Uncertain Input Factors Research Articles

An Improved Copula‐Based Framework for Efficient Global Sensitivity Analysis

AbstractGlobal sensitivity analysis (GSA) enhances our understanding of computational models and simplifies model parameter estimation. VarIance‐based Sensitivity analysis using COpUlaS (VISCOUS) is a variance‐based GSA framework. The advantage of VISCOUS is that it can use existing model input‐output data (e.g., water model parameters‐responses) to estimate the first‐ and total‐order Sobol’ sensitivity indices. This study improves VISCOUS by refining its handling of marginal densities of the Gaussian mixture copula model (GMCM). We then evaluate VISCOUS using three types of generic functions relevant to water system models. We observe that its performance depends on function dimension, input‐output data size, and non‐identifiability. Function dimension refers to the number of uncertain input factors analyzed in GSA, and non‐identifiability refers to the inability to estimate GMCM parameters. VISCOUS proves powerful in estimating first‐order sensitivity with a small amount of input‐output data (e.g., 200 in this study), regardless of function dimension. It always ranks input factors correctly in both first‐ and total‐order terms. For estimating total‐order sensitivity, it is recommended to use VISCOUS when the function dimension is not very high (e.g., less than 20) due to the challenge of producing sufficient input‐output data for accurate GMCM inferences (e.g., more than 10,000 data). In cases where all input factors are equally important (a rarity in practice), VISCOUS faces non‐identifiability issues that impact its performance. We provide a didactic example and an open‐source Python code, pyVISCOUS, for broader user adoption.

A Market-Driven Management Model for Renewable-Powered Undergrid Mini-Grids

Renewable-powered “undergrid mini-grids” (UMGs) are instrumental for electrification in developing countries. An UMG can be installed under a—possibly unreliable— main grid to improve the local reliability or the main grid may “arrive” and connect to a previously isolated mini-grid. Minimising costs is key to reducing risks associated with UMG development. This article presents a novel market-logic strategy for the optimal operation of UMGs that can incorporate multiple types of controllable loads, customer smart curtailment based on reliability requirements, storage management, and exports to and imports from a main grid, which is subject to failure. The formulation results in a mixed-integer linear programming model (MILP) and assumes accurate predictions of the following uncertain parameters: grid spot prices, outages of the main grid, solar availability and demand profiles. An AC hybrid solar-battery-diesel UMG configuration from Nigeria is used as a case example, and numerical simulations are presented. The load-following (LF) and cycle-charging (CC) strategies are compared with our predictive strategy and HOMER Pro’s Predictive dispatch. Results prove the generality and adequacy of the market-logic dispatch model and help assess the relevance of outages of the main grid and of spot prices above the other uncertain input factors. Comparison results show that the proposed market-logic operation approach performs better in terms of cost minimisation, higher renewable fraction and lower diesel use with respect to the conventional LF and CC operating strategies.

Developing an augmented onset model for a thermoacoustically-driven, pulse tube cryocooler

This paper aimed to develop an augmented onset model for a looped-branched, thermoacoustically-driven, pulse tube cryocooler based on the transfer matrix model, introducing a reliable, uncomplicated prediction of the onset features compared to a full transient simulation of the thermoacoustic field. Disciplined successive multiplication of the element's matrices extracted from the linear thermoacoustic equations along with the joint, boundary and periodic conditions establish an eigenvalue onset problem. The corresponding problem solutions are in line with the earlier experimental results for a looped-branched thermoacoustic system. Investigating multiple layouts with specific startup characteristics indicated the ability of a four-stage cryocooler driven by two engines at each stage to reach an onset temperature difference of 45 K at liquid nitrogen temperature. Furthermore, the Morris screening method was adopted to rank the uncertain input factors, followed by the Sobol sensitivity analysis to quantify the uncertainty of model outcomes. The sensitivity quantification highlights that the uncertainty in the gas equation-of-state, specific heat capacity, and the cold regenerator mesh number predominantly affect the onset features. Other influential factors include the dimensions of the hot and cold segments of the unit that respectively affect the onset temperature and the frequency.

Global sensitivity analysis of behavior of energy pile under thermo-mechanical loads

For the predictions and simulations of energy pile behavior under a combination of thermal and mechanical loads, with a complexity of parameters describing the energy pile, the surrounding soil and their interaction, modelers may be faced with the decision of whether it is better to spend more resource on determining the appropriate value of certain model parameters with high precision or on running more simulations to account for various uncertain input factors. In this study global sensitivity analysis is applied to explore the relative importance of the parameters of interest as model inputs and their contributions to the final results of the energy pile numerical model for different outputs. The interaction of uncertainties between different parameters is also analyzed with second order and total indices. Findings of this study indicate that the sensitivity of numerical energy pile predictions is more complex than previously thought. With a varying external forcing like the mechanical load or temperature change, the influence of input factor (e.g. model parameters) for the predictions of different spatially lumped model outputs is found to change but not always monotonically despite a monotonic variation of the output value. Spatial variability in the influence of the input factors which may be hidden by the spatially lumped analysis is also examined and inhomogeneous distribution of the input factor importance can be revealed along the whole length of the energy pile. The input factors that modelers should prioritize will not only differ depending on the assessed model output, but also on the location of the output and the surrounding circumstances which provide external loads and thermal effects.

Parameter uncertainty drives important incongruities between simulated chlorophyll-a and phytoplankton functional group dynamics in a mechanistic management model

Mechanistic phytoplankton functional group (PFG) models are used to develop water quality targets designed to mitigate cyanobacteria blooms, but it remains unclear whether PFG models adequately simulate cyanobacteria dynamics as most are evaluated against observations of chlorophyll-a instead of PFG biomass. To address this challenge, we analyzed an application of CE-QUAL-ICM, a 3D mechanistic PFG model used by water managers and modelers. Global Sensitivity Analysis was employed to assess the sensitivity of modeled chlorophyll-a, cyanobacteria biomass, and eukaryotic phytoplankton biomass to 42 uncertain input factors in CE-QUAL-ICM's PFG growth and loss functions. Results revealed that parameterization of CE-QUAL-ICM captured bloom variation but underpredicted bloom peaks, and simulated chlorophyll-a with greater skill than PFG biomass. Additionally, when run across realistic ranges of PFG parameter values, model outputs were highly sensitive to chlorophyll-to-carbon ratios and phosphorus uptake parameters, indicating that these factors should be the focus of targeted parameterization efforts.

Distribution-based sensitivity analysis from a generic input-output sample

In a previous paper we introduced a distribution-based method for Global Sensitivity Analysis (GSA), called PAWN, which uses cumulative distribution functions of model outputs to assess their sensitivity to the model's uncertain input factors. Over the last three years, PAWN has been employed in the environmental modelling field as a useful alternative or complement to more established variance-based methods. However, a major limitation of PAWN up to now was the need for a tailored sampling strategy to approximate the sensitivity indices. Furthermore, this strategy required three tuning parameters whose optimal choice was rather unclear. In this paper, we present an alternative approximation procedure that tackles both issues and makes PAWN applicable to a generic sample of inputs and outputs while requiring only one tuning parameter. The new implementation therefore allows the user to estimate PAWN indices as complementary metrics in multi-method GSA applications without additional computational cost.

Development of a multi-objective decision-making method to evaluate correlated decarbonization measures under uncertainty – The example of international shipping

Shipping is a major contributor to total global CO2 emissions. In recent years, various operational and technical measures have been proposed to decarbonize the shipping sector. The cost-effectiveness of these mitigation measures is usually evaluated on an individual basis. However, the cost-effectiveness of individual measures could be influenced by the presence of other measures (when selected simultaneously) used to meet the decarbonization targets. As such, it is important to take into consideration such interdependencies when ranking and selecting the mitigation measures. In response to this problem, we propose a method to systematically rank and select the mitigation measures whose cost and carbon abatement potentials depend on the presence of one another. The proposed method is also capable of accounting for uncertain input factors, such as implementation costs and fuel costs. Through a case study considering a set of 14 measures, findings from our study demonstrate the importance of considering the interdependencies of these mitigation measures. We further conduct a sensitivity analysis, in order to ascertain the influence of the relevant input parameters.

Kriging-based inverse uncertainty quantification of nuclear fuel performance code BISON fission gas release model using time series measurement data

In nuclear reactor fuel performance simulation, fission gas release (FGR) and swelling involve treatment of several complicated and interrelated physical processes, which inevitably depend on uncertain input parameters. However, the uncertainties associated with these input parameters are only known by “expert judgment”. In this paper, inverse Uncertainty Quantification (UQ) under the Bayesian framework is applied to BISON code FGR model based on Risø-AN3 time series experimental data. Inverse UQ seeks statistical descriptions of the uncertain input parameters that are consistent with the available measurement data. It always captures the uncertainties in its estimates rather than merely determining the best-fit values. Kriging metamodel is applied to greatly reduce the computational cost during Markov Chain Monte Carlo sampling.We performed a dimension reduction for the FGR time series data using Principal Component Analysis. We also projected the original FGR time series measurement data onto the PC subspace as “transformed experiment data”. A forward uncertainty propagation based on the posterior distributions shows that the agreement between BISON simulation and Risø-AN3 time series measurement data is greatly improved. The posterior distributions for the uncertain input factors can be used to replace the expert specifications for future uncertainty/sensitivity analysis.

Matching decision method for knowledgeable manufacturing system and its production environment

To secure the quick response of knowledgeable manufacturing system (KMS) to the dynamic production environment and its desirable adaptability and competitiveness, we propose a matching decision method that is based on the improved support vector machine (ISVM for short), and the production environment. Taking into account the uncertainty and fuzziness of the production environment, the triangular fuzzy numbers are introduced to represent the uncertain input factors. Independent penalty coefficients are employed for different categories to address the problem of unbalanced samples. To meet the requirement for classifying small, uncertain input, and unbalanced samples, an improved SVM model based on triangular fuzzy theory is put forward. Considering the mutagenic factor and dynamic weight, we improve the particle swarm algorithm to optimize the model parameters. The matching categories of KMS and dynamic production environment are defined, and the corresponding matching decision method based on ISVM model is built. Case study shows that the proposed ISVM matching decision method is feasible and effective.

Quantifying the importance of spatial resolution and other factors through global sensitivity analysis of a flood inundation model

AbstractWhere high‐resolution topographic data are available, modelers are faced with the decision of whether it is better to spend computational resource on resolving topography at finer resolutions or on running more simulations to account for various uncertain input factors (e.g., model parameters). In this paper we apply global sensitivity analysis to explore how influential the choice of spatial resolution is when compared to uncertainties in the Manning's friction coefficient parameters, the inflow hydrograph, and those stemming from the coarsening of topographic data used to produce Digital Elevation Models (DEMs). We apply the hydraulic model LISFLOOD‐FP to produce several temporally and spatially variable model outputs that represent different aspects of flood inundation processes, including flood extent, water depth, and time of inundation. We find that the most influential input factor for flood extent predictions changes during the flood event, starting with the inflow hydrograph during the rising limb before switching to the channel friction parameter during peak flood inundation, and finally to the floodplain friction parameter during the drying phase of the flood event. Spatial resolution and uncertainty introduced by resampling topographic data to coarser resolutions are much more important for water depth predictions, which are also sensitive to different input factors spatially and temporally. Our findings indicate that the sensitivity of LISFLOOD‐FP predictions is more complex than previously thought. Consequently, the input factors that modelers should prioritize will differ depending on the model output assessed, and the location and time of when and where this output is most relevant.

Application of experimental design to estimate hydrocarbons initially in place

When assessing a reservoir’s Hydrocarbon Initially In Place (HIIP) volumes there are often many uncertain input factors. If they are discretized into low, mid and high case scenarios, this can result in tens of thousands of possible combinations of factors and it is often necessary to reduce the amount of uncertain factors to a manageable number. This can reduce the range of model outcomes, and the confidence in the predicted volumes will be overestimated. Experimental design allows a reduced representative set of models to be constructed for uncertainty analysis when it would take too long to construct all possible realizations. This paper uses a case study to demonstrate a refined application of experimental design, whereby uncertain factors were first identified and experts were consulted to specify high, mid and low values with associated probabilities. The analysis was completed in two parts: a screening phase, whereby non-significant factors were eliminated; and an optimization phase, whereby a limited number of model runs were used to train a proxy model for use in a Monte Carlo procedure to generate a probability distribution of HIIP. The key advantage of the method is the comprehensive treatment of uncertainty with a reduced amount of modelling effort.

Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index

Abstract Variance based methods have assessed themselves as versatile and effective among the various available techniques for sensitivity analysis of model output. Practitioners can in principle describe the sensitivity pattern of a model Y = f ( X 1 , X 2 , … , X k ) with k uncertain input factors via a full decomposition of the variance V of Y into terms depending on the factors and their interactions. More often practitioners are satisfied with computing just k first order effects and k total effects, the latter describing synthetically interactions among input factors. In sensitivity analysis a key concern is the computational cost of the analysis, defined in terms of number of evaluations of f ( X 1 , X 2 , … , X k ) needed to complete the analysis, as f ( X 1 , X 2 , … , X k ) is often in the form of a numerical model which may take long processing time. While the computational cost is relatively cheap and weakly dependent on k for estimating first order effects, it remains expensive and strictly k-dependent for total effect indices. In the present note we compare existing and new practices for this index and offer recommendations on which to use.

Estimating uncertainty associated with water stages from a single SAR image

It is the goal of remote sensing to infer information about objects or a natural process from a remote location. This invokes that uncertainty in measurement should be viewed as central to remote sensing. In this study, the uncertainty associated with water stages derived from a single SAR image for the Alzette (G.D. of Luxembourg) 2003 flood is assessed using a stepped GLUE procedure. Main uncertain input factors to the SAR processing chain for estimating water stages include geolocation accuracy, spatial filter window size, image thresholding value, DEM vertical precision and the number of river cross sections at which water stages are estimated. Initial results show that even with plausible parameter values uncertainty in water stages over the entire river reach is 2.8 m on average. Adding spatially distributed field water stages to the GLUE analysis following a one-at-a-time approach helps to considerably reduce SAR water stage uncertainty (0.6 m on average) thereby identifying appropriate value ranges for each uncertain SAR water stage processing factor. For the GLUE analysis a Nash-like efficiency criterion adapted to spatial data is proposed whereby acceptable SAR model simulations are required to outperform a simpler regression model based on the field-surveyed average river bed gradient. Weighted CDFs for all factors based on the proposed efficiency criterion allow the generation of reliable uncertainty quantile ranges and 2D maps that show the uncertainty associated with SAR-derived water stages. The stepped GLUE procedure demonstrated that not all field data collected are necessary to achieve maximum constraining. A possible efficient way to decide on relevant locations at which to sample in the field is proposed. It is also suggested that the resulting uncertainty ranges and flood extent or depth maps may be used to evaluate 1D or 2D flood inundation models in terms of water stages, depths or extents. For this, the extended GLUE approach, which copes with the presence of uncertainty in the observed data, may be adopted.

A dynamic model for cost-benefit analyses of foot-and-mouth disease control strategies

An integrated model for the personal computer is presented, in which a variety of preventive and control strategies with respect to foot-and-mouth disease (FMD) in Dutch cattle and pig herds were examined economically. Special attention is given to the way in which losses due to export bans are determined. Export bans would occur as a result of an outbreak of FMD. Annual costs for the Netherlands would be reduced considerably if the yearly vaccinations were stopped. This conclusion holds even if more pessimistic values are used for some major uncertain input factors. The PC model is flexible with regard to input values, making it possible to fit different conditions.