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Ground motion selection has become increasingly central to the assessment of earthquake resilience. The selection of ground motion records for use in nonlinear dynamic analysis significantly affects structural response. This, in turn, will impact the outcomes of earthquake resilience analysis. This paper presents a new ground motion clustering algorithm, which can be embedded in current ground motion selection methods to properly select representative ground motion records that a structure of interest will probabilistically experience. The proposed clustering-based ground motion selection method includes four main steps: 1) leveraging domain-specific knowledge to pre-select candidate ground motions; 2) using a convolutional autoencoder to learn low-dimensional underlying characteristics of candidate ground motions’ response spectra – i.e., latent features; 3) performing k-means clustering to classify the learned latent features, equivalent to cluster the response spectra of candidate ground motions; and 4) embedding the clusters in the conditional spectra-based ground motion selection. The selected ground motions can represent a given hazard level well (by matching conditional spectra) and fully describe the complete set of candidate ground motions. Three case studies for modified, pulse-type, and non-pulse-type ground motions are designed to evaluate the performance of the proposed ground motion clustering algorithm (convolutional autoencoder + k-means). Considering the limited number of pre-selected candidate ground motions in the last two case studies, the response spectra simulation and transfer learning are used to improve the stability and reproducibility of the proposed ground motion clustering algorithm. The results of the three case studies demonstrate that the convolutional autoencoder + k-means can 1) achieve 100% accuracy in classifying ground motion response spectra, 2) correctly determine the optimal number of clusters, and 3) outperform established clustering algorithms (i.e., autoencoder + k-means, time series k-means, spectral clustering, and k-means on ground motion influence factors). Using the proposed clustering-based ground motion selection method, an application is performed to select ground motions for a structure in San Francisco, California. The developed user-friendly codes are published for practical use. 

Interest in earthquake resilience has increased in recent years, and the use of building cluster performance objectives has been shown to be an effective method for evaluating the resilience of built environment. A building cluster is a portfolio of buildings that share the same role in a community; its performance objectives are defined by considering earthquake scenarios, hazard levels, and individual building performance. The methodology presented in this paper employs performance-based assessments to estimate the probability of achieving building cluster performance objectives immediately following a seismic event. It can be used to assess the immediate post-earthquake community resilience in five steps: 1) hazard analysis, 2) conditional assessment of individual building performance, 3) conditional assessment of building cluster performance, 4) building cluster performance assessment by aggregation, and 5) earthquake resilience assessment of building clusters considering all hazard levels of interest. The design and extreme hazard levels are formulated using ground motion records selected based on the conditional spectra considering characteristics of earthquake scenarios and spatial correlation. Three performance objectives are defined for both individual buildings and building clusters: functionality, safe and usable during repair, and collapse prevention. Two engineering demand parameters – the maximum transient and the permanent interstory drift indices – are used to estimate individual building performance. The probability of achieving building cluster performance objective is calculated using the total probability theorem. The application of the proposed methodology is demonstrated using two clusters of reinforced concrete buildings, corresponding to ASCE 7 Risk Category II and IV structures, in San Francisco, CA. 

In order to evaluate urban earthquake resilience, reliable structural modeling is needed. However, detailed modeling of a large number of structures and carrying out time history analyses for sets of ground motions are not practical at an urban scale. Reduced-order surrogate models can expedite numerical simulations while maintaining necessary engineering accuracy. Neural networks have been shown to be a powerful tool for developing surrogate models, which often outperform classical surrogate models in terms of scalability of complex models. Training a reliable deep learning model, however, requires an immense amount of data that contain a rich input-output relationship, which typically cannot be satisfied in practical applications. In this paper, we propose model-informed symbolic neural networks (MiSNN) that can discover the underlying closed-form formulations (differential equations) for a reduced-order surrogate model. The MiSNN will be trained on datasets obtained from dynamic analyses of detailed reinforced concrete special moment frames designed for San Francisco, California, subject to a series of selected ground motions. Training the MiSNN is equivalent to finding the solution to a sparse optimization problem, which is solved by the Adam optimizer. The earthquake ground acceleration and story displacement, velocity, and acceleration time histories will be used to train 1) an integrated SNN, which takes displacement and velocity states and outputs the absolute acceleration response of the structure; and 2) a distributed SNN, which distills the underlying equation of motion for each story. The results show that the MiSNN can reduce computational cost while maintaining high prediction accuracy of building responses.