Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “probabilistic”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

A probabilistic graphical model based stochastic input model construction

Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Probabilistic Context Neighborhood model for lattices

Here we present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov random field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable order, depending on the neighbors’ values. Our model extends the Probabilistic Context Tree model, originally applicable to one-dimensional space. It retains advantageous properties, such as representing the dependence neighborhood structure as a graph in a tree format, facilitating an understanding of model complexity. Furthermore, we adapt the algorithm used to estimate the Probabilistic Context Tree to estimate the parameters of the proposed model. We illustrate the accuracy of our estimation methodology through simulation studies. Additionally, we apply the Probabilistic Context Neighborhood model to spatial real-world data, showcasing its practical utility.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Operating Dynamic Reserve Dimensioning Using Probabilistic Forecasts

The rapid integration of variable energy sources (VRES) into power grids increases variability and uncertainty of the net demand, making the power system operation challenging. Operating reserve is used by system operators to manage and hedge against such variability and uncertainty. Traditionally, reserve requirements are determined by rules-of-thumb (static reserve requirements, e.g., NERC Reliability Standards), and more recently, dynamic reserve requirements from tools and methods which are in the adoption process (e.g., DynADOR, DRD, and RESERVE, among others). While these methods/tools significantly improve the static rule-of-thumb approaches, they rely exclusively on deterministic data (i.e., best guess only). Consequently, these methods disregard the probabilistic uncertainty thresholds associated with specific days and their weather conditions (i.e., best guess plus probabilistic uncertainty). This work presents practical approaches to determine the operating reserve requirements leveraging the wealth information from probabilistic forecasts. Proposed approaches are validated and tested using actual data from the CAISO system. Furthermore, results show the benefits in terms of risk reduction of considering the probabilistic forecast information into the dimensioning process of operating reserve requirements.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2014

Advanced probabilistic risk analysis using RAVEN and RELAP-7

RAVEN, under the support of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program [1], is advancing its capability to perform statistical analyses of stochastic dynamic systems. This is aligned with its mission to provide the tools needed by the Risk Informed Safety Margin Characterization (RISMC) path-lead [2] under the Department Of Energy (DOE) Light Water Reactor Sustainability program [3]. In particular this task is focused on the synergetic development with the RELAP-7 [4] code to advance the state of the art on the safety analysis of nuclear power plants (NPP). The investigation of the probabilistic evolution of accident scenarios for a complex system such as a nuclear power plant is not a trivial challenge. The complexity of the system to be modeled leads to demanding computational requirements even to simulate one of the many possible evolutions of an accident scenario (tens of CPU/hour). At the same time, the probabilistic analysis requires thousands of runs to investigate outcomes characterized by low probability and severe consequence (tail problem). The milestone reported in June of 2013 [5] described the capability of RAVEN to implement complex control logic and provide an adequate support for the exploration of the probabilistic space using a Monte Carlo sampling strategy. Unfortunately the Monte Carlo approach is ineffective with a problem of this complexity. In the following year of development, the RAVEN code has been extended with more sophisticated sampling strategies (grids, Latin Hypercube, and adaptive sampling). This milestone report illustrates the effectiveness of those methodologies in performing the assessment of the probability of core damage following the onset of a Station Black Out (SBO) situation in a boiling water reactor (BWR). The first part of the report provides an overview of the available probabilistic analysis capabilities, ranging from the different types of distributions available, possible sampling strategies, and post processing analysis capabilities. The first part of the report provides an extensive description of two major developments introduced this year: adaptive sampling for limit surface sampling and multi variate distributions. The document concludes with a description of the demo case (BWR-SBO) and a discussion of the results obtained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Probabilistic Failure Criterion of SiC/SiC Composites Under Multiaxial Loading

Owing to its excellent mechanical properties and stability under high temperature and neutron irradiation conditions, SiC/SiC composites have emerged as a promising material for light water reactors (LWRs) in the development of accident-tolerant fuel (ATF) systems. Structural integrity and retention of hermeticity are two crucial requirements for SiC/SiC claddings during normal operations, and both of them are closely related to the proportional limit stress (PLS) of the material. Understanding the behavior of SiC/SiC composites under multiaxial stress states and developing a probabilistic approach for evaluating the structural vulnerability are of paramount importance for reliability-based analysis and design of SiC/SiC composite claddings. So far, there has been very limited effort towards experimental and analytical investigations of probabilistic failure of SiC/SiC claddings. This critical knowledge gap motivates this research. A probabilistic failure criterion for SiC/SiC composites under multi-axial loading is developed, and this criterion is incorporated into reliability analysis of the structural integrity of SiC/SiC fuel cladding. The research consists of two parts: 1) experimental investigation of multiaxial failure behavior of SiC/SiC composites, and 2) theoretical modeling of time-dependent probabilistic failure of SiC/SiC cladding. In the experimental investigation, the PLS is determined through the examination of stress-strain response, the acoustic emission measurement, as well as the X-ray computed tomography. The theoretical framework is derived by combin- ing the finite weakest-link statistical model and the subcritical damage growth model. This theoretical model captures the time-dependent failure mechanism of the material, which has a major consequence for predicting the lifetime distribution of the cladding. Meanwhile, the model also predicts that the failure statistics of the cladding depends strongly on the cladding length. The results of the multiaxial experiments reveal the level of statistical variation of the PLS of SiC/SiC materials under different stress states. The theoretical model provides a robust analytical tool for extrapolation of small-scale laboratory test results to the behavior of full-scale claddings. These findings establish a scientific foundation for the development of reliability-based design of SiC/SiC fuel claddings, which will play an essential role in improving the structural safety and integrity of LWRs.

42 ENGINEERING↗
DOE OSTI2024

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Pro2R: Procurement of Ramping Product and Regulation in CAISO Using Probabilistic Solar Power Forecasts

This presentation summarizes the objectives and findings from the project titled, "Pro2R: Coordinated Procurement of Ramping Product & Regulation in CAISO Using Probabilistic Solar Power Forecasts," funded by DOE SETO. The goal is to develop cutting edge probabilistic solar power forecasting methods, and integrate them into ISO market operations. The team has integrated in two ways: 1) to procure ramping product and regulation requirements (ancillary services) in the California ISO market, and 2) to develop an open source visitation and ramp alert related situational awareness using probabilistic forecasts. This deck also summarizes the results from the use of machine learning methods to relate probabilistic solar forecasts to the the needs for flexible ramp product in the California ISO system.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2022

Use Probabilistic Forecasts in Reliable and Economic Electricity Market Scheduling and Operations

The value of probabilistic forecasts in electricity market operations is being increasingly recognized lately, however, the use is still limited. This study demonstrates two cases of using probabilistic forecasts in scheduling and operations of the California electricity market. We first develop a data-driven method to give weather-informed estimates of ramping reserves based on short-term probabilistic solar irradiance forecasts. By using forecasts across multiple sites, our proposed method presents advantages over the real-world baseline in terms of system reliability and economics. Our second case uses probabilistic hydro power forecasts in the scheduling of a hydro power plant under economic and environmental constraints. By optimizing the bids into both the day-ahead and real-time markets, our results demonstrate considerable economic benefits.

13 HYDRO ENERGY↗
DOE OSTI2019

Entropy-based closure for probabilistic learning on manifolds

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statistical sample generation is accomplished using a projected Itˆo stochastic differential equation. This probabilistic learning approach has been extended to polynomial chaos representation of databases on manifolds and to probabilistic nonconvex constrained optimization with a fixed budget of function evaluations. The methodology introduces an isotropic-diffusion kernel with hyperparameter ". Currently, " is more or less arbitrarily chosen. In this paper, we propose a selection criterion for identifying an optimal value of ", based on a maximum entropy argument. The result is a comprehensive, closed, probabilistic model for characterizing data sets with hidden constraints. This entropy argument ensures that out of all possible models, this is the one that is the most uncertain beyond any specified constraints, which is selected. Applications are presented for several databases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

QRF4P-NRT: Probabilistic Post-Processing of Near-Real-Time Satellite Precipitation Estimates Using Quantile Regression Forests

Accurate and reliable near-real-time satellite precipitation estimation is of great importance for operational large-scale flood forecasting and drought monitoring. The state-of-the-art precipitation post-processing model is based on a deterministic approach to construct relationships between satellites estimates and ground observations. We propose a probabilistic postprocessor, the Probabilistic Post-Processing of Near-Real-Time Satellite Precipitation Estimates using Quantile Regression Forests (QRF4P-NRT), based on quantile modeling, yielding both deterministic and probabilistic predictions. The experimental design incorporates different solutions of near-real-time predictors to further improve the model performance. Using the Integrated Multi-satellitE Retrievals Early Run for Global Precipitation Measurement Mission (IMERG-E) product as an example, we illustrate that the proposed method significantly improves the overall quality of the raw IMERG-E and is also superior to the bias-corrected product (IMERG Final Run, IMERG-F) at daily scale in a complex mountain basin. Evaluations of the corrected IMERG-E, raw IMERG-E, and IMERG-F using ground observation show that the corrected IMERG-E improves correlation coefficients (0.7), mean error (-0.14 mm/day) and root mean square error (3.3 mm/day) relative to the raw IMERG-E (0.31, -0.72 and 5.5 mm/day) and IMERG-F (0.34, -0.09 and 6.0 mm/day). The error decomposition further confirms that the QRF4P-NRT improves on the various deficiencies of the raw IMERG-E product. The ensemble assessment also demonstrates that the quantile outputs provide reliable prediction spread and sharp prediction intervals. The promising results indicate the great potential of the proposed method for probabilistic post-processing for near-real-time satellite precipitation estimates, and for further applications such as hydrological ensemble forecasting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A comparison of probabilistic generative frameworks for molecular simulations

Generative artificial intelligence is now a widely used tool in molecular science. Despite the popularity of probabilistic generative models, numerical experiments benchmarking their performance on molecular data are lacking. Here, in this work, we introduce and explain several classes of generative models, broadly sorted into two categories: flow-based models and diffusion models. We select three representative models: neural spline flows, conditional flow matching, and denoising diffusion probabilistic models, and examine their accuracy, computational cost, and generation speed across datasets with tunable dimensionality, complexity, and modal asymmetry. Our findings are varied, with no one framework being the best for all purposes. In a nutshell, (i) neural spline flows do best at capturing mode asymmetry present in low-dimensional data, (ii) conditional flow matching outperforms other models for high-dimensional data with low complexity, and (iii) denoising diffusion probabilistic models appear the best for low-dimensional data with high complexity. Our datasets include a Gaussian mixture model and the dihedral torsion angle distribution of the Aib9 peptide, generated via a molecular dynamics simulation. We hope our taxonomy of probabilistic generative frameworks and numerical results may guide model selection for a wide range of molecular tasks.

Artificial intelligence↗
DOE OSTI2025

Probabilistic flux limiters

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters have been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Even for deterministic dynamical models, numerical uncertainty is introduced via coarse-graining required by insufficient computational power to solve all scales of motion. Conventional flux limiters are deterministic and lack the capacity to address uncertainties, both aleatoric (inherent randomness) and epistemic (modeling uncertainty due to limited knowledge), which arise in coarse-grained numerical simulations. Here, we introduce a conceptually distinct type of flux limiter that is designed to handle the effects of randomness in the model and uncertainty in model parameters. Unlike traditional single-function flux limiters, these new probabilistic flux limiters incorporate multiple flux limiting functions, each applied with a learned probability drawn from high-resolution data to mitigate the effects of uncertainty in numerical simulations. This approach departs from traditional single-function limiters by explicitly modeling and incorporating uncertainty into the shock capturing process. Using the example of Burgers' equation as a testbed, we show that a machine learned, probabilistic flux limiter may be used in a shock capturing code to more accurately capture shock profiles. In particular, we show that our probabilistic flux limiter outperforms standard limiters and can be successively improved upon (up to a point) by expanding the set of probabilistically chosen flux limiting functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Occlusion-Perturbed Deep Learning for Probabilistic Solar Forecasting via Sky Images

Solar forecasting is shifting to the probabilistic paradigm due to the inherent uncertainty within the solar resource. Input uncertainty quantification is one of the widely used and best-performing ways to model solar uncertainty. However, compared to other sources of inputs, such as numerical weather prediction models, pure sky image-based probabilistic solar forecasting lags behind. In this research, an occlusion-perturbed convolutional neural network, named the PSolarNet, is developed. The PSolarNet provides very short-term deterministic forecasts, forecast scenarios, and probabilistic forecasts of the global horizontal irradiance from sky image sequences. Case studies based on 6 years of open-source data show that the developed PSolarNet is able to generate accurate 10-minute ahead deterministic forecasts with a 5.62% normalized root mean square error, realistic and diverse forecast scenarios with a 0.966 average correlation with the actual time series, and reliable and sharp probabilistic forecasts with a 2.77% normalized continuous ranked probability score.

Bayesian model averaging↗
DOE OSTI2024

UNDERSTANDING THE SEMI-PROBABILISTIC APPROACHES IN STRUCTURAL RELIABILITY USED TO SET DESIGN RELIABILITY TARGETS FOR GRAPHITE COMPONENTS USING ASME BPVC METHODS

Graphite is a quasi-brittle material, resulting in random variability in tensile strength distributions. To account for the random variability in strength, HHA-3000 of the ASME BPVC provides two semi-probabilistic methods for qualifying nuclear graphite components in the design stage, the simplified and full assessments. The full and simplified assessments apply statistical methods to engineering-based design problems. This is often referred to as reliability-based design. Reliability-based design (RBD) is a method to develop reliable designs by accounting for uncertainties and result in small chances of failure when also considering safety factors. RBDs provide reliability targets using semi-probabilistic approaches. RBD is implemented in ASME BPVC HHA-3000 for nuclear graphite components, but is not specific to that application. There has been much confusion around the methods implemented in ASME BPVC HHA-3000 for qualifying nuclear graphite components. To address the confusion, this paper takes a hierarchical approach. First, the general RBD framework is presented. Then, the semi-probabilistic methods and the underlying assumptions implemented in the assessments are presented. The semi-probabilistic methods are separated from the engineering modifications that have been made to the assessments. After building the framework and underlying assumptions, the specific methods in the full and simplified assessments are explained in three steps: inputs, methods, outputs. The methods are applied to an H-451 reflector block. Tensile strength properties for other graphite grades are provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Efficient Probabilistic Prediction and Uncertainty Quantification of Tropical Cyclone–Driven Storm Tides and Inundation

Abstract This study proposes and assesses a methodology to obtain high-quality probabilistic predictions and uncertainty information of near-landfall tropical cyclone–driven (TC-driven) storm tide and inundation with limited time and resources. Forecasts of TC track, intensity, and size are perturbed according to quasi-random Korobov sequences of historical forecast errors with assumed Gaussian and uniform statistical distributions. These perturbations are run in an ensemble of hydrodynamic storm tide model simulations. The resulting set of maximum water surface elevations are dimensionality reduced using Karhunen–Loève expansions and then used as a training set to develop a polynomial chaos (PC) surrogate model from which global sensitivities and probabilistic predictions can be extracted. The maximum water surface elevation is extrapolated over dry points incorporating energy head loss with distance to properly train the surrogate for predicting inundation. We find that the surrogate constructed with third-order PCs using elastic net penalized regression with leave-one-out cross validation provides the most robust fit across training and test sets. Probabilistic predictions of maximum water surface elevation and inundation area by the surrogate model at 48-h lead time for three past U.S. landfalling hurricanes (Irma in 2017, Florence in 2018, and Laura in 2020) are found to be reliable when compared to best track hindcast simulation results, even when trained with as few as 19 samples. The maximum water surface elevation is most sensitive to perpendicular track-offset errors for all three storms. Laura is also highly sensitive to storm size and has the least reliable prediction. Significance Statement The purpose of this study is to develop and evaluate a methodology that can be used to provide high-quality probabilistic predictions of hurricane-induced storm tide and inundation with limited time and resources. This is important for emergency management purposes during or after the landfall of hurricanes. Our results show that sampling forecast errors using quasi-random sequences combined with machine learning techniques that fit polynomial functions to the data are well suited to this task. The polynomial functions also have the benefit of producing exact sensitivity indices of storm tide and inundation to the forecasted hurricane properties such as path, intensity, and size, which can be used for uncertainty estimation. The code implementing the presented methodology is publicly available on GitHub.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Matilda v1.0: An R package for probabilistic climate projections using a reduced complexity climate model

A primary advantage to using reduced complexity climate models (RCMs) has been their ability to quickly conduct probabilistic climate projections, a key component of uncertainty quantification in many impact studies and multisector systems. Providing frameworks for such analyses has been a target of several RCMs used in studies of the future co-evolution of the human and Earth systems. In this paper, we present Matilda, an open-science R software package that facilitates probabilistic climate projection analysis, implemented here using the Hector simple climate model in a seamless and easily applied framework. The primary goal of Matilda is to provide the user with a turn-key method to build parameter sets from literature-based prior distributions, run Hector iteratively to produce perturbed parameter ensembles (PPEs), weight ensembles for realism against observed historical climate data, and compute probabilistic projections for different climate variables. This workflow gives the user the ability to explore viable parameter space and propagate uncertainty to model ensembles with just a few lines of code. The package provides significant freedom to select different scoring criteria and algorithms to weight ensemble members, as well as the flexibility to implement custom criteria. Additionally, the architecture of the package simplifies the process of building and analyzing PPEs without requiring significant programming expertise, to accommodate diverse use cases. We present a case study that provides illustrative results of a probabilistic analysis of mean global surface temperature as an example of the software application.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Use of limited data to construct Bayesian networks for probabilistic risk assessment.

Probabilistic Risk Assessment (PRA) is a fundamental part of safety/quality assurance for nuclear power and nuclear weapons. Traditional PRA very effectively models complex hardware system risks using binary probabilistic models. However, traditional PRA models are not flexible enough to accommodate non-binary soft-causal factors, such as digital instrumentation&control, passive components, aging, common cause failure, and human errors. Bayesian Networks offer the opportunity to incorporate these risks into the PRA framework. This report describes the results of an early career LDRD project titled %E2%80%9CUse of Limited Data to Construct Bayesian Networks for Probabilistic Risk Assessment%E2%80%9D. The goal of the work was to establish the capability to develop Bayesian Networks from sparse data, and to demonstrate this capability by producing a data-informed Bayesian Network for use in Human Reliability Analysis (HRA) as part of nuclear power plant Probabilistic Risk Assessment (PRA). This report summarizes the research goal and major products of the research.

Groth, Katrina M.↗
DOE OSTI2017

Advanced Seismic Probabilistic Risk Assessment Methodology: Development of Beta 1.0 MASTODON Toolset

Design of nuclear power plant (NPP) facilities to resist natural hazards has been a part of the regulatory process from the beginning of the NPP industry in the United States, but has evolved substantially over time. The original set of approaches and methods was entirely deterministic in nature and focused on a traditional engineering margins-based approach. However, over time probabilistic and risk-informed approaches were also developed and implemented in US Nuclear Regulatory Commission guidance and regulation. A defense-in-depth framework has also been incorporated into US regulatory guidance over time. As a result, today, the US regulatory framework incorporates deterministic and probabilistic approaches for a range of different applications and for a range of natural hazard considerations. Although the US regulatory framework has continued to evolve over time, the tools, methods and data available to the US nuclear industry to meet the changing requirements have not kept pace. Notably, there is room for improvement in the tools and methods available for external event probabilistic risk assessment (PRA), which is the principal assessment approach used in risk-informed regulations and risk-informed decision-making applied to natural hazard assessment and design. Development of a new set of tools and methods that incorporate current knowledge, modern best practice, and state-of-the-art computational resources would lead to more reliable assessment of facility risk and risk insights (e.g., the plant elements and accident sequences that are most risk-significant), with less uncertainty and reduced conservatisms. Development of the next generation tools and methods for external events PRA is ongoing under the Risk Informed Safety Margins Characterization (RISMC) technical pathway. The RISMC toolkit development centers on integration of the tools and methods under a common framework, MOOSE. These tools and methods make use of existing and newly developed tools and methods, coupled with the experience and data gained in the past decades, to define and analyze more realistic risk assessment models. Specific focus in this report is on the capability to model seismic risk using advanced SPRA methods. Over the last year, significant capability has been added to Mastodon to simulate 3-D wave passage effects through nonlinear soil. Verification has demonstrated the capability of Mastodon to model wave passage effects in 1-D, 2-D, and 3-D. Methods have been developed to incorporate probabilistic floor response capabilities. Additional capability will be added to Mastodon over the next year to implement a robust gapping and sliding element for cyclic shaking, web-based verification and user manuals, stochastic finite elements, and frequency independent damping. Verification of added capabilities has occured in parallel with code writing activities.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗