Toward a more robust variance-based global sensitivity analysis of model outputs

Load modeling plays an important role in accessing and enhancing the dynamic stability of power systems. Though the Synthesis Load Model Considering Voltage Regulation of Distribution Network ( $\pi $ model) has high accuracy, its parameters are too many. In order to improve the identification efficiency and reduce the difficulty of identification, a simplified model identification strategy based on parameter sensitivity analysis is proposed. Firstly, based on the global sensitivity analysis, the sensitivity analysis of the model parameters is carried out to obtain the First Order Sensitivity Indices ( FSI )and Total Sensitivity Indices ( TSI ). Secondly, the FSI and TSI of each parameter are analyzed, and the effect on the output of model of each parameter is determined by FSI . For less influential parameters, whether the parameter should be fixed as constant is determined by the value of TSI . The parameter whose TSI equal or approximately equal to zero should be fixed as a constant. Finally, the improved genetic algorithm is used to identify the parameter-simplified model, and the effectiveness of the simplified identification strategy is verified by comparing the fitting effects with the measured curve and the residual and the integrated parameter models.

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.

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. 

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

Evaluation of multiple reduced-order models to enhance confidence in global sensitivity analyses

Global sensitivity analysis has been widely used to detect the relative contributions of input variables to the uncertainty of model output, and then more resources can be assigned to the important input variables to reduce the uncertainty of model output more efficiently. In this paper, a new kind of global sensitivity index based on Gini’s mean difference is proposed. The proposed sensitivity index is more robust than the variance-based first order sensitivity index for the cases with non-normal distributions. Through the decomposition of Gini’s mean difference, it shows that the proposed sensitivity index can be represented by the energy distance, which measures the difference between probability distributions. Therefore, the proposed sensitivity index also takes the probability distribution of model output into consideration. In order to estimate the proposed sensitivity index efficiently, an efficient Monte Carlo simulation method is also proposed, which avoids the nested sampling procedure. The test examples show that the proposed sensitivity index is more robust than the variance-based first order sensitivity index for the cases with non-normal distributions.

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.

Tube hydroforming process is widely used in various industrial applications which consists of combining internal pressure and axial displacement to manufacture tubular parts. Inappropriate choice as small changes in such variables may affect the process stability and, in some cases, lead to failure. Consequently, loading path should be optimised to better control the process and to guarantee hydroformed parts with desired specifications. However, optimisation procedure requires several evaluations of the real models which induces a huge computational time. To cope with this limitation, we propose to compare two metamodelling techniques to solve the problem efficiently: the response surface method and the least squares support vector regression. To enhance the metamodels precision, optimal latin hypercube design is used to generate sampled points. It is obtained through iterative optimisation procedure based on a modified version of the simulated annealing algorithm by minimising simultaneously two optimality criterions. Then, multi-objective optimisation problem is formulated to search for the Pareto optimal solutions. Fuzzy classification is then applied to rank the non-dominated solutions which helps designers in the decision-making phase. Before optimising the process, a global sensitivity analysis is carried out using the variance-based method by coupling metamodels and Monte Carlo simulations in order to identify the relative importance of the design variables in terms of internal pressure and axial displacement on the variance of the responses of interest defined to control the process.

Unraveling the complex dynamics of temporal moments for multispecies contaminant transport in saturated porous media: A global sensitivity analysis approach

This paper presents a step-by-step procedure to study the impact of each thermal phenomenon occurring in electric machines on their internal temperature distribution. First, the Monte-Carlo method is chosen as a global sensitivity analysis technique. This method is applied on a thermal network of a prototype consisting of a permanent magnet based integrated starter-generator machine (ISG). Accordingly, the variation of electric machine critical temperatures in windings and rotor's permanent magnets is evaluated. In addition, a sensitivity index is defined for identifying network parameters that cause significant variation in the machine critical temperatures and should therefore be the focus of attention when designing electric machines. Finally, experimental tests are performed on the prototype and the difference between simulated and a measured temperature is presented.

The design space (DS) is defined as the combination of materials and process conditions that provides assurance of quality for a pharmaceutical product. A model-based approach to identify a probability-based DS requires costly simulations across the entire process parameter space (certain) and the uncertain model parameter space and material properties space. We demonstrate that application of global sensitivity analysis (GSA) can significantly reduce model complexity and reduce computational time for identifying and quantifying a probabilistic DS by screening out nonimportant uncertain parameters. The novelty of this approach is that the use of an indicator function, which takes only binary values as a model function, allows application of a straightforward GSA based on Sobol' sensitivity indices and avoids using more costly Monte Carlo filtering or GSA for constrained problems. We consider a chemical reaction example to illustrate how this formulation results in a model reduction and a significant decrease of model runs.

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.

Constrained Global Sensitivity Analysis: Sobol’ indices for problems in non-rectangular domains

The identification of model effective dimensions using global sensitivity analysis

Benchmarking the PAWN distribution-based method against the variance-based method in global sensitivity analysis: Empirical results