Elementary Effects Method Research Articles

Analyzing parametric influences driving age-associated changes in absorption using a PBPK-GSA approach

The advanced age population may be susceptible to an increased risk of adverse effects due to increased drug exposure after oral dosing. Factors such as high-interindividual variability and lack of data has led to poor characterization of absorption's role in pharmacokinetic changes in this population. Physiologically based pharmacokinetic (PBPK) models are increasingly being used during the drug development process, as their unique qualities are advantageous in atypical scenarios such as drug-drug interactions or special populations such as older people. Along with relying on various sources of data, auxiliary tools including parameter estimation and sensitivity analysis techniques are employed to support model development and other applications. However, sensitivity analyses have mostly been limited to localized techniques in the majority of reported PBPK models using them. This is disadvantageous, since local sensitivity analyses are unsuitable for risk analysis, which require assessment of parametric interactions and proper coverage of the input space to better estimate and subsequently mitigate the effects of the phenomenon of interest. For this reason, this study seeks to integrate a global sensitivity analysis screening method with PBPK models based in PK-Sim® to characterize the consequences of potential changes in absorption that are often associated with advanced age. The Elementary Effects (Morris) method and visualization of the results are implemented in R and three model drugs representing Biopharmaceutical Classification System classes I-III that are expected to exhibit some sensitivity to three age-associated hypotheses were successfully tested.

Are we focusing on the right parameters? Insights from Global Sensitivity Analysis of a Functional-Structural Plant Model

Abstract Performing global sensitivity analysis on functional-structural plant models (FSP models) can greatly benefit both model development and analysis by identifying the relevance of parameters for specific model outputs. Setting unimportant parameters to a fixed value decreases dimensionality of the typically large model parameter space. Efforts can then be concentrated on accurately estimating the most important input parameters. In this work, we apply the Elementary Effects method for dimensional models with arbitrary input types, adapting the method to models with inherent randomness. Our FSP model simulated a maize stand for 160 days of growth, considering three outputs, namely yield, peak biomass and peak leaf area index (LAI). Of 52 input parameters, 12 were identified as important for yield and peak biomass and 14 for LAI. Over 70 % of parameters were deemed unimportant for the outputs under consideration, including most parameters relating to crop architecture. Parameters governing shade avoidance response and leaf appearance rate (phyllochron) were also unimportant; variations in these physiological and developmental parameters do lead to visible changes in plant architecture but not to significant changes in yield, biomass or LAI. Some inputs identified as unimportant due to their low sensitivity index have a relatively high standard deviation of effects, with high fluctuations around a low mean, which could indicate non-linearity or interaction effects. Consequently, parameters with low sensitivity index but high standard deviation should be investigated further. Our study demonstrates that global sensitivity analysis can reveal which parameter values have the most influence on key outputs, predicting specific parameter estimates that need to be carefully characterized.

Morris method supporting building optimization

AbstractAs part of the energy design synthesis method, complex dynamic building simulation database was created with IDA ICE code for all family house building configurations for a considered problem. In this paper, the annual heat energy demand output parameter is considered to serve as basis of a building energy design investigation. The sensitivity analysis performed by Morris' elementary effect method was used. As the result of the sensitivity analysis of the output parameter, the most important input parameters can be identified, that influence the buildings' energy efficiency, that can support further building designs.

Interactions between soil structure dynamics, hydrological processes, and organic matter cycling: A new soil‐crop model

AbstractThe structure of soil is critical for the ecosystem services it provides since it regulates many key soil processes, including water, air and solute movement, root growth and the activity of soil biota. Soil structure is dynamic, driven by external factors such as land management and climate and mediated by a wide range of biological agents and physical processes operating at strongly contrasting time‐scales, from seconds (e.g., tillage) to many decades (e.g., faunal activity and soil aggregation). In this respect, positive feedbacks in the soil–plant system may lead in the longer term to soil physical degradation or to the recovery of structurally poor soils. As far as we are aware, no existing soil‐crop model can account for such processes. In this paper, we describe a new soil‐crop model (USSF, Uppsala model of Soil Structure and Function) that accounts for the effects of soil structure dynamics on water and organic matter cycling at the soil profile scale. Soil structure dynamics are expressed as time‐varying physical (bulk density, porosity) and hydraulic properties (water retention, hydraulic conductivity) responding to the activity of biological agents (i.e., earthworms, plant roots) and physical processes (i.e., tillage, soil swell‐shrink) at seasonal to decadal time‐scales. In this first application of the model, we present the results of 30‐year scenario simulations that illustrate the potential role and importance of soil structure dynamics for the soil water balance, carbon storage in soil, root growth, and winter wheat yields on two soils (loam and clay) in the climate of central Sweden. A sensitivity analysis was also performed for these two scenarios using the Morris method of elementary effects, which revealed that the most sensitive parameters controlling soil structure dynamics in the USSF model are those determining aggregation induced by organic matter turnover and swell/shrink. We suggest that the USSF model is a promising new tool to investigate a wide range of processes and phenomena triggered by land use and climate change. Results from this study show that feedback in the soil‐crop system mediated by the dynamics of soil physical and hydraulic properties are potentially of central importance for long‐term predictions of soil water balance, crop production, and carbon sequestration under global change.

On the selection of Morris trajectories for parametric sensitivity analysis in spectroscopic ellipsometry modeling

Spectroscopic ellipsometry and some other optical metrology techniques, such as reflectometry and scatterometry, are model-based optical measurements and, therefore, require appropriate modeling to determine the geometric and material properties of substrates, thin films, and multilayer structures. Parametric sensitivity analysis (SA) provides essential assistance in the model-building process to quantify the relative importance of model parameters for model output and to identify those with high/little influence. SA can be performed in a variety of ways, and this article discusses an application of the Morris or elementary effect (EE) method, a screening type SA procedure, to spectroscopic ellipsometry modeling. The method is a global SA technique and uses a stepping of m parameters along certain so-called “trajectories” or sequences of points in parameter space, randomly constructed in order to maximally fill the volume of the m-dimensional parameter space. However, it was thought that the EE method relies greatly on a sampling strategy or a way of selecting “optimized trajectories” in the parameter space, i.e., a necessary number of trajectories chosen to be well spread over the space to properly cover the entire realistic ranges of all input factors. Here, we use two sampling methods for selecting trajectories with possibly different distributions and investigate their effects on the estimation of various sensitivity measures in spectroscopic ellipsometry data modeling. The SA results indicate that the performance of the sampling strategy should not be judged only by maximizing the trajectory spread but also include some additional convergence criteria for the sensitivity measures.

Elementary effects for models with dimensional inputs of arbitrary type and range: Scaling and trajectory generation.

The Elementary Effects method is a global sensitivity analysis approach for identifying (un)important parameters in a model. However, it has almost exclusively been used where inputs are dimensionless and take values on [0, 1]. Here, we consider models with dimensional inputs, inputs taking values on arbitrary intervals or discrete inputs. In such cases scaling effects by a function of the input range is essential for correct ranking results. We propose two alternative dimensionless sensitivity indices by normalizing the scaled mean or median of absolute effects. Testing these indices with 9 trajectory generation methods on 4 test functions (including the Penman-Monteith equation for evapotranspiration) reveals that: i) scaled elementary effects are necessary to obtain correct parameter importance rankings; ii) small step-size methods typically produce more accurate rankings; iii) it is beneficial to compute and compare both sensitivity indices; and iv) spread and discrepancy of the simulation points are poor proxies for trajectory generation method performance.

Evaluating the parameter sensitivity and impact of hydrologic modeling decisions on flood simulations

Recent studies argue that hydrological models must be configured for the specific objectives they need to address. Model configuration involves multiple model decision steps, such as choice of model structure, spatial discretization, spatial representation of forcing and performance metrics to calibrate them. We investigated the influence of each of the decisions in turn in a standardized framework to understand how differences in these decisions impact flood simulations. For this purpose, we used the capability of Structure for Unifying Multiple Modeling Alternatives (SUMMA) model as it allows a straightforward comparison of different model structure choices and can easily be reconfigured for different spatial organization. We also employed a sequential sensitivity analysis using the Efficient Elementary Effect (EEE) method to select the sensitive parameters for each model structure considered in this study. This allowed us to check if the dominant hydrological process of the catchment can be captured irrespective of the model structure choice. Identification of the most sensitive parameters also helped us to scale down the dimensionality of the problem both in terms of computational demand and complexity. Based on the various choices of model decisions, 36 unique model configurations are constructed and each of them are separately calibrated by the performance metrics. The impact and relative importance of modeling decisions are quantified by Analysis of Variance(ANOVA) and effect size respectively. As a test case, we use accurate simulation of flood peaks (expressed as deviation in peak flow, deviation in peak time and relative volume error) that occurred in the Netravathi basin of Karnataka, India to study the impact of the model decisions. The extensive sensitivity analysis and model calibration required for the study is carried out by parallel processing using a supercomputer. For floods, the choice of spatial discretization of the modeling domain is the most impacting decision, followed by the choice of objective function during calibration, model structure and spatial representation of forcing, respectively, for the catchment. The results provide key insights regarding the ideal option a modeler must choose for each modeling decision for simulating floods in Netravathi. More generally, this study shows that model configuration decisions that are anecdotally often made based on convenience or habit can strongly impact simulation accuracy for specific modeling purposes. Alongside the need to quantify more traditional uncertainty sources, such as data and parameter uncertainty, there is a need to quantify the impact of these model configuration decisions.

Back analysis of rock mass parameters in tunnel engineering using machine learning techniques

Efficient determination of the rock mass properties is vitally important for calculating and evaluating tunnel stability in tunnel engineering. The back analysis method has been widely used as an indirect method for determining rock mass parameters based on field measurements. However, most back analysis methods are generally time-consuming for numerical simulation and are merely based on the measured displacement, which leads to the identification of rock mass parameters that cannot fully reflect the characteristics of the surrounding rock. To improve the accuracy of the estimation of rock mass parameters, this paper presents a back analysis method based on multi-output support vector regression (MSVR) and differential evolution (DE) algorithms. Firstly, the global sensitivity analysis of rock mass parameters is analyzed using the elementary effects method. Numerical simulation is then carried out to prepare training samples. DE algorithm is used to determine the optimum hyperparameters of MSVR. Based on the monitoring data, the rock mass properties of the selected sensitive parameters are estimated by the constructed MSVR model. A high-speed railway tunnel is utilized to demonstrate the effectiveness of the MSVR with the DE algorithm (DE-MSVR). The results show that the DE-MSVR with mixed monitoring data of vault settlement, convergence, and rock mass stress has higher forecasting performance than these models with a single type of monitoring data. It is feasible to use the monitoring data at the early stages combined with the numerical simulation for parameter back analysis. Moreover, the comparison results show that the presented method exhibits higher prediction accuracy than the existing back analysis models.

A novel equal frequency sampling of factor levels (EFSFL) method is applied to identify the dominant factor inducing the combined toxicities of 13 factors

The research framework combining global sensitivity analysis (GSA) with quantitative high-throughput screening (qHTS), called GSA-qHTS, provides a potentially feasible way to screen for important factors that induce toxicities of complex mixtures. Despite its value, the mixture samples designed using the GSA-qHTS technique still have a shortage of unequal factor levels, which leads to an asymmetry in the importance of elementary effects (EEs). In this study, we developed a novel method for mixture design that enables equal frequency sampling of factor levels (called EFSFL) by optimizing both the trajectory number and the design and expansion of the starting points for the trajectory. The EFSFL has been successfully employed to design 168 mixtures of 13 factors (12 chemicals and time) that each have three levels. By means of high-throughput microplate toxicity analysis, the toxicity change rules of the mixtures are revealed. Based on EE analysis, the important factors affecting the toxicities of the mixtures are screened. It was found that erythromycin is the dominant factor and time is an important non-chemical factor in mixture toxicities. The mixtures can be classified into types A, B, and C mixtures according to their toxicities at 12 h, and all the types B and C mixtures contain erythromycin at the maximum concentration. The toxicities of the type B mixtures increase firstly over time (0.25 ∼ 9 h) and then decrease (12 h), while those of the type C mixtures consistently increase over time. Some type A mixtures produce stimulation that increases with time. With the present new approach to mixture design, the frequency of factor levels in mixture samples is equal. Consequently, the accuracy of screening important factors is improved based on the EE method, providing a new method for the study of mixture toxicity.

Input significance ranking of microalgae continuous culture models

AbstractBackgroundMicroalgal cultures are evolving into a promising ecofriendly technology for a host of applications. To be sustainable, culture conditions need to be optimized and then controlled. One way to develop robust controllers for a cultivation system is by using mathematical growth models to simulate microalga‐based production. In this scenario, engineering design tasks begin by selecting the critical variables of these models.ResultsA new methodology for determining the significance ranking of a model's input factors under steady‐state operation (parameters (e.g. biological, geometrical) and/or process variables) was designed. The sensitivity of biomass response to its inputs was investigated in four different photobioreactor growth models within a nominal operational region. The methodology ranks models’ input factors based on the one‐at‐a‐time Morris method of elementary effects and variance‐based Sobol's method. Such information provided by the presented procedure is valuable as it reveals which input parameters explain most of the variance in model predictions.ConclusionThe methodology allowed the identification of controlled variables and biological parameters to be targeted for enhanced calibration. Furthermore, the presented methodology showed that in continuous reactors the dilution rate is a critical variable of the process. Therefore, it should be controlled. Additionally, most surprisingly, it is observed that controlling the light intensity within the optimum point of operation is not necessarily a crucial task. However, although its manipulation is still important, the accurate calibration of the parameters of the model may represent a greater influence on the biomass response. © 2023 Society of Chemical Industry (SCI).

Sensitivity analysis of structural parameters for PEMFCs based on 1D transient model and elementary effect method

ABSTRACT To investigate the influences of structural parameters on output performances and further quantify the degree of influences, a one-dimensional transient multiphase proton exchange membrane fuel cell (PEMFC) model and a global sensitivity analysis model were established. After rigorous model validation, structural parameters such as the thickness of proton exchange membrane (MEM), catalytic layer (CL), micro-porous layer (MPL), and gas diffusion layer (GDL) as well as the porosity of CL, MPL, and GDL were studied. The ionomer volume fraction of cathode and anode were also studied. Increasing the thickness of MEM and CL decreases the membrane water content and increases the ohmic voltage loss. The increase of thickness leads to longer reaction gas transfer path and increase of transfer resistance. The increase of porosity increases the concentration of the reaction gas . However, too high porosity will reduce the effective ion conductivity . The increase of ionomer volume fraction is beneficial to electrochemical reaction. Based on quantitative sensitivity analysis, the MEM thickness and the anode ionomer volume fraction are defined as highly sensitive parameters. The MPL thickness and the GDL porosity are defined as insensitive parameters. The sensitivity of MEM thickness, CL thickness, and anode ionomer volume fraction become more prominent in large current density regions.

Performance of Compression Yielded FRP-Reinforced Concrete Beams with T Sections

Concrete structures reinforced with fiber-reinforced polymer (FRP) reinforcement have been increasingly applied in civil engineering construction to improve several structural performances of bridges and buildings. However, the major weakness of these structures is that they typically suffer from poor ductility and brittle failure. An innovative mechanism called compression yielding (CY) has recently been proposed to enhance the ductility of FRP-reinforced concrete beams. In this study, the moment capacity and ductility of CY beams with T sections are analyzed based on a layered approach. The key variables in the design of a CY beam with a T section are identified and their importance is comprehensively investigated based on the elementary effects method and a parametric study. It is found that the ductility performance can be effectively improved by using a CY material with postmodulus ratio close to 0, and the moment capacity can be enhanced significantly by increasing the CY material strength. The most effective measure for simultaneously improving the moment capacity and ductility performance is to increase the CY block height.

Comparison of local and global sensitivity analysis methods and application to thermal hydraulic phenomena

The best estimate plus uncertainty analysis have been widely applied for the safety assessment of nuclear systems, and sensitivity analysis is one of the essential steps to identify and rank the important phenomena and parameters. The conventionally used local sensitivity methods are based on linear hypothesis and have limitations in the application process of nonlinear systems, while the more complicated global sensitivity methods may have problem in time costs. To compare and propose the proper method for evaluation of thermal-hydraulic calculation in a reactor system, local methods such as Pearson correlation coefficient, Spearman rank correlation coefficient, and Kendall rank correlation coefficient, global methods such as the variance-based method, moment-independent method, and elementary effects method are reviewed and applied for numerical examples and specific reactor thermal-hydraulic problem in this paper. Results show that the rank of parameter importance measured by various local analysis methods is the same, but away from the global methods. Different types of global sensitivity analysis methods have similar results for parameters with higher importance, and among these methods, the elementary effects method has the lowest computational cost with the same number of samples.

Sensitivity analysis of design variables in life-cycle environmental impacts of buildings

Buildings are responsible for a large portion of global energy consumption and carbon emissions. Improvements in building design contribute to reducing environmental impacts of buildings. In this context, a crucial issue is to understand which design variables should be considered while which variables could be negligible. The objective of this study is to develop a framework for assessing the influence of various design variables throughout the design process in the environmental impacts of a building over its life cycle. This methodological framework combined building information modelling and life cycle assessment tools and a global sensitivity analysis using the Morris elementary effects method. A residential building was applied to demonstrate the developed framework. The influence of six design variables in early design stages (including, floor area, aspect ratio, floor height, orientation, window-to-wall ratio and number of floors), nine variables in detailed design stages (including, structure type of external and internal walls, type of insulation material for external and internal walls, insulation material for floors, waterproofing and insulation material for roof, type of window frame, and glazing type), and four variables in construction design stages (including, type of finishing for external walls, internal walls and floors, and roof tiles) are examined. Three environmental impact criteria (including, embodied, operational, and life-cycle environmental impacts) of a building are considered. The results identified the most influential variables throughout the design process, highlighting aspect ratio in early design stage, the structure and insulation materials for walls in detailed design stages, and the roof title in construction design stages. The outcomes of this research can assist in understanding the importance of design variables in each design stage throughout the design process of a building.

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 Bayesian framework to assess and create risk maps of groundwater flooding

Groundwater flooding can cause severe damages to homes, utilities, and infrastructure and yield significant economic and social costs. Numerical models are used to understand these events and are the basis to produce imagery products for risk management and communication. However, such maps are generally produced using forward model simulations, and most of the mapping products are still deterministic. In contrast to pluvial and fluvial floods, an open issue in the analysis of susceptibility to groundwater flooding is the lack of probabilistic assessment and mapping products recognizing parametric uncertainty. Hence, we propose a Bayesian-based framework to create probabilistic risk maps and to identify the susceptibility to groundwater flood events. We aim to assess the spatial distribution and temporal variability of groundwater flooding by decomposing the uncertainty and the sensitivity of distributed groundwater numerical models. The scheme involves the use of the elementary effects method, the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm, and the exploration of the predictive posterior distributions of the groundwater heads to evaluate the susceptibility according to exceedance levels. We use the proposed Bayesian framework with a numerical model that simulates the groundwater flood event that occurred in the valley of the Alz River in 2013. This study developed two types of susceptibility maps based on the exceedance probability of certain groundwater levels and specific cellar depths. The Bayesian inference supports the parameter estimation and thereby increases the spatial confidence of the areas susceptible to inundation. This study shows that maps of susceptibility to groundwater flooding can be built over one single event models and acknowledge the inherent spatial and temporal uncertainty of such events.

Proposing an Uncertainty Management Framework to Implement the Evidence Theory for Vehicle Crash Applications

Abstract The purpose of this work is to enable the use of the Dempster–Shafer evidence theory (ET) for uncertainty propagation on computationally expensive automotive crash simulations. This is necessary as the results of these simulations are influenced by multiple possibly uncertain aspects. To avoid negative effects, it is important to detect these factors and their consequences. The challenge when pursuing this effort is the prohibitively high computational cost of the ET. To this end, we present a framework of existing methods that is specifically designed to reduce the necessary number of full model evaluations and parameters. An initial screening removes clearly irrelevant parameters to mitigate the curse of dimensionality. Next, we approximate the full-scale simulation using metamodels to accelerate output generation and thus enable the calculation of global sensitivity indices. These indicate effects of the parameters on the considered output and more profoundly sort out irrelevant parameters. After these steps, the ET can be performed rapidly and feasibly due to fast-responding metamodel and reduced input dimension. It yields bounds for the cumulative distribution function of the considered quantity of interest. We apply the proposed framework to a simplified crash test dummy model. The elementary effects method is used for screening, a kriging metamodel emulates the finite element simulation, and Sobol' sensitivity indices are determined before the ET is applied. The outcome of the framework provides engineers with information about the uncertainties they may face in hardware testing and that should be addressed in future vehicle design.

Energy hub-based optimal planning framework for user-level integrated energy systems: Considering synergistic effects under multiple uncertainties

The design of user-level integrated energy systems is challenged by a variety of combinations of energy converters, complex cascade utilization of multiple energy flows, as well as sequential matching between stochastic energy resources and periodic energy demands. These issues can be addressed by an optimal energy-hub based planning framework considering the synergistic effects under multiple uncertainties. The energy hub model is extended to analyze energy-level matching and source–load balance with time-varying coupling factors representing part-load characteristics. The optimization problem is formulated as a bi-level planning model with uncertainties evaluated by a two-stage global sensitivity analysis. The bi-level planning model determines the system structure and component sizing at the upper level and identifies the optimal operation strategy at the lower level by employing piecewise linearization of part-load characteristics of components involved. The global sensitivity analysis reduces model size with the elementary effect method, identifies the most influential uncertain parameters with a variance-based method. A case study in Beijing is demonstrated for the proposed methodology. The results show that the proposed method can effectively plan the integrated energy system considering sequential source–load matching with the rational scheduling strategy of components. The demand-side response influences the system configuration and renewable energy penetration. Integrating the components’ part-load characteristics help avoid the mismatch between the component capacity and energy demand, reducing 6.8% cost compared to the scheme with constant energy efficiency. The three most influential factors identified among 551 uncertain parameters are natural gas price, valley electricity price and nominal efficiency of the gas turbine.

Elementary effects analysis of factors controlling COVID-19 infections in computational simulation reveals the importance of social distancing and mask usage

COVID-19 was declared a pandemic by the World Health Organisation (WHO) on March 11th, 2020. With half of the world's countries in lockdown as of April due to this pandemic, monitoring and understanding the spread of the virus and infection rates and how these factors relate to behavioural and societal parameters is crucial for developing control strategies. This paper aims to investigate the effectiveness of masks, social distancing, lockdown and self-isolation for reducing the spread of SARS-CoV-2 infections. Our findings from an agent-based simulation modelling showed that whilst requiring a lockdown is widely believed to be the most efficient method to quickly reduce infection numbers, the practice of social distancing and the usage of surgical masks can potentially be more effective than requiring a lockdown. Our multivariate analysis of simulation results using the Morris Elementary Effects Method suggests that if a sufficient proportion of the population uses surgical masks and follows social distancing regulations, then SARS-CoV-2 infections can be controlled without requiring a lockdown.

Cluster sampling for Morris method made easy

AbstractIn this paper we provide a thorough investigation of the cluster sampling scheme for Morris' elementary effects method (MM), a popular model‐free factor screening method originated in the setting of design and analysis of computational experiments. We first study the sampling mechanism underpinning the two sampling schemes of MM (i.e., cluster sampling and noncluster sampling) and unveil its nature as a two‐level nested sampling process. This in‐depth understanding sets up a foundation for tackling two important aspects of cluster sampling: budget allocation and sampling plan. On the one hand, we study the budget allocation problem for cluster sampling under the analysis of variance framework and derive optimal budget allocations for efficient estimation of the importance measures. On the other hand, we devise an efficient cluster sampling algorithm with two variants to achieve enhanced statistical properties. The numerical evaluations demonstrate the superiority of the proposed cluster sampling algorithm and the budget allocations derived (when used both separately and in conjunction) to existing cluster and noncluster sampling schemes.