Simplified Identification Strategy of Load Model Based on Global Sensitivity Analysis

Global sensitivity analysis (GSA) measures the variation of a model output as a function of the variations of the model inputs given their ranges. In this paper we consider variance-based GSA methods that do not rely on certain assumptions about the model structure such as linearity or monotonicity. These variance-based methods decompose the output variance into terms of increasing dimensionality called 'sensitivity indices', first introduced by Sobol' [25]. Sobol' developed a method of estimating these sensitivity indices using Monte Carlo simulations. McKay [13] proposed an efficient method using replicated Latin hypercube sampling to compute the 'correlation ratios' or 'main effects', which have been shown to be equivalent to Sobol's first-order sensitivity indices. Practical issues with using these variance estimators are how to choose adequate sample sizes and how to assess the accuracy of the results. This paper proposes a modified McKay main effect method featuring an adaptive procedure for accuracy assessment and improvement. We also extend our adaptive technique to the computation of second-order sensitivity indices. Details of the proposed adaptive procedure as wells as numerical results are included in this paper.

Time series global sensitivity analysis of genetic parameters of CERES-maize model under water stresses at different growth stages

Improved understanding of dynamic hydrological performance of green roof (GR) design parameters towards different model responses is important for maximizing its target design goals at the unit-scale. Replication of an optimally designed GR unit at the catchment-scale significantly contributes to achieving its target design goals (i.e., surface runoff reduction, urban flood reduction, peak flow control, etc.). Moreover, adequate efforts are required to explore and provide appropriate knowledge about the categorization of influential and non-influential design parameters with their suitable design spaces to guide researchers, drainage engineers, and stormwater management practitioners for effective and efficient planning, designing and optimization of GR at catchment-scales.This study employs a robust and comprehensive global sensitivity analysis (GSA) method known as the variogram analysis of response surfaces (VARS) for sensitivity analysis of GR design parameters. Firstly, a total of 13,999 sample points for 14 GR parameters of three layers (i.e., surface, soil and drainage mat) are generated by using the latin hypercube sampling technique and their factor spaces are decided based on design guidelines in current SWMM manuals. Following that, the PySWMM is used to simulate these design samples in a Monte-Carlo-type setting on a conceptual catchment of 0.01km2 (100m2 × 100m2) with 50% treatment area of GR, and the model responses (e.g., surface infiltration, surface outflow, storage volume, and peak flow) are estimated and applied for sensitivity analysis. Finally, VARS evaluates different sensitivity analysis metrics by using different model responses corresponding to their designed samples.Overall, the senstivity analysis results demonstrate that 8 out of 14 design parameters are highly influential on different model responses, however, the parameters’ sensitivity varies towards different model responses under different perturbation scales and rainfall conditions. Moreover, the selection of an effective range of design space of design parameters is necessary as it has a higher influence on model responses, while the parameters’ rankings and contributions to total sensitivity indices change with the range of design spaces. Furthermore, this research also provides an opportunity through VARS directional variogram index (an integrated sensitivity index) to study and understand the underlying mechanisms of design parameters under different perturbation scales with no extra computational burden. Senstivity analysis results will be presented with insights and recommendations for other regions, which will be helpful for decision-makers for effective planning, designing and implementation of GR. The findings of this parametric study would be helpful for the calibration and optimization of design parameters of GR for different case studies. 

The goal of this paper is to solve the global sensitivity analysis for a particular control problem. More precisely, the boundary control problem of an open-water channel is considered, where the boundary conditions are defined by the position of a downstream overflow gate and an upperstream underflow gate. The dynamics of the water depth and of the water velocity are described by the Shallow Water equations, by taking into account the bottom and friction slopes. Since some physical parameters are unknown, a stabilizing boundary control is first computed for their nominal values, and then a sensitivity analysis is performed to measure the impact of the uncertainty in the parameters on a given to-be-controlled output. The unknown physical parameters are described by some probability distribution functions. Numerical simulations are performed to measure the first-order and total sensitivity indices.

Event Abstract Back to Event Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis Olivia Eriksson1, 2*, Alexandra Jauhiainen1, 3, Sara Maad Sasane4, Anu G Nair5, Carolina Sartorius4 and Jeanette Hellgren Kotaleski2, 5, 6 1 Contributed equally to this work, Sweden 2 Stockholm University, Department of Numerical Analysis and Computer Science, Sweden 3 AstraZeneca AB R&D, Early Clinical Biometrics, Sweden 4 Lund University, Centre for Mathematical Sciences, Sweden 5 KTH Royal Institute of Technology, School of Computer Science and Communication, Sweden 6 Karolinska Institute, Department of Neuroscience, Sweden Computational dynamical models describing intracellular signaling pathways of nerve cells are increasing in size and complexity as more information is obtained from experiments. Models describing protein interactions within neurons can contain over hundred protein reactions [1, 2]. These models are built from knowledge about the interaction topology, inferred from e.g. gene knock-out experiments, as well as from experimental quantitative data describing the input-output relationship of the observed system. The quantitative data are often sparse as compared to the size of the system, and translating the experimental information into dynamical models often results in large uncertainties in the parameter (e.g reaction rates) values. This uncertainty is partly due to the sparseness in experimental time series data (practical unidentifiability), but it is also an intrinsic feature of the modeled system (structural unidentifiability) and could reflect the possibility for biological variation [3]; in many biological systems the same function can be achieved in partly different ways due to degeneracy and redundancy. Here we investigate the extent of this parameter uncertainty, in a model describing calcium (Ca)-dependent activation of Calmodulin (CaM), Protein phosphatase 2B (PP2B) and Ca/CaM-dependent protein kinase II (CamKII) [4], which is an intracellular pathway of importance to synaptic plasticity. We presume that the structure of the model is correct and then characterize the uncertainty in the parameters based on data. This is done by sampling the subspace of parameter values which has an equally good fit to data (corresponding to the “viable space” in [5]), through a statistical approach known as Approximate Bayesian Computation (ABC) with Markov Chain Monte Carlo (MCMC) [6]. ABC has been proposed for parameter estimation in system biology models previously, albeit in slightly different settings, e.g. [7, 8], and can be applied to a wide range of problems. In order to characterize the viable space efficiently with several experimental datasets, we employ multivariate probability distributions called copulas as a part of the ABC sampling. The result is a multivariate posterior distribution for the parameters, which represents how much they are constrained by the data (i.e. the uncertainty) as illustrated in Figure 1 (pairwise plots of viable space for four parameters indicating constraints and dependencies before and after calibration to data). The next step is to look into how the parameter uncertainty is translated to uncertainty of the predictions made from the model. We also investigate the role and importance of different parameters, with respect to different model outputs including the predictions, by means of global sensitivity analysis [9]. Figure 2 illustrates the sensitivity of one of the outputs calculated by a method based on the decomposition of the variance [10, 11, 12], showing different types of sensitivity measures. Finally, we explore how the sensitivity of different subsets of parameters change as different parts of the viable space are investigated, which is shown in Figure 3, where sensitivity profiles are clustered into groups with different sensitivity characteristics. Figure 1 Figure 2 Figure 3 Acknowledgements This research was supported by funding from the Swedish e-Science Research Centre and the Human Brain Project References [1] Gutierrez-Arenas O, Eriksson O, Hellgren Kotaleski J (2014) Segregation and Crosstalk of D1 Receptor-Mediated Activation of ERK in Striatal Medium Spiny Neurons upon Acute Administration of Psychostimulants. PLoS Comput Biol 10, e1003445. [2] Nair AG, Gutierrez-Arenas O, Eriksson O, Vincent P, and Hellgren Kotaleski J (2015) Sensing Positive versus Negative Reward Signals through Adenylyl Cyclase-Coupled GPCRs in Direct and Indirect Pathway Striatal Medium Spiny Neurons. J. Neuroscience 35, 14017-14030. [3] Marder E, Goeritz ML, Otopalik AG (2015) Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms. Curr Opin Neurobiol 31, 156-163. [4] Nair AG, Gutierrez-Arenas O, Eriksson O, Jauhiainen A, Blackwell KT and Kotaleski, JH (2014). Modeling intracellular signaling underlying striatal function in health and disease. Progress in molecular biology and translational science, 123, 277 [5] Zamora-Sillero E, Hafner M, Ibig A, Stelling J, and Wagner, A. (2011). Efficient characterization of high-dimensional parameter spaces for systems biology. BMC systems biology 5, 142. [6] Marjoram P, Molitor J, Plagnol V, and Tavare S (2003) Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U.S.A. 100, 15324–15328. [7] Toni T, Welch D, Strelkowa N, Ipsen A, and Stumpf MP. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface, 6, 187–202. [8] Liepe J, Kirk P, Filippi S, Toni T, Barnes CP, and Stumpf MP. A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat Protoc, 9, 439–456. [9] Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S Global sensitivity analysis: the primer. In Wiley 2008 New York, NY:Wiley. [10] Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul. 55, 271–280. [11] Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comp Phys Comm 145, 280 – 297. [12] Halnes G, Ulfhielm E Ljunggren EE, Kotaleski JH and Rospars JP (2009) Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons. Journal of computational neuroscience 27, 471-491. Keywords: sensitivity analysis, Approximate Bayesian Computation, copulas, intracellular signalling, Dynamical Modeling, global sensitivity analysis, Markov chain Monte Carlo, variance decomposition Conference: Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016. Presentation Type: Investigator presentations Topic: Computational neuroscience Citation: Eriksson O, Jauhiainen A, Maad Sasane S, Nair A, Sartorius C and Hellgren Kotaleski J (2016). Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis. Front. Neuroinform. Conference Abstract: Neuroinformatics 2016. doi: 10.3389/conf.fninf.2016.20.00014 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 31 May 2016; Published Online: 18 Jul 2016. * Correspondence: PhD. Olivia Eriksson, Contributed equally to this work, Stockholm, Sweden, olivia@kth.se Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Scholar Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski PubMed Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

In support of ESA's Earth Explorer 8 candidate mission FLEX (FLuorescence EXplorer), a Photosynthesis Study has been initiated to quantitatively link fluorescence to photosynthesis. This led to the development of A-SCOPE, a graphical user interface software package that integrates multiple biochemical models into the soil-vegetation-atmosphere-transfer model SCOPE. Its latest version (v1.53) has been successfully verified and was subsequently evaluated through a global sensitivity analysis. By using the method of Saltelli [4], the relative importance of each input variable to model outputs was quantified through first order and total effect sensitivity indices. Variations in leaf area index (LAI) and chlorophyll content are mostly impacting the reflectance and fluorescence signal. Non-driving variables that can be safely set to default values have been identified and will facilitate consolidating SCOPE into an operational and invertible model.

Global Sensitivity Analysis of Arrhythmic Risk Biomarkers in Cardiac Single Cell Models

The growing body of knowledge on modeling land use systems points to epistemic uncertainty as one of the challenging obstacles in development and application of agent-based models (ABMs). To decrease outcome uncertainty, sensitivity analysis (SA) is performed as part of model verification and validation. Oftentimes, however, it is inadequately addressed, partly because of the lack of tools and techniques that focus on an explicit evaluation of ABM dynamics. The nonlinear processes, inherent in such models, necessitate longitudinal SA with time path investigation of input–output relationships of endogenous variables. In response to the outlined deficiencies, this study investigates the potential of time-dependent global sensitivity analysis (time-GSA) in examining the dynamics of outcome uncertainty of a simple ABM of land use change. Specifically, we apply first and total order sensitivity indices to decompose variance of output landscape fragmentation, apportioned to model inputs for multiple time steps and multiple realizations of the ABM. We focus the analysis on selected complex systems characteristics including preference uncertainty, path dependence, access to information, and magnitude of interactions and feedbacks. We conclude that the factor sensitivity measures vary significantly during model execution. Consequently, a static snapshot of ABM sensitivity, taken at the end of the simulation, is inadequate when deciding on factor prioritization and reduction. Assuming that ABM dynamics is a result of factor interaction, we observe a distinct time lag of nonlinearity, which unfolds after the formation of the seeds of development. Therefore, we argue for further application of time-GSA in ABM as one of the visual quantitative techniques contributing to evaluation of ABM nonlinearity.

Parametric sensitivity analysis (SA) is an essential tool in optical data analysis aiming to quantify the relative importance of optical model parameters and identify those with a low influence which should remain fixed during analysis in order to simplify a model. Typically, such sensitivity studies are performed using a local sensitivity analysis, also referred to as “one-at-a-time” analysis, which estimates parameter sensitivity by evaluating the changes in model output while perturbing one parameter at a time and holding all other parameters fixed. All the pitfalls of the local sensitivity approach are quite obvious and well known; however, local SA is still prevailing in the area of data analysis for spectroscopic ellipsometry. In this study, we discuss applications of a global qualitative analysis introduced by Morris in 1991 which determines an overall significance for each model parameter and describes its nonlinear effect on model’s output and/or interactions with other parameters. The Morris method allows effective separation of the model parameters into different groups such as parameters with negligible effects, parameters with large linear effects without interactions, and parameters with large nonlinear and/or interaction effects. Here, we carried out the Morris sensitivity analysis to reveal the model parameter significance ranking in a test case of the B-spline model for titanium nitride (TiN). Such a screening approach can be considered as a practical tool for the initial global SA strategy prior to true “all-at-a-time” global sensitivity analysis.

In pharmacometrics, understanding a covariate effect on an interested outcome is essential for assessing the importance of the covariate. Variance-based global sensitivity analysis (GSA) can simultaneously quantify contribution of each covariate effect to the variability for the interested outcome considering with random effects. The aim of this study was to apply GSA to pharmacometric models to assess covariate effects. Simulations were conducted with pharmacokinetic models to characterize the GSA for assessment of covariate effects and with an example of quantitative systems pharmacology (QSP) models to apply the GSA to a complex model. In the simulations, covariate and random variables were generated to simulate the outcomes using the models. Ratios of variance explained by each factor (each covariate and random effect) over the overall variance of the outcome were used as sensitivity indices. The sensitivity indices were consistent with the effect size of covariate. The sensitivity indices identified the importance of creatinine clearance on the pharmacokinetic exposure for a renally-excreted drug. These sensitivity indices could be applied to plasma concentrations over time (repeated measurable outcomes over time) as interested outcomes. Using the GSA, each contribution of all of the covariate effects could be efficiently identified even in the complex QSP model. Variance-based GSA can provide insight when considering the importance of covariate effects by simultaneously and quantitatively assessing all covariate and random effects on interested outcomes in pharmacometrics.

This article focuses on reliability-oriented global sensitivity analysis of the fatigue limit state of a steel member stressed by many times repeated loading. The fatigue limit state is associated with fatigue failure, which is caused by brittle fracture due to propagation of a fatigue crack from initial to critical size. The fatigue crack propagation is analysed using linear fracture mechanics. The fundamental question in terms of structural reliability is how significant is the effect of input random quantities on the probability of failure. A new type of global sensitivity analysis subordinated to a contrast identified the equivalent stress range and initial edge crack length as random quantities that most significantly influence the failure probability. The new findings obtained using the contrast-based global sensitivity analyses show interaction effects that are unusually strong in comparison with some results of Sobol’s sensitivity analysis aimed at the reliability of structures. The sensitivity indices are estimated using double-nested-loop simulation of the Latin Hypercube Sampling method.

Global sensitivity analysis (GSA) is useful to recognize important inputs for assigning priority and unimportant inputs for simplifying models by exploring whole distribution ranges. Meanwhile, regional sensitivity analysis (RSA) is also studied for finding the contribution of the critical region of an input, which can be viewed as the complementary of GSA. However, there is a lack of GSA and RSA research in presence of fuzzy uncertainty. Thus, a new global sensitivity index (GSI) under the fuzzy uncertainty is devoted on the credibility distribution function (CrDF), a comprehensive distribution description under the fuzzy uncertainty. The CrDF-based GSI is defined by the fuzzy expectation of the difference between the CrDF and the conditional CrDF of the output on fixing the fuzzy input over its whole distribution range, which can quantify the contribution of the fuzzy input to the output CrDF. Then, a new fuzzy RSA technique, the contribution to this CrDF based index (shortened by CCI) plot, is also proposed, and it can assess the effect of given regions of important inputs on output CrDF. Besides, mathematical properties of the CrDF based GSI and the CCI plot are discussed, and their solution are established by use of the fuzzy simulation with the same set of samples. After the accuracy of established fuzzy simulation solution for the CrDF based GSI and the CCI plot are verified by an analytical example, other examples are used to demonstrate the reasonability and applicability of proposed CrDF based GSI and CCI plot under fuzzy uncertainty.

Sensitivity analyses are frequently used during the design of engineering systems to qualify and quantify the effect of parametric variation in the performance of a system. Two primary types of sensitivity analyses are generally used: local and global. Local analyses, generally involving derivative-based measures, have a significantly lower computational burden than global analyses but only provide measures of sensitivity around a nominal point. Global analyses, generally performed with a Monte Carlo sampling approach, and variation-based measures provide a complete description of sensitivity but incur a large computational burden and require information regarding the distributions of the design parameters in a concept. Local analyses are generally suited to the early stages of design when parametric information is limited, and a large number of concepts must be evaluated (necessitating a light computational burden). Global analyses are more suited to the later stages of design when more information about parametric distributions is available and fewer concepts are under consideration. Current derivative-based local approaches provide a different and incompatible set of measures than a global variation-based analysis. This makes a direct comparison of local to global measures ill posed. To reconcile local and global sensitivity analyses, a hybrid local variation-based sensitivity (HyVar) approach is presented. This approach has a similar computational burden to a local approach but produces measures or percentage contributions. The HyVar approach is directly comparable to global variation-based approaches. In this paper, the HyVar sensitivity analysis method is developed in the context of a functional based behavioral modeling framework. An example application of the method is presented along with a summary of results produced from a more comprehensive example.

Four methods for global sensitivity analysis are studied with respect to their applicability in the finite element analysis of composite structures: (1) sensitivities based on the variance conditional expectation involving experimental design, (2) Morris' elementary effects method (including recent improvements to effective trajectory selection), (3) Sobol's main and total sensitivity indices, and (4) the root mean square of approximate derivatives at sampled points. The sensitivities of the first ten natural frequencies to the composite material properties as well as to the ply stack are determined. The methods are compared and an assessment of their applicability is made in the case of a fairly large number (d > 25) of uncertain parameters.

A re-sampling statistics based imprecise moment independent global sensitivity analysis methodology with limited data of uncorrelated and correlated geotechnical properties