Identifying parametric controls and dependencies in integrated assessment models using global sensitivity analysis

Integrated assessment models for climate change (IAMs) couple representations of economic and natural systems to identify and evaluate strategies for managing the effects of global climate change. In this study we subject three policy scenarios from the globally-aggregated Dynamic Integrated model of Climate and the Economy IAM to a comprehensive global sensitivity analysis using Sobol' variance decomposition. We focus on cost metrics representing diversions of economic resources from global world production. Our study illustrates how the sensitivity ranking of model parameters differs for alternative cost metrics, over time, and for different emission control strategies. This study contributes a comprehensive illustration of the negative consequences associated with using a priori expert elicitations to reduce the set of parameters analyzed in IAM uncertainty analysis. The results also provide a strong argument for conducting comprehensive model diagnostics for IAMs that explicitly account for the parameter interactions between the coupled natural and economic system components.     

A General Probabilistic Framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study

The present study proposes a General Probabilistic Framework (GPF) for uncertainty and global sensitivity analysis of deterministic models in which, in addition to scalar inputs, non-scalar and correlated inputs can be considered as well. The analysis is conducted with the variance-based approach of Sobol/Saltelli where first and total sensitivity indices are estimated. The results of the framework can be used in a loop for model improvement, parameter estimation or model simplification. The framework is applied to SWAP, a 1D hydrological model for the transport of water, solutes and heat in unsaturated and saturated soils. The sources of uncertainty are grouped in five main classes: model structure (soil discretization), input (weather data), time-varying (crop) parameters, scalar parameters (soil properties) and observations (measured soil moisture). For each source of uncertainty, different realizations are created based on direct monitoring activities. Uncertainty of evapotranspiration, soil moisture in the root zone and bottom fluxes below the root zone are considered in the analysis. The results show that the sources of uncertainty are different for each output considered and it is necessary to consider multiple output variables for a proper assessment of the model. Improvements on the performance of the model can be achieved reducing the uncertainty in the observations, in the soil parameters and in the weather data. Overall, the study shows the capability of the GPF to quantify the relative contribution of the different sources of uncertainty and to identify the priorities required to improve the performance of the model. The proposed framework can be extended to a wide variety of modelling applications, also when direct measurements of model output are not available.     

Untangling drivers of species distributions: Global sensitivity and uncertainty analyses of MaxEnt

Untangling drivers of systems and uncertainty for species distribution models (SDMs) is important to provide reliable predictions that are useful for conservation campaigns. This is particularly true for species whose habitat is threatened by climate change that enhances the uncertainty in future species distributions. Global sensitivity and uncertainty analyses (GSUA) is a robust method to globally investigate the uncertainty of SDMs and the importance of species distributions' drivers in space and time.Here we apply GSUA to MaxEnt that is one of the popular presence-only SDMs. We consider the Snowy Plover (Charadrius alexandrinus nivosus) (SP) in Florida that is a shorebird whose habitat is affected by sea level rise due to climate change. The importance of intrinsic and exogenous input factors to the uncertainty of the species distribution is evaluated for MaxEnt. GSUA is applied for three projections of the habitat (2006, 2060, and 2100) according to the A1B sea level rise scenario. The large land cover variation determines a moderate decrease in habitat suitability in 2060 and 2100 prospecting a low risk of decline for the SP. The regularization parameter for the environmental features, the uncertainty into the classification of salt-marsh, transitional marsh, and ocean beach, and the maximum number of iterations for the model training are in this order the most important input factors for the average habitat suitability. These results are related to the SP but, in general MaxEnt appears as a very non-linear model where uncertainty mostly derives from the interactions among input factors.The uncertainty of the output is a species-specific variable. Thus, GSUA need be performed for each case considering local exogenous input factors of the model. GSUA allows quantitative informed species-management decisions by providing scenarios with controlled uncertainty and confidence over factors' importance that can be used by resource managers.     

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.     

非线性末制导系统参数灵敏度分析

末制导系统参数随着飞行环境及飞行条件的改变而存在摄动,针对这一问题本文提出根据动态灵敏度来分析参数摄动对脱靶量的影响.基于伴随法推导出与系统动态方程相同规模的伴随方程,并通过一次伴随求解计算得到脱靶量对所有可调参数及摄动参数的动态灵敏度,有效的提高了计算效率.传统的直接分析法是将系统状态变量直接对参数变量进行微分,需要对每个参数变量求解一组代数或微分方程,对于状态变量及参数变量较多的情况效率较低.本文基于两种方法对末制导系统的参数灵敏度进行分析,分析结果揭示了参数摄动对脱靶量的影响程度,较小的参数灵敏度为提高系统的鲁棒性提供了依据.     

Data envelopment analysis of reservoir system performance

In long-term performance analyses of water systems with surface reservoirs for different operating scenarios, the analyst (or decision maker) is faced with two connected problems: (1) how to handle the extensive output of the simulation model and derive information on the scenarios scores for a prescribed set of performance criteria, and (2) how to compare scenarios in a multi-criterial sense while identifying the most desired. The data sets may overburden the analyst, while an evaluating procedure may be subjective due to personal preferences, attitudes, knowledge and miscellaneous factors. The data envelopment analysis (DEA) approach proposed here seems to be reliable in treating these situations, and sufficiently objective in evaluating and ranking the scenarios. Certain performance indices are defined as evaluating criteria in a standard multi-criterial sense, and then virtually divided into scenarios' output and input measures. By considering scenarios as product units, the DEA optimizes the weights of inputs and outputs, computes productivity efficiency for each unit, and rank them appropriately. Omitting the analyst's personal judgment on the technical parameters that describe system's performance restricts, in this way, the influence of the decision maker. A case study application on the reservoir system in Brazil proved that a methodological connection for solving decision problems with discrete alternatives really exists between the DEA and standard multi-criteria methods.     

Global sensitivity analysis of large-scale numerical landslide models based on Gaussian-Process meta-modeling

Large-scale landslide prediction is typically based on numerical modeling, with computer codes generally involving a large number of input parameters. Addressing the influence of each of them on the final result and providing a ranking procedure may be useful for risk management purposes. This can be performed by a variance-based global sensitivity analysis. Nevertheless, such an analysis requires a large number of computer code simulations, which appears impracticable for computationally demanding simulations, with computation times ranging from several hours to several days. To overcome this difficulty, we propose a “meta-model”-based strategy consisting in replacing the complex simulator by a “statistical approximation” provided by a Gaussian-process (GP) model. This allows computation of sensitivity measures from a limited number of simulations. For illustrative purposes, the proposed methodology is used to rank in terms of importance the properties of the elastoplastic model describing the complex behavior of the slip surface in the La Frasse landslide (Switzerland). One limitation of the GP-based methodology is that the computation of sensitivity measures is associated with uncertainty as the simulator is approximated using a training sample of small size, i.e., a limited knowledge on the “true” simulator. This source of uncertainty can be taken into account by treating the GP model from a Bayesian perspective. This provides the full posterior probability distribution associated with the sensitivity measures, which can be summarized by a confidence interval to outline the regions where the GP model is “unsure.” We show that this methodology is able to provide useful guidelines for the practical decision-making process and suggest further site investigations.     

不确定性参数灵敏度分析的随机响应面法

动力学和控制系统中往往包含有不确定性参数,为此提出了一种基于随机响应面的不确定性参数灵敏度分析方法,以量化参数不确定性对响应变异性的影响.文中首先利用随机响应面建立不确定性参数和响应之间的表达式,然后通过求偏导方式推导参数的灵敏度系数,该系数综合反映了参数均值和标准差的影响.最后通过一根包含几何、材料不确定参数的数值梁来验证所提出方法,并与方差分析法结果进行了比较.     

Extending a global sensitivity analysis technique to models with correlated parameters

The identification and representation of uncertainty is recognized as an essential component in model applications. One important approach in the identification of uncertainty is sensitivity analysis. Sensitivity analysis evaluates how the variations in the model output can be apportioned to variations in model parameters. One of the most popular sensitivity analysis techniques is Fourier amplitude sensitivity test (FAST). The main mechanism of FAST is to assign each parameter with a distinct integer frequency (characteristic frequency) through a periodic sampling function. Then, for a specific parameter, the variance contribution can be singled out of the model output by the characteristic frequency based on a Fourier transformation. One limitation of FAST is that it can only be applied for models with independent parameters. However, in many cases, the parameters are correlated with one another. In this study, we propose to extend FAST to models with correlated parameters. The extension is based on the reordering of the independent sample in the traditional FAST. We apply the improved FAST to linear, nonlinear, nonmonotonic and real application models. The results show that the sensitivity indices derived by FAST are in a good agreement with those from the correlation ratio sensitivity method, which is a nonparametric method for models with correlated parameters.     

深度不确定环境下的决策分析方法—–研究现状与展望

复杂、重大的决策活动经常会面临深度不确定的决策环境,其决策难度和风险远超一般不确定环境下的决策。自21世纪以来,对深度不确定环境下决策分析方法的研究已成为决策分析领域新的重要方向之一。对此,首先梳理了该领域的研究现状,总结了深度不确定环境下决策问题的特征和难点,分类阐述了4种主要方法的起源与发展、核心思想、实现步骤和典型应用;然后进行了案例分析;最后展望了该领域未来的研究方向。     

Global sensitivity analysis of outputs over rice-growth process in ORYZA model

Dynamic crop models usually have a complex structure and a large number of parameters. Those parameter values usually cannot be directly measured, and they vary with crop cultivars, environmental conditions and managements. Thus, parameter estimation and model calibration are always difficult issues for crop models. Therefore, the quantification of parameter sensitivity and the identification of influential parameters are very important and useful. In this work, late-season rice was simulated with meteorological data in Nanchang, China. Furthermore, we conducted a sensitivity analysis of 20 selected parameters in ORYZA_V3 using the Extended FAST method. We presented the sensitivity results for four model outputs (LAI, WAGT, WST and WSO) at four development stages and the results for yield. Meanwhile, we compared the differences among the sensitivity results for the model outputs simulated in cold, normal and hot years. The uncertainty of output variables derived from parameter variation and weather conditions were also quantified. We found that the development rates, RGRLMN and FLV0.5 had strong effects on all model outputs in all conditions, and parameters WGRMX and SPGF had relative high effects on yield in cold year. Only LAI was sensitive to ASLA. Those influential parameters had unequal effects on different outputs, and they had different effects at four development stages. With the interaction effects of parameter variation and different weather conditions, the uncertainty of model outputs varied significantly. However, the weather conditions had negligible effects on the identification of influential parameters, although they had slight effects on the ranks of the parameters' sensitivity for outputs in the panicle-formation phase and the grain-filling phase, including yield at maturity. The results suggested that the influential parameters should be recalibrated in priority and fine-tuned with higher accuracy during model calibration.     

Robust stability analysis of systems with real parametric uncertainty: A global optimization approach

This paper presents an optimization framework for the robustness analysis of linear and nonlinear systems with real parameter uncertainty. For linear systems, a nonlinear programming formulation for the exact calculation of the stability margin is presented. The potential of decomposition-based global optimization methods for the solution of this nonconvex problem is discussed. Next the concept of the stability margin is extended to a class of nonlinear systems. A nonlinear stability margin and a uniqueness margin are defined to address the effect of parametric uncertainty on the stability of a particular steady state, as well as on the number of steady states of the system. This analysis allows for the derivation of necessary and sufficient conditions for robust stability and robust uniqueness of the steady state of the system in the presence of parametric uncertainty.     

基于面积重叠法的概率盒全局灵敏度计算分析

针对随机与认知混合不确定性的概率盒灵敏度分析问题,提出一种利用概率盒缩减前后重叠面积作为不确定性度量的全局灵敏度分析方法.混合不确定性在航空航天仿真系统中广泛存在,概率盒方法用于随机与认知混合不确定性的表征在学术界已被广泛应用.首先,介绍传统概率盒灵敏度分析的不确定性缩减法理论,在此基础上,进一步考虑概率盒在位置和形状上的偏移量;然后,通过计算缩减前后的概率盒面积重叠量来表征各输入不确定性的影响程度,阐述其实施步骤;最后,通过数值算例对所提出方法与传统不确定性缩减方法进行全局灵敏度分析的对比和验证,并应用于发动机总体性能仿真计算灵敏度排序.研究结果表明,所提出面积重叠方法比传统不确定性缩减法适用范围更广,计算结果更准确.     

A parameter estimation and identifiability analysis methodology applied to a street canyon air pollution model

Mathematical models are increasingly used in environmental science thus increasing the importance of uncertainty and sensitivity analyses. In the present study, an iterative parameter estimation and identifiability analysis methodology is applied to an atmospheric model – the Operational Street Pollution Model (OSPM^®). To assess the predictive validity of the model, the data is split into an estimation and a prediction data set using two data splitting approaches and data preparation techniques (clustering and outlier detection) are analysed. The sensitivity analysis, being part of the identifiability analysis, showed that some model parameters were significantly more sensitive than others. The application of the determined optimal parameter values was shown to successfully equilibrate the model biases among the individual streets and species. It was as well shown that the frequentist approach applied for the uncertainty calculations underestimated the parameter uncertainties. The model parameter uncertainty was qualitatively assessed to be significant, and reduction strategies were identified.     

基于EFAST方法的SEBS模型参数全局敏感性分析

应用高效、稳健的EFAST方法,以黑河流域盈科绿洲站为例,从3个方面对SEBS模型的参数敏感性进行了分析:分别以感热通量(H)、潜热通量(λE)、蒸发比(fr)作为SEBS模型的输出结果,分析其对12个输入参数的敏感性;利用气象数据驱动模型,分析H、λE和fr对6个地表特征参数的敏感性;分析了参数取值范围对敏感性分析结果的影响。研究结果表明:H、λE与fr都对参考高度处的气温和风速、地表温度以及植被特征参数的敏感性较高。参数间相互作用对H、λE的间接影响很小,而对fr的影响较大。当气象输入参数确定时,6个地表参数中地表温度对模型输出的直接贡献最大,其主敏感度指数接近0.6。参数采样范围不同时,模型输入参数的敏感性表现不同。     

Selection of outputs for distributed parameter systems by identifiability analysis in the time-scale domain

A method of sensor location selection is introduced for distributed parameter systems. In this method, the sensitivities of spatial outputs to model parameters are computed by a model and transformed via continuous wavelet transforms into the time-scale domain to characterise the shape attributes of output sensitivities and accentuate their differences. Regions are then sought in the time-scale plane wherein the wavelet coefficient of an output sensitivity surpasses all the others’ as indication of the output sensitivity’s distinctness. This yields a comprehensive account of identifiability each output provides to the model parameters as the basis of output selection. The proposed output selection strategy is demonstrated for a numerical case of pollutant dispersion by advection and diffusion in a two-dimensional area.     

Applying undistorted neural network sensitivity analysis in iris plant classification and construction productivity prediction

The present research focuses on the development and applications of a sensitivity analysis technique on multi-layer perceptron (MLP) neural networks (NN), which eliminates distortions on the sensitivity measures due to dissimilar input ranges with different units of measure for input features of both continuous and symbolic types in NNs practical engineering applications. The effect of randomly splitting the dataset into training and testing sets on the stability of a MLP networks sensitivity is also observed and discussed. The IRIS-UCI dataset and a real concreting productivity dataset serve as case studies to illustrate the validity of the undistorted sensitivity measure proposed. The results of the two case studies lead to the conclusion that the sensitivity measures accounting for the relevant input range for each input feature are more accurate and effective for revealing the relevance of each input feature and identifying less significant ones for potential feature reduction on the model. The MLP NN model obtained in such a way can give not only high prediction accuracy, but also valid sensitivity measures on its input features, and hence can be deployed as a predictive tool for supporting the decision process on new scenarios within the engineering problem domain.     

EFAST Method for Global Sensitivity Analysisof Remote Sensing Model’s Parameters

Sensitivity analysis for parameters of remote sensing physical models is a prerequisite for inversion.The EFAST(Extended Fourier Amplitude Sensitivity Test)as a global sensitivity analysis method,can analyze not only a single parameter’s sensitivity but also the coupling effects among parameters.It is usually applied to analyse parameters’ sensitivity of the high-dimensional nonlinear models.In this paper,the SAIL model is taken as an example,the EFAST method and the field measured data of winter wheat in Shunyi district in 2001 were applied to analyze the model parameters’ sensitivity throughout the growing season and in different growth stages respectively.The results are compared with those of the USM (Uncertainty and Sensitivity Matrix) method.The results show that either the EFAST or the USM method for parameters’ sensitivity analysis of the SAIL model is feasible;but the EFAST method,which takes into account of the coupling effects among all the parameters and the analysis result is global,compared to the USM method,is more objective and comprehensive.     

Comparison of variance-based and moment-independent global sensitivity analysis approaches by application to the SWAT model

Global Sensitivity Analysis (GSA) is an essential technique to support the calibration of environmental models by identifying the influential parameters (screening) and ranking them.In this paper, the widely-used variance-based method (Sobol') and the recently proposed moment-independent PAWN method for GSA are applied to the Soil and Water Assessment Tool (SWAT), and compared in terms of ranking and screening results of 26 SWAT parameters. In order to set a threshold for parameter screening, we propose the use of a “dummy parameter”, which has no influence on the model output. The sensitivity index of the dummy parameter is calculated from sampled data, without changing the model equations. We find that Sobol' and PAWN identify the same 12 influential parameters but rank them differently, and discuss how this result may be related to the limitations of the Sobol' method when the output distribution is asymmetric.