Method and system for evaluating seismic performance of large-span building

Abstract

This specification provides a method and system for evaluating the seismic performance of long-span buildings. The method includes: acquiring multidimensional performance response data of the long-span building under seismic motion to form a sample set; determining the initial number of cluster centers based on a preset number K of seismic performance levels; calculating the sensitivity coefficient of each response parameter to overall damage; identifying extreme response samples in the sample set and selecting the point with the largest weighted Euclidean distance from the origin as the first initial cluster center; calculating the local density of unselected candidate sample points and calculating the minimum weighted distance between the sample point and all selected centers; multiplying the local density by the minimum weighted distance to obtain an evaluation index; selecting the sample point with the largest evaluation index as the next center; and using the determined K centers as initial centroids to perform weighted cluster analysis on the performance sample set to obtain a classification of K seismic performance levels.

Description

Technical Field

[0001] This application belongs to the field of assessment, and in particular relates to a method and system for assessing the seismic performance of large-span buildings. Background Technology

[0002] Performance-based seismic planning theory classifies the seismic performance of structures into several levels, such as normal use, basic usability, life safety, and collapse prevention. Time-history analysis methods select multiple sets of ground motion records to calculate the structural model, thereby obtaining structural performance response data, such as maximum inter-story drift angle, vertex displacement, base shear force, and nodal acceleration. Level classification based on engineering experience, which sets preset thresholds for single or a few performance parameters, fails to represent the overall damage state of the structure. Clustering algorithms based on unsupervised learning, such as K-means and fuzzy C-means (FCM), can divide multidimensional performance response samples into different clusters based on the distribution characteristics of the data itself, with each cluster corresponding to a seismic performance level, realizing a shift from single-index threshold to multi-index data-driven approaches. However, partitioning clustering algorithms, such as K-means, randomly select initial cluster centers, leading to high sensitivity of the clustering results to initial values. Multiple runs may yield different partitioning results, exhibiting poor stability and a tendency to get trapped in local optima. Clustering algorithms use standard Euclidean distance when calculating the distance between samples, assuming that all performance response parameters contribute equally to the overall structural damage. However, in reality, different parameters have varying indicative significance and importance for structural damage. Therefore, how to develop an evaluation method that can reasonably balance the importance of each performance parameter and stably select representative initial cluster centers is a pressing technical problem to be solved in the field of seismic performance evaluation of long-span buildings. Summary of the Invention

[0003] This specification provides one or more embodiments of a method for evaluating the seismic performance of large-span buildings, the method comprising the following steps: Multidimensional performance response data of large-span buildings under multiple sets of seismic excitation are obtained to form a performance sample set; the number of initial cluster centers is determined according to the preset number of seismic performance levels K; based on the performance sample set, the sensitivity coefficient of each performance response parameter to the overall structural damage is calculated to form a weight vector. Based on a preset performance response parameter threshold, extreme response samples in the performance sample set are identified, and the sample point with the largest weighted Euclidean distance from the origin is selected from the extreme response samples as the first initial cluster center. The weighted Euclidean distance is calculated using the weight vector. Repeat the operation K-1 times or less to determine the remaining initial cluster centers: For candidate sample points i that are not selected as initial cluster centers, calculate the local density of the sample points. And calculate the minimum weighted distance between the sample point and all selected initial cluster centers. ; wherein, the local density The minimum weighted distance is calculated based on the weighted Euclidean distance between candidate sample point i and other sample points. It is the minimum weighted Euclidean distance between the candidate sample point i and each center point in the selected initial cluster center set, wherein the weighted Euclidean distance is calculated using the weight vector; the local density is... With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center; Using the K predetermined initial cluster centers as initial centroids, a weighted cluster analysis is performed on the performance sample set to obtain K seismic performance level classifications.

[0004] This specification also provides one or more embodiments of a seismic performance evaluation system for large-span buildings, the system comprising the following modules: The calculation module is used to acquire multidimensional performance response data of large-span buildings under multiple sets of seismic excitations to form a performance sample set; determine the number of initial cluster centers according to the preset number of seismic performance levels K; and calculate the sensitivity coefficient of each performance response parameter to the overall structural damage based on the performance sample set to form a weight vector. The selection module is used to identify extreme response samples in the performance sample set based on a preset performance response parameter threshold, and select the sample point with the largest weighted Euclidean distance from the origin of the coordinates from the extreme response samples as the first initial cluster center. The weighted Euclidean distance is calculated using the weight vector. The determination module is used to perform the operation K-1 times or less to determine the remaining initial cluster centers: for candidate sample points i that are not selected as initial cluster centers, the local density of the sample points is calculated. And calculate the minimum weighted distance between the sample point and all selected initial cluster centers. ; wherein, the local density The minimum weighted distance is calculated based on the weighted Euclidean distance between candidate sample point i and other sample points. It is the minimum weighted Euclidean distance between the candidate sample point i and each center point in the selected initial cluster center set, wherein the weighted Euclidean distance is calculated using the weight vector; the local density is... With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center; The analysis module is used to perform weighted cluster analysis on the performance sample set using K predetermined initial cluster centers as initial centroids to obtain K seismic performance level classifications.

[0005] This invention constructs a weight vector by calculating the sensitivity coefficient of performance response parameters to structural damage, and applies this weight vector to the initialization and cluster analysis of cluster centers. This represents the true contribution of each parameter to the overall structural damage, enhancing the rationality of the evaluation results. A deterministic initial cluster center selection strategy is adopted, identifying the center of the most unfavorable performance state by recognizing extreme response samples, and then sequentially determining other initial centers by combining local density and the minimum weighted distance from the selected centers. This ensures that the initial cluster centers have good representativeness and separability, avoiding the problems of unstable clustering results and easy trapping in local optima caused by random selection of initial centers. Therefore, it improves the objectivity and reliability of the seismic performance classification of large-span buildings. Attached Figure Description

[0006] Figure 1 A flowchart of the first embodiment; Figure 2 This is a schematic diagram illustrating the acquisition of multidimensional performance response data. Figure 3 Decision graph for selecting new cluster centers. Detailed Implementation

[0007] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this specification as detailed in the appended claims.

[0008] It should be understood that the terms “comprising” and “having”, and any variations thereof, in the embodiments of this specification are intended to cover but not exclude inclusion. For example, a product or device that includes a series of components is not necessarily limited to those components that are explicitly listed, but may include other components that are not explicitly listed or that are inherent to such product or device.

[0009] This specification provides one or more embodiments of a method for evaluating the seismic performance of large-span buildings, referring to... Figure 1 This includes the following steps: S1: Obtain multidimensional performance response data of large-span buildings under multiple sets of seismic excitation to form a performance sample set; determine the number of initial cluster centers according to the preset number of seismic performance levels K.

[0010] An analysis model of a large-span building is established using finite element analysis software such as ABAQUS or OpenSees. Multiple sets of ground motion records conforming to the site characteristics are selected from the PEERNGA strong earthquake database as input. Incremental dynamic analysis or multi-strip time history analysis is performed on the model to extract the maximum values ​​of multiple performance response parameters of the structure under each analysis case, such as inter-story drift angle, top displacement, story acceleration, or component damage index. The response data of all cases are organized into an N-row, M-column performance sample matrix, where N is the number of ground motion cases and M is the dimension of the performance response parameters. This matrix is ​​the performance sample set. According to the seismic design code or assessment requirements, the seismic performance level is preset to K levels: intact, slightly damaged, moderately damaged, and severely damaged. The number of initial cluster centers is then determined to be K.

[0011] Specifically, the acquisition of multidimensional performance response data of large-span buildings under multiple sets of seismic excitations constitutes a performance sample set, including: S101: Establish a finite element analysis model for large-span buildings; S102: Select 30 natural ground motion records and adjust the peak ground acceleration amplitude to 0.1g, 0.2g, 0.4g and 0.6g respectively to form 120 sets of ground motion excitations; S103: Perform time history analysis on the model to extract the maximum inter-story drift angle, maximum vertex displacement, maximum vertex acceleration, and residual drift angle of the structure under each set of excitations, forming a four-dimensional performance response data sample.

[0012] To obtain reliable performance data, an analytical model capable of representing the actual stress behavior of the structure needs to be established in professional finite element software such as OpenSees, SAP2000, or ABAQUS. The model should simulate the structure's geometry, component cross-sectional properties, and employ constitutive relations that consider the development of material plasticity, such as a bilinear kinematic hardening model for steel, and P-Δ geometric effects. At least 30 representative natural ground motion records covering different site conditions and magnitudes should be selected from authoritative seismic ground motion databases such as PEERNGA-West2. To study the structural response under different seismic intensities, the peak ground acceleration (PGA) of each ground motion is adjusted to multiple levels, such as 0.1g for frequent earthquakes, 0.2g fortification earthquakes, 0.4g rare earthquakes, and 0.6g extremely rare earthquakes, forming a ground motion excitation set.

[0013] Each ground motion from the excitation set is sequentially input into the established finite element model, and dynamic time history analysis is performed. This analysis solves the structure's equations of motion step by step in the time domain, enabling the detection of the detailed response process after the structure enters the nonlinear stage. After each analysis, a set of pre-selected performance indicators representing the structural performance is extracted from the results. The indicator combination includes: maximum inter-story drift angle, representing the degradation of the structure's lateral stiffness and damage to non-structural components; maximum vertex displacement, representing the overall deformation of the structure; maximum vertex acceleration, related to the influence of higher-order vibration modes and equipment safety; and residual displacement angle, representing the difficulty of post-earthquake structural repair. This set of values ​​constitutes a multi-dimensional vector, representing a performance sample under this ground motion excitation, with reference to... Figure 2 After completing all the analyses, a performance sample set containing all sample points is obtained.

[0014] S2: Based on the performance sample set, calculate the sensitivity coefficient of each performance response parameter to the overall structural damage, and form a weight vector; The entropy weight method is used to calculate the weight vector of each performance response parameter. The steps are as follows: Normalize the N x M performance sample matrix to eliminate the influence of dimensions. A commonly used normalization algorithm is min-max scaling. Calculate the proportion of the i-th sample value under the j-th performance response parameter to the sum of all sample values ​​for that parameter. Calculate the entropy value of the j-th performance response parameter based on the proportion. Then, calculate the difference coefficient of the j-th performance response parameter based on the entropy value. The larger the difference coefficient, the more information the parameter provides. Normalize the difference coefficients of each parameter to obtain the weight of each performance response parameter. The weights of all parameters constitute an M-dimensional weight vector.

[0015] To determine the importance of each performance response parameter for weighted clustering analysis, in one embodiment, the sensitivity coefficient of each performance response parameter to overall structural damage is calculated based on the performance sample set, forming a weight vector, including: S201: The overall structural damage index corresponding to each performance sample is calculated using the Park-Ang damage model; S202: Calculate the Pearson correlation coefficient between the sequence of each performance response parameter and the overall structural damage index sequence; S203: Normalize the absolute values ​​of the Pearson correlation coefficients of each performance response parameter, and use the resulting values ​​as the sensitivity coefficients of the parameters. The sensitivity coefficients of all parameters together constitute the weight vector.

[0016] For each sample in the performance sample set, i.e., the multidimensional response result under each seismic excitation, a single overall structural damage index (DI) is calculated using the Park-Ang damage model. This model integrates the maximum deformation of the structure and the energy dissipation accumulated during the earthquake; the calculation formula is as follows: ,in To calculate the maximum inelastic deformation, This refers to the ultimate deformation capacity of the structure under monotonic load. For hysteresis energy dissipation during the earthquake process, The yield strength of the structure, This represents the energy dissipation parameter indicating the impact of cyclic loading damage. Therefore, a sample set containing N multidimensional performance samples will generate an N-dimensional overall damage index sequence.

[0017] If there are M performance response parameters, then calculate the Pearson correlation coefficient between the sequence of each parameter in N samples and the N-dimensional overall damage index sequence obtained in the previous step. The Pearson correlation coefficient ranges from -1 to 1. The closer the absolute value is to 1, the stronger the linear correlation between the performance parameter and the overall structural damage. The absolute value of the correlation coefficient for each parameter is taken and normalized to ensure that the sum of the weights of all parameters is 1. The normalization formula is as follows: ,in The weight of the j-th parameter is the sensitivity coefficient. This is the Pearson correlation coefficient; the summation term sums the absolute values ​​of the correlation coefficients of all performance response parameters. The resulting weight set... This forms the weight vector W.

[0018] S3: Based on a preset performance response parameter threshold, identify extreme response samples in the performance sample set, and select the sample point with the largest weighted Euclidean distance from the origin of the coordinate system from the extreme response samples as the first initial cluster center. The weighted Euclidean distance is calculated using the weight vector.

[0019] According to the seismic design code for buildings or relevant performance evaluation standards, a corresponding limit threshold for collapse or severe damage is set for each performance response parameter. Each sample in the performance sample set is iterated over; if at least one performance response parameter in the sample exceeds the corresponding limit threshold, the sample is identified as an extreme response sample, forming an extreme response sample subset. For each sample point in the extreme response sample subset, the weighted Euclidean distance between the weight vector obtained in the previous step and the origin of the M-dimensional coordinate system is calculated. This distance is calculated by multiplying the squares of the coordinate values ​​of each dimension of the sample point by the corresponding weights, summing the results, and then taking the square root of the sum. Among all extreme response samples, the sample point with the largest calculated weighted Euclidean distance is selected as the first initial cluster center. It should be understood in the art that when calculating the distance, different dimensional values ​​need to be normalized separately. Optionally, the sample set constituting the multidimensional performance response data is standardized, such as by Z-score standardization or Min-Max normalization, to eliminate dimensional differences between different performance response parameters; the weighted Euclidean distance calculation is based on the standardized data.

[0020] To find a sample point that represents the highest damage level as the starting point for clustering, as an optional implementation, the process involves identifying extreme response samples in the performance sample set and selecting the sample point with the largest weighted Euclidean distance from the origin as the first initial cluster center, including: S301: Use the "severe damage" state limit of each performance response parameter as a preset threshold; S302: Traverse the performance sample set. If at least one performance response parameter of a sample point exceeds the "severe damage" state limit corresponding to the sample point, then the sample point is identified as an extreme response sample. S303: Calculate the weighted Euclidean distance between each extreme response sample point and the origin in the multidimensional performance response space; S304: Select the extreme response sample point with the largest calculated weighted Euclidean distance value as the first initial cluster center.

[0021] Define severe failure limits for each performance response parameter. These limits are typically determined based on relevant seismic design codes or research findings. For example, for long-span steel structures, the severe failure limit for the maximum inter-story drift angle can be set to 1 / 50, and the limit for the residual drift angle can be set to 0.005. Iterate through each data point in the performance sample set, checking the values ​​of each dimension, i.e., each performance response parameter. If any dimension value of a sample point exceeds the corresponding limit, for example, the maximum inter-story drift angle of 0.023 is greater than 1 / 50, then that sample point is classified as an extreme response sample.

[0022] After identifying all extreme response samples, the most representative one needs to be selected. To do this, the value of each extreme response sample point is calculated. The weighted Euclidean distance between the origin O and the zero state where the structure is undamaged. The calculation formula is: The summation iterates through all M performance response parameter dimensions. It is the weight of the j-th parameter determined in the previous step. Sample points The coordinate value in the j-th dimension. This distance comprehensively considers the response amplitude of all performance parameters and their contribution to the overall damage; the larger the value, the more severe the overall structural damage state represented by the sample point. The weighted Euclidean distance values ​​calculated for all extreme response samples are compared, and the sample point with the largest distance value is selected as the first initial cluster center. .

[0023] S4: Repeat the operation K-1 times or less to determine the remaining initial cluster centers: For candidate sample points i that were not selected as initial cluster centers, calculate the local density of the sample points. And calculate the minimum weighted distance between the sample point and all selected initial cluster centers. ; wherein, the local density The minimum weighted distance is calculated based on the weighted Euclidean distance between candidate sample point i and other sample points. It is the minimum weighted Euclidean distance between the candidate sample point i and each center point in the selected initial cluster center set, wherein the weighted Euclidean distance is calculated using the weight vector; the local density is... With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center; Initialize a set of selected initial cluster centers and add the first initial cluster center to this set; loop K-1 times, and in each loop, perform the following calculation on all candidate sample points that have not yet been selected as initial cluster centers: Set cutoff distance Typically, the weighted Euclidean distances between all sample points are sorted in ascending order, and the distance values ​​of the top 1% to 2% are taken as the mean. For a candidate sample point i, iterate through all other sample points j in the sample set and calculate the weighted Euclidean distance between i and j. The local density of i is calculated using a Gaussian kernel function. Specifically, for all j, calculate the value of the exponential function and sum all the results to obtain the value. .

[0024] For each candidate sample point i, iterate through each center point c in the selected initial cluster center set and calculate the weighted Euclidean distance between i and c. Select all The minimum value in is used as .

[0025] The calculated local density minimum weighted distance Multiply to obtain the evaluation index. .

[0026] Find the evaluation index among all candidate sample points. The point with the largest value is selected as the initial cluster center for this iteration and added to the set of selected initial cluster centers.

[0027] In one possible embodiment, for candidate sample points i that are not selected as initial cluster centers, the local density of the sample points is calculated. ,include: S401: Set cutoff distance The value is the mean of the first 2% of the weighted Euclidean distances between all sample points in ascending order; S402: For any candidate sample point i, the local density of the sample point The formula, calculated using the Gaussian kernel function, is as follows: The summation iterates through all sample points j except for i. Let be the weighted Euclidean distance between sample point i and sample point j.

[0028] Determine a key parameter, cutoff distance. This defines the neighborhood range considered when calculating local density. To do this, the weighted Euclidean distance between all pairwise points in the performance sample set is first calculated. If the sample set size is N, then a total of N(N-1) / 2 distance values ​​will be generated. These distance values ​​are sorted from smallest to largest, and the distance value located at the 2% quantile after sorting is selected as the cutoff distance. Ensured The choice can adapt to the spatial distribution characteristics of the sample points.

[0029] Determining the cutoff distance Then, the local density of each candidate sample point i can be calculated. The calculation employs a Gaussian kernel function, which is both distance-sensitive and smooth. For sample point i, all other sample points j (excluding i itself) are iterated over, and the weighted Euclidean distance between i and j is calculated. ,calculate The value of represents the density contribution of point j to point i: when j is very close to i, much smaller This value is close to 1; when j is far from i, Much larger This value is close to 0. The sum of the contributions of all points j to point i is the local density of sample point i. . The larger the value, the stronger the performance. Within the neighborhood of the feature scale, the more other sample points clustered around sample point i, and the closer they are.

[0030] To calculate the distance between each candidate sample point and the nearest higher-density dominant point (i.e., the selected cluster center), and to measure the degree of separation at that point, as an optional implementation, the minimum weighted distance between the sample point and all selected initial cluster centers is calculated. ,include: S411: For a candidate sample point i and any selected cluster center k, calculate the weighted Euclidean distance. The calculation formula is: The summation iterates through all m performance response parameter dimensions. The weight of the m-th performance response parameter, and These are the coordinates of sample point i and the selected cluster center k in the m-th dimension, respectively. S412: Take the minimum weighted Euclidean distance among all the calculated weighted Euclidean distances between sample point i and all selected cluster centers as the minimum weighted distance. .

[0031] This calculation is performed after at least one initial cluster center has been determined, for each candidate sample point in the dataset that has not yet been selected as a cluster center. Calculate the set formed by it and all currently selected cluster centers. The weighted Euclidean distance to each center in the cluster. For example, when determining the second cluster center, There is only the first center in the middle. At this point, it is necessary to calculate each candidate point. arrive distance .

[0032] When it is necessary to determine a third cluster center There is already and Two center points. At this point, for each candidate point... Calculate separately and Two distance values ​​are used. After calculation, the smaller of the two distance values ​​is taken as the minimum weighted distance of the candidate point i. ,Right now . The value represents the distance from sample point i to its nearest cluster center. For the sample point with the highest local density, Defined as the maximum weighted distance from all sample points to it. Larger... The value indicates that the sample point is far from other established centers and has the potential to become a candidate for a new center.

[0033] The local density With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center, including: S421: For each candidate sample point i that has not yet been selected as a cluster center, the local density of the sample point is... With the minimum weighted distance Multiply to obtain the evaluation index for the sample points. ; S422: Evaluation metrics for all candidate sample points Sort in descending order; S423: Selecting Evaluation Indicators The largest candidate sample point is selected as the next initial cluster center.

[0034] Ideal cluster centers should possess two characteristics simultaneously: they themselves should be high-density points, i.e., local density. Large, and far from other higher-density points, i.e., the determined cluster centers, i.e., minimum weighted distance. Large. Evaluation indicators It is the combination of these two features. For each candidate sample point i in the dataset that has not yet been selected as a cluster center, the local density calculated in the previous steps is used. and minimum weighted distance Multiplying the two together yields the evaluation index for that point. .

[0035] After calculating all candidate sample points After the value, for The values ​​are compared globally to find the maximum value. The entity possessing this maximum value... The sample point with the highest value is considered to be the most suitable point to become the next cluster center. Figure 3 For example, if the value of sample point 35 is calculated... The value is 89.6, and this value is the largest among all candidate points. If the value is not specified, then sample point 35 is selected as the next initial cluster center. The selected point is added to the set of selected cluster centers, and the remaining candidate points are updated throughout the process. Recalculate And select the largest The process will be repeated until all K-1 remaining initial cluster centers are found.

[0036] S5: Using the K determined initial cluster centers as initial centroids, perform weighted cluster analysis on the performance sample set to obtain K seismic performance level classifications.

[0037] The weighted K-Means clustering algorithm is implemented, and its steps are as follows: The K initial cluster centers determined in the previous step are used as the initial centroids of the K clusters.

[0038] For each sample point in the performance sample set, the weighted Euclidean distance between the sample point and the K centroids is calculated using the weight vector, and the sample point is assigned to the cluster corresponding to the centroid with the smallest weighted Euclidean distance to the sample point.

[0039] For each cluster, the centroid is recalculated. The new centroid is the arithmetic mean of the coordinates of all sample points in each dimension within the cluster.

[0040] Repeat the cluster allocation and centroid update operations until the cluster allocation no longer changes or the preset maximum number of iterations is reached, at which point the algorithm converges; the resulting K clusters represent K seismic performance level classifications, and the sample points within each cluster have similar seismic response characteristics.

[0041] In an optional embodiment, the step of using K predetermined initial cluster centers as initial centroids to perform weighted cluster analysis on the performance sample set to obtain K seismic performance level classifications includes: S501: Use the determined K initial cluster centers as the initial centroids of the weighted K-means clustering algorithm; S502: Assign each sample point in the performance sample set to the cluster containing the centroid that is closest to the weighted Euclidean distance; S503: Recalculate the mean of all sample points within each cluster and update the centroid of the cluster; S504: Repeat steps S502 and S503 until the centroid positions of all clusters no longer change, thus completing the clustering. Each cluster corresponds to a seismic performance level.

[0042] The coordinates of K points are used as the initial centroids of K clusters. The iterative process then proceeds, and in the allocation step, each sample point in the performance sample set is traversed. Using the weighted Euclidean distance formula Calculate the distance from the sample point to the current K centroids. The distance is calculated, and the sample point is assigned to the cluster represented by the nearest centroid.

[0043] After all sample points have been assigned, the update step begins. For each cluster... The centroid position is then recalculated. The new centroid coordinates are the arithmetic mean of the coordinates of all sample points within the cluster. For example, for cluster ... The j-th dimension coordinate of the new centroid ,in It is a cluster The number of sample points in the middle, summing and traversing the cluster All sample points After the update is completed, a new round of iteration begins, that is, the assignment and update steps are repeated. This iterative process continues until a convergence condition is met, for example, the cluster affiliation of all sample points no longer changes after one complete iteration. The clustering process ends when the algorithm converges. The resulting K clusters, due to the initial centers and the rationality of the clustering process, can classify the structural response into different seismic performance levels, ranging from basically intact to severely damaged.

[0044] This specification provides an embodiment of a seismic performance evaluation system for large-span buildings, which includes the following modules: The calculation module is used to acquire multidimensional performance response data of large-span buildings under multiple sets of seismic excitations to form a performance sample set; determine the number of initial cluster centers according to the preset number of seismic performance levels K; and calculate the sensitivity coefficient of each performance response parameter to the overall structural damage based on the performance sample set to form a weight vector. The selection module is used to identify extreme response samples in the performance sample set based on a preset performance response parameter threshold, and select the sample point with the largest weighted Euclidean distance from the origin of the coordinates from the extreme response samples as the first initial cluster center. The weighted Euclidean distance is calculated using the weight vector. The determination module is used to perform the operation K-1 times or less to determine the remaining initial cluster centers: for candidate sample points i that are not selected as initial cluster centers, the local density of the sample points is calculated. And calculate the minimum weighted distance between the sample point and all selected initial cluster centers. ; wherein, the local density The minimum weighted distance is calculated based on the weighted Euclidean distance between candidate sample point i and other sample points. It is the minimum weighted Euclidean distance between the candidate sample point i and each center point in the selected initial cluster center set, wherein the weighted Euclidean distance is calculated using the weight vector; the local density is... With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center; The analysis module is used to perform weighted cluster analysis on the performance sample set using K predetermined initial cluster centers as initial centroids to obtain K seismic performance level classifications.

[0045] In one embodiment, the step of calculating the sensitivity coefficients of each performance response parameter to overall structural damage based on the performance sample set, forming a weight vector, includes: The Park-Ang damage model was used to calculate the overall structural damage index for each performance sample. Calculate the Pearson correlation coefficient between each performance response parameter sequence and the overall structural damage index sequence; The absolute values ​​of the Pearson correlation coefficients of each performance response parameter are normalized, and the resulting values ​​are used as the sensitivity coefficients of the parameters. The sensitivity coefficients of all parameters together constitute the weight vector.

[0046] The process involves identifying extreme response samples from the performance sample set and selecting the sample point with the largest weighted Euclidean distance from the origin as the first initial cluster center, including: The "severe damage" state limit of each performance response parameter is used as the preset threshold. Traverse the performance sample set. If at least one performance response parameter of a sample point exceeds the "severe damage" state limit corresponding to the sample point, then the sample point is identified as an extreme response sample. Calculate the weighted Euclidean distance between each extreme response sample point and the origin in the multidimensional performance response space; The extreme response sample point with the largest calculated weighted Euclidean distance value is selected as the first initial cluster center.

[0047] As an optional implementation, for candidate sample points i that are not selected as initial cluster centers, the local density of the sample points is calculated. ,include: Set cutoff distance The value is the mean of the first 2% of the weighted Euclidean distances between all sample points in ascending order; For any candidate sample point i, the local density of the sample point The formula, calculated using the Gaussian kernel function, is as follows: The summation iterates through all sample points j except for i. Let be the weighted Euclidean distance between sample point i and sample point j.

[0048] Specifically, this involves calculating the minimum weighted distance between the sample point and all selected initial cluster centers. ,include: For a candidate sample point i and any selected cluster center k, calculate the weighted Euclidean distance. The calculation formula is: The summation iterates through all m performance response parameter dimensions. The weight of the m-th performance response parameter, and These are the coordinates of sample point i and the selected cluster center k in the m-th dimension, respectively. The minimum weighted Euclidean distance among all the selected cluster centers calculated for sample point i is taken as the minimum weighted distance. .

[0049] As another optional implementation, the local density is... With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center, including: For each candidate sample point i that has not yet been selected as a cluster center, the local density of the sample point is... With the minimum weighted distance Multiply to obtain the evaluation index for the sample points. ; Evaluation metrics for all candidate sample points Sort in descending order; Selection of evaluation indicators The largest candidate sample point is selected as the next initial cluster center.

[0050] In one possible embodiment, the step of using K predetermined initial cluster centers as initial centroids to perform weighted cluster analysis on the performance sample set to obtain K seismic performance level classifications includes: The determined K initial cluster centers are used as the initial centroids of the weighted K-means clustering algorithm; Each sample point in the performance sample set is assigned to the cluster containing the centroid that is closest to the weighted Euclidean distance. Recalculate the mean of all sample points within each cluster and update the centroid of the cluster; Repeat the above steps until the centroid positions of all clusters no longer change, thus completing the clustering. Each cluster corresponds to a seismic performance level.

[0051] In an optional embodiment, the acquisition of multidimensional performance response data of large-span buildings under multiple sets of seismic excitations to form a performance sample set includes: Establish a finite element analysis model for long-span buildings; Thirty natural ground motion records were selected, and the peak ground acceleration amplitudes were adjusted to 0.1g, 0.2g, 0.4g, and 0.6g, respectively, to form 120 sets of ground motion excitations; Time history analysis was performed on the model to extract the maximum inter-story drift angle, maximum vertex displacement, maximum vertex acceleration, and residual drift angle of the structure under each set of excitations, forming a four-dimensional performance response data sample.

[0052] It should be understood that in the foregoing description of the embodiments in this specification, various features are combined in a single embodiment, drawing, or description for the purpose of simplifying the description and to aid in understanding a feature. However, this does not mean that the combination of these features is necessary, and those skilled in the art, upon reading this specification, may readily identify some of the devices as separate embodiments. That is, the embodiments in this specification can also be understood as an integration of multiple secondary embodiments. And the content of each secondary embodiment is valid even if it contains fewer than all the features of a single foregoing disclosed embodiment.

Claims

1. A method for evaluating the seismic performance of a long-span building, characterized by, Includes the following steps: Acquire multidimensional performance response data of large-span buildings under multiple sets of seismic excitation to form a performance sample set; determine the number of initial cluster centers based on the preset number K of seismic performance levels; Based on the performance sample set, the sensitivity coefficients of each performance response parameter to the overall structural damage are calculated, and a weight vector is formed. Based on a preset performance response parameter threshold, extreme response samples in the performance sample set are identified, and the sample point with the largest weighted Euclidean distance from the origin is selected from the extreme response samples as the first initial cluster center. The weighted Euclidean distance is calculated using the weight vector. Repeat the operation K-1 times or less to determine the remaining initial cluster centers: For candidate sample points i that are not selected as initial cluster centers, calculate the local density of the sample points. And calculate the minimum weighted distance between the sample point and all selected initial cluster centers. ; wherein, the local density The minimum weighted distance is calculated based on the weighted Euclidean distance between candidate sample point i and other sample points. It is the minimum weighted Euclidean distance between the candidate sample point i and each center point in the selected initial cluster center set, wherein the weighted Euclidean distance is calculated using the weight vector; the local density is... With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center; Using the K predetermined initial cluster centers as initial centroids, a weighted cluster analysis is performed on the performance sample set to obtain K seismic performance level classifications.

2. The method according to claim 1, characterized in that, Based on the performance sample set, the sensitivity coefficients of each performance response parameter to overall structural damage are calculated to form a weight vector, including: The Park-Ang damage model was used to calculate the overall structural damage index for each performance sample. Calculate the Pearson correlation coefficient between each performance response parameter sequence and the overall structural damage index sequence; The absolute values ​​of the Pearson correlation coefficients of each performance response parameter are normalized, and the resulting values ​​are used as the sensitivity coefficients of the parameters. The sensitivity coefficients of all parameters together constitute the weight vector.

3. The method according to claim 1, characterized in that, The process involves identifying extreme response samples from the performance sample set and selecting the sample point with the largest weighted Euclidean distance from the origin as the first initial cluster center, including: The "severely damaged" state limit of each performance response parameter is used as the preset threshold. Traverse the performance sample set. If at least one performance response parameter of a sample point exceeds the "severe damage" state limit corresponding to the sample point, then the sample point is identified as an extreme response sample. Calculate the weighted Euclidean distance between each extreme response sample point and the origin in the multidimensional performance response space; The extreme response sample point with the largest calculated weighted Euclidean distance value is selected as the first initial cluster center.

4. The method of claim 1, wherein, For the candidate sample point i that was not selected as the initial cluster center, the local density of the sample point is calculated. ,include: Setting a cutoff distance , the value is the average of the first 2% distance values in ascending order of the weighted Euclidean distance between all sample points; For any candidate sample point i, the local density of the sample point The formula, calculated using the Gaussian kernel function, is as follows: The summation iterates through all sample points j except for i. Let be the weighted Euclidean distance between sample point i and sample point j.

5. The method according to claim 1, characterized in that, calculating the minimum weighted distance between the sample point and all selected initial cluster centers comprising: For a candidate sample point i and any selected cluster center k, calculate the weighted Euclidean distance. The calculation formula is: The summation iterates through all m performance response parameter dimensions. The weight of the m-th performance response parameter, and These are the coordinates of sample point i and the selected cluster center k in the m-th dimension, respectively. The minimum weighted Euclidean distance among all the selected cluster centers calculated for sample point i is taken as the minimum weighted distance. .

6. The method of claim 1, wherein, The local density With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center, including: For each candidate sample point i that has not yet been selected as a cluster center, the local density of the sample point is... With the minimum weighted distance Multiply to obtain the evaluation index for the sample points. ; evaluating the evaluation index of all candidate sample points performing descending arrangement; Selecting evaluation index The largest candidate sample point is selected as the next initial cluster center.

7. The method of claim 1, wherein, The step involves using K predetermined initial cluster centers as initial centroids to perform weighted cluster analysis on the performance sample set, resulting in K seismic performance level classifications, including: The determined K initial cluster centers are used as the initial centroids of the weighted K-means clustering algorithm; Each sample point in the performance sample set is assigned to the cluster containing the centroid that is closest to the weighted Euclidean distance. Recalculate the mean of all sample points within each cluster and update the centroid of the cluster; Repeat the above steps until the centroid positions of all clusters no longer change, thus completing the clustering. Each cluster corresponds to a seismic performance level.

8. The method according to any one of claims 1 to 7, characterized in that, The acquisition of multidimensional performance response data of large-span buildings under multiple sets of seismic excitations constitutes a performance sample set, including: Establish a finite element analysis model for long-span buildings; Thirty natural ground motion records were selected, and the peak ground acceleration amplitudes were adjusted to 0.1g, 0.2g, 0.4g, and 0.6g, respectively, to form 120 sets of ground motion excitations; Time history analysis was performed on the model to extract the maximum inter-story drift angle, maximum vertex displacement, maximum vertex acceleration, and residual drift angle of the structure under each set of excitations, forming a four-dimensional performance response data sample.

9. A system for evaluating seismic performance of a long-span building, the system comprising: Includes the following modules: The calculation module is used to acquire multidimensional performance response data of large-span buildings under multiple sets of seismic excitations to form a performance sample set; and to determine the number of initial cluster centers based on the preset number of seismic performance levels K. Based on the performance sample set, the sensitivity coefficients of each performance response parameter to the overall structural damage are calculated, and a weight vector is formed. The selection module is used to identify extreme response samples in the performance sample set based on a preset performance response parameter threshold, and select the sample point with the largest weighted Euclidean distance from the origin of the coordinates from the extreme response samples as the first initial cluster center. The weighted Euclidean distance is calculated using the weight vector. The determination module is used to perform the operation K-1 times or less to determine the remaining initial cluster centers: for candidate sample points i that are not selected as initial cluster centers, the local density of the sample points is calculated. And calculate the minimum weighted distance between the sample point and all selected initial cluster centers. Wherein, the local density The minimum weighted distance is calculated based on the weighted Euclidean distance between candidate sample point i and other sample points. It is the minimum weighted Euclidean distance between the candidate sample point i and each center point in the selected initial cluster center set, wherein the weighted Euclidean distance is calculated using the weight vector; the local density is... With the minimum weighted distance The product of the products is used as an evaluation index. Selecting evaluation indicators The largest candidate sample point is used as the next initial cluster center; The analysis module is used to perform weighted cluster analysis on the performance sample set using K predetermined initial cluster centers as initial centroids to obtain K seismic performance level classifications.

10. The system of claim 9, wherein, Based on the performance sample set, the sensitivity coefficients of each performance response parameter to overall structural damage are calculated to form a weight vector, including: The Park-Ang damage model was used to calculate the overall structural damage index for each performance sample. Calculate the Pearson correlation coefficient between each performance response parameter sequence and the overall structural damage index sequence; The absolute values ​​of the Pearson correlation coefficients of each performance response parameter are normalized, and the resulting values ​​are used as the sensitivity coefficients of the parameters. The sensitivity coefficients of all parameters together constitute the weight vector.

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