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NASA NTRS1995

Analysis of composite ablators using massively parallel computation

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Shia, David↗
NASA NTRS1995

Electromagnetic scattering analysis of a three-dimensional-cavity-backed aperture in an infinite ground plane using a combined finite element method/method of moments approach

A combined finite element method/method of moments (FEM/MoM) approach is used to analyze the electromagnetic scattering properties of a three-dimensional-cavity-backed aperture in an infinite ground plane. The FEM is used to formulate the fields inside the cavity, and the MoM (with subdomain bases) in both spectral and spatial domains is used to formulate the fields above the ground plane. Fields in the aperture and the cavity are solved using a system of equations resulting from the combination of the FEM and the MoM. By virtue of the FEM, this combined approach is applicable to all arbitrarily shaped cavities with inhomogeneous material fillings, and because of the subdomain bases used in the MoM, the apertures can be of any arbitrary shape. This approach leads to a partly sparse and partly full symmetric matrix, which is efficiently solved using a biconjugate gradient algorithm. Numerical results are presented to validate the analysis.

Reddy, C. J.↗
NASA NTRS1995

Computations of Viscous Flows in Complex Geometries Using Multiblock Grid Systems

Generating high quality, structured, continuous, body-fitted grid systems (multiblock grid systems) for complicated geometries has long been a most labor-intensive and frustrating part of simulating flows in complicated geometries. Recently, new methodologies and software have emerged that greatly reduce the human effort required to generate high quality multiblock grid systems for complicated geometries. These methods and software require minimal input form the user-typically, only information about the topology of the block structure and number of grid points. This paper demonstrates the use of the new breed of multiblock grid systems in simulations of internal flows in complicated geometries. The geometry used in this study is a duct with a sudden expansion, a partition, and an array of cylindrical pins. This geometry has many of the features typical of internal coolant passages in turbine blades. The grid system used in this study was generated using a commercially available grid generator. The simulations were done using a recently developed flow solver, TRAF3D.MB, that was specially designed to use multiblock grid systems.

Steinthorsson, Erlendur↗
NASA NTRS1995

Design of launch systems using continuous improvement process

The purpose of this paper is to identify a systematic process for improving ground operations for future launch systems. This approach is based on the Total Quality Management (TQM) continuous improvement process. While the continuous improvement process is normally identified with making incremental changes to an existing system, it can be used on new systems if they use past experience as a knowledge base. In the case of the Reusable Launch Vehicle (RLV), the Space Shuttle operations provide many lessons. The TQM methodology used for this paper will be borrowed from the United States Air Force 'Quality Air Force' Program. There is a general overview of the continuous improvement process, with concentration on the formulation phase. During this phase critical analyses are conducted to determine the strategy and goals for the remaining development process. These analyses include analyzing the mission from the customers point of view, developing an operations concept for the future, assessing current capabilities and determining the gap to be closed between current capabilities and future needs and requirements. A brief analyses of the RLV, relative to the Space Shuttle, will be used to illustrate the concept. Using the continuous improvement design concept has many advantages. These include a customer oriented process which will develop a more marketable product and a better integration of operations and systems during the design phase. But, the use of TQM techniques will require changes, including more discipline in the design process and more emphasis on data gathering for operational systems. The benefits will far outweigh the additional effort.

Brown, Richard W.↗
NASA NTRS1995

Experimental Investigation of Textile Composite Materials Using Moire Interferometry

The viability as an efficient aircraft material of advanced textile composites is currently being addressed in the NASA Advanced Composites Technology (ACT) Program. One of the expected milestones of the program is to develop standard test methods for these complex material systems. Current test methods for laminated composites may not be optimum for textile composites, since the architecture of the textile induces nonuniform deformation characteristics on the scale of the smallest repeating unit of the architecture. The smallest repeating unit, also called the unit cell, is often larger than the strain gages used for testing of tape composites. As a result, extending laminated composite test practices to textiles can often lead to pronounced scatter in material property measurements. It has been speculated that the fiber architectures produce significant surface strain nonuniformities, however, the magnitudes were not well understood. Moire interferometry, characterized by full-field information, high displacement sensitivity, and high spatial resolution, is well suited to document the surface strain on textile composites. Studies at the NASA Langley Research Center on a variety of textile architectures including 2-D braids and 3-D weaves, has evidenced the merits of using moire interferometry to guide in test method development for textile composites. Moire was used to support tensile testing by validating instrumentation practices and documenting damage mechanisms. It was used to validate shear test methods by mapping the full-field deformation of shear specimens. Moire was used to validate open hole tension experiments to determine the strain concentration and compare then to numeric predictions. It was used for through-the-thickness tensile strength test method development, to verify capabilities for testing of both 2-D and 3-D material systems. For all of these examples, moire interferometry provided vision so that test methods could be developed with less speculation and more documentation.

Ifju, Peter G.↗
NASA NTRS1995

Experiments with explicit filtering for LES using a finite-difference method

The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture most of the energy-containing eddies, and if explicit filtering is used, the mesh must be enlarged so that these motions are passed by the filter. Given the high cost of explicit filtering, the following interesting question arises. Since the mesh must be expanded in order to perform the explicit filter, might it be better to take advantage of the increased resolution and simply perform an unfiltered simulation on the larger mesh? The cost of the two approaches is roughly the same, but the philosophy is rather different. In the filtered simulation, resolution is sacrificed in order to minimize the various forms of numerical error. In the unfiltered simulation, the errors are left intact, but they are concentrated at very small scales that could be dynamically unimportant from a LES perspective. Very little is known about this tradeoff and the objective of this work is to study this relationship in high Reynolds number channel flow simulations using a second-order finite-difference method.

Lund, T. S.↗
NASA NTRS1996

Active Control of Noise Using Actuator/Sensor Arrays

Current research in smart structures is directed toward the integration of many actuators and sensors into a material. In this paper we investigate the possibility of using this instrumentation for active noise control from a vibrating structures. Current technology for reducing radiated sound is limited by the instrumentation for the control system. These control systems employ relatively small numbers of sensors and actuators. Hence, these control systems must rely on a model of the structure to estimate and control the global vibrations that contribute to the far field pressure. For complex, realistic structures the development of such a model is a formidable task. The model is a limiting factor in the continuing development of structural acoustics. In this paper we propose to increase the number of actuators and sensors of a smart material to offset the complexity of the model used for control design. The sensor arrays will be used to directly sense the shape of the structure rather than using a model of the structures to indirectly sense the shape of the structure. The actuator array is used to apply distributed forces to the structure, rather than using the structure itself as a load path. A control system for the active cancellation of sound is derived from standard control system methodologies.

Lindner, Douglas K.↗
NASA NTRS1996

Detection of Delamination in Composite Beams Using Broadband Acoustic Emission Signatures

Delamination in composite structure may be caused by imperfections introduced during the manufacturing process or by impact loads by foreign objects during the operational life. There are some nondestructive evaluation methods to detect delamination in composite structures such as x-radiography, ultrasonic testing, and thermal/infrared inspection. These methods are expensive and hard to use for on line detection. Acoustic emission testing can monitor the material under test even under the presence of noise generated under load. It has been used extensively in proof-testing of fiberglass pressure vessels and beams. In the present work, experimental studies are conducted to investigate the use of broadband acoustic emission signatures to detect delaminations in composite beams. Glass/epoxy beam specimens with full width, prescribed delamination sizes of 2 inches and 4 inches are investigated. The prescribed delamination is produced by inserting Teflon film between laminae during the fabrication of composite laminate. The objectives of this research is to develop a method for predicting delamination size and location in laminated composite beams by combining smart materials concept and broadband AE analysis techniques. More specifically, a piezoceramic (PZT) patch is bonded on the surface of composite beams and used as a pulser. The piezoceramic patch simulates the AE wave source as a 3 cycles, 50KHz, burst sine wave. One broadband AE sensor is fixed near the PZT patch to measure the AE wave near the AE source. A second broadband AE sensor, which is used as a receiver, is scanned along the composite beams at 0.25 inch step to measure propagation of AE wave along the composite beams. The acquired AE waveform is digitized and processed. Signal strength, signal energy, cross-correlation of AE waveforms, and tracking of specific cycle of AE waveforms are used to detect delamination size and location.

Okafor, A. C.↗
NASA NTRS1997

Predictive Attitude Estimation Using Global Positioning System Signals

In this paper, a new algorithm is developed for attitude estimation using Global Positioning System (GPS) signals. The new algorithm is based on a predictive filtering scheme designed for spacecraft without rate measuring devices. The major advantage of this new algorithm over traditional Kalman filter approaches is that the model error is not assumed to represented by an unbiased Gaussian noise process with known covariance, but instead is determined during the estimation process. This is achieved by simultaneously solving system optimality conditions and an output error constraint. This approach is well suited for GPS attitude estimation since some error sources that contribute to attitude inaccuracy, such as signal multipath, are known to be non-Gaussian processes. Also, the predictive filter scheme can use either GPS signals or vector observations or a combination of both for attitude estimation, so that performance characteristics can be maintained during periods of GPS attitude sensor outage. The performance of the new algorithm is tested using flight data from the REX-2 spacecraft. Results are shown using the predictive filter to estimate the attitude from both GPS signals and magnetometer measurements, and comparing that solution to a magnetometer-only based solution. Results using the new estimation algorithm indicate that GPS-based solutions are verified to within 2 degrees using the magnetometer cross-check for the REX-2 spacecraft. GPS attitude accuracy of better than 1 degree is expected per axis, but cannot be reliably proven due to inaccuracies in the magnetic field model.

Crassidis, John L.↗
NASA NTRS1997

Error Analysis System for Spacecraft Navigation Using the Global Positioning System (GPS)

The Flight Dynamics Division (FDD) at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) is currently developing improved space-navigation filtering algorithms to use the Global Positioning System (GPS) for autonomous real-time onboard orbit determination. In connection with a GPS technology demonstration on the Small Satellite Technology Initiative (SSTI)/Lewis spacecraft, FDD analysts and programmers have teamed with the GSFC Guidance, Navigation, and Control Branch to develop the GPS Enhanced Orbit Determination Experiment (GEODE) system. The GEODE system consists of a Kalman filter operating as a navigation tool for estimating the position, velocity, and additional states required to accurately navigate the orbiting Lewis spacecraft by using astrodynamic modeling and GPS measurements from the receiver. A parallel effort at the FDD is the development of a GPS Error Analysis System (GEAS) that will be used to analyze and improve navigation filtering algorithms during development phases and during in-flight calibration. For GEAS, the Kalman filter theory is extended to estimate the errors in position, velocity, and other error states of interest. The estimation of errors in physical variables at regular intervals will allow the time, cause, and effect of navigation system weaknesses to be identified. In addition, by modeling a sufficient set of navigation system errors, a system failure that causes an observed error anomaly can be traced and accounted for. The GEAS software is formulated using Object Oriented Design (OOD) techniques implemented in the C++ programming language on a Sun SPARC workstation. The Phase 1 of this effort is the development of a basic system to be used to evaluate navigation algorithms implemented in the GEODE system. This paper presents the GEAS mathematical methodology, systems and operations concepts, and software design and implementation. Results from the use of the basic system to evaluate navigation algorithms implemented on GEODE are also discussed. In addition, recommendations for generalization of GEAS functions and for new techniques to optimize the accuracy and control of the GPS autonomous onboard navigation are presented.

Truong, S. H.↗
NASA NTRS1997

Attitude and Trajectory Determination using Magnetometers and Estimated Rates

A simultaneous attitude and orbit determination algorithm which uses magnetometer measurements and estimated attitude rates is presented. This is an extension of an algorithm which uses magnetometer and rate gyro measurements. The new algorithm is intended for gyroless spacecraft, or in the case of gyro failures/saturation. Torque control input data is used in forming the rate estimates. Simulation tests of the algorithm are presented. First, tests were performed using the 'true' rate values at each time step. This simulated using accurate gyro measurements. Then, tests were performed estimating the rates. Using estimated rates rather than 'gyro measurements' did not significantly degrade the algorithm's performance if accurate estimates of the initial rates were available. An initial Root-Sum-Square (RSS) position error of 1,400 km was reduced to an average error of approximately 100 km within the first two minutes. The RSS attitude error converged to less than 1.5 degrees within three orbits.

Schierman, J. D.↗
NASA NTRS1997

Fabrication and Evaluation of Graphite Fiber-Reinforced Polyimide Composite Tube Forms Using Modified Resin Transfer Molding

The techniques necessary for the fabrication of a complex three-dimensional tubular form using a PMR-type resin have been developed to allow for the construction of several tubes with good physical and mechanical properties. Employing established resin transfer molding practices, the relatively non-hazardous AMB-21 in acetone formulation was used to successfully impregnate four layers of AS4 braided graphite fiber preform previously loaded around an aluminum cylindrical core in an enclosed mold cavity. Using heat and vacuum, the solvent was evaporated to form a prepreg followed by a partial imidization and removal of condensation products. The aluminum core was replaced by a silicone rubber bladder and the cure cycle continued to the final stage of 550 F with a bladder internal pressure of 200 lbs/sq in while simultaneously applying a strong vacuum to the prepreg for removal of any additional imidization products. A combination of several modifications to the standard resin transfer molding methodology enabled the mold to 'breathe', allowing the imidization products a pathway for escape. AMB-21 resin was chosen because of the carcinogenic nature of the primary commercial polyimide PMR-15. The AMB-21 resin was formulated using commercially available monomers or monomer precursors and dissolved in a mixture of methyl alcohol and acetone. The viscosity of the resulting monomer solution was checked by use of a Brookfield rheometer and adjusted by adding acetone to an easily pumpable viscosity of about 600 cP. In addition, several types of chromatographic and thermal analyses were of the braids, and excess handling of the preforms broke some of the microscopic fibers, needlessly decreasing the strength of the finished part. In addition, three dimensional braided preforms with fibers along the length of the tube will be significantly stronger in tension than the braided preforms used in this study.

Exum, Daniel B.↗
NASA NTRS1996

Understanding gas-surface interactions from direct force measurements using a specialized torsion balance

The first comprehensive measurements of the magnitude and direction of the forces exerted on surfaces by molecular beams are discussed and used to obtain information about the microscopic properties of the gas-surface interactions. This unique approach is not based on microscopic measurements of the scattered molecules. The reduced force coefficients are introduced as a new set of parameters that completely describe the macroscopic average momentum transfer to a surface by an incident molecular beam. By using a specialized torsion balance and molecular beams of N2, CO, CO2, and H2, the reduced force coefficients are determined from direct measurements of the force components exerted on surface of a solar panel array material, Kapton, SiO2-coated Kapton, and Z-93 as a function of the angle of incidence ranging from 0 degrees to 85 degrees. The absolute flux densities of the molecular beams were measured using a different torsion balance with a beam-stop that nullified the force of the scattered molecules. Standard time-of-flight techniques were used to determine the flux-weighted average velocities of the various molecular beams ranging from 1600 m/s to 4600 m/s. The reduced force coefficients can be used to directly obtain macroscopic average properties of the scattered molecules, such as the flux-weighted average velocity and translational energy, that can then be used to determine microscopic details concerning gas-surface interactions without the complications associated with averaging microscopic measurements.

Measuring Methods↗
NASA NTRS1998

LDAR, A Three-Dimensional Lightning Warning System: Its Development and Use by the Government, and Transition to Public Availability

NASA, at the John F. Kennedy Space Center (KSC), developed and operates a unique high precision lightning location system to provide lightning related weather warnings. These warnings are used to stop lightning-sensitive operations such as space vehicle launches and ground operations where equipment and personnel are at risk. The data is provided to the Range Weather Operations [45th Weather Squadron, U. S. Air Force (USAF)] where it is used with other meteorological data to issue weather advisories and warnings for Cape Canaveral Air Station (CCAS) and KSC operations. This system, called Lightning Detection and Ranging (LDAR), provides users with a graphical display in three dimensions of 66 MHz radio frequency events generated by lightning processes. The locations of these events provide a sound basis for the prediction of lightning hazards. NASA and Global Atmospherics, Inc. are developing a new system that will replace the unique LDAR components with commercially available and maintainable components having improved capabilities. These components will be phased in to ensure full continuity and access to this important warning technology. These LDAR systems are expected to eventually be available for installation and use by the public at specialized facilities, such as airports, and for general weather warnings via the National Weather Service (NWS) or television broadcast. The NWS in Melbourne has had access to real-time LDAR data since 1993 on an experimental basis. This use of LDAR has shown promise for the improvement of aviation forecasts and severe weather warnings. More so, it has opened the door to investigate the feasibility of issuing lightning-related public advisories. The success of its early use suggests that this technology may improve safety and potentially save lives, therefore constituting a significant benefit to the public. This paper describes the LDR system, the plans and progress of these upgrades, and the potential benefits of its use.

Starr, Stan↗
NASA NTRS1998

A low cost approach to simultaneous orbit, attitude, and rate estimation using an extended Kalman filter

An innovative approach to autonomous attitude and trajectory estimation is available using only magnetic field data and rate data. The estimation is performed simultaneously using an Extended Kalman Filter (EKF), a well known algorithm used extensively in onboard applications. The magnetic field is measured on a satellite by a magnetometer, an inexpensive and reliable sensor flown on virtually all satellites in low earth orbit. Rate data is provided by a gyro, which can be costly. This system has been developed and successfully tested in a post-processing mode using magnetometer and gyro data from 4 satellites supported by the Flight Dynamics Division at Goddard. In order for this system to be truly low cost, an alternative source for rate data must be utilized. An independent system which estimates spacecraft rate has been successfully developed and tested using only magnetometer data or a combination of magnetometer data and sun sensor data, which is less costly than a gyro. This system also uses an EKF. Merging the two systems will provide an extremely low cost, autonomous approach to attitude and trajectory estimation. In this work we provide the theoretical background of the combined system. The measurement matrix is developed by combining the measurement matrix of the orbit and attitude estimation EKF with the measurement matrix of the rate estimation EKF, which is composed of a pseudo-measurement which makes the effective measurement a function of the angular velocity. Associated with this is the development of the noise covariance matrix associated with the original measurement combined with the new pseudo-measurement. In addition, the combination of the dynamics from the two systems is presented along with preliminary test results.

Deutschmann, Julie↗
NASA NTRS1998

Two-Dimensional High-Lift Aerodynamic Optimization Using Neural Networks

The high-lift performance of a multi-element airfoil was optimized by using neural-net predictions that were trained using a computational data set. The numerical data was generated using a two-dimensional, incompressible, Navier-Stokes algorithm with the Spalart-Allmaras turbulence model. Because it is difficult to predict maximum lift for high-lift systems, an empirically-based maximum lift criteria was used in this study to determine both the maximum lift and the angle at which it occurs. The 'pressure difference rule,' which states that the maximum lift condition corresponds to a certain pressure difference between the peak suction pressure and the pressure at the trailing edge of the element, was applied and verified with experimental observations for this configuration. Multiple input, single output networks were trained using the NASA Ames variation of the Levenberg-Marquardt algorithm for each of the aerodynamic coefficients (lift, drag and moment). The artificial neural networks were integrated with a gradient-based optimizer. Using independent numerical simulations and experimental data for this high-lift configuration, it was shown that this design process successfully optimized flap deflection, gap, overlap, and angle of attack to maximize lift. Once the neural nets were trained and integrated with the optimizer, minimal additional computer resources were required to perform optimization runs with different initial conditions and parameters. Applying the neural networks within the high-lift rigging optimization process reduced the amount of computational time and resources by 44% compared with traditional gradient-based optimization procedures for multiple optimization runs.

Greenman, Roxana M.↗
NASA NTRS1961

Study of a Solar Sensor for use in Space Vehicle Orientation Control Systems

The solar sensor described herein may be used for a variety of space operations requiring solar orientation. The use of silicon solar cells as the sensing elements provides the sensor with sufficient capability to withstand the hazards of a space environment. A method of arranging the cells in a sensor consists simply of mounting them at a large angle to the base. The use of an opaque shield placed between the cells and perpendicular to the base enhances the small-angle sensitivity while adding slightly to the bulk of the sensor. The difference in illumination of these cells as the result of an oblique incidence of the light rays from the reference source causes an electrical error signal which, when used in a battery-bridge circuit, requires a minimum of electrical processing for use in a space-vehicle orientation control system. An error which could occur after prolonged operation of the sensor is that resulting from asymmetrical aging of opposite cells. This could be periodically corrected with a balance potentiometer. A more routine error in the sensor is that produced by reflected earth radiation. This error may be eliminated over a large portion of the operation time by restricting the field of view and, consequently, the capture capability. A more sophisticated method of eliminating this error is to use separate sensors, for capture and fine pointing, along with a switching device. An experimental model has been constructed and tested to yield an output sensitivity of 1.2 millivolts per second of arc with a load resistance of 1,000 ohms and a reference light source of approximately 1,200 foot-candles delivered at the sensor.

Spencer, Paul R.↗
NASA NTRS1998

Using Approximations to Accelerate Engineering Design Optimization

Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.

Torczon, Virginia↗