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Articles 811 - 840 of 1048

Full-Text Articles in Aerospace Engineering

Soldier/Hardware-In-The-Loop Simulation-Based Combat Vehicle Duty Cycle Measurement: Duty Cycle Experiment 2, Mark Brudnak, Mike Pozolo, Victor Paul, Syed Mohammad, Marc Compere, Et Al. Jan 2007

Soldier/Hardware-In-The-Loop Simulation-Based Combat Vehicle Duty Cycle Measurement: Duty Cycle Experiment 2, Mark Brudnak, Mike Pozolo, Victor Paul, Syed Mohammad, Marc Compere, Et Al.

Publications

This paper describes a human-in-the-loop motion-based simulator interfaced to hybrid-electric power system hardware both of which were used to measure the duty cycle of a combat vehicle in a virtual simulation environment. The project discussed is a greatly expanded follow-on to the experiment published in [1]. This paper is written in the context of [1] and therefore highlights the enhancements. The most prominent of these enhancements is the integration (in real-time) of the Power & Electric System Integration Lab (P&E SIL) with a motion base simulator by means of a “long haul” connection over the Internet (a geographical distance of …


The Effects Of Charging By Ultraviolet Light On Granular Lunar Simulant In A Microgravity Environment, Sydney J. Chamberlin, Troy Munro, Sarah Isert, Tracy Garin Savage Jan 2007

The Effects Of Charging By Ultraviolet Light On Granular Lunar Simulant In A Microgravity Environment, Sydney J. Chamberlin, Troy Munro, Sarah Isert, Tracy Garin Savage

Reports and Proposals

No abstract provided.


Modeling Redox-Based Magnetohydrodynamics In Three-Dimensional Microfluidic Channels, Hussameddine S. Kabbani, Aihua Wang, Xiaobing Luo, Shizhi Qian Jan 2007

Modeling Redox-Based Magnetohydrodynamics In Three-Dimensional Microfluidic Channels, Hussameddine S. Kabbani, Aihua Wang, Xiaobing Luo, Shizhi Qian

Mechanical Engineering Faculty Research

RedOx-based magnetohydrodynamic MHD[1] flows in three-dimensional microfluidic channels are investigated theoretically with a coupled mathematical model consisting of the Nernst-Planck equations for the concentrations of ionic species, the local electroneutrality condition for the electric potential, and the Navier-Stokes equations for the flow field. A potential difference is externally applied across two planar electrodes positioned along the opposing walls of a microchannel that is filled with a dilute RedOx electrolyte solution, and a Faradaic current transmitted through the solution results. The entire device is positioned under a magnetic field which can be provided by either a permanent magnet or an electromagnet. …


Neural Network Controller Development And Implementation For Spark Ignition Engines With High Egr Levels, Jonathan B. Vance, Atmika Singh, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier Jan 2007

Neural Network Controller Development And Implementation For Spark Ignition Engines With High Egr Levels, Jonathan B. Vance, Atmika Singh, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier

Electrical and Computer Engineering Faculty Research & Creative Works

Past research has shown substantial reductions in the oxides of nitrogen (NOx) concentrations by using 10% -25% exhaust gas recirculation (EGR) in spark ignition (SI) engines (see Dudek and Sain, 1989). However, under high EGR levels, the engine exhibits strong cyclic dispersion in heat release which may lead to instability and unsatisfactory performance preventing commercial engines to operate with high EGR levels. A neural network (NN)-based output feedback controller is developed to reduce cyclic variation in the heat release under high levels of EGR even when the engine dynamics are unknown by using fuel as the control input. A separate …


Near Optimal Output-Feedback Control Of Nonlinear Discrete-Time Systems In Nonstrict Feedback Form With Application To Engines, Peter Shih, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier Jan 2007

Near Optimal Output-Feedback Control Of Nonlinear Discrete-Time Systems In Nonstrict Feedback Form With Application To Engines, Peter Shih, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier

Electrical and Computer Engineering Faculty Research & Creative Works

A novel reinforcement-learning based output-adaptive neural network (NN) controller, also referred as the adaptive-critic NN controller, is developed to track a desired trajectory for a class of complex nonlinear discrete-time systems in the presence of bounded and unknown disturbances. The controller includes an observer for estimating states and the outputs, critic, and two action NNs for generating virtual, and actual control inputs. The critic approximates certain strategic utility function and the action NNs are used to minimize both the strategic utility function and their outputs. All NN weights adapt online towards minimization of a performance index, utilizing gradient-descent based rule. …


Robust Control Techniques Enabling Duty Cycle Experiments Utilizing A 6-Dof Crewstation Motion Base, A Full Scale Combat Hybrid Electric Power System, And Long Distance Internet Communications, Marc Compere, Jarrett Goodell, Miguel Simon, Wilford Smith, Mark Brudnak Nov 2006

Robust Control Techniques Enabling Duty Cycle Experiments Utilizing A 6-Dof Crewstation Motion Base, A Full Scale Combat Hybrid Electric Power System, And Long Distance Internet Communications, Marc Compere, Jarrett Goodell, Miguel Simon, Wilford Smith, Mark Brudnak

Publications

The RemoteLink effort supports the U.S. Army's objective for developing and fielding next generation hybrid-electric combat vehicles. It is a distributed soldierin- the-Ioop and hardware-in-the-Ioop environment with a 6-DOF motion base for operator realism, a full-scale combat hybrid electric power system, and an operational context provided by OneSAF. The driver/gunner crewstations rest on one of two 6-DOF motion bases at the U.S. Army TARDEC Simulation Laboratory (TSL). The hybrid power system is located 2,450 miles away at the TARDEC Power and Energy System Integration Laboratory (P&E SIL). The primary technical challenge in the RemoteLink is to operate both laboratories together …


Capillary-Driven Flows Along Rounded Interior Corners, Yongkang Chen, Mark M. Weislogel, Cory L. Nardin Nov 2006

Capillary-Driven Flows Along Rounded Interior Corners, Yongkang Chen, Mark M. Weislogel, Cory L. Nardin

Mechanical and Materials Engineering Faculty Publications and Presentations

The problem of low-gravity isothermal capillary flow along interior corners that are rounded is revisited analytically in this work. By careful selection of geometric length scales and through the introduction of a new geometric scaling parameter Tc, the Navier–Stokes equation is reduced to a convenient∼O(1) form for both analytic and numeric solutions for all values of corner half-angle α and corner roundedness ratio λ for perfectly wetting fluids. The scaling and analysis of the problem captures much of the intricate geometric dependence of the viscous resistance and significantly reduces the reliance on numerical data compared with several previous solution methods …


Flow Control Of Airfoil At Post-Stall Conditions By Multiple Frequency Applied Saado Jets, A. Şamil Demirsöz Oct 2006

Flow Control Of Airfoil At Post-Stall Conditions By Multiple Frequency Applied Saado Jets, A. Şamil Demirsöz

Mechanical & Aerospace Engineering Theses & Dissertations

Flow separation over lifting aerodynamic components, such as airfoils and wings, occurs during stall conditions which are caused by adverse changes (i.e.; high angle of attack, inflow conditions, etc.) in the operating conditions of aerodynamic components. During stall conditions, the flow over airfoil loses its momentum, creating high pressure zones on the upper surface of the airfoil and even a small increase in pressure causes the fluid particles to stop and separate to a low pressure zone. In order to eliminate the flow separation, the low momentum flow should be removed in order to maintain the high momentum and low …


Development And Testing Of A High-Speed Real-Time Kinematic Precise Dgps Positioning System Between Two Aircraft, Christopher J. Spinelli Sep 2006

Development And Testing Of A High-Speed Real-Time Kinematic Precise Dgps Positioning System Between Two Aircraft, Christopher J. Spinelli

Theses and Dissertations

This research involves the design, implementation, and testing of a high-speed, real-time kinematic, precise differential GPS positioning system for use in airborne applications such as automated aerial-refueling and close formation flying. Although many of the current ambiguity resolution techniques use the residuals from the least squares position estimation to determine the true ambiguity set, this thesis presents a novel approach to the ambiguity resolution problem, called the minimum indicator. Instead of assuming the ambiguity set with the lowest residuals is the true set, other special characteristics of the residuals are examined. This increases the confidence that the algorithm has selected …


Development And Validation Of Reentry Simulation Using Matlab, Robert E. Jameson Jr. Jun 2006

Development And Validation Of Reentry Simulation Using Matlab, Robert E. Jameson Jr.

Theses and Dissertations

This research effort develops a program using MATLAB to solve the equations of motion for atmospheric reentry and analyzes the validity of the program for use as a tool to expeditiously predict reentry profiles. The reentry vehicle is modeled as a point mass with constant aerodynamic properties as defined by the user. The equations of motion for reentry are based on the two-body problem. The atmosphere is modeled as a single layer exponentially decreasing in density. The MATLAB program has the ability to derive the initial trajectory conditions from the position and velocity relative to the rotating surface of the …


Characterizing A Co-Flow Nozzle For Use In A Filtered Rayleigh Scattering System, David S. Miceli Jun 2006

Characterizing A Co-Flow Nozzle For Use In A Filtered Rayleigh Scattering System, David S. Miceli

Theses and Dissertations

Research was conducted on the flow field exiting a co-annular flow nozzle for use in filtered Rayleigh scattering flow visualizations. More specifically, the flow visualizations were of the flow field exiting a coflow nozzle and illuminated by a tunable, nominal 4.2 watt narrow line width Argon laser operating at 514.5nm. ND:YAG lasers are typically used in this application, but some of the properties of a tunable Argon laser make it an attractive alternative. Before generating flow visualizations, the coflow nozzle was characterized both experimentally and computationally. Due to a flow asymmetry in the outer annulus flow field, the nozzle was …


An Experimental Study Of A Pulsed Dc Plasma Flow Control Actuator, Jennifer D. Wall Jun 2006

An Experimental Study Of A Pulsed Dc Plasma Flow Control Actuator, Jennifer D. Wall

Theses and Dissertations

An experiment on the effects of a pulsed DC plasma actuator on a separated flow in a low speed wind tunnel was conducted. The actuator consisted of two asymmetric copper electrodes oriented normal to the flow separated by a dielectric barrier and mounted on a flat plate in the center of the tunnel. A contoured insert was constructed and used to create an adverse pressure gradient in the test section comparable to a Pak-B low pressure turbine blade distribution. Suction was applied from the upper wall to induce separation along the flat plate over the electrodes. The DC power supply …


2nd Annual Undergraduate Research Conference Abstract Book, University Of Missouri--Rolla Apr 2006

2nd Annual Undergraduate Research Conference Abstract Book, University Of Missouri--Rolla

Undergraduate Research Conference at Missouri S&T

No abstract provided.


Dynamics Of Nonlinear Diffusion Processes, Dustin A. Sipka Apr 2006

Dynamics Of Nonlinear Diffusion Processes, Dustin A. Sipka

Master's Theses - Daytona Beach

The purpose of this thesis is to analyze nonlinear diffusion processes. In particular, some of the results arrived at by Newman and Sagan in their 1981 paper "Galactic Civilizations: Population Dynamics and Interstellar Diffusion," will be reproduced by different means. First, a thorough analysis of the linear diffusion equation will be performed in order to test a numerical algorithm that can solve the nonlinear diffusion equation and look at the processes of interest with sufficient accuracy. Once the algorithm is tested and shows good resolution it is used to solve the nonlinear equation. The post processing is then done to …


Intelligent System Applications Based On Genetic Algorithms, Yasin Volkan Pehlivanoglu Apr 2006

Intelligent System Applications Based On Genetic Algorithms, Yasin Volkan Pehlivanoglu

Mechanical & Aerospace Engineering Theses & Dissertations

As a stochastic search method, evolutionary algorithm (EA) is an emergent optimization algorithm mimicking the natural evolution, where a "biological population" evolves over generations to adapt to an environment by selection, recombination, and mutation. When EA is applied to optimization problems, fitness, individual, and genes usually correspond to an objective function value, a design candidate, and design variables, respectively.

One of the key features of EA is that they search from multiple points in design space, instead of moving from a single point as in gradient-based methods. Furthermore, EA works on function evaluations alone and does not require derivatives or …


Assessing The Potential For Improved Scramjet Performance Through Application Of Electromagnetic Flow Control, Martin F. Lindsey Mar 2006

Assessing The Potential For Improved Scramjet Performance Through Application Of Electromagnetic Flow Control, Martin F. Lindsey

Theses and Dissertations

Hypersonic flight using scramjet propulsion bridges the gap between turbojets and rockets. Recent efforts focus on magnetogasdynamic (MGD) flow control to mitigate the problems of high thermomechanical loads and low efficiencies associated with scramjets. This research is the first flight-scale, three-dimensional computational analysis of a realistic scramjet to assess how MGD flow control improves scramjet performance. Developing a quasi-one dimensional design tool culminated in the first open source scramjet geometry. This geometry was tested with the Air Force Research Laboratory's electromagnetic computational code. To increase fidelity, an algorithm was developed to incorporate thermochemistry, resulting in the only open-source model of …


Spatially-Resolved Temperature Diagnostic For Supersonic Flow Using Cross-Beam Doppler-Limited Laser Saturation Spectroscopy, Grady T. Phillips Mar 2006

Spatially-Resolved Temperature Diagnostic For Supersonic Flow Using Cross-Beam Doppler-Limited Laser Saturation Spectroscopy, Grady T. Phillips

Theses and Dissertations

Optical techniques for measuring the temperature in three-dimensional supersonic reactive flows have typically depended on lineshape measurements using single-beam laser absorption spectroscopy. However, absorption over extended path lengths in flows with symmetric, turbulent eddies can lead to systematically high extracted temperatures due to Doppler shifts resulting from flow along the absorption path. To eliminate these problems, Cross-Beam Saturation Absorption Spectroscopy (CBSAS) and Cross-Beam Inter-Modulated Fluorescence (CBIMF) have been developed which utilize two crossed and nearly copropogating laser beams.to record the spectral signal of an I2 ro-vibrational line in a small three-dimensional volume using a tunable CW dye laser. Temperature …


Control Demonstration Of A Thin Deformable In-Plane Actuated Mirror, Gina A. Peterson Mar 2006

Control Demonstration Of A Thin Deformable In-Plane Actuated Mirror, Gina A. Peterson

Theses and Dissertations

Current imaging satellites are limited in resolution and coverage area by the aperture size of their primary optical mirror. To get a large optical mirror into space, current launch weight and size restrictions must be overcome. Membrane-like optical mirrors can overcome these restrictions with their very lightweight and flexible properties. However, thin, deformable membrane mirrors are very susceptible to the space environment and require active control for surface stabilization and shaping. The primary goal of this research is to demonstrate that an in-plane actuated membrane-like deformable optical mirror can be controlled to optical wavelength tolerances in a closed-loop system. Fabrication …


A Comparison Of Main Rotor Smoothing Adjustments Using Linear And Neural Network Algorithms, Nathan A. Miller Mar 2006

A Comparison Of Main Rotor Smoothing Adjustments Using Linear And Neural Network Algorithms, Nathan A. Miller

Theses and Dissertations

Helicopter main rotor smoothing is a maintenance procedure that is routinely performed to minimize airframe vibrations induced by non-uniform mass and/or aerodynamic distributions in the main rotor system. This important task is both time consuming and expensive, so improvements to the process have long been sought. Traditionally, vibrations have been minimized by calculating adjustments based on an assumed linear relationship between adjustments and vibration response. In recent years, artificial neural networks have been trained to recognize non-linear mappings between adjustments and vibration response. This research was conducted in order observe the character of the adjustment mapping of the Vibration Management …


Macroscopic Computational Model Of Dielectric Barrier Discharge Plasma Actuators, Timothy R. Klein Feb 2006

Macroscopic Computational Model Of Dielectric Barrier Discharge Plasma Actuators, Timothy R. Klein

Theses and Dissertations

Recent progress in the generation and sustainment of gas discharges at atmospheric pressure has energized research in the field of plasma-aerodynamics. Plasma actuators are promising devices that achieve flow control with no moving parts, do not alter the airfoil shape and place no parts in the flow. The operation of a plasma actuator is examined using a macroscopic (force and power addition) computational fluid dynamic model of a dielectric barrier discharge, DBD, in Fluent. A parametric approach is adopted to survey the range of requisite magnitudes of momentum and energy delivered to the flow field and to identify the effects …


Response To "Comment On Variational Approach To The Volume Viscosity Of Fluids" [Phys. Fluids 18, 109101 (2006)], Allen J. Zuckerwar, Robert L. Ash Jan 2006

Response To "Comment On Variational Approach To The Volume Viscosity Of Fluids" [Phys. Fluids 18, 109101 (2006)], Allen J. Zuckerwar, Robert L. Ash

Mechanical & Aerospace Engineering Faculty Publications

We respond to the Comment of Markus Scholle and therewith revise our material entropy constraint to account for the production of entropy. (c) 2006 American Institute of Physics.


Variational Approach To The Volume Viscosity Of Fluids, Allan J. Zuckerwar, Robert L. Ash Jan 2006

Variational Approach To The Volume Viscosity Of Fluids, Allan J. Zuckerwar, Robert L. Ash

Mechanical & Aerospace Engineering Faculty Publications

The variational principle of Hamilton is applied to develop an analytical formulation to describe the volume viscosity in fluids. The procedure described here differs from those used in the past in that a dissipative process is represented by the chemical affinity and progress variable (sometimes called "order parameter") of a reacting species. These state variables appear in the variational integral in two places: first, in the expression for the internal energy, and second, in a subsidiary condition accounting for the conservation of the reacting species. As a result of the variational procedure, two dissipative terms appear in the Navier-Stokes equation. …


An Internet Based Intelligent Argumentation System For Collaborative Engineering Design, Xiaoqing Frank Liu, Samir Raorane, Man Zheng, Ming-Chuan Leu Jan 2006

An Internet Based Intelligent Argumentation System For Collaborative Engineering Design, Xiaoqing Frank Liu, Samir Raorane, Man Zheng, Ming-Chuan Leu

Computer Science Faculty Research & Creative Works

Modern product design is a very complicated process which involves groups of designers, manufacturers, suppliers, and customer representatives. Conflicts are unavoidable in collaboration among multiple stakeholders, who have different objectives, requirements, and priorities. Unfortunately, current web-based collaborative engineering design systems do not support collaborative conflict resolution. In this paper, we will develop an intelligent computational argumentation model to enable management of a large scale argumentation network, and resolution of conflicts based on argumentation from many participants. A web-based intelligent argumentation tool is developed as a part of a web-based collaborative engineering design system based on the above model to resolve …


Neural Network-Based Output Feedback Controller For Lean Operation Of Spark Ignition Engines, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier, Jonathan B. Vance, Pingan He Jan 2006

Neural Network-Based Output Feedback Controller For Lean Operation Of Spark Ignition Engines, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier, Jonathan B. Vance, Pingan He

Electrical and Computer Engineering Faculty Research & Creative Works

Spark ignition (SI) engines running at very lean conditions demonstrate significant nonlinear behavior by exhibiting cycle-to-cycle dispersion of heat release even though such operation can significantly reduce NOx emissions and improve fuel efficiency by as much as 5-10%. A suite of neural network (NN) controller without and with reinforcement learning employing output feedback has shown ability to reduce the nonlinear cyclic dispersion observed under lean operating conditions. The neural network controllers consists of three NN: a) A NN observer to estimate the states of the engine such as total fuel and air; b) a second NN for generating virtual input; …


Numerical Integration Strategy For Generating Root Migration Diagrams, Deepak H. Panduranga Oct 2005

Numerical Integration Strategy For Generating Root Migration Diagrams, Deepak H. Panduranga

Mechanical & Aerospace Engineering Theses & Dissertations

Evans root locus is a graphical method for analyzing or designing the stability and performance of a single channel closed-loop system. The method consists of plotting the locus of closed-loop characteristic equation roots in the complex plane as the loop gain parameter is varied over a wide range of values. Several methods for plotting the root locus graph exist and can be mainly classified into two types: analytical methods and numerical methods. The most common numerical method is based on polynomial factoring or root solving. A less common, alternative method for generating the root locus graph is based on numerical …


Operator State Estimation For Adaptive Aiding In Uninhabited Combat Air Vehicles, Christopher A. Russell Sep 2005

Operator State Estimation For Adaptive Aiding In Uninhabited Combat Air Vehicles, Christopher A. Russell

Theses and Dissertations

This research demonstrated the first closed-loop implementation of adaptive automation using operator functional state in an operationally relevant environment. In the Uninhabited Combat Air Vehicle (UCAV) environment, operators can become cognitively overloaded and their performance may decrease during mission critical events. This research demonstrates an unprecedented closed-loop system, one that adaptively aids UCAV operators based on their cognitive functional state A series of experiments were conducted to 1) determine the best classifiers for estimating operator functional state, 2) determine if physiological measures can be used to develop multiple cognitive models based on information processing demands and task type, 3) determine …


The Use Of X-Ray Pulsars For Aiding Gps Satellite Orbit Determination, Dennis W. Woodfork Ii Mar 2005

The Use Of X-Ray Pulsars For Aiding Gps Satellite Orbit Determination, Dennis W. Woodfork Ii

Theses and Dissertations

This research proposes the use of an existing "signal of opportunity" - namely x-ray pulsars - to improve the accuracy and robustness of the GPS satellite and clock estimation algorithm. Improvement in satellite and clock accuracy results in a direct benefit to the user. A simulation has been developed to determine the effects of using x-ray pulsar measurements on the GPS Operational Control Segment. The epoch-specific position, velocity, and clock errors of all GPS satellites in the constellation were estimated using both pseudoranges and time-difference-of-arrival (TDOA) measurements from pulsars. The primary measure of accuracy is a constellation Signal-In-Space Range Error …


Robust Control Techniques For State Tracking In The Presence Of Variable Time Delays, Jarrett Goodell, Marc Compere, Miguel Simon, Wilford Smith, Ronnie Wright, Mark Brudnak Jan 2005

Robust Control Techniques For State Tracking In The Presence Of Variable Time Delays, Jarrett Goodell, Marc Compere, Miguel Simon, Wilford Smith, Ronnie Wright, Mark Brudnak

Publications

In this paper, a distributed driver-in-the-Ioop and hardware-in-the-Ioop simulator is described with a driver on a motion simulator at the U.S. Army TARDEC Ground Vehicle Simulation Laboratory (GVSL). Realistic power system response is achieved by linking the driver in the GVSL with a full-sized hybrid electric power system located 2,450 miles away at the TARDEC Power and Energy Systems Integration Laboratory (P&E SIL), which is developed and maintained by Science Applications International Corporation (SAIC). The goal is to close the loop between the GVSL and P&E SIL over the Internet to provide a realistic driving experience in addition to realistic …


Performance Analysis And Validation Of A Recoverable Flight Control System In A Simulated Neutron Environment, Hong Zhang, W. Steven Gray, Oscar R. Gonzalez Jan 2005

Performance Analysis And Validation Of A Recoverable Flight Control System In A Simulated Neutron Environment, Hong Zhang, W. Steven Gray, Oscar R. Gonzalez

Electrical & Computer Engineering Faculty Publications

This paper introduces a class of stochastic hybrid models for the analysis of closed-loop control systems implemented with NASA's Recoverable Computer System. Such Recoverable Computer Systems have been proposed to insure reliable control performance in harsh environments. The stochastic hybrid models consist of either a stochastic finite-state automaton or a finite-state machine driven by a Markov input, which in turn drives a switched linear discrete-time dynamical system. Their stability and output tracking performance are analyzed using an extension of the existing theory for Markov jump-linear systems. For illustration, a stochastic hybrid model is used to calculate the tracking error performance …


Quantifying Initial Condition And Parametric Uncertainties In A Nonlinear Aeroelastic System With An Efficient Stochastic Algorithm, Daniel R. Millman Sep 2004

Quantifying Initial Condition And Parametric Uncertainties In A Nonlinear Aeroelastic System With An Efficient Stochastic Algorithm, Daniel R. Millman

Theses and Dissertations

There is a growing interest in understanding how uncertainties in flight conditions and structural parameters affect the character of a limit cycle oscillation (LCO) response, leading to failure of an aeroelastic system. Uncertainty quantification of a stochastic system (parametric uncertainty) with stochastic inputs (initial condition uncertainty) has traditionally been analyzed with Monte Carlo simulations (MCS). Probability density functions (PDF) of the LCO response are obtained from the MCS to estimate the probability of failure. A candidate approach to efficiently estimate the PDF of an LCO response is the stochastic projection method. The objective of this research is to extend the …