Variance-based Sensitivity Analysis Research Articles

Bifurcation Analysis of Brain Connectivity Regulated Neural Oscillations in Schizophrenia

To disclose the pathophysiological mechanism of schizophrenia from the general connectivity among distinct brain regions, the computational model proposed by Szalisznyó et al. is generalized by incorporating the effects of the hippocampus. Based on the center manifold theorem and normal form theory, the emergence of abnormal alpha oscillations, which are directly associated with symptoms of schizophrenia, is analyzed in this network with Hopf bifurcation as a precursor. It is found that the clinically significant hypoconnectivities between the anterior cingulate and the dorsolateral prefrontal cortex or from the dorsolateral prefrontal cortex to the hippocampus are helpful in inhibiting the abnormal alpha oscillations, while disconnection of the coupling from the anterior cingulate cortex to the striatum can induce schizophrenia. Moreover, polynomial chaos expansion and variance-based sensitivity analysis are applied to determine the contributions of these connection strengths to the variance of the neuronal population activity. Our model results are consistent with experimental observations and thus might be meaningful for clinical interference.

Sensitivity analysis of generic deep geologic repository with focus on spatial heterogeneity induced by stochastic fracture network generation

Geologic Disposal Safety Assessment Framework is a state-of-the-art simulation software toolkit for probabilistic post-closure performance assessment of systems for deep geologic disposal of nuclear waste developed by the United States Department of Energy. This paper presents a generic reference case and shows how it is being used to develop and demonstrate performance assessment methods within the Geologic Disposal Safety Assessment Framework that mitigate some of the challenges posed by high uncertainty and limited computational resources. Variance-based global sensitivity analysis is applied to assess the effects of spatial heterogeneity using graph-based summary measures for scalar and time-varying quantities of interest. Behavior of the system with respect to spatial heterogeneity is further investigated using ratios of water fluxes. This analysis shows that spatial heterogeneity is a dominant uncertainty in predictions of repository performance which can be identified in global sensitivity analysis using proxy variables derived from graph descriptions of discrete fracture networks. New quantities of interest defined using water fluxes proved useful for better understanding overall system behavior.

Using DSSAT-MODFLOW to determine the controls of groundwater storage and crop yield in groundwater-based irrigated regions

• Sensitivity analysis was applied to a linked hydro-agronomic system to identify controlling factors on groundwater storage and crop yield. • Sensitivity analysis was conducted using the Sobol’ variance-based sensitivity analysis. • Uncertainty of model responses was quantitatively apportioned to the variation of each input factor. • The linked system is important for quantifying the impact of system properties on groundwater storage. Linked hydro-agronomic modeling systems are often used to evaluate the impact of climate change or management strategies on both groundwater and crop yield. However, these modeling studies have been performed without a detailed assessment of the factors that jointly control groundwater storage and crop yield. The objective of this paper is to present results from a study that applied sensitivity analysis to the linked DSSAT-MODFLOW modeling system to determine the governing environmental and management factors that control groundwater storage and crop yield in an intensively irrigated groundwater region basin. Methods are applied to Finney County, in southwest Kansas, USA. Sensitivity analysis was accomplished using the Morris screening method followed by the Sobol’ variance-based method using random sampling. A combination of soil, hydrologic, plant cultivar, and climate parameters are included in the analysis. A combination of Python scripts and SimLab pre- and post-processing routines were used to generate values of parameters, update model files for DSSAT and MODFLOW, run the model simulations, and calculate sensitivity indices. Results indicate that climatic parameters account for 44%, 29%, 40%, and 36% variation in maize, soybean, winter wheat, and sorghum yields. Hydrogeologic parameters (i.e., hydraulic conductivity, specific yield, and riverbed conductance) have relatively low influence on crop yield. Water table elevation, recharge, and irrigation pumping are considerably sensitive to soil- and climate-related parameters, while evapotranspiration, river leakage, and groundwater discharge are highly influenced by hydrogeological parameters. These results can be used to explore effects of management strategies on groundwater and agricultural sustainability in similar regions in the face of a changing climate.

Measuring the β-decay Properties of Neutron-rich Exotic Pm, Sm, Eu, and Gd Isotopes to Constrain the Nucleosynthesis Yields in the Rare-earth Region

The β-delayed neutron-emission probabilities of 28 exotic neutron-rich isotopes of Pm, Sm, Eu, and Gd were measured for the first time at RIKEN Nishina Center using the Advanced Implantation Detector Array (AIDA) and the BRIKEN neutron detector array. The existing β-decay half-life (T 1/2) database was significantly increased toward more neutron-rich isotopes, and uncertainties for previously measured values were decreased. The new data not only constrain the theoretical predictions of half-lives and β-delayed neutron-emission probabilities, but also allow for probing the mechanisms of formation of the high-mass wing of the rare-earth peak located at A ≈ 160 in the r-process abundance distribution through astrophysical reaction network calculations. An uncertainty quantification of the calculated abundance patterns with the new data shows a reduction of the uncertainty in the rare-earth peak region. The newly introduced variance-based sensitivity analysis method offers valuable insight into the influence of important nuclear physics inputs on the calculated abundance patterns. The analysis has identified the half-lives of 168Sm and of several gadolinium isotopes as some of the key variables among the current experimental data to understand the remaining abundance uncertainty at A = 167–172.

Weakening of tropical sea breeze convective systems through interactions of aerosol, radiation, and soil moisture

Abstract. This study investigates how the enhanced loading of microphysically and radiatively active aerosol particles impacts tropical sea breeze convective systems and whether these impacts are modulated by the many environments that support these cloud systems. Comparisons of two 130-member pristine and polluted ensembles demonstrate that aerosol direct effects reduce the surface incoming shortwave radiation and the surface outgoing longwave radiation. Changes in the ensemble median values of the surface latent heat flux, the mixed layer depth, the mixed layer convective available potential energy, the maximum inland sea breeze extent, and the sea breeze frontal lift suggest that enhanced aerosol loading generally creates a less favorable environment for sea breeze convective systems. However, the sign and magnitude of these aerosol-induced changes are occasionally modulated by the surface, wind, and low-level thermodynamic conditions. As reduced surface fluxes and instability inhibit the convective boundary layer development, updraft velocities of the daytime cumulus convection developing ahead of the sea breeze front are robustly reduced in polluted environments across the environments tested. Statistical emulators and variance-based sensitivity analyses reveal that the soil saturation fraction is the most important environmental factor contributing to the updraft velocity variance of this daytime cumulus convection, but that it becomes a less important contributor with enhanced aerosol loading. It is also demonstrated that increased aerosol loading generally results in a weakening of the sea-breeze-initiated convection. This suppression is particularly robust when the sea-breeze-initiated convection is shallower and, hence, restricted to warm rain processes. While the less favorable convective environment arising from aerosol direct effects also restricts the development of sea-breeze-initiated deep convection in some cases, the response does appear to be environmentally modulated, with some cases producing stronger convective updrafts in more polluted environments. Sea breeze precipitation is ubiquitously suppressed with enhanced aerosol loading across all of the environments tested; however, the magnitude of this suppression remains a function of the initial environment. Altogether, our results highlight the importance of evaluating both direct and indirect aerosol effects on convective systems under the wide range of convective environments.

Variance-Based Sensitivity Analysis of the Biaxial Test on a Cruciform Specimen

Parameter identification is a key aspect in the modeling of the material’s mechanical behavior. The identification quality depends on the sensitivity of the test results to the values of the constitutive parameters. In this context, a variance-based sensitivity analysis is performed, in order to quantify the influence of the material parameters on the results of the biaxial test on a cruciform specimen; in particular the influence of the Swift hardening law parameters and the Hill'48 anisotropic yield criterion on the forces, the principal strains, strain path and thickness reduction. In general, it was concluded that the Swift hardening parameters influence the forces and the major principal strain value, while the anisotropy parameters have the most influence in the principal strains, strain path and thickness reduction along the surface of the cruciform specimen.

Determination of alpha factors for monitoring of aeration systems with the ex situ off-gas method: experience from practical application and estimation of measurement uncertainty

Performance of aeration systems in wastewater treatment plants (WWTP) under process conditions can be monitored with off-gas tests. The ex situ off-gas method transfers activated sludge from an adjacent aeration tank into aerated columns to determine oxygen transfer parameters (e.g., the α-factor). This method is an alternative to in situ off-gas testing with hoods at the tank surface; however, its application and measurement uncertainty have not been examined yet. We outline our experience from long-term off-gas testing with two pilot-scale test reactors (8.3 m3 volume). Global variance-based sensitivity analysis using Sobol’ indices revealed oxygen concentration in off-gas and dissolved oxygen as the most important input quantities to determine α-factors accurately. Measurement uncertainty of other instruments was negligible. These findings are transferable to in situ off-gas hoods because the methods are similar. Random measurement error of α-factors was estimated with uncertainty analysis and comparison measurements to a relative standard deviation of about ± 2.8% for our ex situ pilot setup. Diffuser fouling, biofilm growth, or sensor drift caused systematic errors avoidable by maintenance. Additional mixing of bubble column due to sludge inflow into ex situ tanks led to a systematic overestimation of α-factors at lower airflow rates. Hence, the ex situ off-gas method is not suitable to determine α-factors for the design of aeration systems but offers unique possibilities for research of oxygen transfer dynamics and development of aeration equipment because ex situ columns can be operated independently from a full-scale activated sludge tank.

Short-range near-surface seismic ensemble predictions and uncertainty quantification for layered medium

To make a prediction for seismic signal propagation, one needs to specify physical properties and subsurface ground structure of the site. This information is frequently unknown or estimated with significant uncertainty. This paper describes a methodology for probabilistic seismic ensemble prediction for vertically stratified soils and short ranges with no in situ site characterization. Instead of specifying viscoelastic site properties, the methodology operates with probability distribution functions of these properties taking into account analytical and empirical relationships among viscoelastic variables. This yields ensemble realizations of signal arrivals at specified locations where statistical properties of the signals can be estimated. Such ensemble predictions can be useful for preliminary site characterization, for military applications, and risk analysis for remote or inaccessible locations for which no data can be acquired. Comparison with experiments revealed that measured signals are not always within the predicted ranges of variability. Variance-based global sensitivity analysis has shown that the most significant parameters for signal amplitude predictions in the developed stochastic model are the uncertainty in the shear quality factor and the Poisson ratio above the water table depth.

Deep reinforcement learning-based antilock braking algorithm

Tires play an important role in the performance of vehicular safety systems. Antilock braking system is one of the most important active safety systems that interacts with the tires. Unlike a variety of existing algorithms which are tuned to a specific tire, this research proposes a model-free reinforcement learning-based control algorithm which can adapt to changing tire characteristics and there by effectively utilising the available grip at tire–road interface. The simulation model, consisting of brake actuator dynamics, transportation delays, tire relaxation behaviour, vehicular longitudinal and pitch dynamics, is trained using more than 350,000 random tires. To reduce training time, a parallelisation architecture has been proposed which distributes learning and simulation tasks to different CPU cores. Finally, a conditional variance-based sensitivity analysis with over twelve thousand tires indicate improved grip utilisation at tire–road interface and decreased sensitivity of stopping distance on tire nonlinearity compared to literature version of Bosch algorithm.

Computing Sobol indices in probabilistic graphical models

We show how to apply Sobol’s method of global sensitivity analysis to measure the influence exerted by a set of nodes’ evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to transform the problem of Sobol index estimation into that of marginalization inference and, unlike Monte Carlo based estimators for variance-based sensitivity analysis, it gives exact results when exact inference is used. Moreover, the method supports the case of correlated inputs and it is efficient as long as eliminating the inputs’ ancestors is computationally affordable. The proposed algorithms are inspired by the field of tensor networks and generalize earlier tensor sensitivity techniques from the acyclic to the cyclic case. We demonstrate our method on three medium to large Bayesian networks in the areas of structural reliability and project risk management.

Global sensitivity analysis and optimization for coal–water slurry preheaters based on metamodel of optimal prognosis

Enhancing energy efficiency by coal–water slurry preheaters in the gasification process, the geometry of ladder-type fold helical baffles and shell–inlet velocity have an important effect on thermo-hydraulic performance of preheaters. A variance-based global sensitivity analysis procedure was built by metamodel of prognosis, and optimization results were compared between genetic algorithm and particle swarm optimization. The simulation results illustrate that heat transfer coefficient per unit pressure drop (K/ΔP) increases when folding angle and folding ratio increase, and K/ΔP decreases with increasing relative height and shell–inlet velocity. As for K/ΔP, the coefficient of prognosis of full model is 99.03%, and total effects of shell–inlet velocity, folding angle, folding ratio and relative height is 70.34%, 25.01%, 8.74%, and 7.87%, respectively. Based on reduced spaces with most influential parameters, optimization cases show genetic algorithm is more efficient and provides better results, folding angle, folding ratio, relative height and shell–inlet velocity are 50°, 0.6, 0.5 and 1.4 m s–1 when maximizing K/ΔP. The research results provide theoretical guidance for selection, design and optimization of coal–water slurry preheaters.

Global Sensitivity Analysis of Economic Model Predictive Longitudinal Motion Control of a Battery Electric Vehicle

Global warming forces the automotive industry to reduce real driving emissions and thus, its CO2 footprint. Besides maximizing the individual efficiency of powertrain components, there is also energy-saving potential in the choice of driving strategy. Many research works have noted the potential of model predictive control (MPC) methods to reduce energy consumption. However, this results in a complex control system with many parameters that affect the energy efficiency. Thus, an important question remains: how do these partially uncertain (system or controller) parameters influence the energy efficiency? In this article, a global variance-based sensitivity analysis method is used to answer this question. Therefore, a detailed powertrain model controlled by a longitudinal nonlinear MPC (NMPC) is developed and parameterized. Afterwards, a qualitative Morris screening is performed on this model, in order to reduce the parameter set. Subsequently, the remaining parameters are quantified using Generalized Sobol Indices, in order to take the time dependence of physical processes into account. This analysis reveals that the variations in vehicle mass, battery temperature, rolling resistance and auxiliary consumers have the greatest influence on the energy consumption. In contrast, the parameters of the NMPC only account for a maximum of 5% of the output variance.

Sensitivity analysis of a Ground-Gen Airborne Wind Energy System design

The architecture of a new multidisciplinary design and optimization framework for rigid wing Airborne Wind Energy Systems, named T-GliDe, is introduced and a Ground-Gen AWES is analyzed to illustrate the features of the design approach. T-GliDe features an optimization module and an uncertainty quantification module, allowing for a number of algorithm-based design techniques. T-GliDe performs an AWES design optimizing market-based objective functions, while satisfying constraints related to fight stability. The fight dynamics is modelled with analytical aerodynamic theories, allowing for fast and consistent design evaluations, without the use of time simulation codes and thus of active control. In this work, a reduced optimization problem is run to find optimal working-set points of a Ground-Gen AWES with respect to power production. The reel-out factor and the pitch angle as function of wind speed are considered as design variables and output trends are shown. A variance based sensitivity analysis is then run to investigate how the rigid body eigenvalues are influenced by a set of independent variables. Among the chosen independent variables, a sub-set of variables which bear an impact on the dynamics is identified and they will be considered in future design and optimization activities as design variables.

Field meta modelling for process design in complex sheet metal forming

Actually, new applications of machine learning methods like variance-based sensitivity analysis take place for developing complex sheet metal forming and joining processes. The application of this methods will help to quickly start of production when the simple numerical designing of the processes becomes too complicated. Two investigated examples show the application of the method for complex planning situations. The first one uses variable functions of force and motion during deep drawing to extend the process limits. The second one describes the complex clamping of an assembly of different sheet metal parts. Field meta modelling approaches are shown to automate tasks, visualize results and support engineers to plan and run different complex processes regarding sheet metal parts.

Integrated uncertainty quantification and sensitivity analysis of single-component dynamic column breakthrough experiments

We have carried out the traditional analysis of a set of dynamic breakthrough experiments on the hbox {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 pm 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.

Modelling of wine vinegar acetification bioreactor: Global sensitivity analysis and simplification of the model

First-principles models of any process usually describe its complex underlying mechanisms using differential and algebraic equations including several unknown parameters, whose values must be normally estimated from experimental data. In this context, assessment of the influence of each parameter on model outputs, also known as sensitivity analysis, is an invaluable tool to, for example, simplify the structure of such model. In this work, variance-based Global Sensitivity Analysis (GSA) using Sobol’ main and total effects was carried out on a previously proposed acetification process first-principles model. Three parameters (KSE, KIA and KSO) showed less influence than the remaining nine considering their stated value ranges; KSE presented no influence in all the analysed experimental conditions, value variation of KIA exhibited a slightly greater effect on experiments with higher mean acetic acid concentrations and KSO showed the strongest impact by varying its value in all the experiments. According to these results, the model was simplified and its simulation compared with the initially proposed model and the experimental data. The analysis performed, by way of example, can be of crucial importance for any other process.

Global sensitivity analysis of structural models by active subspace and neural network

PurposeGlobal sensitivity can measure the influence of input variables on model responses and is of positive significance for the improvement design of structural systems. This work aims to study the global sensitivity of structural models by combining the active subspace theory and neural network.Design/methodology/approachThis study aims to improve the efficiency of global sensitivity analysis for high-dimensional structural systems, a novel method based on active subspace and surrogate model is proposed. Active subspace can reduce the dimension of input variables, and an adaptive scaling strategy is proposed to improve the accuracy in finding the active subspace. The uncertainty propagation of active variables and model response is performed through the artificial neural network. Then the global sensitivity analysis is carried out.FindingsSeveral examples are studied by using the Monte Carlo simulation method and the proposed method. Comparison of the results shows that the proposed method has preferable accuracy and low computational cost.Originality/valueThe proposed method provides a practicable tool for the variance-based sensitivity analysis of structural systems. Apart from sensitivity analysis, the method can be also extended for use in other fields relating to uncertainty propagation.

Global sensitivity analysis on debris flow energy dissipation of the artificial step-pool system

For the prevention of debris flow hazards, step-pool and other energy dissipation structures have a bright future due to their economic and efficiency. In this paper, the sensitivity of the debris flow energy dissipation process and the correlation of factors were studied. First, the elementary effect method was adopted to analyze the sensitivity of factors and screen the insensitive factors. Then, the variance-based sensitivity analysis was applied to obtain the higher-order sensitivities of the remaining sensitive factors. Each numerical example was simulated by the material point method (MPM). The results show that the internal friction angle, cohesion and height of artificial step-pool units were the most important factors. These three factors show significant higher-order sensitivities. It is found that the energy dissipation of debris flow mainly depended on its internal friction angle and cohesion. The research method can be extended to most kinds of nonlinear geotechnical engineering problems.

A strategy to personalize a 1D pulse wave propagation model for estimating subject-specific central aortic pressure waveform

The central aortic pressure (CAP) provides insights into the prediction, prevention, diagnosis, and treatment of cardiovascular disease, but can't be directly measured non-invasively. Therefore, the development of a noninvasive CAP estimation method based on the non-invasively measured peripheral pressure waveform is critical for clinical decisions based on the CAP. Some existing widely applied methods, such as the generalized transfer function (GTF) method relating measured peripheral pressure to the CAP, do not or only partly account for inter-subject or intra-subject variability of the cardiovascular system. To overcome this pitfall, we propose a subject-specific central aortic pressure estimation method in this paper. The novel method presented can derive an accurate aortic pressure from the peripheral pressure based on an individualized pulse wave propagation model using a GTF method as a first guess. To develop a strategy to personalize a pulse wave propagation model one usually needs to optimize many input parameters. Therefore, we present a two-step approach with the screening method of Morris and the adaptive sparse generalized polynomial chaos expansion (agPCE) algorithm for the sensitivity analysis of the wave propagation model. First, for a-priori defined output of the model, a subset of important parameters is identified using the screening method of Morris. Next, a quantitative variance-based sensitivity analysis is performed using agPCE. This approach is applied to a 1D pulse wave propagation model to get the personalized parameters of the pulse wave propagation model for the estimation of a subject-specific central aortic pressure waveform and is validated with 26 patients. Compared with the GTF method, the proposed method showed better performance in estimating the central aortic pulse wave and predicting the parameters.

Global Sensitivity Analysis of Four Chamber Heart Hemodynamics Using Surrogate Models.

Computational Fluid Dynamics (CFD) is used to assist in designing artificial valves and planning procedures, focusing on local flow features. However, assessing the impact on overall cardiovascular function or predicting longer-term outcomes may requires more comprehensive whole heart CFD models. Fitting such models to patient data requires numerous computationally expensive simulations, and depends on specific clinical measurements to constrain model parameters, hampering clinical adoption. Surrogate models can help to accelerate the fitting process while accounting for the added uncertainty. We create a validated patient-specific four-chamber heart CFD model based on the Navier-Stokes-Brinkman (NSB) equations and test Gaussian Process Emulators (GPEs) as a surrogate model for performing a variance-based global sensitivity analysis (GSA). GSA identified preload as the dominant driver of flow in both the right and left side of the heart, respectively. Left-right differences were seen in terms of vascular outflow resistances, with pulmonary artery resistance having a much larger impact on flow than aortic resistance. Our results suggest that GPEs can be used to identify parameters in personalized whole heart CFD models, and highlight the importance of accurate preload measurements.