Variance-based Method Research Articles

An efficient sensitivity analysis for energy performance of building envelope: A continuous derivative based approach

Within the framework of building energy assessment, this article proposes to use a derivative based sensitivity analysis of heat transfer models in a building envelope. Two, global and local, estimators are obtained at low computational cost, to evaluate the influence of the parameters on the model outputs. Ranking of these estimators values allows to reduce the number of model unknown parameters by excluding non-significant parameters. A comparison with variance and regression-based methods is carried out and the results highlight the satisfactory accuracy of the continuous-based approach. Moreover, for the carried investigations the approach is $100$ times faster compared to the variance-based methods. A case study applies the method to a real-world building wall. The sensitivity of the thermal loads to local or global variations of the wall thermal is investigated. Additionally, a case study of wall with window is analyzed.

Defining the performance envelope of reactivity-initiated accidents in a high-temperature gas-cooled reactor

The purpose of this study is to define an envelope of possible transient conditions during two reactivity-initiated accidents (RIAs) in a modular high-temperature gas-cooled reactor (mHTGR). The accident scenarios studied were a group control rod withdrawal (CRW), a design basis accident, and a control rod ejection (CRE), a beyond design basis accident. Variance-based sensitivity analysis methods were employed to obtain realistic bounds on the reactor power and maximum temperature, energy deposition, and heating rate in the fuel during these accidents. Key reactor kinetic parameters and the heat transfer properties of the fuel and moderator were varied in a RELAP computer model of a 350-megawatt mHTGR to obtain these bounds. Sobol sensitivity indices were calculated to highlight which inputs account for the most variance in the outputs. Results showed that the kinetic properties and reactivity temperature coefficients were the most dominant inputs, while thermal properties had little impact on the outputs. Compared to previous experimental work, the fuel particle energy deposition from the simulated RIAs would not be expected to cause fuel failure in any design basis or beyond design basis reactivity accident we investigated. The predicted energy deposition in fuel kernels ranged from 98 to 331 J/g-fuel, significantly less than the expected failure threshold of approximately 1500 J/g-fuel. However, the power pulse widths and heating rates used in previous fuel safety experiments were different from the values predicted in this study for both accident scenarios. Regardless of these differences, this analysis shows that the safety margins in graphite-moderated mHTGRs for reactivity accidents are very large, and additional fuel safety tests are not expected to be necessary for this application.

Input modeling and uncertainty quantification for improving volatile residential load forecasting

Residential load forecasting has been playing an increasingly important role in operation and planning of power systems. Over the recent years, accurate forecasts of individual loads have become ever more challenging due to the proliferation of distributed energy resources. This paper identifies and verifies the opportunity of improving load forecasting performance by incorporating suitable input modeling and uncertainty quantification, and proposes a two-stage approach that enjoys the following features. (1) It provides input modeling and quantifies the impact of input errors, rather than neglect or mitigate the impact—a prevalent practice of existing methods. (2) It propagates the impact of input errors into the ultimate point and interval predictions for the target customer’s load for improved predictive performance. (3) A variance-based global sensitivity analysis method is further proposed for input-space dimensionality reduction in both stages to enhance the computational efficiency. Numerical experiments show that the proposed two-stage approach outperforms competing load forecasting methods with respect to both point predictive accuracy and coverage ability of the predictive intervals achieved.

RAAS inhibitors are not associated with mortality in COVID-19 patients: Findings from an observational multicenter study in Italy and a meta-analysis of 19 studies

ObjectiveThe hypothesis that been set forward that use of Renin Angiotensin Aldosterone System (RAAS) inhibitors is associated with COVID−19 severity. We set-up a multicenter Italian collaboration (CORIST Project, ClinicalTrials.gov ID: NCT04318418) to retrospectively investigate the relationship between RAAS inhibitors and COVID−19 in-hospital mortality. We also carried out an updated meta-analysis on the relevant studies. MethodsWe analyzed 4069 unselected patients with laboratory-confirmed SARS-CoV-2 infection and hospitalized in 34 clinical centers in Italy from February 19, 2020 to May 23, 2020. The primary end-point in a time-to event analysis was in-hospital death, comparing patients who received angiotensin-converting–enzyme inhibitors (ACEI) or angiotensin-receptor blockers (ARB) with patients who did not. Articles for the meta-analysis were retrieved until July 13th, 2020 by searching in web-based libraries, and data were combined using the general variance-based method. ResultsOut of 4069 COVID−19 patients, 13.5% and 13.3% received ACE-I or ARB, respectively. Use of neither ACE-I nor ARB was associated with mortality (multivariable hazard ratio (HR) adjusted also for COVID−19 treatments: 0.96, 95% confidence interval 0.77–1.20 and HR = 0.89, 0.67–1.19 for ACE-I and ARB, respectively). Findings were similar restricting the analysis to hypertensive (N = 2057) patients (HR = 1.00, 0.78–1.26 and HR = 0.88, 0.65–1.20) or when ACE-I or ARB were considered as a single group. Results from the meta-analysis (19 studies, 29,057 COVID−19 adult patients, 9700 with hypertension) confirmed the absence of association. ConclusionsIn this observational study and meta-analysis of the literature, ACE-I or ARB use was not associated with severity or in-hospital mortality in COVID−19 patients.

A comprehensive probabilistic approach for integrating and separating natural variability and parametric uncertainty in the prediction of distribution coefficient of radionuclides in rivers

A geochemical speciation model was developed to predict Distribution coefficients (Kds) of radionuclides (RNs) in rivers. The model takes into account complexation of RNs with inorganic ligands, sorption of RNs with hydrous ferric oxides, complexation of RNs with dissolved and particulate organic carbon (DOC and POC) and sorption and/or co-precipitation of RNs to carbonates. A sorption model of Cs onto clay was also integrated. The tool is also designed to conduct uncertainty and sensitivity analysis. Sensitivity analysis follows a stepwise structured approach, starting from computationally ‘inexpensive’ Morris method to most costly variance-based EFAST method. A nested Monte Carlo approach was also implemented to separate natural variability and lack of knowledge in global uncertainty assessment. As case studies, Kd distributions were estimated for Co, Mn, Ag and Cs in seven French rivers. Uncertainty analysis allowed to quantify Kd ranges that can be expected when considering all the sensitive parameters together.

Morris method with improved sampling strategy and Sobol’ variance-based method, as validation tool on numerical model of Richard’s equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters and is suggesting a greater significant digits is required to reduce its input uncertainty range.

PyAEM: A Python toolkit for aquatic ecosystem modelling

Aquatic ecosystem modelling has been a challenging task for scientists partly due to limited tools/software to support. This study attempted to develop a Python toolkit (PyAEM) that was able to support multiple procedures in aquatic ecosystem modelling. PyAEM included improved algorithms for sensitivity analysis, parameter optimization, data assimilation and model visualization. In PyAEM, one-at-a-time and variance-based methods were implemented to identify sensitive parameters in target models. Genetic algorithm was improved for global optimization of model parameters. Ensemble Kalman Filter was implemented for assimilating multi-source measured data to improve model performance. An aquatic ecosystem model viewer was specifically developed for model visualization with the advantages of multi-scenario comparison, model fit evaluation, multi-mesh support and time series data extraction. An application overview of PyAEM in watershed and lake modelling is given, and revealed that PyAEM can be easily adapted to support the implementation of a case for aquatic ecosystem modelling.

Ecosystem Service-Based Sensitivity Analyses of i-Tree Eco

"Trees are known to provide various ecosystem services and disservices to urban communities, which can be quantified using models based on field and environmental data. It is often uncertain how tree structure and environmental variables impact model output. Here we perform a sensitivity analysis (SA) of i-Tree Eco, a common urban forest model, to analyze the relative impact of different model inputs on three module outputs: biogenic volatile organic compound (BVOC)(isoprene and monoterpenes) emissions, carbon storage and sequestration, and dry deposition of nitrogen dioxide, sulfur dioxide, and ozone. The SA methods included novel applications of the Morris one-at-a-time method and a variance-based decomposition method, which integrates Monte Carlo simulation with Latin hypercube sampling and Iman Conover analysis. A case study was performed in New York City, New York, USA, with field plot data collected in 2013. Genus has the largest influence on BVOC emissions by determining base emission rates and its high interactions with other input factors, and BVOC emissions are sensitive to leaf biomass in a concave manner and temperature in a convex manner, while isoprene emissions show a strong linear relationship with photosynthetically active radiation (PAR). Diameter at breast height plays the most important role for both carbon storage and sequestration estimators; crown light exposure and tree condition are also important for carbon sequestration. Dry deposition velocity is sensitive to leaf area index and relative humidity in a nearly linear way, while sensitive to temperature and PAR in a concave manner. The results provide guidance to facilitate future field plot campaigns and model development. The knowledge revealed by the SA is also beneficial for model uncertainty reduction, which in turn facilitates more effective urban forest management and decision-making.

Spatial Exploration of Economic Data—Insight into Attitudes of Students towards Interdisciplinary Knowledge

This paper uses the technology acceptance model (TAM) framework for the research of economic and geography students’ attitudes towards interdisciplinary knowledge. Based on the SmartPLS Structural equation modelling SEM variance-based method, research results were gained through analysis of survey data of economic and geography students. They participated in the Spationomy project in the period of 2017–2019. Online questionnaires were fulfilled before and after students’ participation in the project and their future behavioural intention to use interdisciplinary knowledge was analysed. Based on the research, we can confirm that the Spationomy project has achieved its purpose, as both groups of students (economic and geography students) have acquired interdisciplinary knowledge and students intend to use it also in the future. Therefore, we can argue that the students included in the project in practice gained recognition of systems thinking about the importance of mutual interdisciplinary cooperation towards achieving synergies. The results also show that TAM can be successfully implemented to analyse how students of economics and geography accept the use of interdisciplinary knowledge in the learning process, which is an important implication for management and education as well as from the theoretical implications viewpoint. While effective analysis using TAM has been used successfully and relatively frequently in economics and business field, we have not found relevant examples of its implementation in the broader field of geography. However, the acceptance of geographic information system (GIS) or other information technologies/information software (IT/IS) tool-based approaches of analysis in the geography field may be of most importance. Therefore, also, this represents an important implication for the research area.

A Comparison of Moment-Independent and Variance-Based Global Sensitivity Analysis Approaches for Wheat Yield Estimation with the Aquacrop-OS Model

The present work reports the global sensitivity analysis of the Aquacrop Open Source (AOS) model, which is the open-source version of the original Aquacrop model developed by the Food and Agriculture Organization (FAO). Analysis for identifying the most influential parameters was based on different strategies of global SA, density-based and variance-based, for the wheat crop in two different geographical locations and climates. The main objectives were to distinguish the model’s influential and non-influential parameters and to examine the yield output sensitivity. We compared two different methods of global sensitivity analysis: the most commonly used variance-based method, EFAST, and the moment independent density-based PAWN method developed in recent years. We have also identified non-influential parameters using Morris screening method, so to provide an idea of the use of non-influential parameters with a dummy parameter approach. For both the study areas (located in Italy and in China) and climates, a similar set of influential parameters was found, although with varying sensitivity. When compared with different probability distribution functions, the probability distribution function of yield was found to be best approximated by a Generalized Extreme Values distribution with Kolmogorov–Smirnov statistic of 0.030 and lowest Anderson–Darling statistic of 0.164, as compared to normal distribution function with Kolmogorov–Smirnov statistic of 0.122 and Anderson–Darling statistic of 4.099. This indicates that yield output is not normally distributed but has a rather skewed distribution function. In this case, a variance-based approach was not the best choice, and the density-based method performed better. The dummy parameter approach avoids to use a threshold as it is a subjective question; it advances the approach to setting up a threshold and gives an optimal way to set up a threshold and use it to distinguish between influential and non-influential parameters. The highly sensitive parameters to crop yield were specifically canopy and phenological development parameters, parameters that govern biomass/yield production and temperature stress parameters rather than root development and water stress parameters.

Global Sensitivity Analysis of the Static Performance of Concrete Gravity Dam from the Viewpoint of Structural Health Monitoring

Structural Health Monitoring (SHM) is becoming the fourth driving force of engineering science and technology progress, in addition to the basic theory, numerical simulation and model test. In this paper, a definition of dam SHM is presented, its basic connotation is analyzed, and the general problems in existing researches are summarized. Then the sensitivity analysis of the static performance of concrete gravity dam is reviewed. For a hypothetical concrete gravity dam, a preliminary nonlinear finite element model is established. By means of the variance-based global sensitivity analysis method, phenomenological analysis of the static performance of the dam is carried out from three different horizons. And then the results are discussed in detail according to the common components of SHM. Overall, this paper provides a framework for sensitivity analysis of dams, or a way to explore the complexity of the dam system. In the long run, this paper should still be positioned as a generic and qualitative study in view of the complexity of dam system. There are still many issues as pointed out in the text need to be further understood and studied, and sensitivity analysis is a good tool.

A novel double-spring analytical model for hybrid GLARE joints: Model development, validation, parameter study and global sensitivity analysis

It is significant to theoretically evaluate the mechanical properties of hybrid (bonded/bolted) GLARE joint, especially under the condition of multiple assembly uncertainties. This work develops a double-spring analytical model that predicts the deformation of hybrid joints under the quasi-static load to solve this critical problem in the fabrication process of hybrid joints. Besides the mechanical properties of bolt, the stiffness of adhesive layers is introduced in this novel model in which the factors such as geometrics, properties of adhesive layer, bolt-hole clearance, laminate properties, contact condition, relaxation of pre-torque and types of materials are discussed in detail. Meanwhile, a Monte Carlo simulation (MCS) and a variance-based method are used to calculate their global sensitivity indices that have the ability to quantify the relative importance of those assembly factors in load distribution between the bolt and adhesive layer, fracture displacement at the initial stage and other mechanical properties. It is found that bolt-hole clearance, geometrics of laminate and properties of adhesive layer are the top three sensitive factors, the qualities of which must be strictly controlled in the process of fabrication. This model is able to provide a powerful approach for the future design of hybrid joints to achieve higher reliability and load capacity.

Importance of genetic parameters and uncertainty of MANIHOT, a new mechanistic cassava simulation model.

We identified the most sensitive genotype-specific parameters (GSPs) and their contribution to the uncertainty of the MANIHOT simulation model. We applied a global sensitivity and uncertainty analysis (GSUA) of the GSPs to the simulation outputs for the cassava development, growth, and yield in contrasting environments. We compared enhanced Sampling for Uniformity, a qualitative screening method new to crop simulation modeling, and Sobol, a quantitative, variance-based method. About 80% of the GSPs contributed to most of the variation in maximum leaf area index (LAI), yield, and aboveground biomass at harvest. Relative importance of the GSPs varied between warm and cool temperatures but did not differ between rainfed and no water limitation conditions. Interactions between GSPs explained 20% of the variance in simulated outputs. Overall, the most important GSPs were individual node weight, radiation use efficiency, and maximum individual leaf area. Base temperature for leaf development was more important for cool compared to warm temperatures. Parameter uncertainty had a substantial impact on model predictions in MANIHOT simulations, with the uncertainty 2-5 times larger for warm compared to cool temperatures. Identification of important GSPs provides an objective way to determine the processes of a simulation model that are critical versus those that have little relevance.

Multi-stage Sensitivity Analysis of Distributed Energy Systems: A Variance-based Sobol Method

In the face of the pressing environmental issues, the past decade witnessed the booming development of the distributed energy systems (DESs). A notable problem of DESs is the inevitable uncertainty that may make DESs deviate significantly from the deterministically obtained expectations, in both aspects of optimal design and economic operation. It thus necessitates the sensitivity analysis to quantify the impacts of the massive parametric uncertainties. This paper aims to give a comprehensive quantification, and carries out a multi-stage sensitivity analysis on DESs from the perspectives of evaluation criteria, optimal design and economic operation. First, a mathematical model of a DES is developed to present the solutions to the three stages of the DES. Second, the Monte-Carlo simulation is carried out subject to the probabilistic distributions of the energy, technical and economic parameters. Based on the simulation results, the variance-based Sobol method is applied to calculate the individual importance, interactional importance and total importance of various parameters. The comparison of the multi-stage results shows that only a few parameters play critical roles while the uncertainty of most of the massive parameters has little impact on the system performance. In addition, the influence of parameter interactions in the optimal design stage are much stronger than that in the evaluation criteria and operation strategy stages.

Uncertainty and sensitivity analysis applied to a rammed earth wall: evaluation of the discrepancies between experimental and numerical data

Due to the environmental impact of building materials, researches on sustainable materials, such as bio-based and earth materials, are now widespread. These materials offer numerous qualities such as their availability, recyclability and their ability to dampen the indoor relative humidity variations due to their hygroscopicity. As these materials can absorb large amount of humidity, numerical and experimental studies of their hygrothermal behaviour are crucial to assess their durability. To validate a hygrothermal model, numerical and experimental data have to be confronted. Such confrontation must take into consideration the uncertainties related to the experimental protocol, but also to the model. Statistical tools such as uncertainty and global sensitivity analysis are essential for this task. The uncertainty analysis estimates the robustness of the model, while the global sensitivity analysis identifies the most influential input(s) responsible for this robustness. However, these methods are not commonly used because of the complexity of hygrothermal models, and therefore the prohibitive simulation cost. This study presents a methodology for comparing the numerical and experimental data of a rammed earth wall subjected to varying temperature and relative humidity conditions. The main objectives are the investigation of the uncertainties impact, the estimation of the model robustness, and finally the identification of the input(s) responsible for the discrepancies between numerical and experimental data. To do so, a recent and low-cost global variance-based sensitivity method, named RBD-FAST, is applied. First, the uncertainty propagation through the model is calculated, then the sensitivity indices are estimated. They represent the part of the output variability related to each input variability. The output of interest is the vapour pressure in the middle of the wall to confront it to the experimental measurement. Good agreement is obtained between the experimental and numerical results. It is also highlighted that the sorption isotherm is the main factor influencing the vapour pressure in the material.

Inverse analysis of the residual stress in laser-assisted milling

In laser-assisted milling, higher temperature in shear zone softens the material potentially resulting in a shift of mean residual stress, which significantly affects the damage tolerance and fatigue performance of product. In order to guide the selection of laser and cutting parameters based on the preferred mean residual stress, inverse analysis is conducted by predicting residual stress based on guessed process parameters, which is defined as the forward problem, and applying iterative gradient search to find process parameters for next iteration, which is defined as the inverse problem. An analytical inverse analysis is therefore proposed for the mean residual stress in laser-assisted milling. The forward problem is solved by analytical prediction of mean residual stress after laser-assisted milling. The residual stress profile is predicted through the calculation of thermal stress, by treating laser beam as heat source, and plastic stress by first assuming pure elastic stress in loading process, then obtaining true stress with kinematic hardening followed by the stress relaxation. The variance-based recursive method is applied to solve inverse problem by updating process parameters to match the measured mean residual stress. Three cutting parameters including depth of cut, feed per tooth, and cutting speed, and two laser parameters including laser-tool distance and laser power, are updated with respected to the minimization of resulting residual stress and measurement in each iteration. Experimental measurements are referred on the laser-assisted milling of Ti–6Al–4 V and Si3N4. The percentage difference between experiments and predictions is less than 5% for both materials, and the selection is completed within 50 loops.

A new global sensitivity measure based on the elementary effects method

In the class of global sensitivity analysis methods, the elementary effects method focuses on identifying a few significant input parameters in a mathematical or engineering model including numerous input parameters with very few calculations. It was proved that the sensitivity index based on the elementary effects method is an appropriate proxy of the total sensitivity index based on the variance-based method. Nevertheless, it should be pointed out that two variance-based indices, i.e., the first-order and total sensitivity index, can denote the first-order and total effect of each input parameter to the model output respectively, while the elementary effects based sensitivity index can only reflect the total contribution of the input parameter to the model output, but cannot distinguish this effect resulting from each input parameter alone or the interactions between this input parameter and the others. Therefore, this paper proposes a first-order sensitivity index based on the elementary effects method by employing the high dimensional model representation. Next, the link between the first-order sensitivity index on the variance-based method and the proposed sensitivity index is explored. Subsequently, three computational algorithms, i.e., Monte Carlo simulation method, sparse grid method and dimensional reduction method, are developed to estimate the proposed sensitivity index.

Multivariate sensitivity analysis for dynamic models with both random and random process inputs

Dynamic models with both random and random process inputs are frequently used in engineering. However, sensitivity analysis (SA) for such models is still a challenging problem. This paper, therefore, proposes a new multivariate SA technique to aid the safety design of these models. The new method can decompose the SA of dynamic models into a series of SA of their principle components based on singular value decomposition, which will make the SA of dynamic models much more efficient. It is shown that the effect of both random and random process inputs on the uncertainty of dynamic output can be measured from their effects on both the distributions and directions of the principle components, based on which the individual sensitivities are defined. The generalized sensitivities are then proposed to synthesize the information that is spread between the principal components to assess the influence of each input on the entire uncertainty of dynamic output. The properties of the new sensitivities are derived and an efficient estimation algorithm is proposed based on unscented transformation. Numerical results are discussed with application to a hydrokinetic turbine blade model, where the new method is compared with the existing variance-based method.

Estimation of Link Choice Probabilities Using Monte Carlo Simulation and Maximum Likelihood Estimation Method

Studying the uncertainty of traffic flow takes significant importance for the transport planners because of the variation and fluctuation of temporal traffic flow on all links of the transport network. Uncertainty analysis of traffic flow requires identifying and characterizing two sets of parameters. The first set is the link choice set, which involves the Origin-Destination pairs using this link. The second set is the link choice probabilities set, which includes proportions of the travel demand for the Origin-Destination pairs in the link choice set. For this study, we developed a new methodology based on Monte Carlo simulation for link choice set and link choice probabilities in the context of route choice modeling. This methodology consists of two algorithms: In the first algorithm, we used the sensitivity analysis technique the variance-based method to identify the set of Origin-Destination pairs in each link. In the second algorithm, we used a Gaussian process based on the Maximum Likelihood framework to estimate the link choice probabilities. Furthermore, we applied the proposed methodology in a case study over multiple scenarios representing different traffic flow conditions. The results of this case study show high precision results with low errors' variances.The key contributions of this paper: First, the link choice set can be detected by using sensitivity analysis. Second, the link choice probabilities can be determined by solving an optimization problem in the Maximum likelihood framework. Finally, the prediction errors' parameters of traffic assignment model can be modeled as a Gaussian process.

Information requirements for multi-level-of-development BIM using sensitivity analysis for energy performance

The concept of multi-Level-of-Development (multi-LOD) modelling represents a flexible approach of information management and compilation in building information modelling (BIM) on a set of consistent levels. From an energy perspective during early architectural design, the refinement of design parameters by addition of information allows a more precise prediction of building performance. The need for energy-efficient buildings requires a designer to focus on the parameters in order of their ability to reduce uncertainty in energy performance to prioritise energy relevant decisions. However, there is no method for assigning and prioritising information for a particular level of multi-LOD. In this study, we performed a sensitivity analysis of energy models to estimate the uncertainty caused by the design parameters in energy prediction. This study allows to rank the design parameters in order of their influence on the energy prediction and determine the information required at each level of multi-LOD approach. We have studied the parametric energy model of different building shapes representing architectural design variation at the early design stage. A variance-based sensitivity analysis method is used to calculate the uncertainty contribution of each design parameter. The three levels in the uncertainty contribution by the group of parameters are identified which form the basis of information required at each level of multi-LOD BIM approach. The first level includes geometrical parameters, the second level includes technical specification and operational design parameters, and the third level includes window construction and system efficiency parameters. These findings will be specifically useful in the development of a multi-LOD approach to prioritise performance relevant decisions at early design phases.