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At least 199 records · Page 11

Structural optimization using optimality criteria methods

Optimality criteria methods take advantage of some concepts as those of statically determinate or indeterminate structures, and certain variational principles of structural dynamics, to develop efficient algorithms for the sizing of structures that are subjected to stiffness-related constraints. Some of the methods and iterative strategies developed over the last decade for calculations of the Lagrange multipliers in stressand displacement-limited problems, as well as for satisfying the appropriate optimality criterion, are discussed. The application of these methods are illustrated by solving problems with stress and displacement constraints.

Khot, N. S.↗

Merits and limitations of optimality criteria method for structural optimization

The merits and limitations of the optimality criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement, and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the Optimality Criteria Design Code that was developed for this purpose at NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. Salient features of the code include multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analyzers, and analytical and numerical sensitivities. The performance of the OC method, on the basis of the examples solved, was found to be satisfactory for problems with few active constraints or with small numbers of design variables. For problems with large numbers of behavior constraints and design variables, the OC method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.

Patnaik, Surya N.↗

Analytical investigations in aircraft and spacecraft trajectory optimization and optimal guidance

A collection of analytical studies is presented related to unconstrained and constrained aircraft (a/c) energy-state modeling and to spacecraft (s/c) motion under continuous thrust. With regard to a/c unconstrained energy-state modeling, the physical origin of the singular perturbation parameter that accounts for the observed 2-time-scale behavior of a/c during energy climbs is identified and explained. With regard to the constrained energy-state modeling, optimal control problems are studied involving active state-variable inequality constraints. Departing from the practical deficiencies of the control programs for such problems that result from the traditional formulations, a complete reformulation is proposed for these problems which, in contrast to the old formulation, will presumably lead to practically useful controllers that can track an inequality constraint boundary asymptotically, and even in the presence of 2-sided perturbations about it. Finally, with regard to s/c motion under continuous thrust, a thrust program is proposed for which the equations of 2-dimensional motion of a space vehicle in orbit, viewed as a point mass, afford an exact analytic solution. The thrust program arises under the assumption of tangential thrust from the costate system corresponding to minimum-fuel, power-limited, coplanar transfers between two arbitrary conics. The thrust program can be used not only with power-limited propulsion systems, but also with any propulsion system capable of generating continuous thrust of controllable magnitude, and, for propulsion types and classes of transfers for which it is sufficiently optimal the results of this report suggest a method of maneuvering during planetocentric or heliocentric orbital operations, requiring a minimum amount of computation; thus uniquely suitable for real-time feedback guidance implementations.

Markopoulos, Nikos↗

Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels

We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.

trajectory design↗

End-to-End Trajectory Optimization Using Copernicus and Program to Optimize Simulated Trajectories II

As current and future NASA missions become increasingly more complex, the need to ensure requirements are met across the many phases of flight is more pertinent. Accurately modeling the individual phases of flight is difficult alone, but verifying that the overall mission is characterized properly presents additional challenges. In previous works, there have been successful demonstrations of interfacing multiple software applications to provide a more detailed end-to-end optimized simulation. The work herein will focus on leveraging two NASA built tools that have been successfully utilized on NASA missions: Copernicus and the Program to Optimize Simulated Trajectories II (POST2).

Anthony Williams↗

Optimal PV Inverter Control in Distribution Systems via Data-Driven Distributionally Robust Optimization

Distribution systems with high penetration of uncertain solar generation call for advanced control strategies of photovoltaics (PVs) inverters. This paper proposes a data-driven distributionally robust optimization (DDDRO) approach to optimally controlling the PV inverters to improve the system operation performance under solar power uncertainties. In the proposed DDDRO approach, a Wasserstein ball-based method is proposed to construct the distributional ambiguity set to model the uncertainties of PV generation through partial observations of historical data without knowing exact probability distributions. We further reformulate the computationally intractable DDDRO model to a mixed integer second order cone programming (MISOCP) problem. The effectiveness and out-of-sample performance of the proposed approach have been demonstrated on a modified IEEE 33-node system. We conduct a comparative study to compare the proposed method with traditional chance constrained programming (CCP). It shows that the proposed DDDRO approach can provide a less conservative yet robust solution to minimize the worse-case expectation of the total network loss while maintaining nodal voltages in a secure range.

Xue, Yaosuo↗

Prediction of the Thermal Runaway Limit and Optimal Operation of Heat Transfer-Limited, Fixed-Bed Reactor Systems

Here, we derive a new prediction for thermal runaway starting from the alpha model for fixed-bed reactor systems. This method accounts for thermal resistance internal to the reactor tube and the radial temperature gradients that result. To showcase our method, we compare its predictions to other common criteria for thermal runaway using o-xylene oxidation as the example chemistry. Even in systems where internal heat transfer is negligible, the empirical practical design criterion for thermal runaway is inaccurate. For cases where internal heat transfer is relevant, our runaway limit is more stringent than limits derived from simpler 1-D models. To augment our work, we optimize the product yield with the thermal runaway constraint using orthogonal collocation. Using the alpha model, the results illustrate that the thermal runaway limit can be accurately determined using either numerical or analytical methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimization on Manifolds via Graph Gaussian Processes

This paper integrates manifold learning techniques within a Gaussian process upper confidence bound algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

Bayesian optimization↗

Investigating a Renewable-Resource-Targeting Mobile Aquaculture System Using Route Optimization Based on Optimal Foraging Theory

Aquaculture systems require careful consideration of location, which determines water conditions, pollution impacts, and hazardous conditions. Mobility may be able to address these factors while also supporting the targeting of renewable energy sources such as wind, wave, and solar power throughout the year. In this paper, a purpose-built mobile aquaculture ship is identified and modeled with a combination of renewable energy harvesting capabilities as a case study with the objective of assessing the potential benefits of targeting high renewable energy potentials to power aquaculture operations. A route optimization algorithm is created and tuned to simulate the mobility of the aquaculture platform and cost-basis comparisons are made to a stationary system. The small spatial variability in renewable energy potential when combining multiple resources significantly limits the benefits of a mobile, renewable-targeting aquaculture system. On the other hand, the consistent energy harvest from a blend of renewable energy types (13 kW installed wind capacity, 661 m 2 installed solar, and 1 m characteristic width wave-energy converter) suggests that the potential benefits of a mobile platform for offshore aquaculture (mitigation of environmental and social concerns, any potential positive impact on yields, hazard avoidance, etc.) can likely be pursued without significant increases in energy harvester costs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Optimizing the self-assembly of conjugated polymers and small molecules through structurally programmed non-covalent control

Organic conjugated polymers and oligomers are key electronic materials for applications such as transistors, photovoltaics, and light emitting devices due to their potential for solution processability, mechanical flexibility, and precise structure-based tuning compared to inorganic materials. In dilute environments, the optoelectronic properties of conjugated polymers are largely governed by their constitutional structure and, to a lesser degree, their solution-state intramolecular configuration. In the solid state, intramolecular conformation and intermolecular electronic coupling impact these properties substantially, especially in relation to device performance. Therefore, an increasingly important area of research concerning conjugated materials is developing design strategies aimed at optimizing the solid-state packing for electronic applications. Programming solid-state packing arrangements through discrete non-covalent interactions is an emerging strategy within the context of conjugated polymers. This review focuses on the use of the two most prevalent discrete and directional interactions used to dictate the self-assembly of conjugated polymers and oligomers—hydrogen bonds and chalcogen bonds. Further, we also discuss how these design motifs can imbue conjugated materials with appealing physical properties while simultaneously retaining or improving electronic capabilities.

36 MATERIALS SCIENCE↗

Conservative numerical schemes with optimal dispersive wave relations: Part I. Derivation and analysis

An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived by approximating the Hamiltonian formulation of the inviscid shallow water flows based on the vorticity-divergence variables. These schemes also conserve the first-order moments such as mass and vorticity, as usual. The conservative properties of the schemes stem from the skew-symmetry and singularities of the Poisson brackets, which are carefully retained in the discrete approximations. Here, the schemes operate on unstructured orthogonal dual meshes, over bounded or unbounded domains, and they are also shown to possess the same optimal dispersive wave relations as those of the Z-grid scheme, which is a consequence of the use of the vorticity and divergence variables.

54 ENVIRONMENTAL SCIENCES↗