Variance-based Global Sensitivity Analysis Research Articles

Sensitivity analysis of the SWAP (Soil-Water-Atmosphere-Plant) model under different nitrogen applications and root distributions in saline soils

Sensitivity analysis is important for determining the parameters in the model calibration process. In our study, a variance-based global sensitivity analysis (extended Fourier amplitude sensitivity test, EFAST) was applied to an agro-hydrological model (the SWAP (Soil-Water-Atmosphere-Plant model) model). The sensitivities of 20 parameters belonging to 4 categories (soil hydraulics, solute transport, root water uptake, and environmental stresses) for the simulated accumulated transpiration, dry matter (DM), and yield of sunflowers were analyzed under three nitrogen application rates (N1, N2, and N3), four salinity levels (S1, S2, S3, and S4), and three root distributions (R1, R2, and R3). The results indicated that for predominantly loamy soils, the high-impact parameters for accumulated transpiration, DM, and yield were the soil hydraulic parameters (α and n), critical stress index for compensatory root water uptake (ωc), the salt level at which salt stress starts (Pi), the decline of root water uptake above Pi (SSF), residual water content (θr), saturated water content (θs), and relative uptake of solutes by roots (TSCF). We also found that nitrogen application did not change the order of the parameter impacts on accumulated transpiration, DM, and yield. However, TSCF replaced α as the highest-impact parameter for the accumulated transpiration, DM, and yield at high salinity levels (S2 and S3). Furthermore, α was also the highest-impact parameter for DM and yield under different root distributions, but the highest-impact parameters for transpiration were ωc, α, and θs under R1, R2, and R3, respectively. Nitrogen application could be neglected when considering the interactive effects of nitrogen application, salinity level, and root distribution on the transpiration, DM, and yield. Additionally, the mean values and uncertainties of the transpiration, DM, and yield were similar in all scenarios, except S3, which showed a sharp decrease in the mean values. We suggest determining the above eight parameters (α, n, ωc, Pi, SSF, θr, θs, and TSCF) and the saturated vertical hydraulic conductivity (KS) based on rigorous calibrations with direct or indirect local measurements using economical methods (e.g., a literature review), with limited observations for other parameters when using the SWAP model and other similar agro-hydrological models.

Influence and interactions of input factors in urban flood inundation modeling: An examination with variance-based global sensitivity analysis

Flood risk assessment and management in urbanized area experience an increasing reliance on the supporting information provided by numerical flood modeling as a rapid and efficient tool. Although hydrodynamic modeling based on shallow water equations requires less parameters than hydrologic ones, uncertainties of the input factors describing both the driving forces and the complex urbanized environment still have important influences on the accuracy of the urban flood simulation results once induced into the modeling procedure. The influences of input factors of engineering concern in urban flood hydrodynamic modeling in an intensely urbanized area of 0.58 km2 in the city of Chongqing, China with a mixture of different land-use types are investigated in this study by taking advantage of a variance-based global sensitivity analysis methodology with particular focus upon the interaction between the uncertainties of different input factors describing the external driving force, the underlying urban surface, the drainage loss and the spatial resolution of modeling. The global sensitivity analysis results are examined with regard to maximum values of the flood extent, water depth and discharge and their variation in the course of the urban flood propagation. Influences of the input factors and their interactions are observed to vary for different model outputs. From a spatially-distributed perspective, a dependence of the interactions between input factors is found to be upon the relative location of their acting area associated to the land-use type. Antagonistic effects of the input factors describing the underlying urban surface and the drainage loss for the rainfall-induced flood water accumulations and movements are analyzed with the flood evolution. Main effects of different input factors and their interactions are of a certain consistency with the underlying physical processes of the urban flood propagation from both static and temporal perspective of the global sensitivity analysis results.

Using global variance-based sensitivity analysis to prioritise bridge retrofits in a regional road network subject to seismic hazard

This paper presents a novel method for prioritising bridge retrofits within a regional road network subject to uncertain seismic hazard, using a technique that accounts for network performance while avoiding the combinatoric computational costs of exhaustive searches. Using global variance-based sensitivity analysis, a probabilistic ranking of bridges is determined according to how much their retrofit statuses influence the expected cost of the road network disruption. Bridges’ total-order sensitivity (Sobol’) indices are estimated with respect to the expected cost using the hybrid-point Monte Carlo approximation method. A bridge’s total-order Sobol’ index measures how much its retrofit status influences the variance of the expected cost of the road network performance and accounts for the effect of its interactions with other bridges’ retrofit states. For 71 highway bridges in San Francisco, a retrofit strategy based on bridges’ total-order Sobol’ indices outperforms other heuristic strategies. The proposed method remains computationally tractable while accounting for the probabilistic nature of the seismic hazard, the uniqueness of individual bridges, network effects, and decision-makers’ priorities. Because this method leverages existing risk assessment tools and models without imposing further assumptions, it should be extensible to other types of networks under different types of hazards and to other decision variables.

Modeling Hot-Mix asphalt dynamic modulus using deep residual neural Networks: Parametric and sensitivity analysis study

The dynamic modulus (E*) of hot-mix asphalt mixtures is one of the most tedious and time-consuming laboratory testing material properties. It requires costly, advanced equipment and skills that are not easily accessible in the majority of laboratories yet. Thus, many studies have been dedicated to developing E* predictive models. Unfortunately, it is a complex task due to the many input variables and their non-linear effect on the E*. This study applies a deep residual neural networks (DRNNs) technique for the first time to the problem to enhance the E* prediction capabilities. The proposed DRNNs architecture utilizes residual connections (i.e., shortcuts) that bypass some layers in the deep network structure in order to alleviate the problem of training with high accuracy. An intensive laboratory database is employed in the DRNNs model development considering all influential input parameters such as; mixture gradation, volumetric properties, binder characteristics, and testing conditions parameters. Moreover, a brute force enumeration is integrated in the model to reduce the number of needed input variables and identify the best combinations of them. Then, the proposed DRNNs performance, with the best combination of inputs, is evaluated using representative performance indicators and compared with the well-known E* predictive models, namely; Witczak 1-37A, Witczak 1-40D, and Hirsch models. Finally, a variance-based global sensitivity (VB-GS) analysis is conducted with the Monte Carlo simulation aid to highlight each input variable effect on the E* magnitude in real practice while removing the potential distortion of results due to the input variables correlations. Performance evaluation indicators reveal that the DRNNs model outperforms other E* prediction ones. Furthermore, VB-GS analysis shows that, among all feasible inputs, binder stiffness characteristics and testing temperature are the most significant ones.

Data-driven inverse uncertainty quantification in the transverse tensile response of carbon fiber reinforced composites

Uncertainty quantification is critical for the full exploitation of composite materials’ potential. Inverse methods offer the possibility of indirectly characterizing the uncertainty of microscopic parameters by employing data sets from standard structural tests in higher scales. Two crucial requirements though, are the efficient modeling especially for the nonlinear prediction, and the measurement error availability from the tests which affects the updated scatter. This study employs effective stiffness and strength experimental data in order to quantify uncertainties of a carbon fiber UD composite in the microscale. A polynomial chaos surrogate model is trained from finite element simulations, able to efficiently predict the homogenized stiffness and strength for the uncertainty quantification procedure. The random parameters which are influential enough to be updated, are identified via a variance-based global sensitivity analysis. The inverse problem is solved with the Bayesian inference method, which updates any prior estimation of the probability models of the input parameters, based on output observations from the tests. Results show significant uncertainty reduction in comparison with typically used variance values in the literature and can be used to enrich the composite material databases. The proposed methodology is applied for the transverse tensile load case, although its non-intrusive nature allows applications for more load cases and various setups.

Variance-based global sensitivity analysis and beyond in life cycle assessment: an application to geothermal heating networks

PurposeGlobal sensitivity analysis increasingly replaces manual sensitivity analysis in life cycle assessment (LCA). Variance-based global sensitivity analysis identifies influential uncertain model input parameters by estimating so-called Sobol indices that represent each parameter’s contribution to the variance in model output. However, this technique can potentially be unreliable when analyzing non-normal model outputs, and it does not inform analysts about specific values of the model input or output that may be decision-relevant. We demonstrate three emerging methods that build on variance-based global sensitivity analysis and that can provide new insights on uncertainty in typical LCA applications that present non-normal output distributions, trade-offs between environmental impacts, and interactions between model inputs.MethodsTo identify influential model inputs, trade-offs, and decision-relevant interactions, we implement techniques for distribution-based global sensitivity analysis (PAWN technique), spectral clustering, and scenario discovery (patient rule induction method: PRIM). We choose these techniques because they are applicable with generic Monte Carlo sampling and common LCA software. We compare these techniques with variance-based Sobol indices, using a previously published LCA case study of geothermal heating networks. We assess eight environmental impacts under uncertainty for three design alternatives, spanning different geothermal production temperatures and heating network configurations.ResultsIn the application case on geothermal heating networks, PAWN distribution-based sensitivity indices generally identify influential model parameters consistently with Sobol indices. However, some discrepancies highlight the potentially misleading interpretation of Sobol indices on the non-normal distributions obtained in our analysis, where variance may not meaningfully describe uncertainty. Spectral clustering highlights groups of model results that present different trade-offs between environmental impacts. Compared to second-order Sobol interaction indices, PRIM then provides more precise information regarding the combinations of input values associated with these different groups of calculated impacts. PAWN indices, spectral clustering, and PRIM have a computational advantage because they yield stable results at relatively small sample sizes (n = 12,000), unlike Sobol indices (n = 100,000 for second-order indices).ConclusionsWe recommend adding these new techniques to global sensitivity analysis in LCA as they give more precise as well as additional insights on uncertainty regardless of the distribution of the model outputs. PAWN distribution-based global sensitivity analysis provides a computationally efficient assessment of input sensitivities as compared to variance-based global sensitivity analysis. The combination of clustering and scenario discovery enables analysts to precisely identify combinations of input parameters or uncertainties associated with different outcomes of environmental impacts.

Analytical and numerical modeling, sensitivity analysis, and multi-objective optimization of the acoustic performance of the herschel-quincke tube

This study presents the assessments of the acoustic performance of a Herschel-Quincke (HQ) tube, which includes sensitivity analysis and multi-objective optimization of its design variables. A proper model introduced using the flow characteristics of the HQ tube. Input variables were frequency (f), temperature (T), the ratio of areas (R), and tube length (L). These variables were chosen to be varied in a specified range to best characterize the exhaust flow in internal combustion engines. Then a proper multi-objective genetic algorithm (MOGA) was developed for the acoustic performance and geometry optimization of a two-duct HQ tube; the objectives were maximizing the transmission loss (TL) and at the same time minimizing the backpressure (BP). Besides, the local sensitivity analysis using numerical derivative and variance-based global sensitivity analysis (GSA) using Monte Carlo sampling was performed for the analytical model of the HQ tube. The results showed that the length of the bypass tube is a crucial factor for the maximum sensitivity index (SI) of the TL, while the SI of the BP was maximum for the ratio of areas. The proposed analytical model was proved to be reliable for the TL, showing low values of the error of the sensitivity index (eSI) and less reliable for the BP parameter, showing higher eSI values. For the evaluation of the TL sensitivity, Monte Carlo sampling is relatively inaccurate in the small sample size of 200. It was also observed that the Uniform distribution had lower eSI in lower sample sizes; however, Sobol sampling showed better performance in higher sample sizes. The MOGA optimization proved to be successful in maximizing the TL for the frequencies between 105.84 and 1981.11 Hz, with the TL greater than 20 dB, and the BP less than 0.1. The most efficient solution among the Pareto set after a tradeoff was at 105.84 Hz, for which the TL and the BP were 36.47 dB and 1.50E−02, respectively. The model with the best goodness of fit to represent the Pareto front was the power model with two terms. Then, the acoustic performance of the optimized geometry was investigated using computational aeroacoustics (CAA) in the presence of mean flow in Fluent software. Using the CAA approach, the maximum TL value was obtained for 104 0.4 Hz as 12.14 dB. The simulated TL by CAA had more broadband behaviors with fewer peaks than the analytical approach. The results of this study demonstrated the remarkable potential of the MOGA optimization and sensitivity analysis for acoustic performance and topology optimization for possible applications in internal combustion engines.

Accounting for Uncertainties in the Safety Assessment of Concrete Gravity Dams: A Probabilistic Approach with Sample Optimization

Important advances have been made in the methodologies for assessing the safety of dams, resulting in the review and modification of design guidelines. Many existing dams fail to meet these revised criteria, and structural rehabilitation to achieve the updated standards may be costly and difficult. To this end, probabilistic methods have emerged as a promising alternative and constitute the basis of more adequate procedures of design and assessment. However, such methods, in addition to being computationally expensive, can produce very different solutions, depending on the input parameters, which can greatly influence the final results. Addressing the existing challenges of these procedures to analyze the stability of concrete dams, this study proposes a probabilistic-based methodology for assessing the safety of dams under usual, unusual, and extreme loading conditions. The proposed procedure allows the analysis to be updated while avoiding unnecessary simulation runs by classifying the load cases according to the annual probability of exceedance and by using an efficient progressive sampling strategy. In addition, a variance-based global sensitivity analysis is performed to identify the parameters most affecting the dam stability, and the parameter ranges that meet the safety guidelines are formulated. It is observed that the proposed methodology is more robust, more computationally efficient, and more easily interpretable than conventional methods.

A Global Sensitivity Analysis Method for Multi-Input Multi-Output System and its Application in Structural Design

Commonly, variance-based global sensitivity analysis methods are popular and applicable to quantify the impact of a set of input variables on output response. However, for many engineering practical problems, the output response is not single but multiple, which makes some traditional sensitivity analysis methods difficult or unsuitable. Therefore, a novel global sensitivity analysis method is presented to evaluate the importance of multi-input variables to multi-output responses. First, assume that a multi-input multi-output system (MIMOS) includes [Formula: see text] variables and [Formula: see text] responses. A set of summatory functions [Formula: see text] and [Formula: see text] are constructed by the addition and subtraction of any two response functions. Naturally, each response function is represented using a set of summatory function. Subsequently, the summatory functions [Formula: see text] and [Formula: see text] are further decomposed based on the high dimensional model representation (HDMR), respectively. Due to the orthogonality of all the decomposed function sub-terms, the variance and covariance of each response function can be represented using the partial variances of all the decomposed function sub-terms on the corresponding summatory functions, respectively. The total fluctuation of MIMOS is calculated by the sum of the variances and covariances on all the response functions. Further, the fluctuation is represented as the sum of the total partial variances for all the [Formula: see text]-order function sub-terms, and the total partial variance is the sum of [Formula: see text] partial variances for the corresponding [Formula: see text]-order function sub-terms. Then, the function sensitivity index (FSI) [Formula: see text] for s-order function sub-terms is defined by the ratio of the total partial variance and total fluctuation, which includes first-order, second-order, and high-order FSI. The variable sensitivity index [Formula: see text] of variable [Formula: see text] is calculated by the sum of all the FSIs including the contribution of variable [Formula: see text]. Finally, numerical example and engineering application are employed to demonstrate the accuracy and practicality of the presented global sensitivity analysis method for MIMOS.

Quantifying the Uncertainty of the Future Hydrological Impacts of Climate Change: Comparative Analysis of an Advanced Hierarchical Sensitivity in Humid and Semiarid Basins

AbstractComparison and quantification of different uncertainties of future climate change involved in the modeling of a hydrological system are highly important for both hydrological modelers and policy-makers. However, few studies have accurately estimated the relative importance of different sources of uncertainty at different spatiotemporal scales. Here, a hierarchical sensitivity analysis framework (HSAF) incorporated with a variance-based global sensitivity analysis is developed to quantify the spatiotemporal contributions of different uncertainties in hydrological impacts of climate change in two different climatic (humid and semiarid) basins in China. The uncertainty sources include three emission scenarios (ESs), 20 global climate models (GCs), three hydrological models (HMs), and the associated sensitive hydrological parameters (PAs) screened and sampled by the Morris and Latin hypercube sampling methods, respectively. The results indicate that the overall trend of uncertainty is PA > HM > GC > ES, but their uncertainties have discrepancies in projections of different hydrological variables. The HM uncertainty in annual and monthly discharge projections is generally larger than the PA uncertainty in the humid basin than semiarid basin. The PA has greater uncertainty in extreme hydrological event (annual peak discharge) projections than in annual discharge projections for both basins (particularly for the humid basin), but contributes larger uncertainty to annual and monthly discharge projections in the semiarid basin than humid basin. The GC contributes larger uncertainty in all the hydrological variables projections in the humid basin than semiarid basin, while the ES uncertainty is rather limited in both basins. Overall, our results suggest there is greater spatiotemporal variability of hydrological uncertainty in more arid regions.

Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers

Underplatform dampers are widely used in turbomachinery to mitigate structural vibrations by means of friction dissipation at the interfaces. The modelling of such friction dissipation is challenging because of the high variability observed in experimental measurements of contact parameters. Although this variability is not commonly accounted for in state-of-the-art numerical solvers, probabilistic approaches can be implemented to include it in dynamics simulations in order to significantly improve the estimation of the damper performance. The aim of this work is to obtain uncertainty bands in the dynamic response of turbine blades equipped with dampers by including the variability observed in interfacial contact parameters. This variability is experimentally quantified from a friction rig and used to generate uncertainty bands by combining a deterministic state-of-the-art numerical solver with stochastic Polynomial Chaos Expansion (PCE) models. The bands thus obtained are validated against experimental data from an underplatform damper test rig. In addition, the PCEs are also employed to perform a variance-based global sensitivity analysis to quantify the influence of contact parameters on the variation in the nonlinear dynamic response via Sobol indices. The analysis highlights that the influence of each contact parameter in vibration amplitude strongly varies over the frequency range, and that Sobol indices can be effectively used to analyse uncertainties associated to structures with friction interfaces providing valuable insights into the physics of such complex nonlinear systems.

Investigation of the importance of different factors of flood inundation modeling applied in urbanized area with variance-based global sensitivity analysis

Flood modeling provides useful information to support flood risk assessment and management and reduce flood impacts in urbanized area. The accuracy of urban flood simulation results is highly dependent on the quality of input data for which the appropriate values are generally difficult to determine for complex urbanized environment and from which various uncertainties are induced into the modeling procedure. In this study, variance-based global sensitivity analysis is applied for the hydrodynamic modeling of urban flood to explore the relative importance of the factors of interest as model inputs and their contributions to the final results of the numerical model for different outputs. The factors include the spatial resolution, the forcing condition and the characteristics of the underlying urbanized surface. The global sensitivity analysis results are examined in both spatially lumped and distributed perspective. Findings indicate that importance of the input factors varies with regard to different model output and the influence of the spatial resolution is more tightly related to the flood flow movements whereas that of the rainfall inputs is more relevant to the flood water volume. Spatial variability in the influence of the input factors is revealed to be hidden by the spatially lumped results and the importance of the factors describing the underlying urban surface is found to be largely dependent on the location of the analyzed model output associated with the land-use type. Improved understanding of sensitivity of hydrodynamic modeling of urban floods may help the modelers to decide which input factors to prioritize on according to which model outputs are assessed and where they are assessed.

Land Surface Ecological Status Composition Index (LSESCI): A novel remote sensing-based technique for modeling land surface ecological status

Accurate modeling of Land Surface Ecological Status (LSES) is crucial in environmental applications. Despite valuable benefits, common indices are unable to distinguish LSES of bare soils from lands affected by Anthropogenic Destructive Activities (ADAs). The objective of this study was to present an index to distinguish LSES of different Land Use/Covers (LULCs) particularly bare soils from lands affected by ADAs using remote sensing images. Landsat multi-temporal imagery, National Land Cover Database (NLCD), Imperviousness and High Resolution Layer Imperviousness (HRLI) datasets for Arasbaran protected area in Iran and 13 cities from the United States and Europe were used in this study. First, the surface biophysical characteristics and LULC were derived from Landsat images using the single channel algorithm, spectral indices, and support vector machine. Secondly, a new index was developed based on improved Ridd's conceptual Vegetation-Impervious-Soil triangle model and specified as Land Surface Ecological Status Composition Index (LSESCI). LSESCI was developed by combining Biophysical Composition Index (BCI) information and Land Surface Temperature (LST). In the third step, the LSES was modeled based on Remote Sensing-based Ecological Index (RSEI). Variance-based global sensitivity analysis was used to calculate the impact of input parameters on the modeled LSES. Afterwards, the variations in these indices were modeled using Subtraction, Variance and Principal Component Analysis (PCA) strategies. Finally, the efficiency of these indices was assessed and compared to model from the relationships between LSESCI and RSEI with spectral indices, and LULC classes. There was an overall improvement in modelling LSES accuracy using the LSESCI over RSEI. For instance, the difference between the mean RSEI and LSESCI for the lands affected by ADAs and Bare soil lands in Arasbaran protected area in Iran were 0.04 and 0.27, respectively. LST and Wetness have the most and least impact on LSES modeling, respectively, compared to other input parameters. The mean absolute value of the correlation coefficient (r) between greenness, moisture, dryness, and heat indices and LSESCI (RSEI) were 0.90 (0.84), 0.76 (0.69) and 0.93 (0.88), respectively. The mean absolute values of r between variations of different spectral indices and variations of LSESCI (RSEI) obtained from PCA, Variance and Subtraction strategies were 0.89 (0.87), 0.73 (0.64) and 0.79 (0.73), respectively. Similarly, for selected cities in the United States and Europe, the mean of r values between RSEI and LSESCI and NLCD Imperviousness (HRLI) were 0.58 (0.77) and 0.77 (0.85), respectively. Overall, the LSESCI had high ability to distinguish the LSES of different LULC classes especially bare soils from lands affected by ADAs. Thus, the proposed LSESCI was superior in modeling LSES of the urban and non-urban regions with heterogeneous surface over RSEI.

A predictive discrete-continuum multiscale model of plasticity with quantified uncertainty

Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distribution of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). The outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error.

Reliability Assessment of Converter- Dominated Power Systems Using Variance-Based Global Sensitivity Analysis

With the proliferation of renewable energy and power electronic converters in power systems, the reliability issue has raised more research attention than ever before. This paper proposes a comprehensive framework to assess the reliability of a power system considering the effect from various power converter uncertainties. For the converter stage, we formulate a reliability model for each power converter based on several semiconductor devices, for which ambient uncertainties and converter topologies are considered. For the system stage, we estimate system reliability indicators through a non-sequential Monte Carlo simulation and calculate their variances. Afterward, we leverage machine learning regression algorithms between two stages to establish a nonlinear reliability relation. Moreover, a variance-based sensitivity analysis (SA) is conducted to rank and identify the most influential converter uncertainties with respect to the variance of system EENS. Based on the SA conclusions, system operators can take proactive actions to mitigate the potential risk of the system.

EVs Charging Power Control Participating in Supplementary Frequency Stabilization for Microgrids: Uncertainty and Global Sensitivity Analysis

Electric vehicle (EV) potential has broadly been highlighted in providing ancillary services in a microgrid, such as grid reserve and regulation support. However, uncertain behaviors of EV charging raise crucial concerns for both the utilities and EV owners. In this paper, the impacts of EV charging uncertainties for EV charging power control participating in supplementary frequency stabilization are assessed separately based on the two perspectives, i.e., power capacity for the utility perspective and expected EV energy for the EV owner perspective. On the one hand, the power capacity accessed by the utility directly relates to the stabilization capability, which depends on the number of EVs that are willing to participate in the frequency stabilization program and the rated charging power of EV. On the other hand, the variance of expected EV energy realized by the EV owners is considered in terms of the remaining state of charge (SoC), energy capacity, and available charging time. Besides, a variance-based global sensitivity analysis (GSA) is essentially applied to identify the influential parameters of these uncertainties. The simulation studies are conducted using a microgrid environment via DIgSILENT Powerfactory software to reveal such impacts of EV charging uncertainties based on the two perspectives. The results indicate that the number of participating EVs is the most influential parameter for frequency stabilization capability, followed by the rated charging power of EV. From the EV owner’s perspective, the energy capacity is the dominant parameter affecting the expected EV energy variance, followed by the remaining energy and available charging time.

Analytical description of colloid behavior in single fractures under irreversible deposition

ObjectivesIrreversible colloid deposition in groundwater-saturated fractures is typically modeled using a lumped deposition coefficient (κ) that reflects the system physiochemical conditions. A mathematical relationship between this coefficient and the physicochemical conditions controlling deposition has not yet been defined in the literature; thus, κ is typically fitted using experimental observations. This research develops, for the first time, an analytical relationship between κ and the fraction of colloids retained in single fractures (Fr). This relationship could be subsequently integrated with available models relating Fr to the system’s physicochemical properties to develop an explicit mathematical relationship between κ and these properties. MethodThe Fr-κ analytical relationship was developed through conceptualizing irreversible deposition as first-order decay, as both lead to permanent mass loss, and coupling this with the advection-dispersion equation. The model estimates of colloid deposition were compared to observations from laboratory-scale colloid tracer experiments. A variance-based global sensitivity analysis was applied to identify the parameters controlling deposition. FindingsThe analytical relationship efficiently replicated the experimental observations, and the global sensitivity analysis revealed that colloid deposition variability is controlled by fracture length, aperture size, and deposition coefficient; this supports the accepted understanding that colloid deposition is controlled by the system’s physicochemical properties.

Assessing the Spatiotemporal Uncertainties in Future Meteorological Droughts from CMIP5 Models, Emission Scenarios, and Bias Corrections

AbstractDrought projections are accompanied with large uncertainties due to varying estimates of future warming scenarios from different modeling and forcing data. Using the standardized precipitation index (SPI), this study presents a global assessment of uncertainties in drought characteristics (severity S and frequency Df) projections based on the simulations of 28 general circulation models (GCMs) from phase 5 of the Coupled Model Intercomparison Project (CMIP5). A hierarchical framework incorporating a variance-based global sensitivity analysis was developed to quantify the uncertainties in drought characteristics projections at various spatial (global and regional) and temporal (decadal and 30-yr) scales due to 28 GCMs, three representative concentration pathway scenarios (RCP2.6, RCP4.5, RCP8.5), and two bias-correction (BC) methods. The results indicated that the largest uncertainty contribution in the globally projected S and Df is from the GCM uncertainty (>60%), followed by BC (<35%) and RCP (<16%) uncertainty. Spatially, BC reduces the spreads among GCMs particularly in Northern Hemisphere (NH), leading to smaller GCM uncertainty in the NH than the Southern Hemisphere (SH). In contrast, the BC and RCP uncertainties are larger in the NH than the SH, and the BC uncertainty can be larger than GCM uncertainty for some regions (e.g., southwest Asia). At the decadal and 30-yr time scales, the contributions for three uncertainty sources show larger variability in S than Df projections, especially in the SH. The GCM and BC uncertainties show overall decreasing trends with time, while the RCP uncertainty is expected to increase over time and even can be larger than BC uncertainty for some regions (e.g., northern Asia) by the end of this century.

Global Sensitivity Analysis Based on BP Neural Network for Thermal Design Parameters

In order to obtain the thermal design parameters that have a great influence on the temperature of the spectrometer frame, the sensitivity of the thermal design parameters of a balloon-borne spectrometer system was analyzed and calculated by the global sensitivity analysis (GSA) method based on the backpropagation neural network (BPNN) surrogate model. Firstly, the BPNN with 12 selected thermal design parameters as input and temperature as output was well trained. Then, two kinds of variance-based GSA methods, the Sobol’ method and the extended Fourier amplitude sensitivity test (EFAST), were used to calculate the values and ranking results of sensitivity indices of 12 parameters based on the established BPNN. Moreover, the GSA results were verified based on the finite element model of the balloon-borne spectrometer system built by I-DEAS/TMG (software developed by Structural Dynamics Research Corporation for space thermal analysis), which indicates that the BPNN surrogate-model-based GSA is reliable. Finally, the sensitivity calculation accuracy and speed of two methods, the Spearman rank correlation coefficient formula and the GSA method based on BPNN, were compared, and the EFAST method based on the BPNN surrogate model has been proved to have obvious advantages in the reliability and speed of calculation results. Also, the GSA method based on a surrogate model like BPNN is of great significance in the thermal analysis of an optical remote sensor.

Assessing variable activity for Bayesian regression trees

Bayesian Additive Regression Trees (BART) are non-parametric models that can capture complex exogenous variable effects. In any regression problem, it is often of interest to learn which variables are most active. Variable activity in BART is usually measured by counting the number of times a tree splits for each variable. Such one-way counts have the advantage of fast computations. Despite their convenience, one-way counts have several issues. They are statistically unjustified, cannot distinguish between main effects and interaction effects, and become inflated when measuring interaction effects. An alternative method well-established in the literature is Soboĺ indices, a variance-based global sensitivity analysis technique. However, these indices often require Monte Carlo integration, which can be computationally expensive. This paper provides analytic expressions for Soboĺ indices for BART posterior samples. These expressions are easy to interpret and are computationally feasible. Furthermore, we will show a fascinating connection between first-order (main-effects) Soboĺ indices and one-way counts. We also introduce a novel ranking method, and use this to demonstrate that the proposed indices preserve the Soboĺ-based rank order of variable importance. Finally, we compare these methods using analytic test functions and the En-ROADS climate impacts simulator.