A method for constructing a sea area seismic ground motion intensity index

Abstract

To rationally select seismic intensity indices (IMs) suitable for seismic design of marine engineering structures, a Lasso regression model was established based on nonlinear time history analysis results of 32 seismic IMs and 1400 single-degree-of-freedom (SDOF) structures. The frequency and sensitivity of seismic IMs were defined, and the differences in the ranking results of marine and terrestrial seismic IMs based on both frequency and sensitivity were compared. Furthermore, K-means clustering was used to select the most representative marine seismic IMs. A composite seismic intensity index for marine areas was constructed based on partial least squares regression analysis. I M_PLS Through probabilistic earthquake demand analysis, the composite strength index of the structure is evaluated from both effectiveness and sufficiency perspectives. I M_PLS To conduct an evaluation.

Description

Technical Field

[0001] This application relates to the field of earthquake engineering, specifically to a method for constructing a marine seismic intensity index. Background Technology

[0002] Marine earthquakes pose a significant potential threat to marine engineering structures. Seismic fortification of marine engineering structures is a fundamental issue that must be considered in marine engineering construction to ensure the seismic safety of marine engineering structures. Determining a reasonable intensity measure (IM) for seismic design of marine engineering is the basis for ensuring the seismic safety of marine engineering structures. Domestic and international research on marine ground motion IM mainly focuses on two aspects: (1) research on marine ground motion amplitude parameters, including PGA, PGV, PGD, etc., comprehensively considering the influence of seabed seismic stations and seismic environment on marine ground motion amplitude parameters; (2) considering the needs of seismic design of marine engineering structures, emphasizing the research on marine ground motion spectrum parameters and energy distribution patterns, including acceleration response spectrum values, input energy, etc. All of the above-mentioned research work focuses on exploring the differences between marine and land ground motion IM. The geological environment and site conditions of marine engineering are extremely complex. Due to the coupling effect of seawater and complex topography, the spectrum characteristics of marine ground motion are significantly different from those of land ground motion. However, the seismic design of marine engineering structures still follows the seismic design code for land-based structures, and there is a lack of reasonable design principles for marine engineering structures. Summary of the Invention

[0003] Therefore, this application proposes a method for selecting marine ground motion intensity index (IM) based on Lasso (Least Absolute Selection and Shrinkage Operator) regression, combined with K-means clustering to screen out the most representative marine ground motion IMs. To address the shortcomings of using a single selected IM to characterize the destructive potential of marine ground motions, a composite intensity index (I) for marine ground motions is constructed based on partial least squares (PLS) regression. M_PLS The effectiveness and adequacy of this study will be evaluated through probabilistic seismic demand analysis, aiming to provide a theoretical basis for the screening of marine ground motion IMs and the seismic design of marine engineering structures.

[0004] This application relates to a method for constructing a marine seismic intensity index, which includes the following: S1. Select marine ground motion data and terrestrial ground motion data, and process the ground motion data; S2. Select the ground motion IM and classify the indicators according to amplitude, spectrum, energy and duration indicators, and perform the normal distribution Shapiro-Wilk test. S3. Select a structural restoring force model for assessing the potential damage from seismic motion in the sea area and calculate the damage parameters. S4. Based on the calculation results in S3, establish a Lasso regression model and perform frequency and sensitivity statistical analysis on ground motion IM to obtain a ranking of ground motion IM indices based on sensitivity and frequency. S5. Perform K-means clustering analysis on the marine ground motion samples composed of the ground motion IMs selected in S2 to determine the optimal number of clusters K and obtain K cluster IM groups. S6. Combining the frequency and sensitivity analysis results, the IMs in each cluster are compared and selected to obtain a set of marine ground motion IMs that are decorrelated, have the most information content, and have the strongest ability to characterize the destructive potential of marine ground motion. S7. Determine the optimal number of principal components by combining the cumulative contribution rate Rc with the cross-validity test; S8. Use the ground motion IM set obtained in S6 and the damage parameters obtained in S3 to perform PLS regression analysis, and perform significance test on the PLS regression parameters. S9. Based on the significance test of Bootstrap self-sampling, the marine ground motion IM was screened out and PLS regression modeling was performed to construct the composite IM index IM_PLS. S10. Based on probabilistic earthquake demand analysis, the analysis of single ground motion IM and I in marine seismic motion. M_PLS Statistical analysis was performed.

[0005] This application uses Lasso regression analysis based on the elastoplastic time history analysis results of marine ground motion intensity index (IM) and SDOF structure to provide definitions of IM frequency and sensitivity based on the Lasso regression model. It compares the differences in the ranking results of marine and terrestrial ground motion intensity indexes based on both frequency and sensitivity parameters. Using K-means clustering, it selects the most representative and non-redundant marine ground motion intensity indexes. Based on PLS regression analysis, it constructs a composite intensity index (I) for marine ground motion. M_PLS The probabilistic seismic demand analysis was used to evaluate the effectiveness and adequacy of the marine ground motion IM_PLS (Intense Seismic Ground Situation) model. The main technical results are as follows: 1) The differences between marine and terrestrial ground motion intensity (IM) indices were investigated. Results showed that the structural restoring force model had little impact on the ranking of marine and terrestrial ground motion IMs, ranking them as IMs from 1 to 11. Compared to other IMs, the velocity spectrum intensity (Isv) better characterizes the destructive potential of marine and terrestrial ground motions. Compared to terrestrial ground motions, the Rsv value in marine ground motion IMs is higher. va With R dv The earlier the sorted order, the better the R is. va With R dvIt can effectively characterize the destructive potential of marine earthquakes. This is because, due to the influence of the marine environment, there are significant differences in the frequency characteristics of marine and terrestrial earthquakes. Generally speaking, marine earthquakes have a richer long-period component than terrestrial earthquakes.

[0006] 2) Frequency and sensitivity dual-parameter ranking combined with K-means clustering helps to select the Indicator Model (IM) representing the destructive potential of marine seismic motions, while a single IM has certain limitations in characterizing the destructive potential of marine seismic motions. A marine seismic motion Ik model is constructed based on PLS regression. M_PLS Probabilistic earthquake demand analysis results indicate that, compared with single-area marine ground motion IMo, tectonic marine ground motion IMo is significantly higher. M_PLS It has better effectiveness.

[0007] 3) The single IM screening method based on frequency and sensitivity dual-parameter ranking and K-means clustering analysis proposed in this application, and the marine seismic motion I based on PLS regression M_PLS Construction methods can provide a theoretical basis for the seismic resistance of marine engineering structures. Attached Figure Description

[0008] Figure 1 It shows the distribution of seismic moment magnitude, epicentral distance, and peak ground acceleration in marine and land areas. Figure 2 It is the seismic response spectrum of marine and terrestrial areas; Figure 3 It is the SDOF structural restoring force model; Figure 4 It refers to the MDOF structure and hysteresis rules; Figure 5 Here is an example of seismic motion IM sensitivity and frequency based on Lasso regression; Figure 6 The results are statistical results of marine ground motion IM frequency and sensitivity based on Lasso regression. Figure 7 The results are statistical results of IM frequency and sensitivity of land ground motion based on Lasso regression; Figure 8 This relates the sum of squared errors to the number of K-means clusters. Figure 9 This is the relationship between the mean of the residual standard deviation and the number of marine ground motion IMs in ordinary least squares regression analysis. Figure 10 These are the correlation coefficients of the seven selected marine ground motion IM data. Figure 11 It is the cumulative contribution rate of principal components in a typical SDOF structure; Figure 12 It is the cross-validation coefficient of a typical SDOF structure; Figure 13 σ is the logarithmic standard deviation of ground motion (IM) in different sea areas. ε Calculation results; Figure 14 The goodness of fit R of ground motion IM in different sea areas 2 Calculation results; Figure 15 This is the calculated P-value of the composite IM (instantaneous ground motion) in the marine area; Figure 16 It is the logarithmic standard deviation corresponding to the 2-layer MDOF structure; Figure 17 It is the logarithmic standard deviation corresponding to a 10-layer MDOF structure; Figure 18 It is the logarithmic standard deviation corresponding to a 20-layer MDOF structure; Figure 19 This is the calculated P-value of the composite IM (instantaneous ground motion) in the marine area; Detailed Implementation

[0009] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0010] This application relates to a method for constructing a marine seismic intensity index, which includes the following: S1. Select marine ground motion data and terrestrial ground motion data, and process the ground motion data; S2. Select the ground motion IM and classify the indicators according to amplitude, spectrum, energy and duration indicators, and perform the normal distribution Shapiro-Wilk test. S3. Select a structural restoring force model for assessing the potential damage from seismic motion in the sea area and calculate the damage parameters. S4. Based on the calculation results in S3, establish a Lasso regression model and perform frequency and sensitivity statistical analysis on ground motion IM to obtain a ranking of ground motion IM indices based on sensitivity and frequency. S5. Perform K-means clustering analysis on the marine ground motion samples composed of the ground motion IMs selected in S2 to determine the optimal number of clusters K and obtain K cluster IM groups. S6. Combining the frequency and sensitivity analysis results, the IMs in each cluster are compared and selected to obtain a set of marine ground motion IMs that are decorrelated, have the most information content, and have the strongest ability to characterize the destructive potential of marine ground motion. S7. Determine the optimal number of principal components by combining the cumulative contribution rate Rc with the cross-validity test; S8. Use the ground motion IM set obtained in S6 and the damage parameters obtained in S3 to perform PLS regression analysis, and perform significance test on the PLS regression parameters. S9. Based on the significance test of Bootstrap self-sampling, the marine ground motion IM was screened out and PLS regression modeling was performed to construct the composite IM index IM_PLS. S10. Based on probabilistic earthquake demand analysis, the analysis of single ground motion IM and I in marine seismic motion. M_PLS Statistical analysis was performed.

[0011] Specifically, the principles of Lasso regression and PLS regression in the relevant steps are as follows. Lasso regression is a compressed estimation method that replaces ordinary least squares (OLS). Lasso regression achieves an optimal balance between model simplicity and accuracy by adding a penalty term (L1 regularization term) to the traditional linear regression model. The L1 regularization term encourages sparse solutions, meaning that some coefficients in the regression model are forced to be set to 0. This characteristic makes Lasso efficient in screening variables, and therefore it is widely used for fitting and selecting variables in data with multicollinearity.

[0012] In OLS regression, the regression coefficients can be obtained by minimizing the loss function, which is expressed as follows:

[0013] In the formula: L Los ( β ) is the loss function. X As the independent variable, Y As the dependent variable, β is the regression coefficient.

[0014] Regularization methods are in L Los Add a penalty term to the existing formula, as shown in the following expression.

[0015] In the formula: L Reg ( β ) is the regularization loss function. λ To adjust the parameters, P ( β ) is the penalty function.

[0016] Lasso regression, also known as L1 regularized regression, has a penalty function of: Lasso regression uses the sum of the absolute values ​​of the regression coefficients as a penalty function to compress the regression coefficients. Therefore, the loss function of Lasso regression can be expressed as:

[0017] In the formula WIt is a vector with values ​​of positive and negative 1.

[0018] When adjusting parameters λ When =0, L Lasso ( β Degenerates into OLS loss function L Los ( β This means that the effect of regularization has almost disappeared. λ The larger the value, the stronger the regularization effect, which can effectively control the complexity of the regression model. λ The optimal value can be selected through cross-validation, with the selection criterion being to minimize the mean squared error of the regression model.

[0019] PLS regression is a generalization of OLS regression, used to resolve the interdependencies between two sets of multicollinear variables. By extracting the principal components of the independent and dependent variables to construct the regression model, it not only solves the problem of multicollinearity among independent variables but also allows for effective prediction when there are complex relationships between the independent and dependent variables.

[0020] Let random variable X , Y These are the independent and dependent variables, respectively, and after standardization, they are respectively X 0 and Y 0. t 1= X 0 w 1. u 1= Y 0 c 1 represents the standardized independent variables. X 0 and dependent variable Y The first principal component extracted from 0. Among them, w 1. c All are unit vectors. Principal components extracted during PLS regression analysis. t 1. u 1. All should possess the best possible ability to synthesize and interpret information, and are required to t 1 and u The correlation of 1 reaches its maximum, that is

[0021] In the formula, Cov(), Var(), ρ () represent covariance, variance, and correlation coefficient, respectively.

[0022] The above optimization problems can be addressed by... w T 1 w 1=1 and c T 1 c Solving under the constraint of 1=1. Therefore, the Lagrange multiplier method is employed.

[0023] In the formula λ 1 and λ 2 is a Lagrange multiplier.

[0024] Taking the partial derivative of equation (5), we get:

[0025] In the formula θ 2 1 is and The largest eigenvalue.

[0026] Then the regression equation is obtained:

[0027] The regression coefficients of equations (8) and (9) are respectively:

[0028] Using the residual matrix X 1. Y 1 replaces the original matrix X 0、 Y 0. Repeat the above process until a sufficient number of principal components are extracted. h The final PLS regression model is

[0029] The optimal number of principal components can be determined by combining the cumulative contribution rate with the cross-validation test to achieve the best balance between "retaining enough information" and "avoiding model complexity". The validity test helps to select the optimal number of principal components when the marginal contribution is no longer significant by comparing the prediction error under different numbers of principal components. The marginal contribution is measured by the cross-validation coefficient (as shown in Equation (13)).

[0030]

[0031] In the formula, PRESS( h ) for extraction h Sum of squared prediction errors for each principal component, SSE( h -1) for extraction h The sum of squared prediction errors when there are -1 principal components. Explanation of the first h The marginal contribution of each principal component is significant, and extraction should continue; if This indicates that the addition of principal components does not significantly improve the prediction error, and extraction can be stopped.

[0032] For the ground motion data screening and processing in step S1, refer to the following method to collect strong earthquake records from six submarine stations of the Japan Earthquake Monitoring Center (ETMC) (KNG201~KNG206). Screening criteria: ① PGA greater than 40 cm / s² 2 ② Moment Magnitude M w Greater than 5.0; ③ Focal depth less than 180 km; ④ Epicentral distance D Less than 300 km. Based on the above selection criteria, this application selected 100 sets of horizontal bidirectional ground motions from 892 sets recorded in 273 earthquake events. Of these 100 sets of horizontal bidirectional marine ground motions, only unidirectional ground motion records with larger PGAs were retained. It is worth noting that the PGA of the marine ground motion records from station KNG204 is less than 40 cm / s². 2 Therefore, the records selected in this application do not include records from this station. Furthermore, to compare the differences in potential destructive potential between marine and terrestrial seismic ground motions, 100 terrestrial horizontal ground motion records recorded by adjacent terrestrial stations were selected from the aforementioned 273 earthquake events. The processing of marine and terrestrial ground motion data includes the following steps: (1) Baseline correction: Baseline correction is performed to bring the ground motion record back to the zero baseline position; (2) Filtering: A 4th-order Butterworth noncausal filter is used for processing, with a cutoff frequency of 0.05-25.0Hz; (3) Zeros are padded before and after the acceleration record.

[0033] Figure 1 (a) The earthquake moments and magnitudes for both marine and land areas are given. M w Distance from epicenter D Distribution map, Figure 1 (b) gives the epicentral distances of earthquakes in marine and land areas. D Distribution map of PGA. (From...) Figure 1 It can be known that the earthquake occurred in the sea area. M w - D and M w - The PGA distribution information is quite similar to the corresponding distribution information of land earthquakes, indicating that the selected ground motions come from the same earthquake event and are recorded by adjacent stations. Figure 2 (a), (b), and (c) respectively give the relative displacements of seismic motions in the marine and terrestrial areas. S d Spectrum, pseudo velocity PS v Spectrum and pseudo-acceleration PS a Spectrum. Seismic motions over both marine and land areas throughout the entire period. Sd , PS v and PS a The 10% and 50% quantile spectra match well; in the medium to long period of marine seismic motion... S d , PS v and PS a The 90th percentile spectral value is greater than the elastic spectral value corresponding to land ground motion.

[0034] Regarding the selection and classification of ground motion immobility (IM) indices in step S2, specifically: 32 ground motion immobilities are selected and classified according to amplitude, spectral, energy, and duration indices, as shown in Table 1. The ground motion immobility calculation formula is as follows: a ( t ), v ( t )and d ( t The values ​​are ground motion acceleration, velocity, and displacement time history, respectively. PS a ( T , ξ ), PS v ( T , ξ )and S d ( T , ξ (period) T And damping ratio ξ The value corresponding to 0.05 PS a , PS v and S d Spectrum. t f , T d These are the duration of the earthquake and the 90% significant duration, respectively. t 5. t 95 These are the time points corresponding to 5% and 95% Arias intensity, respectively. v oThis represents the number of times the ground motion acceleration time history crosses the zero line per unit time. A Shapiro-Wilk test for normal distribution was performed on 32 ground motion intensity indices, and the skewness and kurtosis of each ground motion intensity (IM) were calculated. If the absolute value of the kurtosis is less than 10 and the absolute value of the skewness is less than 3, it can be described as basically conforming to a normal distribution, based on the normal distribution histogram. Table 1 shows that the absolute values ​​of the kurtosis of the 32 marine ground motion IMs are all less than 10 and the absolute values ​​of the skewness are all less than 3. Combined with the normal distribution histogram, it can be seen that the selected 32 marine ground motion IMs are basically acceptable as normally distributed.

[0035] Table 1 Preliminary Seismic Motion IMs Tab. 1 The preliminary selection of ground motion IMs

[0036]

[0037] Regarding the selection of the structural restoring force model and the calculation of damage parameters in step S3, the specific methods are as follows: The SDOF structural restoring force model adopts the bilinear plastic (BP) model, the modified Clough (MC) model, and the flag-shaped self-centering (Sc) model, as detailed below. Figure 3 Energy consumption coefficient of the flag-shaped model η Used to describe the energy consumption of the model, and also to determine the height of the "flag" section in the model. η ( F y,pos + F y,neg ),in F y,pos , F y,neg These are the positive yield strength and the negative yield strength, respectively. In this application... η The value is 0.2, therefore the flag-type self-resetting model in the following text is represented as Sc- η =0.2. Table 2 shows the analytical variable values ​​for the SDOF structure used in assessing the seismic damage potential in marine areas. It can be seen that this application established BP, MC, and Sc- η =0.2 The number of SDOF structures in the model is 1400 (40×7×5=1400). Multi-degree-of-freedom (MDOF) structures adopt a link model. Three MDOF structures were established, with 2, 10, and 20 layers, and fundamental periods of 0.16 s, 1.03 s, and 2.09 s respectively. The parameter information of the MDOF structures is as follows: layer height...h = 3.0 m, mass m = 600 t, shear stiffness k 0 = 1 × 10 9 N / m, interlayer yield displacement angle u y = 1 / 400, second (strengthened section) stiffness coefficient α s = 0.05, Stiffness coefficient of the third (softening section) α c = -0.05, nominal ductility coefficient is 6. Parameter information for each layer of the MDOF structure, the link model, and hysteresis rules can be found in [link to MDOF structure]. Figure 4 Maximum displacement response was applied to SDOF and MDOF structures respectively. u max With the maximum inter-story drift angle θ max As a damage parameter, it is used to assess the destructive potential of seismic motion in marine areas.

[0038] Table 2 Analytical variables considered in this application Tab. 2 Variables of SDOF systems selected for the numerical analysis

[0039] The establishment of the Lasso regression model and the ranking of ground motion indices based on sensitivity and frequency in step S4 are as follows: A Lasso regression model is established based on the elastoplastic time history analysis results of 1400 SDOF structures under the action of 100 marine and 100 terrestrial ground motion records. The dependent variable in the Lasso regression model is... u max The independent variables are the 32 ground motion immobiles (IMs) selected in Section 3. Frequency is defined as the number of non-zero regression coefficients of the IMs in the 1400 Lasso regression models, and sensitivity is defined as the sum of squares of the regression coefficients of the IMs in the 1400 Lasso regression models. The 32 IMs are represented as points in a Cartesian coordinate system according to their frequency and sensitivity, as shown below. Figure 5 As shown, 32 selected seismic motion instants (IMs) are sorted based on the Euclidean distance between the midpoint of the Cartesian coordinate system and the origin (0, 0). The greater the distance, the higher the ranking, and the stronger the ability to characterize the destructive potential of the seismic motion. To facilitate the calculation of the Euclidean distance between the 32 seismic motion IMs and the origin (0, 0), the frequency and sensitivity of the 32 seismic motion IMs are normalized. The normalization of frequency and sensitivity is the ratio of the frequency and sensitivity of a particular seismic motion IM to the maximum frequency and sensitivity of all seismic motion IMs, respectively.

[0040] Figure 6 The BP, MC and Sc- parameters are given. η =0.2 Statistical results of ground motion IM frequency and sensitivity of 1400 SDOF structures under marine ground motion loading for three models. Figure 7 The BP, MC and Sc- parameters are given. η =0.2 Statistical results of ground motion IM frequency and sensitivity of 1400 SDOF structures under land-based ground motion loading for three models. Figure 6 It can be seen that under the action of marine seismic motion, BP, MC and Sc- η =0.2 The three models, ranked from 1 to 11 based on the dual parameters of frequency and sensitivity, are respectively I sv , R va , D mi , V ep , I sd , D rms , R dv , I AM , T d , V SI , V rms .Depend on Figure 7 It can be seen that under the action of terrestrial seismic motion, BP, MC and Sc- η =0.2 The three models, ranked from 1 to 11 based on the dual parameters of frequency and sensitivity, are respectively I sv , D rms , D mi , V ep , D rs , I sd , V SI , T d , V rms , V mi , I AMThe ranking of marine and terrestrial ground motion immobilities (IMs) based on both frequency and sensitivity parameters is less affected by the structural restoring force model, especially for IMs ranked 1 to 11. Related authors investigated the correlation between marine ground motion IMs and SDOF structural displacement responses and suggested using peak displacement analysis (PDO). D pg As an inertial motion (IM) analysis tool for seismic resistance analysis of marine engineering structures, this application ranks the marine and terrestrial ground motion IM tools, both based on frequency and sensitivity, as having the velocity spectrum intensity as the primary parameter. I sv That is, compared with other IMs, the velocity spectrum intensity I sv It can better characterize the seismic damage potential in marine and terrestrial areas.

[0041] Comparing the IM ranking results of marine and terrestrial ground motions based on both frequency and sensitivity parameters, it can be seen that for marine ground motions, R va and R dv Sort by first, i.e. R va and R dv It can effectively characterize the destructive potential of seismic motions in marine areas. However, for seismic motions in terrestrial areas, R va and R dv It's listed towards the end. As we all know, A pg , V pg , D pg These are caused by different frequency components of ground motion, respectively reflecting the high-frequency, mid-low-frequency, and low-frequency components of ground motion. R va It mainly reflects the spectral characteristics of ground motion, while R dv This primarily reflects the duration and long-period characteristics of ground motions. Related studies, based on data from the Japanese K-NET submarine network, compared the differences in the elastoplastic response spectrum characteristics of marine and terrestrial ground motions. The research indicates that soft seabed soil layers contribute to a richer long-period component in marine ground motions. Regarding the time-frequency distribution characteristics of nearshore ground motions, related studies have found that marine ground motions possess a richer long-period component than terrestrial ground motions, and that the marine environment (weak sedimentary layers, seawater depth, etc.) has a significant impact on the frequency characteristics of marine ground motions.

[0042] In summary, based on the statistical results using both frequency and sensitivity parameters, the structural restoring force model has a relatively small impact on the ranking of ground motion immobilities (IMs) in both marine and terrestrial areas; it ranks as an IM ranked 1 to 11. Compared to other IMs, the velocity spectrum intensity... Isv It can better characterize the destructive potential of seismic motions in marine and terrestrial areas. Influenced by the marine environment (weak sedimentary layers, seawater depth, etc.), marine and terrestrial seismic motions differ significantly in frequency characteristics. Generally speaking, marine seismic motions have a richer long-period component than terrestrial seismic motions. R va and R dv It can effectively characterize the destructive potential of seismic motion in marine areas.

[0043] The specific steps for K-means clustering analysis and frequency and sensitivity-based seismic motion IM ranking in steps S5 and S6 are as follows: the frequency and sensitivity-based dual-parameter ranking is combined with K-means clustering to select the most representative and non-redundant marine seismic motion IMs. In K-means clustering analysis, Euclidean distance is used to describe the similarity of marine seismic motion IM samples. The sum of squared errors (SSE) is used to evaluate the K-means clustering performance, which represents the sum of squared distances from the marine seismic motion IM sample point to the centroid of its cluster, as shown in the following formula (14).

[0044]

[0045] In the formula, C i For the first i Clusters, μ i As the cluster centroid, x Intra-cluster samples, K This represents the number of clusters.

[0046] In the above formula, SSE reflects the degree of distortion in K-means clustering; the smaller the SSE, the better the clustering effect. To determine the optimal number of clusters for marine seismic IM samples... K ,make And perform K-means clustering analysis and calculate SSE, such as Figure 8 As shown, the optimal number of clusters is determined according to the Elbow method. From... Figure 8 It can be seen that as the number of clusters increases... K As the number of clusters increases, the SSE gradually decreases. K When the SSE value is greater than 7, the decrease is slow, and the slope of the curve is close to horizontal. Therefore, the number of clusters... K When the value is 7, the clustering effect of the marine seismic motion IM samples is better.

[0047] K-means clustering analysis was performed on a marine ground motion sample consisting of 32 ground motion IMs, and the optimal number of clusters was determined based on the elbow rule. KThe 32 marine ground motion imaginary signals (IMs) were divided into 7 clusters. Combining the ranking results of the marine ground motion IMs based on both frequency and sensitivity parameters, only the highest-ranking IM within each cluster was retained. Finally, a set of marine ground motion IMs with the highest decorrelation, the most information content, and the strongest ability to characterize the destructive potential of marine ground motions was selected. I sv , R va , D mi , V ep , D rms , T d , V ca It is worth noting that the selected marine ground motion IM set is not affected by the structural restoring force model. According to the classification of ground motion IMs in Section 3, the selected marine ground motion IM set... D mi For amplitude indicators, I sv , R va , V ep For spectral indicators, D rms , T d , V ca This refers to energy and duration indicators.

[0048] The seven selected marine ground motion IMs were added to the OLS regression model in order of frequency and sensitivity, and the standard deviation of the OLS regression model residuals was calculated sequentially. Figure 9 The mean standard deviation of the residuals for 1400 OLS regression models (corresponding to 1400 SDOF structures) under marine seismic loading is given. When the number of marine seismic IMs included in the OLS regression model is 0, the standard deviation of the residuals is 1.0. When the velocity spectrum intensity... I sv When added to the OLS regression model, BP, MC, and Sc- η The residual standard deviations for the three models with a value of 0.2 were 0.41, 0.39, and 0.41, respectively. When all the seismic motion IMs from the seven sea areas were included in the OLS regression model, the BP, MC, and Sc- ηThe standard deviations of the residuals for the three models were 0.23, 0.20, and 0.22, respectively. Overall, the standard deviation of the OLS regression model residuals gradually decreased with the increase of the number of marine seismic motions (IMs) included, exhibiting a significant decrease in the early stages followed by a stabilization in the later stages. This indicates that ranking based on both frequency and sensitivity parameters helps in selecting IMs that characterize the destructive potential of marine seismic motions, but the selection of a single IM still has certain limitations when used to characterize the destructive potential of marine seismic motions.

[0049] Based on frequency and sensitivity dual-parameter ranking and K-means clustering analysis, there is a strong correlation among the selected marine ground motion IMs, such as... Figure 10 As shown, using a single ground motion intensity (IM) to characterize the destructive potential of marine ground motions still has certain limitations, and there is a strong correlation between ground motion IMs from different marine areas. Therefore, the single ground motion IM selected based on frequency and sensitivity dual-parameter ranking and K-means clustering analysis is still insufficient for the seismic design of marine engineering structures.

[0050] Regarding the cumulative contribution rate in step S7 R c The optimal number of principal components was determined by combining cross-validation tests. Specifically, marine ground motion intensity (IM) selected based on a combination of frequency and sensitivity ranking and K-means clustering analysis was chosen as the independent variable for PLS regression analysis. I M =[ I sv , R va , D mi , V ep , D rms , T d , V ca The damage parameters of the SDOF structure under marine seismic loading are as follows: u max If we take it as the dependent variable in the PLS regression analysis, then according to equation (12), the PLS regression model can be expressed as:

[0051] To more clearly demonstrate the process of marine ground motion composite IM tectonic construction based on PLS regression, this application selected six SDOF structures with different natural periods as typical structures for analysis. The natural periods of the six typical SDOF structures are 0.2s, 0.5s, 1.0s, 1.5s, 2.0s, and 3.0s, respectively denoted as S-0.2, S-0.5, S-1.0, S-1.5, S-2.0, and S-3.0.

[0052] This application uses the cumulative contribution rate. R c The optimal number of principal components for PLS regression is determined by combining cross-validation tests, achieving the best balance between "retaining sufficient information" and "avoiding model complexity". Cumulative contribution rate. R c is used to reflect the effect of the PLS regression principal components on the independent variables. I M and dependent variable u max The ability to synthesize and interpret information. Figure 11 Principal component analysis based on PLS regression analysis of six typical SDOF structures is presented. R c. It can be seen that PLS regresses the principal components. R c gradually increases with the number of principal components. When the number of retained principal components exceeds 2, the independent variable... I M and dependent variable u max corresponding R c is greater than 80%. R A larger c indicates that the PLS regression model has a greater impact on the dependent variable. u max The better the predictive power, the better the predictive power of the PLS regression model for structures S-1.0, S-1.5, S-2.0, and S-3.0, when the number of retained principal components does not exceed 2; the predictive power is significantly better for structures S-0.2 and S-0.5. u max Its predictive ability.

[0053] As can be seen from the above, when the number of retained principal components is 2, the independent variable... I M and dependent variable u max corresponding R Since c is greater than 80%, it indicates that these two principal components have explained the independent variables. I M and dependent variable u maxThe vast majority of useful information is retained. The more principal components retained, the stronger the predictive power of the PLS regression model; however, it is prone to overfitting, leading to poorer predictive performance. Increasing the number of principal components in the PLS regression model is used to assess its improvement in predictive power. Figure 12 The cross-validation coefficients of a typical SDOF structure are given. Q 2 h When the structures S-0.2, S-0.5, S-1.0, and S-3.0 retain the first two principal components, while the structures S-1.5 and S-2.0 retain the first principal component, Q 2 h Greater than 0.0975. This indicates that the optimal number of principal components for PLS regression is 2 for the S-0.2, S-0.5, S-1.0, and S-3.0 structures, and 1 for the S-1.5 and S-2.0 structures.

[0054] PLS regression analysis was performed on the ground motion IM set obtained in step S8 and the damage parameters obtained in S3, and the significance of the PLS regression parameters was tested, specifically by using the cumulative contribution rate. R c The optimal number of principal components is determined by combining cross-validation test, and then the PLS regression model is constructed by equation (12). The significance of the PLS regression parameters needs to be tested based on bootstrap sampling. Random sampling points with replacement are repeated 50 times. n b =50), resulting in a set of Bootstrap samples; repeat the above steps to obtain a total of 100 sets ( r =100) Bootstrap samples. The critical value of the rejection region is obtained by accumulating 100 sets of samples. β α=0.05 ( k );like ,reject H 0, at this time β k The significance level is not zero; otherwise, the null hypothesis is accepted, and the significance test fails. Table 3 shows the significance test results for six typical SDOF structures based on Bootstrap bootstrapping. Through the first PLS regression analysis, only the regression model corresponding to the S-0.5 structure showed a significant difference. R va The significance test failed. , Therefore, in the regression model corresponding to S-0.5... R va Remove from the model, reconstruct a new PLS regression model, and calculate the cumulative contribution rate. R cThe optimal number of principal components is determined by combining cross-validation tests, and a significance test based on Bootstrap sampling is performed. The above steps are repeated until all regression parameters pass the significance test.

[0055] Table 3 Bootstrap test results for typical SDOF structures Tab. 3 The Bootstrap test results of typical SDOF structures

[0056] For step S9, construct the composite IM index. I M_PLS The specific steps are as follows: Based on the significance test of Bootstrap self-sampling, the marine ground motion intensity index (IM) is screened out and PLS regression modeling is performed. The regression coefficients of typical SDOF structures given in Table 3 are substituted into equation (15) to finally construct the marine ground motion composite intensity index. I M_PLS Among them, the S-0.5 structure was deleted based on the significance test of Bootstrap sampling. R va After that, the construction I M_PLS for

[0057] For step S10, based on probabilistic earthquake demand analysis, the single ground motion IM of marine seismic motion and I M_PLS The statistical analysis is conducted through the following steps: This paper analyzes the statistical properties of single ground motion immobilization (IM) and composite ground motion immobilization (IM) in marine areas based on probabilistic seismic demand analysis (PSDA). The probabilistic seismic demand model established based on PSDA is as follows:

[0058] In the formula, For structural seismic demand parameters D The median value, is the logarithmic standard deviation.

[0059] Based on the cloud map method, elastoplastic time history analysis was performed on 1400 SDOF structures under marine seismic loading, and a logarithmic regression model was constructed as follows:

[0060] In the formula εIt is a random error, usually following a log-normal distribution, with a log-standard deviation of . σ ε .

[0061] General assumptions Median values ​​of structural seismic demand parameters and I M The relationship between them follows an exponential relationship, and after taking the logarithm... and I M The relationship between them follows a logarithmic linear relationship. For the elastoplastic time history analysis results of 1400 SDOF structures, the median structural seismic demand parameter is... The logarithmic standard deviation is

[0062] In the formula N This refers to the number of earthquake records in the sea area.

[0063] Based on the PSDA analysis results of 1400 SDOF structures and 3 MDOF structures established in Section 4, the seismic motion intensity (IM) of a single sea area (including...) was analyzed. I sv , R va , D mi , V ep , D rms , T d , V ca )and I M_PLS The statistical properties are evaluated from two aspects: validity and adequacy. Validity is used to reflect... I M With structural seismic demand parameters D The strength of the correlation describes the magnitude of model uncertainty in PSDA. This study uses goodness of fit to assess these factors. R 2 and logarithmic standard deviation σ ε To characterize. Sufficiency is used to describe. I M Earthquake characteristics (moment magnitude) M w Epicenter distance D The strength of the correlation between the logarithm of the residuals and the moment magnitude is usually determined by the relationship between the logarithm of the residuals and the moment magnitude. M w Epicenter distance D Significance level of linear relationship P Use the value to make the judgment. PThe larger the value, the less significant the linear relationship, indicating... I M The better the sufficiency. P The threshold value is usually set to 0.05.

[0064] Figure 13 The log-standard deviations of 1400 SDOF structures are given. σ ε The statistical results show that, within the considered period, the sea-based seismic motion... I M_PLS corresponding σ ε It remains between 0.2 and 0.4. Within the considered period range, compared to the IM of ground motion in a single sea area, I M_PLS corresponding σ ε Minimum. Figure 14 The goodness-of-fit of 1400 SDOF structures is given. R 2 The statistical results show that, within the considered period, compared to the IM of ground motion in a single sea area, I M_PLS corresponding R 2 The minimum. Furthermore, the logarithmic standard deviation of the SDOF structural restoring force model. σ ε and goodness of fit R 2 The statistical results were unaffected. From the perspective of goodness of fit... R 2 and logarithmic standard deviation σ ε The two indicators show that, compared to the IM (instantaneous ground motion) of a single marine area, the marine ground motion induced in this application is significantly more efficient. I M_PLS It is more effective in PSDA.

[0065] Figure 15 Marine seismic motion based on PLS regression structure is presented. I M_PLS Regarding moment magnitude M w and epicenter distance D significance level P The statistical results of the values. As shown in the figure, within the considered period, the moment magnitude... M w and epicenter distance D significance level P The values ​​are all greater than 0.05, indicating that the marine seismic motion constructed in this application is... I M_PLS It is adequate in PSDA.

[0066] For 2, 10, and 20-story MDOF structures, the seismic intensity (IM) of a single sea area was analyzed based on PSDA results. I M_PLS The statistical characteristics are evaluated from the perspectives of validity and adequacy. Figure 16 , 17 The logarithmic standard deviations for 2, 10, and 20-layer MDOF structures are given in sections 1 and 2, respectively. σ ε As shown in the diagram, the sea area experienced earthquakes. I M_PLS Corresponding log standard deviation σ ε Less than the log standard deviation of the IM corresponding to a single sea area ground motion σ ε This indicates that, compared to single-area marine ground motion IM, the marine ground motion induced in this application... I M_PLS It is more effective in PSDA. Figure 19 The sea-based seismic activity was given. I M_PLS Regarding moment magnitude M w and epicenter distance D significance level P The calculated value. As shown in the figure, the moment magnitude... M w and epicenter distance D significance level P The values ​​are all much greater than 0.05, indicating that the marine seismic activity constructed in this application is significant. I M_PLS It is well sufficiency in PSDA.

[0067] Although the embodiments disclosed in this application are as described above, the content is merely for the purpose of facilitating understanding of this application and is not intended to limit this application. Any person skilled in the art to which this application pertains may make any modifications and changes in the form and details of the implementation without departing from the spirit and scope disclosed in this application; however, the scope of patent protection of this application shall still be determined by the scope defined in the appended claims.

Claims

1. A method for constructing a marine seismic intensity index, characterized in that, Includes the following steps: S1. Select marine ground motion data and terrestrial ground motion data, and process the ground motion data; S2. Select the ground motion IM and classify the indicators according to amplitude, spectrum, energy and duration indicators, and perform the normal distribution Shapiro-Wilk test; S3. Select a structural restoring force model for assessing the potential damage from seismic motion in the sea area and calculate the damage parameters. S4. Based on the calculation results in S3, establish a Lasso regression model and perform frequency and sensitivity statistical analysis on ground motion IM to obtain a ranking of ground motion IM indices based on sensitivity and frequency. S5. Perform K-means clustering analysis on the marine ground motion samples composed of the ground motion IMs selected in S2 to determine the optimal number of clusters K and obtain K cluster IM groups. S6. Combining the frequency and sensitivity analysis results, the IMs in each cluster are compared and selected to obtain a set of marine ground motion IMs that are decorrelated, have the most information content, and have the strongest ability to characterize the destructive potential of marine ground motion. S7, based on cumulative contribution rate R c The optimal number of principal components is determined by combining cross-validation tests; S8. Use the ground motion IM set obtained in S6 and the damage parameters obtained in S3 to perform PLS regression analysis, and perform significance test on the PLS regression parameters. S9. Based on the significance test of Bootstrap sampling, marine ground motion intensity (IM) indicators were selected for PLS regression modeling to construct a composite IM index. I M_PLS ; S10. Based on probabilistic earthquake demand analysis, the single ground motion IM of marine seismic motion and... I M_PLS Statistical analysis was performed.

2. The construction method according to claim 1, characterized in that: The damage parameters in step S3 are obtained by applying the maximum displacement response to the SDOF and MDOF structures respectively. u max With the maximum inter-story drift angle θ max .

3. The construction method according to claim 1, characterized in that: In step S4, frequency is defined as the number of non-zero regression coefficients of ground motion IM in the Lasso regression model, and sensitivity is defined as the sum of squares of the regression coefficients of ground motion IM in the Lasso regression model. The selected ground motion IMs are sorted based on the Euclidean distance between the midpoint and the origin (0, 0) of the Cartesian coordinate system. The larger the distance, the higher the ranking, and the stronger the ability to characterize the destructive potential of the ground motion.

4. The construction method according to claim 1, characterized in that: In step S5, the optimal number of clusters K is determined to be 7 based on the elbow rule.

5. The construction method according to claim 1, characterized in that: In step S6, the selection method involves choosing the IM indicator that ranks highest based on sensitivity and frequency analysis as the retention indicator for that cluster. The final selected IM set is... I M =[ I sv , R va , D mi , V ep , D rms , T d , V ca ].

6. The construction method according to claim 1, characterized in that: The number of principal components for determining the optimal PLS regression in step S7 is 2.

7. The construction method according to claim 1, characterized in that: Step S8 specifically includes constructing a PLS regression model, performing a significance test on the PLS regression parameters based on Bootstrap self-sampling, deleting parameters that fail the significance test, and obtaining the marine seismic motion IM set screened out based on the significance test of Bootstrap self-sampling.

8. The construction method according to claim 1, characterized in that: In step S9, the final composite intensity index I for marine seismic motion is constructed. M_PLS for 。 9. The construction method according to claim 1, characterized in that: The specific analysis step in step S10 is to analyze the ground motion of a single sea area based on the PSDA analysis results. I M =[ I sv , R va , D mi , V ep , D rms , T d , V ca [and composite index I] M_PLS The statistical properties are evaluated from two aspects: validity and adequacy. Validity is used to reflect the strength of the correlation between IM and the structural seismic demand parameter D, and to describe the magnitude of model uncertainty during PSDA. The goodness-of-fit R-value is used to evaluate these properties. 2 and logarithmic standard deviation σ ε The sufficiency is used to characterize the correlation between IM and seismic characteristics (moment magnitude Mw, epicentral distance D). The significance level P-value of the linear relationship between the logarithm of the residuals and the moment magnitude Mw and epicentral distance D is used to judge the sufficiency. The larger the P-value, the less significant the linear relationship, indicating that the IM sufficiency is better.

10. The construction method according to claim 1, characterized in that: The screening criteria for ground motion in step S1 include ① PGA greater than 40 cm / s². 2 ② Moment magnitude M w Greater than 5.0; ③ Focal depth less than 180 km; ④ Epicentral distance D less than 300 km; The processing of ground motion includes (1) Baseline correction, which makes the ground motion record return to the zero baseline position; (2) Filtering, which uses a 4th order Butterworth noncausal filter for processing, with a cutoff frequency of 0.05-25.0 Hz; (3) Zeroing before and after the acceleration record.

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