The traditional post-earthquake damage assessment of buildings is done visually through building-by-building inspections, which for a major event might take weeks to months to be completed. The main goal of this study is to establish a framework to quantify the post-event seismic performance of a portfolio of existing structures, in this case soft-story (SS) residential buildings, in near-real-time and an ultra-high resolution. Two main ingredients are required; 1) input ground motion time-series at the sites of the buildings that excite the structures, and 2) well-established nonlinear structural computer models representing the buildings. By having these two ingredients, nonlinear dynamic analyses of the existing structures can be performed, and seismic performance of the portfolio buildings can be quantified. The number of currently available recording instruments is sparse. Therefore, using the Gaussian Process Regression (GPR), a novel approach was developed to generate ground motion time series at un-instrumented target sites (i.e., the sites of the buildings) employing the surrounding recorded ground motions. The methodology has been validated for the physics-based scenario earthquakes in Northern California as well as two events recorded in Southern California: the 2019 M7.1 Ridgecrest and 2020 M4.5 South El Monte earthquakes. In addition, an approach was introduced to generate multiple realizations of ground motions at each target site. The results illustrated that the instrumentation density closer to the target site is crucial in producing accurate and reliable ground motions, especially at long periods. The second ingredient of the framework needs an accurate nonlinear computer structural model for soft-story buildings. There is an inventory of OpenSees models constructed to represent the 13,500 SS buildings in Los Angeles. This inventory includes thirty-two models categorized through four main key features: first-story wall layout, the number of stories, floor plan dimension, and wood-frame shear wall material. I have utilized machine learning methodologies to classify the first two features via visual recognition. I extracted images for 2,681 buildings within Los Angeles via Google Street View (GSV) service through an automated algorithm to train the Convolutional Neural Network (CNN) models for that purpose. The accuracy of the trained model is 80.1% and 91.4% for first-story wall layout and the number of stories classification tasks, respectively. I, then, utilized the OpenStreetMap (OSM) to detect the floor plan area of the target buildings to classify the third required feature. Having both a structural model and input ground motion time series, one can conduct a nonlinear response history analysis to assess the seismic performance of each specific building. As an application of the framework, I generated ground motion time series at over 2,000 SS buildings’ locations within Los Angeles for a scenario M6.7 earthquake based on the 2020 M4.5 El Monte rupture mechanism. I also estimated the structural features through the GSV extracted images to identify the “closest” available OpenSees model. Lastly, a map of the estimated damage state for the 2,000 SS buildings is produced. The results demonstrated that more than 50% of the SS buildings are either severely damaged or collapsed after such an earthquake in Los Angeles, while approximately 15% of them experienced slight damage. The methodology and framework developed in this research can be implemented to assess, in a near-real-time, seismic performance of a large portfolio of structures in moderate-to-severe earthquake events.

Improvement of cognitive function is of great value to many aspects of society. However, identifying robust procedures for training cognitive processes with generalizable benefits remains elusive. Here we present a novel attention regulation training paradigm that incorporates skill application in multiple learning environments. We hypothesized that our training procedure would enhance goal-oriented cognitive function and cognitive control mechanisms. We evaluated training effects using both computerized assessments and self-report questionnaires designed to probe cognitive control in everyday life. We tested for specificity of training effects by employing multiple active control conditions and for generalizability by using assessments that were significantly different from the training tasks as well as a set of secondary self-report questionnaires to explore the extent of far transfer. Training substantially improved performance on multiple tasks that involve goal-oriented cognitive functioning and cognitive control, and these gains were often specific to the group that received attention regulation training and also applied learned skills in varied environments.

Multi-Objective Optimization Problems (MOPs) deal with optimizing several objectives simultaneously and have diverse applications in engineering, economics, logistics, etc. The methods for solving MOPs can generally be classified into stochastic and deterministic approaches. Deterministic approaches are capable of finding the global solution even though they are computationally burdensome. Stochastic methods, on the other hand, can save on computations significantly, although they do not guarantee to find the global solution.

In engineering applications, MOPs can become nonlinear, multi-modal, high dimensional, and have complex structured solutions that makes them more challenging.

This theses follows two major goals. Firstly, it presents new methods and algorithms for solving engineering MOPs by hybridizing the existing methods and comparing their effectiveness by using benchmark problems. The hybrid method combines an evolutionary algorithm with a cell mapping method in order to reduce the computational time while maintaining the quality of the solution. Implementation details on parallel CPU/GPU programming of such methods are discussed as well. The second goal of this thesis is to introduce new applications of MOPs in different areas of engineering such as control design, path planning, fractional systems and airfoil design.

In this work, we study interactions between the curvature of a Riemannian manifold and the geometry of its submanifolds. In particular, we consider manifolds with intermediate Ricci curvature bounded below and manifolds with integral curvature bounds.

First, we develop the tools for studying manifolds with intermediate Ricci curvature bounds. In particular, we prove a comparison theorem for the Hessian of the distance function to a submanifold based on a lower bound for the k-Ricci curvature.

The main result is a generalization of the inequality of E. Heintze and H. Karcher for the volume of tubes around minimal submanifolds to an inequality based on integral bounds for k-Ricci curvature. Even in the case of a pointwise bound, this generalizes the classical inequality by replacing a sectional curvature bound with a k-Ricci bound. This theorem is motivated by the estimates of Petersen-Shteingold-Wei for the volume of tubes around a geodesic and generalizes their result.

Finally, we give several applications of these comparison theorems to the geometry and topology of submanifolds in spaces with curvature bounded below. The first is a uniform lower bound on the volume of minimal submanifolds in spaces with integral curvature bounds. We then bound the relative growth of the fundamental group of a closed minimal submanifold in terms of the growth of the fundamental group of the embedding space when the latter has nonnegative intermediate Ricci curvature. We conclude with an application of the comparison theory for intermediate Ricci curvature to certain geometric inequalities which are motivated by questions in general relativity.

Low-lying coastal areas are susceptible to multiple flooding pathways from seawater, groundwater, and stormwater sources. Focusing on Imperial Beach California, USA, this research studies the vulnerability of coastal stormwater and wastewater systems to compound impacts of changing climate [i.e., Sea-Level Rise (SLR), groundwater shoaling, and precipitation intensification], the capability of decentralized water infrastructure in flood mitigation, and their adoptability by the community.

After presenting the background information and research goals in Chapter 1, Chapter 2 evaluates compound flooding of the stormdrain system under a changing climate. Here, the obtained results for current and high sea-level conditions are presented (SLR = 0 and 2 m). The result illustrates that seawater may intrude into 2/3 of the stormdrain system length by a 2 m rise in current sea level. SLR consequences can be exacerbated by GroundWater Infiltration (GWI) such that the flooding volume may increase six-fold with 0.25% porosity systemwide and impact areas kilometers away from the coastline.

Chapter 3 shows that defect flows currently increase hydraulic loading on the sewer system by 21% and 49% in dry- and wet-weather conditions, respectively. These numbers can be elevated to 84% and 120% at SLR = 2 m placing ~ $3 M cost on the system every year. The excess hydraulic loading also increases the potential of sanitary sewer overflows (i.e., exposing the community and environment to raw sewage pollution). Finally, by involving structural, hydrological, and hydraulic criteria, a holistic approach is presented to prioritize sewer rehabilitation.

Chapter 4 first analyzes a social survey, whose results show that homeowners are more likely to adopt decentralized infrastructure. In addition, gardeners with the intention of reducing water usage in their yards can be targeted as the most prevalent adopters. Moreover, appropriate outreach activities are essential for enhancing public awareness in areas at the future risk of flooding. The engineering model outputs reveal that for a system with 0.25% porosity working under SLR = 0 m and a 1-year rainfall, the flood volume may decrease 56%−99% after implementing an RB system and adding an RG system. Although the RB system implementation can reduce the flood volume only by 24% at future conditions (SLR = 2 m and 25% increase in rainfall intensity), this value can be improved to 77% by adding an RG system. Additionally, the value of harvested rainwater over the lifetime of the RB system is estimated to be $60+ M while its cost will be $4- M. The RG system is also estimated to cost $15 M and occupy 2.4% of the city area.

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