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At least 1,657 records · Page 92

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗

Development and testing of improved statistical wind power forecasting methods.

Wind power forecasting (WPF) provides important inputs to power system operators and electricity market participants. It is therefore not surprising that WPF has attracted increasing interest within the electric power industry. In this report, we document our research on improving statistical WPF algorithms for point, uncertainty, and ramp forecasting. Below, we provide a brief introduction to the research presented in the following chapters. For a detailed overview of the state-of-the-art in wind power forecasting, we refer to [1]. Our related work on the application of WPF in operational decisions is documented in [2]. Point forecasts of wind power are highly dependent on the training criteria used in the statistical algorithms that are used to convert weather forecasts and observational data to a power forecast. In Chapter 2, we explore the application of information theoretic learning (ITL) as opposed to the classical minimum square error (MSE) criterion for point forecasting. In contrast to the MSE criterion, ITL criteria do not assume a Gaussian distribution of the forecasting errors. We investigate to what extent ITL criteria yield better results. In addition, we analyze time-adaptive training algorithms and how they enable WPF algorithms to cope with non-stationary data and, thus, to adapt to new situations without requiring additional offline training of the model. We test the new point forecasting algorithms on two wind farms located in the U.S. Midwest. Although there have been advancements in deterministic WPF, a single-valued forecast cannot provide information on the dispersion of observations around the predicted value. We argue that it is essential to generate, together with (or as an alternative to) point forecasts, a representation of the wind power uncertainty. Wind power uncertainty representation can take the form of probabilistic forecasts (e.g., probability density function, quantiles), risk indices (e.g., prediction risk index) or scenarios (with spatial and/or temporal dependence). Statistical approaches to uncertainty forecasting basically consist of estimating the uncertainty based on observed forecasting errors. Quantile regression (QR) is currently a commonly used approach in uncertainty forecasting. In Chapter 3, we propose new statistical approaches to the uncertainty estimation problem by employing kernel density forecast (KDF) methods. We use two estimators in both offline and time-adaptive modes, namely, the Nadaraya-Watson (NW) and Quantilecopula (QC) estimators. We conduct detailed tests of the new approaches using QR as a benchmark. One of the major issues in wind power generation are sudden and large changes of wind power output over a short period of time, namely ramping events. In Chapter 4, we perform a comparative study of existing definitions and methodologies for ramp forecasting. We also introduce a new probabilistic method for ramp event detection. The method starts with a stochastic algorithm that generates wind power scenarios, which are passed through a high-pass filter for ramp detection and estimation of the likelihood of ramp events to happen. The report is organized as follows: Chapter 2 presents the results of the application of ITL training criteria to deterministic WPF; Chapter 3 reports the study on probabilistic WPF, including new contributions to wind power uncertainty forecasting; Chapter 4 presents a new method to predict and visualize ramp events, comparing it with state-of-the-art methodologies; Chapter 5 briefly summarizes the main findings and contributions of this report.

17 WIND ENERGY↗

Enhancements to Engineering-scale Reactor Pressure Vessel Fracture Capabilities in Grizzly

The Grizzly code is being developed to model the effect of aging in nuclear power plant systems, components, and structures. A significant part of this effort has been to develop capabilites to model the effects of embrittlement in reactor pressure vessels on their integrity. This includes both modeling of microstructure and engineering property evolution, and engineering-scale probabilistic fracture mechanics analysis. This report documents recent advances to the engineering-scale fracture mechanics capability for evaluation of RPV integrity under transient loading in Grizzly. These developments are in three areas: probabilistic fracture mechanics, general reduced order models for fracture a flaw locations, and improvments to the XFEM capability used in Grizzly for fracture mechanics analysis. The combination of these developments brings Grizzly closer to a state where it can be applied in production as a general tool for engineering-scale fracture mechanics analysis. The probabilistic fracture mechanics capabilities are included in the 1.5 testing version of Grizzly, and will be further refined in preparation for production use in the 2.0 released planned for fiscal year 2018.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Probabalistic Modeling of Minibangs and Megabands (Final Report)

This project was original proposed as a fundamental advance in the treatment of probabilistic modeling as it applies to nuclear fission calculations of nuclear database inputs and produced particle distributions in heavy-ion collisions. However, funding decisions made within LLNL and the DOE Office of Science led to the project proceeding through three distinct stages. The first two, probabilistic calculations of the fission and jet energy loss relate follow directly from the proposed research. The fission task led to the development of a proof-of-principle Gaussian Process Emulator for time-dependent generator coordinate method (TDGCM) calculation for the fission of Pu-240. To study energy loss in heavy-ion collisions with a probabilistic model, we generated a training data set using the Pythia event generator superimposed on a heavy-ion background with a single quench-factor parameter. We then used kernel density estimation (KDE) to recover the distribution of quench-factors for a calibration data set. In the third stage, we proceeded to work through collaborations, collecting new data within the ATLAS experiment at the Large Hadron Collider (LHC), and further developing bayesian methodology within the Jet Energy-loss Tomography with a Statistically and Computationally Advanced Program Envelope (JETSCAPE) Collaboration.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Multi-Mechanism Flood Hazard Assessment: Critical Review of Current Practice and Approaches

This report documents the initial findings from the Nuclear Regulatory commission (NRC)-sponsored research project Methods for Estimating Joint Probabilities of Coincident and Correlated Flooding Mechanisms for Nuclear Power Plant Flood Hazard Assessments.1 This research project is a part of NRC’s Probabilistic Flood Hazard Assessment (PFHA) Research Program and will aid the development of guidance on the use of PFHA methods to evaluate infrastructure safety for existing and proposed US nuclear power plants (NPPs). More specifically, this project intends to provide technical background for the development of flood hazard curves for multi-mechanism floods (MMFs). MMFs are flood events caused by more than one flooding mechanism (e.g., flood events due to the simultaneous occurrence of precipitation-induced river flooding and storm surge). Project activities include three main tasks: Task 1—Survey of current concepts and methods in assessing MMF hazards; Task 2—Critical assessment of selected methods and approaches for quantifying probabilistic MMF hazard risk; Task 3—Development of example case studies to illustrate best practices for quantifying probabilistic MMF hazard risk The initial findings from Tasks 1 and 2 are documented in this report. Task 1 comprised a survey of approaches and methods that have been applied to understand and assess flood hazards due to MMFs. Task 2 involved a critical review of the selected approaches and methods. To that end, the scope of this report includes documentation of (1) a reconnaissance-level survey of the current state of concepts and practice for MMF hazard assessment; (2) a generalized MMF assessment framework to address the distinctions among various types of flood-forcing phenomena, flood mechanisms (grouped into three mechanism types), and flood severity metrics; (3) a wide-ranging survey of approaches and methods that have been applied to various flooding phenomena and settings; and (4) a critical assessment of MMF hazard assessment methods. Studies were identified involving MMFs related to coastal flooding mechanisms, fluvial (rivers/streams) flooding mechanisms, and associated combinations of coastal and fluvial flooding mechanisms. Studies were also identified that address MMFs involving coastal and fluvial flooding mechanisms as well as coastal flooding mechanisms along with extreme precipitation (without specific attribution to fluvial or pluvial mechanisms). The studies identified for review in this report included assessments at varying spatial scales (from local to global) with differing geographic regions of focus using both observed and synthetic data. The majority of studies identified and reviewed were site-specific assessments focusing on relatively short return periods. Studies considered a range of flood severity metrics, made differing assumptions regarding the occurrence of extrema, and used multiple statistical techniques; the use of copulas for the development of joint distributions was a particularly popular analysis technique. The literature review highlighted the differences among existing studies relative to terminology used, means of presenting results, framework and techniques employed, and level of sophistication regarding the number and types of variables considered. Despite the significant diversity in existing studies, the review identified several promising techniques that will be considered in future work under this project, including the development of joint distributions for MMFs using copula and Bayesian-motivated approaches.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Final Report on Development of Microwave Resonant Cavity Transducer for Fluid Flow Sensing: Development of Microwave Cavity Flow Meter for Advanced Reactor High Temperature Fluids

We are investigating a microwave resonant cavity transducer for flow sensing in the vessel of a high temperature fluid advanced reactor (AR), such as a molten salt cooled reactor (MSCR) or a sodium fast reactor (SFR). This transducer is a hollow metallic cylindrical cavity, with one of the flat walls of the cylinder flexible enough to undergo microscopic deflection due to dynamic fluid pressure. Membrane deflection leads to a shift in the microwave resonant frequency, which can be detected with a spectrum analyzer. We have developed a continuum electromechanics model of the microwave resonant cavity transducer performance. The deflection of the membrane is calculated using equations from the theory of plates and shells for deflection of radially constrained thin circular disk under uniform load. The microwave frequency shift is calculated using the equations from the microwave cavity perturbation theory. The transducer model was validated with proof-of-concept experimental data of water flow sensing with a Brass 360 right circular cylinder with 22.2mm diameter and 203µm thick wall. The cavity was excited through a subwavelength hole in TE 011 mode with resonant frequency f ≈ 17.8GHz. Subsequently, we have performed a preliminary proof-of-principle test of flow sensing in high temperature liquid sodium in environment. For this test, we have developed a cylindrical resonator with the same dimensions as for the Brass 360 cavity. The resonator for high temperature liquid sodium test was machined from stainless steel 316 and electroplated with silver on the interior surfaces. We have also developed and insertion probe consisting of a 50cm WR-42 brass waveguide enclosed in a protective SS316 tube. The cavity was excited through a subwavelength hole on the side of the wall of the cylinder in the TE 011 mode with resonant frequency f ≈ 17.8GHz. The liquid sodium setup consists of a cylindrical vessel with a center feed line, where a transducer inserted through the top cap of the vessel measures velocity of the impinging liquid jet. The sodium flow sensing study was performed in a liquid sodium vessel at 340°C temperature and ambient pressure. The flow rate was changed by varying sodium pump power, and a frequency shift of several hundred kHz was observed. The transducer was removed after 70 days of testing. No visual damage was observed, and the electromagnetic response remained the same. As a calibration experiment, we have assembled a water vessel with a center feed, and with dimensions similar to those of the liquid sodium setup. Water flow sensing was performed before and after liquid sodium test. The responses in both cases are similar and agree with COMSOL computer simulations. Because long-term (multi-year) experimental tests of transducer resilience to harsh environment are not practical, we have developed a probabilistic model of creep to estimate transducer resilience to the harsh environment. The probabilistic model considers diffusion creep under the condition of high temperature and low stress, where the stress and temperature are allowed to be random variables with Gaussian distributions. Using the probabilistic model, we estimate inelastic membrane deflections due to creep for several temperature ranges. We conclude that for temperatures less than 650°C, creep has negligible long-term effect on the transducer performance.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Assessing Uncertainty in Modeling Stress Corrosion Cracking

This report summarizes the collaboration between Sandia National Laboratories (SNL) and the Nuclear Regulatory Commission (NRC) to improve the state of knowledge on chloride induced stress corrosion cracking (CISCC). The foundation of this work relied on using SNL’s CISCC computer code to assess the current state of knowledge for probabilistically modeling CISCC on stainless steel canisters. This work is presented as three tasks. The first task is exploring and independently comparing crack growth rate (CGR) models typically used in CISCC modeling by the research community. The second task is implementing two of the more conservative CGR models from the first task into SNL’s full CISCC code to understand the impact of the different CGR models on a full probabilistic analysis while studying uncertainty from three key input parameters. The combined work of the first two tasks showed that properly measuring salt deposition rates is impactful to reducing uncertainty when modeling CISCC. The work in Task 2 also showed how probabilistic CGR models can be more appropriate at capturing aleatory uncertainty when modeling SCC. Lastly, appropriate and realistic input parameters relevant for CISCC modeling were documented in the last task as a product of the simulations considered in the first two tasks.

36 MATERIALS SCIENCE↗

Solar and Storage Integration in the U.S. Southeast: Implications for Resource Adequacy

Resource adequacy concerns may be very different in electricity systems that have higher levels of solar and storage, requiring changes to existing planning models. This study explores a novel approach to evaluating resource adequacy under future scenarios with higher solar and storage in the Southeast U.S. It uses NREL’s Probabilistic Resource Adequacy Suite (PRAS), a collection of probabilistic resource adequacy modeling tools, and compares results when interacting PRAS and a portfolio planning tool with a more traditional modeling approach. The results suggest that traditional models perform reasonably well with lower levels of solar PV, but at higher levels of solar probabilistic tools better capture the changes in resource adequacy concerns—such as winter energy availability—associated with higher solar systems. This is the final study in the Preparing Southeast Markets for Reliable and Affordable Integration of Solar into Operations and Planning project. Two prior reports can be found at: Solar and Storage Integration in the Southeastern United States: Economics, Reliability, and Operations. https://emp.lbl.gov/publications/solar-and-storage-integration Solar and Wind Forecast Error Reserve Sharing in a Multi-Utility Region. https://eta-publications.lbl.gov/sites/default/files/2024-11/multiutility_fe_reserve_sharing_final.pdf

14 SOLAR ENERGY↗

The Photometric LSST Astronomical Time-series Classification Challenge PLAsTiCC: Selection of a Performance Metric for Classification Probabilities Balancing Diverse Science Goals

Classification of transient and variable light curves is an essential step in using astronomical observations to develop an understanding of the underlying physical processes from which they arise. However, upcoming deep photometric surveys, including the Large Synoptic Survey Telescope (LSST), will produce a deluge of low signal-to-noise data for which traditional type estimation procedures are inappropriate. Probabilistic classification is more appropriate for such data but is incompatible with the traditional metrics used on deterministic classifications. Furthermore, large survey collaborations like LSST intend to use the resulting classification probabilities for diverse science objectives, indicating a need for a metric that balances a variety of goals. We describe the process used to develop an optimal performance metric for an open classification challenge that seeks to identify probabilistic classifiers that can serve many scientific interests. The Photometric LSST Astronomical Time-series Classification Challenge (PLASTICC) aims to identify promising techniques for obtaining classification probabilities of transient and variable objects by engaging a broader community beyond astronomy. Using mock classification probability submissions emulating realistically complex archetypes of those anticipated of PLASTICC, we compare the sensitivity of two metrics of classification probabilities under various weighting schemes, finding that both yield results that are qualitatively consistent with intuitive notions of classification performance. We thus choose as a metric for PLASTICC a weighted modification of the cross-entropy because it can be meaningfully interpreted in terms of information content. Finally, we propose extensions of our methodology to ever more complex challenge goals and suggest some guiding principles for approaching the choice of a metric of probabilistic data products.

79 ASTRONOMY AND ASTROPHYSICS↗

Assessing Photovoltaic Capacity Factor Variability Using Long-Term Satellite Derived Solar Resource Data Under Brazilian Climate

Accurate estimation of photovoltaic (PV) energy yield and its variability is essential for reducing financial risk and supporting reliable system planning for rapidly expanding PV markets. In Brazil, high solar adoption and increasing levels of distributed energy resources are beginning to introduce operational challenges such as curtailment and evolving grid requirements. Understanding how natural variability in solar resource propagates into PV system performance is therefore increasingly important for both project design and grid integration. Modern PV yield assessments commonly rely on multi-year meteorological datasets and probabilistic exceedance metrics (e.g., P50/P90) to quantify energy yield uncertainty for project financing. However, the implications of long-term solar resource variability for PV system design choices and high-adoption grid conditions remain less well characterized for rapidly expanding markets such as Brazil. In particular, understanding how weather-driven variability propagates into PV production distributions and capacity factor expectations is important for evaluating curtailment exposure, deployment strategies, and storage requirements in regions experiencing rapid growth of distributed and utility-scale PV. Seasonal and interannual variability in atmospheric conditions can produce substantial fluctuations in monthly PV energy production, which propagate into uncertainty in annual energy yield and capacity factor expectations. Characterizing this variability using long-term meteorological datasets allows probabilistic estimation of PV system performance and provides improved insight into the range of expected PV energy outcomes. This study explores the use of long-term satellite-derived meteorological data from the National Solar Radiation Database (NSRDB) to evaluate the variability of photovoltaic system performance across multiple locations in Brazil. Using a 27-year dataset (1998-2024), PV system simulations are performed to characterize the distribution of annual and seasonal capacity factors and energy yield outcomes, while propagating key sources of meteorological variability and model uncertainty through the PV modeling chain. The analysis also investigates the sensitivity of PV performance outcomes to key system design assumptions within the PV modeling chain, including tracking configuration and system sizing parameters. The resulting probabilistic performance characterization provides insight into how weather-driven variability influences PV production expectations and capacity factor distributions. These results provide a foundation for evaluating how weather-driven variability interacts with high PV adoption and potential storage or curtailment mitigation strategies.

14 SOLAR ENERGY↗

An urnful of blinding functions

There is a fundamental connection between the mathematical theory of discrete probability distributions and the parametric curves and surfaces of computer-aided geometric design. It is no accident that the blending functions of Bezier curves and surfaces have an obvious probabilistic interpretation, nor is it a coincidence that the normalized uniform B-spline basis functions also model a simple stochastic process. The link between probability and geometry, and how to exploit simple probabilistic arguments to derive many of the classical geometric properties of the parametric curves and surfaces currently in vogue in computer-aided geometric design is discussed. This probabilistic approach is also used to introduce many new types of curves and surfaces, and it is demonstrated how probability theory can be used to simplify, unify, and generalize many well-known results.

Goldman, R. N.↗

Composite load spectra for select space propulsion structural components

A multiyear program is performed with the objective to develop generic load models with multiple levels of progressive sophistication to simulate the composite (combined) load spectra that are induced in space propulsion system components, representative of Space Shuttle Main Engines (SSME), such as transfer ducts, turbine blades, and liquid oxygen (LOX) posts. Progress of the first year's effort includes completion of a sufficient portion of each task -- probabilistic models, code development, validation, and an initial operational code. This code has from its inception an expert system philosophy that could be added to throughout the program and in the future. The initial operational code is only applicable to turbine blade type loadings. The probabilistic model included in the operational code has fitting routines for loads that utilize a modified Discrete Probabilistic Distribution termed RASCAL, a barrier crossing method and a Monte Carlo method. An initial load model was developed by Battelle that is currently used for the slowly varying duty cycle type loading. The intent is to use the model and related codes essentially in the current form for all loads that are based on measured or calculated data that have followed a slowly varying profile.

Newell, J. F.↗

Management of SSME hardware life utilization

Statistical and probabilistic reliability methodologies were developed for the determination of hardware life limits for the Space Shuttle Main Engine (SSME). Both methodologies require that a mathematical reliability model of the engine (system) performance be developed as a function of the reliabilities of the components and parts. The system reliability model should be developed from the Failute Modes and Effects Analysis/Critical Items List. The statistical reliability methodology establishes hardware life limits directly from the failure distributions of the components and parts obtained from statistically-designed testing. The probabilistic reliability methodology establishes hardware life limits from a decision analysis methodology which incorporates the component/part reliabilities obtained from a probabilistic structural analysis, a calibrated maintenance program, inspection techniques, and fabrication procedures. Probilistic structural analysis is recommended as a tool to prioritize upgrading of the components and parts. The Weibull probability distribution is presently being investigated by NASA/MSFC to characterize the failure distribution of the SSME hardware from a limited data base of failures.

Pauschke, J. M.↗

The NESSUS finite element code

The objective of this development is to provide a new analysis tool which integrates the structural modeling versatility of a modern finite element code with the latest advances in the area of probabilistic modeling and structural reliability. Version 2.0 of the NESSUS finite element code was released last February, and is currently being exercised on a set of problems which are representative of typical Space Shuttle Main Engine (SSME) applications. NESSUS 2.0 allows linear elastostatic and eigenvalue analysis of structures with uncertain geometry, material properties and boundary conditions, which are subjected to a random mechanical and thermal loading environment. The NESSUS finite element code is a key component in a broader software system consisting of five major modules. NESSUS/EXPERT is an expert system under development at Southwest Research Institute, with the objective of centralizing all component-specific knowledge useful for conducting probabilistic analysis of typical Space Shuttle Main Engine (SSME) components. NESSUS/FEM contains the finite element code used for the structural analysis and parameter sensitivity evaluation of these components. The task of parametrizing a finite element mesh in terms of the random variables present is facilitated with the use of the probabilistic data preprocessor in NESSUS/PRE. An external database file is used for managing the bulk of the data generated by NESSUS/FEM.

Dias, J. B.↗

Probability of Failure and Risk Assessment of Propulsion Structural Components

Due to increasing need to account for the uncertainties in material properties, loading conditions, or geometries, a methodology was developed to determine structural reliability and the assess the risk associated with it. The methodology consists of a probabilistic structural analysis by a probabilistic finite element computer code Nonlinear Evaluation of Stochastic Structures Under Stress (NESSUS) and a generic probabilistic material properties model. The methodology is versatile and is equally applicable to high and cryogenic temperature structures. Results obtained demonstrate that the whole issue of structural reliability and risk can be formally evaluated using the methodology developed which is inclusive of uncertainties in material properties, structural parameters and loading conditions. The methodology is described in some detail with illustrative examples.

Shiao, Michael C.↗

Probability of failure and risk assessment of propulsion structural components

The probabilistic structural analysis method (PSAM) was developed to analyze the effects of fluctuating loads, variable material properties, and uncertain analytical models especially for high performance structures such as the Space Shuttle Main Engine turbopump blades. Risk is calculated after expensive service experience. However, probabilistic structural analysis provides a rational alternative method to quantify uncertainties in the structural performance and durability. NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a probabilistic structural analysis computer code which integrates finite element methods and reliability algorithms, capable to predicting the probability distributions of structural response variables such as stress, displacement, natural frequencies, and buckling loads. This computer code is detailed.

Shiao, Michael C.↗

Probability of failure and risk assessment of propulsion structural components

Because of the increasing need to account for the uncertainties in material properties, loading conditions, geometry, etc., a methodology was developed to determine structural reliability and to assess the associated risk. The methodology consists of a probabilistic structural analysis by a probabilistic finite element computer code, numerical evaluation of stochastic structures under stress (NESSUS), and a generic probabilistic material property model. The methodology is versatile and is equally applicable to structures operating at high and cryogenic temperature environments. Results obtained demonstrate that the issues of structural reliability and risk can be formally evaluated by using the methodology developed which is inclusive of the uncertainties in material properties, structural parameters, and loading conditions. The methodology is described in some detail with illustrative examples.

Shiao, Michael C.↗

Composite load spectra for select space propulsion structural components

The objective of this program is to develop generic load models with multiple levels of progressive sophistication to simulate the composite load spectra that are induced in space propulsion system components, representative of Space Shuttle Main Engines (SSME), such as transfer ducts, turbine blades, and liquid oxygen (LOX) posts and system ducting. These models will be developed using two independent approaches. The first approach consists of using state-of-the-art probabilistic methods to describe the individual loading conditions and combinations of these loading conditions to synthesize the composite load spectra simulation. The methodology required to combine the various individual load simulation models (hot-gas dynamic, vibrations, instantaneous position, centrifugal field, etc.) into composite load spectra simulation models will be developed under this program. A computer code incorporating the various individual and composite load spectra models will be developed to construct the specific load model desired. The second approach, which is covered under the options portion of the contract, will consist of developing coupled models for composite load spectra simulation which combine the (deterministic) models for composite load dynamic, acoustic, high-pressure and high rotational speed, etc., load simulation using statistically varying coefficients. These coefficients will then be determined using advanced probabilistic simulation methods with and without strategically selected experimental data. This report covers the efforts of the third year of the contract. The overall program status is that the turbine blade loads have been completed and implemented. The transfer duct loads are defined and are being implemented. The thermal loads for all components are defined and coding is being developed. A dynamic pressure load model is under development. The parallel work on the probabilistic methodology is essentially completed. The overall effort is being integrated in an expert system code specifically developed for this project.

Newell, J. F.↗