Method for evaluating seismic resilience of rc frame based on basis vector guided support vector machine

Abstract

The method for evaluating the seismic resilience of RC frame based on basis vector guided support vector machine, comprising the following steps: 1, collecting the seismic resilience data set of RC frame containing various characteristic variables, and dividing it into training set and test set; 2, establishing a minimum error objective function, solving the objective function to develop a basis vector adaptive selection BVAS algorithm to actively select the optimal basis vector; 3, extracting a small number of samples as basis vectors from a large-scale data set based on the BVAS algorithm, mapping them into a high-dimensional feature space, and establishing a BVAS-LS-SVMR model; 4, training the BVAS-LS-SVMR model using the training set data, and establishing the seismic resilience prediction model of RC frame; 5, based on the test set data, the performance of the seismic resilience prediction model of RC frame is tested, and the performance evaluation index is obtained; the present application solves the inverse of a small-scale matrix, significantly improves the calculation efficiency and reduces the computer memory requirement.

Description

Technical Field

[0001] This invention relates to the field of structural seismic technology, and in particular to a method for evaluating the seismic toughness of RC frames based on a basis vector-guided support vector machine. Background Technology

[0002] With the continuous development of seismic design and construction technology, building structural design has gradually shifted from collapse-resistant design to seismic toughness design. In recent years, some buildings have been able to withstand significant seismic forces without collapsing, but they may be demolished due to high maintenance costs. For example, in the 2011 Christchurch earthquake in New Zealand, many buildings, although not collapsed, required reconstruction due to damage to non-structural components and loss of internal items, resulting in huge economic losses. Therefore, in structural engineering and architectural design, the assessment of building seismic toughness has gradually gained importance among scholars, researchers, and structural design practitioners. Currently, the assessment of building seismic losses mainly relies on four standards or systems, including FEMA P-58, REDi, USRC, and China's "Standard for Evaluation of Building Seismic Toughness" (GB / T 38591-2020). These standards or systems are based on EDPs (Engineering Demand Parameters) and assess the seismic losses of building structures through parameters such as IDRs (Interstory Drift Ratio) and PFAs (Peak Floor Acceleration).

[0003] Traditional seismic toughness assessment requires extensive elastoplastic time-history analysis using the Finite Element Method (FEM), which consumes significant computational time and resources, resulting in low computational efficiency. In recent years, Machine Learning (ML) and big data technologies have brought new research avenues to civil engineering, effectively improving computational efficiency. For example, the article "Seismic Damage Prediction of Regional Reinforced Frame Structures Based on Component Performance" published in the 2022 issue of the *Journal of Civil Engineering* (Vol. 55, S01) proposes a seismic performance assessment system based on component deformation and a machine learning algorithm for regional RC (Reinforced Frame) structures. A method for predicting seismic damage in reinforced concrete frame structures was developed. Results showed that the CatBoost machine learning method can efficiently predict the performance state distribution of each component in the regional structure and intuitively present the performance level of the regional structure. The paper "Sensitivity Analysis and Damage Potential Assessment of Seismic Ground Motion Intensity Indicators Based on Machine Learning" published in the *Journal of Building Structures* (Vol. 44, No. 11, 2023) proposed a method for sensitivity analysis using the extreme random forest algorithm to quantify the influence of seismic intensity indicators on damage indicators. Results showed that extreme random forest can better assess damage potential, and its advantage in assessment accuracy increases with the increase of the basic period of the structure. The paper "Research on Seismic Damage Level Prediction of Mega-Structure Isolation Systems Based on Machine Learning" published in *Vibration and Shock* (Vol. 42, No. 20, 2023) proposed a seismic damage level prediction method that uses machine learning to correlate structural information, seismic ground motion information, and structural damage level. Comparison of damage level prediction results for mega-structure isolation systems using various machine learning methods showed that the overall prediction accuracy of extreme gradient boosting tree, gradient boosting tree, random forest, and decision tree all reached over 80%, with the extreme gradient boosting tree algorithm performing best at an accuracy of 86.6%. These machine learning-based methods can process and analyze large amounts of complex data, showing significant potential in the field of seismic toughness assessment. However, because these methods only consider the impact of structural components on seismic damage and do not take into account the complex ground motion, the nonlinear relationship between non-structural components and seismic toughness, they exhibit the problem of performing well under specific types of structures or seismic conditions but poorly under new structures outside the dataset. Therefore, it is necessary to consider non-structural information that has a significant impact on structural toughness and to establish ML (Machine Learning) models for seismic toughness assessment.

[0004] For example, CN114741758A discloses a preliminary design method and system for building seismic resilience based on machine learning, belonging to the field of building seismic resilience design. It includes steps such as collecting basic data, establishing seismic resilience targets, extracting seismic hazard characteristics, identifying building design characteristics, determining structural design characteristics and upgrade measures, and processing and determining an optimized model for building seismic resilience. By using building design models and structural design models, all available structural design features and structural and non-structural component upgrade measures are identified to form a design space. By integrating machine learning to improve the preliminary design process of buildings, focusing on the relationship between seismic hazard characteristics, building design characteristics, structural design characteristics, and resilience targets, the aim is to improve design quality and efficiency, especially in improving the seismic resistance of buildings. This invention, by considering the relationship between seismic hazard characteristics, building design characteristics, structural design characteristics, and resilience targets, can improve the quality and efficiency of structural design. However, training the machine learning model requires a large amount of building seismic resilience data, which may lead to long training times and require more computational resources and time to achieve satisfactory performance, thus limiting the generalization ability of the machine learning method to the scale of the training data.

[0005] Machine Learning (ML) methods can transform complex physics-based analytical calculations into simple data matrix calculations by adaptively fitting training samples, forming a predictive model (i.e., the training process), given a training sample. When using the established predictive model to predict results, it is essentially equivalent to the product of a matrix and a vector, thus offering high computational efficiency. However, when the training sample size is large, the training process of ML methods requires solving for the inverse matrix of the matrix formed by the training samples, which places high demands on computer memory and significantly reduces computational efficiency. Therefore, it is urgent to provide a novel ML model capable of handling large-scale training samples for evaluating seismic toughness. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a method for assessing the seismic toughness of RC frames based on basis vector guided support vector machines, thereby addressing the two key issues of low computational efficiency of existing seismic toughness assessment methods and high computer memory consumption when traditional machine learning models process large-scale data.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by this invention is a method for evaluating the seismic toughness of RC frames based on basis vector-guided support vector machines, comprising the following steps: Step 1: Collect seismic toughness data of various classic RC (Reinforced Concrete) frame structures, including a seismic toughness dataset of RC frames with multiple feature variables, and divide the data into training set and test set; Step 2: By establishing the minimum error objective function, solve the objective function to develop the basis vector adaptive selection (BVAS) algorithm to actively select the optimal basis vector; Step 3: Based on the BVAS algorithm, extract small-scale sub-samples from the large-scale dataset as basis vectors, and map them to a high-dimensional feature space to establish the BVAS-LS-SVMR model; Step 4: Use the training set data to train the BVAS-LS-SVMR model and establish a seismic toughness prediction model for RC (Reinforced Concrete) frames. Step 5: Based on the test set data, verify the performance of the seismic toughness prediction model for RC (Reinforced Concrete) frames and obtain the performance evaluation index of the method.

[0008] In the preferred embodiment, step 1 includes 14 variables related to building information and 8 variables related to ground motion, totaling 22 variables that have a significant impact on the seismic toughness index of buildings, which serve as the feature variables of the dataset.

[0009] In the preferred embodiment, the twenty-two variables specifically include: fourteen building information items such as the number of stories, bearing capacity degradation parameter D, beam width, beam height, first-floor column section height, first-floor column section width, standard-floor column section height, standard-floor column section width, first-floor column longitudinal reinforcement ratio, standard-floor column longitudinal reinforcement ratio, first-floor beam longitudinal reinforcement ratio, intermediate-floor beam longitudinal reinforcement ratio, top-floor beam longitudinal reinforcement ratio, and first-order natural vibration period T1; and eight seismic motion parameters such as peak ground acceleration PGA, peak ground velocity PGV, peak ground displacement PGD, Vs30 fault distance, 5~95% energy duration, 5~75% energy duration, magnitude, and spectral acceleration Sa.

[0010] In the preferred embodiment, the theoretical basis of the BVAS algorithm described in Step 2 is to establish a minimum error objective function by calculating the Euclidean distance between the estimated sample data points (approximately estimated by basis vectors) and the actual sample data values ​​in Hilbert space. Solving the objective function allows for the development of a basis vector adaptive selection BVAS algorithm that actively selects the optimal basis vector. Its mathematical principle can be expressed as follows: For each sample vector Both can be subsets consisting of M subsamples An approximate estimation table, denoted as:

[0011] (1)

[0012] In the formula, This is the weight vector;

[0013] Euclidean distance It can be represented as:

[0014] (2)

[0015] Minimizing the Euclidean distance can be expressed as: (3)

[0016] in, (4)

[0017] (5)

[0018] (6)

[0019] In the formula, Let L be the square of the L2 norm of the sample vector, which represents the length of the vector in Euclidean space. and This is a matrix representation of the Euclidean distance between sample vectors and subsample vectors. Represents sample vector and subsamples Geometric distance in Hilbert space.

[0020] Therefore, a minimum error objective function can be established: (7)

[0021] In the preferred embodiment, the establishment of the BVAS-LS-SVMR model in Step 3 is based on the BVAS algorithm to extract small-scale subsamples from a large-scale dataset, and then mapping the selected subsamples to a high-dimensional feature space as basis vectors to approximate the least squares support vector machine LS-SVMR model. (8)

[0022] Parameters in And a constant b, and then establish a basis vector adaptive selection algorithm to guide the support vector machine regression model BVAS-LS-SVMR, reducing the computational complexity and memory requirements of the traditional LS-SVMR model training process.

[0023] In the preferred embodiment, the structural learning and parameter learning in Step 4 involve using optimization algorithms to adjust the structure and parameters of the BVAS-LS-SVMR model in order to achieve the best fit to the seismic toughness characteristics of different RC (Reinforced Concrete) frame structures.

[0024] In the preferred embodiment, the validation and performance evaluation in Step 5 involves comparing the BVAS-LS-SVMR model with common machine learning methods, including Ridge Regression, Lasso Regression, ElasticNet Regression, and Artificial Neural Networks (ANNs), by analyzing the coefficients of determination of each model on the training and test sets. The mean absolute error (MAE) of the test set and the model training time were used to comprehensively evaluate the training efficiency and prediction accuracy of these models. Through comparative analysis with existing technologies, the application value of this invention in the field of seismic toughness assessment of RC (Reinforced Concrete) frames was confirmed.

[0025] The seismic toughness assessment method for RC frames based on basis vector guided support vector machine provided by this invention has the following beneficial effects: 1. The seismic toughness assessment method for RC frames proposed in this invention effectively solves the problem of low computational efficiency of seismic toughness assessment methods based on the traditional finite element method (FEM), and is nearly 10,689 times faster than FEM, further improving the computational efficiency of seismic toughness assessment methods. 2. The seismic toughness assessment method for RC frames proposed in this invention selects the most suitable basis vector approximation LS-SVMR model by developing the BVAS algorithm. In This improves the robustness of the BVAS-LS-SVMR model's prediction performance;

[0026] 3. This invention compares the BVAS-LS-SVMR model with common machine learning methods, verifying the significant advantages of the BVAS-LS-SVMR model in terms of prediction accuracy and training efficiency, and solving the problem of high computer memory consumption when traditional machine learning models process large-scale data. Attached Figure Description

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a technical roadmap of the present invention; Figure 2 This is the main working principle of the BVAS-LS-SVMR model of this invention. Detailed Implementation

[0028] like Figures 1-2 As shown, the seismic toughness assessment method for RC frames based on basis vector guided support vector machines includes the following steps: Step 1: Collect seismic toughness data of various classic RC (Reinforced Concrete) frame structures, including a seismic toughness dataset of RC (Reinforced Concrete) frame structures with multiple feature variables, and divide the data into training set dataset and test set dataset; Step 2: By establishing the minimum error objective function, solve the objective function to develop the basis vector adaptive selection (BVAS) algorithm to actively select the optimal basis vector; Step 3: Based on the BVAS algorithm, extract small-scale sub-samples from the large-scale dataset as basis vectors, and map them to a high-dimensional feature space to establish the BVAS-LS-SVMR model; Step 4: Use the training set data to perform structural learning and parameter learning for BVAS-LS-SVMR, and establish a seismic toughness prediction model for the RC frame. Step 5: Based on the test set data, the established seismic toughness prediction model of the RC (Reinforced Concrete) frame is validated, and the performance evaluation index of the method is obtained.

[0029] In step 1, there are 14 building information-related variables and 8 seismic motion-related variables, totaling 22 variables that have a significant impact on the seismic resilience index of buildings, which serve as the feature variables of the dataset.

[0030] The twenty-two variables specifically include: fourteen building information items such as number of stories, bearing capacity degradation parameter D, beam width, beam height, first-floor column section height, first-floor column section width, standard-floor column section height, standard-floor column section width, first-floor column longitudinal reinforcement ratio, standard-floor column longitudinal reinforcement ratio, first-floor beam longitudinal reinforcement ratio, intermediate-floor beam longitudinal reinforcement ratio, top-floor beam longitudinal reinforcement ratio, and first-order natural vibration period T1; and eight ground motion parameters such as peak ground acceleration PGA, peak ground velocity PGV, peak ground displacement PGD, Vs30 fault distance, 5~95% energy duration, 5~75% energy duration, magnitude, and spectral acceleration Sa.

[0031] The theoretical basis of the BVAS algorithm described in Step 2 is that by calculating the Euclidean distance between the estimated sample data points (approximately estimated by basis vectors) and the actual sample data values ​​in Hilbert space, a minimum error objective function is established. Solving the objective function develops the basis vector adaptive selection BVAS algorithm, which actively selects the optimal basis vector. Its mathematical principle can be expressed as follows: For each sample vector Both can be subsets consisting of M subsamples An approximate estimation table, denoted as:

[0032] (1)

[0033] In the formula, This is the weight vector;

[0034] Euclidean distance It can be represented as:

[0035] (2)

[0036] Minimizing the Euclidean distance can be expressed as: (3)

[0037] in, (4)

[0038] (5)

[0039] (6)

[0040] In the formula, Let L be the square of the L2 norm of the sample vector, which represents the length of the vector in Euclidean space. and This is a matrix representation of the Euclidean distance between sample vectors and subsample vectors. Represents sample vector and subsamples Geometric distance in Hilbert space.

[0041] Therefore, a minimum error objective function can be established: (7)

[0042] The BVAS-LS-SVMR model established in Step 3 is based on the BVAS algorithm to extract small-scale subsamples from a large-scale dataset, and then mapping the selected subsamples to a high-dimensional feature space as basis vectors to approximate the least squares support vector machine LS-SVMR model. (8)

[0043] Parameters in With the constant b, a basis vector adaptive selection algorithm is established to guide the support vector machine regression model BVAS-LS-SVMR, reducing the computational complexity and memory requirements of the traditional LS-SVMR model training process.

[0044] The BVAS-LS-SVMR model proposed in this invention is as follows: (9)

[0045] In the formula, For the new linear combination coefficients, , , Let f(x) represent the mapping function from p-dimensional space to a high-dimensional Hilbert space with h dimensions. It is a constant. Subsample input variables selected for the BVAS algorithm The high-dimensional feature vector formed by mapping to a high-dimensional feature space is denoted as .

[0046] The structural learning and parameter learning in Step 4 involve using optimization algorithms to adjust the structure and parameters of the BVAS-LS-SVMR model in order to achieve the best fit to the seismic toughness characteristics of different RC (Reinforced Concrete) frame structures.

[0047] The validation and performance evaluation in Step 5 compares the BVAS-LS-SVMR model with common machine learning methods, including Ridge regression, Lasso regression, ElasticNet regression, and ANN (Artificial Neural Network). This is achieved by analyzing the performance of each model on the training and test sets. The training efficiency and prediction accuracy of these models were comprehensively evaluated using R squared (coefficient of determination), MAE (mean absolute error) of the test set, and model training time. Comparative analysis with existing technologies confirmed the application value of this invention in the field of seismic toughness assessment of RC (reinforced concrete) frames. Specific results are shown in Table 1.

[0048] Table 1 Performance comparison of BVAS-LS-SVMR and various ML models

[0049] Table 1 provides a more detailed breakdown of the performance metrics for various Machine Learning (ML) models. In Table 1, the computation time for the BVAS-LS-SVMR model represents the average of 10 training iterations, while the prediction performance metrics represent the average of 10 predictions. The BVAS-LS-SVMR model demonstrates excellent performance on both the training and test sets. The values ​​reached 0.982 and 0.974 respectively, while possessing an extremely low MAE on the test set (0.0297). Furthermore, the model's training time was only 1.55 seconds, demonstrating its efficient training capabilities. In contrast, although ANN performs poorly on the test set... The value (0.984) is slightly higher than BVAS-LS-SVMR, but its training time is significantly longer at 76.11 seconds. Among other algorithms, the Ridge regression model, Lasso regression model, and ElasticNet regression model perform relatively poorly. Their performance on the test set... The values ​​were 0.730, 0.700, and 0.707, respectively, and the MAEs were 0.1034, 0.1045, and 0.1033, respectively. This indicates a significant gap in prediction accuracy. Although the ElasticNet regression model has an extremely short training time of only 0.078 seconds, its overall performance is far inferior to the prediction performance of the BVAS-LS-SVMR model.

[0050] In summary, this invention provides a method for assessing the seismic toughness of RC (Reinforced Concrete) frames based on basis vector-guided support vector machines. This method addresses two key issues: the low efficiency of FEM (Finite Element Method) in calculating building seismic toughness indices, and the inefficiency of ML (Machine Learning) training with large-scale training samples. Comparative analysis with various ML methods verifies the computational efficiency and predictive performance of the established RC (Reinforced Concrete) frame seismic toughness prediction model, providing important reference for the development of building seismic toughness assessment methods.

Claims

1. A method for assessing the seismic toughness of RC frames based on basis vector-guided support vector machines, characterized in that, The method includes the following steps: Step 1: Collect seismic toughness data of various RC frame structures, including a seismic toughness dataset of RC frames with multiple feature variables, and divide the data into training set and test set; Step 2: By establishing a minimum error objective function and solving the objective function, the BVAS (Boundary Vector Adaptive Selection) algorithm is developed to actively select the optimal basis vectors. The theoretical basis of the BVAS algorithm is to establish a minimum error objective function by calculating the Euclidean distance between the estimated sample data points (approximately estimated by the basis vectors) and the actual sample data values ​​in Hilbert space. Solving the objective function allows the BVAS algorithm to actively select the optimal basis vectors. Its mathematical principle is expressed as follows: For each sample vector... All passed A subset consisting of subsamples An approximate estimation table, denoted as: （1）； In the formula, This is the weight vector; Euclidean distance Represented as: （2）； Minimize the Euclidean distance as follows: （3）； in, （4）； （5）； （6）； In the formula, Let be the square of the L2 norm of the sample vector, and let be the length of the vector in Euclidean space. and It is a matrix representation of the Euclidean distance between sample vectors and subsample vectors; Represents sample vector and subsamples Geometric distance in Hilbert space; Therefore, the objective function for minimizing error is established as follows: （7）； Step 3: Extract small-scale subsamples from a large-scale dataset using the BVAS algorithm as basis vectors, and map them to a high-dimensional feature space to establish the BVAS-LS-SVMR model. The BVAS-LS-SVMR model is based on the BVAS algorithm to extract small-scale subsamples from a large-scale dataset, and then mapping the selected subsamples to a high-dimensional feature space as basis vectors, which are used to approximate the parameters in the least squares support vector machine (LS-SVMR) model. and constant Furthermore, a basis vector adaptive selection algorithm is established to guide the support vector machine regression model BVAS-LS-SVMR: （9）； In the formula, For the new linear combination coefficients; , , Indicates from Dimension to have Mapping functions for high-dimensional Hilbert spaces; It is a constant; Subsample input variables selected for the BVAS algorithm High-dimensional feature vectors are formed by mapping onto a high-dimensional feature space; Step 4: Use the training set data to train the BVAS-LS-SVMR model and establish a seismic toughness prediction model for the RC frame. Step 5: Based on the test set data, verify the performance of the seismic toughness prediction model of the RC frame and obtain the performance evaluation index of the method.

2. The seismic toughness assessment method for RC frames based on basis vector guided support vector machine according to claim 1, characterized in that: The Step 1 section includes 14 variables related to building information and 8 variables related to ground motion, totaling 22 variables that have a significant impact on the seismic resilience index of buildings, which serve as the feature variables of the dataset.

3. The method for evaluating the seismic toughness of RC frames based on basis vector guided support vector machine according to claim 2, characterized in that: The twenty-two variables specifically include: Fourteen building information items: number of stories, bearing capacity degradation parameter D, beam width, beam height, first-floor column section height, first-floor column section width, standard-floor column section height, standard-floor column section width, first-floor column longitudinal reinforcement ratio, standard-floor column longitudinal reinforcement ratio, first-floor beam longitudinal reinforcement ratio, intermediate-floor beam longitudinal reinforcement ratio, top-floor beam longitudinal reinforcement ratio, and first-order natural vibration period T1; Eight ground motion parameters: peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), Vs30 fault distance, 5-95% energy duration, 5-75% energy duration, magnitude, and spectral acceleration (Sa).

4. The seismic toughness assessment method for RC frames based on basis vector guided support vector machine according to claim 1, characterized in that: The expression for the LS-SVMR model in Step 3 is as follows: （8）。 5. The method for assessing the seismic toughness of RC frames based on basis vector guided support vector machine according to claim 1, characterized in that: The training of the BVAS-LS-SVMR model in Step 4 involves using an optimization algorithm to adjust the structure and parameters of the BVAS-LS-SVMR model in order to achieve the best fit to the seismic toughness characteristics of different RC frame structures.

6. The method for assessing the seismic toughness of RC frames based on basis vector guided support vector machine according to claim 1, characterized in that, The validation and performance evaluation in Step 5 involves comparing the BVAS-LS-SVMR model with common machine learning methods, including Ridge Regression, Lasso Regression, ElasticNet Regression, and Artificial Neural Networks (ANNs), by analyzing the coefficients of determination of each model on the training and test sets. The mean absolute error (MAE) of the test set and the model training time are used to comprehensively evaluate the training efficiency and prediction accuracy of these models.

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