52 results found
Bilokon P, Kucherenko S, Williams C, 2022, Quasi-Monte Carlo Methods for Calculating Derivatives Sensitivities on the GPU
Bai Z, Wei H, Xiao Y, et al., 2021, A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables, MATHEMATICS, Vol: 9
Zhou C, Shi Z, Kucherenko S, et al., 2021, A unified approach for global sensitivity analysis based on active subspace and Kriging, RELIABILITY ENGINEERING & SYSTEM SAFETY, Vol: 217, ISSN: 0951-8320
Song S, Bai Z, Kucherenko S, et al., 2021, Quantile sensitivity measures based on subset simulation importance sampling, Reliability Engineering & System Safety, Vol: 208, Pages: 1-13, ISSN: 0951-8320
Global sensitivity measures based on quantiles of the output are an efficient tool in measuring the effect of input variables for problems in which α - th quantiles are the functions of interest and for identification of inputs which are the most important in achieving the specific values of the model output. Previously proposed methods for numerical estimation of such measures are costly and not practically feasible in cases in which the quantile level α is very small or high. It is shown that the subset simulation importance sampling (SS-IS) method previously applied for solving small failure probability problems can be efficiently used for estimating quantile global sensitivity measures (QGSM). Considered test cases and engineering examples show that the proposed SS-IS method is more efficient than the previously proposed Monte Carlo method.
Lamboni M, Kucherenko S, 2021, Multivariate sensitivity analysis and derivative-based global sensitivity measures with dependent variables, RELIABILITY ENGINEERING & SYSTEM SAFETY, Vol: 212, ISSN: 0951-8320
Razavi S, Jakeman A, Saltelli A, et al., 2021, The future of sensitivity analysis: An essential discipline for systems modeling and policy support, Environmental Modelling & Software, Vol: 137, Pages: 1-22, ISSN: 1364-8152
Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society.
Kucherenko S, Klymenko O, Shah N, 2021, Application of Machine Learning and Global Sensitivity Analysis for Identification and Visualization of Design Space, Computer Aided Chemical Engineering, Pages: 875-881
The design space (DS) is defined as the combination of materials and process conditions which provides assurance of quality for a pharmaceutical. 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 (e.g. material properties). We demonstrate that application of metamodel-based filters and global sensitivity analysis (GSA) can significantly reduce model complexity and reduce computational time for identifying and quantifying DS. Once DS is identified it is necessary to present it graphically. The output of identification of DS is a multi-dimensional probability map. The projection of the multi-dimensional DS to a 2D representation is still unavoidable irrespectively of the method used to reach such probability mapping. We showed that application of constraint GSA can dramatically reduce the number of required for visualization 2D projections.
Kucherenko S, Giamalakis D, Shah N, et al., 2020, Computationally efficient identification of probabilistic design spaces through application of metamodeling and adaptive sampling, Computers & Chemical Engineering, Vol: 132, Pages: 1-9, ISSN: 0098-1354
The design space (DS) is defined as the combination of materials and process conditions which provides assurance of quality for a pharmaceutical product (e.g. purity, potency, uniformity). A model-based approach to identify a probability-based design space requires simulations across the entire process parameter space (certain) and the uncertain model parameter space and material properties space if explicitly considered by the model. This exercise is a demanding task. A novel theoretical and numerical framework for determining probabilistic DS using metamodelling and adaptive sampling is developed. Several approaches were proposed and tested among which the most efficient is a new multi-step adaptive technique based using a metamodel for a probability map as an acceptance-rejection criterion to optimize sampling to identify the DS. It is shown that application of metamodel-based filters can significantly reduce model complexity and computational costs with speed up of two orders of magnitude observed here.
Atanassov E, Kucherenko S, Karaivanova A, 2020, Global Sensitivity Analysis of Various Numerical Schemes for the Heston Model, 20th Annual International Conference on Computational Science (ICCS), Publisher: SPRINGER INTERNATIONAL PUBLISHING AG, Pages: 520-528, ISSN: 0302-9743
Spiessl SM, Kucherenko S, Becker D-A, et al., 2019, Higher-order sensitivity analysis of a final repository model with discontinuous behaviour using the RS-HDMR meta-modeling approach, Reliability Engineering and System Safety, Vol: 187, Pages: 149-158, ISSN: 0951-8320
Sensitivity analysis is considered a useful tool for determining sensitivities and assessing uncertainties of computational models, which is critical for the performance assessment of final repository models. One group of methods of sensitivity analysis is variance-based methods, which can identify sensitivities of individual parameters and parameter interactions. This is done via computation of Sobol’ sensitivity indices of first and higher orders.Models describing complex physical systems can behave in a highly nonlinear, non-monotonic or even discontinuous manner. Many methods of sensitivity analysis perform poorly or even fail completely on such models. In former investigations with a model of this kind, we could not identify any method capable of calculating reliably second- or higher-order sensitivity indices.This paper demonstrates that the Random-Sampling High Dimensional Model Representation (RS-HDMR) meta-modelling approach is able to compute efficiently sensitivity indices of the first, second and total orders for a complex, highly nonlinear model describing the long-term behaviour of a final repository for low- and intermediate-level radioactive waste, and that the results are consistent and plausible. The efficiency of the RS-HDMR approach in computing sensitivity indices of the first order is compared to that of two other methods: EASI and the State-Dependent-Parameter (SDP) meta-modelling approach.
Song S, Zhou T, Wang L, et al., 2019, Derivative-based new upper bound of Sobol' sensitivity measure, Reliability Engineering and System Safety, Vol: 187, Pages: 142-148, ISSN: 0951-8320
Global sensitivity (also called “uncertainty importance measure”) can reflect the effect of input variables onoutput response. The variance-based importance measure proposed by Sobol’ has highly general applicability.The Sobol’ total sensitivity index Sitotcan estimate the total contribution of input variables to the model output,including the self-influence of variable and the intercross influence of variable vectors. However, the computational load of Sitot is extremely heavy for double-loop simulation. The main sensitivity index Si is the lowerbound of Sitot, and new upper bounds of Sitot based derivative are derived and proposed. New upper bounds of Sitotfor different variable distribution types (such as uniform, normal, exponential, triangular, beta and gamma) areanalyzed, and the process and formulas are presented comprehensively according to functional analysis and theEuler–Lagrange equation. Derivative-based upper bounds are easy to implement and evaluate numerically.Several numerical and engineering examples are adopted to verify the efficiency and applicability of the presented upper bounds, which can effectively estimate the Sitot value.
Kucherenko S, Song S, Wang L, 2019, Quantile based global sensitivity measures, RELIABILITY ENGINEERING & SYSTEM SAFETY, Vol: 185, Pages: 35-48, ISSN: 0951-8320
Klymenko OV, Kucherenko S, Shah N, 2017, Constrained Global Sensitivity Analysis: Sobol' indices for problems in non-rectangular domains, 27th European Symposium on Computer-Aided Process Engineering (ESCAPE), Publisher: ELSEVIER SCIENCE BV, Pages: 151-156, ISSN: 1570-7946
Kucherenko S, Song S, 2017, Different numerical estimators for main effect global sensitivity indices, Reliability Engineering and System Safety, Vol: 165, Pages: 222-238, ISSN: 0951-8320
The variance-based method of global sensitivity indices based on Sobol' sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol' indices generally requires a large number of function evaluations to achieve reasonable convergence. Four different direct formulas for computing Sobol’ main effect sensitivity indices are compared on a set of test models for which there are analytical results. Considered test functions represent various types of models that are found in practice. Formulas are based on high-dimensional integrals which are evaluated using Monte Carlo (MC) and Quasi Monte Carlo (QMC) techniques. Direct formulas are also compared with a different approach based on the so-called “double loop reordering” formula. It is found that the “double loop reordering” (DLR) approach shows a superior performance among all methods both for models with independent and dependent variables.
Molkenthin C, Scherbaum F, Griewank A, et al., 2017, Derivative-Based Global Sensitivity Analysis: Upper Bounding of Sensitivities in Seismic-Hazard Assessment Using Automatic Differentiation, BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA, Vol: 107, Pages: 984-1004, ISSN: 0037-1106
Scoleri S, Bianchetti M, Kucherenko S, 2017, Application of Quasi Monte Carlo and Global Sensitivity Analysis to Option Pricing and Greeks
Kucherenko S, Klymenko OV, Shah N, 2016, Sobol' indices for problems defined in non-rectangular domains
A novel theoretical and numerical framework for the estimation of Sobol sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical methods, namely the quadrature integration method which may be very efficient for problems of low and medium dimensionality and the MC/QMC estimators based on the acceptance-rejection sampling method are proposed for the numerical estimation of Sobol sensitivity indices. Several model test functions with constraints are considered for which analytical solutions for Sobol sensitivity indices were found. These solutions were used as benchmarks for verifying numerical estimates. The method is shown to be general and efficient.
Lambert R, Lemke F, Song S, et al., 2016, Global sensitivity analysis using sparse high dimensional model representations generated by the group method of data handling, Mathematics and Computers in Simulation, Vol: 128, Pages: 42-54, ISSN: 1872-7166
In this paper, the parameter selection capabilities of the group method of data handling (GMDH) as an inductive self-organizing modelling method are used to construct sparse random sampling high dimensional model representations (RS-HDMR), from which the Sobol’s first and second order global sensitivity indices can be derived. The proposed method is capable of dealing with high-dimensional problems without the prior use of a screening technique and can perform with a relatively limited number of function evaluations, even in the case of under-determined modelling problems. Four classical benchmark test functions are used for the evaluation of the proposed technique.
Kucherenko S, Song S, 2016, Derivative-Based Global Sensitivity Measures and Their Link with Sobol' Sensitivity Indices, 11th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC), Publisher: SPRINGER INTERNATIONAL PUBLISHING AG, Pages: 455-469, ISSN: 2194-1009
Bianchetti M, Kucherenko S, Scoleri S, 2015, Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and Global Sensitivity Analysis, Wilmott, volume 2015
Kucherenko S, Delpuech B, Iooss B, et al., 2015, Application of the control variate technique to estimation of total sensitivity indices, RELIABILITY ENGINEERING & SYSTEM SAFETY, Vol: 134, Pages: 251-259, ISSN: 0951-8320
Kucherenko S, Song S, 2015, Comparison of different numerical estimators for main effect global sensitivity indices, Pages: 607-638
The variance-based method of global sensitivity indices based on Sobol' sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol' indices generally requires a large number of function evaluations to achieve reasonable convergence. Four different direct formulas for computing Sobol' main effect sensitivity indices for models with independent variables are compared on a set of test problems for which there are analytical results. These formulas are based on high-dimensional integrals which are evaluated using MC and QMC techniques. Direct formulas are also compared with a different approach based on the so-called "double loop reordering" formula. It is found that the "double loop reordering" (DLR) approach shows a superior performance among all methods both for models with independent and dependent variables.
Todri E, Amenaghawon AN, Jimenez del Val I, et al., 2014, Global sensitivity analysis and meta-modeling of an ethanol production process, Chemical Engineering Science, Vol: 114, Pages: 114-127
Traditional ethanol fermentation becomes inhibitory to microbial growth at ethanol concentrations that depend on the producer organism, leading to reduced ethanol productivity. Continuous ethanol removal from the fermenter could increase productivity and potentially reduce the cost of product recovery. In this work, continuous ethanol removal via in situ gas stripping in a stirred tank reactor has been investigated as a means of reducing growth inhibition and improving productivity. A dynamic mathematical model that couples ethanol fermentation with gas stripping has been developed. This has been linked to a flash separation model to represent the initial steps of product recovery. Global sensitivity analysis was used to reduce the number of uncertain parameters, the values of which were estimated with satisfactory accuracy using experimental data for ethanol production from a metabolically engineered strain of the thermophile Geobacillus thermoglucosidasius growing on cellobiose. Simulation results show that continuous ethanol fermentation with product removal by gas stripping is feasible, with the associated energy requirement, costs of gas compression and fermenter agitation being a function of the stripping gas flow rate. Finally, the conditions under which gas stripping is a practical product recovery method were established.
Zuniga MM, Kucherenko S, Shah N, 2013, Metamodelling with independent and dependent inputs, COMPUTER PHYSICS COMMUNICATIONS, Vol: 184, Pages: 1570-1580, ISSN: 0010-4655
Kucherenko S, 2013, SOBOLHDMR: A General-Purpose Modeling Software, SYNTHETI C BIOLOGY, Vol: 1073, Pages: 191-224, ISSN: 1064-3745
Kucherenko S, Tarantola S, Annoni P, 2012, Estimation of global sensitivity indices for models with dependent variables, COMPUTER PHYSICS COMMUNICATIONS, Vol: 183, Pages: 937-946, ISSN: 0010-4655
Kucherenko S, Feil B, Shah N, et al., 2011, The identification of model effective dimensions using global sensitivity analysis, RELIABILITY ENGINEERING & SYSTEM SAFETY, Vol: 96, Pages: 440-449, ISSN: 0951-8320
Kucherenko S, Zuniga MM, Tarantola S, et al., 2011, Metamodelling and Global Sensitivity Analysis of Models with Dependent Variables, International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Publisher: AMER INST PHYSICS, ISSN: 0094-243X
Hosseini SA, Lambert R, Kucherenko S, et al., 2010, Multiscale Modeling of Hydrothermal Pretreatment: From Hemicellulose Hydrolysis to Biomass Size Optimization, ENERGY & FUELS, Vol: 24, Pages: 4673-4680, ISSN: 0887-0624
Lambert RSC, Shah N, Kucherenko SS, 2010, Quasi-random-sampling high dimensional model representations for the construction of reduced discrete time state space dynamic models, Procedia - Social and Behavioral Sciences, Vol: 2, Pages: 7696-7697, ISSN: 1877-0428
In the context of real time model-based applications, complex high fidelity models may be computationally too expensive. Model order reduction and system identification techniques have been employed to transform complex models into equivalent reduced order models. However, most of the literature on model order reduction concerns linear time invariant dynamic systems, and the research into non linear model reduction is still on early stage. In this paper, we present a novel approach using quasi random sampling - high dimensional model representation (QRS-HDMR) to generate reduced discrete time state space dynamic models. The approach has the advantages of being able to handle the high dimensional case and produce affine discrete state space models, readily usable in control engineering applications.
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