Probabilistic Analysis of a Metamorphic Mechanism Based on a Global Sensitivity Analysis: A Preliminary Study

Kinematic Model ◽

Mathematical Structure ◽

Motion Path ◽

Model Parameters ◽

Global Sensitivity ◽

Sensitivity Indices ◽

Mathematical modeling is an important part of the engineering design cycle. Most models require application specific input parameters that are established by calculation or experiment. The accuracy of model predictions depends on underlying model assumptions as well as how uncertainty in knowledge of the parameters is transmitted through the mathematical structure of the model. Knowledge about the relative impact of individual parameters can help establish priorities in developing/choosing specific parameters and provide insight into a range of parameters that produce ‘equally good’ designs. In this work Global Sensitivity Analysis (GSA) is examined as a technique that can contribute to this insight by developing Sensitivity Indices, a measure of the relative importance, for each parameter. The approach is illustrated on a kinematic model of a metamorphic 4-bar mechanism. The model parameters are the lengths of the four links. The results of this probabilistic analysis highlight the synergy that must exist between all four link lengths to create a design that can follow the desired motion path. The impact of individual link lengths, however, rises and falls depending on where the mechanism is along its motion path.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4041622 ◽

2019 ◽

Vol 14 (2) ◽

Cited By ~ 1

Author(s):

Souransu Nandi ◽

Tarunraj Singh

Keyword(s):

Sensitivity Analysis ◽

Linear Systems ◽

Benchmark Problems ◽

Model Parameters ◽

Parameter Uncertainties ◽

Sobol Indices ◽

Global Sensitivity ◽

Time Invariant ◽

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

10.5194/egusphere-egu21-6131 ◽

2021 ◽

Author(s):

Sabine M. Spiessl ◽

Dirk-A. Becker ◽

Sergei Kucherenko

Keyword(s):

Sensitivity Analysis ◽

Higher Order ◽

Model Parameters ◽

High Dimensional Model Representation ◽

Model Output ◽

Global Sensitivity ◽

Sparse Polynomial ◽

Sensitivity Indices ◽

Highly Nonlinear

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.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.[1] M. Zuniga, S. Kucherenko, N. Shah (2013). Metamodelling with independent and dependent inputs. Computer Physics Communications, 184 (6): 1570-1580.[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.[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.[4] SobolGSA software (2021). User manual https://www.imperial.ac.uk/process-systems-engineering/research/free-software/sobolgsa-software/.

Sensitivity analysis and the challenges posed by multiple approaches: a multifaceted mess

10.5194/egusphere-egu2020-6626 ◽

2020 ◽

Author(s):

Monica Riva ◽

Aronne Dell'Oca ◽

Alberto Guadagnini

Keyword(s):

Sensitivity Analysis ◽

Model Calibration ◽

System Model ◽

Model Parameters ◽

Model Output ◽

Multiple Model ◽

Total Uncertainty ◽

Global Sensitivity ◽

Sensitivity Indices

Modern models of environmental and industrial systems have reached a relatively high level of complexity. The latter aspect could hamper an unambiguous understanding of the functioning of a model, i.e., how it drives relationships and dependencies among inputs and outputs of interest. Sensitivity Analysis tools can be employed to examine this issue.Global sensitivity analysis (GSA) approaches rest on the evaluation of sensitivity across the entire support within which system model parameters are supposed to vary. In this broad context, it is important to note that the definition of a sensitivity metric must be linked to the nature of the question(s) the GSA is meant to address. These include, for example: (i) which are the most important model parameters with respect to given model output(s)?; (ii) could we set some parameter(s) (thus assisting model calibration) at prescribed value(s) without significantly affecting model results?; (iii) at which space/time locations can one expect the highest sensitivity of model output(s) to model parameters and/or knowledge of which parameter(s) could be most beneficial for model calibration?The variance-based Sobol&#8217; Indices (e.g., Sobol, 2001) represent one of the most widespread GSA metrics, quantifying the average reduction in the variance of a model output stemming from knowledge of the input. Amongst other techniques, Dell&#8217;Oca et al. [2017] proposed a moment-based GSA approach which enables one to quantify the influence of uncertain model parameters on the (statistical) moments of a target model output.Here, we embed in these sensitivity indices the effect of uncertainties both in the system model conceptualization and in the ensuing model(s) parameters. The study is grounded on the observation that physical processes and natural systems within which they take place are complex, rendering target state variables amenable to multiple interpretations and mathematical descriptions. As such, predictions and uncertainty analyses based on a single model formulation can result in statistical bias and possible misrepresentation of the total uncertainty, thus justifying the assessment of multiple model system conceptualizations. We then introduce copula-based sensitivity metrics which allow characterizing the global (with respect to the input) value of the sensitivity and the degree of variability (across the whole range of the input values) of the sensitivity for each value that the prescribed model output can possibly undertake, as driven by a governing model. In this sense, such an approach to sensitivity is global with respect to model input(s) and local with respect to model output, thus enabling one to discriminate the relevance of an input across the entire range of values of the modeling goal of interest. The methodology is demonstrated in the context of flow and reactive transport scenarios.&#160;ReferencesSobol, I. M., 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Sim., 55, 271-280.Dell&#8217;Oca, A., Riva, M., Guadagnini, A., 2017. Moment-based metrics for global sensitivity analysis of hydrological systems. Hydr. Earth Syst. Sci., 21, 6219-6234.

How to perform global sensitivity analysis of a catchment-scale, distributed pesticide transfer model? Application to the PESHMELBA model

10.5194/gmd-2021-425 ◽

2021 ◽

Author(s):

Emilie Rouzies ◽

Claire Lauvernet ◽

Bruno Sudret ◽

Arthur Vidard

Keyword(s):

Water Quality ◽

Sensitivity Analysis ◽

Transfer Model ◽

Valuable Insight ◽

Catchment Scale ◽

Sobol Indices ◽

Global Sensitivity ◽

Sensitivity Indices ◽

Abstract. Pesticide transfers in agricultural catchments are responsible for diffuse but major risks to water quality. Spatialized pesticide transfer models are useful tools to assess the impact of the structure of the landscape on water quality. Before considering using these tools in operational contexts, quantifying their uncertainties is a preliminary necessary step. In this study, we explored how global sensitivity analysis can be applied to the recent PESHMELBA pesticide transfer model to quantify uncertainties on transfer simulations. We set up a virtual catchment based on a real one and we compared different approaches for sensitivity analysis that could handle the specificities of the model: high number of input parameters, limited size of sample due to computational cost and spatialized output. We compared Sobol' indices obtained from Polynomial Chaos Expansion, HSIC dependence measures and feature importance measures obtained from Random Forest surrogate model. Results showed the consistency of the different methods and they highlighted the relevance of Sobol' indices to capture interactions between parameters. Sensitivity indices were first computed for each landscape element (site sensitivity indices). Second, we proposed to aggregate them at the hillslope and the catchment scale in order to get a summary of the model sensitivity and a valuable insight into the model hydrodynamical behaviour. The methodology proposed in this paper may be extended to other modular and distributed hydrological models as there has been a growing interest in these methods in recent years.

Considerations and Caveats when Applying Global Sensitivity Analysis Methods to Physiologically Based Pharmacokinetic Models

The AAPS Journal ◽

10.1208/s12248-020-00480-x ◽

2020 ◽

Vol 22 (5) ◽

Author(s):

Dan Liu ◽

Linzhong Li ◽

Amin Rostami-Hodjegan ◽

Frederic Y. Bois ◽

Masoud Jamei

Keyword(s):

Sensitivity Analysis ◽

Plasma Concentration ◽

Model Parameters ◽

Model Parameter ◽

Global Sensitivity ◽

Physiologically Based ◽

The Impact ◽

Influential Parameters

Abstract Three global sensitivity analysis (GSA) methods (Morris, Sobol and extended Sobol) are applied to a minimal physiologically based PK (mPBPK) model using three model drugs given orally, namely quinidine, alprazolam, and midazolam. We investigated how correlations among input parameters affect the determination of the key parameters influencing pharmacokinetic (PK) properties of general interest, i.e., the maximal plasma concentration (Cmax) time at which Cmax is reached (Tmax), and area under plasma concentration (AUC). The influential parameters determined by the Morris and Sobol methods (suitable for independent model parameters) were compared to those determined by the extended Sobol method (which considers model parameter correlations). For the three drugs investigated, the Morris method was as informative as the Sobol method. The extended Sobol method identified different sets of influential parameters to Morris and Sobol. These methods overestimated the influence of volume of distribution at steady state (Vss) on AUC24h for quinidine and alprazolam. They also underestimated the effect of volume of liver (Vliver) for all three drugs, the impact of enzyme intrinsic clearance of CYP2C9 and CYP2E1 for quinidine, and that of UGT1A4 abundance for midazolam. Our investigation showed that the interpretation of GSA results is not straightforward. Dismissing existing model parameter correlations, GSA methods such as Morris and Sobol can lead to biased determination of the key parameters for the selected outputs of interest. Decisions regarding parameters’ influence (or otherwise) should be made in light of available knowledge including the model assumptions, GSA method limitations, and inter-correlations between model parameters, particularly in complex models.

Investigation of determinism-related issues in the Sobol′ low-discrepancy sequence for producing sound global sensitivity analysis indices

ANZIAM Journal ◽

10.21914/anziamj.v62.16094 ◽

2021 ◽

Vol 62 ◽

pp. C84-C97

Author(s):

Xifu Sun ◽

Barry Croke ◽

Stephen Roberts ◽

Anthony Jakeman

Keyword(s):

Sensitivity Analysis ◽

Model Parameters ◽

Type I ◽

Random Sequences ◽

Global Sensitivity ◽

Low Discrepancy Sequences ◽

Sensitivity Indices ◽

Sequence Generator ◽

Math Phys

A computationally efficient and robust sampling scheme can support a sensitivity analysis of models to discover their behaviour through Quasi Monte Carlo approximation. This is especially useful for complex models, as often occur in environmental domains when model runtime can be prohibitive. The Sobol' sequence is one of the most used quasi-random low-discrepancy sequences as it can explore the parameter space significantly more evenly than pseudo-random sequences. The built-in determinism of the Sobol' sequence assists in achieving this attractive property. However, the Sobol' sequence tends to deteriorate in the sense that the estimated errors are distributed inconsistently across model parameters as the dimensions of a model increase. By testing multiple Sobol' sequence implementations, it is clear that the deterministic nature of the Sobol' sequence occasionally introduces relatively large errors in sensitivity indices produced by well-known global sensitivity analysis methods, and that the errors do not diminish by averaging through multiple replications. Problematic sensitivity indices may mistakenly guide modellers to make type I and II errors in trying to identify sensitive parameters, and this will potentially impact model reduction attempts based on these sensitivity measurements. This work investigates the cause of the Sobol' sequence's determinism-related issues. References I. A. Antonov and V. M. Saleev. An economic method of computing LPτ-sequences. USSR Comput. Math. Math. Phys. 19.1 (1979), pp. 252–256. doi: 10.1016/0041-5553(79)90085-5 P. Bratley and B. L. Fox. Algorithm 659: Implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Soft. 14.1 (1988), pp. 88–100. doi: 10.1145/42288.214372 J. Feinberg and H. P. Langtangen. Chaospy: An open source tool for designing methods of uncertainty quantification. J. Comput. Sci. 11 (2015), pp. 46–57. doi: 10.1016/j.jocs.2015.08.008 on p. C90). S. Joe and F. Y. Kuo. Constructing Sobol sequences with better two-dimensional projections. SIAM J. Sci. Comput. 30.5 (2008), pp. 2635–2654. doi: 10.1137/070709359 S. Joe and F. Y. Kuo. Remark on algorithm 659: Implementing Sobol’s quasirandom sequence generator. ACM Trans. Math. Soft. 29.1 (2003), pp. 49–57. doi: 10.1145/641876.641879 W. J. Morokoff and R. E. Caflisch. Quasi-random sequences and their discrepancies. SIAM J. Sci. Comput. 15.6 (1994), pp. 1251–1279. doi: 10.1137/0915077 X. Sun, B. Croke, S. Roberts, and A. Jakeman. Comparing methods of randomizing Sobol’ sequences for improving uncertainty of metrics in variance-based global sensitivity estimation. Reliab. Eng. Sys. Safety 210 (2021), p. 107499. doi: 10.1016/j.ress.2021.107499 S. Tarantola, W. Becker, and D. Zeitz. A comparison of two sampling methods for global sensitivity analysis. Comput. Phys. Com. 183.5 (2012), pp. 1061–1072. doi: 10.1016/j.cpc.2011.12.015 S. Tezuka. Discrepancy between QMC and RQMC, II. Uniform Dist. Theory 6.1 (2011), pp. 57–64. url: https://pcwww.liv.ac.uk/~karpenk/JournalUDT/vol06/no1/5Tezuka11-1.pdf I. M. Sobol′. On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys. 7.4 (1967), pp. 86–112. doi: 10.1016/0041-5553(67)90144-9 I. M. Sobol′. Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp 1.4 (1993), pp. 407–414.

Hierarchical Sensitivity Analysis for Large Scale Process-based Hydrological Modeling with Application in an Amazonian Watershed

10.5194/hess-2019-246 ◽

2019 ◽

Author(s):

Haifan Liu ◽

Heng Dai ◽

Jie Niu ◽

Bill X. Hu ◽

Han Qiu ◽

...

Keyword(s):

Sensitivity Analysis ◽

Large Scale ◽

Overland Flow ◽

Hydrologic Model ◽

Model Parameters ◽

Hydrological Models ◽

Global Sensitivity ◽

Uncertainty Sources ◽

Sensitivity Indices

Abstract. Sensitivity analysis is an effective tool for identifying important uncertainty sources and improving model calibration and predictions, especially for integrated systems with heterogeneous parameter inputs and complex processes coevolution. In this work, an advanced hierarchical global sensitivity analysis framework, which integrates a hierarchical uncertainty framework and a variance-based global sensitivity analysis, was implemented to quantitatively analyze several uncertainties of a three-dimensional, process-based hydrologic model (PAWS). The uncertainty sources considered include model parameters, model structures (with/without overland flow module), and climate forcing. We apply the approach in a ~ 9000 km2 Amazon catchment modeled at 1 km resolution to provide a demonstration of multiple uncertainty source quantification using a large-scale process-based hydrologic model. The sensitivity indices are assessed based on three important hydrologic outputs: evapotranspiration (ET), ground evaporation (EG), and groundwater contribution to streamflow (QG). It is found that, in general, model parameters (especially those within the streamside model grid cells) are the most important uncertainty contributor for all sensitivity indices. In addition, the overland flow module significantly contributes to model predictive uncertainty. These results can assist model calibration and provide modelers a better understanding of the general sources of uncertainty in predictions of complex hydrological systems in Amazonia. We demonstrated a pilot example for comprehensive global sensitivity analysis of large-scale complex hydrological models in this research. The hierarchical sensitivity analysis methodology used is mathematically rigorous and can be applied to a wide range of large-scale hydrological models with various sources of uncertainty.

Global sensitivity analysis for a stochastic flow problem

Monte Carlo Methods and Applications ◽

10.1515/mcma-2018-2022 ◽

2018 ◽

Vol 24 (4) ◽

pp. 263-270

Author(s):

Dmitriy Kolyukhin

Keyword(s):

Sensitivity Analysis ◽

Single Phase ◽

Numerical Procedure ◽

Model Parameters ◽

Saturated Porous Media ◽

Global Sensitivity ◽

Flow Through ◽

The Impact ◽

Total Model

Abstract The paper is devoted to the modeling of a single-phase flow through saturated porous media. A statistical approach where permeability is considered as a lognormal random field is applied. The impact of permeability, random boundary conditions and wells pressure on the flow in a production well is studied. A numerical procedure to generate an ensemble of realizations of the numerical solution of the problem is developed. A global sensitivity analysis is performed using Sobol indices. The impact of different model parameters on the total model uncertainty is studied.

Global Sensitivity Analysis for Field Response Based on the Manifold of Feature Covariance Matrix

10.1115/detc2021-69086 ◽

2021 ◽

Author(s):

Zhouzhou Song ◽

Zhao Liu ◽

Can Xu ◽

Ping Zhu

Keyword(s):

Sensitivity Analysis ◽

Covariance Matrix ◽

Computational Models ◽

Feature Selection Method ◽

Global Sensitivity ◽

Sensitivity Indices ◽

Field Response ◽

Input Variables ◽

Abstract In real-world applications, it is commonplace that the computational models have field responses, i.e., the temporal or spatial fields. It has become a critical task to develop global sensitivity analysis (GSA) methods to measure the effect of each input variable on the full-field. In this paper, a new sensitivity analysis method based on the manifold of feature covariance matrix (FCM) is developed for quantifying the impact of input variables on the field response. The method firstly performs feature extraction on the field response to obtain a low-dimensional FCM. An adaptive feature selection method is proposed to avoid the FCM from singularity. Thereby, the field response is represented by a FCM, which lies on a symmetric positive-definite matrix manifold. Then, the GSA technique based on the Cramér-von Mises distance for output valued on the Riemannian manifold is introduced for estimating the sensitivity indices for field response. An example of a temporal field and an example of a 2-D displacement field are introduced to demonstrate the applicability of the proposed method in estimating global sensitivity indices for field solution. Results show that the proposed method can distinguish the important input variables correctly and can yield robust index values. Besides, the proposed method can be implemented for GSA for field responses of different dimensionalities.

Exploring the impact of forcing error characteristics on physically based snow simulations within a global sensitivity analysis framework

Hydrology and Earth System Sciences ◽

10.5194/hess-19-3153-2015 ◽

2015 ◽

Vol 19 (7) ◽

pp. 3153-3179 ◽

Cited By ~ 68

Author(s):

M. S. Raleigh ◽

J. D. Lundquist ◽

M. P. Clark

Keyword(s):

Sensitivity Analysis ◽

Snow Water Equivalent ◽

Model Parameters ◽

Random Errors ◽

Global Sensitivity ◽

Error Characteristics ◽

Physically Based ◽

Snow Water ◽

Abstract. Physically based models provide insights into key hydrologic processes but are associated with uncertainties due to deficiencies in forcing data, model parameters, and model structure. Forcing uncertainty is enhanced in snow-affected catchments, where weather stations are scarce and prone to measurement errors, and meteorological variables exhibit high variability. Hence, there is limited understanding of how forcing error characteristics affect simulations of cold region hydrology and which error characteristics are most important. Here we employ global sensitivity analysis to explore how (1) different error types (i.e., bias, random errors), (2) different error probability distributions, and (3) different error magnitudes influence physically based simulations of four snow variables (snow water equivalent, ablation rates, snow disappearance, and sublimation). We use the Sobol' global sensitivity analysis, which is typically used for model parameters but adapted here for testing model sensitivity to coexisting errors in all forcings. We quantify the Utah Energy Balance model's sensitivity to forcing errors with 1 840 000 Monte Carlo simulations across four sites and five different scenarios. Model outputs were (1) consistently more sensitive to forcing biases than random errors, (2) generally less sensitive to forcing error distributions, and (3) critically sensitive to different forcings depending on the relative magnitude of errors. For typical error magnitudes found in areas with drifting snow, precipitation bias was the most important factor for snow water equivalent, ablation rates, and snow disappearance timing, but other forcings had a more dominant impact when precipitation uncertainty was due solely to gauge undercatch. Additionally, the relative importance of forcing errors depended on the model output of interest. Sensitivity analysis can reveal which forcing error characteristics matter most for hydrologic modeling.