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NASA NTRSDate not supplied

4pPA1 - Turbulence Effects on Shaped Booms: Central Composite Design of Modeled Atmospheric Turbulence Parameters for Sonic Boom Propagation

Propagation of sonic booms through turbulence reduces mean sonic boom perception metric levels and also causes considerable variability. NASA’s PCBoom suite of sonic boom acoustic propagation modules includes an approximate method for accounting for the effects of turbulence on traditional N-wave sonic booms. The current implementation is ineffective for shaped sonic booms or low-booms, and it also has limited values for turbulence and ambient input parameters. NASA’s future X-59 low-boom community noise surveys require an accurate estimate of the effects of turbulence in regions across the USA, so the module must be improved. This work presents the methods of selecting which ambient and turbulence parameters should be included in an improved PCBoom turbulence module. Turbulence and ambient data were collected from two atmospheric model databases, the Climate Forecast System Version 2 and European Centre for Medium-Range Weather Forecast Reanalysis Version 5 (ERA5), hourly from 7 AM to 7 PM local time for 10 years at 19 locations across the USA. A fully-factorial propagation analysis using these parameters would be exceedingly computationally expensive. Instead, a central composite design was chosen resulting in 45 combinations of ambient and turbulence parameters. These 45 cases effectively sample the space balancing computational burden.

turbulence↗

NASA NTRS2010

Tuning Parameters in Heuristics by Using Design of Experiments Methods

With the growing complexity of today's large scale problems, it has become more difficult to find optimal solutions by using exact mathematical methods. The need to find near-optimal solutions in an acceptable time frame requires heuristic approaches. In many cases, however, most heuristics have several parameters that need to be "tuned" before they can reach good results. The problem then turns into "finding best parameter setting" for the heuristics to solve the problems efficiently and timely. One-Factor-At-a-Time (OFAT) approach for parameter tuning neglects the interactions between parameters. Design of Experiments (DOE) tools can be instead employed to tune the parameters more effectively. In this paper, we seek the best parameter setting for a Genetic Algorithm (GA) to solve the single machine total weighted tardiness problem in which n jobs must be scheduled on a single machine without preemption, and the objective is to minimize the total weighted tardiness. Benchmark instances for the problem are available in the literature. To fine tune the GA parameters in the most efficient way, we compare multiple DOE models including 2-level (2k ) full factorial design, orthogonal array design, central composite design, D-optimal design and signal-to-noise (SIN) ratios. In each DOE method, a mathematical model is created using regression analysis, and solved to obtain the best parameter setting. After verification runs using the tuned parameter setting, the preliminary results for optimal solutions of multiple instances were found efficiently.

Arin, Arif↗

NASA NTRS1993

Space transportation vehicle design evaluation using saturated designs

An important objective in the preliminary design and evaluation of space transportation vehicles is to find the best values of design variables that optimize the performance characteristic (e.g. dry weight). For a given configuration, the vehicle performance can be determined by the use of complex sizing and performance evaluation computer programs. These complex computer programs utilize iterative algorithms and they are generally too expensive and/or difficult to use directly in multidisciplinary design optimization. An alternative is to use response surface methodology (RSM) and obtain quadratic polynomial approximations to the functional relationships between performance characteristics and design variables. In RSM, these approximation models are then used to determine optimum design parameter values and for rapid sensitivity studies. Constructing a second-order model requires that 'n' design parameters be studied at least at 3 levels (values) so that the coefficients in the model can be estimated. There, 3(n) factorial experiments (point designs or observations) may be necessary. For small values of 'n' such as two or three, this design works well. However, when a large number of design parameters are under study, the number of design points required for a full-factorial design may become excessive. Fortunately, these quadratic polynomial approximations can be obtained by selecting an efficient design matrix using central composite designs (CCD) from design of experiments theory. Each unique point design from the CCD matrix is then conducted using computerized analysis tools (e.g. POST, CONSIZ, etc.). In the next step, least squares regression analysis is used to calculate the quadratic polynomial coefficients from the data. However, in some multidisciplinary applications involving a large number of design variables and several disciplines, the computerized performance synthesis programs may get too time consuming and expensive to run even with the use of efficient central composite designs. In such cases, it may be preferable to keep the number of design points to an absolute minimum and trade some model accuracy with cost. For this purpose, another class of experimental designs, called saturated D-optimal designs may be utilized for generating a matrix of vehicle designs. A design is called saturated when the number of design points is exactly equal to the number of terms in the model to be fitted. As a result, saturated designs require the absolute minimum number of design points ((n+1)(n+2)/s) to estimate the quadratic polynomial model coefficients. Saturated designs can be generated using the D-optimality criterion. A good saturated design should give rise to least squares estimates with minimum generalized variance.

Unal, Resit↗

NASA NTRS2010

Estimation of Supersonic Stage Separation Aerodynamics of Winged-Body Launch Vehicles Using Response Surface Methods

Response surface methodology was used to estimate the longitudinal stage separation aerodynamic characteristics of a generic, bimese, winged multi-stage launch vehicle configuration at supersonic speeds in the NASA LaRC Unitary Plan Wind Tunnel. The Mach 3 staging was dominated by shock wave interactions between the orbiter and booster vehicles throughout the relative spatial locations of interest. The inference space was partitioned into several contiguous regions within which the separation aerodynamics were presumed to be well-behaved and estimable using central composite designs capable of fitting full second-order response functions. The underlying aerodynamic response surfaces of the booster vehicle in belly-to-belly proximity to the orbiter vehicle were estimated using piecewise-continuous lower-order polynomial functions. The quality of fit and prediction capabilities of the empirical models were assessed in detail, and the issue of subspace boundary discontinuities was addressed. Augmenting the central composite designs to full third-order using computer-generated D-optimality criteria was evaluated. The usefulness of central composite designs, the subspace sizing, and the practicality of fitting lower-order response functions over a partitioned inference space dominated by highly nonlinear and possibly discontinuous shock-induced aerodynamics are discussed.

Erickson, Gary E.↗

NASA NTRS2008

Estimation of Supersonic Stage Separation Aerodynamics of Winged-Body Launch Vehicles Using Response Surface Methods

A collection of statistical and mathematical techniques referred to as response surface methodology was used to estimate the longitudinal stage separation aerodynamic characteristics of a generic, bimese, winged multi-stage launch vehicle configuration using data obtained on small-scale models at supersonic speeds in the NASA Langley Research Center Unitary Plan Wind Tunnel. The simulated Mach 3 staging was dominated by multiple shock wave interactions between the orbiter and booster vehicles throughout the relative spatial locations of interest. This motivated a partitioning of the overall inference space into several contiguous regions within which the separation aerodynamics were presumed to be well-behaved and estimable using cuboidal and spherical central composite designs capable of fitting full second-order response functions. The primary goal was to approximate the underlying overall aerodynamic response surfaces of the booster vehicle in belly-to-belly proximity to the orbiter vehicle using relatively simple, lower-order polynomial functions that were piecewise-continuous across the full independent variable ranges of interest. The quality of fit and prediction capabilities of the empirical models were assessed in detail, and the issue of subspace boundary discontinuities was addressed. The potential benefits of augmenting the central composite designs to full third order using computer-generated D-optimality criteria were also evaluated. The usefulness of central composite designs, the subspace sizing, and the practicality of fitting low-order response functions over a partitioned inference space dominated by highly nonlinear and possibly discontinuous shock-induced aerodynamics are discussed.

Erickson, Gary E.↗

NASA NTRS1998

Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Designs

This paper discusses response surface methods for approximation model building and multidisciplinary design optimization. The response surface methods discussed are central composite designs, Bayesian methods and D-optimal designs. An over-determined D-optimal design is applied to a configuration design and optimization study of a wing-body, launch vehicle. Results suggest that over determined D-optimal designs may provide an efficient approach for approximation model building and for multidisciplinary design optimization.

Unal, Resit↗

NASA NTRS1986

The effect of Cr, Co, Al, Mo and Ta on a series of cast Ni-base superalloys on the stability of an aluminide coating during cyclic oxidation in Mach 0.3 burner rig

The influence of varying the content of Co, Cr, Mo, Ta, and Al in a series of cast Ni-based gamma/gamma'superalloys on the behavior of aluminide coatings was studied in burner rig cyclic oxidation tests at 1100 C. The alloys had nominally fixed levels of Ti, W, Cb, Zr, C, and B. The alloy compositions were based on a full 2(sup 5)-fractional statistical design supplemented by 10 star point alloys and a center point alloy. This full central composite design of 43 alloys plus two additional alloys with extreme Al levels allowed a complete second degree estimating equation to be derived from the 5-compositional variables. The weight change/time data for the coated samples fitted well to the paralinear oxidation model and enabled a modified oxidation attack parameter, K'(sub a) to be derived to rank the alloys and log K' (sub a ) to be used as the dependent variable in the estimating equation to determine the oxidation resistance of the coating as a function of the underlying alloy content. The most protective aluminide coatings are associated with the highest possible base ally contents of CR and Al and at a 4 percent Ta level. The Mo and Co effects interact but at fixed levels of 0, 5, or 10% Co. A 4% Mo level is optimum.

Zaplatynsky, I.↗

NASA NTRS2009

Experimental Investigation of the Application of Microramp Flow Control to an Oblique Shock Interaction

The effectiveness of microramp flow control devices in controlling an oblique shock interaction was tested in the 15- by 15-Centimeter Supersonic Wind Tunnel at NASA Glenn Research Center. Fifteen microramp geometries were tested varying the height, chord length, and spacing between ramps. Measurements of the boundary layer properties downstream of the shock reflection were analyzed using design of experiments methods. Results from main effects, D-optimal, full factorial, and central composite designs were compared. The designs provided consistent results for a single variable optimization.

Hirt, Stefanie M.↗

NASA NTRS1993

Multidisciplinary Design Techniques Applied to Conceptual Aerospace Vehicle Design

Multidisciplinary design optimization (MDO) is an emerging discipline within aerospace engineering. Its goal is to bring structure and efficiency to the complex design process associated with advanced aerospace launch vehicles. Aerospace vehicles generally require input from a variety of traditional aerospace disciplines - aerodynamics, structures, performance, etc. As such, traditional optimization methods cannot always be applied. Several multidisciplinary techniques and methods were proposed as potentially applicable to this class of design problem. Among the candidate options are calculus-based (or gradient-based) optimization schemes and parametric schemes based on design of experiments theory. A brief overview of several applicable multidisciplinary design optimization methods is included. Methods from the calculus-based class and the parametric class are reviewed, but the research application reported focuses on methods from the parametric class. A vehicle of current interest was chosen as a test application for this research. The rocket-based combined-cycle (RBCC) single-stage-to-orbit (SSTO) launch vehicle combines elements of rocket and airbreathing propulsion in an attempt to produce an attractive option for launching medium sized payloads into low earth orbit. The RBCC SSTO presents a particularly difficult problem for traditional one-variable-at-a-time optimization methods because of the lack of an adequate experience base and the highly coupled nature of the design variables. MDO, however, with it's structured approach to design, is well suited to this problem. The result of the application of Taguchi methods, central composite designs, and response surface methods to the design optimization of the RBCC SSTO are presented. Attention is given to the aspect of Taguchi methods that attempts to locate a 'robust' design - that is, a design that is least sensitive to uncontrollable influences on the design. Near-optimum minimum dry weight solutions are determined for the vehicle. A summary and evaluation of the various parametric MDO methods employed in the research are included. Recommendations for additional research are provided.

Olds, John Robert↗

NASA NTRSDate not supplied

Evaluation of Response Surface Experiment Designs for Distributed Propulsion Aircraft Aero-Propulsive Modeling

Modern distributed hybrid and electric propulsion aircraft, including vertical, short, and conventional takeoff and landing configurations, exhibit significant aero-propulsive complexity and a large number of interacting test factors. This paper presents the development and evaluation of experiment designs for aero-propulsive characterization of distributed propulsion aircraft. Five different foundational response surface designs are evaluated to inform the development of two sequential design approaches tailored to complex aircraft aerodynamic characterization experiments. The first approach, which builds on sequential face-centered central composite designs, has been used previously to develop aero-propulsive models for complex aircraft using wind tunnel testing. The second approach is a new design strategy leveraging a regular I-optimal and nested I-optimal design that was developed for this study. The two sequential design strategies are compared for experiments with a large number of test factors using pre-experiment design evaluation metrics, as well as modeling results obtained from simulated wind tunnel data for the NASA LA-8 aircraft. The design evaluation metrics show that the sequential I-optimal base design has higher statistical power, lower correlation among candidate regressors, lower prediction variance, and more precise parameter estimates. The simulated wind tunnel experiments conducted using each design reveal that the sequential I-optimal base design has better predictive capability with fewer test points. The experiment design and evaluation procedures are described in detail to inform future aerodynamic characterization experiments for complex aircraft.

design of experiments↗

NASA NTRS1993

Aerodynamic configuration design using response surface methodology analysis

An investigation has been conducted to determine a set of optimal design parameters for a single-stage-to-orbit reentry vehicle. Several configuration geometry parameters which had a large impact on the entry vehicle flying characteristics were selected as design variables: the fuselage fineness ratio, the nose to body length ratio, the nose camber value, the wing planform area scale factor, and the wing location. The optimal geometry parameter values were chosen using a response surface methodology (RSM) technique which allowed for a minimum dry weight configuration design that met a set of aerodynamic performance constraints on the landing speed, and on the subsonic, supersonic, and hypersonic trim and stability levels. The RSM technique utilized, specifically the central composite design method, is presented, along with the general vehicle conceptual design process. Results are presented for an optimized configuration along with several design trade cases.

Engelund, Walter C.↗

NASA NTRS2008

A Piloted Simulator Evaluation of Transport Aircraft Rudder Pedal Force/Feel Characteristics

A piloted simulation study has been conducted in a fixed-base research simulator to assess the directional handling qualities for various rudder pedal feel characteristics for commercial transport airplanes. That is, the effects of static pedal force at maximum pedal travel, breakout force, and maximum pedal travel on handling qualities were studied. An artificial maneuver with a severe lateral wind shear and requiring runway tracking at an altitude of 50 feet in a crosswind was used to fully exercise the rudder pedals. Twelve active airline pilots voluntarily participated in the study and flew approximately 500 maneuvers. The pilots rated the maneuver performance with various rudder pedal feel characteristics using the Cooper- Harper rating scale. The test matrix had 15 unique combinations of the 3 static pedal feel characteristics. A 10-term, second-order equation for the Cooper-Harper pilot rating as a function of the 3 independent pedal feel parameters was fit to the data. The test matrix utilized a Central Composite Design that is very efficient for fitting an equation of this form. The equation was used to produce contour plots of constant pilot ratings as a function of two of the parameters with the third parameter held constant. These contour plots showed regions of good handling qualities as well as regions of degraded handling qualities. In addition, a numerical equation solver was used to predict the optimum parameter values (those with the lowest pilot rating). Quantitative pilot performance data were also analyzed. This analysis found that the peak values of the cross power spectra of the pedal force and heading angle could be used to quantify the tendency toward directional pilot induced oscillations (PIO). Larger peak values of the cross power spectra were correlated with larger (degraded) Cooper-Harper pilot ratings. Thus, the subjective data (Cooper-Harper pilot ratings) were consistent with the objective data (peak values of the cross power spectra).

Stewart, Eric C.↗

NASA NTRS2013

Effects of Hybrid Flow Control on a Normal Shock Boundary-Layer Interaction

Hybrid flow control, a combination of micro-ramps and steady micro-jets, was experimentally investigated in the 15x15 cm Supersonic Wind Tunnel at the NASA Glenn Research Center. A central composite design of experiments method, was used to develop response surfaces for boundary-layer thickness and reversed-flow thickness, with factor variables of inter-ramp spacing, ramp height and chord length, and flow injection ratio. Boundary-layer measurements and wall static pressure data were used to understand flow separation characteristics. A limited number of profiles were measured in the corners of the tunnel to aid in understanding the three-dimensional characteristics of the flowfield.

Hirt, Stefanie M.↗

NASA NTRS2003

Fuel Injector Design Optimization for an Annular Scramjet Geometry

A four-parameter, three-level, central composite experiment design has been used to optimize the configuration of an annular scramjet injector geometry using computational fluid dynamics. The computational fluid dynamic solutions played the role of computer experiments, and response surface methodology was used to capture the simulation results for mixing efficiency and total pressure recovery within the scramjet flowpath. An optimization procedure, based upon the response surface results of mixing efficiency, was used to compare the optimal design configuration against the target efficiency value of 92.5%. The results of three different optimization procedures are presented and all point to the need to look outside the current design space for different injector geometries that can meet or exceed the stated mixing efficiency target.

Steffen, Christopher J., Jr.↗

NASA NTRS2010

Calibration Designs for Non-Monolithic Wind Tunnel Force Balances

This research paper investigates current experimental designs and regression models for calibrating internal wind tunnel force balances of non-monolithic design. Such calibration methods are necessary for this class of balance because it has an electrical response that is dependent upon the sign of the applied forces and moments. This dependency gives rise to discontinuities in the response surfaces that are not easily modeled using traditional response surface methodologies. An analysis of current recommended calibration models is shown to lead to correlated response model terms. Alternative modeling methods are explored which feature orthogonal or near-orthogonal terms.

Wind tunnel models↗

NASA NTRS1985

Evaluation of alpha-SiC sintering using statistical methods

The effect of time and temperature on the density and strength of alpha-SiC was studied and mathematically modeled using a central composite experimental design. A sintering temperature of 2150 C for 1.7 h maximized the flexural strength and densification values. However, temperatures above 2200 C promoted abnormal grain growth, with resulting appreciable decreases in strength. Flexural strength increased exponentially with increasing density for specimens with densities less than or equal to 92 percent of theoretical.

Hurst, J. B.↗

NASA NTRS2006

Life Test Approach for Refractory Metal/Sodium Heat Pipes

Heat pipe life tests described in the literature have seldom been conducted on a systematic basis. Typically one or more heat pipes are built and tested for an extended period at a single temperature with simple condenser loading. This paper describes an approach to generate carefully controlled data that can conclusively establish heat pipe operating life with material-fluid combinations capable of extended operation. Approximately 10 years of operational life might be compressed into 3 years of laboratory testing through a combination of increased temperature and mass fluence. Two specific test series have been identified and include: investigation of long term corrosion rates based on the guidelines contained in ASTM G-68-80 (using 7 heat pipes); and investigation of corrosion trends in a cross correlation sequence at various temperatures and mass fluences based on a central composite test design (using 9 heat pipes). The heat pipes selected for demonstration purposes are fabricated from a Mo-44.5%Re alloy with a length of 0.3 meters and a diameter of 1.59 cm(to conserve material) with a condenser to evaporator length ratio of approximately 3. The wick is a crescent annular design formed from 400-mesh Mo-Re alloy material hot isostatically pressed to produce a final wick core of 20 microns or less.

Martin, James J.↗

NASA NTRS1980

Effect of sodium, potassium, magnesium, calcium, and chlorine on the high temperature corrosion of IN-100, U-700, IN-792, and Mar M-509

The effects of potential impurities such as Na, K, Mg, Ca, and Cl, in coal-derived liquid fuels on accelerated corrosion of IN-100, U-700, IN-792, and Mar M-509 were investigated using a Mach 0.3 burner rig for times to 200 hours in one hour cycles. These impurities were injected in combination as aqueous solutions into the combustor. Other variables were time, temperature, and fuel-to-air ratio. The experimental matrix was a central composite fractional fractorial design divided into blocks to allow modification of the design as data was gathered. The extent of corrosion was determined by metal consumption. The time exponent was near 1.0 for the least corrosion resistant alloys, U-700 and IN-100; near 0.8 for the moderately resistant IN-792; and close to Mar M-509, the most corrosion resistant alloy. As anticipated, corrosion rapidly increased with increasing temperature as well as Na and K concentrations, while corrosion decreased somewhat as the Ca concentration increased for all alloys. Mg was beneficial for the Ni-base alloys but had little effect on the Co-base alloy. Surprisingly, the effect of increasing Cl was to decrease the corrosion of all alloys. Little interaction among the dopants was noted.

Lowell, C. E.↗