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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Using Bayesian Networks for Sensitivity Analysis of Complex Biogeochemical Models

Sensitivity analysis is a vital tool in numerical modeling to identify important parameters and processes that contribute to the overall uncertainty in model outputs. We developed a new sensitivity analysis method to quantify the relative importance of uncertain model processes that contain multiple uncertain parameters. The method is based on the concepts of Bayesian networks (BNs) to account for complex hierarchical uncertainty structure of a model system. We derived a new set of sensitivity indices using the methodology of variance-based global sensitivity analysis with the Bayesian inference. The framework is capable of representing the detailed uncertainty information of a complex model system using BNs and affords flexible grouping of different uncertain inputs given their characteristics and dependency structures. We have implemented the method on a real-world biogeochemical model at the groundwater-surface water interface within the Hanford Site’s 300 Area. The uncertainty sources of the model were first grouped into forcing scenario and three different processes based on our understanding of the complex system. The sensitivity analysis results indicate that both the reactive transport and groundwater flow processes are important sources of uncertainty for carbon-consumption predictions. Within the groundwater flow process, the structure of geological formations is more important than the permeability heterogeneity within a given geological formation. Our new sensitivity analysis framework based on BNs offers substantial flexibility for investigating the importance of combinations of interacting uncertainty sources in a hierarchical order, and it is expected to be applicable to a wide range of multi-physics models for complex systems.

Dai, Heng↗
DOE OSTI2015

Modern sensitivity analysis - 15651

Sensitivity analysis has been applied to complex models, such as performance assessment models, since at least the advent of computational tools to support such an approach to model evaluation. Initially, sensitivity analysis methods were applied to deterministic models and focused on changing one input variable at a time. Probabilistic modeling opened the door to evaluating changes in all input variables simultaneously. Standardized rank regression methods were primarily used in the last century to evaluate probabilistic models. These methods assume linearity in the rank response of the model to the inputs. At the very least this assumes monotonicity in the response, but for the most part the response needs to be near-linear. This is highly unlikely for performance assessment models that are based on differential equations, multiplication and division of variables that are usually not correlated, and conservatism that is not well understood. There are better statistical methods for evaluating highly non-linear and dynamic probabilistic models. Some of these methods were founded in the data mining industry. This century has seen a rapid development of the internet that led directly to the development of data mining techniques for massive databases. Although the goals were different, these techniques can be adapted to sensitivity analysis for complex probabilistic models, which, also, form large, or even massive, databases. These modern sensitivity analysis procedures assess the importance of every explanatory variable (input parameters) used in a probabilistic model. In practice, this means that for each endpoint of interest, every explanatory variable in the model is associated with a quantitative measure of importance. For a given explanatory variable, the importance value depends on the endpoint of interest. This global approach to sensitivity analysis allows all levels of interactions to be evaluated, so that the variation in the output can be measured at every level of possible interaction. The effects are collected together during sensitivity analysis processing, and then separated out to attribute the overall contribution of each input parameter to the model output. These global sensitivity analysis procedures have the ability to characterize non-linear and non-monotonic relationships between explanatory variables and endpoints of interest. This is critically important because of the need to characterize complex interactions among multiple explanatory variables in PA models that often have non-linear and non-monotonic effects. The options for sensitivity analysis are fully explored, including an evaluation of several methods when applying them to a well-known complex non-linear non-monotonic model. The results clearly demonstrate the relative benefit of using data mining methods over simple statistical approaches such as standardized rank regression. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

State-of-the-Art Reactor Consequence Analysis Project: Sensitivity Analysis Using Dakota

The State-of-the-Art Reactor Consequence Analyses (SOARCA) project has focused on best estimate analyses and uncertainty analysis for postulated accidents at specific nuclear power plants. The consequences of these accidents are estimated using the simulation tools MELCOR and MACCS. To understand which uncertain input variables are important to determining these consequences, analysts have performed sensitivity analyses. The tool used to perform these sensitivity analyses in previous SOARCA work, CompModSA, is no longer supported. Therefore, the current work focuses on migrating these analyses to another tool and evaluating its performance. Dakota, which is a tool developed at Sandia National Laboratories, is used in this work. Sensitivity results are created for three analyses from the SOARCA Surry UA. Though CompModSA and Dakota vary slightly in their algorithms and implementation, their sensitivity results generally agree, which gives confidence in the Dakota approach and increases confidence in the original analyses. It is likely that this methodology is extendable to the rest of SOARCA analyses.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching [Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems]

Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields.

42 ENGINEERING↗
DOE OSTI2015

Parametric sensitivity analysis for stochastic molecular systems using information theoretic metrics

In this paper, we present a parametric sensitivity analysis (SA) methodology for continuous time and continuous space Markov processes represented by stochastic differential equations. Particularly, we focus on stochastic molecular dynamics as described by the Langevin equation. The utilized SA method is based on the computation of the information-theoretic (and thermodynamic) quantity of relative entropy rate (RER) and the associated Fisher information matrix (FIM) between path distributions, and it is an extension of the work proposed by Y. Pantazis and M. A. Katsoulakis [J. Chem. Phys. 138, 054115 (2013)]. A major advantage of the pathwise SA method is that both RER and pathwise FIM depend only on averages of the force field; therefore, they are tractable and computable as ergodic averages from a single run of the molecular dynamics simulation both in equilibrium and in non-equilibrium steady state regimes. We validate the performance of the extended SA method to two different molecular stochastic systems, a standard Lennard-Jones fluid and an all-atom methane liquid, and compare the obtained parameter sensitivities with parameter sensitivities on three popular and well-studied observable functions, namely, the radial distribution function, the mean squared displacement, and the pressure. Results show that the RER-based sensitivities are highly correlated with the observable-based sensitivities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Modified GMDH-NN algorithm and its application for global sensitivity analysis

Global sensitivity analysis (GSA) is a very useful tool to evaluate the influence of input variables in the whole distribution range. Sobol' method is the most commonly used among variance-based methods, which are efficient and popular GSA techniques. High dimensional model representation (HDMR) is a popular way to compute Sobol' indices, however, its drawbacks cannot be ignored. We show that modified GMDH-NN algorithm can calculate coefficients of metamodel efficiently, so this paper aims at combining it with HDMR and proposes GMDH-HDMR method. The new method shows higher precision and faster convergent rate. Several numerical and engineering examples are used to confirm its advantages. - Highlights: • The GMDH-NN is improved to construct the explicit polynomial model of optimal complexity by self-organization. • The paper aims at combining improved GMDH-NN with HDMR expansions and using it to compute Sobol' indices directly. • The method can be applied in uniform, normal and exponential distribution by using suitable orthogonal polynomials. • Engineering examples, e.g., electronic circuit models can be solved by the presented method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Sensitivity analysis of simulated SOA loadings using a variance-based statistical approach: SENSITIVITY ANALYSIS OF SOA

We investigate the sensitivity of secondary organic aerosol (SOA) loadings simulated by a regional chemical transport model to 7 selected tunable model parameters: 4 involving emissions of anthropogenic and biogenic volatile organic compounds, anthropogenic semi-volatile and intermediate volatility organics (SIVOCs), and NOx, 2 involving dry deposition of SOA precursor gases, and one involving particle-phase transformation of SOA to low volatility. We adopt a quasi-Monte Carlo sampling approach to effectively sample the high-dimensional parameter space, and perform a 250 member ensemble of simulations using a regional model, accounting for some of the latest advances in SOA treatments based on our recent work. We then conduct a variance-based sensitivity analysis using the generalized linear model method to study the responses of simulated SOA loadings to the tunable parameters. Analysis of SOA variance from all 250 simulations shows that the volatility transformation parameter, which controls whether particle-phase transformation of SOA from semi-volatile SOA to non-volatile is on or off, is the dominant contributor to variance of simulated surface-level daytime SOA (65% domain average contribution). We also split the simulations into 2 subsets of 125 each, depending on whether the volatility transformation is turned on/off. For each subset, the SOA variances are dominated by the parameters involving biogenic VOC and anthropogenic SIVOC emissions. Furthermore, biogenic VOC emissions have a larger contribution to SOA variance when the SOA transformation to non-volatile is on, while anthropogenic SIVOC emissions have a larger contribution when the transformation is off. NOx contributes less than 4.3% to SOA variance, and this low contribution is mainly attributed to dominance of intermediate to high NOx conditions throughout the simulated domain. The two parameters related to dry deposition of SOA precursor gases also have very low contributions to SOA variance. This study highlights the large sensitivity of SOA loadings to the particle-phase transformation of SOA volatility, which is neglected in most previous models.

Shrivastava, Manish↗
DOE OSTI2018

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the system’s stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. In conclusion, these methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2017

Sensitivity analysis for III–V/Si tandem solar cells: A theoretical study

Material and structural parameters may affect the efficiency of a tandem solar cell differently from the way they do in a single-junction solar cell. Here, we fabricated a III–V/Si four-terminal tandem solar cell and developed an opto-electronic model simulating this device. The optical properties were simulated with the transfer matrix method, while the electrical properties were simulated using the numerical device simulator PC1D. For this simulated tandem structure, we determined the parameters which have the largest potential impact on the device efficiency. A sensitivity analysis of the impact of these parameters on the device efficiency was also performed. Furthermore, to reduce the cost of the tandem solar cells, we identified the parameters that do not require tight control during the manufacturing process. The Si cell was simulated both as a single-junction cell and as the bottom cell of a tandem device. Lastly, we determined those device parameters that are more critical in a tandem configuration than in a single-junction configuration.

14 SOLAR ENERGY↗
DOE OSTI2022

Uncertainty quantification in elastic constants of SiC f /SiC m tubular composites using global sensitivity analysis

Silicon carbide fiber and silicon carbide matrix (SiC f /SiC m ) tubes produced through the chemical vapor infiltration process have become a candidate cladding material in nuclear applications. The performance of this composite is influenced by many variables such as braiding angle, porosity, material properties, etc., which vary over a range of values due to the inherent fluctuations in the manufacturing process. In this study, the variability in elastic constants of SiC f /SiC m composite has been quantified through multiscale finite element (FE) simulations, variable screening, and high-fidelity surrogate modeling. The key variables dominantly affecting the elastic constants of SiC f /SiC m tubes were identified using global sensitivity analysis. A surrogate to the high-fidelity FE-based model was used in Monte Carlo simulations to generate a hundred thousand samples from which the uncertainty in elastic constants was assessed. It turned out that the coefficient of variation was less than 10%.

Materials Science↗
DOE OSTI2014

Integrated Sensitivity Analysis Workflow

Sensitivity analysis is a crucial element of rigorous engineering analysis, but performing such an analysis on a complex model is difficult and time consuming. The mission of the DART Workbench team at Sandia National Laboratories is to lower the barriers to adoption of advanced analysis tools through software integration. The integrated environment guides the engineer in the use of these integrated tools and greatly reduces the cycle time for engineering analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Sensitivity Analysis of Wind Plant Performance to Key Turbine Design Parameters: A Systems Engineering Approach; Preprint

This paper introduces the development of a new software framework for research, design, and development of wind energy systems which is meant to 1) represent a full wind plant including all physical and nonphysical assets and associated costs up to the point of grid interconnection, 2) allow use of interchangeable models of varying fidelity for different aspects of the system, and 3) support system level multidisciplinary analyses and optimizations. This paper describes the design of the overall software capability and applies it to a global sensitivity analysis of wind turbine and plant performance and cost. The analysis was performed using three different model configurations involving different levels of fidelity, which illustrate how increasing fidelity can preserve important system interactions that build up to overall system performance and cost. Analyses were performed for a reference wind plant based on the National Renewable Energy Laboratory's 5-MW reference turbine at a mid-Atlantic offshore location within the United States.

17 WIND ENERGY↗
DOE OSTI2017

Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)

This paper develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗