Elementary Effects Method Research Articles

An Efficient Sensitivity Analysis Approach for Computationally Expensive Microscopic Traffic Simulation Models

Microscopic traffic simulators are useful tools for designing, evaluating and optimizing transportation systems. In order for a simulator to accurately describe reality, the corresponding traffic model must be properly calibrated. However, the calibration can be rather difficult when the model is computationally expensive and has many parameters. To overcome these difficulties, Sensitivity Analysis (SA) can be applied as an essential instrument for supporting model calibration. Through SA the practitioners can obtain valuable information about the relationship between model inputs and outputs, and hence focus on the proper set of most influential parameters for the calibration. Notice, however, that many quantitative SA techniques may also fail with computationally expensive models. To address the above issues, in this paper we developed the quasi-OTEE method, an efficient and qualitative SA approach based on the Elementary Effects (EE) method. The quasi-OTEE approach is able to screen the most influential parameters of a complex model through computing and comparing their Sensitivity Indexes. With the improved sampling strategy, this approach is much more efficient than the original EE method. The approach is validated through a numerical analysis, and a case study of a small synthetic network in Aimsun. A more detailed case study of the Zurich network in VISSIM is then provided to illustrate its application. The results demonstrate that the proposed approach is an effective SA tool for the computationally expensive microscopic traffic models, as well as other complex models in the general scientific community.

Global Sensitivity Analysis for UNSATCHEM Simulations of Crop Production with Degraded Waters

One strategy for maintaining irrigated agricultural productivity in the face of diminishing resource availability is to make greater use of marginal quality waters and lands. A key to sustaining systems using degraded irrigation waters is salinity management. Advanced simulation models and decision support tools can aid in the design and management of water reuse systems, but at present model predictions and related management recommendations contain significant uncertainty. Sensitivity analyses can help characterize and reduce uncertainties by revealing which parameter variations or uncertainties have the greatest impact on model outputs. In this work, the elementary effects method was used to obtain global sensitivity analyses of UNSATCHEM seasonal simulations of forage corn (Zea mays L.) production with differing irrigation rates and water compositions. Sensitivities were determined with respect to four model outcomes: crop yield, average root zone salinity, water leaching fraction, and salt leaching fraction. For a multiple‐season, quasi‐steady scenario, the sensitivity analysis found that overall the most important model parameters were the plant salt tolerance parameters, followed by the solute dispersivity. For a single‐season scenario with irrigation scheduling based on soil water deficit, soil hydraulic parameters were the most important; the computed salt leaching fraction was also strongly affected by the initial ionic composition of the exchange phase because of its impact on mineral precipitation. In general, parameter sensitivities depend of the specifics of a given modeling scenario, and procedures for routine use of models for site‐specific degraded irrigation water management should include site‐specific uncertainty and sensitivity analyses. The elementary effects method used in this work is a useful approach for obtaining parameter sensitivity information at relatively low computational cost.

On the elastic properties of mineralized turkey leg tendon tissue: multiscale model and experiment

The key parameters influencing the elastic properties of the mineralized turkey leg tendon (MTLT) were investigated. Two structurally different tissue types appearing in the MTLT were considered: circumferential and interstitial tissue. These differ in their amount of micropores and their average diameter of the mineralized collagen fibril bundles. A multiscale model representing the apparent elastic stiffness tensor of MTLT tissue was developed using the Mori-Tanaka and the self-consistent homogenization schemes. The volume fraction of mineral (hydroxyapatite) in the fibril bundle, [Formula: see text], and the tissue microporosity are the variables of the model. The MTLT model was analyzed performing a global sensitivity analysis (Elementary Effects method) and a parametric study. The stiffnesses parallel (axial) and perpendicular (transverse) to the MTLT long axis were the only significantly sensitive components of the apparent stiffness tensor of MTLT tissue. The most important parameters influencing these apparent stiffnesses are [Formula: see text], tissue microporosity, as well as shape and distribution of the minerals in the fibril bundle (intra- vs. interfibrillar). The predicted apparent stiffness was converted to acoustic impedance for model validation. From measurements on embedded MTLT samples, including 50- and 200-MHz scanning acoustic microscopy as well as synchrotron radiation micro-computed tomography, we obtained site-matched acoustic impedance and [Formula: see text] data of circumferential and interstitial tissue. The experimental and the model data compare very well for both tissue types (relative error 6-8%).

Scheduling of Changes in Complex Engineering Design Process via Genetic Algorithm and Elementary Effects Method

Engineering design changes constantly occur in a complex engineering design process. Designers have to put an appropriate procedure in place to handle these changes in order to realize successful product development in a timely and cost-effective manner. When many change propagation paths are present, selection of the best change evolution paths and distribution of change results to downstream tasks become critical to the progress management of the project. In this paper, based on the available change propagation simulation algorithm, a global sensitivity analysis method known as elementary effects (EE) is employed to rank the importance of each potential propagation path with those involved design dependencies in the process. Further, an EE-based heuristic design dependency encoding method is applied to the genetic algorithm which is then adopted to schedule the change updating process. Finally, the optimal results obtained by the complete search and the heuristic dependency encoding methods are compared to illustrate the improvements and effectiveness of the latter method.

Global sensitivity analysis for subsoil parameter estimation in mechanized tunneling

The present paper validates two alternative global sensitivity analysis methods, namely variance-based and elementary effect, for the purpose of detecting key subsoil parameters that influence the output of mechanized tunnel finite element simulation. In the elementary effect method, a strategy for considering the dependencies, that result from a set of constraints between different parameters, is proposed. Moreover, because the numerical implementation of variance-based sensitivity estimates, in particular, has been proven to require intensive evaluations of the system under investigation, a practical surrogate modeling technique is utilized. This technique is based on quadratic polynomial regression and represents a reliable approximation of the computationally expensive mechanized tunnel simulation. Furthermore, a convergence analysis based on Central Limit Theorem for the numerical implementation of the methods is introduced. The adopted analysis highlights model evaluations needed for the sensitivity measures to converge, as well as the uncertainty involved in these measures.

Calibration of VISSIM for Indian Heterogeneous Traffic Conditions

Efficient modeling of vehicular traffic remains a largely debated issue especially in context of Indian heterogeneous driving conditions. VISSIM is a microscopic traffic simulation software that is gaining increasing recognition in India. However, modifications to the default behavioral parameters are essential to effectively simulate Indian heterogeneous traffic conditions. This paper presents a method and results on sensitivity analysis and automatic calibration of VISSIM model using data from an intersection in Chennai. This intersection has heavy flows during the peak time. VISSIM parameters affecting driving behaviour in Indian heterogeneous conditions were found using sensitivity analysis. ANOVA and elementary effects method were used in sensitivity analysis. The model was calibrated using Visual C++ COM interface of VISSIM. Genetic Algorithm was used to find the optimal combination of sensitive parameters during calibration.

Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations

The effect of the chain length, the temperature and the strain rate on the yield stress and the elastic modulus of glassy polyethylene is systematically studied using united-atom molecular dynamics (MD) simulations. Based on our MD results, a sensitivity analysis (SA) is carried out in order to quantify the influence of the uncertain input parameters on the predicted yield stress and elastic modulus. The SA is based on response surface (RS) models (polynomial regression and moving least squares). We use partial derivatives (local SA) and variance-based methods (global SA) where we compute first-order and total sensitivity indices. In addition, we use the elementary effects method on the mechanical model. All stochastic methods predict that the key parameter influencing the yield stress and elastic modulus is the temperature, followed by the strain rate.

Two-Step Sensitivity Testing of Parametrized and Regionalized Life Cycle Assessments: Methodology and Case Study

Comprehensive sensitivity analysis is a significant tool to interpret and improve life cycle assessment (LCA) models, but is rarely performed. Sensitivity analysis will increase in importance as inventory databases become regionalized, increasing the number of system parameters, and parametrized, adding complexity through variables and nonlinear formulas. We propose and implement a new two-step approach to sensitivity analysis. First, we identify parameters with high global sensitivities for further examination and analysis with a screening step, the method of elementary effects. Second, the more computationally intensive contribution to variance test is used to quantify the relative importance of these parameters. The two-step sensitivity test is illustrated on a regionalized, nonlinear case study of the biodiversity impacts from land use of cocoa production, including a worldwide cocoa products trade model. Our simplified trade model can be used for transformable commodities where one is assessing market shares that vary over time. In the case study, the highly uncertain characterization factors for the Ivory Coast and Ghana contributed more than 50% of variance for almost all countries and years examined. The two-step sensitivity test allows for the interpretation, understanding, and improvement of large, complex, and nonlinear LCA systems.

Energy potential of a Massive Solar-Thermal Collector design in European climates

The aim of this work is to investigate the energy potential of using exposed concrete structures as solar energy absorbers (here denoted with the general term of Massive Solar-Thermal Collectors, MSTCs) during the heating period and in particular the design of a Concrete Solar Collector (CSC) is then presented. The CSC is a particular kind of MSTC, conceived as an exposed free standing structure that embeds a coiled pipe heat exchanger in a massive-concrete matrix. A numerical design model has been developed and parametric simulations have been conducted in order to get a figure of the energy potential of the CSC under different European climate conditions. The CSC has reached an energy yield of 460.77kWh/m2/y and an average heat flux of 93.07W/m2 for the reference climate of Stuttgart (Germany) during the winter season (inlet fluid temperature of −5°C and mass-flow rate of 45kg/h/m2). The Elementary Effect Method has been adopted as Sensitivity Analysis procedure with the aim of understanding the dependency of design parameters on the energy output. Finally, an economic analysis has been carried out by comparing investment costs and energy outputs.

Application of sensitivity analysis in building energy simulations: Combining first- and second-order elementary effects methods

Sensitivity analysis plays an important role in the understanding of complex models. It helps to identify the influence of input parameters in relation to the outputs. It can also be a tool to understand the behavior of the model and can then facilitate its development stage. This study aims to analyze and illustrate the potential usefulness of combining first and second-order sensitivity analysis, applied to a building energy model (ESP-r). Through the example of an apartment building, a sensitivity analysis is performed using the method of elementary effects (also known as the Morris method), including an analysis of the interactions between the input parameters (second-order analysis). The usefulness of higher-order analysis is highlighted to support the results of the first-order analysis better. Several aspects are tackled to implement the multi-order sensitivity analysis efficiently: interval size of the variables, the management of non-linearity and the usefulness of various outputs.

From screening to quantitative sensitivity analysis. A unified approach

The present work is a sequel to a recent one published on this journal where the superiority of ‘radial design’ to compute the ‘total sensitivity index’ was ascertained. Both concepts belong to sensitivity analysis of model output. A radial design is the one whereby starting from a random point in the hyperspace of the input factors one step in turn is taken for each factor. The procedure is iterated a number of times with a different starting random point as to collect a sample of elementary shifts for each factor. The total sensitivity index is a powerful sensitivity measure which can be estimated based on such a sample. Given the similarity between the total sensitivity index and a screening test known as method of the elementary effects (or method of Morris), we test the radial design on this method. Both methods are best practices: the total sensitivity index in the class of the quantitative measures and the elementary effects in that of the screening methods. We find that the radial design is indeed superior even for the computation of the elementary effects method. This opens the door to a sensitivity analysis strategy whereby the analyst can start with a small number of points (screening-wise) and then – depending on the results – possibly increase the numeral of points up to compute a fully quantitative measure. Also of interest to practitioners is that a radial design is nothing else than an iterated ‘One factor At a Time’ (OAT) approach. OAT is a radial design of size one. While OAT is not a good practice, modelers in all domains keep using it for sensitivity analysis for reasons discussed elsewhere (Saltelli and Annoni, 2010) [23]. With the present approach modelers are offered a straightforward and economic upgrade of their OAT which maintain OAT's appeal of having just one factor moved at each step.

Simplex-based screening designs for estimating metamodels

The screening method proposed by Morris in 1991 allows to identify the important factors of a model, including those involved in interactions. This method, known as the elementary effects method, relies on a “one-factor-at-a-time” (OAT) design of experiments, i.e. two successive points differ only by one factor. In this article, we introduce a non-OAT simplex-based design for the elementary effects method. Its main advantage, compared to Morris's OAT design, is that the sample size does not collapse when the design is projected on sub-spaces spanned by groups of factors. The use of this design to estimate a metamodel depending only on the (screened) important factors is discussed.

An effective screening design for sensitivity analysis of large models

In 1991 Morris proposed an effective screening sensitivity measure to identify the few important factors in models with many factors. The method is based on computing for each input a number of incremental ratios, namely elementary effects, which are then averaged to assess the overall importance of the input. Despite its value, the method is still rarely used and instead local analyses varying one factor at a time around a baseline point are usually employed. In this piece of work we propose a revised version of the elementary effects method, improved in terms of both the definition of the measure and the sampling strategy. In the present form the method shares many of the positive qualities of the variance-based techniques, having the advantage of a lower computational cost, as demonstrated by the analytical examples. The method is employed to assess the sensitivity of a chemical reaction model for dimethylsulphide (DMS), a gas involved in climate change. Results of the sensitivity analysis open up the ground for model reconsideration: some model components may need a more thorough modelling effort while some others may need to be simplified.