Variance-based Global Sensitivity Analysis Research Articles

Uncertainty sensitivity analysis for vibration properties of composite doubly-curved shallow shells using Kriging method

This paper presents a Kriging based global sensitivity analysis (GSA) method for the frequency response of displacements of composite doubly-curved shallow shells. A unified solution is utilized to develop the dynamic vibration formulation using the First-order Shear Deformation Theory (FSDT) and the Rayleigh-Ritz method. Kriging surrogate model is employed to substitute the frequency response function (FRF) of displacements. Ten parameters including materials and geometrical dimension are considered as input uncertain variables. A variance-based GSA method for dynamic model is employed to quantify the influence of each uncertain parameter. In addition, to avoid the computational burden of Monte Carlo simulation method (MCS), the presented sensitivity indices are computed analytically based on the Kriging mode, which further improves computational efficiency. Based on the convergence studies and comparison with traditional methods, the accuracy and efficiency of the present method are validated. The results shows that the frequency response of displacements exhibits greater sensitivity to changes in width, and thickness is more influential than others in the example from this article. Finally, the presented numerical results demonstrate vibration characteristics of different types of shells and observation points, which can also serve as a reference for further study on uncertainty-propagation analysis.

Variance-based global sensitivity analysis of the performance of a proton exchange membrane water electrolyzer

This study is threefold objective. First, a nonlinear one-dimensional steady-state simulation model for hydrogen production from proton exchange membrane water electrolyzer (PEMWE) is established. The model comprehensively addresses activation, diffusion overpotentials and ohmic potential drop, and particularly incorporating Nafion membrane properties in the presence of liquid water. The model is enhanced by analyzing the hydrogen crossover, introducing corresponding diffusion equations to evaluate Faraday efficiency. The model accurately quantifies voltage efficiency, hydrogen production rate and specific energy consumption, and it is validated with published experimental data found in the scientific literature. Second, a variance-based global sensitivity analysis (GSA) on the model, is employed as a metric to assess the impact of operating conditions and material characteristics on three objective functions: the hydrogen production rate; the voltage efficiency and the specific energy consumption. Third, to support the GSA analysis, genetic algorithm (GA) technique is performed to maximize hydrogen production rate while minimizing specific energy consumption. In the course of this novel investigation, it was discerned that the number of cells, the cross-sectional area of the electrolyzer, the current density and temperature all exerted a significant impact on the three objective functions. This combined approach GSA-GA provides a thorough exploration of parameter influences and an efficient optimization strategy for enhancing the model's performance. These findings provide valuable insights that can guide analysis of the performance and the optimization of the PEMWE system.

Modeling green recycled aggregate concrete using machine learning and variance-based sensitivity analysis

Recycled aggregate concrete (RAC) is commonly used to lessen the environmental effect of concrete building and demolition waste. The compressive strength of the RAC is one of the most critical factors influencing concrete quality. The compressive strength is assessed by a compression test, which takes a large number of materials and is expensive and time-consuming. With the development of novel concrete mixes and applications, academics are obliged to seek accurate models for forecasting mechanical strength. A significant source of difficulty in compressive strength modeling is that there are many mixture components and testing conditions whose variation significantly influences the predicted values. To this end, this study explores the mixture design of sustainable concrete in order to generate eco-friendly concrete mixes. Tests are conducted on 18 different mixtures comprising different proportions of waste tires, plastic, cement, and red brick to experiment with new green RAC mixtures. For the modeling part, the deep residual neural networks (DRNNs) method is first presented to the problem, aided by a database from the literature for a pretraining task. The proposed DRNNs structure uses shortcuts (i.e., residual connections) that bypass some layers in the deep network structure to alleviate the problem of training with high accuracy. The performance of the proposed DRNNs is evaluated using different goodness of fit measures and compared with well-known machine learning tools. The findings showed that the suggested model could provide credible predictions about the desired mechanical parameter, saving the required lab efforts by 40 %. Finally, a variance-based global sensitivity analysis is performed with the Latin hypercube simulation method to help rank/prioritize each mixture component's impact on determining the compressive strength in practice while mitigating the potential misrepresentation of results due to the correlations between the input parameters. The analysis showed that cement and waste contents are the most significant ones in their first and total order effects.

A compartmental model for smoking dynamics in Italy: a pipeline for inference, validation, and forecasting under hypothetical scenarios

We propose a compartmental model for investigating smoking dynamics in an Italian region (Tuscany). Calibrating the model on local data from 1993 to 2019, we estimate the probabilities of starting and quitting smoking and the probability of smoking relapse. Then, we forecast the evolution of smoking prevalence until 2043 and assess the impact on mortality in terms of attributable deaths. We introduce elements of novelty with respect to previous studies in this field, including a formal definition of the equations governing the model dynamics and a flexible modelling of smoking probabilities based on cubic regression splines. We estimate model parameters by defining a two-step procedure and quantify the sampling variability via a parametric bootstrap. We propose the implementation of cross-validation on a rolling basis and variance-based Global Sensitivity Analysis to check the robustness of the results and support our findings. Our results suggest a decrease in smoking prevalence among males and stability among females, over the next two decades. We estimate that, in 2023, 18% of deaths among males and 8% among females are due to smoking. We test the use of the model in assessing the impact on smoking prevalence and mortality of different tobacco control policies, including the tobacco-free generation ban recently introduced in New Zealand.

Effectiveness of Adjacent and Bivariate Maps in Communicating Global Sensitivity Analysis for Geodiversity Assessment

This study compares adjacent and bivariate maps in communicating variance-based global sensitivity analysis (GSA) results for a geodiversity assessment spatial multi-criteria model and examines the influence of prior exposure to geodiversity and map reading skills on interpretation. It analyzes the quality of map interpretation, confidence levels, and map communication effectiveness. The findings indicate that there is no significant difference in the quality of map interpretation or confidence levels between the two map types. However, there are nuanced differences in interpretive patterns, suggesting the need for further investigation into factors affecting map interpretation. Adjacent maps are more effective in identifying factors linked to uncertainty in high geodiversity values, while bivariate maps excel in understanding spatial variability. Prior exposure to geodiversity and map reading skills do not significantly impact interpretation quality or confidence levels. Future research could explore other factors influencing map effectiveness and explore the cognitive processes underlying map interpretation. Understanding these processes could lead to more effective strategies for communicating the results of a GSA for spatial models through maps.

Investigating the effects of spatial scales on social vulnerability index: A hybrid uncertainty and sensitivity analysis approach combined with remote sensing land cover data.

Investigating the effects of spatial scales on the uncertainty and sensitivity analysis of the social vulnerability index (SoVI) model output is critical, especially for spatial scales finer than the census block group or census block. This study applied the intelligent dasymetric mapping approach to spatially disaggregate the census tract scale SoVI model into a 300-m grids resolution SoVI map in Davidson County, Nashville. Then, uncertainty analysis and variance-based global sensitivity analysis were conducted on two scales of SoVI models: (a) census tract scale; (b) 300-m grids scale. Uncertainty analysis results indicate that the SoVI model has better confidence in identifying places with a higher socially vulnerable status, no matter the spatial scales in which the SoVI is constructed. However, the spatial scale of SoVI does affect the sensitivity analysis results. The sensitivity analysis suggests that for census tract scale SoVI, the indicator transformation and weighting scheme are the two major uncertainty contributors in the SoVI index modeling stages. While for finer spatial scales like the 300-m grid's resolution, the weighting scheme becomes the uttermost dominant uncertainty contributor, absorbing uncertainty contributions from indicator transformation.

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics.

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Global sensitivity analysis with limited data via sparsity-promoting D-MORPH regression: Application to char combustion

In uncertainty quantification, variance-based global sensitivity analysis quantitatively determines the effect of each input random variable on the output by partitioning the total output variance into contributions from each input. However, computing conditional expectations can be prohibitively costly when working with expensive-to-evaluate models. Surrogate models can accelerate this, yet their accuracy depends on the quality and quantity of training data, which is expensive to generate (experimentally or computationally) for complex engineering systems. Thus, methods that work with limited data are desirable. We propose a diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression to train a polynomial dimensional decomposition surrogate of the output that minimizes the number of training data. The new method first computes a sparse Lasso solution and uses it to define the cost function. A subsequent D-MORPH regression minimizes the difference between the D-MORPH and Lasso solution. The resulting D-MORPH based surrogate is more robust to input variations and more accurate with limited training data. We illustrate the accuracy and computational efficiency of the new surrogate for global sensitivity analysis using mathematical functions and an expensive-to-simulate model of char combustion. The new method is highly efficient, requiring only 15% of the training data compared to conventional regression.

An Improved Sobol Sensitivity Analysis Method

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.

Global sensitivity analysis and optimization of multi-stage TEG based on random and fuzzy mixed input variables

In practical engineering, uncertainties in thermoelectric power generation arise from various factors such as material properties, geometric dimensions, assembly processes, and operational fluctuations of the thermoelectric components. Addressing subjective and objective uncertainties in the design parameters of multi-stage thermoelectric generators (TEGs), this study establishes a robust TEG model incorporating non-equilibrium thermodynamics. Fuzzy and stochastic theories are employed for uncertainty representation, and a variance-based global sensitivity analysis is conducted. The results indicate that the uncertainties in the design variables have varying effects on the output responses of the three-stage TEG. Among them, the temperature of the hot and cold sources has the most significant impact on the output responses（STHP: 0.5018, STLP:0.2199, STHη: 0.5436, STLη: 0.3336）, Parameters like Seebeck coefficient, thermal resistance, thermal conductivity, and operating current exhibit relatively minor effects. The coefficient of variation of the output response varies consistently with changes in the standard deviation or coefficient of variation of input variables, following a similar order as the sensitivity indicators. The variations in the distribution parameters of the key design variable, i.e., the temperature of the hot and cold sources, do not affect the sensitivity index rankings of the variables concerning the system output responses. As the distribution parameters of the hot and cold source temperatures gradually increase, the sensitivity indices of the design variables to the system output responses exhibit different trends, indicating a change in the degree of sensitivity to the variations in distribution parameters of the design variables. Optimization based on global sensitivity analysis enhances power output by 43.37 %, reaching a maximum of 11.37 W under constraints compared to the original 7.93 W. This research provides guidance for designing and optimizing thermoelectric power systems under mixed uncertainties.

Multi-objective optimization for sustainable and economical polycarbonate production with reaction kinetics inference for real-world industrial process

Polycarbonate has a wide range of applications in electronic devices and medicine because of its remarkable properties such as transparency and mechanical strength. However, the polycarbonate production process using diphenyl carbonate leads to the inevitable generation of nitrogen oxide (NOx) from byproduct incineration. Therefore, it is essential to optimize the process conditions while simultaneously considering the production costs and NOx emissions. Herein, we propose a multi-objective optimization model for sustainable and economical polycarbonate production using a high-fidelity reaction model for real-world industrial processes. Additionally, a data-driven model was developed using industrial data to identify the operating conditions that minimize NOx emissions and maximize profitability. Four of the ten reaction parameters were selected through variance-based global sensitivity analysis, and the posterior distribution of each parameter was determined through Bayesian inference. In addition, NOx emissions were predicted using the data-driven model developed from industrial data. A process model with coefficients of determination above 0.7 and a data-driven model with R-squared value above 0.99 for pilot-scale experimental and industrial data were generated using our approach. The Pareto optimality, identified based on the developed models, suggested operating conditions that optimize both economic and environmental benefits. Consequently, NOx emissions could be reduced by 27.2%–27.4% and the unit costs of production could be reduced by 0.8%–1.6% compared with the base case.

Advancement in ice-jam flood risk management: Integrating dynamic adaptive behavior by an agent-based modeling in Fort McMurray, Canada

Ice-jam flooding is a prevalent extreme event that impacts flood hazard and vulnerability. We introduce a conceptual model framework for Dynamic Ice-jam Flood Risk Assessment (DIFRA). DIFRA integrates ice-jam flood hazard, ice-jam flood risk, and human adaptation. Using agent-based modeling, we captured top-down (artificial breakup) and bottom-up (flood-proofing) adaptive behavior. Our study in Fort McMurray, Canada, shows the complex interaction between micro-level behaviors and macro-level phenomena over time. Our variance-based global sensitivity analysis shows the role of dynamic adaptive behavior in ice-jam flood risk, where the artificial breakage by the government can lead to a regime shift and a decrease in the ice-jam flood risk. However, it can also decrease the number of newly adapted residents to flood-proofing and the role of residents in ice-jam flood risk. DIFRA offers a comprehensive approach to understanding and managing ice-jam flood risk, with potential applications to similar riverine communities in cold regions.

Identification of parameter importance for benzene transport in the unsaturated zone using global sensitivity analysis

Abstract. One of the greatest threats to groundwater is contamination from fuel derivatives. Benzene, a highly mobile and toxic fuel derivative, can easily reach groundwater from fuel sources and lead to extensive groundwater contamination and drinking water disqualification. Modelling benzene transport in the unsaturated zone can quantify the risk for groundwater contamination and provide needed remediation strategies. Yet, characterization of the problem is often complicated, due to typical soil heterogeneity, numerous unknown site and solute parameters, and the difficulty of distinguishing important from non-important parameters. Thus, sensitivity analysis (SA) methods, such as global SA (GSA), are applied to reduce uncertainty and detect key parameters for groundwater contamination and remediation. Nevertheless, studies devoted to identifying the parameters that determine transport of fuel derivatives in the unsaturated zone are scarce. In this study, we performed GSA to assess benzene transport in the unsaturated zone. First, a simple GSA (Morris) screening method was used for a homogenous sandy vadose zone. Then, a more computationally demanding (Sobol) variance-based GSA was run on the most influential parameters. Finally, the Morris method was tested for a heterogeneous medium containing clay layers. To overcome model crashes during GSA, several methods were tested for imputation of missing data. The GSA results indicate that benzene degradation rate (λk) is the utmost influential parameter controlling benzene mobility, followed by aquifer depth (z). The adsorption coefficient (Kd) and the van Genuchten n parameter of the sandy soil (n1) were also highly influential. The study emphasizes the significance of λk and the presence of clay layers in predicting aquifer contamination. The study also indicates the importance of heterogenous media representation in the GSA. Though identical parameters control the transport in the different soil types, in the presence of both sand and clay, parameters directly affecting the solute concentration like λk and Kd have increased influence in clay, whereas n is more influential for sand comprising most of the profile. Overall, GSA is demonstrated here as an important tool for the analysis of transport models. The results also show that in higher dimensionality models, the radial basis function (RBF) is an efficient surrogate model for missing data imputation.

Sensitivity analysis of multiple time-scale building energy using Bayesian adaptive spline surfaces

Sensitivity analysis has been widely used in building energy analysis to identify key variables influencing building energy and carbon emissions. However, most previous studies only focus on the single time scale energy use of buildings when conducting sensitivity analysis. The multiple time-scale sensitivity analysis would lead to increased complexity and challenges in building energy analysis. This paper proposes a new systematical procedure for global variance-based sensitivity analysis of multiple time-scale energy use of buildings. A case study of an office building is used to demonstrate the application of this approach using the Bayesian adaptive spline surface (BASS) models at three different time scales (annual, monthly, and daily). The results indicate that the procedure proposed here can provide fast and reliable sensitivity results for the multiple time-scale building energy assessment. The BASS learning models have the advantages of high predictive performance and the fast computation of sensitivity indicators in a closed form without Monte Carlo integrals. The application of principal component analysis can deal with the highly correlated multi-output energy use at a smaller time scale, which can further reduce computational costs. Moreover, the sensitivity analysis at the different time scales can provide new insights into energy characteristics due to the intrinsic variations of weather conditions. This systematical procedure can provide useful guidance for the multiple time-scale model calibration and multi-step ahead predictions of buildings. Moreover, the method proposed here can be extended to the sensitivity analysis of energy use in different time scales (sub-hourly, hourly, or daily) for other energy systems (such as PV, solar thermal, and wind).

Variance-based Global Sensitivity Analysis of Surface Runoff Parameters for Hydrological Modeling of a Real Peri-urban Ungauged Basin

Variance-based Global Sensitivity Analysis of Surface Runoff Parameters for Hydrological Modeling of a Real Peri-urban Ungauged Basin

EXTREME LEARNING MACHINES FOR VARIANCE-BASED GLOBAL SENSITIVITY ANALYSIS

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost, which often renders it unfeasible in practice. An appealing alternative is to instead analyze the sensitivity of a surrogate model with the goal of lowering computational costs while maintaining sufficient accuracy. Should a surrogate be "simple" enough to be amenable to the analytical calculations of its Sobol' indices, the cost of GSA is essentially reduced to the construction of the surrogate.We propose a new class of sparse-weight extreme learning machines (ELMs), which, when considered as surrogates in the context of GSA, admit analytical formulas for their Sobol' indices and, unlike the standard ELMs, yield accurate approximations of these indices. The effectiveness of this approach is illustrated through both traditional benchmarks in the field and on a chemical reaction network.

Sensitivity analysis of fifth generation district heating and cooling coupled with borehole thermal energy storage with respect to cooling adoption

Fifth generation district heating and cooling (5GDHC) is a promising solution for decarbonising building thermal demands, as it allows for simultaneous heating and cooling through a bi-directional network. This paper aims to investigate the general performance of 5GDHC under uncertainty. Initially, an uncertainty analysis is performed on a 5GDHC model in a case study, revealing significant variation in economic, technical, and environmental performance due to uncertain parameters. Subsequently, variance-based global sensitivity analysis is used to rank the uncertain parameters based on their impact on the economic performance of 5GDHC. The results identify cooling adoption rate, borehole pricing, and discount rate as the most influential parameters. Lastly, factors mapping demonstrates that cooling adoption rate within 0.6-0.9, low borehole costs, low discount rates, and high gas prices will drive the switch to 5GDHC. Overall, this study emphasizes the general applicability of 5GDHC.

Estimating global identifiability using conditional mutual information in a Bayesian framework

A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual information, an estimate of information gained for each model parameter is used to quantify the identifiability with practical considerations. No assumptions are made about the structure of the statistical model or the prior distribution while constructing the estimator. The estimator has the following notable advantages: first, no controlled experiment or data is required to conduct the practical identifiability analysis; second, unlike popular variance-based global sensitivity analysis methods, different forms of uncertainties, such as model-form, parameter, or measurement can be taken into account; third, the identifiability analysis is global, and therefore independent of a realization of the parameters. If an individual parameter has low identifiability, it can belong to an identifiable subset such that parameters within the subset have a functional relationship and thus have a combined effect on the statistical model. The practical identifiability framework is extended to highlight the dependencies between parameter pairs that emerge a posteriori to find identifiable parameter subsets. The applicability of the proposed approach is demonstrated using a linear Gaussian model and a non-linear methane-air reduced kinetics model. It is shown that by examining the information gained for each model parameter along with its dependencies with other parameters, a subset of parameters that can be estimated with high posterior certainty can be found.

Iterative hierarchical clustering algorithm for automated operational modal analysis

Recent developments in sensors and data processing made the structural health monitoring (SHM) sector expanding to big-data field, particularly when continuous long-term strategies are implemented. Nevertheless, main shortcomings are due to the identification and extraction of modal features. In fact, although machine learning methods have been implemented to automate modal identification processes, intense user interaction and time-consuming procedures are still required, limiting the extensive use of these techniques. In order to provide a fully automated procedure capable of identifying and extracting modal properties from covariance driven SSI analyses, an innovative and flexible algorithm for Iterative Hierarchical Clustering Analysis (IHCA) is proposed. To evaluate the stability and robustness of the IHCA method, a Variance-Based Global sensitivity Analysis (VBGA) was performed considering a numerical and experimental case study. The outcomes demonstrated that the IHCA is stable in clustering the physical structural modes and selecting the most representative modal features.

Effect of uncertainty of material parameters on stress triaxiality and Lode angle in finite elasto-plasticity—A variance-based global sensitivity analysis

This work establishes a computational framework for the quantification of the effect of uncertainty of material model parameters on extremal stress triaxiality and Lode angle values in plastically deformed devices, whereby stress triaxiality and Lode angle are accepted as key indicators for damage initiation in metal forming processes. Attention is paid to components, the material response of which can be represented as elasto-plastic with proportional hardening as a prototype model, whereby the finite element method is used as a simulation approach generally suitable for complex geometries and loading conditions. Uncertainty about material parameters is characterized resorting to probability theory. The effects of material parameter uncertainty on stress triaxiality and Lode angle are quantified by means of a variance-based global sensitivity analysis. Such sensitivity analysis is most useful for apportioning the variance of the stress triaxiality and Lode angle to the uncertainty on material properties. The practical implementation of this sensitivity analysis is carried out resorting to a Gaussian process regression, Bayesian probabilistic integration and active learning in order to decrease the associated numerical costs. An example illustrates the proposed framework, revealing that parameters governing plasticity affect stress triaxiality and Lode angle the most.