Comprehensive sensitivity analysis of rotational stability of a super-deep underground spherical structure considering uncertainty

2020 ◽  
Vol 24 (1) ◽  
pp. 65-78
Author(s):  
Hua-Ping Wan ◽  
Yanfeng Zheng ◽  
Yaozhi Luo ◽  
Chao Yang ◽  
Xian Xu
Keyword(s):  
Sensitivity Analysis ◽  
Sensitivity Analyses ◽  
Rotational Stability ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Global Sensitivity ◽  
Evaluation Indicator ◽  
Spherical Structure ◽  
Central Detector ◽  
Deep Underground

Jiangmen Underground Neutrino Observatory central detector is located 700 m below the ground and also submerged into an ultrapure water pool. The main structure of the Jiangmen Underground Neutrino Observatory central detector is a hybrid spherical shell that is vulnerable to rotation under the buoyancy effect. The influences of the model parameters on the rotational stability of this complex and unique structure are investigated. Since the model parameters are inevitably subjected to many sources of uncertainties (e.g. manufacturing tolerances and geometrical imperfections), the parameter uncertainty is taken into account. In addition, linear and nonlinear rotational stabilities of this super-deep underground spherical structure are also under consideration. Specifically, the critical loading multiplier is used as the evaluation indicator of linear rotational stability and the load proportionality factor- θ curve is considered as the evaluation indicator of nonlinear rotational stability. The sensitivity of linear and nonlinear rotational stabilities to uncertain parameters is systematically studied in terms of univariate and multivariate global sensitivity analyses. The univariate global sensitivity analysis is able to evaluate the effects of uncertain parameters on each evaluation indicator, whereas multivariate global sensitivity analysis enables to assess the global influence of uncertain parameters on all evaluation indicators. A polynomial chaos expansion surrogate model is utilized to replace the time-consuming simulation model for analytical implementation of the univariate and multivariate global sensitivity analyses. The present polynomial chaos expansion-based univariate and multivariate global sensitivity analyses effectively and efficiently reveal the sensitivity of the rotational stability of this super-deep underground spherical structure to uncertain parameters, and provide a practical method for comprehensive sensitivity analysis of similar structures.

scholarly journals Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling

2021 ◽  
Author(s):  
Sebastian Brandstaeter ◽  
Sebastian L. Fuchs ◽  
Jonas Biehler ◽  
Roland C. Aydin ◽  
Wolfgang A. Wall ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Computational Studies ◽  
Growth And Remodeling ◽  
Global Sensitivity ◽  
Output Variability ◽  
Constrained Mixture ◽  
The One ◽  
Influential Parameters

AbstractGrowth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Comprehensive global sensitivity analysis of a repository model using different types of transformations and metamodeling techniques

2021 ◽  
Author(s):  
Sabine M. Spiessl ◽  
Dirk-A. Becker ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Higher Order ◽  
Model Parameters ◽  
High Dimensional Model Representation ◽  
Model Output ◽  
Global Sensitivity ◽  
Sparse Polynomial ◽  
Sensitivity Indices ◽  
Highly Nonlinear

<p>Due to their highly nonlinear, non-monotonic or even discontinuous behavior, sensitivity analysis of final repository models can be a demanding task. Most of the output of repository models is typically distributed over several orders of magnitude and highly skewed. Many values of a probabilistic investigation are very low or even zero. Although this is desirable in view of repository safety it can distort the evidence of sensitivity analysis. For the safety assessment of the system, the highest values of outputs are mainly essential and if those are only a few, their dependence on specific parameters may appear insignificant. By applying a transformation, different model output values are differently weighed, according to their magnitude, in sensitivity analysis. Probabilistic methods of higher-order sensitivity analysis, applied on appropriately transformed model output values, provide a possibility for more robust identification of relevant parameters and their interactions. This type of sensitivity analysis is typically done by decomposing the total unconditional variance of the model output into partial variances corresponding to different terms in the ANOVA decomposition. From this, sensitivity indices of increasing order can be computed. The key indices used most often are the first-order index (SI1) and the total-order index (SIT). SI1 refers to the individual impact of one parameter on the model and SIT represents the total effect of one parameter on the output in interactions with all other parameters. The second-order sensitivity indices (SI2) describe the interactions between two model parameters.</p><p>In this work global sensitivity analysis has been performed with three different kinds of output transformations (log, shifted and Box-Cox transformation) and two metamodeling approaches, namely the Random-Sampling High Dimensional Model Representation (RS-HDMR) [1] and the Bayesian Sparse PCE (BSPCE) [2] approaches. Both approaches are implemented in the SobolGSA software [3, 4] which was used in this work. We analyzed the time-dependent output with two approaches for sensitivity analysis, i.e., the pointwise and generalized approaches. With the pointwise approach, the output at each time step is analyzed independently. The generalized approach considers averaged output contributions at all previous time steps in the analysis of the current step. Obtained results indicate that robustness can be improved by using appropriate transformations and choice of coefficients for the transformation and the metamodel.</p><p>[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.</p><p>[2] Q. Shao, A. Younes, M. Fahs, T.A. Mara (2017). Bayesian sparse polynomial chaos expansion for global sensitivity analysis. Computer Methods in Applied Mechanics and Engineering, 318: 474-496.</p><p>[3] S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus (2018). Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004.</p><p>[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.</p>

Global sensitivity analysis of statistical models by double randomization method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dmitriy Kolyukhin
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Models ◽  
Global Sensitivity Analysis ◽  
Uncertain Parameters ◽  
Suggested Approach ◽  
Global Sensitivity ◽  
Double Randomization Method ◽  
Complex Models ◽  
Monte Carlo Estimation ◽  
Randomization Method

Abstract The paper addresses a global sensitivity analysis of complex models. The work presents a generalization of the hierarchical statistical models where uncertain parameters determine the distribution of statistical models. The double randomization method is applied to increase the efficiency of the Monte Carlo estimation of Sobol indices. Numerical computations are provided to study the accuracy and efficiency of the proposed technique. The issue of optimization of the suggested approach is considered.

scholarly journals Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active subspaces

2020 ◽  
Vol 34 (11) ◽  
pp. 1813-1830
Author(s):  
Daniel Erdal ◽  
Sinan Xiao ◽  
Wolfgang Nowak ◽  
Olaf A. Cirpka
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Process ◽  
Parameter Space ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Large Sample Size ◽  
Global Sensitivity ◽  
Environmental Models ◽  
Additional Costs ◽  
Active Subspace

Abstract Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70–90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs.

scholarly journals Global sensitivity analysis of parameter uncertainty in landscape evolution models

2018 ◽  
Vol 11 (12) ◽  
pp. 4873-4888 ◽  
Author(s):  
Christopher J. Skinner ◽  
Tom J. Coulthard ◽  
Wolfgang Schwanghart ◽  
Marco J. Van De Wiel ◽  
Greg Hancock
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Landscape Evolution ◽  
Relative Sensitivity ◽  
Function Approach ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Model Function ◽  
Sediment Yields ◽  
Statistical Measures

Abstract. The evaluation and verification of landscape evolution models (LEMs) has long been limited by a lack of suitable observational data and statistical measures which can fully capture the complexity of landscape changes. This lack of data limits the use of objective function based evaluation prolific in other modelling fields, and restricts the application of sensitivity analyses in the models and the consequent assessment of model uncertainties. To overcome this deficiency, a novel model function approach has been developed, with each model function representing an aspect of model behaviour, which allows for the application of sensitivity analyses. The model function approach is used to assess the relative sensitivity of the CAESAR-Lisflood LEM to a set of model parameters by applying the Morris method sensitivity analysis for two contrasting catchments. The test revealed that the model was most sensitive to the choice of the sediment transport formula for both catchments, and that each parameter influenced model behaviours differently, with model functions relating to internal geomorphic changes responding in a different way to those relating to the sediment yields from the catchment outlet. The model functions proved useful for providing a way of evaluating the sensitivity of LEMs in the absence of data and methods for an objective function approach.

scholarly journals Global sensitivity analysis, probabilistic calibration, and predictive assessment for the Data Assimilation Linked Ecosystem Carbon model

2014 ◽  
Vol 7 (5) ◽  
pp. 6893-6948
Author(s):  
C. Safta ◽  
D. Ricciuto ◽  
K. Sargsyan ◽  
B. Debusschere ◽  
H. N. Najm ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Data Assimilation ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Forest Site ◽  
Carbon Cycle Model ◽  
Global Sensitivity ◽  
Predictive Skill ◽  
Ecosystem Carbon

Abstract. In this paper we propose a probabilistic framework for an uncertainty quantification study of a carbon cycle model. A Global Sensitivity Analysis (GSA) study indicates the parameters and parameter couplings that are important at different times of the year for Quantities of Interest obtained with the Data Assimilation Linked Ecosystem Carbon (DALEC) model. We then employ a Bayesian approach to calibrate the parameters of DALEC using net ecosystem exchange observations at the Harvard Forest site. The calibration exercise is guided by GSA and by Fisher information matrix results that quantify the amount of information carried by the experimental data about specific model parameters. The calibration results are employed in the second part of the paper to assess the predictive skill of the model via posterior predictive checks. These checks show a better performance for the non-steady state model during the growing season compared to the one employing steady state assumptions. Overall, this study leads to a 40% improvement in the predictive skill of DALEC and highlights the importance of considering correlations in the model parameters as informed by the data.

How well do we know our models?

2020 ◽  
Author(s):  
Denise Degen ◽  
Karen Veroy ◽  
Mauro Cacace ◽  
Magdalena Scheck-Wenderoth ◽  
Florian Wellmann
Keyword(s):  
Finite Element ◽  
Surrogate Model ◽  
Sensitivity Study ◽  
Reduced Basis Method ◽  
Sensitivity Analyses ◽  
Model Parameters ◽  
Reduced Basis ◽  
Global Sensitivity ◽  
Sensitivity Studies ◽  
Basis Method

<p>In Geosciences, we face the challenge of characterizing uncertainties to provide reliable predictions of the earth surface to allow, for instance, a sustainable and renewable energy management. In order, to address the uncertainties we need a good understanding of our geological models and their associated subsurface processes.</p><p>Therefore, the essential pre-step for uncertainty analyses are sensitivity studies. Sensitivity studies aim at determining the most influencing model parameters. Hence, we require them to significantly reduce the parameter space to avoid unfeasibly large compute times.</p><p>We distinguish two types of sensitivity analyses: local and global studies. In contrast, to the local sensitivity study, the global one accounts for parameter correlations. That is the reason, why we employ in this work a global sensitivity study. Unfortunately, global sensitivity studies have the disadvantage that they are computationally extremely demanding. Hence, they are prohibitive even for state-of-the-art finite element simulations.</p><p>For this reason, we construct a surrogate model by employing the reduced basis method. The reduced basis method is a model order reduction technique that aims at significantly reducing the spatial and temporal degrees of freedom of, for instance, finite element solves. In contrast to other surrogate models, we obtain a surrogate model that preserves the physics and is not restricted to the observation space. As we will show, the reduced basis method leads to a speed-up of five to six orders of magnitude with respect to our original problem while retaining an accuracy higher than the measurement accuracy.</p><p>In this work, we elaborate on the advantages of global sensitivity studies in comparison to local ones. We use several case studies, from large-scale European sedimentary basins to demonstrate how the global sensitivity studies are used to learn about the influence of transient, such as paleoclimate effects, and stationary effects. We also demonstrate how the results can be used in further analyses, such as deterministic and stochastic model calibrations. Furthermore, we show how we can use the analyses to learn about the subsurface processes and to identify model short comes.</p>

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