SEARCH · Engineering Papers

Results for “sum of squares”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

All sources NASA NTRS DOE OSTI

NASA NTRS1995

Influence of the helicopter environment on patient care capabilities: flight crew perceptions

INTRODUCTION: Flight crew perceptions of the effect of the rotary-wing environment on patient-care capabilities have not been subject to statistical analysis. We hypothesized that flight crew members perceived significant difficulties in performing patient-care tasks during air medical transport. METHODS: A survey was distributed to a convenience sample of flight crew members from 20 flight programs. Respondents were asked to compare the difficulty of performing patient-care tasks in rotary-wing and standard (emergency department or intensive care unit) settings. Demographic data collected on respondents included years of flight experience, flights per month, crew duty position and primary aircraft in which the respondent worked. Statistical analysis was performed as appropriate using Student's t-test, type III sum of squares, and analysis of variance. Alpha was defined as p < 0.05. RESULTS: Fifty-five percent of programs (90 individuals) responded. All tasks were significantly rated more difficult in the rotary-wing environment. Ratings were not significantly correlated with flight experience, duty position, flights per month or aircraft used. CONCLUSIONS: We conclude that the performance of patient-care tasks are perceived by air medical flight crew to be significantly more difficult during rotary-wing air medical transport than in hospital settings.

Noise, Transportation/adverse effects↗

NASA NTRS2006

A LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR (LASSO) FOR NONLINEAR SYSTEM IDENTIFICATION

Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.

Kukreja, Sunil L.↗

NASA NTRS2000

Maxium-Likelihood Template Matching

In image matching applications such as tracking and stereo matching, it is common to use the sum-of-squared-differences (SSD) measure to determine the best match for an image template.

maximum-likeihood estimation template matching obj↗

NASA NTRS2007

Aeroelastic Model Structure Computation for Envelope Expansion

Structure detection is a procedure for selecting a subset of candidate terms, from a full model description, that best describes the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modelling may be of critical importance in the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion which may save significant development time and costs. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear aeroelastic systems. The LASSO minimises the residual sum of squares by the addition of an l(sub 1) penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. Applicability of this technique for model structure computation for the F/A-18 Active Aeroelastic Wing using flight test data is shown for several flight conditions (Mach numbers) by identifying a parsimonious system description with a high percent fit for cross-validated data.

Kukreja, Sunil L.↗

NASA NTRS2007

Aeroelastic Model Structure Computation for Envelope Expansion

Structure detection is a procedure for selecting a subset of candidate terms, from a full model description, that best describes the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modeling may be of critical importance in the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion that may save significant development time and costs. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of non-linear aeroelastic systems. The LASSO minimises the residual sum of squares with the addition of an l(Sub 1) penalty term on the parameter vector of the traditional l(sub 2) minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudo-linear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. Applicability of this technique for model structure computation for the F/A-18 (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) Active Aeroelastic Wing project using flight test data is shown for several flight conditions (Mach numbers) by identifying a parsimonious system description with a high percent fit for cross-validated data.

Kukreja, Sunil L.↗

NASA NTRS2008

Spline-Based Smoothing of Airfoil Curvatures

Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).

Li, W.↗

NASA NTRS2006

Multichannel Phase and Power Detector

An electronic signal-processing system determines the phases of input signals arriving in multiple channels, relative to the phase of a reference signal with which the input signals are known to be coherent in both phase and frequency. The system also gives an estimate of the power levels of the input signals. A prototype of the system has four input channels that handle signals at a frequency of 9.5 MHz, but the basic principles of design and operation are extensible to other signal frequencies and greater numbers of channels. The prototype system consists mostly of three parts: An analog-to-digital-converter (ADC) board, which coherently digitizes the input signals in synchronism with the reference signal and performs some simple processing; A digital signal processor (DSP) in the form of a field-programmable gate array (FPGA) board, which performs most of the phase- and power-measurement computations on the digital samples generated by the ADC board; and A carrier board, which allows a personal computer to retrieve the phase and power data. The DSP contains four independent phase-only tracking loops, each of which tracks the phase of one of the preprocessed input signals relative to that of the reference signal (see figure). The phase values computed by these loops are averaged over intervals, the length of which is chosen to obtain output from the DSP at a desired rate. In addition, a simple sum of squares is computed for each channel as an estimate of the power of the signal in that channel. The relative phases and the power level estimates computed by the DSP could be used for diverse purposes in different settings. For example, if the input signals come from different elements of a phased-array antenna, the phases could be used as indications of the direction of arrival of a received signal and/or as feedback for electronic or mechanical beam steering. The power levels could be used as feedback for automatic gain control in preprocessing of incoming signals. For another example, the system could be used to measure the phases and power levels of outputs of multiple power amplifiers to enable adjustment of the amplifiers for optimal power combining.

Li, Samuel↗

NASA NTRS2011

Uncertainty Analysis via Failure Domain Characterization: Polynomial Requirement Functions

This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. A Bernstein expansion approach is used to size hyper-rectangular subsets while a sum of squares programming approach is used to size quasi-ellipsoidal subsets. These methods are applicable to requirement functions whose functional dependency on the uncertainty is a known polynomial. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the uncertainty model assumed (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.

Crespo, Luis G.↗

NASA NTRS2005

Fitting Nonlinear Curves by use of Optimization Techniques

MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon-Fletcher-Goldfarb-Shanno (BFGS) variable-metric method for unconstrained minimization in conjunction with a one-dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.

Hill, Scott A.↗

NASA NTRS2004

Reducing Errors by Use of Redundancy in Gravity Measurements

A methodology for improving gravity-gradient measurement data exploits the constraints imposed upon the components of the gravity-gradient tensor by the conditions of integrability needed for reconstruction of the gravitational potential. These constraints are derived from the basic equation for the gravitational potential and from mathematical identities that apply to the gravitational potential and its partial derivatives with respect to spatial coordinates. Consider the gravitational potential in a Cartesian coordinate system {x1,x2,x3}. If one measures all the components of the gravity-gradient tensor at all points of interest within a region of space in which one seeks to characterize the gravitational field, one obtains redundant information. One could utilize the constraints to select a minimum (that is, nonredundant) set of measurements from which the gravitational potential could be reconstructed. Alternatively, one could exploit the redundancy to reduce errors from noisy measurements. A convenient example is that of the selection of a minimum set of measurements to characterize the gravitational field at n3 points (where n is an integer) in a cube. Without the benefit of such a selection, it would be necessary to make 9n3 measurements because the gravitygradient tensor has 9 components at each point. The problem of utilizing the redundancy to reduce errors in noisy measurements is an optimization problem: Given a set of noisy values of the components of the gravity-gradient tensor at the measurement points, one seeks a set of corrected values - a set that is optimum in that it minimizes some measure of error (e.g., the sum of squares of the differences between the corrected and noisy measurement values) while taking account of the fact that the constraints must apply to the exact values. The problem as thus posed leads to a vector equation that can be solved to obtain the corrected values.

Kulikov, Igor↗

NASA NTRS2015

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor selection metrics are presented for two types of estimators including a Kalman filter and a maximum a posteriori estimator. For each type of performance estimator, sensor selection is based on minimizing the theoretical sum of squared estimation errors in health parameters representing performance deterioration in the major rotating modules of the engine. For gas path fault diagnostics, the sensor selection metric is set up to maximize correct classification rate for a diagnostic strategy that performs fault classification by identifying the fault type that most closely matches the observed measurement signature in a weighted least squares sense. Results from the application of the sensor selection metrics to a linear engine model are presented and discussed. Given a baseline sensor suite and a candidate list of optional sensors, an exhaustive search is performed to determine the optimal sensor suites for performance estimation and fault diagnostics. For any given sensor suite, Monte Carlo simulation results are found to exhibit good agreement with theoretical predictions of estimation and diagnostic accuracies.

Gas Turbine Engines↗

NASA NTRS2015

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

Gas Turbine Engines↗

NASA NTRS2016

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

Diagnosis↗

NASA NTRS2016

Image Correlation Pattern Optimization for Micro-Scale In-Situ Strain Measurements

The accuracy and precision of digital image correlation (DIC) is a function of three primary ingredients: image acquisition, image analysis, and the subject of the image. Development of the first two (i.e. image acquisition techniques and image correlation algorithms) has led to widespread use of DIC; however, fewer developments have been focused on the third ingredient. Typically, subjects of DIC images are mechanical specimens with either a natural surface pattern or a pattern applied to the surface. Research in the area of DIC patterns has primarily been aimed at identifying which surface patterns are best suited for DIC, by comparing patterns to each other. Because the easiest and most widespread methods of applying patterns have a high degree of randomness associated with them (e.g., airbrush, spray paint, particle decoration, etc.), less effort has been spent on exact construction of ideal patterns. With the development of patterning techniques such as microstamping and lithography, patterns can be applied to a specimen pixel by pixel from a patterned image. In these cases, especially because the patterns are reused many times, an optimal pattern is sought such that error introduced into DIC from the pattern is minimized. DIC consists of tracking the motion of an array of nodes from a reference image to a deformed image. Every pixel in the images has an associated intensity (grayscale) value, with discretization depending on the bit depth of the image. Because individual pixel matching by intensity value yields a non-unique scale-dependent problem, subsets around each node are used for identification. A correlation criteria is used to find the best match of a particular subset of a reference image within a deformed image. The reader is referred to references for enumerations of typical correlation criteria. As illustrated by Schreier and Sutton and Lu and Cary systematic errors can be introduced by representing the underlying deformation with under-matched shape functions. An important implication, as discussed by Sutton et al., is that in the presence of highly localized deformations (e.g., crack fronts), error can be reduced by minimizing the subset size. In other words, smaller subsets allow the more accurate resolution of localized deformations. Contrarily, the choice of optimal subset size has been widely studied and a general consensus is that larger subsets with more information content are less prone to random error. Thus, an optimal subset size balances the systematic error from under matched deformations with random error from measurement noise. The alternative approach pursued in the current work is to choose a small subset size and optimize the information content within (i.e., optimizing an applied DIC pattern), rather than finding an optimal subset size. In the literature, many pattern quality metrics have been proposed, e.g., sum of square intensity gradient (SSSIG), mean subset fluctuation, gray level co-occurrence, autocorrelation-based metrics, and speckle-based metrics. The majority of these metrics were developed to quantify the quality of common pseudo-random patterns after they have been applied, and were not created with the intent of pattern generation. As such, it is found that none of the metrics examined in this study are fit to be the objective function of a pattern generation optimization. In some cases, such as with speckle-based metrics, application to pixel by pixel patterns is ill-conditioned and requires somewhat arbitrary extensions. In other cases, such as with the SSSIG, it is shown that trivial solutions exist for the optimum of the metric which are ill-suited for DIC (such as a checkerboard pattern). In the current work, a multi-metric optimization method is proposed whereby quality is viewed as a combination of individual quality metrics. Specifically, SSSIG and two auto-correlation metrics are used which have generally competitive objectives. Thus, each metric could be viewed as a constraint imposed upon the others, thereby precluding the achievement of their trivial solutions. In this way, optimization produces a pattern which balances the benefits of multiple quality metrics. The resulting pattern, along with randomly generated patterns, is subjected to numerical deformations and analyzed with DIC software. The optimal pattern is shown to outperform randomly generated patterns.

Bomarito, G. F.↗

NASA NTRS2017

Interval Predictor Models for Data with Measurement Uncertainty

An interval predictor model (IPM) is a computational model that predicts the range of an output variable given input-output data. This paper proposes strategies for constructing IPMs based on semidefinite programming and sum of squares (SOS). The models are optimal in the sense that they yield an interval valued function of minimal spread containing all the observations. Two different scenarios are considered. The first one is applicable to situations where the data is measured precisely whereas the second one is applicable to data subject to known biases and measurement error. In the latter case, the IPMs are designed to fully contain regions in the input-output space where the data is expected to fall. Moreover, we propose a strategy for reducing the computational cost associated with generating IPMs as well as means to simulate them. Numerical examples illustrate the usage and performance of the proposed formulations.

Lacerda, Marcio J.↗

NASA NTRS2018

Super Resolution of Remote Sensing Images Using Edge-Directed Radial Basis Functions

Edge-Directed Radial Basis Functions (EDRBF) are used to compute super resolution(SR) image from a given set of low resolution (LR) images differing in subpixel shifts. The algorithm is tested on remote sensing images and compared for accuracy with other well-known algorithms such as Iterative Back Projection (IBP), Maximum Likelihood (ML) algorithm, interpolation of scattered points using Nearest Neighbor (NN) and Inversed Distance Weighted (IDW) interpolation, and Radial Basis Functin(RBF) . The accuracy of SR depends on various factors besides the algorithm (i) number of subpixel shifted LR images (ii) accuracy with which the LR shifts are estimated by registration algorithms (iii) and the targeted spatial resolution of SR. In our studies, the accuracy of EDRBF is compared with other algorithms keeping these factors constant. The algorithm has two steps: i) registration of low resolution images and (ii) estimating the pixels in High Resolution (HR) grid using EDRBF. Experiments are conducted by simulating LR images from a input HR image with different sub-pixel shifts. The reconstructed SR image is compared with input HR image to measure the accuracy of the algorithm using sum of squared errors (SSE). The algorithm has outperformed all of the algorithms mentioned above. The algorithm is robust and is not overly sensitive to the registration inaccuracies.

Mareboyana, Manohar M.↗

NASA NTRSDate not supplied

A Convex Optimization Approach to Improving Suboptimal Hyperparameters of Sliced Normal Distributions

Sliced Normal (SN) distributions are a generalization of Gaussian distributions where the quadratic argument of the exponential is replaced with a sum of squares polynomial. SNs may be used to represent the distribution of a diverse set of random variables including multi-modal, non-symmetric, and skewed distributions. Unfortunately, the likelihood function of a SN includes a normalization constant and the inclusion of this normalization constant makes the likelihood a non-convex function of the hyperparameters which define the SN. In previous work, suboptimal fitting of the hyperparameters was performed by transforming the given data into a higher dimensional monomial basis and selecting the optimal hyperparameters of a Gaussian fit in this space. However, this approach did not account for the effect of lifting on the normalization constant. Indeed, it was observed that as the number of monomials is increased the likelihood of the Sliced Normal can decrease. In this paper, we increase the likelihood of Sliced Normals found using the previous method by developing a convex formulation which scales the covariance matrix of the Gaussian fit such that the likelihood of the Sliced Normal is maximized. The result is significant improvements of the log likelihood of fitted SN distributions, including a significant increase, especially for problems with 500+ monomials.

Convex optimization approach to improving suboptim↗

DOE OSTI2020

How Wrong Can the Operational AEP Uncertainty Estimate Be When We Ignore the Correlations Between the Uncertainty Components?

Calculations of wind farm annual energy production (AEP) on operational data are essential for a variety of financial transactions during the life of wind plants. The AEP estimate is associated with an uncertainty value, which is calculated by combining contributions connected to on-site measurements, long-term reference measurements, losses, regression, windiness adjustment, and wind resource interannual variability. Although very limited documentation on the topic exists, the conventional approach currently used by the wind energy community to assess the uncertainty connected to the operational AEP estimate assume that the different uncertainty components are uncorrelated and therefore calculates the overall uncertainty with a sum of squares approach. In this analysis, we contrast the traditional technique to estimate the overall AEP uncertainty by ignoring the correlation between its different components with a novel Monte Carlo based approach, which can instead take into account the correlation between different uncertainty categories. We consider monthly operational data from 472 wind farms from the Energy Information Administration (EIA) 923 database to assess the difference between the two approaches. Long-term wind speed data needed for the AEP assessment are taken from three reanalysis products: the Modern-Era Retrospective analysis for Research and Applications v2 (MERRA-2), the European Reanalysis Interim (ERA-interim), and the National Centers for Environmental Prediction v2 (NCEP-2). The results of the Monte Carlo approach show that three pairs of AEP uncertainty components do show a statistically significant correlation: the uncertainty connected with wind resource inter-annual variability is positively correlated with the one related to the windiness correction and negatively correlated with the one due to the regression, and the wind measurement uncertainty is positively correlated with the regression uncertainty. All these correlations, which are found between uncertainty components which are not only part of an operational analysis, but also of a wind resource assessment, are currently ignored in the conventional techniques used as industry standard. We further investigate the causes of these correlations, in terms of common dependencies of different uncertainty components on wind resource variability, number of data points, and quality of the regression between wind speed and energy production data. Next, we quantify the error in the current industry standard technique, in terms of the percentage difference in total uncertainty calculated with the two considered approaches, for all the analyzed wind farms. We find a mean absolute percentage difference of about 6%, with the largest differences being greater than 20%. The data clearly confirm that ignoring the actual correlation between the uncertainty components can lead to large errors in the assessment of the operational AEP uncertainty, and the proposed Monte Carlo approach should be preferred.

Monte Carlo↗