Results for “Model Based System Engineering” — Page 25

NASA NTRS2007

Design for Reliability and Safety Approach for the NASA New Launch Vehicle

The United States National Aeronautics and Space Administration (NASA) is in the midst of a space exploration program intended for sending crew and cargo to the international Space Station (ISS), to the moon, and beyond. This program is called Constellation. As part of the Constellation program, NASA is developing new launch vehicles aimed at significantly increase safety and reliability, reduce the cost of accessing space, and provide a growth path for manned space exploration. Achieving these goals requires a rigorous process that addresses reliability, safety, and cost upfront and throughout all the phases of the life cycle of the program. This paper discusses the "Design for Reliability and Safety" approach for the NASA new crew launch vehicle called ARES I. The ARES I is being developed by NASA Marshall Space Flight Center (MSFC) in support of the Constellation program. The ARES I consists of three major Elements: A solid First Stage (FS), an Upper Stage (US), and liquid Upper Stage Engine (USE). Stacked on top of the ARES I is the Crew exploration vehicle (CEV). The CEV consists of a Launch Abort System (LAS), Crew Module (CM), Service Module (SM), and a Spacecraft Adapter (SA). The CEV development is being led by NASA Johnson Space Center (JSC). Designing for high reliability and safety require a good integrated working environment and a sound technical design approach. The "Design for Reliability and Safety" approach addressed in this paper discusses both the environment and the technical process put in place to support the ARES I design. To address the integrated working environment, the ARES I project office has established a risk based design group called "Operability Design and Analysis" (OD&A) group. This group is an integrated group intended to bring together the engineering, design, and safety organizations together to optimize the system design for safety, reliability, and cost. On the technical side, the ARES I project has, through the OD&A environment, implemented a probabilistic approach to analyze and evaluate design uncertainties and understand their impact on safety, reliability, and cost. This paper focuses on the use of the various probabilistic approaches that have been pursued by the ARES I project. Specifically, the paper discusses an integrated functional probabilistic analysis approach that addresses upffont some key areas to support the ARES I Design Analysis Cycle (DAC) pre Preliminary Design (PD) Phase. This functional approach is a probabilistic physics based approach that combines failure probabilities with system dynamics and engineering failure impact models to identify key system risk drivers and potential system design requirements. The paper also discusses other probabilistic risk assessment approaches planned by the ARES I project to support the PD phase and beyond.

Safie, Fayssal, M.↗

NASA NTRS2018

Integration of Information Management System, Workflow and Computational Tools Enabling Multiscale Modeling Within an ICME Paradigm

With the increased emphasis on reducing the cost and time to market of new materials, the need for analytical tools that enable the virtual design and optimization of materials throughout their processing - internal structure - property - performance envelope, along with the capturing and storing of the associated material and model information across its lifecycle, has become critical. This need is also fueled by the demands for higher efficiency in material testing; consistency, quality and traceability of data; product design; engineering analysis; as well as control of access to proprietary or sensitive information. Fortunately, material information management systems and physics-based multiscale modeling methods have kept pace with the growing user demands. Herein, recent efforts to develop a set of Python functions that exchange information between NASA GRC's Integrated multiscale Micromechanics Analysis Code (ImMAC) software toolset and its Integrated Computational Materials Engineering (ICME), Granta MI® database schema is presented. The goal is to enable seamless coupling between both test data and simulation data, which is captured and tracked automatically within Granta MI®, with full model pedigree information. These tools, and this type of linkage, are foundational to realizing the full potential of ICME, in which materials processing, microstructure, properties, and performance are coupled to enable application-driven design and optimization of materials and structures.

multiscale modeling; Micromechanics; Computational↗

NASA NTRS2013

Integrated Main Propulsion System Performance Reconstruction Process/Models

The Integrated Main Propulsion System (MPS) Performance Reconstruction process provides the MPS post-flight data files needed for postflight reporting to the project integration management and key customers to verify flight performance. This process/model was used as the baseline for the currently ongoing Space Launch System (SLS) work. The process utilizes several methodologies, including multiple software programs, to model integrated propulsion system performance through space shuttle ascent. It is used to evaluate integrated propulsion systems, including propellant tanks, feed systems, rocket engine, and pressurization systems performance throughout ascent based on flight pressure and temperature data. The latest revision incorporates new methods based on main engine power balance model updates to model higher mixture ratio operation at lower engine power levels.

Lopez, Eduardo↗

NASA NTRSDate not supplied

Design, Formalization, and Verification of Decision Making for Intelligent Systems

The development of autonomous systems requires a rigorous process that can guarantee a system’s reliability in critical applications. At its core, an autonomous system bases its behavior on a well-defined decision making system. In this paper, we present a methodological basis for the design, formalization and formal verification of Decision Making systems for autonomous agents. The approach is generally applicable to operational objectives that can be functionally decomposed and subsequently represented as Hierarchical Finite State Machines. As a case study, we present the application of this method to implement a Decision Making model in Simulink. Furthermore, we present how we use NASA’s FRET tool to write requirements in structured natural language and generate formal specifications that can be automatically digested by NASA’s CoCoSim tool. Finally, we present how, by leveraging CoCoSim, we perform formal verification against the Simulink model and present analysis results.

Model-based development↗

NASA NTRSDate not supplied

Design, Formalization, and Verification of Decision Making for Intelligent Systems

The development of autonomous systems requires a rigorous process that can guarantee a system’s reliability in critical applications. At its core, an autonomous system bases its behavior on a well-defined decision making system. In this paper, we present a methodological basis for the design, formalization and formal verification of Decision Making systems for autonomous agents. The approach is generally applicable to operational objectives that can be functionally decomposed and subsequently represented as Hierarchical Finite State Machines. As a case study, we present the application of this method to implement a Decision Making model in Simulink. Furthermore, we present how we use NASA’s FRET tool to write requirements in structured natural language and generate formal specifications that can be automatically digested by NASA’s CoCoSim tool. Finally, we present how, by leveraging CoCoSim, we perform formal verification against the Simulink model and present analysis results.

Model-based development↗

NASA NTRS1986

Prototyping and implementing flight qualifiable semicustom CMOS P-well bulk integrated circuits in the JPL environment

Presently, there are many difficulties associated with implementing application specific custom or semi-custom (standard cell based) integrated circuits (ICs) into JPL flight projects. One of the primary difficulties is developing prototype semi-custom integrated circuits for use and evaluation in engineering prototype flight hardware. The prototype semi-custom ICs must be extremely cost-effective and yet still representative of flight qualifiable versions of the design. A second difficulty is encountered in the transport of the design from engineering prototype quality to flight quality. Normally, flight quality integrated circuits have stringent quality standards, must be radiation resistant and should consume minimal power. It is often not necessary or cost effective, however, to impose such stringent quality standards on engineering models developed for systems analysis in controlled lab environments. This article presents work originally initiated for ground based applications that also addresses these two problems. Furthermore, this article suggests a method that has been shown successful in prototyping flight quality semi-custom ICs through the Metal Oxide Semiconductor Implementation Service (MOSIS) program run by the University of Southern California's Information Sciences Institute. The method has been used successfully to design and fabricate through the MOSIS three different semi-custom prototype CMOS p-well chips. The three designs make use of the work presented and were designed consistent with design techniques and structures that are flight qualifiable, allowing one hour transfer of the design from engineering model status to flight qualifiable foundry-ready status through methods outlined in this article.

Olson, E. M.↗

NASA NTRS2020

Space Launch Vehicle Transient Particle Redistribution Modeling and Implications for Optically Sensitive Payloads

The performance of contamination sensitive components—such as optical components—can be degraded by particulate matter depositing on the surfaces. Particles can accumulate during manufacturing, handling and operation. For a space-based system, particles can shed from the fairing and redistribute onto sensitive surfaces during launch. An engineering modeling approach has been developed for modeling particle migration during launch. The approach involves particle detachment from the fairing, particle transport through the venting atmosphere inside the fairing, and attachment to the receiving surface. Particle size and amounts on the fairing surface can be modeled using distributions from standards, such as IEST-STD-CC1246E, as well as from empirical data obtained from tape lifts. Surface interactions are modeled using theoretical as well as empirical data. Commercial computational fluid dynamics codes are used to calculate the gas flow in the fairing during depressurization during launch. This approach not only provides insight into particle redistribution during launch but also can be used to establish fairing cleanliness requirements.

Brieda, Lubos↗

NASA NTRS2006

Marshall Space Flight Center Propulsion Systems Department (PSD) KM Initiative

NASA Marshall Space Flight Center s Propulsion Systems Department (PSD) is four months into a fifteen month Knowledge Management (KM) initiative to support enhanced engineering decision making and analyses, faster resolution of anomalies (near-term) and effective, efficient knowledge infused engineering processes, reduced knowledge attrition, and reduced anomaly occurrences (long-term). The near-term objective of this initiative is developing a KM Pilot project, within the context of a 3-5 year KM strategy, to introduce and evaluate the use of KM within PSD. An internal NASA/MSFC PSD KM team was established early in project formulation to maintain a practitioner, user-centric focus throughout the conceptual development, planning and deployment of KM technologies and capabilities with in the PSD. The PSD internal team is supported by the University of Alabama's Aging Infrastructure Systems Center Of Excellence (AISCE), Intergraph Corporation, and The Knowledge Institute. The principle product of the initial four month effort has been strategic planning of PSD KM implementation by first determining the "as is" state of KM capabilities and developing, planning and documenting the roadmap to achieve the desired "to be" state. Activities undertaken to support the planning phase have included data gathering; cultural surveys, group work-sessions, interviews, documentation review, and independent research. Assessments and analyses have been performed including industry benchmarking, related local and Agency initiatives, specific tools and techniques used and strategies for leveraging existing resources, people and technology to achieve common KM goals. Key findings captured in the PSD KM Strategic Plan include the system vision, purpose, stakeholders, prioritized strategic objectives mapped to the top ten practitioner needs and analysis of current resource usage. Opportunities identified from research, analyses, cultural/KM surveys and practitioner interviews include: executive and senior management sponsorship, KM awareness, promotion and training, cultural change management, process improvement, leveraging existing resources and new innovative technologies to align with other NASA KM initiatives (convergence: the big picture). To enable results based incremental implementation and future growth of the KM initiative, key performance measures have been identified including stakeholder value, system utility, learning and growth (knowledge capture, sharing, reduced anomaly recurrence), cultural change, process improvement and return-on-investment. The next steps for the initial implementation spiral (focused on SSME Turbomachinery) have been identified, largely based on the organization and compilation of summary level engineering process models, data capture matrices, functional models and conceptual-level systems architecture. Key elements include detailed KM requirements definition, KM technology architecture assessment, evaluation and selection, deployable KM Pilot design, development, implementation and evaluation, and justifying full implementation (estimated Return-on-Investment). Features identified for the notional system architecture include the knowledge presentation layer (and its components), knowledge network layer (and its components), knowledge storage layer (and its components), User Interface and capabilities. This paper provides a snapshot of the progress to date, the near term planning for deploying the KM pilot project and a forward look at results based growth of KM capabilities with-in the MSFC PSD.

Caraccioli, Paul↗

NASA NTRS2012

Integrating Engineering Data Systems for NASA Spaceflight Projects

NASA has a large range of custom-built and commercial data systems to support spaceflight programs. Some of the systems are re-used by many programs and projects over time. Management and systems engineering processes require integration of data across many of these systems, a difficult problem given the widely diverse nature of system interfaces and data models. This paper describes an ongoing project to use a central data model with a web services architecture to support the integration and access of linked data across engineering functions for multiple NASA programs. The work involves the implementation of a web service-based middleware system called Data Aggregator to bring together data from a variety of systems to support space exploration. Data Aggregator includes a central data model registry for storing and managing links between the data in disparate systems. Initially developed for NASA's Constellation Program needs, Data Aggregator is currently being repurposed to support the International Space Station Program and new NASA projects with processes that involve significant aggregating and linking of data. This change in user needs led to development of a more streamlined data model registry for Data Aggregator in order to simplify adding new project application data as well as standardization of the Data Aggregator query syntax to facilitate cross-application querying by client applications. This paper documents the approach from a set of stand-alone engineering systems from which data are manually retrieved and integrated, to a web of engineering data systems from which the latest data are automatically retrieved and more quickly and accurately integrated. This paper includes the lessons learned through these efforts, including the design and development of a service-oriented architecture and the evolution of the data model registry approaches as the effort continues to evolve and adapt to support multiple NASA programs and priorities.

Carvalho, Robert E.↗

NASA NTRSDate not supplied

BERT-based Topic Modeling and Information Retrieval to Support Fishbone Diagramming for Safe Integration of Unmanned Aircraft Systems in Wildfire Response

Recent concepts for emerging wildfire response operations have included unmanned aircraft systems (UAS) due to their increasing accessibility and capabilities. To integrate UAS into wildfire response safely, researchers have studied the use of large repositories of historic incident reports to improve the scope of root cause analysis. Recent work has emphasized applying state-of-the-art natural language processing techniques to extract useful information from these repositories. However, it has not yet been studied how these results can be interpreted and integrated into the systems engineering process. In this work, we propose a process in which Bidirectional Encoder Representations from Transformers (BERT)-based topic modeling and information retrieval are applied to a relevant set of documents in order to support the development of a fishbone diagram in a semiautomated process. High-level themes in the document set are identified using topic modeling, which are then refined and interpreted by a human analyst. Then, the themes are used to guide a finer search using information retrieval, which returns specific incident reports of relevance. This provides traceability to specific incidents as well as broader categorizations that comprise the fishbone branches. We apply the proposed process to relevant documents from NASA’s Aviation Safety Reporting System (ASRS). The proposed process is widely applicable when relevant documents are available, and the results from this study will be useful to identifying potential causes of wildfire response UAS incidents.

hazard analysis↗

NASA NTRSDate not supplied

BERT-based Topic Modeling and Information Retrieval to Support Fishbone Diagramming for Safe Integration of Unmanned Aircraft Systems in Wildfire Response

Recent concepts for emerging wildfire response operations have included unmanned aircraft systems (UAS) due to their increasing accessibility and capabilities. To integrate UAS into wildfire response safely, researchers have studied the use of large repositories of historic incident reports to improve the scope of root cause analysis. Recent work has emphasized applying state-of-the-art natural language processing techniques to extract useful information from these repositories. However, it has not yet been studied how these results can be interpreted and integrated into the systems engineering process. In this work, we propose a process in which Bidirectional Encoder Representations from Transformers (BERT)-based topic modeling and information retrieval are applied to a relevant set of documents in order to support the development of a fishbone diagram in a semiautomated process. High-level themes in the document set are identified using topic modeling, which are then refined and interpreted by a human analyst. Then, the themes are used to guide a finer search using information retrieval, which returns specific incident reports of relevance. This provides traceability to specific incidents as well as broader categorizations that comprise the fishbone branches. We apply the proposed process to relevant documents from NASA’s Aviation Safety Reporting System (ASRS). The proposed process is widely applicable when relevant documents are available, and the results from this study will be useful to identifying potential causes of wildfire response UAS incidents.

hazard analysis↗

NASA NTRS2023

BERT-Based Topic Modeling and Information Retrieval to Support Fishbone Diagramming for Safe Integration of Unmanned Aircraft Systems in Wildfire Response

Recent concepts for emerging wildfire response operations have included unmanned aircraft systems (UAS) due to their increasing accessibility and capabilities. To integrate UAS into wildfire response safely, researchers have studied the use of large repositories of historic incident reports to improve the scope of root cause analysis. Recent work has emphasized applying state-of-the-art natural language processing techniques to extract useful information from these repositories. However, it has not yet been studied how these results can be interpreted and integrated into the systems engineering process. In this work, we propose a process in which Bidirectional Encoder Representations from Transformers (BERT)-based topic modeling and information retrieval are applied to a relevant set of documents in order to support the development of a fishbone diagram in a semiautomated process. High-level themes in the document set are identified using topic modeling, which are then refined and interpreted by a human analyst. Then, the themes are used to guide a finer search using information retrieval, which returns specific incident reports of relevance. This provides traceability to specific incidents as well as broader categorizations that comprise the fishbone branches. We apply the proposed process to relevant documents from NASA’s Aviation Safety Reporting System (ASRS). The proposed process is widely applicable when relevant documents are available, and the results from this study will be useful to identifying potential causes of wildfire response UAS incidents.

Hazard analysis↗

NASA NTRS1991

Modeling structural dynamic behavior of SSME components

FEM studies are presented of the nozzle and the low-pressure fuel-pump inducer designs for the Space Shuttle Main Engine (SSME) to analyze the effects of structural vibrations. FEM preprocessing software based on a CAD system is employed to develop a model of the component's sophisticated geometry. The nozzle geometry is also defined by means of the preprocessing technique and subsequently analyzed with respect to time-transient loading. The analysis is conducted with a Cray supercomputer using the SPAR/EAL FEM program. The investigation of the nozzle demonstrates the advantageous use of symmetry in the determination of nozzle response to SSME start-up transients. Plots of time vs strain are developed for gages on the nozzle wall and steerhorn tubing. The results of the inducer modeling are found to be adequate for investigating the component's principle modes, and the nozzle results indicate the suitability of the FEM techniques for optimizing the design of engine components.

Kiefling, Larry A.↗

NASA NTRS2013

Software Tools to Support the Assessment of System Health

This presentation provides an overview of three software tools that were developed by the NASA Glenn Research Center to support the assessment of system health: the Propulsion Diagnostic Method Evaluation Strategy (ProDIMES), the Systematic Sensor Selection Strategy (S4), and the Extended Testability Analysis (ETA) tool. Originally developed to support specific NASA projects in aeronautics and space, these software tools are currently available to U.S. citizens through the NASA Glenn Software Catalog. The ProDiMES software tool was developed to support a uniform comparison of propulsion gas path diagnostic methods. Methods published in the open literature are typically applied to dissimilar platforms with different levels of complexity. They often address different diagnostic problems and use inconsistent metrics for evaluating performance. As a result, it is difficult to perform a one ]to ]one comparison of the various diagnostic methods. ProDIMES solves this problem by serving as a theme problem to aid in propulsion gas path diagnostic technology development and evaluation. The overall goal is to provide a tool that will serve as an industry standard, and will truly facilitate the development and evaluation of significant Engine Health Management (EHM) capabilities. ProDiMES has been developed under a collaborative project of The Technical Cooperation Program (TTCP) based on feedback provided by individuals within the aircraft engine health management community. The S4 software tool provides a framework that supports the optimal selection of sensors for health management assessments. S4 is structured to accommodate user ]defined applications, diagnostic systems, search techniques, and system requirements/constraints. One or more sensor suites that maximize this performance while meeting other user ]defined system requirements that are presumed to exist. S4 provides a systematic approach for evaluating combinations of sensors to determine the set or sets of sensors that optimally meet the performance goals and the constraints. It identifies optimal sensor suite solutions by utilizing a merit (i.e., cost) function with one of several available optimization approaches. As part of its analysis, S4 can expose fault conditions that are difficult to diagnose due to an incomplete diagnostic philosophy and/or a lack of sensors. S4 was originally developed and applied to liquid rocket engines. It was subsequently used to study the optimized selection of sensors for a simulation ]based aircraft engine diagnostic system. The ETA Tool is a software ]based analysis tool that augments the testability analysis and reporting capabilities of a commercial ]off ]the ]shelf (COTS) package. An initial diagnostic assessment is performed by the COTS software using a user ]developed, qualitative, directed ]graph model of the system being analyzed. The ETA Tool accesses system design information captured within the model and the associated testability analysis output to create a series of six reports for various system engineering needs. These reports are highlighted in the presentation. The ETA Tool was developed by NASA to support the verification of fault management requirements early in the Launch Vehicle process. Due to their early development during the design process, the TEAMS ]based diagnostic model and the ETA Tool were able to positively influence the system design by highlighting gaps in failure detection, fault isolation, and failure recovery.

Melcher, Kevin J.↗

NASA NTRS2011

Hybrid CFD/CAA Modeling for Liftoff Acoustic Predictions

This paper presents development efforts at the NASA Marshall Space flight Center to establish a hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) simulation system for launch vehicle liftoff acoustics environment analysis. Acoustic prediction engineering tools based on empirical jet acoustic strength and directivity models or scaled historical measurements are of limited value in efforts to proactively design and optimize launch vehicles and launch facility configurations for liftoff acoustics. CFD based modeling approaches are now able to capture the important details of vehicle specific plume flow environment, identifY the noise generation sources, and allow assessment of the influence of launch pad geometric details and sound mitigation measures such as water injection. However, CFD methodologies are numerically too dissipative to accurately capture the propagation of the acoustic waves in the large CFD models. The hybrid CFD/CAA approach combines the high-fidelity CFD analysis capable of identifYing the acoustic sources with a fast and efficient Boundary Element Method (BEM) that accurately propagates the acoustic field from the source locations. The BEM approach was chosen for its ability to properly account for reflections and scattering of acoustic waves from launch pad structures. The paper will present an overview of the technology components of the CFD/CAA framework and discuss plans for demonstration and validation against test data.

Strutzenberg, Louise L.↗

NASA NTRS1998

Injector Design Tool Improvements: User's manual for FDNS V.4.5

The major emphasis of the current effort is in the development and validation of an efficient parallel machine computational model, based on the FDNS code, to analyze the fluid dynamics of a wide variety of liquid jet configurations for general liquid rocket engine injection system applications. This model includes physical models for droplet atomization, breakup/coalescence, evaporation, turbulence mixing and gas-phase combustion. Benchmark validation cases for liquid rocket engine chamber combustion conditions will be performed for model validation purpose. Test cases may include shear coaxial, swirl coaxial and impinging injection systems with combinations LOXIH2 or LOXISP-1 propellant injector elements used in rocket engine designs. As a final goal of this project, a well tested parallel CFD performance methodology together with a user's operation description in a final technical report will be reported at the end of the proposed research effort.

Chen, Yen-Sen↗

NASA NTRS2003

Methods Developed by the Tools for Engine Diagnostics Task to Monitor and Predict Rotor Damage in Real Time

Tools for Engine Diagnostics is a major task in the Propulsion System Health Management area of the Single Aircraft Accident Prevention project under NASA s Aviation Safety Program. The major goal of the Aviation Safety Program is to reduce fatal aircraft accidents by 80 percent within 10 years and by 90 percent within 25 years. The goal of the Propulsion System Health Management area is to eliminate propulsion system malfunctions as a primary or contributing factor to the cause of aircraft accidents. The purpose of Tools for Engine Diagnostics, a 2-yr-old task, is to establish and improve tools for engine diagnostics and prognostics that measure the deformation and damage of rotating engine components at the ground level and that perform intermittent or continuous monitoring on the engine wing. In this work, nondestructive-evaluation- (NDE-) based technology is combined with model-dependent disk spin experimental simulation systems, like finite element modeling (FEM) and modal norms, to monitor and predict rotor damage in real time. Fracture mechanics time-dependent fatigue crack growth and damage-mechanics-based life estimation are being developed, and their potential use investigated. In addition, wireless eddy current and advanced acoustics are being developed for on-wing and just-in-time NDE engine inspection to provide deeper access and higher sensitivity to extend on-wing capabilities and improve inspection readiness. In the long run, these methods could establish a base for prognostic sensing while an engine is running, without any overt actions, like inspections. This damage-detection strategy includes experimentally acquired vibration-, eddy-current- and capacitance-based displacement measurements and analytically computed FEM-, modal norms-, and conventional rotordynamics-based models of well-defined damages and critical mass imbalances in rotating disks and rotors.

Baaklini, George Y.↗

NASA NTRS1997

The Application of New Software Technology to the Architecture of the National Cycle Program

As part of the Numerical Propulsion System Simulation (NPSS) effort of NASA Lewis in conjunction with the United States aeropropulsion industry, a new system simulation framework, the National Cycle Program (NCP), capable of combining existing empirical engine models with new detailed component-based computational models is being developed. The software architecture of the NCP program involves a generalized object- oriented framework and a base-set of engine component models along with supporting tool kits which will support engine simulation in a distributed environment. As the models are extended to contain two and three dimensions the computing load increases rapidly and it is intended that this load be distributed across multiple work stations executing concurrently in order to get acceptably fast results. The research carried out was directed toward performance analysis of the distributed object system. More specifically, the performance of the actor-based distributed object design I created earlier was desired. To this end, the research was directed toward the design and implementation of suitable performance-analysis techniques and software to demonstrate those techniques. There were three specific results which are reported in two separate reports submitted separately as NASA Technical Memoranda. The results are: (1) Design, implementation, and testing of a performance analysis program for a set of active objects (actor based objects) which allowed the individual actors to be assigned to arbitrary processes on an arbitrary set of machines. (2) The global-balance-equation approach has the fundamental limitation that the number of equations increases exponentially with the number of actors. Hence, unlike many approximate approaches to this problem, the nearest-neighbor approach allows checking of the solution and an estimate of the error. The technique was demonstrated in a prototype analysis program as part of this research. The results of the program were checked against the global-balance solution discussed above. Late during the grant, a much better approximation was developed and this is discussed in result below. As a consequence, a proposal was submitted to continue the research by developing the new approximation including development of a complete program from the prototype. (3) The source of approximation in the nearest-neighbor algorithm is the requirement for estimating some joint probabilities from some marginal distributions. A completely ad hoc estimate was used in the prototype.

Schoeffler, James D.↗