Publications

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We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural error in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.

Large-scale computational models have become common tools for analyzing complex man-made systems. However, when coupled with optimization or uncertainty quantification methods in order to conduct extensive model exploration and analysis, the computational expense quickly becomes intractable. Furthermore, these models may have both continuous and discrete parameters. One common approach to mitigating the computational expense is the use of response surface approximations. While well developed for models with continuous parameters, they are still new and largely untested for models with both continuous and discrete parameters. In this work, we describe and investigate the performance of three types of response surfaces developed for mixed-variable models: Adaptive Component Selection and Shrinkage Operator, Treed Gaussian Process, and Gaussian Process with Special Correlation Functions. We focus our efforts on test problems with a small number of parameters of interest, a characteristic of many physics-based engineering models. We present the results of our studies and offer some insights regarding the performance of each response surface approximation method. © 2014 Springer International Publishing Switzerland.

The objective is to calculate the probability, PF, that a device will fail when its inputs, x, are randomly distributed with probability density, p (x), e.g., the probability that a device will fracture when subject to varying loads. Here failure is defined as some scalar function, y (x), exceeding a threshold, T. If evaluating y (x) via physical or numerical experiments is sufficiently expensive or PF is sufficiently small, then Monte Carlo (MC) methods to estimate PF will be unfeasible due to the large number of function evaluations required for a specified accuracy. Importance sampling (IS), i.e., preferentially sampling from “important” regions in the input space and appropriately down-weighting to obtain an unbiased estimate, is one approach to assess PF more efficiently. The inputs are sampled from an importance density, pʹ (x). We present an adaptive importance sampling (AIS) approach which endeavors to adaptively improve the estimate of the ideal importance density, p* (x), during the sampling process. Our approach uses a mixture of component probability densities that each approximate p* (x). An iterative process is used to construct the sequence of improving component probability densities. At each iteration, a Gaussian process (GP) surrogate is used to help identify areas in the space where failure is likely to occur. The GPs are not used to directly calculate the failure probability; they are only used to approximate the importance density. Thus, our Gaussian process adaptive importance sampling (GPAIS) algorithm overcomes limitations involving using a potentially inaccurate surrogate model directly in IS calculations. This robust GPAIS algorithm performs surprisingly well on a pathological test function.

The objective is to calculate the probability, PF, that a device will fail when its inputs, x, are randomly distributed with probability density, p (x), e.g., the probability that a device will fracture when subject to varying loads. Here failure is defined as some scalar function, y (x), exceeding a threshold, T. If evaluating y (x) via physical or numerical experiments is sufficiently expensive or PF is sufficiently small, then Monte Carlo (MC) methods to estimate PF will be unfeasible due to the large number of function evaluations required for a specified accuracy. Importance sampling (IS), i.e., preferentially sampling from “important” regions in the input space and appropriately down-weighting to obtain an unbiased estimate, is one approach to assess PF more efficiently. The inputs are sampled from an importance density, pʹ (x). We present an adaptive importance sampling (AIS) approach which endeavors to adaptively improve the estimate of the ideal importance density, p* (x), during the sampling process. Our approach uses a mixture of component probability densities that each approximate p* (x). An iterative process is used to construct the sequence of improving component probability densities. At each iteration, a Gaussian process (GP) surrogate is used to help identify areas in the space where failure is likely to occur. The GPs are not used to directly calculate the failure probability; they are only used to approximate the importance density. Thus, our Gaussian process adaptive importance sampling (GPAIS) algorithm overcomes limitations involving using a potentially inaccurate surrogate model directly in IS calculations. This robust GPAIS algorithm performs surprisingly well on a pathological test function.

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This report discusses the treatment of uncertainties stemming from relatively few samples of random quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse data samples it is not practical to have a goal of accurately estimating the underlying probability density function (PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a specified percentile range of the actual PDF, say the range between 0.025 and .975 percentiles, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the desired percentile range of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem interesting and difficult. In this report, five uncertainty representation techniques are characterized for their performance on twenty-one test problems (over thousands of trials for each problem) according to these two opposing objectives and other performance measures. Two of the methods, statistical Tolerance Intervals and a kernel density approach specifically developed for handling sparse data, exhibit significantly better overall performance than the others.

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This report summarizes the result of a NEAMS project focused on the use of reliability methods within the RAVEN and RELAP-7 software framework for assessing failure probabilities as part of probabilistic risk assessment for nuclear power plants. RAVEN is a software tool under development at the Idaho National Laboratory that acts as the control logic driver and post-processing tool for the newly developed Thermal-Hydraulic code RELAP-7. Dakota is a software tool developed at Sandia National Laboratories containing optimization, sensitivity analysis, and uncertainty quantification algorithms. Reliability methods are algorithms which transform the uncertainty problem to an optimization problem to solve for the failure probability, given uncertainty on problem inputs and a failure threshold on an output response. The goal of this work is to demonstrate the use of reliability methods in Dakota with RAVEN/RELAP-7. These capabilities are demonstrated on a demonstration of a Station Blackout analysis of a simplified Pressurized Water Reactor (PWR).

This paper discusses the treatment of uncertainties corresponding to relatively few samples of random-variable quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse samples it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem an interesting and difficult one. In this paper the performance of five uncertainty representation techniques is characterized on twenty-one test problems (over thousands of trials for each problem) according to these two opposing objectives and other performance measures. Two of the methods exhibit significantly better overall performance than the others according to the objectives and performance measures emphasized. © 2012 AIAA.

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This report summarizes the result of a NEAMS project focused on sensitivity analysis of a new model for the fission gas behavior (release and swelling) in the BISON fuel performance code of Idaho National Laboratory. Using the new model in BISON, the sensitivity of the calculated fission gas release and swelling to the involved parameters and the associated uncertainties is investigated. The study results in a quantitative assessment of the role of intrinsic uncertainties in the analysis of fission gas behavior in nuclear fuel.

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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.

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Many of the Performance Shaping Factors (PSFs) used in Human Reliability Analysis (HRA) methods are not directly measurable or observable. Methods like SPAR-H require the analyst to assign values for all of the PSFs, regardless of the PSF observability; this introduces subjectivity into the human error probability (HEP) calculation. One method to reduce the subjectivity of HRA estimates is to formally incorporate information about the probability of the PSFs into the methodology for calculating the HEP. This can be accomplished by encoding prior information in a Bayesian Network (BN) and updating the network using available observations. We translated an existing HRA methodology, SPAR-H, into a Bayesian Network to demonstrate the usefulness of the BN framework. We focus on the ability to incorporate prior information about PSF probabilities into the HRA process. This paper discusses how we produced the model by combining information from two sources, and how the BN model can be used to estimate HEPs despite missing observations. Use of the prior information allows HRA analysts to use partial information to estimate HEPs, and to rely on the prior information (from data or cognitive literature) when they are unable to gather information about the state of a particular PSF. The SPAR-H BN model is a starting point for future research activities to create a more robust HRA BN model using data from multiple sources.