Variance-based Sensitivity Analysis Research Articles

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 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.

Evaluating spray drift from Uncrewed Aerial Spray Systems: A machine learning and variance-based sensitivity analysis of environmental and spray system parameters

Uncrewed Aerial Spray Systems (UASS), commonly called drones, have become an important application technique for plant protection products in Asia and worldwide. As such, environmental variables and spray system parameters influencing spray drift deserve detailed investigations. This study presents the data analysis of 114 UASS drift trials conducted between December 2021 and December 2022 in China. Study design was based on the ISO 22866:2005 protocol for spray drift trials and considered different UASS platforms, nozzles, and release heights, and specifically continuously measured weather conditions. The relative importance of the environmental variables and spray system parameters was evaluated by a random forest (RF) feature importance analysis, a Sobol sensitivity analysis and partial dependence plots. This approach was preferred to linear ranking techniques such as ANOVA (analysis of variance) due to the non-linearity of the system. In addition, partial dependence plots are proposed to visualize the relationship between specific input parameters within the system.Drift deposition curves calculated from the 114 trials show good agreement with previous UASS trials reported in the literature. As reported in previous studies, spray drift following UASS applications is lower than for manned aerial vehicles, greater than for ground spray applications, and similar to drift observed from orchard air blast applications. In addition, 9 trials were conducted on corn fields in order to evaluate the potential effect of crop cover on spray drift. Spray drift was observed to be reduced over the cropped soil, suggesting that plant cover might possibly reduce spray drift. These findings could help supporting drift mitigation policies, stewardship advice and product labelling around the world.

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.

A mathematical model of competition between fiber and mucin degraders in the gut provides a possible explanation for mucus thinning

The human gut microbiota relies on complex carbohydrates (glycans) for energy and growth, primarily dietary fiber and host-derived mucins. We introduce a mathematical model of a glycan generalist and a mucin specialist in a two-compartment chemostat model of the human colon. Our objective is to characterize the influence of dietary fiber and mucin supply on the abundance of mucin-degrading species within the gut ecosystem. Current mathematical gut reactor models that include the enzymatic degradation of glycans do not differentiate between glycan types and their degraders. The model we present distinguishes between a generalist that can degrade both dietary fiber and mucin, and a specialist species that can only degrade mucin. The integrity of the colonic mucus barrier is essential for overall human health and well-being, with the mucin specialist Akkermanisa muciniphila being associated with a healthy mucus layer. Competition, particularly between the specialist and generalists like Bacteroides thetaiotaomicron, may lead to mucus layer erosion, especially during periods of dietary fiber deprivation. Our model treats the colon as a gut reactor system, dividing it into two compartments that represent the lumen and the mucus of the gut, resulting in a complex system of ordinary differential equations with a large and uncertain parameter space. To understand the influence of model parameters on long-term behavior, we employ a random forest classifier, a supervised machine learning method. Additionally, a variance-based sensitivity analysis is utilized to determine the sensitivity of steady-state values to changes in model parameter inputs. By constructing this model, we can investigate the underlying mechanisms that control gut microbiota composition and function, free from confounding factors.

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).

Prediction of the Waviness Error in Ultra-Precision Fly Cutting Using the Direct Integration Method

Abstract Fly cutting is widely used in manufacturing of large-scale, high-precision optical components. However, the discontinuity of fly cutting machining leads to significant relative vibrations between the tool and the workpiece. The cutting process generates periodic waves along the cutting direction, which will deteriorate the wavefront characteristics of optical components. Based on the machining dynamics, this paper proposes a direct integration method to predict the waviness error of the machined surface. The cutting force model of fly cutting is established. The multi-mode characteristics of the spindle-tool system are measured by the experimental method. Then, the influence of uncertainties on the calculation results is analyzed by the variance-based sensitivity analysis method. Finally, the plane cutting experiment verifies that the direct integration method effectively predicts the waviness error and its variation trend, and the waviness prediction research is important for optimization of the machining parameters.

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

Sensitivity assessment of the crack propagation behavior in welded stiffened panels

ABSTRACT Welded stiffened panels play an integral role in maintaining the strength, stability, and lightweight characteristics of marine vessels. The stiffeners also affect the service life of the structure under propagating cracks. In this context, properly quantifying the effect of various input parameters on the fatigue crack propagation behavior is crucial to accurately predict the service life. This paper quantifies the influence of relevant input parameters, covering geometric and mechanical properties, on the crack propagation and fatigue service life of welded stiffened panels. Three-dimensional finite element analysis, artificial neural networks, and an elastic-plastic crack advancement rule are integrated to predict the crack propagation. Variance-based sensitivity analysis is conducted to evaluate the effect of variability in the considered input parameters on the variance of the fatigue service life of these panels. It was found that neglecting the uncertainties associated with the geometric parameters can lead to unconservative estimates of the fatigue reliability.

Validating ensemble historical simulations of Upernavik Isstrøm (1985–2019) using observations of surface velocity and elevation

Abstract The future of tidewater glaciers in response to climate warming is one of the largest sources of uncertainty in the contribution of the Greenland ice sheet to global sea-level rise. In this study, we investigate the ability of an ice-sheet model to reproduce the past evolution of the velocity and surface elevation of a tidewater glacier, Upernavik Isstrøm, by prescribing front positions. To achieve this, we run two ensembles of simulations with a Weertman and a regularised-Coulomb friction law. We show that the ice-flow model has to include a reduction in friction in the first 15 km upstream of the ice front in fast-flowing regions to capture the trends observed during the 1985–2019 period. Without this process, the ensemble model overestimates the ice flow before the retreat of the front in 2005 and does not fully reproduce its acceleration during the retreat. This results in an overestimation of the total mass loss between 1985 and 2019 of 50% (300 vs 200 Gt). Using a variance-based sensitivity analysis, we show that uncertainties in the friction law and the ice-flow law have a greater impact on the model results than surface mass balance and initial surface elevation.

Impact of Polymer Interlayers on All-Solid-State Battery Performance Using a Physicochemical Modeling Approach

Recent studies presented the advantages of incorporating solid-polymer-electrolyte (SPE) interlayers in all-solid-state batteries (ASSB). Still, drawbacks regarding the cell performance are expected due to additional polymer-related overpotentials. The pseudo-two-dimensional (p2D) physicochemical model is extended to account for Li-ion transport in the SPE interlayer and in the ceramic LLZO solid electrolyte (SE), as well as for the charge transfer at the SPE∣LLZO interface using Butler-Volmer-like kinetics. The overpotential analysis for a reference parameterization disclosed a dominant overpotential contribution from the SPE∣LLZO charge transfer and a facilitation with increasing discharge C-rate. Variance-based global sensitivity analyses demonstrate that as the exchange current density between SPE and LLZO increases, polarization losses exhibit an exponential-like reduction. Additionally, the radius of the active material (AM) particles within the composite cathode exerts a significant and dominant influence on cell performance. With an optimization of the SPE∣LLZO exchange current density, the accessible capacity could be increased compared to the reference parameterization from 41% to 61% for a 2C discharge.

Sensitivity Assessment of Building Energy Performance Simulations Using MARS Meta-Modeling in Combination with Sobol’ Method

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.

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.

Torsional Vibration and Sensitivity Analysis of Microcantilever in Liquid

Development of microsystems and ever-increasing advances of nanotechnology have resulted in growing applications of microcantilevers (MCs), including Atomic Force Microscopy (AFM). In AFM, transverse vibration of microfiber from a liquid medium results in resonance of unwanted hydrodynamic and electrostatic forces, which can be minimized by torsional mode. In the present study, the differential equation of the vibrational motion is extracted by acquiring the hydrodynamic force applied to MCs aiming to investigate the torsional vibration behavior of MCs in a liquid medium; and the extracted equation is solved to study the behavior of MCs in a liquid medium. Considering the significant effect of MC geometry on its torsional vibrations in a liquid medium, Sobol's variance-based sensitivity analysis method was utilized to investigate the effectiveness of MC geometry on torsional vibration. The sensitivity analysis results show that length and width have the most significant effects on the quality factor and the resonance frequency of MCs.

Machine learning method for shale gas adsorption capacity prediction and key influencing factors evaluation

Shale gas plays a pivotal role in the global energy landscape, emphasizing the need for accurate shale gas-in-place (GIP) prediction to facilitate effective production planning. Adsorbed gas in shale, the primary form of gas storage under reservoir conditions, is a critical aspect of this prediction. In this study, a machine learning Gaussian process regression (GPR) model for methane adsorption prediction was established and validated using published experimental data. Five typical variables, i.e., total organic carbon (TOC), clay minerals, temperature, pressure, and moisture were considered, which were derived from the Marine shale of the Longmaxi formation in the Sichuan Basin through correlation analysis. The performance of the GPR model was compared with the widely used an extreme gradient boosting model. It turned out that our GPR model had better accuracy for predicting methane adsorption in shale with an average relative error of less than 3%. Furthermore, a variance-based sensitivity analysis method in conjunction with kernel density estimation theory was employed to conduct a global sensitivity analysis, quantifying the nonlinear influence of each variable methane adsorption. The findings indicate that TOC is the most significant factor affecting methane adsorption, while clay minerals have a limited direct impact but can enhance their influence through interactions with other influencing factors. Finally, based on the GPR model, a GIP prediction method was proposed that eliminates the need for calculating the density of the adsorbed phase. These findings are expected to extend the shale gas reserve assessment methodologies and offer valuable insight for further exploring the adsorption mechanisms of shale gas.

Stochastic critical buckling speed analysis of rim-driven rotating composite plate using NURBS-based isogeometric approach and HSDT

This article is the first attempt in the open literature to investigate the impact of uncertainty in material properties on the critical buckling speed of rim-driven rotating laminated plates. The formulations are constructed using the isogeometric approach (IGA) and higher-order shear deformation theory (HSDT). Coriolis and centrifugal forces resulting from rotation are taken into consideration. The results of the current formulation are compared to the previous results and validated. The accuracy and flexibility of the RBFN-based surrogate model, designed for uncertainty analysis, is verified by comparing the result with Monte Carlo simulation (MCS). Through a variety of parametric experiments, the critical buckling speed of rotating laminates driven by a rim is stochastically analyzed. Variance-based sensitivity analysis is employed to identify the influence of individual material properties on the critical buckling speed. Further, the impact of sensitive properties on the probability of structural failure is estimated. This research can be used to forecast the probability of failure of a structure at various levels of material uncertainty associated with it.

Efficient sensitivity analysis for biomechanical models with correlated inputs.

In most variance-based sensitivity analysis (SA) approaches applied to biomechanical models, statistical independence of the model input is assumed. However, often the model inputs are correlated. This might alter the interpretation of the SA results, which may severely impact the guidance provided during model development and personalization. Potential reasons for the infrequent usage of SA techniques that account for input correlation are the associated high computational costs, especially for models with many parameters, and the fact that the input correlation structure is often unknown. The aim of this study was to propose an efficient correlated global sensitivity analysis method by applying a surrogate model-based approach. Furthermore, this article demonstrates how correlated SA should be interpreted and how the applied method can guide the modeler during model development and personalization, even when the correlation structure is not entirely known beforehand. The proposed methodology was applied to a typical example of a pulse wave propagation model and resulted in accurate SA results that could be obtained at a theoretically 27,000× lower computational cost compared to the correlated SA approach without employing a surrogate model. Furthermore, our results demonstrate that input correlations can significantly affect SA results, which emphasizes the need to thoroughly investigate the effect of input correlations during model development. We conclude that our proposed surrogate-based SA approach allows modelers to efficiently perform correlated SA to complex biomechanical models and allows modelers to focus on input prioritization, input fixing and model reduction, or assessing the dependency structure between parameters.

Assessing Climate Sensitivity and Mechanisms in a One-Dimensional Climate Energy Balance Model

Addressing the pressing concerns surrounding climate sensitivity, particularly within the context of Earth's changing climate, remains a pivotal endeavor. In this paper, the earth global temperature variation modeled by a one-dimensional climate energy balance model (EBM) is studied using a variance-based sensitivity analysis. The outcomes of this study offer a comprehensive analysis on each parameter that govern Earth's climate dynamics. Specifically, the analyses highlight that land albedo possesses the most substantial First-Order Sobol indices; the solar multiplier and the constant coefficient in the linearized Stefan-Boltzmann Law emerge as the second and third-largest contributor to Sobol indices, while the sensitivity of albedo of ice, temperature dependent coefficient of linearized Stefan-Boltzmann Law, and Transfer Coefficient remain insignificance. The analysis also suggests the non-negligible role of ice-albedo feedback and supports the hypothesis of the "Snowball Earth". This research holds significance as it uniquely addresses Earth's climate sensitivity using a one-dimensional Energy Balance Model, offering fundamental yet essential insights into the dynamics of earth's climate system, particularly its temperature variations.