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Chen, Lixin, Zhongxiang Xu, Desuo Huang, and Zhining Chen. "An Improved Sobol Sensitivity Analysis Method." Journal of Physics: Conference Series 2747, no. 1 (2024): 012025. http://dx.doi.org/10.1088/1742-6596/2747/1/012025.
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Abstract The Sobol method is a variance-based global sensitivity analysis method that evaluates single-input and multiple-input interaction effects by calculating the contribution of a single input to the output variance and the contribution of multiple inputs to the output variance. The Sobol method requires each input to obey a uniform distribution of U [0,1], but it is difficult to meet the requirements in practice. Taking the sum function as an example, this paper analyzes the inapplicability of the existing Sobol method when the input does not obey the uniform distribution U [0,1]. To solve the inapplicability of the Sobol method and broaden the application scope, an improved Sobol sensitivity analysis method is proposed. First, the effect of the joint probability density function not 1 on sensitivity calculation is studied; second, the input parameters are changed to uniform distribution U [0,1] through variable substitution; finally, a complete algorithm model is presented and logical sensitivity analysis results are obtained. Application verification shows that the improved Sobol method is more scientific, applicable and practical.
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Alves Borges, Luiz Felipe, Fabio Freitas Ferreira, Fábio Gonçalves, Antônio Espósito Junior, Aline Fernanda Da Silva Oliveira, and Wagner Rambaldi Telles. "IPSAL: Implementation of the module to generate the Sobol sequence and indices." VETOR - Revista de Ciências Exatas e Engenharias 33, no. 2 (2023): 60–69. http://dx.doi.org/10.14295/vetor.v33i2.16439.
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Sensitivity and uncertainty analysis hold significant importance across a range of applications, spanning from industrial problems to climate change, financial risk assessment, as well as mathematical and computational models. These analyses involve identifying influential input parameters in models to comprehend their impact on the output. Sensitivity analysis can be performed locally, examining parameter effects at a fixed value, or globally, evaluating the model across a range of parameter values. The Sobol method stands as a robust approach for global sensitivity analysis, employing a Sobol sequence to create samples more uniformly within the input parameter space, thus enabling efficient exploration of model inputs. This paper aims to introduce a computational implementation in Scilab to generate the Sobol sequence for utilization in sensitivity analysis through the Sobol method. A test case was applied to generate Sobol sequences and discuss the obtained results.
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Herman, J. D., J. B. Kollat, P. M. Reed, and T. Wagener. "Technical Note: Method of Morris effectively reduces the computational demands of global sensitivity analysis for distributed watershed models." Hydrology and Earth System Sciences 17, no. 7 (2013): 2893–903. http://dx.doi.org/10.5194/hess-17-2893-2013.
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Abstract. The increase in spatially distributed hydrologic modeling warrants a corresponding increase in diagnostic methods capable of analyzing complex models with large numbers of parameters. Sobol' sensitivity analysis has proven to be a valuable tool for diagnostic analyses of hydrologic models. However, for many spatially distributed models, the Sobol' method requires a prohibitive number of model evaluations to reliably decompose output variance across the full set of parameters. We investigate the potential of the method of Morris, a screening-based sensitivity approach, to provide results sufficiently similar to those of the Sobol' method at a greatly reduced computational expense. The methods are benchmarked on the Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM) over a six-month period in the Blue River watershed, Oklahoma, USA. The Sobol' method required over six million model evaluations to ensure reliable sensitivity indices, corresponding to more than 30 000 computing hours and roughly 180 gigabytes of storage space. We find that the method of Morris is able to correctly screen the most and least sensitive parameters with 300 times fewer model evaluations, requiring only 100 computing hours and 1 gigabyte of storage space. The method of Morris proves to be a promising diagnostic approach for global sensitivity analysis of highly parameterized, spatially distributed hydrologic models.
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Herman, J. D., J. B. Kollat, P. M. Reed, and T. Wagener. "Technical note: Method of Morris effectively reduces the computational demands of global sensitivity analysis for distributed watershed models." Hydrology and Earth System Sciences Discussions 10, no. 4 (2013): 4275–99. http://dx.doi.org/10.5194/hessd-10-4275-2013.
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Abstract. The increase in spatially distributed hydrologic modeling warrants a corresponding increase in diagnostic methods capable of analyzing complex models with large numbers of parameters. Sobol' sensitivity analysis has proven to be a valuable tool for diagnostic analyses of hydrologic models. However, for many spatially distributed models, the Sobol' method requires a prohibitive number of model evaluations to reliably decompose output variance across the full set of parameters. We investigate the potential of the method of Morris, a screening-based sensitivity approach, to provide results sufficiently similar to those of the Sobol' method at a greatly reduced computational expense. The methods are benchmarked on the Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM) model over a six-month period in the Blue River Watershed, Oklahoma, USA. The Sobol' method required over six million model evaluations to ensure reliable sensitivity indices, corresponding to more than 30 000 computing hours and roughly 180 gigabytes of storage space. We find that the method of Morris is able to correctly identify sensitive and insensitive parameters with 300 times fewer model evaluations, requiring only 100 computing hours and 1 gigabyte of storage space. Method of Morris proves to be a promising diagnostic approach for global sensitivity analysis of highly parameterized, spatially distributed hydrologic models.
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Pannier, Marie-Lise, Patrick Schalbart, and Bruno Peuportier. "Computationally efficient sensitivity analysis for building ecodesign with many-level categorical input factors." International Journal of Metrology and Quality Engineering 14 (2023): 15. http://dx.doi.org/10.1051/ijmqe/2023016.
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Dynamic building energy simulation and life cycle assessment (LCA) are useful ecodesign tools to mitigate the energy and environmental impacts of buildings. Various uncertain factors can affect the building energy and environmental modelling, including continuous and categorical factors (i.e., discrete factors without logical ranking). Sensitivity analysis (SA) is applied to identify the most influential factors on which additional research efforts are needed to increase the robustness of results. The Sobol method (Sobol) is the reference SA method, but it requires a significant amount of computation. Less time-consuming methods, such as an adaptation of the Morris screening (Morris), have shown a good ability to quantify the influence of factors, but their performance has not been investigated for categorical factors having many (more than two) levels. Two strategies (2LA-Morris and MA-Morris) based on the adaptation of Morris are proposed to handle many-level factors. Their performance is compared to that of Sobol based on four criteria: computation time, factor's relative influence, factor's ranking, and ability to detect interactions. For the LCA of a house including 24 uncertain factors, MA-Morris was able to quantify the influence of factors in the same way as Sobol, while reducing the computation time by a factor of 12.
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Wang, Qi, Haiyang Li, Lin Lu, Luyi Yang, and Shenquan Wang. "Global Sensitivity Analysis of Earth-Moon Transfer Orbit Parameters Based on Sobol Method." International Journal of Aerospace Engineering 2022 (May 29, 2022): 1–22. http://dx.doi.org/10.1155/2022/6587890.
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In the process of Earth-Moon transfer orbit, many parameters are involved and the degree of influence varies among the parameters. How to accurately distinguish the influence relationship between different parameters is of great significance to engineering missions. Based on Sobol sequence sampling method and Sobol global sensitivity analysis method, a calculation process of global sensitivity analysis is proposed in this paper for high-fidelity Earth-Moon transfer orbit. A numerical simulation method is used to verify that the Sobol sequence sampling method has better convergence and higher precision than other sampling methods and has better adaptability in global sensitivity analysis. The effects of different state parameters and the combination of different parameters on the perilune parameters of Earth-Moon transfer orbit are given by simulation examples, which verifies the effectiveness and feasibility of the calculation process proposed in this paper. Simulation results show that the radial position and tangential velocity at the trans-lunar injection point are the main sensitivity parameters, and the other parameters have little effect on the results. The sensitivity of the orbital elements at the trans-lunar injection point to the perilune parameters is different and needs to be determined according to the specific parameters. The results of this study can provide important reference for future Earth-Moon transfer orbit design and related engineering missions.
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Kalra, Tarandeep S., Alfredo Aretxabaleta, Pranay Seshadri, Neil K. Ganju, and Alexis Beudin. "Sensitivity analysis of a coupled hydrodynamic-vegetation model using the effectively subsampled quadratures method (ESQM v5.2)." Geoscientific Model Development 10, no. 12 (2017): 4511–23. http://dx.doi.org/10.5194/gmd-10-4511-2017.
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Abstract. Coastal hydrodynamics can be greatly affected by the presence of submerged aquatic vegetation. The effect of vegetation has been incorporated into the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modeling system. The vegetation implementation includes the plant-induced three-dimensional drag, in-canopy wave-induced streaming, and the production of turbulent kinetic energy by the presence of vegetation. In this study, we evaluate the sensitivity of the flow and wave dynamics to vegetation parameters using Sobol' indices and a least squares polynomial approach referred to as the Effective Quadratures method. This method reduces the number of simulations needed for evaluating Sobol' indices and provides a robust, practical, and efficient approach for the parameter sensitivity analysis. The evaluation of Sobol' indices shows that kinetic energy, turbulent kinetic energy, and water level changes are affected by plant stem density, height, and, to a lesser degree, diameter. Wave dissipation is mostly dependent on the variation in plant stem density. Performing sensitivity analyses for the vegetation module in COAWST provides guidance to optimize efforts and reduce exploration of parameter space for future observational and modeling work.
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Derakhshanfard, Rasoul, Ali Nourali, Moein Taheri, and Hamed Safikhani. "Performance analysis in square cyclones using Sobol statistical sensitivity analysis method." Mechanic of Advanced and Smart Materials 2, no. 4 (2023): 401–12. http://dx.doi.org/10.52547/masm.2.4.401.
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Guo, Jianbin, Shaohua Du, Yao Wang, and Shengkui Zeng. "Time-Dependent Global Sensitivity Analysis for Long-Term Degeneracy Model Using Polynomial Chaos." Advances in Mechanical Engineering 6 (January 1, 2014): 719825. http://dx.doi.org/10.1155/2014/719825.
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Global sensitivity is used to quantify the influence of uncertain model inputs on the output variability of static models in general. However, very few approaches can be applied for the sensitivity analysis of long-term degeneracy models, as far as time-dependent reliability is concerned. The reason is that the static sensitivity may not reflect the completed sensitivity during the entire life circle. This paper presents time-dependent global sensitivity analysis for long-term degeneracy models based on polynomial chaos expansion (PCE). Sobol’ indices are employed as the time-dependent global sensitivity since they provide accurate information on the selected uncertain inputs. In order to compute Sobol’ indices more efficiently, this paper proposes a moving least squares (MLS) method to obtain the time-dependent PCE coefficients with acceptable simulation effort. Then Sobol’ indices can be calculated analytically as a postprocessing of the time-dependent PCE coefficients with almost no additional cost. A test case is used to show how to conduct the proposed method, then this approach is applied to an engineering case, and the time-dependent global sensitivity is obtained for the long-term degeneracy mechanism model.
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Sun, Xifu, Barry Croke, Stephen Roberts, and Anthony Jakeman. "Investigation of determinism-related issues in the Sobol′ low-discrepancy sequence for producing sound global sensitivity analysis indices." ANZIAM Journal 62 (December 7, 2021): C84—C97. http://dx.doi.org/10.21914/anziamj.v62.16094.
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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.
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Kotidis, Pavlos, and Cleo Kontoravdi. "Strategic Framework for Parameterization of Cell Culture Models." Processes 7, no. 3 (2019): 174. http://dx.doi.org/10.3390/pr7030174.
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Global Sensitivity Analysis (GSA) is a technique that numerically evaluates the significance of model parameters with the aim of reducing the number of parameters that need to be estimated accurately from experimental data. In the work presented herein, we explore different methods and criteria in the sensitivity analysis of a recently developed mathematical model to describe Chinese hamster ovary (CHO) cell metabolism in order to establish a strategic, transferable framework for parameterizing mechanistic cell culture models. For that reason, several types of GSA employing different sampling methods (Sobol’, Pseudo-random and Scrambled-Sobol’), parameter deviations (10%, 30% and 50%) and sensitivity index significance thresholds (0.05, 0.1 and 0.2) were examined. The results were evaluated according to the goodness of fit between the simulation results and experimental data from fed-batch CHO cell cultures. Then, the predictive capability of the model was tested against four different feeding experiments. Parameter value deviation levels proved not to have a significant effect on the results of the sensitivity analysis, while the Sobol’ and Scrambled-Sobol’ sampling methods and a 0.1 significance threshold were found to be the optimum settings. The resulting framework was finally used to calibrate the model for another CHO cell line, resulting in a good overall fit. The results of this work set the basis for the use of a single mechanistic metabolic model that can be easily adapted through the proposed sensitivity analysis method to the behavior of different cell lines and therefore minimize the experimental cost of model development.
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Kolyukhin, Dmitriy. "Global sensitivity analysis of statistical models by double randomization method." Monte Carlo Methods and Applications 27, no. 4 (2021): 341–46. http://dx.doi.org/10.1515/mcma-2021-2096.
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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.
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Chen, Jie, Richard Arsenault, and François P. Brissette. "An experimental approach to reduce the parametric dimensionality for rainfall–runoff models." Hydrology Research 48, no. 1 (2016): 48–65. http://dx.doi.org/10.2166/nh.2016.145.
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Sobol’ sensitivity analysis has been used successfully in the past to reduce the parametric dimensionality for hydrological models. However, the effects of its limitation, in that it assumes an independence of parameters, need to be investigated. This study proposes an experimental approach to assess the commonly used Sobol’ analysis for reducing the parameter dimensionality of hydrological models. In this approach, the number of model parameters is directly pitted against an efficiency criterion within a multi-objective genetic algorithm (MOGA), thus allowing both the identification of key model parameters and the optimal number of parameters to be used within the same analysis. The proposed approach was tested and compared with the Sobol’ method based on a conceptual lumped hydrological model (HSAMI) with 23 free parameters. The results show that both methods performed very similarly, and allowed 11 out of 23 HSAMI parameters to be reduced with little loss in model performance. Based on this comparison, Sobol’ appears to be an effective and robust method despite its limitations. On the other hand, the MOGA algorithm outperformed Sobol’ analysis for further reduction of the parametric space and found optimal solutions with as few as eight parameters with minimal performance loss in validation.
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Ganji, Arman, Holger R. Maier, and Graeme C. Dandy. "A modified Sobol′ sensitivity analysis method for decision-making in environmental problems." Environmental Modelling & Software 75 (January 2016): 15–27. http://dx.doi.org/10.1016/j.envsoft.2015.10.001.
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Feng, Kaixuan, Zhenzhou Lu, and Caiqiong Yang. "Enhanced Morris method for global sensitivity analysis: good proxy of Sobol’ index." Structural and Multidisciplinary Optimization 59, no. 2 (2018): 373–87. http://dx.doi.org/10.1007/s00158-018-2071-7.
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Jaxa-Rozen, Marc, Astu Sam Pratiwi, and Evelina Trutnevyte. "Variance-based global sensitivity analysis and beyond in life cycle assessment: an application to geothermal heating networks." International Journal of Life Cycle Assessment 26, no. 5 (2021): 1008–26. http://dx.doi.org/10.1007/s11367-021-01921-1.
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Abstract Purpose Global sensitivity analysis increasingly replaces manual sensitivity analysis in life cycle assessment (LCA). Variance-based global sensitivity analysis identifies influential uncertain model input parameters by estimating so-called Sobol indices that represent each parameter’s contribution to the variance in model output. However, this technique can potentially be unreliable when analyzing non-normal model outputs, and it does not inform analysts about specific values of the model input or output that may be decision-relevant. We demonstrate three emerging methods that build on variance-based global sensitivity analysis and that can provide new insights on uncertainty in typical LCA applications that present non-normal output distributions, trade-offs between environmental impacts, and interactions between model inputs. Methods To identify influential model inputs, trade-offs, and decision-relevant interactions, we implement techniques for distribution-based global sensitivity analysis (PAWN technique), spectral clustering, and scenario discovery (patient rule induction method: PRIM). We choose these techniques because they are applicable with generic Monte Carlo sampling and common LCA software. We compare these techniques with variance-based Sobol indices, using a previously published LCA case study of geothermal heating networks. We assess eight environmental impacts under uncertainty for three design alternatives, spanning different geothermal production temperatures and heating network configurations. Results In the application case on geothermal heating networks, PAWN distribution-based sensitivity indices generally identify influential model parameters consistently with Sobol indices. However, some discrepancies highlight the potentially misleading interpretation of Sobol indices on the non-normal distributions obtained in our analysis, where variance may not meaningfully describe uncertainty. Spectral clustering highlights groups of model results that present different trade-offs between environmental impacts. Compared to second-order Sobol interaction indices, PRIM then provides more precise information regarding the combinations of input values associated with these different groups of calculated impacts. PAWN indices, spectral clustering, and PRIM have a computational advantage because they yield stable results at relatively small sample sizes (n = 12,000), unlike Sobol indices (n = 100,000 for second-order indices). Conclusions We recommend adding these new techniques to global sensitivity analysis in LCA as they give more precise as well as additional insights on uncertainty regardless of the distribution of the model outputs. PAWN distribution-based global sensitivity analysis provides a computationally efficient assessment of input sensitivities as compared to variance-based global sensitivity analysis. The combination of clustering and scenario discovery enables analysts to precisely identify combinations of input parameters or uncertainties associated with different outcomes of environmental impacts.
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Parreira, Tomás G., Diogo C. Rodrigues, Marta C. Oliveira, Nataliya A. Sakharova, Pedro A. Prates, and André F. G. Pereira. "Sensitivity Analysis of the Square Cup Forming Process Using PAWN and Sobol Indices." Metals 14, no. 4 (2024): 432. http://dx.doi.org/10.3390/met14040432.
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This study investigates the sensitivity of the square cup forming process. It analyses how the uncertainties in the material properties, friction and process conditions affect the results of the square cup, such as equivalent plastic strain, geometry change, thickness reduction, punch force and springback. The cup flange and the die curvature region are identified as highly affected areas, while the cup bottom is least affected by the uncertainties. Two sensitivity analysis techniques, PAWN and Sobol indices, are compared. In particular, the study shows that PAWN indices require a significantly smaller number of simulations than Sobol indices, making them a more efficient choice for sensitivity analysis. While both PAWN and Sobol indices generally give comparable results, discrepancies arise in the analysis of springback, where PAWN indices show superior accuracy, particularly when dealing with multimodal distributions. This observation highlights the importance of selecting the appropriate sensitivity analysis method based on the nature of the data being analysed. These results provide insights for optimizing stamping processes to reduce production time and costs.
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Liu, Zifa, Heyang Huai, and Yusen Yao. "Static voltage bilayer optimization for distribution networks based on Sobol’ method." Journal of Physics: Conference Series 2918, no. 1 (2024): 012004. https://doi.org/10.1088/1742-6596/2918/1/012004.
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Abstract In active distribution networks, the uncertainty of a large number of distributed power sources makes the voltage stability problem of distribution networks more and more prominent. The existing optimization methods tend to deal with the economy and voltage stability of distribution networks as independent objectives, with less consideration of their connection, making it difficult to realize the efficient use of flexible resources. The paper introduces upper and lower connection factors and proposes a two-layer optimization model for distribution network voltage using the Sobol’ method. First, taking into account the uncertainty of distributed power sources and loads in active distribution networks, a probabilistic tidal current calculation model for active distribution networks is constructed, based on which the impact of load fluctuations on the L index is quantitatively analyzed by the global sensitivity of the Sobol’ method. Secondly, the upper and lower connection factors are calculated based on the sensitivity analysis results. The upper economic objective and the lower stability objective are connected through the connection factors to establish a two-layer optimization model to solve the flexible resources in the system optimally. Finally, simulations on the modified IEEE33 node system validate that the proposed optimization model enhances distribution network security while considering economic factors.
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Lyu, Jingye, Chong Li, Wenwen Zhou, and Jinsuo Zhang. "Sensitivity Analysis of Factors Influencing Coal Prices in China." Mathematics 12, no. 24 (2024): 4019. https://doi.org/10.3390/math12244019.
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A scientific assessment of the sensitivity of the Chinese coal market has become an important research topic. This paper combines Gaussian Process Regression (GPR) and Sobol sensitivity analysis to construct a GPR–Sobol hybrid model innovatively applied to the Chinese coal market, thus addressing a gap in the economic applications of this method. The model is used to analyze the sensitivity of factors influencing coal prices in China. The GPR–Sobol model effectively handles nonlinear relationships, enabling an in-depth exploration of key factors affecting price volatility and quantifying their impacts, thus overcoming the limitations of traditional econometric models in nonlinear data processing. The results indicate that economic growth, energy prices, interest rates, exchange rates, and uncertainty factors exhibit high sensitivity and significantly impact coal price fluctuations in China. Coal prices in northwest China are more sensitive to interest rates and geopolitical risks, while prices in east and south China are more responsive to exchange rates but less so to economic policy uncertainty. Additionally, coal prices in north, south, and east China are highly sensitive to international energy prices, indicating that coal prices are dominated by the global energy market, yet their weak response to macroeconomic indicators suggests these regions is still insufficiently mature.
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Liu, Jiacheng, Haiyun Liu, Cong Zhang, Jiyin Cao, Aibo Xu, and Jiwei Hu. "Derivative-Variance Hybrid Global Sensitivity Measure with Optimal Sampling Method Selection." Mathematics 12, no. 3 (2024): 396. http://dx.doi.org/10.3390/math12030396.
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This paper proposes a derivative-variance hybrid global sensitivity measure with optimal sampling method selection. The proposed sensitivity measure is as computationally efficient as the derivative-based global sensitivity measure, which also serves as the conservative estimation of the corresponding variance-based global sensitivity measure. Moreover, the optimal sampling method for the proposed sensitivity measure is studied. In search of the optimal sampling method, we investigated the performances of six widely used sampling methods, namely Monte Carlo sampling, Latin hypercube sampling, stratified sampling, Latinized stratified sampling, and quasi-Monte Carlo sampling using the Sobol and Halton sequences. In addition, the proposed sensitivity measure is validated through its application to a rural bridge.
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Wang, Yuan, Jie Ren, Shaobin Hu, and Di Feng. "Global Sensitivity Analysis to Assess Salt Precipitation for CO2 Geological Storage in Deep Saline Aquifers." Geofluids 2017 (2017): 1–16. http://dx.doi.org/10.1155/2017/5603923.
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Salt precipitation is generated near the injection well when dry supercritical carbon dioxide (scCO2) is injected into saline aquifers, and it can seriously impair the CO2 injectivity of the well. We used solid saturation (Ss) to map CO2 injectivity. Ss was used as the response variable for the sensitivity analysis, and the input variables included the CO2 injection rate (QCO2), salinity of the aquifer (XNaCl), empirical parameter m, air entry pressure (P0), maximum capillary pressure (Pmax), and liquid residual saturation (Splr and Sclr). Global sensitivity analysis methods, namely, the Morris method and Sobol method, were used. A significant increase in Ss was observed near the injection well, and the results of the two methods were similar: XNaCl had the greatest effect on Ss; the effect of P0 and Pmax on Ss was negligible. On the other hand, with these two methods, QCO2 had various effects on Ss: QCO2 had a large effect on Ss in the Morris method, but it had little effect on Ss in the Sobol method. We also found that a low QCO2 had a profound effect on Ss but that a high QCO2 had almost no effect on the Ss value.
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Widyanugraha, A. D., N. Atikah, and D. Hardiansyah. "Estimation of The Main Effect and Total Effect of a PBPK Model Based on The Uncertainty of Individual Parameter for Treatment Planning in PSMA Therapy." IOP Conference Series: Earth and Environmental Science 913, no. 1 (2021): 012101. http://dx.doi.org/10.1088/1755-1315/913/1/012101.
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Abstract The purpose of this study was to identify the most important physiologically-based pharmacokinetic (PBPK) model parameters determining the absorbed dose (AD) in prostate-specific membrane antigen (PSMA) therapy. The extended-Sobol’ global sensitivity analysis method was used to analyze the sensitivity of the PBPK model parameters obtained from 3 patients. The investigated PBPK model parameters were the blood flow to the organs, PSMA binding rate, biological release rates, and density of organs receptor. The outputs of extended Sobol method were the main effect Si and the total effect STi of the parameter of interests for each ADs. The sampling strategy of extended Sobol has been implemented based on the mean and covariance matrix of the parameters. From the simulations, the most important parameters which determine the ADs to the kidney was the kidney receptor density (Si=0,4, STi=0,8). For tumors, it was shown that tumor receptor density was the most essential parameter (Si=0,7, STi=0,8). In conclusion, measurement of the blood flow and organ receptor densities might be of interest to improve individualized treatment of PSMA therapy.
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Silva, Arthur Santos, and Enedir Ghisi. "Evaluation of capabilities of different global sensitivity analysis techniques for building energy simulation: experiment on design variables." Ambiente Construído 21, no. 2 (2021): 89–111. http://dx.doi.org/10.1590/s1678-86212021000200516.
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Abstract The objective of this study is to investigate the capabilities of different global sensitivity analysis methods applied to building performance simulation, i.e. Morris, Monte Carlo, Design of Experiments, and Sobol methods. A single-zone commercial building located in Florianópolis, southern Brazil, was used as a case study. Fifteen inputs related to design variables were considered, such as thermal properties of the construction envelope, solar orientation, and fenestration characteristics. The performance measures were the annual heating and cooling loads. It was found that each method can provide different visual capabilities and measures of interpretation, but, in general, there was little difference in showing the most influent and least influent variables. For the heating loads, the thermal transmittances were the most influent variables, while for the cooling loads, the solar absorptances stood out. The Morris method showed to be the most feasible method due to its simplicity and low computational cost. However, as the building simulation model is still complex and non-linear, the variance-based method such as the Sobol is still necessary for general purposes.
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Wei, Shangshang, Yiguo Li, Xianhua Gao, Kwang Y. Lee, and Li Sun. "Multi-stage Sensitivity Analysis of Distributed Energy Systems: A Variance-based Sobol Method." Journal of Modern Power Systems and Clean Energy 8, no. 5 (2020): 895–905. http://dx.doi.org/10.35833/mpce.2020.000134.
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Rosolem, Rafael, Hoshin V. Gupta, W. James Shuttleworth, Xubin Zeng, and Luis Gustavo Gonçalves de Gonçalves. "A fully multiple-criteria implementation of the Sobol′ method for parameter sensitivity analysis." Journal of Geophysical Research: Atmospheres 117, no. D7 (2012): n/a. http://dx.doi.org/10.1029/2011jd016355.
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Cao, Xiaoqun, ShiPeng Su, HongZe Leng, and BaiNian Liu. "Global Sensitivity Analysis of Parameters in the ENSO model Based on Sobol' Method." Journal of Coastal Research 99, sp1 (2020): 340. http://dx.doi.org/10.2112/si99-047.1.
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Le Guyadec, Mathias, Laurent Gerbaud, Emmanuel Vinot, and Benoit Delinchant. "Sensitivity analysis using Sobol indices for the thermal modelling of an electrical machine for sizing by optimization." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 3 (2019): 965–76. http://dx.doi.org/10.1108/compel-09-2018-0360.
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Purpose The thermal modelling of an electrical machine is difficult because the thermal behavior depends on its geometry, the used materials and its manufacturing process. In the paper, such a thermal model is used during the sizing process by optimization of a hybrid electric vehicle (HEV). This paper aims to deal with the sensitivities of thermal parameters on temperatures inside the electrical machine to allow the assessment of the influence of thermal parameters that are hard to assess. Design/methodology/approach A sensitivity analysis by Sobol indices is used to assess the sensitivities of the thermal parameters on electrical machine temperatures. As the optimization process needs fast computations, a lumped parameter thermal network (LPTN) is proposed for the thermal modelling of the machine, because of its fastness. This is also useful for the Sobol method that needs too many calls to this thermal model. This model is also used in a global model of a hybrid vehicle. Findings The difficulty is the thermal modelling of the machine on the validity domain of the sizing problem. The Sobol indices allow to find where a modelling effort has to be carried out. Research limitations/implications The Sobol indices have a significant value according to the number of calls of the model and their type (first-order, total, etc.). Therefore, the quality of the thermal sensitivity analysis is a compromise between computation times and modelling accuracy. Practical implications Thermal modelling of an electrical machine in a sizing process by optimization. Originality/value The use of Sobol indices for the sensitivity analysis of the thermal parameters of an electrical machine.
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Ryan, Edmund, Oliver Wild, Apostolos Voulgarakis, and Lindsay Lee. "Fast sensitivity analysis methods for computationally expensive models with multi-dimensional output." Geoscientific Model Development 11, no. 8 (2018): 3131–46. http://dx.doi.org/10.5194/gmd-11-3131-2018.
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Abstract. Global sensitivity analysis (GSA) is a powerful approach in identifying which inputs or parameters most affect a model's output. This determines which inputs to include when performing model calibration or uncertainty analysis. GSA allows quantification of the sensitivity index (SI) of a particular input – the percentage of the total variability in the output attributed to the changes in that input – by averaging over the other inputs rather than fixing them at specific values. Traditional methods of computing the SIs using the Sobol and extended Fourier Amplitude Sensitivity Test (eFAST) methods involve running a model thousands of times, but this may not be feasible for computationally expensive Earth system models. GSA methods that use a statistical emulator in place of the expensive model are popular, as they require far fewer model runs. We performed an eight-input GSA, using the Sobol and eFAST methods, on two computationally expensive atmospheric chemical transport models using emulators that were trained with 80 runs of the models. We considered two methods to further reduce the computational cost of GSA: (1) a dimension reduction approach and (2) an emulator-free approach. When the output of a model is multi-dimensional, it is common practice to build a separate emulator for each dimension of the output space. Here, we used principal component analysis (PCA) to reduce the output dimension, built an emulator for each of the transformed outputs, and then computed SIs of the reconstructed output using the Sobol method. We considered the global distribution of the annual column mean lifetime of atmospheric methane, which requires ∼ 2000 emulators without PCA but only 5–40 emulators with PCA. We also applied an emulator-free method using a generalised additive model (GAM) to estimate the SIs using only the training runs. Compared to the emulator-only methods, the emulator–PCA and GAM methods accurately estimated the SIs of the ∼ 2000 methane lifetime outputs but were on average 24 and 37 times faster, respectively.
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Zelelew, M. B., and K. Alfredsen. "Sensitivity-guided evaluation of the HBV hydrological model parameterization." Journal of Hydroinformatics 15, no. 3 (2012): 967–90. http://dx.doi.org/10.2166/hydro.2012.011.
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Applying hydrological models for river basin management depends on the availability of the relevant data information to constrain the model residuals. The estimation of reliable parameter values for parameterized models is not guaranteed. Identification of influential model parameters controlling the model response variations either by main or interaction effects is therefore critical for minimizing model parametric dimensions and limiting prediction uncertainty. In this study, the Sobol variance-based sensitivity analysis method was applied to quantify the importance of the HBV conceptual hydrological model parameterization. The analysis was also supplemented by the generalized sensitivity analysis method to assess relative model parameter sensitivities in cases of negative Sobol sensitivity index computations. The study was applied to simulate runoff responses at twelve catchments varying in size. The result showed that varying up to a minimum of four to six influential model parameters for high flow conditions, and up to a minimum of six influential model parameters for low flow conditions can sufficiently capture the catchments' responses characteristics. To the contrary, varying more than nine out of 15 model parameters will not make substantial model performance changes on any of the case studies.
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Korayem, M. H., M. Taheri, and S. D. Ghahnaviyeh. "Sobol method application in dimensional sensitivity analyses of different AFM cantilevers for biological particles." Modern Physics Letters B 29, no. 22 (2015): 1550123. http://dx.doi.org/10.1142/s0217984915501237.
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Due to the more delicate nature of biological micro/nanoparticles, it is necessary to compute the critical force of manipulation. The modeling and simulation of reactions and nanomanipulator dynamics in a precise manipulation process require an exact modeling of cantilevers stiffness, especially the stiffness of dagger cantilevers because the previous model is not useful for this investigation. The stiffness values for V-shaped cantilevers can be obtained through several methods. One of them is the PBA method. In another approach, the cantilever is divided into two sections: a triangular head section and two slanted rectangular beams. Then, deformations along different directions are computed and used to obtain the stiffness values in different directions. The stiffness formulations of dagger cantilever are needed for this sensitivity analyses so the formulations have been driven first and then sensitivity analyses has been started. In examining the stiffness of the dagger-shaped cantilever, the micro-beam has been divided into two triangular and rectangular sections and by computing the displacements along different directions and using the existing relations, the stiffness values for dagger cantilever have been obtained. In this paper, after investigating the stiffness of common types of cantilevers, Sobol sensitivity analyses of the effects of various geometric parameters on the stiffness of these types of cantilevers have been carried out. Also, the effects of different cantilevers on the dynamic behavior of nanoparticles have been studied and the dagger-shaped cantilever has been deemed more suitable for the manipulation of biological particles.
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Sabino, Marlus, and Adilson Pacheco de Souza. "Global Sensitivity of Penman–Monteith Reference Evapotranspiration to Climatic Variables in Mato Grosso, Brazil." Earth 4, no. 3 (2023): 714–27. http://dx.doi.org/10.3390/earth4030038.
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Understanding how climatic variables impact the reference evapotranspiration (ETo) is essential for water resource management, especially considering potential fluctuations due to climate change. Therefore, we used the Sobol’ method to analyze the spatiotemporal variations of Penman–Monteith ETo sensitivity to the climatic variables: downward solar radiation, relative humidity, maximum and minimum air temperature, and wind speed. The Sobol’ indices variances were estimated by Monte Carlo integration, with sample limits set to the 2.5th and 97.5th percentiles of the daily data of 33 automatic weather stations located in the state of Mato Grosso, Brazil. The results of the Sobol’ analysis indicate considerable spatiotemporal variations in the sensitivity of ETo to climatic variables and their interactions. The dominant climatic variable responsible for ETo fluctuations in Mato Grosso is incident solar radiation (53% to 93% of annual total sensitivity—Stot), which has a more significant impact in humid environments (70% to 90% of Stot), as observed in the areas of the Amazon biome in the state. Air relative humidity and wind speed have higher sensitivity indices during the dry season in the Cerrado biome (savanna) areas in Mato Grosso (20% and 30% of the Stot, respectively). Our findings show that changes in solar radiation, relative humidity, and wind speed are the main driving forces that impact the reference evapotranspiration.
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Yu, Liang, Xiaoquan Yi, Ran Wang, Chenyu Zhang, Tongdong Wang, and Xiaopeng Zhang. "Uncertainty Quantification for Infrasound Propagation in the Atmospheric Environment." Applied Sciences 12, no. 17 (2022): 8850. http://dx.doi.org/10.3390/app12178850.
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The propagation of infrasound in the atmosphere is influenced by atmospheric environmental parameters, which affect the precise localization of the infrasound source. Therefore, it has become crucial to quantify the influence of atmospheric environmental parameters on infrasound propagation. First, in this paper, the tau-p model is chosen as the physical model of infrasound propagation in a non-uniform moving medium. The atmospheric environmental parameters affecting infrasound propagation are determined. Secondly, the atmospheric environmental parameter distribution data are generated using the Sobol sampling method. Third, the generated atmospheric data are incorporated into the physical model of infrasound propagation to solve the output. Finally, Sobol sensitivity analysis is performed for each parameter, and the atmospheric parameter with the largest Sobol index is identified as the one with the most significant influence on infrasound propagation.
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Wang, Shujuan, Qiuyang Li, and Gordon J. Savage. "Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/280940.
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This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.
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Wu, Mengli, Xianqu Yue, Weibin Chen, Qi Nie, and Yue Zhang. "Accuracy analysis and synthesis of asymmetric parallel mechanism based on Sobol-QMC." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 21 (2020): 4200–4214. http://dx.doi.org/10.1177/0954406220920702.
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Aiming at the aircraft composite skin grinding, a new three degree-of-freedom (DOF) parallel mechanism with asymmetrical structure (TAM) is proposed to replace manual grinding. The TAM is achieved by integrating one of active limbs into the passive limb while keeping the required DOF unchanged, which is divided into two closed-loop chains: telescopic rod and parallelogram. The inverse kinematics models of the two chains are established according to closed-loop vector method. Thus, the actuation and the constraint Jacobian matrix are obtained. Based on the perturbation principle, the error modeling of the TAM is built. Adopting the constraint Jacobian matrix, 15 uncompensated errors are distinguished from the error model. In order to improve the working accuracy of the TAM, accuracy analysis and synthesis are necessary for all the uncompensated errors. The mapping function reflects the influence of uncompensated errors on the pose accuracy. The global sensitivity evaluation indexes are established by mapping function. Since Sobol sequences are superior in uniformity and convergence, the Quasi-Monte Carlo method based on Sobol sequences (Sobol-QMC) is introduced for sensitivity analysis. Taking the minimum manufacturing and installation costs as the optimization target, the objective function of accuracy synthesis is constructed. Ultimately, the reasonable tolerance zone of each uncompensated error is calculated by genetic algorithm. Simulation is performed by Sobol-QMC to verify the rationality of the optimization. The results show the probability is above 97% where most pose errors are in [[Formula: see text], [Formula: see text]] within the workspace. Therefore, accuracy synthesis is correct and practical.
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Kala, Zdeněk. "Global Sensitivity Analysis of Structural Reliability Using Cliff Delta." Mathematics 12, no. 13 (2024): 2129. http://dx.doi.org/10.3390/math12132129.
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This paper introduces innovative sensitivity indices based on Cliff’s Delta for the global sensitivity analysis of structural reliability. These indices build on the Sobol’ method, using binary outcomes (success or failure), but avoid the need to calculate failure probability Pf and the associated distributional assumptions of resistance R and load F. Cliff’s Delta, originally used for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff’s Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff’s Delta δC2, exhibit properties analogous to those in the Sobol’ sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a framework for evaluating the contributions of input variables on structural reliability. The results demonstrate that the Cliff’s Delta method provides a more accurate estimate of Pf. In one case study, the Cliff’s Delta approach reduces the standard deviation of Pf estimates across various Monte Carlo run counts. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff’s Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff’s Delta is a disadvantage. Future research should optimize computational demands, especially for small values of Pf.
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Ye, Xin, Pan Liu, Zhijing Zhang, Chao Shao, and Yan Li. "Error sensitivity analysis of a microassembly system with coaxial alignment function." Assembly Automation 36, no. 1 (2016): 25–33. http://dx.doi.org/10.1108/aa-02-2015-010.
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Purpose – The purpose of this paper is to analyze the sensitivity of the motion error parameters in microassembly process, thereby improving the assembly accuracy. The motion errors of the precision motion stages directly affect the final assembly quality after the machine visual alignment. Design/methodology/approach – This paper presents the error parameters of the in-house microassembly system with coaxial alignment function, builds the error transfer model by the multi-body system theory, analyzes the error sensitivity on the sensitive direction using the Sobol method, which was based on variance, and then gets the ones which made a great degree of influence. Before the sensitivity analyzing, parts of the error sources have been measured to obtain their distribution ranges. Findings – The results of the sensitivity analysis by the Sobol method, which was based on variance, are coincident with the theoretical analysis. Besides, the results provide a reference for the error compensation in control process, for the selection of the precision motion stages and for the installation index of the motion stages of the assembly system with coaxial alignment. Originality/value – This kind of error sensitivity analysis method is of great significance for improving the assembly accuracy after visual system positioning, and increasing efficiency from the initial motion stage selection to final error compensation for designers. It is suitable for general precision motion systems be of multi-degree of freedom, for the method of modeling, measuring and analyzing used in this paper are all universal and applicative.
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Dimov, Ivan, Venelin Todorov, and Slavi Georgiev. "A Super-Convergent Stochastic Method Based on the Sobol Sequence for Multidimensional Sensitivity Analysis in Environmental Protection." Axioms 12, no. 2 (2023): 146. http://dx.doi.org/10.3390/axioms12020146.
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Environmental security is among the top priorities worldwide, and there are many difficulties in this area. The reason for this is a painful subject for society and healthcare systems. Multidimensional sensitivity analysis is fundamental in the process of validating the accuracy and reliability of large-scale computational models of air pollution. In this paper, we present an improved version of the well-known Sobol sequence, which shows a significant improvement over the best available existing sequences in the measurement of the sensitivity indices of the digital ecosystem under consideration. We performed a complicated comparison with the best available low-discrepancy sequences for multidimensional sensitivity analysis to study the model’s output with respect to variations in the input emissions of anthropogenic pollutants and to evaluate the rates of several chemical reactions. Our results, which are presented in this paper through a sensitivity analysis, will play an extremely important multi-sided role.
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Tsokanas, Nikolaos, Roland Pastorino, and Božidar Stojadinović. "A Comparison of Surrogate Modeling Techniques for Global Sensitivity Analysis in Hybrid Simulation." Machine Learning and Knowledge Extraction 4, no. 1 (2021): 1–21. http://dx.doi.org/10.3390/make4010001.
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Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario. The system under consideration is divided into multiple individual substructures, out of which one or more are tested physically, whereas the remaining are simulated numerically. The coupling of all substructures forms the so-called hybrid model. Although hybrid simulation is extensively used across various engineering disciplines, it is often the case that the hybrid model and related excitation are conceived as being deterministic. However, associated uncertainties are present, whilst simulation deviation, due to their presence, could be significant. In this regard, global sensitivity analysis based on Sobol’ indices can be used to determine the sensitivity of the hybrid model response due to the presence of the associated uncertainties. Nonetheless, estimation of the Sobol’ sensitivity indices requires an unaffordable amount of hybrid simulation evaluations. Therefore, surrogate modeling techniques using machine learning data-driven regression are utilized to alleviate this burden. This study extends the current global sensitivity analysis practices in hybrid simulation by employing various different surrogate modeling methodologies as well as providing comparative results. In particular, polynomial chaos expansion, Kriging and polynomial chaos Kriging are used. A case study encompassing a virtual hybrid model is employed, and hybrid model response quantities of interest are selected. Their respective surrogates are developed, using all three aforementioned techniques. The Sobol’ indices obtained utilizing each examined surrogate are compared with each other, and the results highlight potential deviations when different surrogates are used.
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Wang, Haixia, Ying Zhao, and Wenyuan Fu. "Utilizing the Sobol’ Sensitivity Analysis Method to Address the Multi-Objective Operation Model of Reservoirs." Water 15, no. 21 (2023): 3795. http://dx.doi.org/10.3390/w15213795.
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The operation of reservoirs has significantly influenced the river ecological system. Upholding the ecological integrity of rivers during reservoir operations has been the focus of research over the years. When the Dahuofang reservoir project started, focus moved to ecological goals to address the Biliuhe reservoir’s environmental issues. The water strategy limits usage for various purposes and outlines the diversion route, complicating Biliuhe operations. In this study, to comprehend the effects of individual water level guidelines and their combined influence on these goals, the Sobol’ sensitivity analysis was introduced as an initial measure to tackle the optimization challenge. The results show that removing the insensitive water levels during specific periods of reservoir scheduling lines and beginning with sensitive water levels for local optimization to identify viable solutions, and then moving to wider optimization, significantly enhances the search efficiency, solution quality, and operational speed compared with an exhaustive search without any preceding steps. This sensitivity analysis technique is crucial for fine-tuning multi-objective reservoir operations.
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Nouri, Amin, Christoph van Treeck, and Jérôme Frisch. "Sensitivity Assessment of Building Energy Performance Simulations Using MARS Meta-Modeling in Combination with Sobol’ Method." Energies 17, no. 3 (2024): 695. http://dx.doi.org/10.3390/en17030695.
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Large discrepancies can occur between building energy performance simulation (BEPS) outputs and reference data. Uncertainty and sensitivity analyses are performed to discover the significant contributions of each input parameter to these discrepancies. Variance-based sensitivity analyses typically require many stochastic simulations, which is computationally demanding (especially in the case of the large number of input parameters involved in the analysis). To overcome these impediments, this study proposes a reliable meta-model-based sensitivity analysis, including validation, Morris’ method, multivariate adaptive regression splines (MARS) meta-modeling, and Sobol’ method, to identify the most influential input parameters on BEPS prediction (annual energy consumption) at the early building design process. A hypothetical building is used to analyze the proposed methodology. Six statistical metrics are applied to verify and quantify the accuracy of the model. It is concluded that the cooling set-point temperature and g-value of the window are the most influential input parameters for the analyzed case study.
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Tahmasbi, Vahid, Majid Ghoreishi, and Mojtaba Zolfaghari. "Sensitivity analysis of temperature and force in robotic bone drilling process using Sobol statistical method." Biotechnology & Biotechnological Equipment 32, no. 1 (2017): 130–41. http://dx.doi.org/10.1080/13102818.2017.1403863.
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Guo, Ganggui, Shanshan Li, Yakun Liu, Ze Cao, and Yangyu Deng. "Prediction of Cavity Length Using an Interpretable Ensemble Learning Approach." International Journal of Environmental Research and Public Health 20, no. 1 (2022): 702. http://dx.doi.org/10.3390/ijerph20010702.
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The cavity length, which is a vital index in aeration and corrosion reduction engineering, is affected by many factors and is challenging to calculate. In this study, 10-fold cross-validation was performed to select the optimal input configuration. Additionally, the hyperparameters of three ensemble learning models—random forest (RF), gradient boosting decision tree (GBDT), and extreme gradient boosting tree (XGBOOST)—were fine-tuned by the Bayesian optimization (BO) algorithm to improve the prediction accuracy and compare the five empirical methods. The XGBOOST method was observed to present the highest prediction accuracy. Further interpretability analysis carried out using the Sobol method demonstrated its ability to reasonably capture the varying relative significance of different input features under different flow conditions. The Sobol sensitivity analysis also observed two patterns of extracting information from the input features in ML models: (1) the main effect of individual features in ensemble learning and (2) the interactive effect between each feature in SVR. From the results, the models obtaining individual information both predict the cavity length more accurately than that using interactive information. Subsequently, the XGBOOST captures more correct information from features, which leads to the varied Sobol index in accordance with outside phenomena; meanwhile, the predicted results fit the experimental points best.
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Morris, David J., Douglas C. Speir, Angus I. Cameron, and Michael R. Heath. "Global sensitivity analysis of an end-to-end marine ecosystem model of the North Sea: Factors affecting the biomass of fish and benthos." Ecological modelling 273 (February 10, 2014): 251–63. https://doi.org/10.1016/j.ecolmodel.2013.11.019.
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Comprehensive analysis of parameter and driver sensitivity is key to establishing the credibility of models representing complex systems. This is especially so for models of natural systems where experimental manipulation of the real-world to provide controlled validation data is not possible. End-to-end ecosystem models (nutrients to birds and mammals) of marine ecosystems fall into this category with applications for evaluating the effects of climate change and fishing on nutrient fluxes and the abundances of flora and fauna. Here we present results of both ‘one-at-a-time’ (OAT) and variance based global sensitivity analyses (GSA) of the fish and fishery aspects of StrathE2E, an end-to-end ecosystem model of the North Sea. The sensitivity of the model was examined with respect to internal biological parameters, and external drivers related to climate and human activity. The OAT Morris method was first used to screen for factors most influential on model outputs. The Sobol GSA method was then used to calculate quantitative sensitivity indices. The results indicated that the fish and shellfish components of the model (demersal and pelagic fish, filter/deposit and scavenge/carnivore feeding benthos) were influenced by different sets of factors. Harvesting rates were highly influential on demersal and pelagic fish biomasses. Suspension/deposit feeding benthos were directly sensitive to changes in temperature, while the temperature acted indirectly on pelagic fish through the connectivity between model components of the food web. Biomass conversion efficiency was the most important factor for scavenge/carnivorous feeding benthos. The results indicate the primacy of fishing as the most important process affecting total fish biomass, together with varying responses to environmental factors which may be relevant in the context of climate change. The non-linear responses and parameter interactions identified by the analysis also highlight the necessity to use global rather than local methods for the sensitivity analysis of ecosystem models.
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Puszyński, K., P. Lachor, M. Kardyńska, and J. Śmieja. "Sensitivity analysis of deterministic signaling pathways models." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 3 (2012): 471–79. http://dx.doi.org/10.2478/v10175-012-0060-3.
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Abstract The paper is focused on application of sensitivity methods to analysis of signaling pathway models. Two basic methods are compared: local, based on standard sensitivity functions, and global, based on Sobol indices. Firstly, a general outline of modeling of signaling pathways by means of ordinary differential equations is briefly described. Afterwards, the methods of sensitivity analysis, known from literature, are introduced and illustrated with a simple example of a dynamical system of the second order. Subsequently, the analysis of the p53/Mdm2 regulatory module, which is a key element of any pathway involving p53 protein, is presented. The results of this analysis suggest that no single method should be chosen for investigation of any signaling pathway model but several of them should be applied to answer important questions about sources of heterogeneity in cells behavior, robustness of signaling pathways and possible molecular drug targets.
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Baki, Harish, Sandeep Chinta, and Balaji Srinivasan. "Determining the sensitive parameters of the Weather Research and Forecasting (WRF) model for the simulation of tropical cyclones in the Bay of Bengal using global sensitivity analysis and machine learning." Geoscientific Model Development 15, no. 5 (2022): 2133–55. http://dx.doi.org/10.5194/gmd-15-2133-2022.
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Abstract. The present study focuses on identifying the parameters from the Weather Research and Forecasting (WRF) model that strongly influence the simulation of tropical cyclones over the Bay of Bengal (BoB) region. Three global sensitivity analysis (SA) methods, namely, the Morris One-at-A-Time (MOAT), multivariate adaptive regression splines (MARS), and surrogate-based Sobol', are employed to identify the most sensitive parameters out of 24 tunable parameters corresponding to seven parameterization schemes of the WRF model. Ten tropical cyclones across different categories, such as cyclonic storms, severe cyclonic storms, and very severe cyclonic storms over BoB between 2011 and 2018, are selected in this study. The sensitivity scores of 24 parameters are evaluated for eight meteorological variables. The parameter sensitivity results are consistent across three SA methods for all the variables, and 8 out of the 24 parameters contribute 80 %–90 % to the overall sensitivity scores. It is found that the Sobol' method with Gaussian progress regression as a surrogate model can produce reliable sensitivity results when the available samples exceed 200. The parameters with which the model simulations have the least RMSE values when compared with the observations are considered the optimal parameters. Comparing observations and model simulations with the default and optimal parameters shows that simulations with the optimal set of parameters yield a 16.74 % improvement in the 10 m wind speed, 3.13 % in surface air temperature, 0.73 % in surface air pressure, and 9.18 % in precipitation simulations compared to the default set of parameters.
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Jin, Shousong, Shulong Shang, Suqi Jiang, Mengyi Cao, and Yaliang Wang. "Sensitivity Analysis of RV Reducer Rotation Error Based on Deep Gaussian Processes." Sensors 23, no. 7 (2023): 3579. http://dx.doi.org/10.3390/s23073579.
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The rotation error is the most important quality characteristic index of a rotate vector (RV) reducer, and it is difficult to accurately optimize the design of a RV reducer, such as the Taguchi type, due to the many factors affecting the rotation error and the serious coupling effect among the factors. This paper analyzes the RV reducer rotation error and each factor based on the deep Gaussian processes (DeepGP) model and Sobol sensitivity analysis(SA) method. Firstly, using the optimal Latin hypercube sampling (OLHS) approach and the DeepGP model, a high-precision regression prediction model of the rotation error and each affecting factor was created. On the basis of the prediction model, the Sobol method was used to conduct a global SA of the factors influencing the rotation error and to compare the coupling relationship between the factors. The results show that the OLHS method and the DeepGP model are suitable for predicting the rotation error in this paper, and the accuracy of the prediction model constructed based on both of them is as high as 95%. The rotation error mainly depends on the influencing factors in the second stage cycloidal pinwheel drive part. The primary involute planetary part and planetary output carrier’s rotation error factors have little effect. The coupling effects between the matching clearance between the pin gear and needle gear hole (δJ) and the circular position error of the needle gear hole (δt) is noticeably stronger.
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Buzzard, Gregery T., and Dongbin Xiu. "Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature." Communications in Computational Physics 9, no. 3 (2011): 542–67. http://dx.doi.org/10.4208/cicp.230909.160310s.
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AbstractThe stochastic collocation method using sparse grids has become a popular choice for performing stochastic computations in high dimensional (random) parameter space. In addition to providing highly accurate stochastic solutions, the sparse grid collocation results naturally contain sensitivity information with respect to the input random parameters. In this paper, we use the sparse grid interpolation and cubature methods of Smolyak together with combinatorial analysis to give a computationally efficient method for computing the global sensitivity values of Sobol’. This method allows for approximation of all main effect and total effect values from evaluation of f on a single set of sparse grids. We discuss convergence of this method, apply it to several test cases and compare to existing methods. As a result which may be of independent interest, we recover an explicit formula for evaluating a Lagrange basis interpolating polynomial associated with the Chebyshev extrema. This allows one to manipulate the sparse grid collocation results in a highly efficient manner.
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Zhao, Wei, Na Zhou, and Yi Min Zhang. "Global Sensitivity of Random Parameters in Vibration Transfer Path Systems." Applied Mechanics and Materials 635-637 (September 2014): 274–80. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.274.
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Based on the Sobol’ theory, Hamma and Saltelli indicator system, the path parameters were divided into the different subsets for the vibration transfer path systems with random paths in this paper. The object function was constructed and decomposed, thus the global sensitivity based on variances was formed. The first-order and total sensitivities of various parameter subsets were calculated using Monte-Carlo simulation method combined with Latin hypercube sampling technique. Through the analysis example, the way is feasible to analyze the interaction of paths or path parameters in the vibration transfer path systems with uncertainty.
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Guan, Guan, Shuai Zhou, Zhengmao Zhuang, and Qu Yang. "Resistance Optimization of Fishing Boat Based on Parametric Modeling Method and Sensitivity Analysis." Marine Technology Society Journal 55, no. 6 (2021): 117–28. http://dx.doi.org/10.4031/mtsj.55.6.15.
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Abstract In the conventional process of parametric ship optimization, the selection of design variables mostly relies on design experience. The lack of a clear and quantitative method of parameter selection leads to a certain degree of blindness and inefficiency. In this article, a parametric hull modeling method is proposed. The sensitivity analysis based on orthogonal experimental design is performed to select the design variables of optimization. Through variance and range analysis, the parameters that have a significant influence on the optimization objective are selected as the design variables. A combination of Sobol and tangent search method is applied during the optimization. The shape optimization of a fishing boat with minimum resistance is taken as an example. The optimization result proves the efficiency of the proposed parametric modeling method and the sensitivity analysis, which are significant for the shape optimization of a fishing boat.
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Buzzard, Gregery T. "Efficient Basis Change for Sparse-Grid Interpolating Polynomials with Application to T-Cell Sensitivity Analysis." Computational Biology Journal 2013 (April 11, 2013): 1–10. http://dx.doi.org/10.1155/2013/562767.
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Sparse-grid interpolation provides good approximations to smooth functions in high dimensions based on relatively few function evaluations, but in standard form it is expressed in Lagrange polynomials. Here, we give a block-diagonal factorization of the basis-change matrix to give an efficient conversion of a sparse-grid interpolant to a tensored orthogonal polynomial (or gPC) representation. We describe how to use this representation to give an efficient method for estimating Sobol' sensitivity coefficients and apply this method to analyze and efficiently approximate a complex model of T-cell signaling events.