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At least 163 records · Page 9

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NASA NTRS2000

A Probabilistic Framework for the Validation and Certification of Computer Simulations

The paper presents a methodology for quantifying, propagating, and managing the uncertainty in the data required to initialize computer simulations of complex phenomena. The purpose of the methodology is to permit the quantitative assessment of a certification level to be associated with the predictions from the simulations, as well as the design of a data acquisition strategy to achieve a target level of certification. The value of a methodology that can address the above issues is obvious, specially in light of the trend in the availability of computational resources, as well as the trend in sensor technology. These two trends make it possible to probe physical phenomena both with physical sensors, as well as with complex models, at previously inconceivable levels. With these new abilities arises the need to develop the knowledge to integrate the information from sensors and computer simulations. This is achieved in the present work by tracing both activities back to a level of abstraction that highlights their commonalities, thus allowing them to be manipulated in a mathematically consistent fashion. In particular, the mathematical theory underlying computer simulations has long been associated with partial differential equations and functional analysis concepts such as Hilbert spares and orthogonal projections. By relying on a probabilistic framework for the modeling of data, a Hilbert space framework emerges that permits the modeling of coefficients in the governing equations as random variables, or equivalently, as elements in a Hilbert space. This permits the development of an approximation theory for probabilistic problems that parallels that of deterministic approximation theory. According to this formalism, the solution of the problem is identified by its projection on a basis in the Hilbert space of random variables, as opposed to more traditional techniques where the solution is approximated by its first or second-order statistics. The present representation, in addition to capturing significantly more information than the traditional approach, facilitates the linkage between different interacting stochastic systems as is typically observed in real-life situations.

Ghanem, Roger↗

NASA NTRS2014

Upset Recovery Human Factors

Accident and incident analyses as well as industry group concerns and recommendations have justified taking a second look at proficiency standards related to upset recovery training and performance. Quite a number of factors and theories have been suggested-- leading the NASA Aviation Safety Program to reconsider manual handling skills in highly automated aircraft particularly in conditions that can potentially lead to Loss of Control events. Our team of Subject Matter Experts (SMEs) first identified 76 Basic Recovery Skills that were important for effective crew response under five different anomaly conditions. In addition to manual handling skills, the skill set included knowledge and cognitive skills, as well as decision making and management skills. Advanced Recovery Skills were identified by combining skills, integrating with crew resource management skills, and developing heuristics for decision making.Using the Advanced Recovery Skill set, the SMEs then developed a generic process flow starting from the problem discovery phase (e.g., identifying an anomaly) through the decision making and management phase (e.g., assessing response options), through the recovery phase (e.g., controlling the aircraft). The generic process flow was refined by testing it against six additional scenarios. The next part of the project was to develop an approach for assessing and revising a generic training curriculum (we used an operators Advanced Qualification Program (AQP) as a framework). Although many of the Basic and Advanced Recovery Skills could be found in the Job Task Listing, they were not always structured or combined in the most effective way. Recommendations were developed for assessing relevant aspects of the Job Task Listing and Continuing Qualification curriculum so that the more comprehensive set of Upset Recovery skillsincluding Human Factors--could be trained and assessed in the most appropriate and effective context. The existing AQP methodology provides a natural way to insert targeted Upset Recovery skills into its system of proficiency objectives, training devices, training activities, and ultimately, into the event sets of a simulator training scenario.

AQP training↗

NASA NTRSDate not supplied

Explaining Soft-Goal Conflicts through Constraint Relaxations

Recent work suggests to explain trade-offs between soft goals in terms of their conflicts, i. e., minimal unsolvable soft-goal subsets. But this does not explain the conflicts themselves: Why can a given set of soft-goals not be jointly achieved? Here we approach that question in terms of the underlying constraints on plans in the task at hand, namely resource availability and time windows. In this context, a natural form of explanation for a soft-goal conflict is a minimal constraint relaxation under which the conflict disappears (“if the deadline was 1 hour later, it would work”). We explore algorithms for computing such explanations. A baseline is to simply loop over all relaxed tasks and compute the conflicts for each separately. We improve over this by two algorithms that leverage information – conflicts, reachable states – across relaxed tasks. We show that these algorithms can exponentially outperform the baseline in theory, and we run experiments confirming that advantage in practice.

Planning↗

NASA NTRS2008

Control Architecture for Robotic Agent Command and Sensing

Control Architecture for Robotic Agent Command and Sensing (CARACaS) is a recent product of a continuing effort to develop architectures for controlling either a single autonomous robotic vehicle or multiple cooperating but otherwise autonomous robotic vehicles. CARACaS is potentially applicable to diverse robotic systems that could include aircraft, spacecraft, ground vehicles, surface water vessels, and/or underwater vessels. CARACaS incudes an integral combination of three coupled agents: a dynamic planning engine, a behavior engine, and a perception engine. The perception and dynamic planning en - gines are also coupled with a memory in the form of a world model. CARACaS is intended to satisfy the need for two major capabilities essential for proper functioning of an autonomous robotic system: a capability for deterministic reaction to unanticipated occurrences and a capability for re-planning in the face of changing goals, conditions, or resources. The behavior engine incorporates the multi-agent control architecture, called CAMPOUT, described in An Architecture for Controlling Multiple Robots (NPO-30345), NASA Tech Briefs, Vol. 28, No. 11 (November 2004), page 65. CAMPOUT is used to develop behavior-composition and -coordination mechanisms. Real-time process algebra operators are used to compose a behavior network for any given mission scenario. These operators afford a capability for producing a formally correct kernel of behaviors that guarantee predictable performance. By use of a method based on multi-objective decision theory (MODT), recommendations from multiple behaviors are combined to form a set of control actions that represents their consensus. In this approach, all behaviors contribute simultaneously to the control of the robotic system in a cooperative rather than a competitive manner. This approach guarantees a solution that is good enough with respect to resolution of complex, possibly conflicting goals within the constraints of the mission to be accomplished by the vehicle(s).

Huntsberger, Terrance↗

NASA NTRS1995

Viscous-flow analysis of a subsonic transport aircraft high-lift system and correlation with flight data

High-lift system aerodynamics has been gaining attention in recent years. In an effort to improve aircraft performance, comprehensive studies of multi-element airfoil systems are being undertaken in wind-tunnel and flight experiments. Recent developments in Computational Fluid Dynamics (CFD) offer a relatively inexpensive alternative for studying complex viscous flows by numerically solving the Navier-Stokes (N-S) equations. Current limitations in computer resources restrict practical high-lift N-S computations to two dimensions, but CFD predictions can yield tremendous insight into flow structure, interactions between airfoil elements, and effects of changes in airfoil geometry or free-stream conditions. These codes are very accurate when compared to strictly 2D data provided by wind-tunnel testing, as will be shown here. Yet, additional challenges must be faced in the analysis of a production aircraft wing section, such as that of the NASA Langley Transport Systems Research Vehicle (TSRV). A primary issue is the sweep theory used to correlate 2D predictions with 3D flight results, accounting for sweep, taper, and finite wing effects. Other computational issues addressed here include the effects of surface roughness of the geometry, cove shape modeling, grid topology, and transition specification. The sensitivity of the flow to changing free-stream conditions is investigated. In addition, the effects of Gurney flaps on the aerodynamic characteristics of the airfoil system are predicted.

Potter, R. C.↗

NASA NTRS2019

Complex Dynamics of Air Traffic Flow

Air traffic in the United States has continued to grow at a steady pace since 1980, except for a dip immediately after the tragic events of September 11, 2001. There are different growth scenarios associated both with the magnitude and the composition of the future air traffic. The Terminal Area Forecast (TAF), prepared every year by the FAA, projects the growth of traffic in the United States. Both Boeing and Airbus publish market outlooks for air travel annually. Although predicting the future growth of traffic is difficult, there are two significant trends: heavily congested major airports continue to see an increase in traffic, and the emergence of regional jets and other smaller aircraft with fewer passengers operating directly between non-major airports. The interaction between air traffic demand and the ability of the system to provide the necessary airport and airspace resources can be modeled as a network. The size of the resulting network varies depending on the choice of its nodes. It would be useful to understand the properties of this network to guide future design and development. Many questions, such as the growth of delay with increasing traffic demand and impact of the en route weather on future air traffic, require a systematic understanding of the properties of the air traffic network. There has been a major advance in the understanding of the behavior of networks with a large number of components. Several theories have been advanced about the evolution of large biological and engineering networks by authors in diversified disciplines like physics, mathematics, biology and computer science. Several networks exhibit a scale-free property in the sense that the probabilistic distribution of their nodes as a function of connections decreases slower than an exponential. These networks are characterized by the fact that a small number of components have a disproportionate influence on the performance of the network. Scale-free networks are tolerant to random failure of components, but are vulnerable to selective attack on components. This paper examines two network representations for the baseline air traffic system. A network defined with the 40 major airports as nodes and with standard flight routes as links has a characteristic scale: all nodes have 60 or more links and no node has more than 460 links. Another network is defined with baseline aircraft routing structure exhibits an exponentially truncated scale-free behavior. Its degree ranges from 2 connections to 2900 connections, and 225 nodes have more than 250 connections. Furthermore, those high-degree nodes are homogeneously distributed in the airspace. A consequence of this scale-free behavior is that the random loss of a single node has little impact, but the loss of multiple high-degree nodes (such as occurs during major storms in busy airspace) can adversely impact the system. Two future scenarios of air traffic growth are used to predict the growth of air traffic in the United States. It is shown that a three-times growth in the overall traffic may result in a ten-times impact on the density of traffic in certain parts of the United States.

Scale-free Networks↗

NASA NTRS1980

A model of plant canopy polarization

A model for the amount of linearly polarized light reflected by the shiny leaves of grain crops is based on the morphological and phenological characteristics of the plant canopy and upon the Fresnel equations which describe the light reflection process at the smooth boundary separating two dielectrics. The theory used demonstrates that, potentially, measurements of the linearly polarized light from a crop canopy may be used as an additional feature to discriminate between crops such as wheat and barley, two crops which are so spectrally similar that they are misclassified with unacceptable frequency. Examination of the model suggests that, potentially, satellite polarization measurements may be used to monitor crop development stage, leaf water content, leaf area index, hail damage, and certain plant diseases. The information content of these measurements is needed to evaluate the proposed polarization sensor for the satellite-borne multispectral resource sampler.

Vanderbilt, V. C.↗

NASA NTRS1994

Building brains for bodies

We describe a project to capitalize on newly available levels of computational resources in order to understand human cognition. We will build an integrated physical system including vision, sound input and output, and dextrous manipulation, all controlled by a continuously operating large scale parallel MIMD computer. The resulting system will learn to 'think' by building on its bodily experiences to accomplish progressively more abstract tasks. Past experience suggests that in attempting to build such an integrated system we will have to fundamentally change the way artificial intelligence, cognitive science, linguistics, and philosophy think about the organization of intelligence. We expect to be able to better reconcile the theories that will be developed with current work in neuroscience.

Brooks, Rodney Allen↗

NASA NTRS1996

Induction as Knowledge Integration

Two key issues for induction algorithms are the accuracy of the learned hypothesis and the computational resources consumed in inducing that hypothesis. One of the most promising ways to improve performance along both dimensions is to make use of additional knowledge. Multi-strategy learning algorithms tackle this problem by employing several strategies for handling different kinds of knowledge in different ways. However, integrating knowledge into an induction algorithm can be difficult when the new knowledge differs significantly from the knowledge the algorithm already uses. In many cases the algorithm must be rewritten. This paper presents Knowledge Integration framework for Induction (KII), a KII, that provides a uniform mechanism for integrating knowledge into induction. In theory, arbitrary knowledge can be integrated with this mechanism, but in practice the knowledge representation language determines both the knowledge that can be integrated, and the costs of integration and induction. By instantiating KII with various set representations, algorithms can be generated at different trade-off points along these dimensions. One instantiation of KII, called RS-KII, is presented that can implement hybrid induction algorithms, depending on which knowledge it utilizes. RS-KII is demonstrated to implement AQ-11, as well as a hybrid algorithm that utilizes a domain theory and noisy examples. Other algorithms are also possible.

Smith, Benjamin D.↗

NASA NTRS2023

Broader Impacts and Outreach Videos on Ocean Physics and Biogeochemistry

This is just a preliminary NF1676 in advance of filming for a project....A convergent team of experts in biology, chemistry, physics, engineering, mathematics, and computational modeling examine how dynamic and coupled phytoplankton-pathogen-particle-predator linkages coalesce to explain the observed high spatial variability in the efficiency of the export of particulate organic carbon (POC) to the deep ocean. They elucidate and quantify the linkages between viruses and ballast minerals to increase understanding of carbon cycling in the oceanic biological carbon pump and the impact of viruses within it. By providing knowledge than can be used to improve the parameterization of carbon export in Earth system models, the project will help reduce uncertainty in regional marine biogeochemical projections, potentially improving marine ecosystem and fisheries management on timescales from seasons to decades. The project includes activities that provide teaching resources and hands-on training to educators within a ‘Tools of Science’ program that provides a simple and succinct way to communicate the process of scientific research to students in a way that is useful to teachers. The project couples laboratory-based experiments on model host-virus-grazer systems with extensive field based observational and manipulative studies on natural populations of diatoms and coccolithophores, the two phytoplankton groups that account for most of the estimated particulate organic matter flux to the deep ocean. Experiments and measurements integrate diagnostic biological and chemical controls on infection and particle coagulation theory with microscale physics and grazing to quantify links to each hypothesized export mechanism under field-relevant turbulent conditions. Cutting-edge engineering and analytical tools are used to diagnose and track infection dynamics while characterizing and quantifying particle aggregation and disaggregation, mineral dissolution, sinking dynamics, grazing rates, and fecal pellet production at unprecedented resolution and under well-defined, microscale physical regimes. Field campaigns elucidate the relative efficiency of hypothesized mechanisms in stimulating POC export in natural blooms, while providing bulk and size-resolved estimates of POC flux.

Daniel B Whitt↗

NASA NTRS1995

The role and status of Euler solvers in impulsive rotor noise computations

Several recent applications (in the last five years) of Euler solvers in the computation of impulsive noise from rotor blades emphasize their emerging role in complementing other methods and experimental work. In the area of high-speed impulsive noise the use of Euler solvers as research tools has become fairly mature with very favorable comparisons with experimental data, especially in hover. The grid sizes and resulting computational times are reasonable when compared to those required for accurate surface aerodynamics alone. Furthermore, Euler solvers have provided a rich database with the resolution and accuracy needed for input to Kirchhoff and acoustic analogy methods for predicting the far-field noise. On the other hand, the application of Euler solvers to calculate blade-vortex interaction noise is still far from mature. The computational resources required for accurate calculations away from the blade are much larger than for high-speed impulsive noise. Current calculations help improve the basic understanding of the phenomena involved, but to date no comparisons with experiment have been made. Fortunately, the use of coupled Euler solver/Kirchhoff methods seems to offer promise for a robust and efficient technique for predicting both high-speed impulsive noise and blade-vortex interaction noise. Finally, a simple model problem of an isolated vortex interacting with an arbitrarily prescribed pitching airfoil demonstrates the feasibility of using Euler solvers to examine noise reduction techniques. The use of simple aerodynamic quasi-static theory and the computed lift time history as feedback to determine the required pitching motion appears sufficient to significantly dampen the unsteady loading and subsequent acoustics by an order of magnitude within a few blade passages.

Baeder, James D.↗

NASA NTRS2009

Prominence Structure and Dynamics

Nonerupting prominences are not dull, static objects. Rather, they are composed of fine-scale blobs and threads that are highly dynamic, often appearing to travel in opposite directions on adjacent tracks (denoted counterstreaming). Because the plasma is largely constrained to travel along the magnetic field, these cool, dense features can serve as tracers of the prominence magnetic structure, a valuable resource in view of the long-standing difficulty of observing the coronal field. Conversely, greater understanding of the fundamental magnetic geometry of filament channels can provide important constraints on the physical processes governing the accumulation, support, motion, and eruption of the cool plasma. Despite over a century of detailed observations, large gaps remain in our knowledge of filament channel/plasma formation and evolution. Resolving these issues will shed light on the physics of coronal heating, helicity transport throughout the solar cycle, and the origins of eruptive activity on the Sun. I will discuss the leading models for the magnetic and plasma structure, and outline how new observations and theory /modeling could solve long-standing uncertainties regarding this majestic solar phenomenon.

Karpen, Judy T.↗

NASA NTRSDate not supplied

Preliminary Steps in Developing Rapid Aero Modeling Technology

The Rapid Aero Modeling (RAM) approach is a method to efficiently and automatically obtain aerodynamic models during testing, significantly saving time and resources. Motivation for this technology results from demand for experimental efficiency and model fidelity that has increased with growing aircraft complexity and aerodynamic nonlinearities. These issues are typical in the responses presented by a class of vehicles categorized as Urban Air Mobility aircraft where many features from both airplane and rotorcraft are present. For UAM configurations, with typically many more factors than conventional aircraft, traditional test methods can lead to increased costs and missed interactions. RAM guides the test to obtain high-fidelity, statistically rigorous aircraft models, and the approach is applicable to computational, ground, or flight-test experiments. It combines concepts from Design of Experiment theory and Aircraft System Identification theory that allow the user the freedom to choose, in advance of the test, a specific level of fidelity typically, in terms of prediction error. RAM only collects data required to meet the user-specified fidelity and fidelity is only limited by the facility and test article capabilities. An initial wind tunnel test to support development of RAM was conducted to assess potential metrics, algorithms, and procedures. This paper presents results from initial tests for the development of RAM technology and highlights some of the unique features of RAM applied toa conventional configuration during a ground-based, static, wind-tunnel test.

Patrick C Murphy↗

NASA NTRS1981

Biomass measurement from LANDSAT: Drought and energy applications

The theory supporting the use of vegetation indices derived from LANDSAT data for the direct measurement of biomass is reviewed. The use of multispectral data to measure biomass is a natural and viable application since the photosynthetic production of biomass gives vegetation its unique spectral properties. Vegetation indices also perform a normalization function which tends to make them insensitive to atmospheric and soil color variations. Optical and digital LANDSAT products are discussed relative to the use of vegetation indices to monitor drought impact. Based on results obtained in Colorado, operational use of LANDSAT to monitor drought is cost effective, practical and ready for implementation today. The direct measurement of biomass energy resources may also benefit from LANDSAT technology. Measurement of total biomass and annual primary production may be feasible. Identification of that component of biomass resources available for energy use will require other sources of information, however.

Maxwell, E. L.↗

NASA NTRS1997

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Baysal, Oktay↗

NASA NTRS1994

High speed civil transport: Sonic boom softening and aerodynamic optimization

An improvement in sonic boom extrapolation techniques has been the desire of aerospace designers for years. This is because the linear acoustic theory developed in the 60's is incapable of predicting the nonlinear phenomenon of shock wave propagation. On the other hand, CFD techniques are too computationally expensive to employ on sonic boom problems. Therefore, this research focused on the development of a fast and accurate sonic boom extrapolation method that solves the Euler equations for axisymmetric flow. This new technique has brought the sonic boom extrapolation techniques up to the standards of the 90's. Parallel computing is a fast growing subject in the field of computer science because of its promising speed. A new optimizer (IIOWA) for the parallel computing environment has been developed and tested for aerodynamic drag minimization. This is a promising method for CFD optimization making use of the computational resources of workstations, which unlike supercomputers can spend most of their time idle. Finally, the OAW concept is attractive because of its overall theoretical performance. In order to fully understand the concept, a wind-tunnel model was built and is currently being tested at NASA Ames Research Center. The CFD calculations performed under this cooperative agreement helped to identify the problem of the flow separation, and also aided the design by optimizing the wing deflection for roll trim.

Cheung, Samson↗

NASA NTRS1996

Ra: The Sun for Science and Humanity

To guide the development of the Ra Strategic Framework, we defined scientific and applications objectives. For our primary areas of scientific interest, we choose the corona, the solar wind, the Sun's effect on the Earth, and solar theory and model development. For secondary areas of scientific interest, we selected sunspots, the solar constant, the Sun's gravitational field, helioseismology and the galactic cosmic rays. We stress the importance of stereoscopic imaging, observations at high spatial, spectral, and temporal resolutions, as well as of long duration measurements. Further exploration of the Sun's polar regions is also important, as shown already by the Ulysses mission. From an applications perspective, we adopted three broad objectives that would derive complementary inputs for the Strategic Framework. These were to identify and investigate: possible application spin-offs from science missions, possible solar-terrestrial missions dedicated to a particular application, and possible future applications that require technology development. The Sun can be viewed as both a source of resources and of threats. Our principal applications focus was that of threat mitigation, by examining ways to improve solar threat monitoring and early warning systems. We compared these objectives to the mission objectives of past, current, and planned international solar missions. Past missions (1962-1980) seem to have been focused on improvement of scientific knowledge, using multiple instrument spacecraft. A ten year gap followed this period, during which the results from previous missions were analyzed and solar study programmes were prepared in international organizations. Current missions (1990-1996) focus on particular topics such as the corona, solar flares, and coronal mass ejections. In planned missions, Sun/Earth interactions and environmental effects of solar activity are becoming more important. The corona is the centre of interest of almost all planned missions. It seems that no international long-term strategy has yet been adopted. For these plans the number of necessary future missions can be reduced and the onboard instrumentation can be optimized by performing a comparative analysis. The study of the corona must be done from different observing locations, orbits closer to the Sun, and by different means. The Cluster mission replacement is in progress; however, if the replacement is not implemented, the ISTP programme will fade after 1998. Furthermore, the physics of the Sun's interior should be emphasized more in the Mid- and Far-Term programmes. Finally, more emphasis should be placed on monitoring space weather and forecasting Sun/Earth interactions.

Source record↗

NASA NTRS1989

Development of a funding, cost, and spending model for satellite projects

The need for a predictive budget/funging model is obvious. The current models used by the Resource Analysis Office (RAO) are used to predict the total costs of satellite projects. An effort to extend the modeling capabilities from total budget analysis to total budget and budget outlays over time analysis was conducted. A statistical based and data driven methodology was used to derive and develop the model. Th budget data for the last 18 GSFC-sponsored satellite projects were analyzed and used to build a funding model which would describe the historical spending patterns. This raw data consisted of dollars spent in that specific year and their 1989 dollar equivalent. This data was converted to the standard format used by the RAO group and placed in a database. A simple statistical analysis was performed to calculate the gross statistics associated with project length and project cost ant the conditional statistics on project length and project cost. The modeling approach used is derived form the theory of embedded statistics which states that properly analyzed data will produce the underlying generating function. The process of funding large scale projects over extended periods of time is described by Life Cycle Cost Models (LCCM). The data was analyzed to find a model in the generic form of a LCCM. The model developed is based on a Weibull function whose parameters are found by both nonlinear optimization and nonlinear regression. In order to use this model it is necessary to transform the problem from a dollar/time space to a percentage of total budget/time space. This transformation is equivalent to moving to a probability space. By using the basic rules of probability, the validity of both the optimization and the regression steps are insured. This statistically significant model is then integrated and inverted. The resulting output represents a project schedule which relates the amount of money spent to the percentage of project completion.

Johnson, Jesse P.↗