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A new technique for locating simultaneous roots of a set of functions is described. The technique is based on the property of the Kreisselmeier-Steinhauser function which descends to a minimum at each root location. It is shown that the ensuing algorithm may be merged into any nonlinear programming method for solving optimization problems with equality constraints.
A new technique for locating simultaneous roots of a set of functions is described. The technique is based on the property of the Kreisselmeier-Steinhauser function which descends to a minimum at each root location. It is shown that the ensuing algorithm may be merged into any nonlinear programming method for solving optimization problems with equality constraints.
Manufactured homes provide affordable housing for over 20 million Americans. The U.S. Department of Energy’s Efficient New Homes (ENH) program has introduced new energy certification requirements that manufacturers can optionally target to ensure outstanding levels of energy savings, comfort, health, and durability. In collaboration with Clayton Homes (under User Agreement (NN-23-1469)), Oak Ridge National Laboratory evaluated multiple wall assembly options to meet ENH requirements in HUD Climate Zones 2 and 3, with a target maximum cost premium of 5%. After analyzing thermal performance, cost, and manufacturability, insulated structural sheathing was identified as the most practical and effective solution. A full-scale manufactured home prototype demonstrated that this approach meets energy performance goals with minimal disruption to existing manufacturing processes and a cost premium of less than 10% with a path to further lower costs, offering a promising path forward for more efficient manufactured housing.
Digital simulation of boundary value problems of trajectory optimization, using variational and functional analysis and IBM-FORMAC language
In engineering, simulation software is often used as a convenient means for carrying out experiments to evaluate physical systems. The benefit of using simulations as 'numerical' experiments is that the experimental conditions can be easily modified and repeated at much lower cost than the comparable physical experiment. The goal of these experiments is to 'improve' the process or result of the experiment. In most cases, the computational experiments employ the same trial and error approach as their physical counterparts. When using this approach for complex systems, the cause and effect relationship of the system may never be fully understood and efficient strategies for improvement never utilized. However, it is possible when running simulations to accurately and efficiently determine the sensitivity of the system results with respect to simulation to accurately and efficiently determine the sensitivity of the system results with respect to simulation parameters (e.g., initial conditions, boundary conditions, and material properties) by manipulating the underlying computations. This results in a better understanding of the system dynamics and gives us efficient means to improve processing conditions. We begin by discussing the steps involved in performing simulations. Then we consider how sensitivity information about simulation results can be obtained and ways this information may be used to improve the process or result of the experiment. Next, we discuss optimization and the efficient algorithms which use sensitivity information. We draw on all this information to propose a generalized approach for integrating simulation and optimization, with an emphasis on software programming issues. After discussing our approach to simulation and optimization we consider an application involving crystal growth. This application is interesting because it includes radiative heat transfer. We discuss the computation of radiative new factors and the impact this mode of heat transfer has on our approach. Finally, we will demonstrate the results of our optimization.
A key aspect of the new space exploration programs will be the approach to optimize launch operations. A STS Derived Launch Vehicle (SDLV) Program can provide a cost effective, low risk, and logical step to launch all of the elements of the exploration program. Many benefits can be gained by utilizing the synergy of a common launch site as an exploration spaceport as well as evolving the resources of the current Space Shuttle Program (SSP) to meet the challenges of the Vision for Space Exploration. In particular, the launch operation resources of the SSP can be transitioned to the exploration program and combined with the operations efficiencies of unmanned EELVs to obtain the best of both worlds, resulting in lean launch operations for crew and cargo missions of the exploration program. The SDLV Program would then not only capture the extensive human space flight launch operations knowledge, but also provide for the safe fly-out of the SSP through continuity of system critical skills, manufacturing infrastructure, and ability to maintain and attract critical skill personnel. Thus, a SDLV Program can smoothly transition resources from the SSP and meet the transportation needs to continue the voyage of discovery of the space exploration program.
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This paper is a discussion of the supersonic nonlinear point design optimization efforts at McDonnell Douglas Aerospace under the High-Speed Research (HSR) program. The baseline for these optimization efforts has been the M2.4-7A configuration which represents an arrow-wing technology for the High-Speed Civil Transport (HSCT). Optimization work on this configuration began in early 1994 and continued into 1996. Initial work focused on optimization of the wing camber and twist on a wing/body configuration and reductions of 3.5 drag counts (Euler) were realized. The next phase of the optimization effort included fuselage camber along with the wing and a drag reduction of 5.0 counts was achieved. Including the effects of the nacelles and diverters into the optimization problem became the next focus where a reduction of 6.6 counts (Euler W/B/N/D) was eventually realized. The final two phases of the effort included a large set of constraints designed to make the final optimized configuration more realistic and they were successful albeit with a loss of performance.
The design of a High-Speed Civil Transport (HSCT) air-breathing propulsion system for multimission, variable-cycle operations was successfully optimized through a soft coupling of the engine performance analyzer NASA Engine Performance Program (NEPP) to a multidisciplinary optimization tool COMETBOARDS that was developed at the NASA Lewis Research Center. The design optimization of this engine was cast as a nonlinear optimization problem, with engine thrust as the merit function and the bypass ratios, r-values of fans, fuel flow, and other factors as important active design variables. Constraints were specified on factors including the maximum speed of the compressors, the positive surge margins for the compressors with specified safety factors, the discharge temperature, the pressure ratios, and the mixer extreme Mach number. Solving the problem by using the most reliable optimization algorithm available in COMETBOARDS would provide feasible optimum results only for a portion of the aircraft flight regime because of the large number of mission points (defined by altitudes, Mach numbers, flow rates, and other factors), diverse constraint types, and overall poor conditioning of the design space. Only the cascade optimization strategy of COMETBOARDS, which was devised especially for difficult multidisciplinary applications, could successfully solve a number of engine design problems for their flight regimes. Furthermore, the cascade strategy converged to the same global optimum solution even when it was initiated from different design points. Multiple optimizers in a specified sequence, pseudorandom damping, and reduction of the design space distortion via a global scaling scheme are some of the key features of the cascade strategy. HSCT engine concept, optimized solution for HSCT engine concept. A COMETBOARDS solution for an HSCT engine (Mach-2.4 mixed-flow turbofan) along with its configuration is shown. The optimum thrust is normalized with respect to NEPP results. COMETBOARDS added value in the design optimization of the HSCT engine.
The Integrated Medical Model (IMM) is a probabilistic model that estimates medical event occurrences and mission outcomes for different mission profiles. IMM simulation outcomes describing the impact of medical events on the mission may be used to optimize the allocation of resources in medical kits. Efficient allocation of medical resources, subject to certain mass and volume constraints, is crucial to ensuring the best outcomes of in-flight medical events. We implement a new approach to this medical kit optimization problem. METHODS We frame medical kit optimization as a modified knapsack problem and implement an algorithm utilizing a dynamic programming technique. Using this algorithm, optimized medical kits were generated for 3 different mission scenarios with the goal of minimizing the probability of evacuation and maximizing the Crew Health Index (CHI) for each mission subject to mass and volume constraints. Simulation outcomes using these kits were also compared to outcomes using kits optimized..RESULTS The optimized medical kits generated by the algorithm described here resulted in predicted mission outcomes more closely approached the unlimited-resource scenario for Crew Health Index (CHI) than the implementation in under all optimization priorities. Furthermore, the approach described here improves upon in reducing evacuation when the optimization priority is minimizing the probability of evacuation. CONCLUSIONS This algorithm provides an efficient, effective means to objectively allocate medical resources for spaceflight missions using the Integrated Medical Model.
McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.
Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.
The Magnetospheric Multiscale Mission (MMS) is a NASA mission intended to make fundamental advancements in our understanding of the Earth's Magnetosphere. There are three processes that MMS is intended to study including magnetic recon- nection, charged particle acceleration, and turbulence. There are four phases of the MMS mission and each phase is designed to study a particular region of the Earth's magnetosphere. The mission is composed of a formation of four spacecraft that are nominally in a regular tetrahedron formation. In this work, we present optimal orbit designs for Phase I and II. This entails designing optimal reference orbits so that the spacecraft dwell-time in the region of interest is a maximum. This is non-trivial because the Earth's magnetosphere is dynamic and its shape and position are not constant in inertial space. Optimal orbit design for MMS also entails designing the formation so that the relative motion of the four spacecraft yields the greatest science return. We develop performance metrics that are related to the science return, and use Sequential Quadratic Programming (SQP) to determine optimal relative motion solutions. We also ensure that practical constraints such as maximum eclipse time and minimum inter-spacecraft separation distances are not violated.
This is a report of work in support of the Computational Aerosciences (CAS) element of the Federal HPCC program. Specifically, CFD and aerodynamic optimization are being performed on parallel computers. The long-range goal of this work is to facilitate teraflops-rate multidisciplinary optimization of aerospace vehicles. This year's work is targeted for application to the High Speed Civil Transport (HSCT), one of four CAS grand challenges identified in the HPCC FY 1995 Blue Book. This vehicle is to be a passenger aircraft, with the promise of cutting overseas flight time by more than half. To meet fuel economy, operational costs, environmental impact, noise production, and range requirements, improved design tools are required, and these tools must eventually integrate optimization, external aerodynamics, propulsion, structures, heat transfer, controls, and perhaps other disciplines. The fundamental goal of this project is to contribute to improved design tools for U.S. industry, and thus to the nation's economic competitiveness.
A computer program, SCAP2D (Solar Cell Analysis Program in 2-Dimensions), is used to evaluate the Etched Multiple Vertical Junction (EMVJ) and grating solar cells. The aim is to demonstrate how SCAP2D can be used to evaluate cell designs. The cell designs studied are by no means optimal designs. The SCAP2D program solves the three coupled, nonlinear partial differential equations, Poisson's Equation and the hole and electron continuity equations, simultaneously in two-dimensions using finite differences to discretize the equations and Newton's Method to linearize them. The variables solved for are the electrostatic potential and the hole and electron concentrations. Each linear system of equations is solved directly by Gaussian Elimination. Convergence of the Newton Iteration is assumed when the largest correction to the electrostatic potential or hole or electron quasi-potential is less than some predetermined error. A typical problem involves 2000 nodes with a Jacobi matrix of order 6000 and a bandwidth of 243.
The Magnetospheric Multiscale Mission (MMS) is a NASA mission intended to make fundamental advancements in our understanding of the Earth s magnetosphere. There are three processes that MMS is intended to study including magnetic reconnection, charged particle acceleration, and turbulence. There are four phases of the MMS mission and each phase is designed to study a particular region of the Earth's magnetosphere. The mission is composed of a formation of four spacecraft that are nominally in a regular tetrahedron formation. In this work, we present optimal orbit designs for Phase I and II. This entails designing reference orbits such that the spacecraft dwell-time in the region of interest is a maximum. This is non-trivial because the Earth's magnetosphere is dynamic and its shape and position are not constant in inertial space. Optimal orbit design for MMS also entails designing the formation so that the relative motion of the four spacecraft yields the greatest science return. We develop performance metrics that are directly related to the science return, and use Sequential Quadratic Programming (SQP) to determine optimal relative motion solutions. While designing for optimal science return, we also consider practical constraints such as maximum eclipse time and minimum inter-spacecraft separation distances. Data are presented that illustrates how long we can ensure that the formation remains in the relevant region of the Earth's magnetosphere. We also draw general conclusions about where in the orbit acceptable tetrahedron configurations can be provided and for how long.