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A Simulated Annealing Algorithm for the Optimization of Multistage Depressed Collector Efficiency

The microwave traveling wave tube amplifier (TWTA) is widely used as a high-power transmitting source for space and airborne communications. One critical factor in designing a TWTA is the overall efficiency. However, overall efficiency is highly dependent upon collector efficiency; so collector design is critical to the performance of a TWTA. Therefore, NASA Glenn Research Center has developed an optimization algorithm based on Simulated Annealing to quickly design highly efficient multi-stage depressed collectors (MDC).

Vaden, Karl R.

Discrete-State Simulated Annealing For Traveling-Wave Tube Slow-Wave Circuit Optimization

Algorithms based on the global optimization technique of simulated annealing (SA) have proven useful in designing traveling-wave tube (TWT) slow-wave circuits for high RF power efficiency. The characteristic of SA that enables it to determine a globally optimized solution is its ability to accept non-improving moves in a controlled manner. In the initial stages of the optimization, the algorithm moves freely through configuration space, accepting most of the proposed designs. This freedom of movement allows non-intuitive designs to be explored rather than restricting the optimization to local improvement upon the initial configuration. As the optimization proceeds, the rate of acceptance of non-improving moves is gradually reduced until the algorithm converges to the optimized solution. The rate at which the freedom of movement is decreased is known as the annealing or cooling schedule of the SA algorithm. The main disadvantage of SA is that there is not a rigorous theoretical foundation for determining the parameters of the cooling schedule. The choice of these parameters is highly problem dependent and the designer needs to experiment in order to determine values that will provide a good optimization in a reasonable amount of computational time. This experimentation can absorb a large amount of time especially when the algorithm is being applied to a new type of design. In order to eliminate this disadvantage, a variation of SA known as discrete-state simulated annealing (DSSA), was recently developed. DSSA provides the theoretical foundation for a generic cooling schedule which is problem independent, Results of similar quality to SA can be obtained, but without the extra computational time required to tune the cooling parameters. Two algorithm variations based on DSSA were developed and programmed into a Microsoft Excel spreadsheet graphical user interface (GUI) to the two-dimensional nonlinear multisignal helix traveling-wave amplifier analysis program TWA3. The algorithms were used to optimize the computed RF efficiency of a TWT by determining the phase velocity profile of the slow-wave circuit. The mathematical theory and computational details of the DSSA algorithms will be presented and results will be compared to those obtained with a SA algorithm.

Wilson, Jeffrey D.

Motion Cueing Algorithm Development: Human-Centered Linear and Nonlinear Approaches

While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. Prior research identified viable features from two algorithms: the nonlinear "adaptive algorithm", and the "optimal algorithm" that incorporates human vestibular models. A novel approach to motion cueing, the "nonlinear algorithm" is introduced that combines features from both approaches. This algorithm is formulated by optimal control, and incorporates a new integrated perception model that includes both visual and vestibular sensation and the interaction between the stimuli. Using a time-varying control law, the matrix Riccati equation is updated in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. The neurocomputing approach was crucial in that the number of presentations of an input vector could be reduced to meet the real time requirement without degrading the quality of the motion cues.

Houck, Jacob A.

Optimal placement of tuning masses on truss structures by genetic algorithms

Optimal placement of tuning masses, actuators and other peripherals on large space structures is a combinatorial optimization problem. This paper surveys several techniques for solving this problem. The genetic algorithm approach to the solution of the placement problem is described in detail. An example of minimizing the difference between the two lowest frequencies of a laboratory truss by adding tuning masses is used for demonstrating some of the advantages of genetic algorithms. The relative efficiencies of different codings are compared using the results of a large number of optimization runs.

Ponslet, Eric

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian

Three-dimensional unstructured grid generation via incremental insertion and local optimization

Algorithms for the generation of 3D unstructured surface and volume grids are discussed. These algorithms are based on incremental insertion and local optimization. The present algorithms are very general and permit local grid optimization based on various measures of grid quality. This is very important; unlike the 2D Delaunay triangulation, the 3D Delaunay triangulation appears not to have a lexicographic characterization of angularity. (The Delaunay triangulation is known to minimize that maximum containment sphere, but unfortunately this is not true lexicographically). Consequently, Delaunay triangulations in three-space can result in poorly shaped tetrahedral elements. Using the present algorithms, 3D meshes can be constructed which optimize a certain angle measure, albeit locally. We also discuss the combinatorial aspects of the algorithm as well as implementational details.

Barth, Timothy J.

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

low thrust

An approximation based global optimization strategy for structural synthesis

A global optimization strategy for structural synthesis based on approximation concepts is presented. The methodology involves the solution of a sequence of highly accurate approximate problems using a global optimization algorithm. The global optimization algorithm implemented consists of a branch and bound strategy based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm. The approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure setforth.

Sepulveda, A. E.

Motion Cueing Algorithm Development: Piloted Performance Testing of the Cueing Algorithms

The relative effectiveness in simulating aircraft maneuvers with both current and newly developed motion cueing algorithms was assessed with an eleven-subject piloted performance evaluation conducted on the NASA Langley Visual Motion Simulator (VMS). In addition to the current NASA adaptive algorithm, two new cueing algorithms were evaluated: the optimal algorithm and the nonlinear algorithm. The test maneuvers included a straight-in approach with a rotating wind vector, an offset approach with severe turbulence and an on/off lateral gust that occurs as the aircraft approaches the runway threshold, and a takeoff both with and without engine failure after liftoff. The maneuvers were executed with each cueing algorithm with added visual display delay conditions ranging from zero to 200 msec. Two methods, the quasi-objective NASA Task Load Index (TLX), and power spectral density analysis of pilot control, were used to assess pilot workload. Piloted performance parameters for the approach maneuvers, the vertical velocity upon touchdown and the runway touchdown position, were also analyzed but did not show any noticeable difference among the cueing algorithms. TLX analysis reveals, in most cases, less workload and variation among pilots with the nonlinear algorithm. Control input analysis shows pilot-induced oscillations on a straight-in approach were less prevalent compared to the optimal algorithm. The augmented turbulence cues increased workload on an offset approach that the pilots deemed more realistic compared to the NASA adaptive algorithm. The takeoff with engine failure showed the least roll activity for the nonlinear algorithm, with the least rudder pedal activity for the optimal algorithm.

Houck, Jacob A.

An efficient algorithm for numerical airfoil optimization

A new optimization algorithm is presented. The method is based on sequential application of a second-order Taylor's series approximation to the airfoil characteristics. Compared to previous methods, design efficiency improvements of more than a factor of 2 are demonstrated. If multiple optimizations are performed, the efficiency improvements are more dramatic due to the ability of the technique to utilize existing data. The method is demonstrated by application to subsonic and transonic airfoil design but is a general optimization technique and is not limited to a particular application or aerodynamic analysis.

Vanderplaats, G. N.

Integration and Optimization of a Waste Heat Driven Organic Rankine Cycle for Power Generation in Wastewater Treatment Plants

The study focuses on achieving energy self-sufficiency in Wastewater Treatment Plants by proposing a comprehensive model for integrating, sizing, and optimizing an Organic Rankine Cycle system. The Organic Rankine Cycle system is designed to utilize waste heat from the gensets at As Samra Wastewater Treatment Plant in Jordan, where it will contribute to the overall electrical energy supply of the plant. Real data from As Samra Wastewater Treatment Plant is used to model and calculate the available waste heat using TRNSYS® software. The Organic Rankine Cycle model is then developed using ASPEN PLUS® software to explore the impact of operational parameters and determine their optimal values for maximizing the plant's energy profile. An economic analysis is conducted to assess the feasibility of the proposed model, considering system components, installation, operation, and maintenance costs. To optimize the Organic Rankine Cycle system, the study employs the Multi-Output Support Vector Regression technique to capture nonlinear relationships between independent variables (fluid type, turbine inlet pressure, turbine inlet temperature, turbine outlet pressure, and mass flow rate) and dependent variables (pump power input, waste heat input, and turbine specific work). The Osprey optimization algorithm is used to address the multi-objective optimization problem, with the proposed Pareto-based Osprey Optimization Algorithm and the Multi-Objective Particle Swarm Optimization technique being employed to evaluate critical performance and economic parameters such as system thermal efficiency, net power output, and the levelized cost of electricity. The results of the optimization strategies indicate that the M-SVR model's prediction accuracy is significantly improved after parameter optimization, with the model returning high R 2 and low Mean Square Error values of 0.991 and 0.00216, respectively. The Pareto-Based Osprey Optimization Algorithm optimizer identifies the best working fluid as Isobutane/Isopentane in a ratio of 66:34, with optimal turbine inlet pressure and temperature of 15 bars and 218 °C, respectively. In conclusion, the Organic Rankine Cycle model at these optimal conditions achieves a cycle efficiency of 19.93% and an Levelized Cost of Electricity value of 0.0353 USD/kWh.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented that optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented which optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.

A reliable algorithm for optimal control synthesis

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Vansteenwyk, Brett