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A relaxation method is demonstrated which reliably solves the nonlinear two point boundary value problem which arises when optimal control theory is applied to determination of large angle maneuvers of flexible spacecraft. The basic ideas are summarized and several idealized maneuvers are determined. The emphasis is upon demonstrating the basic ideas and practical aspects of the methodology.
A new spectral-spatial method for classification of hyperspectral images is proposed. The HSegClas method is based on the integration of probabilistic classification and shape analysis within the hierarchical step-wise optimization algorithm. First, probabilistic support vector machines classification is applied. Then, at each iteration two neighboring regions with the smallest Dissimilarity Criterion (DC) are merged, and classification probabilities are recomputed. The important contribution of this work consists in estimating a DC between regions as a function of statistical, classification and geometrical (area and rectangularity) features. Experimental results are presented on a 102-band ROSIS image of the Center of Pavia, Italy. The developed approach yields more accurate classification results when compared to previously proposed methods.
Numerical computations are performed to investigate the potential for transition control in an axisymmetric boundary layer via fully realizable, streamwise stationary streaks induced by an azimuthally periodic array of surface mounted vortex generators (VGs). Previous work has shown that suitable streaks of this type can significantly reduce the growth of Mack’s second mode instabilities, but large streak amplitudes can make the flow susceptible to previously absent streak instabilities that can become the leading cause of transition. Here, we use the adjoint capabilities of the SU2 flow solver to optimize the VG shape to maximize the reduction in the growth of second-mode disturbances while also preventing the streak amplitudes from reaching large enough values to precipitate an earlier onset of transition via streak instabilities. The geometry and the freestream flow conditions are selected to match a relevant trajectory lo-cation from the HIFiRE-1 flight experiment. Results show that the optimized VGs can increase the mean streak amplitude by 117% with respect to a manually developed baseline design. The stability of this optimized basic state is analyzed via the plane-marching parabolized stability equations, predicting a fully laminar flow over the entire cone, or equivalently, yielding transition delay of 130% versus the 17% for the baseline VGs.
This paper presents a cohesive set of engine-in-the-loop (EIL) studies examining the use of hierarchical model-predictive control for fuel consumption minimization in a class-8 heavy-duty truck intended to be equipped with Level-1 connectivity/automation. This work is motivated by the potential of connected/automated vehicle technologies to reduce fuel consumption in both urban/suburban and highway scenarios. The authors begin by presenting a hierarchical model-predictive control scheme that optimizes multiple chassis and powertrain functionalities for fuel consumption. These functionalities include: vehicle routing, arrival/departure at signalized intersections, speed trajectory optimization, platooning, predictive optimal gear shifting, and engine demand torque shaping. The primary optimization goal is to minimize fuel consumption, but the hierarchical controller explicitly accounts for other key objectives/constraints, including operator comfort and safe inter-vehicle spacing. This work is experimentally experimentally validated via a sequence of EIL studies intended for evaluating the computational costs and fuel savings associated with these algorithms. These EIL studies involve the closed-loop validation of the proposed control strategies, both individually and combined. These studies show that this hierarchy of algorithms is capable of running online, with the round-trip communication delay inherent in EIL simulation being one of the key factors affecting the EIL results. Moreover, the EIL studies are encouraging, both in terms of the successful hierarchical integration of the underlying algorithms and also in the resulting fuel savings seen in the EIL tests. In particular, the EIL results suggest that an aggressive overall goal of reducing vehicle fuel consumption by 15-20% or more is potentially achievable, especially in urban/suburban scenarios.
Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.
A new cap design eliminates thermal disruptions in the destruction of sand–polymer shaping mandrels when manufacturing polymer composite parts.
Dual-laser beams interacting with small droplets of liquid tin are currently the most efficient systems for producing the 13.5 nm EUV photon radiation source required for the next generation microchips. Usually, EUV light is produced during the second main-pulse stage, while the pre-pulse (PP) is used for target preparation, i.e., droplet preheating, vaporization, and target deformation. However, the PP laser energy can be utilized more efficiently if the EUV producing plasma is being developed during the PP stage as well. In this work, we study the ways of optimization of the PP laser temporal shape to achieve conditions for maximum EUV output during the pre-pulse. The size of the deformed droplet is kept optimized for the following main laser pulse. Our simulations showed a significant increase in the EUV output at the pre-pulse stage when a ramping profile is used for the laser temporal shape. Using the ramped square pre-pulse produces 24% gain in the EUV output in comparison with the standard Gaussian temporal profile (i.e., regular Nd:YAG shape) for the same energy of the laser pulse.
A generalized layout problem involving sizing, shape, and topology optimization is solved by using the homogenization method for three-dimensional linearly elastic shell structures in order to seek a possibility of establishment of an integrated design system of automotive car bodies, as an extension of the previous work by Bendsoe and Kikuchi. A formulation of a three-dimensional homogenized shell, a solution algorithm, and several examples of computing the optimum layout are presented in this first part of the two articles.
An application of numerical optimization to the design of advanced airfoils for transonic aircraft showed that low-drag sections can be developed for a given design Mach number without an accompanying drag increase at lower Mach numbers. This is achieved by imposing a constraint on the drag coefficient at an off-design Mach number while minimizing the drag coefficient at the design Mach number. This multiple design-point numerical optimization has been implemented with the use of airfoil shape functions which permit a wide range of attainable profiles during the optimization process. Analytical data for the starting airfoil shape, a single design-point optimized shape, and a double design-point optimized shape are presented. Experimental data obtained in the NASA Ames two-by two-foot wind tunnel are also presented and discussed.
The present paper details the design of the counter rotating fans for a Turboelectric Distributed Propulsion (TeDP) system. Sixteen propulsors installed in mail-slot-shape nacelles are embedded on an aerodynamically optimized hybrid wing-body configuration. The hybrid-wing/body (HWB) configuration which was previously designed to satisfy the conditions of trim, longitudinally static stability and specific cargo space is employed as the baseline configuration in pursuing an optimal distributed propulsion system. A set of distributed propulsors is conceptually designed and the collective performance is evaluated against the target thrust mandated by the mission requirements. The concept of the distributed propulsion allows the fan pressure ratio to be around 1.27~1.32 for the target thrust. In addition, further splitting of the fan pressure ratio by using the counter-rotating fans for each slot realizes the target pressure ratio with low tip speed. In the distributed propulsion system, the nature of the flow conditions and/or the thickness of the ingested boundary layer may differ and result in different propulsive reaction of each individual propulsor. The optimization is, thus, approached from both the propulsion system and individual propulsor perspectives. An optimal distribution of the thrust and power output is determined by how the system utilizes each passage's propulsive characteristics and its interaction with the airframe. These system level analysis and optimization are conducted using an actuator disk model to account for the propulsion-airframe integration numerically. With respect to the propulsor level, aerodynamic shape optimizations of the fan blades are performed in a sequential multi-objective optimization process for various design objectives, such as mass flow rate condition, fan pressure ratio, efficiency and the exit flow angle of the fan stage by using a genetic algorithm, NSGA-II. The radial chord distribution, and meanline distribution of the rotors are designed on the circumferentially averaged axi-symmetric inlet profiles and tested on the six inlet profiles from six divided sectors to reckon flow distortion. The performances of the counter rotating fans are, thus, evaluated accordingly for obtaining distortion tolerant fan. The performance of the distributed propulsion system is evaluated by two CFD tools, i.e., a multi-stage turbo-machinery CFD code and one propulsion-airframe integration flow solver coupled with a body-force model. The optimized boundary layer ingestion propulsion system of 16 distributed slots not only reaches the system target thrust, but also delivers a close to 20% fuel saving benefit against its counterpart 12 distributed clean inlet propulsion system.
This paper describes a joint NASA/Army research activity at the Langley Research Center to develop optimization procedures aimed at improving the rotor blade design process by integrating appropriate disciplines and accounting for important interactions among the disciplines. The activity is being guided by a Steering Committee made up of key NASA and Army researchers and managers. The paper describes the optimization formulation in terms of the objective function, design variables, and constraints. The analysis aspects are discussed, and the interdisciplinary interactions are defined in terms of the information that must be transferred among disciplinary analyses as well as the trade-offs between disciplines in determining the details of the design. At this writing, some significant progress has been made. Results given in the paper represent accomplishments in rotor aerodynamic performance optimization for minimum horsepower, rotor dynamic optimization for vibration reduction, approximate analysis of frequencies and mode shapes, rotor structural optimization for minimum weight, and integrated aerodynamic load/dynamics optimization for minimum vibration and weight.
Super high quality aspherical x-ray mirrors with a residual slope error of ~100 nrad (root-mean-square) and a height error of ~1-2 nm (peak-to-valley), and even lower, are now available from a number of the most advanced vendors utilizing deterministic polishing techniques. The mirror specification for the fabrication is based on the simulations of the desired performance of the mirror in the beamline optical system and is normally given with the acceptable level of deviation of the mirror figure and finish from the desired ideal shape. For example, in the case of aspherical x-ray mirrors designed for the Advanced Light Source (ALS) QERLIN beamline, the ideal shape is defined with the beamline application (conjugate) parameters and their tolerances. Here, we first introduce an original procedure and dedicated software developed at the ALS X-Ray Optics Laboratory (XROL) for optimization of beamline performance of pre-shaped hyperbolic and elliptical mirrors. The optimization is based on results of ex situ surface slope metrology and consists in minimization of the mirror shape error by determining the conjugate parameters of the best-fit ideal shape within the specified tolerances. We describe novel optical metrology instrumentation, measuring techniques, and analytical methods used at the XROL for acquisition of surface slope data and optimization of the optic’s beamline performance. The high efficacy of the developed experimental methods and data analysis procedures is reflected in results of measurements with and performance optimization of hyperbolic and elliptical cylinder mirrors designed and fabricated for the ALS QERLIN beamline.
Advances in theoretical modeling across multiple disciplines have yielded generative models capable of high veracity in predicting macroscopic functional responses of materials emerging as a result of complex non-local interactions. Correspondingly, of interest is the inverse problem of finding the model parameter that will yield desired macroscopic responses, such as stress–strain curves, ferroelectric hysteresis loops, etc. Here, we suggest and implement Gaussian process based methods that allow to effectively sample the degenerate parameter space of a complex non-local model to output regions of parameter space which yield desired functionalities. In this work, we discuss the specific adaptation of the acquisition function and sampling function to make the process efficient and balance the efficient exploration of parameter space for multiple possible minima and exploitation to densely sample the regions of interest where target behaviors are optimized. Additionally, this approach is illustrated via the hysteresis loop engineering in ferroelectric materials but can be adapted to other functionalities and generative models.
Uniform linear phased arrays where many radiating elements share a relatively small number of phase shifters are investigated. Such architectures arise in arrays which derive the time delays in the signal paths from a small group of independent phase shifters. In particular, a true time-delay device which has been suggested recently for optically controlled arrays is used as the basic phase shifter. Different architectures, viz. alternative procedures of deriving the necessary time delay for each antenna in the face of phase-shifter inaccuracies, are examined. The variance of the steered beam's direction is used as the performance criterion. The direction-optimal architecture is obtained by means of quadratic programming, and is shown not to be unique. The nonuniqueness of the optimal architecture is exploited to improve other characteristics of the array's beam shape, and the optimal solution is shown to compare favorably with a suboptimal interleaved solution which is easier to implement.
Lestofire is an academic software for the automated design of engineering components. It finds the optimal geometry of a system to minimize a given cost function while constrained by a given set of physics equations. Using a level set function to describe the geometry, lestofire uses shapes derivative to evolve the system until its optimal shape. It leverages the compilation of variational forms in Firedrake (https://www.firedrakeproject.org/) and the automated calculation of shape derivatives via pyadjoint (http://www.dolfin-adjoint.or/en/latest/) to allow fast prototyping of different physics, cost functions and design parametrizations.
A method is presented for numerical airfoil optimization whereby a reduced number of design coordinates are used to define the airfoil shape. The approach is to define the airfoil as a linear combination of shapes. These basic shapes may be analytically or numerically defined, allowing the designer to use his insight to propose candidate designs. The design problem becomes one of determining the participation of each such function in defining the optimum airfoil. Examples are presented for two-dimensional airfoil design and are compared with previous results based on a polynomial representation of the airfoil shape. Four existing NACA airfoils are used as basic shapes. Solutions equivalent to previous results are achieved with a factor of more than 3 improvements in efficiency, while superior designs are demonstrated with an efficiency greater than 2 over previous methods. With this shape definition, the optimization process is shown to exploit the simplifying assumptions in the inviscid aerodynamic analysis used here, thus demonstrating the need to use more advanced aerodynamics for airfoil optimization.
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape in this paper. Specifically, we consider an objective (tracking) functional for surface shape with the prescribed mean curvature equation in graph form as a state constraint. The control variable is the prescribed curvature. We prove existence of an optimal control, and using improved regularity estimates, we show sufficient differentiability to make sense of the first order optimality conditions. This allows us to rigorously compute the gradient of the objective functional for both the continuous and discrete (finite element) formulations of the problem. Numerical results are shown to illustrate the minimizers and optimal controls on different domains.
Three algorithms are developed for designing finite impulse response digital filters to be used for pulse shaping and channel equalization. The first is the Minimax algorithm which uses linear programming to design a frequency-sampling filter with a pulse shape that approximates the specification in a minimax sense. Design examples are included which accurately approximate a specified impulse response with a maximum error of 0.03 using only six resonators. The second algorithm is an extension of the Minimax algorithm to design preset equalizers for channels with known impulse responses. Both transversal and frequency-sampling equalizer structures are designed to produce a minimax approximation of a specified channel output waveform. Examples of these designs are compared as to the accuracy of the approximation, the resultant intersymbol interference (ISI), and the required transmitted energy. While the transversal designs are slightly more accurate, the frequency-sampling designs using six resonators have smaller ISI and energy values.