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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Multidisciplinary design optimization using multiobjective formulation techniques

This report addresses the development of a multidisciplinary optimization procedure using an efficient semi-analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles. A semi-analytical sensitivity analysis procedure is developed for calculating computational grid sensitivities and aerodynamic design sensitivities. Accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique. The developed sensitivity analysis technique are then used within a multidisciplinary optimization procedure for designing aerospace vehicles. The optimization problem, with the integration of aerodynamics and structures, is decomposed into two levels. Optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level. Aerodynamic analysis is performed by solving the three-dimensional parabolized Navier Stokes equations. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The proceduredeveloped is applied to design the wing of a high speed aircraft. Results obtained show significant improvements in the aircraft aerodynamic and structural performance when compared to a reference or baseline configuration. The use of the semi-analytical sensitivity technique provides significant computational savings.

Chattopadhyay, Aditi↗
NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗
NASA NTRS1994

A genetic technique for planning a control sequence to navigate the state space with a quasi-minimum-cost output trajectory for a non-linear multi-dimnensional system

There are many multi-stage optimization problems that are not easily solved through any known direct method when the stages are coupled. For instance, we have investigated the problem of planning a vehicle's control sequence to negotiate obstacles and reach a goal in minimum time. The vehicle has a known mass, and the controlling forces have finite limits. We have developed a technique that finds admissible control trajectories which tend to minimize the vehicle's transit time through the obstacle field. The immediate applications is that of a space robot which must rapidly traverse around 2-or-3 dimensional structures via application of a rotating thruster or non-rotating on-off for such vehicles is located at the Marshall Space Flight Center in Huntsville Alabama. However, it appears that the development method is applicable to a general set of optimization problems in which the cost function and the multi-dimensional multi-state system can be any nonlinear functions, which are continuous in the operating regions. Other applications included the planning of optimal navigation pathways through a transversability graph; the planning of control input for under-water maneuvering vehicles which have complex control state-space relationships; the planning of control sequences for milling and manufacturing robots; the planning of control and trajectories for automated delivery vehicles; and the optimization and athletic training in slalom sports.

Hein, C.↗
NASA NTRS1972

Optimal horizontal guidance law for aircraft in the terminal area.

A complete nonlinear control law is derived for guiding an aircraft in minimum time from an arbitrary initial position and heading to a prescribed terminal position and heading in the horizontal plane. The solution is obtained with the aid of the maximum principle, and is implemented by constructing a digital-computer program for the resulting switching logic.

Pecsvaradi, T.↗
NASA NTRS1984

Inverse Modelling to Obtain Head Movement Controller Signal

Experimentally obtained dynamics of time-optimal, horizontal head rotations have previously been simulated by a sixth order, nonlinear model driven by rectangular control signals. Electromyography (EMG) recordings have spects which differ in detail from the theoretical rectangular pulsed control signal. Control signals for time-optimal as well as sub-optimal horizontal head rotations were obtained by means of an inverse modelling procedures. With experimentally measured dynamical data serving as the input, this procedure inverts the model to produce the neurological control signals driving muscles and plant. The relationships between these controller signals, and EMG records should contribute to the understanding of the neurological control of movements.

Kim, W. S.↗
NASA NTRS1997

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

Lewis, Robert Michael↗
DOE OSTI2026

Cs X Si 15 P 21 ( X = Sn or Pb): Polar Noncentrosymmetric Si–P Frameworks Stabilized by Covalent X –P Bonding

Metal silicon phosphides composed of earth-abundant Si and P tend to exhibit semiconducting properties and adopt diverse crystal structures with relatively small additions of structure-directing elements. The potential of silicon phosphide materials in nonlinear optical applications has been hindered by the inability to systematically produce noncentrosymmetric structures with such a flexible framework. Here, in this work, two isostructural compounds with a novel noncentrosymmetric structure were made possible by the inclusion of elements with stereochemically active lone pairs (Sn 2+ and Pb 2+ ). The structures were determined through single-crystal and synchrotron powder X-ray diffraction. Analysis of chemical bonding in real space through the electron localization function revealed stereochemically active Pb 2+ and Sn 2+ species in a trigonal pyramidal coordination with {Pb/Sn}–P bonds. Such covalent bonding between Pb and P is quite uncommon in extended solids and has been reported in a few rare instances. Band structure calculations and linear optical measurements confirm the semiconducting nature of Cs X Si 15 P 21 ( X = Sn or Pb). The synthesis was optimized to yield high-purity polycrystalline samples. The nonlinear optical properties show promising second-harmonic generation (SHG) coefficients from the Kurtz–Perry method. First-principles calculations of the nonlinear optical properties support the experimentally determined SHG values and provide moderate values of birefringence, suggesting Cs X Si 15 P 21 could be phase-matchable and practical nonlinear optical materials in the mid-IR region.

crystal structure↗
NASA NTRS2006

Optimization of Blended Wing Body Composite Panels Using Both NASTRAN and Genetic Algorithm

The blended wing body (BWB) is a concept that has been investigated for improving the performance of transport aircraft. A trade study was conducted by evaluating four regions from a BWB design characterized by three fuselage bays and a 400,000 lb. gross take-off weight (GTW). This report describes the structural optimization of these regions via computational analysis and compares them to the baseline designs of the same construction. The identified regions were simplified for use in the optimization. The regions were represented by flat panels having appropriate classical boundary conditions and uniform force resultants along the panel edges. Panel-edge tractions and internal pressure values applied during the study were those determined by nonlinear NASTRAN analyses. Only one load case was considered in the optimization analysis for each panel region. Optimization was accomplished using both NASTRAN solution 200 and Genetic Algorithm (GA), with constraints imposed on stress, buckling, and minimum thicknesses. The NASTRAN optimization analyses often resulted in infeasible solutions due to violation of the constraints, whereas the GA enforced satisfaction of the constraints and, therefore, always ensured a feasible solution. However, both optimization methods encountered difficulties when the number of design variables was increased. In general, the optimized panels weighed less than the comparable baseline panels.

Lovejoy, Andrew E.↗
DOE OSTI2020

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Control of second-harmonic generation in all-dielectric intersubband metasurfaces by controlling the polarity of χ (2)

All-dielectric metasurfaces have recently led to a paradigm shift in nonlinear optics as they allow for circumventing the phase matching constraints of bulk crystals and offer high nonlinear conversion efficiencies when normalized by the light-matter interaction volume. Unlike bulk crystals, in all-dielectric metasurfaces nonlinear conversion efficiencies primarily rely on the material nonlinearity, field enhancements, and the modal overlaps, therefore most efforts to date have only focused on utilizing these degrees of freedom. In this work, we demonstrate that for second-harmonic generation in all-dielectric metasurfaces, an additional degree of freedom is the control of the polarity of the nonlinear susceptibility. We demonstrate that semiconductor heterostructures that support resonant nonlinearities based on quantum-engineered intersubband transitions provide this new degree of freedom. We can flip and control the polarity of the nonlinear susceptibility of the dielectric medium along the growth direction and couple it to the Mie-type photonic modes. Here we demonstrate that engineering the χ (2) polarity in the meta-atom enables the control of the second-harmonic radiation pattern and conversion efficiency. Our results therefore open a new direction for engineering and optimizing second-harmonic generation using all-dielectric intersubband nonlinear metasurfaces.

42 ENGINEERING↗
NASA NTRS1987

Optimization of shallow arches against instability using sensitivity derivatives

The author discusses the problem of optimization of shallow frame structures which involve a coupling of axial and bending responses. A shallow arch of a given shape and of given weight is optimized such that its limit point load is maximized. The cross-sectional area, A(x) and the moment of inertia, I(x) of the arch obey the relationship I(x) = rho A(x) sup n, n = 1,2,3 and rho is a specified constant. Analysis of the arch for its limit point calculation involves a geometric nonlinear analysis which is performed using a corotational formulation. The optimization is carried out using a second-order projected Lagrangian algorithm and the sensitivity derivatives of the critical load parameter with respect to the areas of the finite elements of the arch are calculated using implicit differentation. Results are presented for an arch of a specified rise to span ratio under two different loadings and the limitations of the approach for the intermediate rise arches are addressed.

Kamat, Manohar P.↗
NASA NTRS2000

Synthesis Methods for Robust Passification and Control

The research effort under this cooperative agreement has been essentially the continuation of the work from previous grants. The ongoing work has primarily focused on developing passivity-based control techniques for Linear Time-Invariant (LTI) systems. During this period, there has been a significant progress made in the area of passivity-based control of LTI systems and some preliminary results have also been obtained for nonlinear systems, as well. The prior work has addressed optimal control design for inherently passive as well as non- passive linear systems. For exploiting the robustness characteristics of passivity-based controllers the passification methodology was developed for LTI systems that are not inherently passive. Various methods of passification were first proposed in and further developed. The robustness of passification was addressed for multi-input multi-output (MIMO) systems for certain classes of uncertainties using frequency-domain methods. For MIMO systems, a state-space approach using Linear Matrix Inequality (LMI)-based formulation was presented, for passification of non-passive LTI systems. An LMI-based robust passification technique was presented for systems with redundant actuators and sensors. The redundancy in actuators and sensors was used effectively for robust passification using the LMI formulation. The passification was designed to be robust to an interval-type uncertainties in system parameters. The passification techniques were used to design a robust controller for Benchmark Active Control Technology wing under parametric uncertainties. The results on passive nonlinear systems, however, are very limited to date. Our recent work in this area was presented, wherein some stability results were obtained for passive nonlinear systems that are affine in control.

Kelkar, Atul G.↗
DOE OSTI2026

Energy-Optimal Vehicle Longitudinal Motion Control via Pontryagin’s Minimum Principle and Ultra-Local Model

Longitudinal vehicle motion control is essential for enhancing performance and optimizing a vehicle’s energy usage. However, it remains a challenging task due to the nonlinear and uncertain nature of vehicle dynamics, along with varying driving conditions. This paper presents a novel ultra-local optimal control approach based on Pontryagin’s Minimum Principle (PMP) that circumvents the need for detailed system identification by employing an ultra-local model. The control objective is to minimize the total energy consumption under boundary conditions while ensuring smooth traction force generation. The proposed approach is evaluated using a high-fidelity vehicle model in three representative scenarios: (i) nominal driving, (ii) a change in tire road friction coefficient (TRFC) from 0.5 to 0.65 and road slope from 0% to 5% during the maneuver, with target velocity unchanged, and (iii) a change in target velocity from 20 m/s to 0 m/s during the maneuver, while maintaining nominal TRFC and slope conditions. The simulation results demonstrate that the proposed method delivers robust performance, effectively balancing consumption and tracking accuracy in all tested scenarios.

Waleed khan, Muhammad [The University of Texas at ↗
NASA NTRS1971

Analytical methods for performance evaluation of nonlinear filters.

In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.

Bejczy, A. K.↗
DOE OSTI2022

Deterministic modeling of hybrid nonlinear effects in epsilon-near-zero thin films

In nonlinear optics, significant effort is concentrated on improving the strength and efficiency of interactions; however, experimentally investigating nonlinear materials is a complex, time-consuming, and costly investment. Moreover, it is often challenging to isolate, study, and optimize material parameters in an experiment due to complexities in the growth process. Recently, epsilon-near-zero materials have received a great deal of attention as promising nonlinear optical materials, but like many up-and-coming materials, the ability to explore and optimize their properties has been challenging. Here, we establish a framework to rapidly evaluate the performance of nonlinear epsilon-near-zero materials for both inter- and intraband effects in silico, requiring only an energy-momentum (E-k) diagram, linear optical properties, and experimental conditions. Measured nonlinear reflection and transmission in gallium-doped zinc oxide films are compared to the numerical framework for both intra- and interband excitation to verify accuracy across wavelength and irradiance while two figures of merit (FoMs) are introduced to quickly evaluate the performance of films without a full numerical framework. This capability is used to predict the performance of highly doped gallium nitride, cadmium oxide, zinc oxide, and indium tin oxide films, and efficient intra- and interband operation conditions are identified. Through this numerical framework and the FoMs, the exploration of unstudied epsilon-near-zero materials is enabled without the need for a nonlinear experiment, thereby accelerating the search for more efficient nonlinear materials and excitation conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Topology optimization of 3D photonic crystals with complete bandgaps

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Multi-objective optimization of peel and shear strengths in ultrasonic metal welding using machine learning-based response surface methodology

Ultrasonic metal welding (UMW) is a solid-state joining technique with varied industrial applications. Despite of its numerous advantages, UMW has a relative narrow operating window and is sensitive to variations in process conditions. As such, it is imperative to quantitatively characterize the influence of welding parameters on the resulting joint quality. The quantification model can be subsequently used to optimize the parameters. Conventional response surface methodology (RSM) usually employs linear or polynomial models, which may not be able to capture the intricate, nonlinear input-output relationships in UMW. Furthermore, some UMW applications call for simultaneous optimization of multiple quality indices such as peel strength, shear strength, electrical conductivity, and thermal conductivity. To address these challenges, this paper develops a machine learning (ML)-based RSM to model the input-output relationships in UMW and jointly optimize two quality indices, namely, peel and shear strengths. The performance of various ML methods including spline regression, Gaussian process regression (GPR), support vector regression (SVR), and conventional polynomial regression models with different orders is compared. A case study using experimental data shows that GPR with radial basis function (RBF) kernel and SVR with RBF kernel achieve the best prediction accuracy. The obtained response surface models are then used to optimize a compound joint strength indicator that is defined as the average of normalized shear and peel strengths. In addition, the case study reveals different patterns in the response surfaces of shear and peel strengths, which has not been systematically studied in the literature. While developed for the UMW application, the method can be extended to other manufacturing processes.

42 ENGINEERING↗