Structure earthquake risk assessment method based on WiBS-PLS-RSM

Abstract

The invention discloses a structure earthquake risk assessment method based on WiBS-PLS-RSM. Firstly, design parameters of structural earthquake risk assessment and damage indexes of a to-be-assessed structure are determined; then, a training set (TrainX, TrainY) is determined, and the training set (TrainX, TrainY) is input into a width-adjustable basic spline partial least square response surface model (WiBS-PLS-RSM) for training; a test set (TestX, TestY) is input into the trained WiBS-PLS-RSM, verification is carried out through a decision coefficient R2, and finally, a total data set input variable sample TotalX is input into the verified WiBS-PLS-RSM to obtain a damage index considering design parameter uncertainty. According to the method, the problem of over-fitting or under-fitting of a traditional response surface model in earthquake risk assessment which is high in nonlinearity, multi-dimension and strong in data correlation and considers parameter uncertainty is effectively solved.

Description

TECHNICAL FIELD

[0001] The application relates to a structure seismic risk assessment method based on a WiBS-PLS-RSM (Width-tunable Basis Spline Partial Least Squares Response Surface Model), which is used for performing nonlinear time-history analysis on a calibrated numerical model to obtain structure seismic response, and efficiently and accurately constructing a structure seismic risk assessment model by using an improved response surface as a substitute model, and belongs to the technical field of improved response surface model prediction of structure risk values. BACKGROUND

[0002] Due to natural disasters, material aging, human damage and inherent structural defects, building structures and components suffer severe damage in previous earthquakes, resulting in a large number of casualties and property losses. In the performance-based seismic engineering framework, efficient and accurate pre-earthquake risk assessment of structures has become a key task. In the structure seismic risk assessment considering parameter uncertainty, nonlinear time-history analysis of the calibrated numerical model requires high data, time and operation costs. The traditional response surface model is used to replace the nonlinear time-history analysis process to obtain the structure seismic response, which can improve the analysis efficiency, but the prediction accuracy is difficult to meet the engineering requirements. In contrast, the basis spline partial least squares response surface model performs well in structure seismic response substitution modeling, but due to the fixed width of the spline function, only relying on the change of the number of segments can easily lead to overfitting or underfitting of the substitute model, thereby affecting the fitting effect of the nonlinear time-history analysis substitution modeling. SUMMARY

[0003] In view of the above problems, the application provides a structure seismic risk assessment method based on a WiBS-PLS-RSM. The WiBS-PLS-RSM introduces a width parameter on the basis of the traditional response surface model and cooperates with the number of segments to effectively solve the overfitting or underfitting problem of the traditional response surface model in the seismic risk assessment considering parameter uncertainty with high nonlinearity, multidimensionality and strong data correlation. Based on the verified WiBS-PLS-RSM, all structure damage indicators considering parameter uncertainty are generated, so as to efficiently and accurately construct a structure risk assessment model and provide a theoretical basis for subsequent seismic reinforcement.

[0004] The above object is achieved by the following technical scheme.

[0005] The structure seismic risk assessment method based on the WiBS-PLS-RSM is characterized in that the method comprises the following steps:

[0006] S1. Sensitivity analysis is used to determine the material parameters and geometric parameters of the finite element model of the structure to be evaluated, which is referred to as the design parameter of the structure seismic risk assessment. According to the research purpose, the damage index (DI) of the structure to be evaluated is determined;

[0007] S2. The distribution form, value range and sample size of the design parameter are determined by existing literature research or experiment, which is referred to as the statistical distribution of the design parameter. The statistical distribution of the design parameter is randomly sampled to obtain the total data set input variable sample Total_X. The uniform design table is used to determine the training set input variable sample Train_X of the response surface model. The number of samples randomly selected from the samples other than Train_X is not less than 0.25 times of it, which is used as the test set input variable sample Test_X of the response surface model. The finite element model corresponding to Train_X and Test_X is established in the existing modeling software, and the nonlinear time history analysis of the structure finite element model is carried out to obtain the damage index, that is, the training set output variable sample Train_Y and the test set output variable sample Test_Y of the response surface model are obtained;

[0008] S3. The training set (Train_X, Train_Y) is input into the width-adjustable basis spline partial least squares response surface model (WiBS-PLS-RSM) for training;

[0009] S4. The test set (Test_X, Test_Y) is input into the trained WiBS-PLS-RSM, and the coefficient of determination R 2 Verification, if R 2 ≥ 0.9, the WiBS-PLS-RSM training is completed, if R 2 < 0.9, adjust the width parameter and the number of segments of the WiBS-PLS-RSM, and reiterate the training until R 2 ≥ 0.9;

[0010] S5. The total data set input variable sample Total_X is input into the WiBS-PLS-RSM verified in step S4 to obtain the damage index considering the uncertainty of the design parameter. The seismic vulnerability analysis, seismic risk analysis and seismic loss analysis are used to obtain the structure vulnerability curve, the seismic risk curve and the structure damage curve respectively, and finally the structure seismic risk assessment model is obtained, so as to realize the efficient and accurate pre-earthquake risk assessment of the structure and the component, and provide a theoretical basis for subsequent seismic reinforcement.

[0011] Further, the sensitivity analysis in step S1 is used to determine the material parameters and geometric parameters of the finite element model of the structure to be evaluated, and the specific steps are as follows:

[0012] S11, initially select the parameters X_Initial which have influence on the structural finite element model, determine the sample of the parameter X_Initial according to engineering experience, then change the sample of the parameter, the change rate is 2%, the changed parameter is X_adjust, that is, X_adjust = (1+2%)·X_Initial;

[0013] S12, establish the finite element model corresponding to X_Initial and X_adjust in the existing modeling software and perform nonlinear time history analysis, respectively obtain the damage index Y_Initial corresponding to the initially selected parameter X_Initial and the damage index Y_adjust corresponding to the changed parameter X_adjust,

[0014] S13, calculate the sensitivity S of the parameter to the damage index, and select the parameter with S>0.8 as the input variable X, that is, .

[0015] Further, the training set (Train_X, Train_Y) in step S3 is input into the width-adjustable basis spline partial least squares response surface model (WiBS-PLS-RSM) for training, and the specific steps are as follows:

[0016] S31, define the number of segments M i , so as to determine the segment length h i , the node , that is, , , where x i is the i-th input variable of the training set; M i , h i and ξ i,l-1 are the spline space segment number, the spline space segment length and the l-1-th node of the i-th input variable, respectively; is the l-th node of the spline space;

[0017] S32, define the width parameter w, and convert the i-th input variable x i of the training set into the spline space variable z i , that is, , where is the value of the j-th sample of x i at the l-th node of the spline space; is the b-th spline basis function; is the j-th sample point of the i-th input variable of the training set;

[0018] S33, constructing a multiple linear function in the spline space, obtaining the regression coefficient by using the partial least squares method, and finally converting to the original space to construct the WiBS-PLS-RSM, that is, , , , wherein is the predicted value of the WiBS-PLS-RSM; β0and β i,l are self-defined parameters in the original space; p is the number of input variables of the training set; ε is the error term of the WiBS-PLS-RSM; is the mean of the output variable samples of the training set; is the mean of ; is the standard deviation of the output variable samples of the training set; s i,l is the standard deviation of ; a i,l is the regression coefficient of the multiple linear function;

[0019] Further, the step S4 is inputting the test set (Test_X, Test_Y) into the trained WiBS-PLS-RSM, and verifying by the coefficient of determination R 2 , and the specific formula is: , wherein is the predicted value of the WiBS-PLS-RSM, is the measured value of the nonlinear time history analysis, is the mean of the measured value.

[0020] Further, the step S5 is obtaining the structure vulnerability curve, the seismic risk curve and the structure loss curve by using the seismic vulnerability analysis, the seismic risk analysis and the seismic loss analysis respectively, and finally obtaining the structure seismic risk assessment model, and the specific steps are:

[0021] S51, inputting the total data set input variable sample Total_X into the verified WiBS-PLS-RSM to obtain all damage indexes considering the uncertainty of the design parameters, that is, the total data set output variable sample Total_Y, and constructing the structure vulnerability curve by using the seismic vulnerability analysis, that is, , , wherein is the structure vulnerability curve, DS is the structural damage state, DS b LS is the bth structural damage state, LS c n(DI ≥ LS c ) is the number of damage indices greater than or equal to the limit state, N is the number of damage index samples, and d is the number of total data set output variable samples Total_Y;

[0022] S52, constructing a seismic hazard curve using a seismic hazard analysis, i.e., ,

[0023] Table 1 Shape parameter k values for different fortification intensities Basic intensity 6 7 8 9 Shape parameter 9.793 8.334 6.871 5.403 where P h (IM) is the seismic hazard curve, IM is the seismic intensity, I0 is the fortification intensity, which can be obtained by consulting the Code for Seismic Design of Buildings GB 50011-2010, and k is the shape parameter for different fortification intensities, as shown in Table 1.

[0024] S53, constructing a structure loss curve using a seismic loss analysis, i.e., , , , , where L[IM] is the structure loss curve, L[DS b ], P L (DS b ), and P S (DS b ) are the economic loss, direct economic loss, and indirect economic loss of the structure in the damage state DS b , respectively, C h is the reconstruction cost of the building structure, C is the construction cost of the building structure, S is the damaged area of the building structure during an earthquake, X B , X BT , and DR are the building structure protection level coefficient, protection level adjustment coefficient, and damage loss ratio, respectively, which can be obtained by consulting the specification;

[0025] S54, constructing a structure seismic risk assessment model using the structure vulnerability curve of step S51, the seismic hazard curve of step S52, and the structure loss curve of step S53, i.e., , where R is the structure seismic risk value, which can be classified by the structure seismic risk grade classification table defined by the specification; BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 Flowchart for the present application

[0027] Figure 2 Sensitivity analysis of the top story peak displacement to design parameters

[0028] Figure 3 WiBS-PLS-RSM training iteration process for the mean of the top story peak displacement

[0029] Figure 4 WiBS-PLS-RSM training iteration process for the standard deviation of the top story peak displacement

[0030] Figure 5 Fitting results of the WiBS-PLS-RSM training set for the mean of the top story peak displacement

[0031] Figure 6 Fitting results of the WiBS-PLS-RSM training set for the standard deviation of the top story peak displacement

[0032] Figure 7 Prediction results of the WiBS-PLS-RSM test set for the mean of the top story peak displacement

[0033] Figure 8 Prediction results of the WiBS-PLS-RSM test set for the standard deviation of the top story peak displacement

[0034] Figure 9 Structural fragility curve

[0035] Figure 10 Seismic hazard curve

[0036] Figure 11 Structural loss curve

[0037] Figure 12 Structural seismic risk value curve DETAILED DESCRIPTION

[0038] The present application will be further described in conjunction with the embodiments and specific working examples. However, it should not be understood that the scope of the present application is limited to the following examples only, and any technology realized based on the content of the present application falls within the scope of the present application.

[0039] EMBODIMENT

[0040] Taking a masonry ancient tower structure as an example, the structural seismic risk assessment method based on WiBS-PLS-RSM of the present embodiment includes the following steps:

[0041] S1. Sensitivity analysis is used to determine the material parameters and geometric parameters of the finite element model of the masonry ancient tower structure, which is referred to as the design parameter of the structural seismic risk assessment. According to the research purpose, the damage index (DI) of the masonry ancient tower structure is determined, that is, the peak displacement of the tower top;

[0042] S2. The distribution form, value range and sample number of the design parameter are determined through existing literature research or test, which is referred to as the statistical distribution of the design parameter. The total data set input variable sample Total_X is obtained by random sampling of the statistical distribution of the design parameter. The training set input variable sample Train_X of the response surface model is determined by using the uniform design table on Total_X. The number of samples randomly selected from the samples other than Train_X is not less than 0.25 times of it, which is the test set input variable sample Test_X of the response surface model. The structure finite element model corresponding to Train_X and Test_X is established in the existing modeling software, and the nonlinear time history analysis is carried out on the structure finite element model to obtain the damage index, that is, the training set output variable sample Train_Y and the test set output variable sample Test_Y of the response surface model are obtained;

[0043] S3. The training set (Train_X, Train_Y) is input into the width-adjustable basis spline partial least squares response surface model (WiBS-PLS-RSM) for training;

[0044] S4. The test set (Test_X, Test_Y) is input into the trained WiBS-PLS-RSM, and the coefficient of determination R 2 Verification, if R 2 ≥ 0.9, the WiBS-PLS-RSM training is completed, if R 2 < 0.9, adjust the width parameter and the number of segments of the WiBS-PLS-RSM, and reiterate the training until R 2 ≥ 0.9 is met;

[0045] S5. The total data set input variable sample Total_X is input into the WiBS-PLS-RSM verified in step S4 to obtain the damage index considering the uncertainty of the design parameter. The seismic vulnerability analysis, seismic risk analysis and seismic loss analysis are used to obtain the structure vulnerability curve, the seismic risk curve and the structure damage curve respectively, and finally the structure seismic risk assessment model is obtained, so as to realize the efficient and accurate pre-earthquake risk assessment of the structure and the component, and provide a theoretical basis for subsequent seismic reinforcement.

[0046] The masonry ancient tower structure in step S1, the specific information of the masonry ancient tower is:

[0047] The tower is 34.246 m high, with a bottom diameter of 9.72 m. The tower body is built with blue bricks, in a cylindrical shape. The elastic modulus of the masonry material E = 818.7 MPa, the average compressive strength of the masonry f m = 2.44 MPa, the Poisson's ratio λ = 0.15, and the density ρ = 1707 kg / m 3 .

[0048] The sensitivity analysis in step S1 is used to determine the material parameters and geometric parameters of the finite element model affecting the masonry ancient tower structure. The specific steps are as follows:

[0049] S11, initially select parameters X_Initial that have an impact on the finite element model of the masonry ancient tower structure, including density ρ, masonry compressive peak stress f m , masonry compressive peak strain ε c , masonry compressive ultimate stress f cu , masonry compressive ultimate strain ε cu , masonry tensile ultimate strength f t , main tower bottom inner radius r mbi , main tower bottom outer radius r mbo , main tower top inner radius r mti , main tower top outer radius r mto , small tower bottom radius r sb , small tower top radius r st . Change each parameter sample by 2%, and the changed parameter is X_adjust, i.e., X_adjust = (1+2%)·X_Initial.

[0050] S12, establish the finite element model corresponding to X_Initial and X_adjust in the existing modeling software and perform nonlinear time history analysis, respectively, to obtain the damage index Y_Initial corresponding to the initially selected parameter X_Initial and the damage index Y_adjust corresponding to the changed parameter X_adjust. The modeling software used in this embodiment is OpenSees.

[0051] S13, calculate the sensitivity S of the parameter to the peak displacement of the tower top, i.e., .

[0052] S14, Figure 2 is the sensitivity analysis of 12 design parameters to the peak displacement of the tower top. Select parameters with S > 0.8 as input variables X, including 11 parameters other than the main tower top outer radius r mto .

[0053] The specific steps for determining the training set input variable samples Train_X of the response surface model using a uniform design table for Total_X in step S2 are as follows:

[0054] S21, based on the total dataset, determine the number of variables s=11 and the sample size of each variable a=60, and query the uniform design table U. 60 (60 11 This will give you 60 training set input variable samples, Train_X;

[0055] The steps described in step S3, which involve inputting the training set (Train_X, Train_Y) into a width-adjustable basic spline partial least squares response surface model (WiBS-PLS-RSM) for training, are as follows:

[0056] S31, Initially set the number of segments M i The value is 1, thus determining the segment length h. i ,node ,Right now, , , Where x i M is the i-th input variable in the training set; i h i and ξ i,l-1 These represent the number of spline space segments, the length of the spline space segment, and the (l-1)th node of the i-th input variable, respectively. Let l be the l-th node in the spline space;

[0057] S32, Define the width parameter w, and input the i-th variable x from the training set. i Transform into spline space variable z i ,Right now, , in For x i The value of the j-th sample at the l-th node in the spline space; These are third-order spline basis functions; For the j-th sample point of the i-th input variable in the training set;

[0058] S33, construct a multivariate linear function in spline space, obtain the regression coefficients using partial least squares method, and finally transform it into the original space to construct WiBS-PLS-RSM, i.e. , , , in is the predicted value of WiBS-PLS-RSM; β0and β i,l is the custom parameter of original space; p is the number of input variables of training set; ε is the error term of WiBS-PLS-RSM; is the mean of output variable samples of training set; is the mean of ; is the standard deviation of output variable samples of training set; s i,l is the standard deviation of ; a i,l is the regression coefficient of multivariate linear function;

[0059] In step S4, the test set (Test_X, Test_Y) is input into the trained WiBS-PLS-RSM, and the coefficient of determination R 2 is verified, and the specific process is as follows:

[0060] The fitting effect of the training set (Train_X, Train_Y) in step S3 and the prediction effect of the test set (Test_X, Test_Y) are compared, and the training iteration process, the fitting effect of the training set, and the prediction effect of the test set of the WiBS-PLS-RSM of the mean of the top peak displacement are respectively Figure 3 , Figure 5 and Figure 7 , the training iteration process, the fitting effect of the training set, and the prediction effect of the test set of the WiBS-PLS-RSM of the standard deviation of the top peak displacement are respectively Figure 4 , Figure 6 and Figure 8 . In the optimal WiBS-PLS-RSM of the mean of the top peak displacement, the number of segments is 9, the width parameter is 5.0, the training set verification index is 0.974, and the prediction set verification index is 0.985. For the optimal WiBS-PLS-RSM of the standard deviation of the top peak displacement, the number of segments is 2, the width parameter is 1.6, the training set verification index is 0.9, and the prediction set verification index is 0.955. The coefficients of determination are all greater than 0.9, indicating that the WiBS-PLS-RSM has high precision.

[0061] In step S5, the structure vulnerability curve, the seismic risk curve, and the structure loss curve are obtained by using the seismic vulnerability analysis, the seismic risk analysis, and the seismic loss analysis respectively, and finally the structure seismic risk assessment model is obtained, and the specific steps are as follows:

[0062] S51, the total data set input variable sample Total_X is input into the verified WiBS-PLS-RSM to obtain all damage indexes considering the uncertainty of design parameters, i.e. the total data set output variable sample Total_Y. The seismic vulnerability analysis is used to construct a structure vulnerability curve as Figure 9The brick masonry tower structure fragility curve, through which the probability of the structure being in a failure state under ground motion intensity can be analyzed, is , , wherein P is the structure fragility curve, is the structure vulnerability curve, DS b is the bth structure failure state, LS c is the cth structure limit state, n(SDI ≥ LS c ) is the number of structure damage indexes greater than or equal to the structure limit state, N is the number of structure damage index samples, and d is the number of samples generated by the WiBS-PLS-RSM for all output variables.

[0063] S52, a seismic hazard analysis is used to construct a seismic hazard curve as shown in Figure 10 The ground motion intensity parameter S a (T1) is the seismic hazard curve, through which the probability of each intensity earthquake occurring can be analyzed, i.e., ,

[0064] Table 1 Shape parameter k values for different fortification intensities Basic intensity 6 7 8 9 Shape parameter 9.793 8.334 6.871 5.403 wherein P h (IM) is the seismic hazard curve, S a (T1) is the acceleration response spectrum, I0 is the fortification intensity, which can be obtained from the Code for Seismic Design of Buildings GB 50011-2010, and k is the shape parameter for different fortification intensities, as shown in Table 1.

[0065] S53, a seismic loss analysis is used to construct a brick masonry tower structure loss curve as shown in Figure 11 Through the curve, the economic loss of the structure under ground motion intensity can be analyzed, i.e., , , , , wherein L[IM] is the structure loss curve, L[DS b ], P L (DS b ), and P S (DS b ) are the economic loss, direct economic loss, and indirect economic loss of the structure under the failure state DS b , respectively, and C hFor the building structure reconstruction cost, C is the building structure engineering cost, S is the building structure damage area, X B , BT and DR are building structure protection level coefficient, protection level adjustment coefficient and damage loss ratio respectively, which can be obtained by consulting the specification;

[0066] S54, the masonry tower structure vulnerability curve of step S51, the seismic risk curve of step S52 and the masonry structure loss curve of step S53 are used to construct the masonry tower structure seismic risk curve as shown in Figure 12 The masonry tower structure risk value R is less than 2.5 million yuan / (year·seat) when the seismic intensity S a (T1) is located in the interval of 0~0.5g, R is classified by the structure seismic risk grade division table defined by the specification, the masonry tower structure is in the medium risk level, and measures should be taken to reduce the risk, which provides a theoretical basis for subsequent seismic reinforcement, that is, , where R[IM] is the structure seismic risk value.

Claims

1. A structural seismic risk assessment method based on WiBS-PLS-RSM, characterized in that, The method includes the following steps: S1. Sensitivity analysis is used to determine the material and geometric parameters of the finite element model that affect the structure to be evaluated, referred to as the design parameters for structural seismic risk assessment. The damage index (DI) of the structure to be evaluated is determined according to the research purpose. S2. Determine the distribution form, value range, and sample size of the design parameters through existing literature research or experiments, referred to as the statistical distribution of the design parameters. Randomly sample the statistical distribution of the design parameters to obtain the total dataset input variable sample Total_X. Use a uniform design table to determine the training set input variable sample Train_X of the response surface model from Total_X. Randomly select samples from Total_X other than Train_X, with a number not less than 0.25 times that of Total_X, as the test set input variable sample Test_X of the response surface model. Establish the structural finite element model corresponding to Train_X and Test_X in existing modeling software, and perform nonlinear time history analysis on the structural finite element model to obtain the damage index, that is, obtain the training set output variable sample Train_Y and the test set output variable sample Test_Y of the response surface model, respectively. S3. Input the training set (Train_X, Train_Y) into the width-adjustable basic spline partial least squares response surface model (WiBS-PLS-RSM) for training; S4. Input the test set (Test_X, Test_Y) into the trained WiBS-PLS-RSM and use the coefficient of determination R0 to... 2 Verify that if R 2 If R ≥ 0.9, then WiBS-PLS-RSM training is complete. 2 If the value is less than 0.9, adjust the width parameter and the number of segments of WiBS-PLS-RSM, and re-iterate the training until R is satisfied. 2 ≥ 0.9; S5. Input the total dataset into the input variable sample Total_X and input it into the WiBS-PLS-RSM validated in step S4 to obtain the damage index considering the uncertainty of design parameters. Use seismic vulnerability analysis, seismic hazard analysis and seismic loss analysis to obtain the structural vulnerability curve, seismic hazard curve and structural damage curve respectively. Finally, obtain the structural seismic risk assessment model, thereby realizing efficient and accurate pre-earthquake risk assessment of structures and components, and providing a theoretical basis for subsequent seismic reinforcement.

2. The structural seismic risk assessment method based on WiBS-PLS-RSM according to claim 1, characterized in that, The specific steps for determining the material and geometric parameters of the finite element model affecting the structure to be evaluated using sensitivity analysis in step S1 are as follows: S11, initially select the parameter X_Initial that affects the structural finite element model. Determine a sample of parameter X_Initial based on engineering experience, then change the parameter sample by a change rate of 2%. The changed parameter is X_adjust, i.e. X_adjust = (1+2%)·X_Initial; S12, finite element models corresponding to X_Initial and X_adjust are established in existing modeling software, and nonlinear time history analysis is performed to obtain the damage index Y_Initial corresponding to the initially selected parameter X_Initial and the damage index Y_adjust corresponding to the changed parameter X_adjust. S13, calculate the sensitivity S of the parameter to the damage index, and select the parameter with S > 0.8 as the input variable X, that is, 。 3. The structural seismic risk assessment method based on WiBS-PLS-RSM according to claim 1, characterized in that, The specific steps for determining the training set input variable samples Train_X of the response surface model using a uniform design table for Total_X in step S2 are as follows: S21, based on the total dataset, determine the number of variables s and the sample size a for each variable, and query the uniform design table U. a (a s This will give you a training set input variable samples Train_X.

4. The structural seismic risk assessment method based on WiBS-PLS-RSM according to claim 1, characterized in that, The steps described in step S3, which involve inputting the training set (Train_X, Train_Y) into a width-adjustable basic spline partial least squares response surface model (WiBS-PLS-RSM) for training, are as follows: S31, Define the number of segments M i Thus, the segment length h is determined. i ,node ,Right now, Where x i M is the i-th input variable in the training set; i h i and ξ i,l-1 These represent the number of spline space segments, the length of the spline space segment, and the (l-1)th node of the i-th input variable, respectively. Let l be the l-th node in the spline space; S32, Define the width parameter w, and input the i-th variable x from the training set. i Transform into spline space variable z i ,Right now, in For x i The value of the j-th sample at the l-th node in the spline space; For b-order spline basis functions; For the j-th sample point of the i-th input variable in the training set; S33, construct a multivariate linear function in spline space, obtain the regression coefficients using partial least squares method, and finally transform it into the original space to construct WiBS-PLS-RSM, i.e. in The predicted values ​​for WiBS-PLS-RSM; β0 and β i,l is a user-defined parameter for the original space; p is the number of input variables in the training set; ε is the error term of WiBS-PLS-RSM; Output the mean of the variable samples for the training set; for The mean; The standard deviation of the output variable samples in the training set; s i,l for Standard deviation; a i,l represents the regression coefficients of a multivariate linear function.

5. The structural seismic risk assessment method based on WiBS-PLS-RSM according to claim 1, characterized in that, Step S4 involves inputting the test set (Test_X, Test_Y) into the trained WiBS-PLS-RSM and using the coefficient of determination R... 2 Verification, the specific formula is as follows: in The predicted value for WiBS-PLS-RSM. These are measured values ​​from nonlinear time history analysis. This represents the average of the measured values.

6. The structural seismic risk assessment method based on WiBS-PLS-RSM according to claim 1, characterized in that, Step S5 involves using seismic vulnerability analysis, seismic hazard analysis, and seismic loss analysis to obtain structural vulnerability curves, seismic hazard curves, and structural loss curves, ultimately leading to a structural seismic risk assessment model. The specific steps are as follows: S51, input the total dataset input variable sample Total_X into the validated WiBS-PLS-RSM to obtain all damage indices considering design parameter uncertainties, i.e., the total dataset output variable sample Total_Y. Seismic vulnerability analysis is then used to construct the structural vulnerability curve, i.e., Among them Structural fragility curve The DS curve represents the structural fragility profile. b For the b-th structural failure state, LS c For the c-th limiting state, n(DI ≥ LS) c ) represents the number of damage indicators greater than or equal to the limit state, N represents the number of damage indicator samples, and d represents the number of total dataset output variable samples Total_Y; S52, seismic hazard curves are constructed using seismic hazard analysis, namely, Where P h (IM) is the seismic hazard curve, where IM is the seismic intensity, I0 is the design intensity (obtained from the "Code for Seismic Design of Buildings" GB 50011-2010), and k is the shape parameter for different design intensities. S53, using seismic loss analysis to construct structural loss curves, namely, Where L[IM] is the structural loss curve, and L[DS] is the structural loss curve. b ]、P L (DS b ) and P S (DS b ) represent the structure in the failure state DS b The economic losses, direct economic losses, and indirect economic losses, C h C is the cost of rebuilding the building structure, S is the cost of the building structure project, and X is the area of ​​damage to the building structure during the earthquake. B X BT DR and DR are respectively the building structure protection level coefficient, protection level adjustment coefficient and damage loss ratio, all of which are obtained by consulting the specifications; S54, using the structural vulnerability curve from step S51, the seismic hazard curve from step S52, and the structural loss curve from step S53, a structural seismic risk assessment model is constructed, that is, R represents the structural seismic risk value, which is classified according to the structural seismic risk level classification table defined in the code.

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