Decision Making under Uncertainty for Design of Resilient Engineered Systems

Designing resilient engineered systems that can sense and withstand adverse events and recover from the effects of the adverse events is increasingly seen as an important goal of engineering design. This paper proposes a value-driven design for resilience (VD2R) framework in order to enable the assessment of system resilience and the optimization of decision variables (or design characteristics) that maximize the value of the system for a firm. The VD2R framework possesses three unique features that allow system resilience and value to be addressed in a theoretically founded and explicit way. First, it assesses the time-dependent resilience of an engineered system by explicitly modeling the redundancy, robustness, and restoration of the system. This assessment captures the stochastic behavior of degradation and restoration and their impact on system resilience. Second, it encompasses a value model that links time-dependent system resilience to a design firm\u27s future profit. Third, the VD2R framework offers an efficient optimization method to solve high-dimension, mixed-integer decision-making models. The proposed framework is demonstrated with a case study, where the resilience of a series-parallel system is modeled and its design characteristics optimized

Optimizing Design for Resilience for Risk-Averse Firms Using Expected Utility and Value-at-Risk

Research Problem •Determine how resilience should be integrated into a firm’s design decisions •Optimize design for a risk-averse firm that incorporates resilienc

A multi-stage optimization model for flexibility in engineering design

Engineered systems often operate in uncertain environments. Understanding different environments under which a system will operate is important in engineering design. Thus, there is a need to design systems with the capability to respond to future changes. This research explores designing a hybrid renewable energy system while taking into account long-range uncertainties of 20 years. The objective is to minimize the expected cost of the hybrid renewable energy system over the next 20 years. A design solution may be flexible, which means that the design can be adapted or modified to meet different scenarios in the future. The value of flexibility can be measured by comparing the expected cost without flexibility and expected cost with flexibility. The results show that a flexible design for hybrid renewable systems can decrease the expected cost by approximately 30%

Design Optimization Under Long-Range Uncertainty

Designing complex systems with many parameters requires computationally expensive simulations and selecting both discrete and continuous design parameters. How to optimize design when future conditions may change, or when system is used differently than expected

An absorbing boundary formulation for the stratified, linearized, ideal MHD equations based on an unsplit, convolutional perfectly matched layer

Perfectly matched layers are a very efficient and accurate way to absorb waves in media. We present a stable convolutional unsplit perfectly matched formulation designed for the linearized stratified Euler equations. However, the technique as applied to the Magneto-hydrodynamic (MHD) equations requires the use of a sponge, which, despite placing the perfectly matched status in question, is still highly efficient at absorbing outgoing waves. We study solutions of the equations in the backdrop of models of linearized wave propagation in the Sun. We test the numerical stability of the schemes by integrating the equations over a large number of wave periods.Comment: 8 pages, 7 figures, accepted, A &

Capacity Planning and Production Scheduling for Aircraft Painting Operations

Long-term capacity planning and production scheduling present significant challenges for the aviation industry. Our research has integrated three different modeling methodologies to effectively forecast future demand for aircraft painting and then assess and manage the capacity that is needed to meet these requirements. First, an innovative forecasting approach was developed in which stochastic processes were used to model aircraft demand over a selected time interval. These demand forecasts were used as inputs to an integer programming model, which was used to find optimal monthly aircraft painting schedules. This approach supports for resource allocation that is based on optimal scheduling, rather than the existing heuristic-based methods. The optimal monthly schedules can then serve as inputs to a discrete event simulation model of the painting operation, which can be used to test the robustness of the optimal schedules under conditions of uncertain demand and processing times

Probabilistic Methods for Long-Term Demand Forecasting for Aviation Production Planning

The aviation industry represents a complex system with low-volume high-value manufacturing, long lead times, large capital investments, and highly variable demand. Making important decisions with intensive capital investments requires accurate forecasting of future demand. However, this can be challenging because of significant variability in future scenarios. The use of probabilistic methods such as Brownian motion in forecasting has been well studied especially in the financial industry. Applying these probabilistic methods to forecast demand in the aerospace industry can be problematic because of the independence assumptions and no consideration of production system in these models. We used two forecasting models based on stochastic processes to forecast demand for commercial aircraft models. A modified Brownian motion model was developed to account for dependency between observations. Geometric Brownian motion at different starting points was used to accurately account for increasing variation. The modified Brownian motion and the geometric Brownian motion models were used to forecast demand for aircraft production in the next 20 years

Recalibrating R\mathbb{R}-order trees and \mbox{Homeo}_+(S^1)-representations of link groups

In this paper we study the left-orderability of $3$-manifold groups using an enhancement, called recalibration, of Calegari and Dunfield's "flipping" construction, used for modifying \mbox{Homeo}_+(S^1)-representations of the fundamental groups of closed $3$-manifolds. The added flexibility accorded by recalibration allows us to produce \mbox{Homeo}_+(S^1)-representations of hyperbolic link exteriors so that a chosen element in the peripheral subgroup is sent to any given rational rotation. We apply these representations to show that the branched covers of families of links associated to arbitrary epimorphisms of the link group onto a finite cyclic group are left-orderable. This applies, for instance, to fibered hyperbolic strongly quasipositive links. Our result on the orderability of branched covers implies that the degeneracy locus of any pseudo-Anosov flow on an alternating knot complement must be meridional, which generalizes the known result that the fractional Dehn twist coefficient of any hyperbolic fibered alternating knot is zero. Applications of these representations to order-detection of slopes are also discussed in the paper.Comment: 43 pages, 12 figure

JSJ decompositions of knot exteriors, Dehn surgery and the LL-space conjecture

In this article, we apply slope detection techniques to study properties of toroidal $3$-manifolds obtained by performing Dehn surgeries on satellite knots in the context of the $L$-space conjecture. We show that if $K$ is an $L$-space knot or admits an irreducible rational surgery with non-left-orderable fundamental group, then the JSJ graph of its exterior is a rooted interval. Consequently, any rational surgery on a composite knot has a left-orderable fundamental group. This is the left-orderable counterpart of Krcatovich's result on the primeness of $L$-space knots, which we reprove using our methods. Analogous results on the existence of co-orientable taut foliations are proved when the knot has a fibred companion. Our results suggest a new approach to establishing the counterpart of Krcatovich's result for surgeries with co-orientable taut foliations, on which partial results have been achieved by Delman and Roberts. Finally, we prove results on left-orderable $p/q$-surgeries on knots with $|p|$ small.Comment: 25 pages, 1 appendi

Phase-field approach to heterogeneous nucleation

We consider the problem of heterogeneous nucleation and growth. The system is described by a phase field model in which the temperature is included through thermal noise. We show that this phase field approach is suitable to describe homogeneous as well as heterogeneous nucleation starting from several general hypotheses. Thus we can investigate the influence of grain boundaries, localized impurities, or any general kind of imperfections in a systematic way. We also put forward the applicability of our model to study other physical situations such as island formation, amorphous crystallization, or recrystallization.Comment: 8 pages including 7 figures. Accepted for publication in Physical Review