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At least 325 records · Page 18

Active vibration mitigation of distributed parameter, smart-type structures using Pseudo-Feedback Optimal Control (PFOC)

A new, near-optimal feedback control technique is introduced that is shown to provide excellent vibration attenuation for those distributed parameter systems that are often encountered in the areas of aeroservoelasticity and large space systems. The technique relies on a novel solution methodology for the classical optimal control problem. Specifically, the quadratic regulator control problem for a flexible vibrating structure is first cast in a weak functional form that admits an approximate solution. The necessary conditions (first-order) are then solved via a time finite-element method. The procedure produces a low dimensional, algebraic parameterization of the optimal control problem that provides a rigorous basis for a discrete controller with a first-order like hold output. Simulation has shown that the algorithm can successfully control a wide variety of plant forms including multi-input/multi-output systems and systems exhibiting significant nonlinearities. In order to firmly establish the efficacy of the algorithm, a laboratory control experiment was implemented to provide planar (bending) vibration attenuation of a highly flexible beam (with a first clamped-free mode of approximately 0.5 Hz).

Patten, W. N.↗

Model reduction using new optimal Routh approximant technique

An optimal Routh approximant of a single-input single-output dynamic system is a reduced-order transfer function of which the denominator is obtained by the Routh approximation method while the numerator is determined by minimizing a time-response integral-squared-error (ISE) criterion. In this paper, a new elegant approach is presented for obtaining the optimal Routh approximants for linear time-invariant continuous-time systems. The approach is based on the Routh canonical expansion, which is a finite-term orthogonal series of rational basis functions, and minimization of the ISE criterion. A procedure for combining the above approach with the bilinear transformation is also presented in order to obtain the optimal bilinear Routh approximants of linear time-invariant discrete-time systems. The proposed technique is simple in formulation and is amenable to practical implementation.

Hwang, Chyi↗

FUN3D Manual: 13.7

This manual describes the installation and execution of FUN3D version 13.7, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver may be used for formal design optimization, error estimation, and mesh adaptation. FUN3D also offers a reacting, real-gas capability and provides GPU acceleration of many common simulation options.

FUN3D↗

FUN3D Manual: 14.0.2

This manual describes the installation and execution of FUN3D version 14.0.2, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver may be used for formal design optimization, error estimation, and mesh adaptation. FUN3D also offers a reacting, real-gas capability and provides GPU acceleration of many common simulation options.

William K Anderson↗

FUN3D Manual: 14.1

This manual describes the installation and execution of FUN3D version 14.1, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver may be used for formal design optimization, error estimation, and mesh adaptation. FUN3D also offers a reacting, real-gas capability and provides GPU acceleration of many common simulation options.

William K Anderson↗

Optimal block cosine transform image coding for noisy channels

The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimization of a scheme based on the 2-D block cosine transform when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noisy channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered.

Vaishampayan, V.↗

Discretized energy minimization in a wave guide with point sources

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Propst, G.↗

Recursive Branching Simulated Annealing Algorithm

This innovation is a variation of a simulated-annealing optimization algorithm that uses a recursive-branching structure to parallelize the search of a parameter space for the globally optimal solution to an objective. The algorithm has been demonstrated to be more effective at searching a parameter space than traditional simulated-annealing methods for a particular problem of interest, and it can readily be applied to a wide variety of optimization problems, including those with a parameter space having both discrete-value parameters (combinatorial) and continuous-variable parameters. It can take the place of a conventional simulated- annealing, Monte-Carlo, or random- walk algorithm. In a conventional simulated-annealing (SA) algorithm, a starting configuration is randomly selected within the parameter space. The algorithm randomly selects another configuration from the parameter space and evaluates the objective function for that configuration. If the objective function value is better than the previous value, the new configuration is adopted as the new point of interest in the parameter space. If the objective function value is worse than the previous value, the new configuration may be adopted, with a probability determined by a temperature parameter, used in analogy to annealing in metals. As the optimization continues, the region of the parameter space from which new configurations can be selected shrinks, and in conjunction with lowering the annealing temperature (and thus lowering the probability for adopting configurations in parameter space with worse objective functions), the algorithm can converge on the globally optimal configuration. The Recursive Branching Simulated Annealing (RBSA) algorithm shares some features with the SA algorithm, notably including the basic principles that a starting configuration is randomly selected from within the parameter space, the algorithm tests other configurations with the goal of finding the globally optimal solution, and the region from which new configurations can be selected shrinks as the search continues. The key difference between these algorithms is that in the SA algorithm, a single path, or trajectory, is taken in parameter space, from the starting point to the globally optimal solution, while in the RBSA algorithm, many trajectories are taken; by exploring multiple regions of the parameter space simultaneously, the algorithm has been shown to converge on the globally optimal solution about an order of magnitude faster than when using conventional algorithms. Novel features of the RBSA algorithm include: 1. More efficient searching of the parameter space due to the branching structure, in which multiple random configurations are generated and multiple promising regions of the parameter space are explored; 2. The implementation of a trust region for each parameter in the parameter space, which provides a natural way of enforcing upper- and lower-bound constraints on the parameters; and 3. The optional use of a constrained gradient- search optimization, performed on the continuous variables around each branch s configuration in parameter space to improve search efficiency by allowing for fast fine-tuning of the continuous variables within the trust region at that configuration point.

Bolcar, Matthew↗

Modeling the human controller in environments that include continuous and discrete tasks

In complex environments where the human operator is a supervisor, he must allocate his attention between different kinds of tasks for satisfactory overall performance. When a portion of the future reference trajectory for a continuous control task is available for preview, scheduling various other discrete activities is possible. A model has been developed for this situation using dynamic programming to solve an optimal control problem. An experiment was conducted where subjects controlled an airplane symbol over a map, shown a fixed distance into the future. Discrete tasks were introduced as data entry tasks. Results showed that the model compared favorably with experimental results.

Govindaraj, T.↗

Hybrid state-space self-tuning control using dual-rate sampling

This paper presents a hybrid state-space self-tuning control scheme using dual-rate sampling for suboptimal digital adaptive control of linear time-invariant continuous-time multivariable stochastic systems with unknown parameters. An equivalent fast-rate discrete-time state-space innovation model (with estimated states) of the continuous-time system is constructed by using the estimated system parameters and Kalman gain. To utilize the existing optimal regional-pole assignment method developed in the continuous-time domain, the constructed fast-rate discrete-time model is converted into an equivalent continuous-time model for the development of a state-feedback optimal control law with pole placement in a specific region. The developed analog optimal control law is then converted into an equivalent pseudo-slow-rate digital control law via the proposed digital redesign technique, which can be realized via slow-rate digital electronics. The proposed method enables the development of a digitally implementable advanced control algorithm for digital adaptive control of continuous-time multivariable stochastic systems which may be unstable and/or have nonminimum phase.

Shieh, Leang S.↗

Multiresolution Representation Using Biorthogonal Multiwavelets

We generalize Harten's multiresolution representation to biorthogonal multiwavelets. Several variants are considered. For example, a given array of discrete point values is transformed to point values and derivatives or point 'values and cell averages'. Compact Hermite interpolation is used in the decomposition and reconstruction algorithm. The resulting basis functions that are symmetric or skewsymmetric, compact, and smooth with optimal order accuracy. Harten's approach has several advantages: the multiresolution scheme is inherently discrete, non-periodic boundary conditions are easy to implement, and the representation can be extended to unstructured grids in bounded domains. We demonstrate the compression features of the new mutliwavelets by application to variable scale piecewise smooth functions with jump discontinuities typical of numerical solutions of nonlinear hyperbolic conservation laws.

Warming, Robert F.↗

MADS Users' Guide

MADS (Minimization Assistant for Dynamical Systems) is a trajectory optimization code in which a user-specified performance measure is directly minimized, subject to constraints placed on a low-order discretization of user-supplied plant ordinary differential equations. This document describes the mathematical formulation of the set of trajectory optimization problems for which MADS is suitable, and describes the user interface. Usage examples are provided.

Moerder, Daniel D.↗

MColl: Monte Collocation Trajectory Design Tool

In this paper we describe a prototype low-thrust optimization software being developed at JPL. The software tool is based on a collocation algorithm where a trajectory discretization is fitted and adjusted until the underlying dynamics equations of motion are satisfied. The resulting large scale non-linear programming problem may either be optimized with IPOPT or KNITRO. The user specifies path constraints, boundary constraints, and objectives. We describe the collocation algorithm as well as various mesh refinement strategies, and apply the software tool to solve various example problems.

Grebow, Daniel J.↗

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗

Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme

Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.

Lee, Duck-Joo↗

Design and fabrication of a stringer stiffened discrete-tube actively cooled panel for a hypersonic aircraft

A 0.61 x 1.22 m (2 x 4 ft) test panel was fabricated and delivered to the Langley Research Center for assessment of the thermal and structural features of the optimized panel design. The panel concept incorporated an aluminum alloy surface panel actively cooled by a network of discrete, parallel, redundant, counterflow passage interconnected with appropriate manifolding, and assembled by adhesive bonding. The cooled skin was stiffened with a mechanically fastened conventional substructure of stringers and frames. A 40 water/60 glycol solution was the coolant. Low pressure leak testing, radiography, holography and infrared scanning were applied at various stages of fabrication to assess integrity and uniformity. By nondestructively inspecting selected specimens which were subsequently tested to destruction, it was possible to refine inspection standards as applied to this cooled panel design.

Anthony, F. M.↗

Implementation of a multiblock sensitivity analysis method in numerical aerodynamic shape optimization

A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.

Lacasse, James M.↗