Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “First Order Second Moment”

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.

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

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

A First and Second Order Moment Approach to Probabilistic Control Synthesis

This paper presents a robust control design methodology based on the estimation of the first two order moments of the random variables and processes that describe the controlled response. Synthesis is performed by solving an multi-objective optimization problem where stability and performance requirements in time- and frequency domains are integrated. The use of the first two order moments allows for the efficient estimation of the cost function thus for a faster synthesis algorithm. While reliability requirements are taken into account by using bounds to failure probabilities, requirements related to undesirable variability are implemented by quantifying the concentration of the random outcome about a deterministic target. The Hammersley Sequence Sampling and the First- and Second-Moment- Second-Order approximations are used to estimate the moments, whose accuracy and associated computational complexity are compared numerically. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

Crespo, Luis G.↗
NASA NTRS2013

Analytical Algorithms to Quantify the Uncertainty in Remaining Useful Life Prediction

This paper investigates the use of analytical algorithms to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in aerospace applications. The prediction of RUL is affected by several sources of uncertainty and it is important to systematically quantify their combined effect by computing the uncertainty in the RUL prediction in order to aid risk assessment, risk mitigation, and decisionmaking. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical algorithms are computationally cheaper and sometimes, are better suited for online decision-making. While exact analytical algorithms are available only for certain special cases (for e.g., linear models with Gaussian variables), effective approximations can be made using the the first-order second moment method (FOSM), the first-order reliability method (FORM), and the inverse first-order reliability method (Inverse FORM). These methods can be used not only to calculate the entire probability distribution of RUL but also to obtain probability bounds on RUL. This paper explains these three methods in detail and illustrates them using the state-space model of a lithium-ion battery.

Sankararaman, Shankar↗
NASA NTRS2003

Towards a Probabilistic Preliminary Design Criterion for Buckling Critical Composite Shells

A probability-based analysis method for predicting buckling loads of compression-loaded laminated-composite shells is presented, and its potential as a basis for a new shell-stability design criterion is demonstrated and discussed. In particular, a database containing information about specimen geometry, material properties, and measured initial geometric imperfections for a selected group of laminated-composite cylindrical shells is used to calculate new buckling-load "knockdown factors". These knockdown factors are shown to be substantially improved, and hence much less conservative than the corresponding deterministic knockdown factors that are presently used by industry. The probability integral associated with the analysis is evaluated by using two methods; that is, by using the exact Monte Carlo method and by using an approximate First-Order Second- Moment method. A comparison of the results from these two methods indicates that the First-Order Second-Moment method yields results that are conservative for the shells considered. Furthermore, the results show that the improved, reliability-based knockdown factor presented always yields a safe estimate of the buckling load for the shells examined.

Arbocz, Johann↗
DOE OSTI2019

Deep Direct-Use Feasibility Study Numerical Modeling and Uncertainty Analysis using iTOUGH2 for West Virginia University

To reduce the geothermal exploration risk, a feasibility study is performed for a deep direct-use system proposed at the West Virginia University (WVU) Morgantown campus. This study applies numerical simulations to investigate reservoir impedance and thermal production. Because of the great depth of the geothermal reservoir, few data are available to characterize reservoir features and properties. As a result, the study focuses on the following three aspects: 1. model choice for predicting reservoir impedance and thermal breakthrough: after investigating three potential models (one single permeability model and two dual permeability models) for flow through fractured rock, it is decided to use single permeability model for further analysis; 2. well placement (horizontal vs. vertical) options: horizontal well placement seems to be more robust to heterogeneity and the impedance is more acceptable; 3. Prediction uncertainty: the most influential parameters are identified using a First-Order-Second-Moment uncertainty propagation analysis, and the uncertain range of the model predictions is estimated by performing a Monte Carlo simulation. Heterogeneity has a large impact on the perdition, therefore, is considered in the predictive model and uncertainty analysis. The numerical model results and uncertainty analysis are used for economic analysis. The dataset submitted here support the described study. Manuscript is submitted to Geothermics, will be linked once paper is accepted.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

Direct sensitivity analysis on the parameterization of crystal plasticity models

Various methods for calibrating crystal plasticity finite element (CPFE) models lead to non-unique input parameter values, which subsequently introduce uncertainty in the predicted mechanical response. Sensitivity analysis (SA) conducted on crystal plasticity models is used to identify how variability in these parameters contribute to output uncertainty. Traditional SA on CPFE parameters uses simplified surrogate models to save computational time. However, the accuracy of the surrogate models depends on the quantity of training data used, and any modeling error can propagate into the SA results, potentially affecting their reliability. In this work, the elementary effects test (EET) method, a global SA technique using direct CPFE simulations was employed, and the results obtained were compared with the First Order Second Moment (FOSM) method. ExaConstit, an open-source GPU-enabled CPFE code, was used to perform the simulations and direct SA. The EET method was accurately able to capture the non-linear effects of all the input parameters on the output and is a valuable approach for reliably attributing parameter sensitivities in CPFE models. Based on the results, efficient strategies to perform future parameter calibration and SA are discussed. Additionally, the SA trends observed in different single crystal orientations closely mirrored the activity of the slip systems.

Elementary Effects Test↗
DOE OSTI2020

Modeling study of deep direct use geothermal on the West Virginia university campus-morgantown, WV

To reduce the geothermal exploration risk, a feasibility study is performed for a deep direct-use (DDU) system proposed at the West Virginia University (WVU) Morgantown campus. This study applies numerical simulations to investigate reservoir impedance and thermal production. Because of the great depth of the geothermal reservoir, few data are available to characterize reservoir features and properties. Consequently, the study focuses on the following three aspects: 1. model choice for predicting reservoir impedance and thermal breakthrough: after investigating three potential models (one single permeability model and two dual permeability models) for flow through fractured rock, it is decided only the single permeability model is needed; 2. well placement (horizontal vs. vertical) options: horizontal well placement seems to be more robust to heterogeneity and the impedance is more acceptable; 3. Prediction uncertainty: the most influential parameters are identified using a First-Order-Second-Moment uncertainty propagation analysis, and the uncertain range of the model predictions is estimated by performing a Monte Carlo simulation. Heterogeneity has a large impact on the prediction, therefore, heterogeneity is included in the predictive model and uncertainty analysis. The numerical model results and uncertainty analysis will be used for further economic studies.

15 GEOTHERMAL ENERGY↗
NASA NTRS1991

Reliable fusion of control and sensing in intelligent machines

Although robotics research has produced a wealth of sophisticated control and sensing algorithms, very little research has been aimed at reliably combining these control and sensing strategies so that a specific task can be executed. To improve the reliability of robotic systems, analytic techniques are developed for calculating the probability that a particular combination of control and sensing algorithms will satisfy the required specifications. The probability can then be used to assess the reliability of the design. An entropy formulation is first used to quickly eliminate designs not capable of meeting the specifications. Next, a framework for analyzing reliability based on the first order second moment methods of structural engineering is proposed. To ensure performance over an interval of time, lower bounds on the reliability of meeting a set of quadratic specifications with a Gaussian discrete time invariant control system are derived. A case study analyzing visual positioning in robotic system is considered. The reliability of meeting timing and positioning specifications in the presence of camera pixel truncation, forward and inverse kinematic errors, and Gaussian joint measurement noise is determined. This information is used to select a visual sensing strategy, a kinematic algorithm, and a discrete compensator capable of accomplishing the desired task. Simulation results using PUMA 560 kinematic and dynamic characteristics are presented.

Mcinroy, John E.↗
NASA NTRS1994

Probability techniques for reliability analysis of composite materials

Traditional design approaches for composite materials have employed deterministic criteria for failure analysis. New approaches are required to predict the reliability of composite structures since strengths and stresses may be random variables. This report will examine and compare methods used to evaluate the reliability of composite laminae. The two types of methods that will be evaluated are fast probability integration (FPI) methods and Monte Carlo methods. In these methods, reliability is formulated as the probability that an explicit function of random variables is less than a given constant. Using failure criteria developed for composite materials, a function of design variables can be generated which defines a 'failure surface' in probability space. A number of methods are available to evaluate the integration over the probability space bounded by this surface; this integration delivers the required reliability. The methods which will be evaluated are: the first order, second moment FPI methods; second order, second moment FPI methods; the simple Monte Carlo; and an advanced Monte Carlo technique which utilizes importance sampling. The methods are compared for accuracy, efficiency, and for the conservativism of the reliability estimation. The methodology involved in determining the sensitivity of the reliability estimate to the design variables (strength distributions) and importance factors is also presented.

Wetherhold, Robert C.↗
DOE OSTI2021

A surrogate-model-based approach for estimating the first and second-order moments of offshore wind power

Power curve, the functional relationship that governs the process of converting a set of weather variables experienced by a wind turbine into electric power, is widely used in the wind industry to estimate power output for planning and operational purposes. Existing methods for power curve estimation have three main limitations: (i) they mostly rely on wind speed as the sole input, thus ignoring the secondary, yet possibly significant effects of other environmental factors, (ii) they largely overlook the complex marine environment in which offshore turbines operate, potentially compromising their value in offshore wind energy applications, and (ii) they solely focus on the first-order properties of wind power, with little (or null) information about the variation around the mean behavior, which is important for ensuring reliable grid integration, asset health monitoring, and energy storage, among others. In light of that, this study investigates the impact of several wind-and wave-related factors on offshore wind power variability, with the ultimate goal of accurately predicting its first two moments. Further, our approach couples OpenFAST—a multi-physics wind turbine simulator—with Gaussian Process (GP) regression to reveal the underlying relationships governing offshore weather-to-power conversion. We first find that a multi-input power curve which captures the combined impact of wind speed, direction, and air density, can provide double-digit improvements, in terms of prediction accuracy, relative to univariate methods which rely on wind speed as the sole explanatory variable (e.g. the standard method of bins). Wave-related variables are found not important for predicting the average power output, but interestingly, appear to be extremely relevant in describing the fluctuation of the offshore power around its mean. Tested on real-world data collected at the New York/New Jersey bight, our proposed multi-input models demonstrate a high explanatory power in predicting the first two moments of offshore wind generation, testifying their potential value to the offshore wind industry.

17 WIND ENERGY↗
NASA NTRS1978

Design of a compensation for an ARMA model of a discrete time system

The design of an optimal dynamic compensator for a multivariable discrete time system is studied. Also the design of compensators to achieve minimum variance control strategies for single input single output systems is analyzed. In the first problem the initial conditions of the plant are random variables with known first and second order moments, and the cost is the expected value of the standard cost, quadratic in the states and controls. The compensator is based on the minimum order Luenberger observer and it is found optimally by minimizing a performance index. Necessary and sufficient conditions for optimality of the compensator are derived. The second problem is solved in three different ways; two of them working directly in the frequency domain and one working in the time domain. The first and second order moments of the initial conditions are irrelevant to the solution. Necessary and sufficient conditions are derived for the compensator to minimize the variance of the output.

Mainemer, C. I.↗
NASA NTRS2002

Effect of Random Geometric Uncertainty on the Computational Design of a 3-D Flexible Wing

The effect of geometric uncertainty due to statistically independent, random, normally distributed shape parameters is demonstrated in the computational design of a 3-D flexible wing. A first-order second-moment statistical approximation method is used to propagate the assumed input uncertainty through coupled Euler CFD aerodynamic / finite element structural codes for both analysis and sensitivity analysis. First-order sensitivity derivatives obtained by automatic differentiation are used in the input uncertainty propagation. These propagated uncertainties are then used to perform a robust design of a simple 3-D flexible wing at supercritical flow conditions. The effect of the random input uncertainties is shown by comparison with conventional deterministic design results. Sample results are shown for wing planform, airfoil section, and structural sizing variables.

Gumbert, C. R.↗
NASA NTRS2002

Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗
NASA NTRS2004

The Extended Parabolic Equation Method and Implication of Results for Atmospheric Millimeter-Wave and Optical Propagation

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the -correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

Manning, Robert M.↗
NASA NTRS2004

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

Manning, Robert M.↗
NASA NTRS2001

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗
NASA NTRS1993

Probabilistic nonlinear finite element analysis of composite structures

A probabilistic finite element analysis procedure for laminated composite shells is developed. A total Lagrangian finite element formulation, employing a degenerated three-dimensional laminated composite shell element with the full Green-Lagrange strains and first-order shear deformable kinematics, is used. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed, and results are presented in the form of mean and variance of the structural response. Reliability calculations are made by using the first-order reliability method combined with sensitivity derivatives from the finite element analysis. Both ply-level and micromechanics-level random variables are incorporated, the latter by means of the Aboudi micromechanics model. Two sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. In general, the procedure is quite effective in determining the response statistics and reliability for linear and geometric nonlinear behavior of laminated composite shells.

Engelstad, S. P.↗
NASA NTRS1984

Criteria and algorithms for spectrum parameterization of MST radar signals

The power spectra S(f) of MST radar signals contain useful information about the variance of refractivity fluctuations, the mean radial velocity, and the radial velocity variance in the atmosphere. When noise and other contaminating signals are absent, these quantities can be obtained directly from the zeroth, first and second order moments of the spectra. A step-by-step procedure is outlined that can be used effectively to reduce large amounts of MST radar data-averaged periodograms measured in range and time to a parameterized form. The parameters to which a periodogram can be reduced are outlined and the steps in the procedure, that may be followed selectively, to arrive at the final set of reduced parameters are given. Examples of the performance of the procedure are given and its use with other radars are commented on.

Rastogi, P. K.↗
NASA NTRS1993

Nonlinear probabilistic finite element models of laminated composite shells

A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.

Engelstad, S. P.↗