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Statistical model to perform error analysis of curve fits of wind tunnel test data using the techniques of analysis of variance and regression analysis

The considered research had the objective to design a statistical model that could perform an error analysis of curve fits of wind tunnel test data using analysis of variance and regression analysis techniques. Four related subproblems were defined, and by solving each of these a solution to the general research problem was obtained. The capabilities of the evolved true statistical model are considered. The least squares fit is used to determine the nature of the force, moment, and pressure data. The order of the curve fit is increased in order to delete the quadratic effect in the residuals. The analysis of variance is used to determine the magnitude and effect of the error factor associated with the experimental data.

Alston, D. W.↗

Development of a User Interface for a Regression Analysis Software Tool

An easy-to -use user interface was implemented in a highly automated regression analysis tool. The user interface was developed from the start to run on computers that use the Windows, Macintosh, Linux, or UNIX operating system. Many user interface features were specifically designed such that a novice or inexperienced user can apply the regression analysis tool with confidence. Therefore, the user interface s design minimizes interactive input from the user. In addition, reasonable default combinations are assigned to those analysis settings that influence the outcome of the regression analysis. These default combinations will lead to a successful regression analysis result for most experimental data sets. The user interface comes in two versions. The text user interface version is used for the ongoing development of the regression analysis tool. The official release of the regression analysis tool, on the other hand, has a graphical user interface that is more efficient to use. This graphical user interface displays all input file names, output file names, and analysis settings for a specific software application mode on a single screen which makes it easier to generate reliable analysis results and to perform input parameter studies. An object-oriented approach was used for the development of the graphical user interface. This choice keeps future software maintenance costs to a reasonable limit. Examples of both the text user interface and graphical user interface are discussed in order to illustrate the user interface s overall design approach.

Ulbrich, Norbert Manfred↗

External Tank Liquid Hydrogen (LH2) Prepress Regression Analysis Independent Review Technical Consultation Report

The request to conduct an independent review of regression models, developed for determining the expected Launch Commit Criteria (LCC) External Tank (ET)-04 cycle count for the Space Shuttle ET tanking process, was submitted to the NASA Engineering and Safety Center NESC on September 20, 2005. The NESC team performed an independent review of regression models documented in Prepress Regression Analysis, Tom Clark and Angela Krenn, 10/27/05. This consultation consisted of a peer review by statistical experts of the proposed regression models provided in the Prepress Regression Analysis. This document is the consultation's final report.

Parsons, Vickie s.↗

Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials

Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.

42 ENGINEERING↗

Notes on Regression Analysis for Radar Parameter Estimation

A fundamental task of radar, beyond merely detecting a target, is to estimate some parameters associated with it. For example, this might include range, direction, velocity, etc. In any case, multiple measurements, often noisy, need to be processed to yield a ‘best estimate’ of the parameter. A common mathematical method for doing so is called “Regression” analysis. The goal is to minimize the expected squared error in the estimate. Even when alternate algorithms are considered, the least squared-error regression analysis is the benchmark against which alternatives are compared.

47 OTHER INSTRUMENTATION↗

Performance of an Axisymmetric Rocket Based Combined Cycle Engine During Rocket Only Operation Using Linear Regression Analysis

The all rocket mode of operation is shown to be a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. An axisymmetric RBCC engine was used to determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and multiple linear regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inlet diameter ratio. A perfect gas computational fluid dynamics analysis, using both the Spalart-Allmaras and k-omega turbulence models, was performed with the NPARC code to obtain values of vacuum specific impulse. Results from the multiple linear regression analysis showed that for both the full flow and gas generator configurations increasing mixer-ejector area ratio and rocket area ratio increase performance, while increasing mixer-ejector inlet area ratio and mixer-ejector length-to-diameter ratio decrease performance. Increasing injected secondary flow increased performance for the gas generator analysis, but was not statistically significant for the full flow analysis. Chamber pressure was found to be not statistically significant.

Smith, Timothy D.↗

A method for nonlinear exponential regression analysis

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Junkin, B. G.↗

A New Global Regression Analysis Method for the Prediction of Wind Tunnel Model Weight Corrections

A new global regression analysis method is discussed that predicts wind tunnel model weight corrections for strain-gage balance loads during a wind tunnel test. The method determines corrections by combining "wind-on" model attitude measurements with least squares estimates of the model weight and center of gravity coordinates that are obtained from "wind-off" data points. The method treats the least squares fit of the model weight separate from the fit of the center of gravity coordinates. Therefore, it performs two fits of "wind- off" data points and uses the least squares estimator of the model weight as an input for the fit of the center of gravity coordinates. Explicit equations for the least squares estimators of the weight and center of gravity coordinates are derived that simplify the implementation of the method in the data system software of a wind tunnel. In addition, recommendations for sets of "wind-off" data points are made that take typical model support system constraints into account. Explicit equations of the confidence intervals on the model weight and center of gravity coordinates and two different error analyses of the model weight prediction are also discussed in the appendices of the paper.

strain-gage balance↗

A multiple linear regression analysis of hot corrosion attack on a series of nickel base turbine alloys

Multiple linear regression analysis was used to determine an equation for estimating hot corrosion attack for a series of Ni base cast turbine alloys. The U transform (i.e., 1/sin (% A/100) to the 1/2) was shown to give the best estimate of the dependent variable, y. A complete second degree equation is described for the centered" weight chemistries for the elements Cr, Al, Ti, Mo, W, Cb, Ta, and Co. In addition linear terms for the minor elements C, B, and Zr were added for a basic 47 term equation. The best reduced equation was determined by the stepwise selection method with essentially 13 terms. The Cr term was found to be the most important accounting for 60 percent of the explained variability hot corrosion attack.

Barrett, C. A.↗

Regression Analysis of Top of Descent Location for Idle-thrust Descents

In this paper, multiple regression analysis is used to model the top of descent (TOD) location of user-preferred descent trajectories computed by the flight management system (FMS) on over 1000 commercial flights into Melbourne, Australia. The independent variables cruise altitude, final altitude, cruise Mach, descent speed, wind, and engine type were also recorded or computed post-operations. Both first-order and second-order models are considered, where cross-validation, hypothesis testing, and additional analysis are used to compare models. This identifies the models that should give the smallest errors if used to predict TOD location for new data in the future. A model that is linear in TOD altitude, final altitude, descent speed, and wind gives an estimated standard deviation of 3.9 nmi for TOD location given the trajec- tory parameters, which means about 80% of predictions would have error less than 5 nmi in absolute value. This accuracy is better than demonstrated by other ground automation predictions using kinetic models. Furthermore, this approach would enable online learning of the model. Additional data or further knowl- edge of algorithms is necessary to conclude definitively that no second-order terms are appropriate. Possible applications of the linear model are described, including enabling arriving aircraft to fly optimized descents computed by the FMS even in congested airspace. In particular, a model for TOD location that is linear in the independent variables would enable decision support tool human-machine interfaces for which a kinetic approach would be computationally too slow.

trajectory prediction↗

Method for nonlinear exponential regression analysis

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

Junkin, B. G.↗

Fast and Non-Destructive Determination of Water Content in Ionic Liquids at Varying Temperatures by Raman Spectroscopy and Multivariate Regression Analysis

Imidazolium acetate ionic liquids (ILs) have been utilized as promising solvents in many applications that involve varying water content and temperature. These experimental variables affect the anion-cation intermolecular interactions, which in turn influence the performance of the ILs in these applications. Here, this paper shows Raman spectroscopy can be used as an operando method to measure water content in IL solvents when simultaneous temperature changes may occur. The Raman spectra of 1-alkyl-3-methylimidazolium acetate ILs (alkyl chain length n = 2, 4, 6, 8) with varying water content (from 0.028 to 0.899 water mole fraction) and temperature (from 78.1 K to 423.1 K) were measured. Increasing the water content or decreasing the temperature of the tested ILs weakens the anion-cation intermolecular interactions. The water content of these ILs can be quantified even in conditions when the temperature is changing using Raman spectroscopy combined with multivariate regression analysis, including principal component regression (PCR), partial-least-squares regression (PLSR), and artificial neural networks (ANNs). The ANN model combined with partial-least-squares (PLS) achieves the highest prediction accuracy of water content in ILs at varying temperatures (RMSECV = 0.017, R 2 CV = 99.1%, RMSEP = 0.019, R 2 P = 98.8%, RPD = 8.93). Raman spectroscopy provides a potential fast non-destructive operando method to monitor the water content of ILs even in applications when the temperature may be simultaneously altered; this information can lead to the optimized use of these ILs in many applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗