghaiwan Cross-sea Bridge as an example, the displacement time history data under the action of main shock and aftershock earthquake motions are predicted by the method of the present invention.

[0168] S1. Determine the main shock and aftershock ground motions

[0169] (1) Determination of the main shock stage after induction

[0170] 200 main earthquake ground motions that meet the site conditions are selected, and one main earthquake ground motion (Duzce, Turkey) is taken as an example:

[0171] ① Magnitude of the main earthquake (m) s =7.14;

[0172] ② The peak acceleration PGA of each main shock ground motion record is 0.35g;

[0173] ③ The peak velocity of each main shock ground motion record is PGV = 59.99 cm / s;

[0174] ④ The focal mechanism of the earthquake is a thrust fault or a strike-slip layer;

[0175] ⑤ The epicenter distance of the main earthquake is x ee =20km;

[0176] ⑥ The effective period of the seismic wave of the main shock is T e =4.86s;

[0177] The peak acceleration PGA of these 200 main shock ground motions ms After induction, the peak acceleration PGA of the main shock phase is mso as follows:

[0178]

[0179] (2) The duration of the gap phase after induction is set to 30 s;

[0180] (3) Determination of aftershock stages after induction

[0181] The peak acceleration PGA of the aftershock ground motion corresponding to each selected main shock ground motion zo as follows:

[0182]

[0183] Calculated PGA zo Should conform to the normal distribution, the 200 PGA zo The peak acceleration PGA of the aftershock phase after induction is zoo as follows:

[0184]

[0185] According to the calculated PGA mso and PGA zoo Determine the acceleration time sequence of the main aftershock earthquake motion. Take one of them as an example. The acceleration time sequence of the main aftershock earthquake motion is combined with Figure 2 shown.

[0186] S2. Establish finite element model

[0187] Taking into account the uncertainty of key parameters in actual situations, an error value is added or subtracted for each key parameter to form the corresponding allowable range of key parameters, and the allowable range of key parameters is divided into 10 equal parts. The probability interval of each partition is 1 / 10, so that the eight-dimensional space is divided into 10 8 Partitions are selected, and a sampling point is randomly selected from each partition in the allowable range of each key parameter, that is, 10 sampling points are selected from each allowable range of each key parameter, and a total of 80 sampling points are selected. The design of key parameters and the parameters extracted considering the uncertainty of key parameters in actual situations are shown in Table 1:

[0188] Table 1 Key design parameters and parameters extracted considering the uncertainty of key parameters in actual situations

[0189]

[0190]

[0191] The vectors of the sampling point combinations extracted from the allowed range of the eight key parameters are combined to obtain the sampling matrix X, which is expressed as follows:

[0192]

[0193] Sampling is performed in the sampling matrix X, one point is randomly sampled in each row, and a corresponding acceleration time sequence of the main shock and aftershock ground motion is selected to form 10 groups of sample pairs, and the sample set A of the main shock and aftershock ground motion-anchored steel truss suspension bridge structure is constructed.η It is expressed as follows:

[0194]

[0195] Finite element model was established using finite element software. Sample set A η A finite element model is established for each pair of samples in a row, and a total of 10 finite element models are established.

[0196] S3. Collect bridge output parameters

[0197] Output the longitudinal displacement wave Δδ1,...,Δδ of the main beam corresponding to each finite element model in the finite element software j , establish the data set T corresponding to the input and output of each finite element model o , dataset T o Some of the data are shown in Table 2:

[0198] Table 2 Collection output parameters (partial)

[0199]

[0200]

[0201] S4. Processing Dataset

[0202] For the data set T o The data in are normalized to be within the range of 0 to 1, and the normalized training set and validation set are obtained. Some of the data are shown in Table 3:

[0203] Table 3 Normalized data set (part)

[0204]

[0205]

[0206] S5. Establish physical constraint equations

[0207] The TensorFlow open source library is called to build a spatiotemporal correlation mechanism model, and the optimizer and loss function are selected. The physical constraint equation is established in the compute_physics_constraint function, and the longitudinal displacement wave eta_p of the main beam mid-span under the physical constraint is calculated.

[0208] S6. Build a machine learning model

[0209] Create ANN layer: This part is the ANN network constructed by the ANN_model method to extract features from the input data.

[0210] Create an input layer: The input layer receives data through the Conv1D layer, where the input shape is (4838,1), that is, the data dimension of each time step is 4838, and there is only 1 feature at each time step.

[0211] Create LSTM layer: This is done through TensorFlow's LSTM layer. We have already extracted features through the ANN layer, and we can use matrix operations (tf.matmul) in the LSTM layer to calculate eta_t and eta_tt.

[0212] Create the output layer: The output layer is used to predict the target variables: eta_pred and eta_tt_pred based on the model's calculation results. Through the self.net_structure() function, the model can calculate these outputs and finally get the predicted values ​​through the network structure.

[0213] The training cycle is specified as 10,000 iterations, and the model is trained using the train method. The batch size is set to 32 for batch gradient updates. The Adam optimizer is used with a learning rate of 1e-3 and a loss function combined with physical constraints for training.

[0214] The AM attention mechanism is implemented through the Multi Head Attention layer in TensorFlow.

[0215] S7. Establishing the loss function of the machine learning model

[0216] The loss function is established by the calculate_loss function. The data loss establishes the mean square error between eta_tt and eta_tt_pred, and the physical constraint loss calls the compute_physics_constraint function to establish the mean square error between eta_p and eta_tt.

[0217] S8. Validate the machine learning model

[0218] The verification results are shown in Table 4:

[0219] Table 4 Prediction results of validation set data (partial)

[0220]

[0221]

[0222] The calculated root mean square error RMSE = 0.017, the mean absolute error MAE = 0.014, R 2 =0.989. S9. Prediction using machine learning models

[0223] Some of the predicted results are shown in Table 5:

[0224] Table 5 Results of model prediction (partial)

[0225]

[0226]

[0227] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0228] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for predicting the dynamic response of a suspension bridge under main and aftershock shocks driven by a combination of physics and data, characterized by: The following steps are involved: Step 1: Determine the main and aftershock ground motions The summarized mainshock-aftershock ground motion consists of three stages, including the mainshock stage, the gap stage and the aftershock stage; (1) Determination of the main shock stage after induction: Select n main shock ground motions, whose peak acceleration should conform to the normal distribution. The peak acceleration of the main shock stage after induction is recorded as PGA mso ; (2) The duration of the gap phase after induction is set to 30 s; (3) Determination of the aftershock stage after induction: Calculate the peak acceleration of the aftershock ground motion corresponding to each main shock ground motion, which should conform to the normal distribution. The peak acceleration of the aftershock stage after induction is recorded as PGA zoo ; According to the calculated PGA mso and PGA zoo Determine the acceleration time history of the main aftershock ground motion and record the acceleration time history of the main shock stage as The gap stage is recorded as The acceleration time history of the aftershock stage is recorded as Then the analytical expression of the acceleration time series of the main aftershock ground motion is: Step 2: Create a finite element model For the ground-anchored steel truss suspension bridge, eight key design parameters are determined, including the main beam span l span , initial strain of main cable ε0, main cable diameter d d1 , boom diameter d d2 , bridge tower height h tower , concrete strength E c , Suspension steel strength E sd and the main beam steel strength E sz ; Taking into account the uncertainty of key parameters in actual situations, an error value is added or subtracted for each key parameter according to the requirements to form the corresponding allowable range of the key parameters, and the allowable range of the key parameters is divided into m equal parts. M sampling points are randomly selected from each partition of the allowable range of the key parameters, and then the sampling matrix X is obtained by combining them as follows: Sampling is performed in the sampling matrix X, one point is randomly sampled in each row, and a corresponding acceleration time sequence of the main shock and aftershock ground motion is selected to form m groups of sample pairs, and the sample set A of the main shock and aftershock ground motion-anchored steel truss suspension bridge structure is constructed. η It is expressed as follows: Finite element model was established using finite element software. Sample set A η A finite element model is established for each pair of samples in a row, and a total of m finite element models are established; Step 3: Collect bridge output parameters Output the longitudinal displacement wave Δδ1,...,Δδ of the main beam corresponding to each finite element model in the finite element software j , establish the data set T corresponding to the input and output of each finite element model o It is expressed as follows: The dataset T o Divide into training set T according to 7:3 o1 and validation set T o2 , which is expressed as follows: Step 4: Process the dataset For the data set T o The data in are normalized to be in the range of 0 to 1, and the normalized training set and validation set are obtained; Step 5: Establish physical constraint equations Using physical constraint equations to construct the acceleration time sequence of mainshock and aftershock ground motions The longitudinal displacement wave Δδ of the main beam at mid-span under physical constraints p =Δδ p,1 ,...,Δδ p,j The relationship between them is expressed as follows: In the formula, M represents the mass matrix of the structure, C represents the damping matrix, and K represents the stiffness matrix; At the initial condition In the case of , the gradient recursive method is used to solve the longitudinal displacement wave Δδ of the main beam mid-span under the physical constraints of each finite element model in the training set. p , which is expressed as follows: In the formula, Δδ p,t Denotes Δδ p The displacement of the node at time t, t = 1, ..., j, ζ represents the damping ratio, ω represents the fundamental frequency of the structure, f t represents the system mass recovery force, Δt represents the time interval; Step 6: Build a machine learning model Input any row in the normalized training set as parameter Denoted as y η , the corresponding output parameters Δδ1,...,Δδ j Denoted as c η =c1,...,c j , the transfer function s is determined by ANN artificial neural network modeling, which is expressed as follows: c η =s(y η W i +b i ) Where W i and b i Represent the weight and bias term of nonlinear mapping respectively; The LSTM long short-term memory model is modeled as a machine learning model, which consists of an input gate, a forget gate, and an output gate, expressed as: Input gate: r η =s(W t y η +U t y η-1 +b t ) Forget gate: h η =s(W h y η +U h y η-1 +b h ) f η =tanh(W f y η +U f y η-1 +b f ) o η =s(W o y η +U o y η-1 +b o ) Output gate: c η =h η *c η-1 +r η *f η h η =o η *tanh(c η ) Where W t , W h , W f , W o represents the corresponding weight, U t , U h , U f , U o represents the corresponding hidden weight, b t , b h , b f , b o represents the corresponding bias term; Step 7: Establish a machine learning model loss function The longitudinal displacement wave of the main beam at mid-span predicted by the machine learning model is denoted as χ η =χ1,...,χ j , use the loss function to quantify the error between the predicted value and the true value, and the loss function of the physical constraint is recorded as L p , the data-constrained loss function is recorded as L d , using mean square error as the objective function, the total function of the constraint is recorded as L, which is expressed as follows: L=αL p +βL d α+β＝1 In the formula, λ p and λ d Represent the overfitting adjustment value introduced by the loss function of physical constraints and data constraints, ω p and ω d Represent the optimization parameters of the loss functions for physical constraints and data constraints respectively; Step 8: Validate the machine learning model The normalized validation set is imported into the machine learning model for validation. The prediction accuracy of the machine learning model is evaluated by the evaluation index. If the prediction value meets the required accuracy, it is used as the final machine learning model. If not, return to step 6 to retrain the machine learning model until it meets the requirements. Step 9: Use machine learning models to make predictions By inputting the selected new acceleration time sequence of mainshock and aftershock earthquake motions into the final machine learning model, the predicted longitudinal displacement wave of the main beam mid-span can be output.

2. The method for predicting dynamic response of suspension bridge under main and aftershocks driven by physical and data hybrid according to claim 1 is characterized by: In step 1, the selection rule of the main earthquake ground motion is: ① The magnitude of the main earthquake is greater than 6.5; ②The peak acceleration of each main shock ground motion record is greater than 0.2g; ③The peak velocity of each main shock ground motion record is greater than 15 cm / s; ④ The focal mechanism of the earthquake is a thrust fault or a strike-slip layer; ⑤ The epicenter distance of the main earthquake is not less than 10 km; ⑥ The effective period of the seismic wave of the main earthquake is not less than 4s.

3. The method for predicting dynamic response of suspension bridge under main and aftershocks driven by physical and data hybrid according to claim 1 is characterized by: In step 2, m sampling points are randomly selected from the allowable range of key parameters, and the error values ​​corresponding to each key parameter are expressed as follows: L span =(l span,1 ,...,l span,m ) T ,l span -2m≤l span,1 ,...,l span,m ≤l span +2m E0=(e 0,1 ,...,eh 0,m ) T ,ε0-0.0001≤ε 0,1 ,...,eh 0,m ≤ε0+0.0001 D d1 =(d d1,1 ,...,d d1,m ) T ,d d1 -5mm≤d d1,1 ,...,d d1,m ≤d d1 +5mm D d2 =(d d2,1 ,...,d d2,m ) T ,d d2 -2mm≤d d2,1 ,...,d d2,m ≤d d2 +2mm H tower =(h tower，1 ,...,h tower，m ) T ,h tower -1m≤h tower，1 ,...,h tower，m ≤h tower +1m Where, L span , E0, D d1 , D d2 , H tower , They respectively represent the vectors of sampling point combinations extracted from the allowed range of the corresponding key parameters.

4. The method for predicting dynamic response of suspension bridge under main and aftershocks driven by physical and data hybrid according to claim 1 is characterized by: In step 6, the AM attention mechanism is used to improve the accuracy of the machine learning model, as shown below: have been η =vtanh(W e h η +b e ) In the formula, e η represents the attention score function, v represents the weight vector of the attention score function, W e represents the weight matrix of the attention score function, b e represents the bias term of the attention score function, γ η Attention weight, s η Represents the output layer of the attention mechanism.

5. The method for predicting dynamic response of suspension bridge under main and aftershocks driven by physics and data hybrid according to claim 1 is characterized by: In step 8, the root mean square error RMSE, mean absolute error MAE or R 2 Evaluation indicators.

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