Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.

RISK-BASED MULTIOBJECTIVE PATH PLANNING AND DESIGN OPTIMIZATION FOR UNMANNED AERIAL VEHICLES

Safe operation of unmanned aerial vehicles (UAVs) over populated areas requires reducing the risk posed by a UAV if it crashed during its operation. We considered several types of UAV risk-based path planning problems and developed techniques for estimating the risk to third parties on the ground. The path planning problem requires making trade-offs between risk and flight time. Four optimization approaches for solving the problem were tested; a network-based approach that used a greedy algorithm to improve the original solution generated the best solutions with the least computational effort. Additionally, an approach for solving a combined design and path planning problems was developed and tested. This approach was extended to solve robust risk-based path planning problem in which uncertainty about wind conditions would affect the risk posed by a UAV.

Evaluating Risks of Dam-Reservoir Systems Using Efficient Importance Sampling

The occurrence frequency of failure events serve as critical indexes representing the safety status of dam-reservoir systems. Although overtopping is the most common failure mode with significant consequences, this type of event, in most cases, has a small probability. Estimation of such rare event risks for dam-reservoir systems with crude Monte Carlo (CMC) simulation techniques requires a prohibitively large number of trials, where significant computational resources are required to reach the satisfied estimation results. Otherwise, estimation of the disturbances would not be accurate enough. In order to reduce the computation expenses and improve the risk estimation efficiency, an importance sampling (IS) based simulation approach is proposed in this dissertation to address the overtopping risks of dam-reservoir systems. Deliverables of this study mainly include the following five aspects: 1) the reservoir inflow hydrograph model; 2) the dam-reservoir system operation model; 3) the CMC simulation framework; 4) the IS-based Monte Carlo (ISMC) simulation framework; and 5) the overtopping risk estimation comparison of both CMC and ISMC simulation. In a broader sense, this study meets the following three expectations: 1) to address the natural stochastic characteristics of the dam-reservoir system, such as the reservoir inflow rate; 2) to build up the fundamental CMC and ISMC simulation frameworks of the dam-reservoir system in order to estimate the overtopping risks; and 3) to compare the simulation results and the computational performance in order to demonstrate the ISMC simulation advantages. The estimation results of overtopping probability could be used to guide the future dam safety investigations and studies, and to supplement the conventional analyses in decision making on the dam-reservoir system improvements. At the same time, the proposed methodology of ISMC simulation is reasonably robust and proved to improve the overtopping risk estimation. The more accurate estimation, the smaller variance, and the reduced CPU time, expand the application of Monte Carlo (MC) technique on evaluating rare event risks for infrastructures.

Physical Design Methodologies for Low Power and Reliable 3D ICs

As the semiconductor industry struggles to maintain its momentum down the path following the Moore's Law, three dimensional integrated circuit (3D IC) technology has emerged as a promising solution to achieve higher integration density, better performance, and lower power consumption. However, despite its significant improvement in electrical performance, 3D IC presents several serious physical design challenges. In this dissertation, we investigate physical design methodologies for 3D ICs with primary focus on two areas: low power 3D clock tree design, and reliability degradation modeling and management. Clock trees are essential parts for digital system which dissipate a large amount of power due to high capacitive loads. The majority of existing 3D clock tree designs focus on minimizing the total wire length, which produces sub-optimal results for power optimization. In this dissertation, we formulate a 3D clock tree design flow which directly optimizes for clock power. Besides, we also investigate the design methodology for clock gating a 3D clock tree, which uses shutdown gates to selectively turn off unnecessary clock activities. Different from the common assumption in 2D ICs that shutdown gates are cheap thus can be applied at every clock node, shutdown gates in 3D ICs introduce additional control TSVs, which compete with clock TSVs for placement resources. We explore the design methodologies to produce the optimal allocation and placement for clock and control TSVs so that the clock power is minimized. We show that the proposed synthesis flow saves significant clock power while accounting for available TSV placement area. Vertical integration also brings new reliability challenges including TSV's electromigration (EM) and several other reliability loss mechanisms caused by TSV-induced stress. These reliability loss models involve complex inter-dependencies between electrical and thermal conditions, which have not been investigated in the past. In this dissertation we set up an electrical/thermal/reliability co-simulation framework to capture the transient of reliability loss in 3D ICs. We further derive and validate an analytical reliability objective function that can be integrated into the 3D placement design flow. The reliability aware placement scheme enables co-design and co-optimization of both the electrical and reliability property, thus improves both the circuit's performance and its lifetime. Our electrical/reliability co-design scheme avoids unnecessary design cycles or application of ad-hoc fixes that lead to sub-optimal performance. Vertical integration also enables stacking DRAM on top of CPU, providing high bandwidth and short latency. However, non-uniform voltage fluctuation and local thermal hotspot in CPU layers are coupled into DRAM layers, causing a non-uniform bit-cell leakage (thereby bit flip) distribution. We propose a performance-power-resilience simulation framework to capture DRAM soft error in 3D multi-core CPU systems. In addition, a dynamic resilience management (DRM) scheme is investigated, which adaptively tunes CPU's operating points to adjust DRAM's voltage noise and thermal condition during runtime. The DRM uses dynamic frequency scaling to achieve a resilience borrow-in strategy, which effectively enhances DRAM's resilience without sacrificing performance. The proposed physical design methodologies should act as important building blocks for 3D ICs and push 3D ICs toward mainstream acceptance in the near future.

ADVERTISEMENT ALLOCATION AND TRUST MECHANISMS DESIGN IN SOCIAL NETWORKS

Social network sites (SNS), such as Facebook, Google+ and Twitter, have attracted hundreds of millions of users daily since their appearance. Within SNS, users connect to each other, express their identity, disseminate information and form cooperation by interacting with their connected peers. The increasing popularity and ubiquity of SNS usage and the invaluable user behaviors and connections give birth to many applications and business models. We look into several important problems within the social network ecosystem. The first one is the SNS advertisement allocation problem. The other two are related to trust mechanisms design in social network setting, including local trust inference and global trust evaluation. In SNS advertising, we study the problem of advertisement allocation from the ad platform's angle, and discuss its differences with the advertising model in the search engine setting. By leveraging the connection between social networks and hyperbolic geometry, we propose to solve the problem via approximation using hyperbolic embedding and convex optimization. A hyperbolic embedding method, \hcm, is designed for the SNS ad allocation problem, and several components are introduced to realize the optimization formulation. We show the advantages of our new approach in solving the problem compared to the baseline integer programming (IP) formulation. In studying the problem of trust mechanisms in social networks, we consider the existence of distrust (i.e. negative trust) relationships, and differentiate between the concept of local trust and global trust in social network setting. In the problem of local trust inference, we propose a 2-D trust model. Based on the model, we develop a semiring-based trust inference framework. In global trust evaluation, we consider a general setting with conflicting opinions, and propose a consensus-based approach to solve the complex problem in signed trust networks.

THE STOCHASTIC NAVIER STOKES EQUATIONS FOR HEAT CONDUCTING, COMPRESSIBLE FLUIDS

This dissertation is devoted to the equations of motion governing the evolution of a fluid or gas at the macroscopic scale. The classical model is a PDE description known as the Navier-Stokes equations. The behavior of solutions is notoriously complex, leading many in the scientific community to describe fluid mechanics using a statistical language. In the physics literature, this is often done in an ad-hoc manner with limited precision about the sense in which the randomness enters the evolution equation. The stochastic PDE community has begun proposing precise models, where a random perturbation appears explicitly in the evolution equation. Although this has been an active area of study in recent years, the existing literature is almost entirely devoted to incompressible fluids. The purpose of this thesis is to take a step forward in addressing this statistical perspective in the setting of compressible fluids. In particular, we study the well posedness for the corresponding system of Stochastic Navier Stokes equations, satisfied by the density, velocity, and temperature. The evolution of the momentum involves a random forcing which is Brownian in time and colored in space. We allow for multiplicative noise, meaning that spatial correlations may depend locally on the fluid variables. Our main result is a proof of global existence of weak martingale solutions to the Cauchy problem set within a bounded domain, emanating from large initial datum. The proof involves a mix of deterministic and stochastic analysis tools. Fundamentally, the approach is based on weak compactness techniques from the deterministic theory combined with martingale methods. Four layers of approximate stochastic PDE's are built and analyzed. A careful study of the probability laws of our approximating sequences is required. We prove appropriate tightness results and appeal to a recent generalization of the Skorohod theorem. This ultimately allows us to deduce analogues of the weak compactness tools of Lions and Feireisl, appropriately interpreted in the stochastic setting.