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Several recent theoretical studies have indicated that a relatively simple secretion control mechanism in the epithelial cells lining the stomach may be responsible for maintaining a neutral (healthy) pH adjacent to the stomach wall, even in the face of enormous electrodiffusive acid transport from the interior of the stomach. Subsequent work used Sobol’ Indices (SIs) to quantify the degree to which this secretion mechanism is “self-regulating” i.e. the degree to which the wall pH is held neutral as mathematical parameters vary. However, questions remain regarding the nature of the control that specific parameters exert over the maintenance of a healthy stomach wall pH. Studying the sensitivity of higher moments of the statistical distribution of a model output can provide useful information, for example, how one parameter may skew the distribution towards or away from a physiologically advantageous regime. In this work, we prove a relationship between SIs and the higher moments and show how it can potentially reduce the cost of computing sensitivity of said moments. We define γ -indices to quantify sensitivity of variance, skewness, and kurtosis to the choice of value of a parameter, and we propose an efficient strategy that uses both SIs and γ -indices for a more comprehensive sensitivity analysis. Our analysis uncovers a control parameter which governs the “tightness of control” that the secretion mechanism exerts on wall pH. Finally, we discuss how uncertainty in this parameter can be reduced using expert information about higher moments, and speculate about the physiological advantage conferred by this control mechanism. [ABSTRACT FROM AUTHOR]

In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to "normal" in-person operations, but it is not clear if-or for how long-campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced's student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals.

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. [ABSTRACT FROM AUTHOR]

This study aims to analyze the historical trends of evapotranspiration at annual and seasonal scales and assess the sensitivity to various meteorological factors in Gia Lai province from 1980 to 2019. The modified innovative-Şen trend method and Sobol analysis are employed for trend identification and sensitivity assessment, respectively. The results obtained indicate significant downward trends using both the innovative-Şen trend analysis and the improved version of the innovative trend analysis method across different stations and time scales. Furthermore, in the low-value subgroups of the rainy season at Pleiku and An Khe stations, there were notable increasing trends with quantitative values of approximately 6%. Sensitivity analysis reveals that evapotranspiration is most sensitive to sunshine duration across most stations on annual and seasonal time scales, followed by relative humidity and minimum temperature. Overall, this research provides valuable insights into the relationship between evapotranspiration and relevant climate variables, contributing to the assessment of water demand for agricultural irrigation. HIGHLIGHTS The tendency rate of historical evapotranspiration data was evaluated in the Gia Lai province from 1980 to 2019 in this study.; The improved visualization trend analysis known as the non-parametric detection test was explored, which was proposed to identify the percentage of the fluctuations.; The temporal characteristics of the sensitivity coefficients between evapotranspiration and key climatic parameters across Gia Lai province were determined.;

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.

Failure of dams and dikes often leads to devastating consequences in protected areas. Numerical models are instrumental tools to assess flood risk and guide emergency management, but numerous uncertainties affect model outcomes. Identifying uncertain model input parameters that induce high uncertainties in model outputs is essential. This paper focuses on two model outputs: the maximum breach discharge and the time to reach this peak. Using our implementation of a simplified physically based dam breaching model developed by Wu (2016), a global sensitivity analysis was conducted based on Sobol indices of total order. Unlike in most previous studies, many different configurations (twenty‐seven), both at laboratory and field scales, were considered. For each of them, input variables were ranked according to the significance of the contribution of their uncertainty to the output variability, and the dependency between reference configurations and sensitivity analysis results was highlighted. Depending on the considered case study, input parameter uncertainties with the largest impact on output variability were different, and so was the magnitude of output uncertainties. We demonstrate that sensitivity analysis results obtained for a specific configuration cannot be transferred as it to other configurations. Finally, sensitivity and uncertainty quantification results were combined in a decision tree to determine which input parameter uncertainty is the most critical in each configuration and what standard deviation in the output variables is expected. The global sensitivity analysis procedure presented here may apply to a wide variety of models in environmental sciences. Key Points: Based on a simplified physically based dam breaching model, a global sensitivity analysis was conducted using Sobol indices of total orderThe analysis was applied on twenty‐seven configurations at both laboratory and field scalesMost influential parameters and output uncertainty magnitudes were assessed and turned out to strongly depend on the dam configuration [ABSTRACT FROM AUTHOR]

The numerical modeling of cardiac electrophysiology has reached a mature and advanced state that allows for quantitative modeling of many clinically relevant processes. As a result, complex computational tasks such as the creation of a variety of electrocardiograms (ECGs) from virtual cohorts of models representing biological variation are within reach. This requires a correct representation of the variability of a population by suitable distributions of a number of input parameters. Hence, the assessment of the dependence and variation of model outputs by sensitivity analysis and uncertainty quantification become crucial. Since the standard metrological approach of using Monte–Carlo simulations is computationally prohibitive, we use a nonintrusive polynomial chaos-based approximation of the forward model used for obtaining the atrial contribution to a realistic electrocardiogram. The surrogate increases the speed of computations for varying parameters by orders of magnitude and thereby greatly enhances the versatility of uncertainty quantification. It further allows for the quantification of parameter influences via Sobol indices for the time series of 12 lead ECGs and provides bounds for the accuracy of the obtained sensitivities derived from an estimation of the surrogate approximation error. Thus, it is capable of supporting and improving the creation of synthetic databases of ECGs from a virtual cohort mapping a representative sample of the human population based on physiologically and anatomically realistic three-dimensional models.

The numerical modeling of cardiac electrophysiology has reached a mature and advanced state that allows for quantitative modeling of many clinically relevant processes. As a result, complex computational tasks such as the creation of a variety of electrocardiograms (ECGs) from virtual cohorts of models representing biological variation are within reach. This requires a correct representation of the variability of a population by suitable distributions of a number of input parameters. Hence, the assessment of the dependence and variation of model outputs by sensitivity analysis and uncertainty quantification become crucial. Since the standard metrological approach of using Monte–Carlo simulations is computationally prohibitive, we use a nonintrusive polynomial chaos-based approximation of the forward model used for obtaining the atrial contribution to a realistic electrocardiogram. The surrogate increases the speed of computations for varying parameters by orders of magnitude and thereby greatly enhances the versatility of uncertainty quantification. It further allows for the quantification of parameter influences via Sobol indices for the time series of 12 lead ECGs and provides bounds for the accuracy of the obtained sensitivities derived from an estimation of the surrogate approximation error. Thus, it is capable of supporting and improving the creation of synthetic databases of ECGs from a virtual cohort mapping a representative sample of the human population based on physiologically and anatomically realistic three-dimensional models. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Informed decision-making for sustainable manufacturing requires accurate manufacturing process environmental impact models with uncertainty quantification (UQ). For emerging manufacturing technologies, there is often insufficient process data available to derive accurate data-driven models. This paper explores an alternative mechanistic modeling approach using easy-to-access data from a given machine to perform Bayesian inference and reduce the uncertainty of model parameters. First, we derive mechanistic models of the cumulative energy demand (CED) for making aluminum (AlSi10) and nylon (PA12) parts using laser powder bed fusion (L-PBF). Initial parametric uncertainty is assigned to the model inputs informed by literature reviews and interviews with industry experts. Second, we identify the most critical sources of uncertainty using variance-based global sensitivity analyses; therefore, reducing the dimension of the problem. For metal and polymer L-PBF, critical uncertainty is related to the adiabatic efficiency of the process (a measure of the efficiency with which the laser energy is used to fuse the powder) and the recoating time per layer between laser scans. Data pertinent to both of these parameters include the part geometry (height and volume) and total build time. Between three and eight data points on part geometry and build time were collected on two different L-PBF machines and Bayesian inference was performed to reduce the uncertainty of the adiabatic efficiency and recoating time per layer on each machine. This approach was validated by subsequently taking direct parameter measurements on these machines during operation. The delivered electricity uncertainty is reduced by 40-70% after performing inference, highlighting the potential to construct accurate energy and environmental impact models of manufacturing processes using small easy-to-access datasets without interfering with the operations of the manufacturing facility. [ABSTRACT FROM AUTHOR]

Recently a lumped-parameter model of the cardiovascular system was proposed to simulate the hemodynamics response to partial hepatectomy and evaluate the risk of portal hypertension (PHT) due to this surgery. Model parameters are tuned based on each patient data. This work focuses on a global sensitivity analysis (SA) study of such model to better understand the main drivers of the clinical outputs of interest. The analysis suggests which parameters should be considered patient-specific and which can be assumed constant without losing in accuracy in the predictions. While performing the SA, model outputs need to be constrained to physiological ranges. An innovative approach exploits the features of the polynomial chaos expansion method to reduce the overall computational cost. The computed results give new insights on how to improve the calibration of some model parameters. Moreover the final parameter distributions enable the creation of a virtual population available for future works. Although this work is focused on partial hepatectomy, the pipeline can be applied to other cardiovascular hemodynamics models to gain insights for patient-specific parameterization and to define a physiologically relevant virtual population. [ABSTRACT FROM AUTHOR]

Accurately determining the hydraulic conductivity of unsaturated bentonite is important for modeling subsurface thermo-hydro-mechanical and chemical processes. This study introduced a new hybrid model that employs a constrained categorial boosting (CatBoost) algorithm, combined with a genetic algorithm for hyperparameter tuning, to estimate the hydraulic conductivity of unsaturated compacted bentonite The performance of the constrained CatBoost model was benchmarked against a diverse set of data-driven baseline regression models, including lasso, elastic net, polynomial, k-nearest neighbors, decision tree, bagging tree, random forest, and CatBoost. The results indicated that the constrained CatBoost model offers a superior balance between model robustness and predictive accuracy in estimating the hydraulic conductivity of compacted bentonite-based materials during the wetting phase. The model effectively captured the U-shape relationship between hydraulic conductivity and suction, a key characteristic of bentonite behavior. Additionally, bootstrapping analyses confirmed the model's reliability under data variability, further validating its applicability in environmental and geotechnical applications. • Developed a constrained CatBoost model for hydraulic conductivity of compacted bentonite. • The model demonstrated higher accuracy and robustness compared to traditional data-driven models. • The model captured the U-shaped relationship between hydraulic conductivity and suction. [ABSTRACT FROM AUTHOR]

• An ensemble polynomial chaos expansion (EPCE) method is proposed. • An active learning hybrid criterion is proposed to update the accuracy of EPCE for Sobol index estimation. • The model correlation and sensitivity pursuit criteria are developed to improve the local accuracy of EPCE. • The performance of the proposed method is validated by four benchmark functions and an engineering example. Global sensitivity analysis (GSA) techniques, especially Sobol indices, have gained prominence in assessing the impact of uncertainty across all input variables on the variation of model response. However, GSA can incur intensive computational costs, particularly when dealing with time-consuming models. To address this issue, an ensemble polynomial chaos expansion (EPCE) surrogate model based on an active learning hybrid (ALH) criterion is proposed. The proposed method integrates a weighted combination of multiple sparse PCE surrogate models to formulate the EPCE method. To enhance the performance, the ALH criterion, which balances local exploitation and global exploration, is developed to sequentially select samples for updating the EPCE model. In terms of local exploitation, the model correlation and sensitivity pursuit criteria are derived to identify the local region displaying both the largest discrepancy among multiple sparse PCE methods and the most substantial contribution to the total variance. The ALH criterion also incorporates a minimum distance-based measure for global exploration. The performance of the proposed method is evaluated by four benchmark functions and an engineering application. The numerical studies demonstrate that the proposed method exhibits favorable performance for conducting GSA. [ABSTRACT FROM AUTHOR]

Aseisimic earth fissures are complex consequences of groundwater withdrawal and natural hydrogeologic conditions. This paper aims to improve the understanding of the mechanism of earth fissuring and investigate the relative importance of various factors to fissure activity, including bedrock geometry, piezometric depletion, compressibility and thickness of the exploited aquifer. For these purposes, a test case characterized by an impermeable and incompressible rock ridge in a subsiding basin is developed, where stress/displacement analyses and fissure state are predicted using an interface-finite element model. Three different methods for global sensitivity analysis are used to quantify the extent of the fissure opening to the aforementioned factors. The conventional sampling based Sobol' sensitivity analysis is compared to two surrogate based methods, the general polynomial chaos expansion based Sobol' analysis and a feature importance evaluation of a gradient boosting decision tree model. Numerical results indicate that earth fissure is forming in response to tensile stress accumulation above the ridge associated to pore-pressure depletion, inducing the fissure opening at land surface with further downward propagation. Sensitivity analysis highlights that the geometry of bedrock ridge is the most influential feature. Specifically, the fissure grows more when the ridge is steeper and closer to the land surface. Pore pressure depletion is a secondary feature and required to reach a certain threshold to activate the fissure. As for this specific application, the gradient boosting tree is the most suitable method for its better performance in capturing fissure characteristics. [ABSTRACT FROM AUTHOR]

Most temperature predictions for deep geothermal applications rely on correcting bottom-hole temperatures (BHTs) to undisturbed or static formation temperatures (SFTs). The data used for BHT correction are usually of low quality due to a lack of information and poor documentation, and the uncertainty of the corrected SFT is therefore unknown. It is supposed that the error within the input data exceeds the error due to the uncertainty of the different correction schemes. To verify this, we combined a global sensitivity study with Sobol indices of six easy-to-use conventional correction schemes of the BHT data set of the Bavarian Molasse Basin with an uncertainty study and developed a workflow that aims at presenting a valid error range of the corrected SFTs depending on the quality of their input data. The results give an indication of which of the investigated correction methods should be used depending on the input data, as well as show that the unknown error in the input parameters exceeds the error of the individual BHT correction methods as such. The developed a priori uncertainty-based BHT correction helps to provide a real estimate of the subsurface temperatures needed for geothermal prospecting and probabilistic risk assessment. [ABSTRACT FROM AUTHOR]

The present study addresses the sensitivity analysis of particle concentration dispersion in the turbulent flow. A stochastic spectral model of turbulence is used to simulate the particle transfer. Sensitivity analysis is performed by estimations of Morris and Sobol indices. This study allows to define the significant and nonsignificant model parameters. It also gives an idea of the qualitative behavior of the stochastic model used. [ABSTRACT FROM AUTHOR]

We have carried out the traditional analysis of a set of dynamic breakthrough experiments on the CO 2 /He system adsorbing onto activated carbon by fitting a 1D dynamic column breakthrough model to the transient experimental profiles. We have quantified the uncertainties in the fitted model parameters using the techniques of Bayesian inference, and have propagated these parametric uncertainties through the dynamic model to assess the robustness of the modelling. We have found significant uncertainties in the outlet mole fraction profile, internal temperature profile and internal adsorption profiles of approximately ± 15 % . To assess routes to reduce these uncertainties we have applied a global variance-based sensitivity analysis to the dynamic model using the Sobol method. We have found that approximately 70 % of the observed variability in the modelling outputs can be attributed to uncertainties in the adsorption isotherm parameters that describe its temperature dependence. We also make various recommendations for practitioners, using the developed Bayesian statistical tools, regarding the choice of the isotherm model, the choice of the fitting data for the extraction of system specific parameters and the simplification of the wall energy balance. [ABSTRACT FROM AUTHOR]

Reliability based design approaches are usually adopted to explicitly consider uncertainties in the rock mass and make decisions on selecting design parameters for tunnel-support problems. However, it is difficult to accurately characterize the input random variables due to fewer sample availability and costly observations. Thus, it is necessary to focus on the characterization and reduction of epistemic uncertainty of those input variables, which have higher relative contributions towards the variability in output. These input variables are identified using global sensitivity analysis based on Sobol indices conducted for the supported circular tunnel in Hoek–Brown rock mass. Convergent confinement analysis method is applied to obtain the output—radius of yield zone ( R pl ), tunnel convergence ( u r D ) and induced load on installed support ( p s D ). The analysis is conducted for both uncorrelated and correlated input parameters. For uncorrelated input, the sensitivity measures are divided into correlated and uncorrelated contributions to provide insights into the mechanism of the tunnel-support system. The results obtained by assuming input variables as uncorrelated suggest that the relative contribution of variation in uniaxial compressive strength (UCS) of rock is highest towards the variation in the outputs followed by geological strength index (GSI) of the rock mass, its Young's modulus ( E i ) and thickness of the liner support. However, by considering the correlation between input parameters, the sensitivity measures change significantly. The ranking of input parameters in descending orders of their relative contribution also changed due to the presence of high correlated contributions. The strong correlation between UCS and E i makes them most sensitive, followed by GSI, while thickness of the liner impacts p s D the most. It is found that strong correlations do not necessarily mean higher correlated contributions, rather, it depends on the physics of the tunnel-support system. The 95% confidence interval of ground response curve and longitudinal deformation profile changes considerably for correlated rock mass parameters compared to the uncorrelated case resulting in higher variance of u r D and lower variances of R pl and p s D . Additionally, the investigation of average error in the variance of output, induced by keeping individual parameters as deterministic, yielded high values for highly sensitive inputs and vice versa. [ABSTRACT FROM AUTHOR]

The paper presents a hierarchical polynomial chaos expansion-based probabilistic approach to analyze the single diode solar cell model under Gaussian parametric uncertainty. It is important to analyze single diode solar cell model response under random events or factors due to uncertainty propagation. The optimal values of five electrical parameters associated with the single diode model are estimated using six deterministic optimization techniques through the root-mean-square minimization approach. Values corresponding to the best objective function response are further utilized to describe the probabilistic design space of each random electrical parameter under uncertainty. Adequate samples of each parameter corresponding Gaussian uncertain distribution are generated using Latin hypercube sampling. Furthermore, a multistage probabilistic approach is adopted to evaluate the model response using low-cost polynomial chaos series expansion and perform global sensitivity analysis under specified Gaussian distribution. Coefficients of polynomial basis functions are calculated using least square and least angle regression techniques. Unlike the highly non-linear and complex single diode representation of solar cells, the polynomial chaos expansion model provides a low computational burden and reduced complexity. To ensure reproducibility, probabilistic output response computed using proposed polynomial chaos expansion model is compared with the true model response. Finally, a multidimensional sensitivity analysis is performed through Sobol decomposition of polynomial chaos series representation to quantify the contribution of each parameter to the variance of the probabilistic response. The validation and assessment result shows that the output probabilistic response of the solar cell under Gaussian parametric uncertainty correlates to a Rayleigh probability distribution function. Output response is characterized by a mean value of 0.0060 and 0.0760 for RTC France and Solarex MSX83 solar cells, respectively. The standard deviation of ± 0.0034 and ± 0.0052 was observed in the probabilistic response for RTC France and Solarex MSX83 solar cells, respectively. [ABSTRACT FROM AUTHOR]

A surrogate model is developed to accurately approximate a two-dimensional hydrodynamics numerical solver in order to conduct a reduced-cost variance-based global sensitivity analysis of the hydraulic state. The impact of uncertainties in river bottom friction and boundary conditions on the simulated water depth is analyzed for quasi-unsteady flows. An autoencoder technique adapted to non-linear variable dimension reduction is used to reduce the multi-dimensional model output so that the formulation of the surrogate remains computationally parsimonious. In addition, following the divide-and-conquer principle, a mixture of local polynomial chaos expansions is proposed to deal with non-linearity in the hydraulic state with respect to uncertain inputs. Machine learning techniques are used to automatically partition the input space into clusters that are not affected by non-linearities and support accurate surrogates. This combined strategy is applied to a reach of the Garonne River where river and floodplains dynamics are simulated by the numerical solver Telemac-2D. The merits of this strategy are highlighted when the flood front reaches regions where the topography features a strong gradient and where, consequently, strong non-linearities occur between the water depth and friction as well as hydrologic input forcing. By applying this strategy, the Q 2 metric improves by 90% compared to a classical polynomial chaos expansion surrogate, resulting in a much more reliable sensitivity analysis. This is particularly important in floodplain areas where human and economic activities are at stake. [ABSTRACT FROM AUTHOR]

The use of epidemic modelling in connection with spread of diseases plays an important role in understanding dynamics and providing forecasts for informed analysis and decision-making. In this regard, it is crucial to quantify the effects of uncertainty in the modelling and in model-based predictions to trustfully communicate results and limitations. We propose to do efficient uncertainty quantification in compartmental epidemic models using the generalized Polynomial Chaos (gPC) framework. This framework uses a suitable polynomial basis that can be tailored to the underlying distribution for the parameter uncertainty to do forward propagation through efficient sampling via a mathematical model to quantify the effect on the output. By evaluating the model in a small number of selected points, gPC provides illuminating statistics and sensitivity analysis at a low computational cost. Through two particular case studies based on Danish data for the spread of Covid-19, we demonstrate the applicability of the technique. The test cases consider epidemic peak time estimation and the dynamics between superspreading and partial lockdown measures. The computational results show the efficiency and feasibility of the uncertainty quantification techniques based on gPC, and highlight the relevance of computational uncertainty quantification in epidemic modelling. [ABSTRACT FROM AUTHOR]

This paper presents the results of a sensitivity analysis of the characteristics of discrete fracture network (DFN) connectivity. The sizes of the maximum and mean clusters comprising the DFN and the distribution of the connectivity index were estimated. Attention was primarily directed to the global sensitivity analysis of these characteristics. Sobol sensitivity indices were used to determine the relative contribution of the DFN model parameter uncertainty to the total uncertainty of the studied problem. Dominant Sobol indices for different DFN models and each fracture connectivity characteristic were determined. The analysis of the results allowed the identification of the parameters whose relevant probability distributions are most important for the correct description of the studied statistical model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The paper presents a probabilistic approach to study uncertainty quantification in electrical parameters associated with single diode model of a solar cell. Five parameters which governs the electrical behavior of a solar cell needs to be estimated for analyzing the performance of a solar cell. Here, three deterministic techniques for parameter estimation namely Black Widow Optimization, multi-variable Newton Raphson and Particle Swarm Optimization are presented. For verifying the proposed techniques, Solarex MSX83 experimental (Current-Voltage) I-V data is considered. I-V and (Power-Voltage) P-V curves are plotted under standard test conditions (1000 W / m 2 , 1.5 A.M. spectrum, 25 ∘ C ) for three deterministic techniques and are compared with experimental curves. Black Widow Optimization shows increased convergence speed and accuracy. Additionally, uncertainty quantification analysis is presented to study the behaviour of deterministic response of single diode model under Gaussian random parametric uncertainity. Random samples of uncertain electrical parameters are obtained using Latin hypercube and Monte Carlo sampling methods to estimate the output probabilistic response. It can be observed that the objective function shows a bi-modal distribution under random parametric variations primarily due to measurement error, shading losses, surface defects, uneven thermal management and manufacturing issues. Alternatively, Bayesian approach is performed using Markov chain Monte Carlo sampling to estimate the probabilistic distribution of model parameters from given set of observations. To avoid computational complexity, Gaussian process model is also considered using polynomial choas expansion. The expected variance in the model response is statistically explained using multi-variate global sensitivity analysis based on Sobol Indices. Based on computed values of first order, second order and total Sobol indices, it can be concluded that reverse saturation current ' I O ' is the most influential parameter among five electrical parameters and contributes about 68.9 % to the variance in model response under random uncertainties. [ABSTRACT FROM AUTHOR]

This paper presents an analysis and optimization of Airborne Wind Energy Systems (AWESs), designed to maximize the Annual Energy Production (AEP) and, in the second part, the economic profit. A gradient-based optimization algorithm is used to perform the preliminary design of the main AWES sub-systems. A global sensitivity analysis is carried out to study how the design process, represented by the optimization problem, is influenced by aleatory and epistemic uncertainties. In particular, Ground-Gen and Fly-Gen AWESs are studied with a unified model to allow for a quantitative comparison. In the first part of the work, an ideal hybrid AWES design with ground and on-board power generation is considered. With this approach, the common characteristics of Ground-Gen and Fly-Gen AWES designs that maximize AEP are found. In the second part, Ground-Gen and Fly-Gen AWES optimal economic designs are analyzed individually. It is found that a fully developed AWES has strong potential to be highly competitive in the energy market, by providing cheap renewable energy. Fly-Gen AWESs are found to be slightly more profitable than Ground-Gen if the airborne unit is not replaced often. The main physical and economical characteristics of optimal designs are highlighted. • AWESs are optimized to maximize AEP and profit. • Optimal designs are studied with global sensitivity analyses. • Optimal designs of Fly-Gen and Ground-Gen AWESs are compared. [ABSTRACT FROM AUTHOR]

Suppose that Y = ψ (X 1 , ... , X p) , where (X 1 , ... , X p) ⊤ are random inputs, Y is the output, and ψ (·) is an unknown link function. The Sobol indices gauge the sensitivity of each X against Y by estimating the regression curve's variability between them. In this paper, we estimate these curves with a kernel-based method. The method allows to estimate the first order indices when the link between the independent and dependent variables is unknown. The kernel-based methods need a bandwidth to average the observations. For finite samples, the cross-validation method is famous to decide this bandwidth. However, it produces a structural bias. To remedy this, we propose a bootstrap procedure which reconstruct the model residuals and re-estimate the non-parametric regression curve. With the new set of curves, the procedure corrects the bias in the Sobol index. To test the developed method, we implemented simulated numerical examples with complex functions. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis (GSA) of voltage to uncertain power injection variations plays an important role for appropriate Volt-VAR optimization. This paper proposes a data-driven GSA method for large-scale distribution systems with a large number of uncertain sources. Specifically, the deep Gaussian process is used to identify the mapping relationship between uncertain power injections and voltages. This allows resorting to the analysis of variance framework to calculate the Sobol indices for GSA. Unlike the existing polynomial chaos expansion and Gaussian process-based approaches, our proposed method has much better scalability. Test results on the EPRI 1747-node K1 circuit with different numbers of uncertain sources with various uncertain levels and different PV distributions demonstrate that the proposed method can achieve accurate GSA. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis (GSA) of distribution system with respect to stochastic PV and load variations plays an important role in designing optimal voltage control schemes. This paper proposes a data-driven framework for GSA of distribution system. In particular, two representative surrogate modeling-based approaches are developed, including the traditional Gaussian process-based and the analysis of variance (ANOVA) kernel ones. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol indices can be conveniently calculated through either the sampling-based method or the analytical method to assess the global sensitivity of voltage to variations of load and PV power injections. The sampling-based method estimates the Sobol indices using Monte Carlo simulations while the analytical method calculates them by resorting to the ANOVA expansion framework. Comparison results with other model-based GSA methods on the unbalanced three-phase IEEE 37-bus and 123-bus distribution systems show that the proposed framework can achieve much higher computational efficiency with negligible loss of accuracy. The results on a real 240-bus distribution system using actual smart meter data further validate the feasibility and scalability of the proposed framework. [ABSTRACT FROM AUTHOR]

Sobol's method is one of the most powerful and widely used frameworks for global sensitivity analysis, and it maps every possible combination of input variables to an associated Sobol index. However, these indices are often challenging to analyze in depth, due in part to the lack of suitable, flexible enough, and fast‐to‐query data access structures as well as visualization techniques. We propose a visualization tool that leverages tensor decomposition, a compressed data format that can quickly and approximately answer sophisticated queries over exponential‐sized sets of Sobol indices. This way, we are able to capture the complete global sensitivity information of high‐dimensional scalar models. Our application is based on a three‐stage visualization, to which variables to be analyzed can be added or removed interactively. It includes a novel hourglass‐like diagram presenting the relative importance for any single variable or combination of input variables with respect to any composition of the rest of the input variables. We showcase our visualization with a range of example models, whereby we demonstrate the high expressive power and analytical capability made possible with the proposed method. [ABSTRACT FROM AUTHOR]

Predictive flame spread models based on temperature dependent pyrolysis rates require numerous material properties as input parameters. These parameters are often derived by optimisation and inverse modelling using data from bench scale experiments such as the Cone Calorimeter. The estimated parameters are then transferred to flame spread simulations, where self-sustained propagation is expected. A fundamental requirement for this transfer is that the simulation model used in the optimisation is sufficiently sensitive to the input parameters that are important to flame spread. Otherwise, the estimated parameters will have an increased associated uncertainty that will be transferred to the flame spread simulation. This is investigated here using a variance-based global sensitivity analysis method, the Sobol indices. The sensitivities of a Cone Calorimeter and a horizontal flame spread simulation to 15 effective properties of polymethyl methacrylate (PMMA) are compared. Results show significant differences between the setups: the Cone Calorimeter is dominated by strong interaction effects between two temperature dependent specific heat values, whereas the flame spread is influenced by several parameters. Furthermore, the importance of some parameters for the Cone Calorimeter is found to be time-varying, suggesting that single-value cost functions may not be sufficient to account for all sensitive parameters during optimisation. [ABSTRACT FROM AUTHOR]

Most temperature predictions for deep geothermal applications rely on correcting bottom-hole temperatures (BHTs) to undisturbed or static formation temperatures (SFTs). The data used for BHT correction are usually of low quality due to a lack of information and poor documentation, and the uncertainty of the corrected SFT is therefore unknown. It is supposed that the error within the input data exceeds the error due to the uncertainty of the different correction schemes. To verify this, we combined a global sensitivity study with Sobol indices of six easy-to-use conventional correction schemes of the BHT data set of the Bavarian Molasse Basin with an uncertainty study and developed a workflow that aims at presenting a valid error range of the corrected SFTs depending on the quality of their input data. The results give an indication of which of the investigated correction methods should be used depending on the input data, as well as show that the unknown error in the input parameters exceeds the error of the individual BHT correction methods as such. The developed a priori uncertainty-based BHT correction helps to provide a real estimate of the subsurface temperatures needed for geothermal prospecting and probabilistic risk assessment.

Historical masonry constructions are difficult to mimic in hygrothermal models. The material properties of the walls are often highly uncertain due to the natural origin of the aggregates and the various, manual production processes used through time. Therefore, sensitivity analyses based on probabilistic simulations are powerful tools to indicate the risks on damage in masonry constructions. Damage criteria for relevant pathologies such as frost damage, potential decay of wooden beam heads and mould growth at the interior surface are used. The assessment methods (Scatter plots, Classification trees and Sobol indices) are based on 1D Heat, Air and Moisture simulations, including realistic variations on climate parameters and wall properties. These methodologies are applied to probabilistic simulations in which a potential damage risk is expected in historic masonries. The application of interior insulation, the use of hydrophobic treatments, and the impact of potential water infiltrations through cracks are discussed. In most of these situations a high dependency of each of the damage criteria on the rain intensity, the trend of the moisture retention/liquid conductivity curve and the absorption coefficient is evident, but also additional insights are found. For example, the thermal impact of interior insulation is negligible compared to its reduction of the first phase drying potential towards the interior. For hydrophobic treatments, the risk for damage typically decreases, but in combination with a rain water infiltration rate above approximately 5% of the wind driven rain the risk on mould growth at the interior surface significantly increases. [ABSTRACT FROM AUTHOR]

The inverse problem of electromagnetic (EM) non‐destructive testing (NdT) consists of reconstructing material defect parameters invoking EM field measurements. Uncertainties of the configuration (e.g. imprecise constitutive and geometrical parameters) are inevitably present; hence, the reconstructed defect parameters are also uncertain. In this study, the different sources of uncertainty are ranked by means of sensitivity analysis. The model‐based inversion (involving EM simulation) is computationally demanding; moreover, sensitivity analysis usually requires a vast number of repeated runs of the inversion. To overcome the computational complexity, surrogate models are applied at different levels. Interpolation on a sparse grid is used as a surrogate model of the EM simulation. The sensitivity of the reconstructed defect parameters concerning configuration uncertainties is characterised by means of Sobol indices. The Sobol indices are obtained from a polynomial chaos expansion surrogate model of the entire inversion scheme. A numerical example drawn from eddy‐current NdT is thoroughly analysed to illustrate the proposed methodology and to demonstrate its performance. [ABSTRACT FROM AUTHOR]

Markov models have a long tradition in modeling and simulation of dynamic systems. In this article, we look at certain properties of a discrete-time Markov chain, including entropy, trace, and second-largest eigenvalue to better understand their role for time-series analysis. We simulate a number of possible input signals, fit a discrete-time Markov chain, and explore properties with the help of Sobol indices, partial correlation coefficients, and the Morris elementary effect screening method. Our analysis suggests that the presence of a trend, periodicity, and autocorrelation impact entropy, trace, and second-largest eigenvalue to varying degrees but not independently of each other and with Markov chain parameter settings as other influencing factors. The properties of interest are promising to distinguish time-series data, as evidenced for the entropy measure by recent results in the analysis of cell development for Xenopus laevis in cell biology. [ABSTRACT FROM AUTHOR]

This paper presents a new framework for stochastic updating of a finite element model for a composite plate, considering the influence of temperature on Lamb wave propagation. The framework involves deterministic updating to optimize mechanical properties and stochastic updating to derive probability density functions for key parameters. It utilizes sensitivity analysis and Bayesian inference with Markov-Chain Monte Carlo simulations and the Metropolis–Hastings sampling algorithm. This paper proposes a machine learning surrogate model based on artificial neural networks to improve computational efficiency. This surrogate modeling approach allows parallelized Monte Carlo simulations, reducing updating time significantly without compromising the accuracy of the resulting probability density functions for model parameters. These advancements show a promising way to enhance composite plate modeling and Lamb wave propagation studies, providing a more efficient and accurate approach to verify and validate finite element models with potential applications in engineering simulations. [ABSTRACT FROM AUTHOR]

The aim of the presented study was to perform a global sensitivity analysis of various design parameters affecting the lost motion of the harmonic drive. A detailed virtual model of a harmonic drive was developed, including the wave generator, the flexible ball bearing, the flexible spline and the circular spline. Finite element analyses were performed to observe which parameter from the harmonic drive geometry parameter group affects the lost motion value most. The analyses were carried out using 4% of the rated harmonic drive output torque by the locked wave generator and fixed circular spline according the requirements for the high accuracy harmonic drive units. The described approach was applied to two harmonic drive units with the same ratio, but various dimensions and rated power were used to generalize and interpret the global sensitivity analysis results properly. The most important variable was for both harmonic drives the offset from the nominal tooth shape.

The effects of atmospheric icing can be anticipated by Computational Fluid Dynamics (CFD). Past studies show that the convective heat transfer influences the ice accretion and is itself a function of surface roughness. Uncertainty quantification (UQ) could help quantify the impact of surface roughness parameters on the reliability of ice accretion prediction. This paper aims to quantify ice accretion uncertainties and identify the key surface roughness correction parameters contributing the most to the uncertainties in a Reynolds-Averaged Navier-Stokes (RANS) formulation. Ice accretion simulations over a rough flat plate using two thermal correction models are used to construct a RANS database. Non-Intrusive Polynomial Chaos Expansion (NIPCE) metamodels are developed to predict the convective heat transfer and icing characteristics of the RANS database. The metamodels allow for the computation of the 95% confidence intervals of the output probability distribution (PDF) and of the sensitivity indexes of the roughness parameters according to their level of influence on the outputs. For one of the thermal correction models, the most influential parameter is the roughness height, whereas for the second model it is the surface correction coefficient. In addition, the uncertainty on the freestream temperature has a minor impact on the ice accretion sensitivity compared to the uncertainty on the roughness parameters.

The role of simulation keeps increasing for the reliability analysis of complex systems. Most of the time, these analyses can be reduced to estimating the probability of occurrence of an undesirable event, also called failure probability, using a stochastic model of the system. If the considered event is rare, sophisticated sample-based procedures are generally introduced to get a relevant estimate of the failure probability. Based on the samples constructed for the evaluation of this estimate, this work considers two types of reliability-oriented sensitivity indices (ROSI). The first ones are introduced to identify the model inputs whose variability has to be reduced in priority to decrease this probability. The second ones are used to find the model inputs whose distribution has to be particularly well-characterized for the available estimate to be realistic. It is also shown how these ROSI can be derived when the true model is approximated by a surrogate model. In particular, an innovative procedure is proposed to take into account the surrogate model uncertainty in the estimation of these ROSI. The proposed approach is then applied to the reliability analysis of a series of numerical and industrial examples. [ABSTRACT FROM AUTHOR]

Highlights • This paper presents an original updating method that enables to update the model parameters one-at-a-time. • For each model parameter, the model outputs are transformed into a new output which is sensitive to this parameter only. • The sensitivity is quantified using Sobol indices. • The proposed approached is robust with respect to modelling errors. Abstract This paper is interested in model updating problems which consists in identifying optimal values of model parameters by comparing the model outputs with the experimental outputs. Such a problem generally yields a challenging multivariate inverse problem to be solved in high dimension. The high-dimensionality requires the use of a global optimization algorithm in order the explore efficiently the parameters space. In this paper we propose an alternative algorithm which allows each model parameters to be identified separately and sequentially by solving separated univariate inverse problems. For each parameter, a devoted inverse problem is introduced by identifying an output which is sensitive to this parameter only, the sensitivity being quantified using Sobol indices. The proposed method is illustrated through a three-storey structure for which experimental measurements are collected. [ABSTRACT FROM AUTHOR]

Complex mechanistic computer models often produce functional or multivariate output. Sensitivity analysis can be used to determine what input parameters are responsible for uncertainty in the output. Much of the literature around sensitivity analysis has focused on univariate output. Recent advances have been made in sensitivity analysis for multivariate output. However, these methods often depend on a significant number of model runs and may still be computationally intensive for practical purposes. Emulators have been a proven method for reducing the required number of model runs for univariate sensitivity analysis, with some recent development for multivariate computer models. We propose the use of generalized additive models and random forests combined with a principal component analysis for emulation for a multivariate sensitivity analysis. We demonstrate our method using a complex agricultural simulators. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

Highlights • We propose the Sobol tensor train, a data structure containing all Sobol indices of a surrogate model compressed using the tensor train decomposition • We show how to extract the proposed tensor from any tensor train surrogate, and how such surrogates can be learned • We derive all total, closed, and superset indices from our representation at very small cost • We are able to answer advanced queries among the set of all sensitivity indices • Our algorithms are demonstrated with two high-dimensional analytical functions and an engineering simulation example Abstract Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (TT) as a unified framework for surrogate modeling and sensitivity analysis via Sobol indices. We first overview several strategies to build a TT surrogate using either an adaptive sampling strategy or a predefined set of samples. Our main contribution is the introduction of the Sobol TT, which compactly represents variance components for all possible joint variable interactions of any order. Our formulation allows efficient aggregation and subselection operations, and we are able to obtain related Sobol indices (closed, total, and superset indices) at negligible cost. Furthermore, we exploit an existing global optimization procedure within the TT framework for variable selection and model analysis tasks. We demonstrate our algorithms with two analytical models and a parallel computing simulation data set. [ABSTRACT FROM AUTHOR]