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Based on partial differential equations of motion the closed form solution for the optimal estimation of a spatially continuous state vector is derived, using a continuously distributed sensor. Local control is shown to be the feedback that minimizes a quadratic performance index of sensor and process disturbances. A detailed example of the control of a string in tension is presented.
A transform-domain method for deriving the generating function of the acquisition process resulting from an arbitrary serial search strategy is presented. The method relies on equivalent circular state diagrams, uses Mason's formula from flow-graph theory, and employs a minimum number of required parameters. The transform-domain approach is briefly described and the concept of equivalent circular state diagrams is introduced and exploited to derive the generating function and resulting mean acquisition time for three particular cases of interest, the continuous/center Z search, the broken/center Z search, and the expanding window search. An optimization of the latter technique is performed whereby the number of partial windows which minimizes the mean acquisition time is determined. The numerical results satisfy certain intuitive predictions and provide useful design guidelines for such systems.
Commercialization of lithium-air batteries faces many challenges, such as electrolyte decomposition, short cycle life, low energy and power density, etc. However, commercialization of Li-O2 batteries for aeronautics is much more challenging due to additional safety constraints on cyclability and performance (high specific power and specific energy). For this presentation, we will discuss inter-related aspects of physics-based modeling of a pack: cell and battery model calibration. In addition, we will evaluate and present optimal battery designs for high discharge current density, high discharge time, and low battery mass using simulation-based optimization.The Finite Element Model (FEM) used to simulate a Li-O2 cell is based on the work of Bevara [1]. The different aspects of the model are based on: porous electrode theory and concentrated electrolyte theory; quantum tunneling model for the resistance of conformal layer of discharge product (Li2O2) [1]; Butler-Volmer kinetics for electrochemical reaction; Fick's diffusion for oxygen transport; and an oxygen dissolution model is applied at the air/electrolyte interface [2]. The electrolyte properties such as ion conductivity, ion diffusion, oxygen diffusion, and mass density of the electrolyte were taken from Molecular Dynamics (MD) simulations [3]; while the other model parameters, which includes mass of cell components, were calibrated to match experiments at high discharge current densities. The cell mass includes the anode, cathode, separator, electrolyte, and other components (such as current collector). This calibrated model is used to perform parametric studies on cathode thickness, porosity, tortuosity, carbon particle size, electrolyte transport and material properties, partial pressure of oxygen, discharge time, and discharge current density to study optimal designs for high specific power and energy. References:1. Bevara, V. & Andrei, P. (2014), J. Electrochem. Soc. 161 (14), A2068-A2079.2.Mehta, M. & Andrei, P. (2015), J. Power Sources. 286, 299-308.3.Liyana-Arachchi, T.; Haskins, J.; Burke, C.; Diederichsen, K.; McCloskey, B.; & Lawson, J. (2018), J. Phys. Chem. B. 122 (36), 8548 - 8559.4.Choi, W.; Kikumoto, H.; Choudhary, R. & Ooka, R. (2018), Applied Energy, 209, 306-321.
A partially supervised classification problem is addressed, especially when the class definition and corresponding training samples are provided a priori only for just one particular class. In practical applications of pattern classification techniques, a frequently observed characteristic is the heavy, often nearly impossible requirements on representative prior statistical class characteristics of all classes in a given data set. Considering the effort in both time and man-power required to have a well-defined, exhaustive list of classes with a corresponding representative set of training samples, this 'partially' supervised capability would be very desirable, assuming adequate classifier performance can be obtained. Two different classification algorithms are developed to achieve simplicity in classifier design by reducing the requirement of prior statistical information without sacrificing significant classifying capability. The first one is based on optimal significance testing, where the optimal acceptance probability is estimated directly from the data set. In the second approach, the partially supervised classification is considered as a problem of unsupervised clustering with initially one known cluster or class. A weighted unsupervised clustering procedure is developed to automatically define other classes and estimate their class statistics. The operational simplicity thus realized should make these partially supervised classification schemes very viable tools in pattern classification.
The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of re- producible experiments. In the first phase of the study, three MDO methods were implemented in the SIGHT: framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, other formulations, optimality conditions, and sensitivity of solutions to various perturbations. Optimization algorithms are used to solve a particular MDO formulation. It is then appropriate to speak of local convergence rates and of global convergence properties of an optimization algorithm applied to a specific formulation. An analogous distinction exists in the field of partial differential equations. On the one hand, equations are analyzed in terms of regularity, well-posedness, and the existence and unique- ness of solutions. On the other, one considers numerous algorithms for solving differential equations. The area of MDO methods studies MDO formulations combined with optimization algorithms, although at times the distinction is blurred. It is important to
Electrified aircraft are being developed to increase the efficiency and reduce the cost of operating subsonic transport aircraft. Achieving a substantial impact necessitates focusing on single- and twin-aisle aircraft which use propulsion systems with >20 MW ratings. For these aircraft, multi-MW superconducting electric machines are being developed due to their high specific power and high efficiency. Cryogenic electric machines are a promising technology for multi megawatt electric aircraft drivetrains. Second generation high temperature superconductors (HTS) are the ideal conductor for the field winding (typically the rotor) of superconducting machines, and they have attractive features for the armature winding (typically the stator) of these machines. However, their use in armature windings has been severely limited due to excessive AC losses in conventional electric machines. This presentation will present the working principle, design, and a performance trade study of a novel electric machine – termed a Helmholtz machine – that enables HTS armatures by significantly reducing AC losses. The working principle of the patent pending Helmholtz motor is to optimize the rotor-produced magnetic field (i.e., the field winding) so that it produces a magnetic field almost purely in the plane of the HTS. This is accomplished using 2 rotors that contain a set of matched Helmholtz coil pairs (or matched permanent magnet Halbach arrays). The armature (stator) HTS coils are positioned between the rotors and oriented to minimize the out of plane magnetic field. The armature HTS coils are also designed to minimize the out of plane component of their self field. The presentation will include the lessons learned in the sizing and design of this motor, including equations for how to match the magnet arrays. A performance trade study will be presented for a partially superconducting, radial flux version of the motor. The trade study involved an optimization of a motor design code based on analytical calculations (electromagnetic, AC loss, thermofluid, mechanical, and motor sizing) that determine the motor’s total efficiency and total specific power. The design code will be described in the presentation, with an emphasis on the calculation of magnetic fields, AC loss, and temperature distribution.
The objective is to simulate and optimize distributed cooperation among a network of robots tasked with cooperative excavation on an extra-terrestrial surface. Additionally to examine the concept of directed Emergence among a group of limited artificially intelligent agents. Emergence is the concept of achieving complex results from very simple rules or interactions. For example, in a termite mound each individual termite does not carry a blueprint of how to make their home in a global sense, but their interactions based strictly on local desires create a complex superstructure. Leveraging this Emergence concept applied to a simulation of cooperative agents (robots) will allow an examination of the success of non-directed group strategy achieving specific results. Specifically the simulation will be a testbed to evaluate population based robotic exploration and cooperative strategies while leveraging the evolutionary teamwork approach in the face of uncertainty about the environment and partial loss of sensors. Checking against a cost function and 'social' constraints will optimize cooperation when excavating a simulated tunnel. Agents will act locally with non-local results. The rules by which the simulated robots interact will be optimized to the simplest possible for the desired result, leveraging Emergence. Sensor malfunction and line of sight issues will be incorporated into the simulation. This approach falls under Swarm Robotics, a subset of robot control concerned with finding ways to control large groups of robots. Swarm Robotics often contains biologically inspired approaches, research comes from social insect observation but also data from among groups of herding, schooling, and flocking animals. Biomimetic algorithms applied to manned space exploration is the method under consideration for further study.
The simulation of propulsive flows inherently involves chemical activity. Recent years have seen substantial strides made in the development of numerical schemes for reacting flowfields, in particular those involving finite-rate chemistry. However, finite-rate calculations are computationally intensive and require knowledge of the actual kinetics, which are not always known with sufficient accuracy. Alternatively, flow simulations based on the assumption of local chemical equilibrium are capable of obtaining physically reasonable results at far less computational cost. The present study summarizes the development of efficient numerical techniques for the simulation of flows in local chemical equilibrium, whereby a 'Black Box' chemical equilibrium solver is coupled to the usual gasdynamic equations. The generalization of the methods enables the modelling of any arbitrary mixture of thermally perfect gases, including air, combustion mixtures and plasmas. As demonstration of the potential of the methodologies, several solutions, involving reacting and perfect gas flows, will be presented. Included is a preliminary simulation of the SSME startup transient. Future enhancements to the proposed techniques will be discussed, including more efficient finite-rate and hybrid (partial equilibrium) schemes. The algorithms that have been developed and are being optimized provide for an efficient and general tool for the design and analysis of propulsion systems.
In developing the automated methodologies for simulation-based optimal shape designs, their accuracy, efficiency and practicality are the defining factors to their success. To that end, four recent improvements to the building blocks of such a methodology, intended for more practical design optimization, have been reported. First, in addition to a polynomial-based parameterization, a partial differential equation (PDE) based parameterization was shown to be a practical tool for a number of reasons. Second, an alternative has been incorporated to one of the tedious phases of developing such a methodology, namely, the automatic differentiation of the computer code for the flow analysis in order to generate the sensitivities. Third, by extending the methodology for the thin-layer Navier-Stokes (TLNS) based flow simulations, the more accurate flow physics was made available. However, the computer storage requirement for a shape optimization of a practical configuration with the -fidelity simulations (TLNS and dense-grid based simulations), required substantial computational resources. Therefore, the final improvement reported herein responded to this point by including the alternating-direct-implicit (ADI) based system solver as an alternative to the preconditioned biconjugate (PbCG) and other direct solvers.
The optimization of spacecraft protective structures design to defeat hypervelocity impacts of meteoroids and space debris is presented. A space debris environment model is incorporated into an overall optimization methodology employing engineering models developed to predict protective structures design requirements for hypervelocity impact loads. Several nonlinear optimization techniques are used to generate design parametrics based on environment, mission, and configuration variables for the Space Station Core Module Configuration. Results indicate that careful consideration of the spacecraft structural configuration and materials can partially offset the design consequences of dramatic increases in the orbital space debris environment. Furthermore, the use of nonlinear optimization techniques coupled with hypervelocity impact engineering models can provide significant design tradeoff insight through the use of parametric analyses.
A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition.
The design of filters for detection and estimation in radar and communications systems is considered, with inequality constraints on the maximum output sidelobe levels. A constrained optimization problem in Hilbert space is formulated, incorporating the sidelobe constraints via a partial ordering of continuous functions. Generalized versions (in Hilbert space) of the Kuhn-Tucker and Duality Theorems allow the reduction of this problem to an unconstrained one in the dual space of regular Borel measures. A convergent algorithm is presented for computational solution of the dual problem.
The design of filters for detection and estimation in radar and communications systems is considered, with inequality constraints on the maximum output sidelobe levels. A constrained optimization problem in Hilbert space is formulated, incorporating the sidelobe constraints via a partial ordering of continuous functions. Generalized versions (in Hilbert space) of the Kuhn-Tucker and duality theorems allow the reduction of this problem to an unconstrained one in the dual space of regular Borel measures.
A CFD analysis was performed on a Blended Wing Body (BWB) aircraft with advanced, turbofan engines analyzing various inlet configurations atop the aft end of the aircraft. The results are presented showing that the optimal design for best aircraft fuel efficiency would be a configuration with a partially buried engine, short offset diffuser using active flow control, and a D-shaped inlet duct that partially ingests the boundary layer air in flight. The CFD models showed that if active flow control technology can be satisfactorily developed, it might be able to control the inlet flow distortion to the engine fan face and reduce the powerplant performance losses to an acceptable level. The weight and surface area drag benefits of a partially submerged engine shows that it might offset the penalties of ingesting the low energy boundary layer air. The combined airplane performance of such a design might deliver approximately 5.5% better aircraft fuel efficiency over a conventionally designed, pod-mounted engine.
Transistor design for extremely high frequency applications requires consideration of the interaction between the device and the circuit to which it is connected. Traditional analytical transistor models are to approximate at some of these frequencies and may not account for variations of dopants and semiconductor materials (especially some of the newer materials) within the device. Physically based models of device performance are required. These are based on coupled systems of partial differential equations and typically require 20 minutes of Cray computer time for a single AC operating point. A technique is presented to extract parameters from a few partial differential equation solutions for the device to create a nonlinear equivalent circuit model which runs in approximately 1 second of personal computer time. This nonlinear equivalent circuit model accurately replicates the contact current properties of the device as computed by the partial differential solver on which it is based. Using the nonlinear equivalent circuit model of the device, optimization of systems design can be performed based on device/circuit interactions.
An experimental system is analyzed which is designed to determine the angular and polarization properties of low frequency radio sources from measurements made on a spinning spacecraft. The system has been optimized to provide high accuracies for sources at high as well as low elevation angles. Theoretical expressions are derived for the response of this system to a partially polarized point source. Integrations are then carried out to get the system response to a uniform circular distributed source. Data processing techniques are derived so that computer simulations can be carried out to investigate the accuracy of this technique. It is shown that using 24 measurements of a partially polarized source (with Q = U = V = 0.5), taken in one spacecraft rotation, the resulting rms errors in angular position are less than one degree and the errors in determining the Stokes parameters are generally 1-10% for a wide range of source elevations.
Two distinct parametrization procedures of generating free-form surfaces to represent aerospace vehicles are presented. The first procedure is the representation using spline functions such as nonuniform rational b-splines (NURBS) and the second is a novel (geometrical) parametrization using solutions to a suitably chosen partial differential equation. The main idea is to develop a surface which is more versatile and can be used in an optimization process. Unstructured volume grid is generated by an advancing front algorithm and solutions obtained using an Euler solver. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an automatic differentiator precompiler software tool. Aerodynamic shape optimization of a complete aircraft with twenty four design variables is performed. High speed civil transport aircraft (HSCT) configurations are targeted to demonstrate the process.
Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.