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At least 865 records · Page 48

Space Station Furnace Facility. Volume 2: Requirements Definition and Conceptual Design Study. Appendix 3: Environment Analysis

A Preliminary Safety Analysis (PSA) is being accomplished as part of the Space Station Furnace Facility (SSFF) contract. This analysis is intended to support SSFF activities by analyzing concepts and designs as they mature to develop essential safety requirements for inclusion in the appropriate specifications, and designs, as early as possible. In addition, the analysis identifies significant safety concerns that may warrant specific trade studies or design definition, etc. The analysis activity to date concentrated on hazard and hazard cause identification and requirements development with the goal of developing a baseline set of detailed requirements to support trade study, specifications development, and preliminary design activities. The analysis activity will continue as the design and concepts mature. Section 2 defines what was analyzed, but it is likely that the SSFF definitions will undergo further changes. The safety analysis activity will reflect these changes as they occur. The analysis provides the foundation for later safety activities. The hazards identified will in most cases have Preliminary Design Review (PDR) applicability. The requirements and recommendations developed for each hazard will be tracked to ensure proper and early resolution of safety concerns.

Source record↗

A study of the application of power-spectral methods of generalized harmonic analysis to gust loads on airplanes

The applicability of some results from the theory of generalized harmonic analysis (or power-spectral analysis) to the analysis of gust loads on airplanes in continuous rough air is examined. The general relations for linear systems between power spectrums of a random input disturbance and an output response are used to relate the spectrum of airplane load in rough air to the spectrum of atmospheric gust velocity. The power spectrum of loads is shown to provide a measure of the load intensity in terms of the standard deviation (root mean square) of the load distribution for an airplane in flight through continuous rough air. For the case of a load output having a normal distribution, which appears from experimental evidence to apply to homogeneous rough air, the standard deviation is shown to describe the probability distribution of loads or the proportion of total time that the load has given values. Thus, for airplane in flight through homogeneous rough air, the probability distribution of loads may be determined from a power-spectral analysis. In order to illustrate the application of power-spectral analysis to gust-load analysis and to obtain an insight into the relations between loads and airplane gust-response characteristics, two selected series of calculations are presented. The results indicate that both methods of analysis yield results that are consistent to a first approximation.

Press, Harry↗

ROSAT data analysis with EXSAS

For the x-ray observatory ROSAT, data from survey and pointed mission phases taken with different focal plane instruments and according to a complex mission timeline have to be handled. Data analysis therefore puts high demands on appropriate software tools. With EXSAS - the Extended Scientific Analysis System developed with an effort of 20 man years by the German ROSAT Scientific Data Center - a comfortable system for the reduction of data from the ROSAT x-ray and XUV instruments has been made available. EXSAS comprises a large collection of application modules as typically required in analyzing data of this wavelength regime and runs as a specific context in the wide-spread ESO-MIDAS environment. EXSAS, completely written in FORTRAN 77, takes full advantage of all the standards used in MIDAS and therefore, reflects the same portability (different UNIX installations and VMS). If required, the FORTRAN code also enables users to adapt the software in an easy way to their specific needs. To maintain independence from the specifics of different operating systems also on the data input side, all ROSAT data redistributed in the widely accepted FITS format. Although EXSAS has been developed specifically for data analysis of the ROSAT instruments, its structural design is sufficiently general to serve equally well also data from other X-ray and XUV instruments. EXSAS analysis modules are grouped into 4 application packages dealing with Data Preparation and Instrument Correction, Spatial Analysis, Spectral Analysis and Timing Analysis. A special EXSAS header, read and updated by each application, maintains the general information transfer on the origin, the history and the parameter space of the data stored in tables and images. About 100 genuine commands (most of which offer several additional options) allow to interactively explore the functionality of the system. Up to now 40 institutes all over the world have requested the EXSAS software. Maintenance and regular updates of the software and the comprehensive documentation are provided by the ROSAT Scientific Data Center at Garching.

Zimmermann, H. U.↗

Advanced composites structural concepts and materials technologies for primary aircraft structures: Structural response and failure analysis

Non-linear analysis methods were adapted and incorporated in a finite element based DIAL code. These methods are necessary to evaluate the global response of a stiffened structure under combined in-plane and out-of-plane loading. These methods include the Arc Length method and target point analysis procedure. A new interface material model was implemented that can model elastic-plastic behavior of the bond adhesive. Direct application of this method is in skin/stiffener interface failure assessment. Addition of the AML (angle minus longitudinal or load) failure procedure and Hasin's failure criteria provides added capability in the failure predictions. Interactive Stiffened Panel Analysis modules were developed as interactive pre-and post-processors. Each module provides the means of performing self-initiated finite elements based analysis of primary structures such as a flat or curved stiffened panel; a corrugated flat sandwich panel; and a curved geodesic fuselage panel. This module brings finite element analysis into the design of composite structures without the requirement for the user to know much about the techniques and procedures needed to actually perform a finite element analysis from scratch. An interactive finite element code was developed to predict bolted joint strength considering material and geometrical non-linearity. The developed method conducts an ultimate strength failure analysis using a set of material degradation models.

Dorris, William J.↗

Applying AI tools to operational space environmental analysis

The U.S. Air Force and National Oceanic Atmospheric Agency (NOAA) space environmental operations centers are facing increasingly complex challenges meeting the needs of their growing user community. These centers provide current space environmental information and short term forecasts of geomagnetic activity. Recent advances in modeling and data access have provided sophisticated tools for making accurate and timely forecasts, but have introduced new problems associated with handling and analyzing large quantities of complex data. AI (Artificial Intelligence) techniques have been considered as potential solutions to some of these problems. Fielding AI systems has proven more difficult than expected, in part because of operational constraints. Using systems which have been demonstrated successfully in the operational environment will provide a basis for a useful data fusion and analysis capability. Our approach uses a general purpose AI system already in operational use within the military intelligence community, called the Temporal Analysis System (TAS). TAS is an operational suite of tools supporting data processing, data visualization, historical analysis, situation assessment and predictive analysis. TAS includes expert system tools to analyze incoming events for indications of particular situations and predicts future activity. The expert system operates on a knowledge base of temporal patterns encoded using a knowledge representation called Temporal Transition Models (TTM's) and an event database maintained by the other TAS tools. The system also includes a robust knowledge acquisition and maintenance tool for creating TTM's using a graphical specification language. The ability to manipulate TTM's in a graphical format gives non-computer specialists an intuitive way of accessing and editing the knowledge base. To support space environmental analyses, we used TAS's ability to define domain specific event analysis abstractions. The prototype system defines events covering reports of natural phenomena such as solar flares, bursts, geomagnetic storms, and five others pertinent to space environmental analysis. With our preliminary event definitions we experimented with TAS's support for temporal pattern analysis using X-ray flare and geomagnetic storm forecasts as case studies. We are currently working on a framework for integrating advanced graphics and space environmental models into this analytical environment.

Krajnak, Mike↗

Analysis of filter tuning techniques for sequential orbit determination

This paper examines filter tuning techniques for a sequential orbit determination (OD) covariance analysis. Recently, there has been a renewed interest in sequential OD, primarily due to the successful flight qualification of the Tracking and Data Relay Satellite System (TDRSS) Onboard Navigation System (TONS) using Doppler data extracted onboard the Extreme Ultraviolet Explorer (EUVE) spacecraft. TONS computes highly accurate orbit solutions onboard the spacecraft in realtime using a sequential filter. As the result of the successful TONS-EUVE flight qualification experiment, the Earth Observing System (EOS) AM-1 Project has selected TONS as the prime navigation system. In addition, sequential OD methods can be used successfully for ground OD. Whether data are processed onboard or on the ground, a sequential OD procedure is generally favored over a batch technique when a realtime automated OD system is desired. Recently, OD covariance analyses were performed for the TONS-EUVE and TONS-EOS missions using the sequential processing options of the Orbit Determination Error Analysis System (ODEAS). ODEAS is the primary covariance analysis system used by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). The results of these analyses revealed a high sensitivity of the OD solutions to the state process noise filter tuning parameters. The covariance analysis results show that the state estimate error contributions from measurement-related error sources, especially those due to the random noise and satellite-to-satellite ionospheric refraction correction errors, increase rapidly as the state process noise increases. These results prompted an in-depth investigation of the role of the filter tuning parameters in sequential OD covariance analysis. This paper analyzes how the spacecraft state estimate errors due to dynamic and measurement-related error sources are affected by the process noise level used. This information is then used to establish guidelines for determining optimal filter tuning parameters in a given sequential OD scenario for both covariance analysis and actual OD. Comparisons are also made with corresponding definitive OD results available from the TONS-EUVE analysis.

Lee, T.↗

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.↗

Active Control of Fan Noise: Feasibility Study: Theoretical Analysis for Coupling of Active Noise Control Actuator Ring Sources to an Annular Duct with Flow - Volume 6

The objective of this effort is to develop an analytical model for the coupling of active noise control (ANC) piston-type actuators that are mounted flush to the inner and outer walls of an annular duct to the modes in the duct generated by the actuator motion. The analysis will be used to couple the ANC actuators to the modal analysis propagation computer program for the annular duct, to predict the effects of active suppression of fan-generated engine noise sources. This combined program will then be available to assist in the design or evaluation of ANC systems in fan engine annular exhaust ducts. An analysis has been developed to predict the modes generated in an annular duct due to the coupling of flush-mounted ring actuators on the inner and outer walls of the duct. The analysis has been combined with a previous analysis for the coupling of modes to a cylindrical duct in a FORTRAN computer program to perform the computations. The method includes the effects of uniform mean flow in the duct. The program can be used for design or evaluation purposes for active noise control hardware for turbofan engines. Predictions for some sample cases modeled after the geometry of the NASA Lewis ANC Fan indicate very efficient coupling in both the inlet and exhaust ducts for the m = 6 spinning mode at frequencies where only a single radial mode is cut-on. Radial mode content in higher order cut-off modes at the source plane and the required actuator displacement amplitude to achieve 110 dB SPL levels in the desired mode were predicted. Equivalent cases with and without flow were examined for the cylindrical and annular geometry, and little difference was found for a duct flow Mach number of 0.1. The actuator ring coupling program will be adapted as a subroutine to the cylindrical duct modal analysis and the exhaust duct modal analysis. This will allow the fan source to be defined in terms of characteristic modes at the fan source plane and predict the propagation to the arbitrarily-located ANC source plane. The actuator velocities can then be determined to generate the anti-phase mode. The resulting combined fan source/ANC pressure can then be calculated at any desired wall sensor position. The actuator velocities can be determined manually or using a simulation of a control system feedback loop. This will provide a very useful ANC system design and evaluation tool.

Kraft, R. E.↗

TADS--A CFD-Based Turbomachinery Analysis and Design System with GUI: User's Manual

The primary objective of this study was the development of a Computational Fluid Dynamics (CFD) based turbomachinery airfoil analysis and design system, controlled by a Graphical User Interface (GUI). The computer codes resulting from this effort are referred to as TADS (Turbomachinery Analysis and Design System). This document is intended to serve as a User's Manual for the computer programs which comprise the TADS system, developed under Task 18 of NASA Contract NAS3-27350, ADPAC System Coupling to Blade Analysis & Design System GUI and Task 10 of NASA Contract NAS3-27394, ADPAC System Coupling to Blade Analysis & Design System GUI, Phase II-Loss, Design and, Multi-stage Analysis. TADS couples a throughflow solver (ADPAC) with a quasi-3D blade-to-blade solver (RVCQ3D) in an interactive package. Throughflow analysis and design capability was developed in ADPAC through the addition of blade force and blockage terms to the governing equations. A GUI was developed to simplify user input and automate the many tasks required to perform turbomachinery analysis and design. The coupling of the various programs was done in such a way that alternative solvers or grid generators could be easily incorporated into the TADS framework. Results of aerodynamic calculations using the TADS system are presented for a highly loaded fan, a compressor stator, a low speed turbine blade and a transonic turbine vane.

Koiro, M. J.↗

Overview of Current Turbine Aerodynamic Analysis and Testing at MSFC

An overview of the current turbine aerodynamic analysis and testing activities at NASA/Marshall Space Flight Center (MSFC) is presented. The presentation is divided into three areas. The first area is the three-dimensional (3D), unsteady Computational Fluid Dynamics (CFD) analysis of the Fastrac turbine. Results from a coupled nozzle, blade, and exit guide vane analysis and from an uncoupled nozzle and coupled blade and exit guide vane will be presented. Unsteady pressure distributions, frequencies, and exit profiles from each analysis will be compared and contrasted. The second area is the testing and analysis of the Space Shuttle Main Engine (SSME) High Pressure Fuel Turbopump (HPFTP) turbine with instrumented first stage blades. The SSME HPFTP turbine was tested in air at the MSFC Turbine Test Equipment (TTE). Pressure transducers were mounted on the first stage blades. Unsteady, 3D CFD analysis was performed for this geometry and flow conditions. A sampling of the results will be shown. The third area is a status of the Turbine Performance Optimization task. The objective of this task is to improve the efficiency of a turbine for potential use on a next generation launch vehicle. This task includes global optimization for the preliminary design, detailed optimization for blade shapes and spacing, and application of advanced CFD analysis. The final design will be tested in the MSFC TTE.

Griffin, Lisa W.↗

Aerothermo-Structural Analysis of Low Cost Composite Nozzle/Inlet Components

This research is a cooperative effort among the Turbomachinery and Propulsion Division of NASA Glenn, CCMR of NC A&T State University, and the Tuskegee University. The NC A&T is the lead center and Tuskegee University is the participating institution. Objectives of the research were to develop an integrated aerodynamic, thermal and structural analysis code for design of aircraft engine components, such as, nozzles and inlets made of textile composites; conduct design studies on typical inlets for hypersonic transportation vehicles and setup standards test examples and finally manufacture a scaled down composite inlet. These objectives are accomplished through the following seven tasks: (1) identify the relevant public domain codes for all three types of analysis; (2) evaluate the codes for the accuracy of results and computational efficiency; (3) develop aero-thermal and thermal structural mapping algorithms; (4) integrate all the codes into one single code; (5) write a graphical user interface to improve the user friendliness of the code; (6) conduct test studies for rocket based combined-cycle engine inlet; and finally (7) fabricate a demonstration inlet model using textile preform composites. Tasks one, two and six are being pursued. Selected and evaluated NPARC for flow field analysis, CSTEM for in-depth thermal analysis of inlets and nozzles and FRAC3D for stress analysis. These codes have been independently verified for accuracy and performance. In addition, graphical user interface based on micromechanics analysis for laminated as well as textile composites was developed. Demonstration of this code will be made at the conference. A rocket based combined cycle engine was selected for test studies. Flow field analysis of various inlet geometries were studied. Integration of codes is being continued. The codes developed are being applied to a candidate example of trailblazer engine proposed for space transportation. A successful development of the code will provide a simpler, faster and user-friendly tool for conducting design studies of aircraft and spacecraft engines, applicable in high speed civil transport and space missions.

Shivakumar, Kuwigai↗

High Fidelity Failure Analysis for a Composite Fuselage Section

A high fidelity delamination failure analysis was developed by combining a local failure analysis with a global full-scale finite element structural analysis to address strength and delamination failure in a single package. The methodology was demonstrated through a local three-dimensional pull-off failure analysis and a geometrically nonlinear structural analysis of a five-foot composite helicopter fuselage section. Pull-off specimens were used to identify potential debonding failure of co-cured skin-stringer/frame fuselage structures. An investigation of the failed pull-off specimens was performed to determine the location of the failure initiation. Three-dimensional strain energy release rate analysis indicates that the delamination initiation and growth is controlled by Mode 1 opening mode. The bending moment at the delamination tip was identified as the crucial factor controlling the failure. The geometrically nonlinear structural analysis of a five-foot composite fuselage section was performed using a detailed finite element model. Loads were applied along the periphery of the subcomponent using displacement fields generated from solutions of a full-vehicle model.

Li, Jain↗

Coupled Aerodynamic and Structural Sensitivity Analysis of a High-Speed Civil Transport

An objective of the High Performance Computing and Communication Program at the NASA Langley Research Center is to demonstrate multidisciplinary shape and sizing optimization of a complete aerospace vehicle configuration by using high-fidelity, finite-element structural analysis and computational fluid dynamics aerodynamic analysis. In a previous study, a multi-disciplinary analysis system for a high-speed civil transport was formulated to integrate a set of existing discipline analysis codes, some of them computationally intensive, This paper is an extension of the previous study, in which the sensitivity analysis for the coupled aerodynamic and structural analysis problem is formulated and implemented. Uncoupled stress sensitivities computed with a constant load vector in a commercial finite element analysis code are compared to coupled aeroelastic sensitivities computed by finite differences. The computational expense of these sensitivity calculation methods is discussed.

Mason, B. H.↗

Hierarchical Strategy for Rapid Analysis Environment

A new philosophy is developed wherein the hierarchical definition of data is made use of in creating a better environment to conduct analyses of practical problems. This system can be adapted to conduct virtually any type of analysis, since this philosophy is not bound to any specific kind of analysis. It provides a framework to manage different models and its results and more importantly, the interaction between the different models. Thus, it is ideal for many types of finite element analyses like globalAoca1 analysis and those that involve multiple scales and fields. The system developed during the course of this work is just a demonstrator of the basic concepts. A complete implementation of this strategy could potentially make a major impact on the way analyses are conducted. It could considerably reduce the time frame required to conduct the analysis of real-life problems by efficient management of the data involved and reducing the human effort involved. It also helps in better decision making because of more ways to interpret the results. The strategy has been currently implemented for structural analysis, but with more work it could be extended to other fields of science when the finite element method is used to solve the differential equations numerically. This report details the work that has been done during the course of this project and its achievements and results. The following section discusses the meaning of the word hierarchical and the different references to the term in the literature. It talks about the development of the finite element method, its different versions and how hierarchy has been used to improve the methodology. The next section describes the hierarchical philosophy in detail and explains the different concepts and terms associated with it. It goes on to describe the implementation and the features of the demonstrator. A couple of problems are analyzed using the demonstrator program to show the working of the system. The two problems considered are two dimensional plane stress analysis problems. The results are compared with those obtained using conventional analysis. The different challenges faced during the development of this system are discussed. Finally, we conclude with suggestions for future work to add more features and extend it to a wider range of problems.

Whitcomb, John↗

Analysis and Test Correlation of Proof of Concept Box for Blended Wing Body-Low Speed Vehicle

The Low Speed Vehicle (LSV) is a 14.2% scale remotely piloted vehicle of the revolutionary Blended Wing Body concept. The design of the LSV includes an all composite airframe. Due to internal manufacturing capability restrictions, room temperature layups were necessary. An extensive materials testing and manufacturing process development effort was underwent to establish a process that would achieve the high modulus/low weight properties required to meet the design requirements. The analysis process involved a loads development effort that incorporated aero loads to determine internal forces that could be applied to a traditional FEM of the vehicle and to conduct detailed component analyses. A new tool, Hypersizer, was added to the design process to address various composite failure modes and to optimize the skin panel thickness of the upper and lower skins for the vehicle. The analysis required an iterative approach as material properties were continually changing. As a part of the material characterization effort, test articles, including a proof of concept wing box and a full-scale wing, were fabricated. The proof of concept box was fabricated based on very preliminary material studies and tested in bending, torsion, and shear. The box was then tested to failure under shear. The proof of concept box was also analyzed using Nastran and Hypersizer. The results of both analyses were scaled to determine the predicted failure load. The test results were compared to both the Nastran and Hypersizer analytical predictions. The actual failure occurred at 899 lbs. The failure was predicted at 1167 lbs based on the Nastran analysis. The Hypersizer analysis predicted a lower failure load of 960 lbs. The Nastran analysis alone was not sufficient to predict the failure load because it does not identify local composite failure modes. This analysis has traditionally been done using closed form solutions. Although Hypersizer is typically used as an optimizer for the design process, the failure prediction was used to help gain acceptance and confidence in this new tool. The correlated models and process were to be used to analyze the full BWB-LSV airframe design. The analysis and correlation with test results of the proof of concept box is presented here, including the comparison of the Nastran and Hypersizer results.

Spellman, Regina L.↗

Subsonic and Supersonic Flutter Analysis of a Highly Tapered Swept-Wing Planform, Including Effects of Density Variation and Finite Wing Thickness, and Comparison with Experiments

The flutter characteristics of several wings with an aspect-ratio of 4.0, a taper ratio of 0.2, and a quarter-chord sweepback of 45 deg. have been investigated analytically for Mach numbers up to 2.0. The calculations were based on the modified-strip-analysis method, the subsonic-kernel-function method, piston theory, and quasi-steady second-order theory. Results of t h e analysis and comparisons with experiment indicated that: (1) Flutter speeds were accurately predicted by the modified strip analysis, although accuracy at t h e highest Mach numbers required the use of nonlinear aerodynamic theory (which accounts for effects of wing thickness) for the calculation of the aerodynamic parameters. (2) An abrupt increase of flutter-speed coefficient with increasing Mach number, observed experimentally in the transonic range, was also indicated by the modified strip analysis. (3) In the low supersonic range for some densities, a discontinuous variation of flutter frequency with Mach number was indicated by the modified strip analysis. An abrupt change of frequency appeared experimentally in the transonic range. (4) Differences in flutter-speed-coefficient levels obtained from tests at low supersonic Mach numbers in two wind tunnels were also predicted by the modified strip analysis and were shown to be caused primarily by differences in mass ratio. (5) Flutter speeds calculated by the subsonic-kernel-function method were in good agreement with experiment and with the results of the modified strip analysis. (6) Flutter speed obtained from piston theory and from quasi-steady second-order theory were higher than experimental values by at least 38 percent.

Yates, Carson, Jr.↗

Validation of Design and Analysis Techniques of Tailored Composite Structures

Aeroelasticity is the relationship between the elasticity of an aircraft structure and its aerodynamics. This relationship can cause instabilities such as flutter in a wing. Engineers have long studied aeroelasticity to ensure such instabilities do not become a problem within normal operating conditions. In recent decades structural tailoring has been used to take advantage of aeroelasticity. It is possible to tailor an aircraft structure to respond favorably to multiple different flight regimes such as takeoff, landing, cruise, 2-g pull up, etc. Structures can be designed so that these responses provide an aerodynamic advantage. This research investigates the ability to design and analyze tailored structures made from filamentary composites. Specifically the accuracy of tailored composite analysis must be verified if this design technique is to become feasible. To pursue this idea, a validation experiment has been performed on a small-scale filamentary composite wing box. The box is tailored such that its cover panels induce a global bend-twist coupling under an applied load. Two types of analysis were chosen for the experiment. The first is a closed form analysis based on a theoretical model of a single cell tailored box beam and the second is a finite element analysis. The predicted results are compared with the measured data to validate the analyses. The comparison of results show that the finite element analysis is capable of predicting displacements and strains to within 10% on the small-scale structure. The closed form code is consistently able to predict the wing box bending to 25% of the measured value. This error is expected due to simplifying assumptions in the closed form analysis. Differences between the closed form code representation and the wing box specimen caused large errors in the twist prediction. The closed form analysis prediction of twist has not been validated from this test.

Jegley, Dawn C.↗

Probabilistic Parameter Uncertainty Analysis of Single Input Single Output Control Systems

The current standards for handling uncertainty in control systems use interval bounds for definition of the uncertain parameters. This approach gives no information about the likelihood of system performance, but simply gives the response bounds. When used in design, current methods of m-analysis and can lead to overly conservative controller design. With these methods, worst case conditions are weighted equally with the most likely conditions. This research explores a unique approach for probabilistic analysis of control systems. Current reliability methods are examined showing the strong areas of each in handling probability. A hybrid method is developed using these reliability tools for efficiently propagating probabilistic uncertainty through classical control analysis problems. The method developed is applied to classical response analysis as well as analysis methods that explore the effects of the uncertain parameters on stability and performance metrics. The benefits of using this hybrid approach for calculating the mean and variance of responses cumulative distribution functions are shown. Results of the probabilistic analysis of a missile pitch control system, and a non-collocated mass spring system, show the added information provided by this hybrid analysis.

Smith, Brett A.↗