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A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASAs Space Launch System

The engineering development of the National Aeronautics and Space Administration's (NASA) new Space Launch System (SLS) requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The nominal and off-nominal characteristics of SLS's elements and subsystems must be understood and matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large and complex systems engineering challenge, which is being addressed in part by focusing on the specific subsystems involved in the handling of off-nominal mission and fault tolerance with response management. Using traditional model-based system and software engineering design principles from the Unified Modeling Language (UML) and Systems Modeling Language (SysML), the Mission and Fault Management (M&FM) algorithms for the vehicle are crafted and vetted in Integrated Development Teams (IDTs) composed of multiple development disciplines such as Systems Engineering (SE), Flight Software (FSW), Safety and Mission Assurance (S&MA) and the major subsystems and vehicle elements such as Main Propulsion Systems (MPS), boosters, avionics, Guidance, Navigation, and Control (GNC), Thrust Vector Control (TVC), and liquid engines. These model-based algorithms and their development lifecycle from inception through FSW certification are an important focus of SLS's development effort to further ensure reliable detection and response to off-nominal vehicle states during all phases of vehicle operation from pre-launch through end of flight. To test and validate these M&FM algorithms a dedicated test-bed was developed for full Vehicle Management End-to-End Testing (VMET). For addressing fault management (FM) early in the development lifecycle for the SLS program, NASA formed the M&FM team as part of the Integrated Systems Health Management and Automation Branch under the Spacecraft Vehicle Systems Department at the Marshall Space Flight Center (MSFC). To support the development of the FM algorithms, the VMET developed by the M&FM team provides the ability to integrate the algorithms, perform test cases, and integrate vendor-supplied physics-based launch vehicle (LV) subsystem models. Additionally, the team has developed processes for implementing and validating the M&FM algorithms for concept validation and risk reduction. The flexibility of the VMET capabilities enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the developed algorithms utilizing actual subsystem models such as MPS, GNC, and others. One of the principal functions of VMET is to validate the M&FM algorithms and substantiate them with performance baselines for each of the target vehicle subsystems in an independent platform exterior to the flight software test and validation processes. In any software development process there is inherent risk in the interpretation and implementation of concepts from requirements and test cases into flight software compounded with potential human errors throughout the development and regression testing lifecycle. Risk reduction is addressed by the M&FM group but in particular by the Analysis Team working with other organizations such as S&MA, Structures and Environments, GNC, Orion, Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission (LOM) and Loss of Crew (LOC) probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and associated detection and responses to be tested in VMET to ensure reliable failure detection, and confirm responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - the ARINC 6535-partitioned Operating System, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM such as telemetry packing and processing. The baseline plan for use of VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by FSW. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure their effectiveness and performance in the exterior FSW development and test processes. This paper is outlined in a systematic fashion analogous to a lifecycle process flow for engineering development of algorithms into software and testing. Section I describes the NASA SLS M&FM context, presenting the current infrastructure, leading principles, methods, and participants. Section II defines the testing philosophy of the M&FM algorithms as related to VMET followed by section III, which presents the modeling methods of the algorithms to be tested and validated in VMET. Its details are then further presented in section IV followed by Section V presenting integration, test status, and state analysis. Finally, section VI addresses the summary and forward directions followed by the appendices presenting relevant information on terminology and documentation.

Trevino, Luis↗

User's Guide for GAA_JET_FV (v1): A Jet Noise Prediction Code Based on the Generalized Acoustic Analogy

This document is a user’s guide for the jet noise prediction code GAA_JET_FV, which can be used to make predictions of turbulent mixing noise in high-speed free jets (ie. in the absence of any solid surfaces) of arbitrary cross section. The code requires a Reynolds-averaged Navier-Stokes (RANS) solution for the mean flow and turbulence as input. A script is provided in the code package which can be used to interpolate structured or unstructured RANS solutions onto a structured grid suitable for the noise calculations. Output file formats for two commonly used RANS solvers are currently supported by this script. The document describes how the code can be obtained and installed on a user’s system. A simple test case is provided that can be run with minimal user knowledge of the code details. General instructions for running the interpolation script and the main code are given along with descriptions of the input and output data files and individual code modules. Several additional test cases are provided which allow the user to exercise additional features of the code. This document is Version 1, Revision 0 of the User’s Guide, which contains examples of round and non-axisymmetric unheated jet test cases. Future versions are planned which will include additional functionality for the code and more complex test cases.

Jet Noise↗

Installed Transonic 2D Nozzle Nacelle Boattail Drag Study

The Transonic Nozzle Boattail Drag Study was initiated in 1995 to develop an understanding of how external nozzle transonic aerodynamics effect airplane performance and how strongly those effects are dependent on nozzle configuration (2D vs. axisymmetric). MDC analyzed the axisymmetric nozzle. Boeing subcontracted Northrop-Grumman to analyze the 2D nozzle. AU participants analyzed the AGARD nozzle as a check-out and validation case. Once the codes were checked out and the gridding resolution necessary for modeling the separated flow in this region determined, the analysis moved to the installed wing/body/nacelle/diverter cases. The boat tail drag validation case was the AGARD B.4 rectangular nozzle. This test case offered both test data and previous CFD analyses for comparison. Results were obtained for test cases B.4.1 (M=0.6) and B.4.2 (M=0.938) and compared very well with the experimental data. Once the validation was complete a CFD grid was constructed for the full Ref. H configuration (wing/body/nacelle/diverter) using a combination of patched and overlapped (Chimera) grids. This was done to ensure that the grid topologies and density would be adequate for the full model. The use of overlapped grids allowed the same grids from the full configuration model to be used for the wing/body alone cases, thus eliminating the risk of grid differences affecting the determination of the installation effects. Once the full configuration model was run and deemed to be suitable the nacelle/diverter grids were removed and the wing/body analysis performed. Reference H wing/body results were completed for M=0.9 (a=0.0, 2.0, 4.0, 6.0 and 8.0), M=1.1 (a=4.0 and 6.0) and M=2.4 (a=0.0, 2.0, 4.4, 6.0 and 8.0). Comparisons of the M=0.9 and M=2.4 cases were made with available wind tunnel data and overall comparisons were good. The axi-inlet/2D nozzle nacelle was analyzed isolated. The isolated nacelle data coupled with the wing/body result enabled the interference effects of the installed nacelles to be determined. Isolated nacelle mm were made at M=0.9 and M=1.1 for both the supersonic and transonic nozzle settings. AU of the isolated nacelle cases were run at alpha=0. Full configuration runs were to be made at Mach numbers of 0.9, 1.1, and 2.4 (the same as the wing/body and isolated nacelles). Both the isolated nacelles and installed nacelles were run with inlet conditions designed to give zero spillage. This was to be done in order to isolate the boattail effects as much as possible. Full configuration runs with the supersonic nozzles were completed for M=0.9 and 1.1 at a=4.0 and 6.0 (4 runs total) and with the transonic nozzles at M=0.9 and 1.1 at a=2.0, 4.0 and 6.0 (6 runs total). Drag breakdowns were completed for the M=0.9 and M= 1.1 showing favorable interference drag for both cases.

Malone, Michael B.↗

Assessment of Numerical and Modeling Errors of RANS based Transition Models for Low-Reynolds Numbers 2-D Flows

In this paper we report the outcome of selected workshops organized as part of the NATO Applied Vehicle Technology (AVT)-313 activity Incompressible Laminar-to-Turbulent Flow Transition Study that focused on assessing the numerical and modeling accuracy of the γ−Reθ and γ transition models coupled to the k−ω Shear-Stress Transport (SST) two-equation eddy-viscosity model. Three different test cases involving nominally 2D flow configurations were selected: flow over a flat plate with two different levels of turbulence intensity at the inlet; flow around the Eppler 387 foil at a Reynolds number of 3×10^5 and angles of attack of 1 deg. and 7 deg. flow around the NACA 0015 foil at a Reynolds number of 1.8×10^5 and angles of attack of 5 deg. and10 deg. The flat plate flow conditions correspond to natural and by-pass transition, whereas the other two test cases include laminar separation bubbles that lead to separation-induced transition. For each test case, the selected quantities of interest include both integral and local flow quantities. Geometrically similar grids with a wide range of grid refinement ratios were generated for each of the test cases to allow the estimation of numerical uncertainties for all quantities of interest selected for this study. Several RANS flow solvers were used, employing common grids with the same boundary conditions and mathematical models. Therefore, it is possible to analyze the consistency of the results, i.e., to check if the intervals defined by the different numerical solutions with their respective uncertainties overlap with each other. Modeling errors can also be addressed for the selected flow quantities that have experimental data available. However, the experimental information available in these cases is not sufficient to guarantee that experiments and simulations are performed with the same settings. Nonetheless, the available experimental data is sufficient to guarantee that modeling errors are significantly reduced with the use of the transition models when compared to simulations performed using only the k−ω SST model.

CFD Modeling↗

Automated unit-level testing with heuristic rules

Software testing plays a significant role in the development of complex software systems. Current testing methods generally require significant effort to generate meaningful test cases. The QUEST/Ada system is a prototype system designed using CLIPS to experiment with expert system based test case generation. The prototype is designed to test for condition coverage, and attempts to generate test cases to cover all feasible branches contained in an Ada program. This paper reports on heuristics sued by the system. These heuristics vary according to the amount of knowledge obtained by preprocessing and execution of the boolean conditions in the program.

Carlisle, W. Homer↗

Report on Workshop on Artificial Intelligence in Strategic Planning and Science Prioritization

This report details the observations from a two-day virtual workshop, held May 12-13, 2020, focused on whether, and how, artificial intelligence (AI) could assist humans in strategic planning, specifically in science and technology prioritization. The participants identified several “key challenges” that AI might tackle in this area. To further understand the value of these key challenges the workshop then developed related test cases that would demonstrate specifically how AI/machine learning (ML) could provide assistance to humans. Approximately 40 subject matter experts (SMEs), with backgrounds in AI, strategic planning for science, and scientific data, were gathered for the conference. This report collates the details of the output of the workshop. The “best” test cases include (in no particular order):Use of AI to assist in selecting Decadal Survey priorities. * Use of AI to identify new, or previously unidentified, science topics for prioritization. * Using AI to better label and increase discoverability of scientific literature and proposals. * Use of AI to enhance current observation capabilities for scientific missions. * Using AI to mitigate biases in selection of proposal reviewers and membership of advisory committees. Examination of these test cases indicates that Natural Language Processing (NLP) is a common capability found in most of the ”best” (top-rated) test cases and is a valuable, multi-purpose tool which enables ML in this area.

strategic planning↗

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASA's Space Launch System

The engineering development of the new Space Launch System (SLS) launch vehicle requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The characteristics of these spacecraft systems must be matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large and complex system engineering challenge, which is being addressed in part by focusing on the specific subsystems involved in the handling of off-nominal mission and fault tolerance with response management. Using traditional model based system and software engineering design principles from the Unified Modeling Language (UML) and Systems Modeling Language (SysML), the Mission and Fault Management (M&FM) algorithms for the vehicle are crafted and vetted in specialized Integrated Development Teams (IDTs) composed of multiple development disciplines such as Systems Engineering (SE), Flight Software (FSW), Safety and Mission Assurance (S&MA) and the major subsystems and vehicle elements such as Main Propulsion Systems (MPS), boosters, avionics, Guidance, Navigation, and Control (GNC), Thrust Vector Control (TVC), and liquid engines. These model based algorithms and their development lifecycle from inception through Flight Software certification are an important focus of this development effort to further insure reliable detection and response to off-nominal vehicle states during all phases of vehicle operation from pre-launch through end of flight. NASA formed a dedicated M&FM team for addressing fault management early in the development lifecycle for the SLS initiative. As part of the development of the M&FM capabilities, this team has developed a dedicated testbed that integrates specific M&FM algorithms, specialized nominal and off-nominal test cases, and vendor-supplied physics-based launch vehicle subsystem models. Additionally, the team has developed processes for implementing and validating these algorithms for concept validation and risk reduction for the SLS program. The flexibility of the Vehicle Management End-to-end Testbed (VMET) enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the developed algorithms utilizing actual subsystem models such as MPS. The intent of VMET is to validate the M&FM algorithms and substantiate them with performance baselines for each of the target vehicle subsystems in an independent platform exterior to the flight software development infrastructure and its related testing entities. In any software development process there is inherent risk in the interpretation and implementation of concepts into software through requirements and test cases into flight software compounded with potential human errors throughout the development lifecycle. Risk reduction is addressed by the M&FM analysis group working with other organizations such as S&MA, Structures and Environments, GNC, Orion, the Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission and Loss of Crew probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and associated detection and responses that can be tested in VMET to ensure that failures can be detected, and confirm that responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - ARINC 653 partitioned OS, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM such as telemetry packing and processing. The baseline plan for use of VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by Flight Software. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure the effectiveness of M&FM algorithms performance in the FSW development and test processes.

Trevino, Luis↗

The 1992-1993 advanced design program. Part 1: The Mars methane engine project. Part 2: The Mars oxygen processor new furnace

Three constituents of the Martian atmosphere, methane, carbon dioxide, and oxygen, can be used for internal combustion in engines utilized for future space exploration on Mars. These three gases, considered as the test case in this research, will be examined to determine required flow rates needed for combustion and optimization of engine performance. Results of the test case are examined in relation to a base case of methane and air for comparative purposes. Testing of exhaust temperatures, cylinder pressure, and exhaust gas analysis were performed for the base case and test case. Also described is a study utilizing a zirconia cell to convert carbon dioxide into usable oxygen to help support future Mars missions.

Lauer, Stephen↗

Numerical study of laminar and turbulent flows inside a turnaround duct with and without guide vanes

The purpose of this study is to examine in detail incompressible laminar and turbulent flows inside a turnaround duct with and without guide vanes and to investigate the effects of vanes on the flow characteristics. To perform this study, an implicit finite difference code cast in general curvilinear coordinates is further developed. The code is based on the method of pseudo-compressibility and utilize ADI or implicit approximate factorization algorithm to achieve computational efficiency. Method of segmental sweeping is developed to overcome the multiple-zone problem due to imposition of guide vanes. In the present study, several test cases have been computed. These test cases include laminar and turbulent flows inside a turnaround duct without and with two or three guide vanes. The study reveals that: (1) there exists large recirculation zones inside the duct if no vanes are present; (2) properly shaped and positional guide vanes are effective in eliminating flow separation; and (3) laminar and turbulent flows have similar flow features. But turbulent flow has less total pressure drop.

Lin, S.-J.↗

Automating symbolic analysis with CLIPS

Symbolic Analysis is a methodology first applied as an aid in selecting and generating test cases for 'white box' type testing of computer software programs. The feasibility of automating this analysis process has recently been demonstrated through the development of a CLIPS-based prototype tool. Symbolic analysis is based on separating the logic flow diagram of a computer program into its basic elements, and then systematically examining those elements and their relationships to provide a detailed static analysis of the process that those diagrams represent. The basic logic flow diagram elements are flow structure (connections), predicates (decisions), and computations (actions). The symbolic analysis approach supplies a disciplined step-by-step process to identify all executable program paths and produce a truth table that defines the input and output domains for each path identified. The resulting truth table is the tool that allows software test cases to be generated in a comprehensive manner to achieve total program path, input domain, and output domain coverage. Since the manual application of symbolic analysis is extremely labor intensive and is itself error prone, automation of the process is highly desirable. Earlier attempts at automation, utilizing conventional software approaches, had only limited success. This paper briefly describes the automation problems, the symbolic analysis expert's problem solving heuristics, and the implementation of those heuristics as a CLIPS based prototype, and the manual augmentation required. A simple application example is also provided for illustration purposes. The paper concludes with a discussion of implementation experiences, automation limitations, usage experiences, and future development suggestions.

Morris, Keith E.↗

Computational considerations for the simulation of shock-induced sound

The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved, because the chosen algorithm must also resolve discontinuities in the solution. The extent to which a high-order-accurate shock-capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified. Such a study is initiated in this work. A fourth-order-accurate essentially nonoscillatory (ENO) method is used to investigate the solutions of inviscid, compressible flows with shocks in a quasi-one-dimensional nozzle flow. The design order of accuracy is achieved in the smooth regions of a steady-state test case. However, in an unsteady test case, only first-order results are obtained downstream of a sound-shock interaction. The difficulty in obtaining a globally high-order-accurate solution in such a case with a shock-capturing method is demonstrated through the study of a simplified, linear model problem. Some of the difficult issues and ramifications for aeroacoustics simulations of flows with shocks that are raised by these results are discussed.

Casper, Jay↗

Statistical Analysis of CFD Solutions from the Third AIAA Drag Prediction Workshop

The first AIAA Drag Prediction Workshop, held in June 2001, evaluated the results from an extensive N-version test of a collection of Reynolds-Averaged Navier-Stokes CFD codes. The code-to-code scatter was more than an order of magnitude larger than desired for design and experimental validation of cruise conditions for a subsonic transport configuration. The second AIAA Drag Prediction Workshop, held in June 2003, emphasized the determination of installed pylon-nacelle drag increments and grid refinement studies. The code-to-code scatter was significantly reduced compared to the first DPW, but still larger than desired. However, grid refinement studies showed no significant improvement in code-to-code scatter with increasing grid refinement. The third Drag Prediction Workshop focused on the determination of installed side-of-body fairing drag increments and grid refinement studies for clean attached flow on wing alone configurations and for separated flow on the DLR-F6 subsonic transport model. This work evaluated the effect of grid refinement on the code-to-code scatter for the clean attached flow test cases and the separated flow test cases.

Statistical analysis↗

Lag Model Predictions for UFAST SBLI Flowfield

Presentation for Shock Boundary Layer Interaction Workshop. Shows results for Lag turbulence model on one of the international workshop test cases the UFAST 8 degree test case. Comparison with PIV velocity measurements as well as computed tunnel wall flowfields are shown, emphasizing that the interaction is a 3D phenomena, and is reasonably well predicted.

Olsen, Mike↗

A Model-Based Anomaly Detection Approach for Analyzing Streaming Aircraft Engine Measurement Data

This paper presents a model-based anomaly detection architecture designed for analyzing streaming transient aircraft engine measurement data. The technique calculates and monitors residuals between sensed engine outputs and model predicted outputs for anomaly detection purposes. Pivotal to the performance of this technique is the ability to construct a model that accurately reflects the nominal operating performance of the engine. The dynamic model applied in the architecture is a piecewise linear design comprising steady-state trim points and dynamic state space matrices. A simple curve-fitting technique for updating the model trim point information based on steadystate information extracted from available nominal engine measurement data is presented. Results from the application of the model-based approach for processing actual engine test data are shown. These include both nominal fault-free test case data and seeded fault test case data. The results indicate that the updates applied to improve the model trim point information also improve anomaly detection performance. Recommendations for follow-on enhancements to the technique are also presented and discussed.

Propulsion System Performance↗

A Model-Based Anomaly Detection Approach for Analyzing Streaming Aircraft Engine Measurement Data

This paper presents a model-based anomaly detection architecture designed for analyzing streaming transient aircraft engine measurement data. The technique calculates and monitors residuals between sensed engine outputs and model predicted outputs for anomaly detection purposes. Pivotal to the performance of this technique is the ability to construct a model that accurately reflects the nominal operating performance of the engine. The dynamic model applied in the architecture is a piecewise linear design comprising steady-state trim points and dynamic state space matrices. A simple curve-fitting technique for updating the model trim point information based on steadystate information extracted from available nominal engine measurement data is presented. Results from the application of the model-based approach for processing actual engine test data are shown. These include both nominal fault-free test case data and seeded fault test case data. The results indicate that the updates applied to improve the model trim point information also improve anomaly detection performance. Recommendations for follow-on enhancements to the technique are also presented and discussed.

Propulsion System Performance↗

Iterated Sigma-Point Kalman Filtering for Trajectory Reconstruction

Two second-order Kalman filtering methods are added to the New Statistical Trajec-tory Estimation Program (NewSTEP). The two filters are of the class of Sigma-Point Kalman Filters, namely the Unscented Kalman Filter and the Divided Difference Filter. Both filters are implemented with an iterative measurement update step. Results from simulation test case and a flight data test case are provided to show the filter performance. The results indicate that the new second-order filters pro-duce trajectory estimates with reduced uncertainties when compared to the existing first-order filtering method.

Sophia Vedvik↗

Effect of density gradients in confined supersonic shear layers, part 1

The effect of density gradients on the supersonic wall modes (acoustic modes) of a 2-D confined compressible shear layer were investigated using linear analysis. Due to the inadequacies of the hyperbolic tangent profile, the boundary layer basic profiles were used. First a test case was taken with the same parameters as in Tam and Hu's analysis with convective Mach number M(sub c) = 1.836 and density ratio of 1.398. Three generalized inflection points were found giving rise to three modes. The first two show similar properties to the Class A and B modes, and the third is an 'inner mode' which will be called a Class C mode. As the density ratio is increased, the smallest of the three neutral phase speeds tends towards the speed of the lower velocity stream, and the other two eventually coalesce and then disappear. These two effects lead to a linear resonance between the Class B modes which increases the cutoff frequency and growth rate of the lowest mode. In fact, growth rates of 2-4 times the test case were found as the density ratio was increased to 7. A similar trend is observed for the Class A modes when the density ratio is decreased from the test case, but the growth rate is not changed by much from the test case.

Peroomian, Oshin↗

Structural Reliability Using Probability Density Estimation Methods Within NESSUS

A reliability analysis studies a mathematical model of a physical system taking into account uncertainties of design variables and common results are estimations of a response density, which also implies estimations of its parameters. Some common density parameters include the mean value, the standard deviation, and specific percentile(s) of the response, which are measures of central tendency, variation, and probability regions, respectively. Reliability analyses are important since the results can lead to different designs by calculating the probability of observing safe responses in each of the proposed designs. All of this is done at the expense of added computational time as compared to a single deterministic analysis which will result in one value of the response out of many that make up the density of the response. Sampling methods, such as monte carlo (MC) and latin hypercube sampling (LHS), can be used to perform reliability analyses and can compute nonlinear response density parameters even if the response is dependent on many random variables. Hence, both methods are very robust; however, they are computationally expensive to use in the estimation of the response density parameters. Both methods are 2 of 13 stochastic methods that are contained within the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) program. NESSUS is a probabilistic finite element analysis (FEA) program that was developed through funding from NASA Glenn Research Center (GRC). It has the additional capability of being linked to other analysis programs; therefore, probabilistic fluid dynamics, fracture mechanics, and heat transfer are only a few of what is possible with this software. The LHS method is the newest addition to the stochastic methods within NESSUS. Part of this work was to enhance NESSUS with the LHS method. The new LHS module is complete, has been successfully integrated with NESSUS, and been used to study four different test cases that have been proposed by the Society of Automotive Engineers (SAE). The test cases compare different probabilistic methods within NESSUS because it is important that a user can have confidence that estimates of stochastic parameters of a response will be within an acceptable error limit. For each response, the mean, standard deviation, and 0.99 percentile, are repeatedly estimated which allows confidence statements to be made for each parameter estimated, and for each method. Thus, the ability of several stochastic methods to efficiently and accurately estimate density parameters is compared using four valid test cases. While all of the reliability methods used performed quite well, for the new LHS module within NESSUS it was found that it had a lower estimation error than MC when they were used to estimate the mean, standard deviation, and 0.99 percentile of the four different stochastic responses. Also, LHS required a smaller amount of calculations to obtain low error answers with a high amount of confidence than MC. It can therefore be stated that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ and the newest LHS module is a valuable new enhancement of the program.

Chamis, Chrisos C.↗