Sensitivity Analysis Framework Research Articles

Diagnostic Framework for Evaluating How Parametric Uncertainty Influences Agro‐Hydrologic Model Projections of Crop Yields Under Climate Change

AbstractDespite the prevalence of climate change assessments of crop yields, there are significant limits to our understanding of how parametric uncertainty in the underlying agro‐hydrologic models as well as the stationarity assumptions tacit to their commonly employed calibration procedures are influencing projections. This study addresses this knowledge gap by clarifying how parametric uncertainty in agro‐hydrologic models influences yield projections under changing future climate. We focus on rain‐fed winter wheat systems in the drylands of United States Pacific Northwest. We use a tightly coupled agro‐hydrologic model, VIC‐CropSyst, as a representative of this class of models. Our contributed diagnostic global sensitivity analysis framework identifies differences in how influential factors (e.g., temperature during early growth stages or the growing degree‐day required to reach peak leaf area index) vary across zones during historical and future periods. Our results show that the dominant parametric controls for yield projection and their sensitivities change subject to agro‐climatic zones and differences in the specific temperature‐precipitation trends in future climate scenarios. Our results also indicate that the stationarity assumptions tacit to using historical observations to calibrate agro‐hydrologic model parameters and their subsequent use in future yield projections may introduce significant bias. Employing the stationarity assumption in future projections problematically ignores how shifts in climate influence the relative dominance of underlying agro‐hydrologic processes in the model. This study's contributed diagnostic exploratory modeling framework has promise for advancing our understanding of how calibration, parametric uncertainties, and climate induced changes in the dominance of model biophysical processes shape crop yield projections.

Uncertainty quantification of wind turbine airfoil aerodynamics with geometric uncertainty

An artificial neural network based reduced order model (ROM) is developed to predict the load coefficients and performance of wind turbine airfoils. The model is trained using a representative database of 972 wind turbine airfoil shapes generated by perturbing the design parameters in each of 12 baseline airfoils defining commercially relevant modern wind turbines. The predictions from our ROM show excellent agreement with the CFD data, with a 99th percentile maximum errors of 0.03 in lift-coefficient, 2 in lift-to-drag ratio and 0.002 in pitching moment coefficient. A Monte-Carlo based uncertainty quantification (UQ) and global sensitivity analysis (GSA) framework is developed using this computationally economical ROM. Using UQ, we observed the stall behavior to be very sensitive to geometric uncertainty, with more than 10% deviation in lift coefficient associated to 5% deviation in geometric features. Sobol’s analysis is used to identify the most influencing geometric feature for the stall behavior to be concentrated at the maximum thickness location on the airfoil suction surface.

Opening the Black Box: Bootstrapping Sensitivity Measures in Neural Networks for Interpretable Machine Learning

Artificial neural networks are powerful tools for data analysis, particularly in the context of highly nonlinear regression models. However, their utility is critically limited due to the lack of interpretation of the model given its black-box nature. To partially address the problem, the paper focuses on the important problem of feature selection. It proposes and discusses a statistical test procedure for selecting a set of input variables that are relevant to the model while taking into account the multiple testing nature of the problem. The approach is within the general framework of sensitivity analysis and uses the conditional expectation of functions of the partial derivatives of the output with respect to the inputs as a sensitivity measure. The proposed procedure extensively uses the bootstrap to approximate the test statistic distribution under the null while controlling the familywise error rate to correct for data snooping arising from multiple testing. In particular, a pair bootstrap scheme was implemented in order to obtain consistent results when using misspecified statistical models, a typical characteristic of neural networks. Numerical examples and a Monte Carlo simulation were carried out to verify the ability of the proposed test procedure to correctly identify the set of relevant features.

Aerodynamic shape optimization using a time spectral coupled adjoint for nonlinear aeroelastic problems

In this work, prediction of flutter and Limit Cycle Oscillations (LCO) for the aircraft wing has been carried out using a coupled, time spectral computational fluid dynamics (CFD) and computational structural dynamics (CSD) method. Flutter related shape design has also been carried out using a coupled, adjoint based sensitivity analysis framework. A discrete adjoint solver was developed in time-spectral form to calculate coupled sensitivity of the dynamic aeroelastic motion. The total structural energy was constrained at different levels to determine the flutter onset conditions or different LCO solutions. Compared to the time-marching approach, the time-spectral method not only enables faster convergence for unsteady problems, but also leads to significant improvement in implementation of adjoint based sensitivity analysis. Unlike the time-marching approach, there is no high memory requirement for time-spectral approach. The proposed method was applied to a pitch-plunge airfoil section at transonic flight conditions. The flutter and LCO results showed great agreements with time-marching results. The adjoint based sensitivity values were validated by finite difference based results, showing great agreement with errors less than 2%. Finally, aerodynamic shape optimization was carried out with the design objective of maximizing the flutter velocity, with and without constraint on the drag coefficient, respectively. Significant increase in flutter boundary velocity was observed in both cases.

Revisiting driving factor influences on uncertain cascading disaster evolutions: From perspective of global sensitivity

For the simulation of a cascading disaster (or failure), the quantitative relationship between the disaster level and the parameters that define the driving factors of the cascade dynamics assist in identifying the critical factors and their thresholds to suppress the disaster outbreak. The variation of the disaster level, as well as the synchronous influences of all parameters and their interactions on this variation, conditional on global uncertain parameters, have long been neglected in previous analysis paradigm. This study revisited these issues using a global sensitivity analysis framework based on the extended Fourier amplitude sensitivity test (EFAST). The demonstrative experiment on a disaster causality model demonstrated that the uniform distribution of each parameter with bounds at only ± 20% of their default could increase the disaster level by thousands times. However, the individual or interactive influence of a small fraction of the parameters dominated this variation, and the influence of each parameter was significantly time-varying and different from each other. The disaster evolution and parameter influence on each network component were significantly affected by the propagation structure and distance from the initial disturbance. A comparison with the past research paradigm verified the merit of the EFAST, which acquires the time-dependent influences of all parameters and their interactions in a synchronous manner. This capability makes this method superior to instruct interventions on disaster cascade by identifying the influential driving factors.

A sustainable circular economic supply chain system with waste minimization using 3D printing and emissions reduction in plastic reforming industry

A circular supply chain consists of emission and wastes minimization technologies with a remarkable gain in profit, which is the aim of any industry that is concerned about environmental conservation. One of the most critical hurdles to the transition to sustainability is waste management. This study proposes a circular sustainable integrated model in a plastic reforming industry with investment in 3D printing techniques to minimize waste, emission reduction, and ordering cost reduction and it led to optimal profit. The customer's demand and the unit profit depend on the circularity index of the item. This paper looked at three scenarios with partial backlogging: (a) linear demand versus linear unit profit; (b) linear demand versus exponential unit profit; and (c) linear demand versus logistic unit profit. An algorithm was used to optimize the profit of the plastic reforming industry with optimal values of ordering quantity, circularity index, and investment in waste minimization, emission reduction, and ordering cost under carbon cap policy. This model establishes that the plastic reforming industry will get more profit and an optimal level of circularity index when it works with high efficiency of emission and waste minimization technologies under low investment, a rise in the carbon tax, and less opportunity cost. Sensitivity analysis and managerial framework in the plastic reforming industry were given to realize the sensitivity of decision variables with variation in key parameters.

Robust fuzzy gain scheduling power control of a generation IV nuclear reactor

Gen-IV nuclear reactors are deemed to actively participate in the load following operations in order to meet the ever increasing energy demands. Robust fuzzy gain scheduling is proposed in this work as an advanced and efficient control strategy for the power cycling of the BREST design of lead cooled fast reactors (LFR). To this end, a reasonably accurate coupled thermo-neutronic simulator is developed at first. System identification techniques are employed thereafter to extract a multi-model set at various operating levels relying on the data obtained from this simulator. Uncertainties incurred as a result of the statistically based identification schemes are moreover accounted for using a narrow band (99%) confidence level for the determined model parameters. A set of robust controllers are contrived through a mixed sensitivity analysis framework and are blended afterwards by way of a fuzzy inference mechanism to appropriately schedule this regulation practice with the reactor power level. Certain load following scenarios are finally examined wherein the closed loop system exhibits an efficient and quite feasible control attempt.

Uncertainty quantification and global sensitivity analysis of composite wind turbine blades

In this paper, a framework for uncertainty quantification (UQ) and global sensitivity analysis (GSA) of composite wind turbine blades is presented. Because of the presence of uncertainties, the performance and reliability of wind turbine blades are adversely affected. Uncertainties must therefore be accounted for during the design phase. However, performing UQ of composite blades while considering a large number of random parameters is computationally intensive. To make the process tractable, this work is based on an approach referred to as polynomial chaos expansion (PCE) with l1-minimization. PCE also enables one to perform GSA to assess the relative importance of random parameters using Sobol Indices. This article also introduces an anisotropic formulation of PCE for dimension adaptive basis expansion. In addition, the UQ framework can handle random inputs with arbitrary distributions as well as spatial variations of material and geometric properties using Karhunen–Loève expansion. The presented framework was applied to three composite wind turbine blade problems – modal analysis, failure analysis, and buckling analysis – by considering the randomness in material and geometric parameters as well as loading conditions. The test case selected in this study is a blade from the National Renewable Energy Laboratory 5 Megawatt wind turbine. Results obtained with PCE were compared to Monte Carlo simulations. In addition, the influential random parameters were identified using Sobol Indices, obtained as an inexpensive sub-product of the PCE approximation.

Approximate profile likelihood estimation for Cox regression with covariate measurement error.

In nutritional epidemiology, measurement error in covariates is a well-known problem since dietary intakes are usually assessed through self-reporting. In this article, we consider an additive error model in which error variables are highly correlated, and propose a new method called approximate profile likelihood estimation (APLE) for covariates measured with error in the Cox regression. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to examine the finite sample performance of the proposed estimator empirically. Moreover, the popular correction method called regression calibration is shown to be a special case of APLE. We then apply APLE to deal with measurement error in some nutrients of interest in the EPIC-InterAct Study under a sensitivity analysis framework.

A Framework for Sensitivity Analysis of Real-Time Power Hardware-in-the-Loop (PHIL) Systems

Power hardware-in-the-loop (PHIL) simulation leverages the advanced real-time emulation based technique to carry out in-depth investigations on novel real-world power components. Power amplifiers, sensors, and signal conversion units based power interfaces (PI) incorporate physical hardware systems and real-time simulation platforms into PHIL setups. However, the employment of any interfacing technique inevitably introduces disturbances such as sensor noise, switching harmonics, or quantization noise to PHIL systems. To facilitate quantitatively analyzing and assessing the impact of external disturbances on PHIL simulation systems, a framework for sensitivity analysis of PHIL setups has been developed in this paper. Detailed modelling principles related to the sensitivity analysis of PHIL systems and the inherent relationship between sensitivity transfer functions and stability criteria are elaborated along with theoretical and experimental validation. Based on this concept, accuracy assessment methods are employed in this framework to quantify generic sensitivity criteria. Moreover, physical passive load and converter-based PHIL setups are applied and experimental results are presented to characterize and demonstrate the applicability of the proposed framework.

A Global Sensitivity Analysis Framework for Hybrid Simulation with Stochastic Substructures

Hybrid simulation is an experimental method used to investigate the dynamic response of a reference prototype structure by decomposing it to physically-tested and numerically-simulated substructures. The latter substructures interact with each other in a real-time feedback loop and their coupling forms the hybrid model. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic, as nominally identical specimens are, in practice, never actually identical. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol’ sensitivity indices are computed for substructure quantity of interest response quantiles. Normally, several repetitions of every single sample of the inputs parameters would be required to replicate the response of a stochastic hybrid model. In this regard, a great advantage of the proposed framework is that the generalized lambda surrogate model does not require repeated evaluations of the same sample. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.

Optimization of long-distance and large-scale transmission of renewable hydrogen in China: Pipelines vs. UHV

The reverse distribution of renewable energy resources and load centers makes exploring the optimal transmission mode of long-distance and large-scale renewable hydrogen the key to solving the bottleneck of renewable hydrogen development. This study incorporates hydrogen pipeline (HGP), natural gas pipeline (NGP), and Ultra High Voltage (UHV) into an optimal planning model framework and analyzes the optimal transmission mode, quantity, network, and cost of large-scale renewable hydrogen in China. Constructing a sensitivity analysis framework, this study also investigates the optimal transmission mode changes under different scenarios. The results show that the optimal mode of large-scale renewable hydrogen transmission in the province is NGP, and 5.4% of supply level is the critical point to export renewable hydrogen inter-provincially. It switches to the combination of NGP and HGP when the unit transmission costs of these elements decrease to a certain proportion simultaneously or switches to HGP when the unit transmission cost of HGP decreases more than that of NGP. The complementary transmission mode of NGP and UHV is the optimal mode for inter-provincial transmission, and the HGP can be put into use for inter-provincial transmission only when the unit transmission cost of which is reduced to less than 25%. Jilin is the key node in the NGP network, and Tibet and Gansu are the key nodes in UHV network, and the participation or absence of which will have significant impact on the renewable hydrogen transmission system. Only minor adjustments to the transmission technical parameters of NGP or HGP can promote the qualitative overflight of the optimal transmission volume of them so as to achieve the target optimization at the minimum cost.

An adjoint sensitivity analysis of the Telegrapher’s neutron kinetic equations

The work presented herein is an approach to the kinetic uncertainty analysis of the Telegrapher’s neutron kinetic equations. The adjoint sensitivity analysis framework has been resorted to meet this end. Burnup induced uncertainty in the value of the delayed neutron fraction is addressed and its impact on the neutron population (as an observable quantity by the way of flux detectors) is investigated. Results compared against those obtained through an exact forward analysis approach confirm quite satisfactory accuracy of the proposed variational method. The effect of relaxation time on the adjoint system dynamics is moreover explored.

Sensitivity analysis in classification using Bayesian smoothing spline ANOVA probit regression

For many classification problems, in addition to providing accurate classification results, very often it is equally important to determine which predictors are contributing to the results, and by how much. This motivates this article, where a new sensitivity analysis framework is developed for classification problems to address this issue. The effectiveness of this framework is illustrated through simulation studies and application to real data. Notice that this framework can be coupled with different classification methods. However, in practice it is recommended to pair it with a classification method called Bayesian smoothing spline ANOVA probit regression (BSSANOVA). When compared with other existing methods through numerical experiments, BSSANOVA performs extremely well for both classification and sensitivity analysis.

A novel sensitivity analysis of commercial building hybrid energy-structure performance

The Architecture, Engineering, and Construction community is highly focused on designing buildings that can improve energy efficiency while maintaining adequate structural behavior (termed herein as energy-structure performance). Sensitivity analysis is a fundamental tool to identify the influential factors under this multidisciplinary setting which can be used for model calibration, model reduction, and design optimization. To enhance the study of energy-structure performance, a novel framework of sensitivity analysis, including initial studies and global sensitivity analysis, was developed based on a general and automated platform of multi-physics simulation. This platform meets the requirements of object-orientation and provides compatibility with parametrical representation, including geometric/non-geometric parameters and detailed modeling. A systematic methodology of sensitivity analysis considering sensitivity auditing and a Scaled Morris Method is developed within the context of hybrid building energy-structure performance. The refined global screening sensitivity analysis (Scaled Morris Method) is proposed to deal with different types of data inputs and multiple-output sensitivity index comparison problems. A building case study was part of the research, which included two types of façades totaling 15 input factors. More than 2000 simulations were conducted producing the yearly/peak energy performance indicators over four climate zones along with static/dynamic structural performance indicators. The results from the initial studies and global sensitivity analysis provided varying/sensitivity effects of building topology/layout, structural/nonstructural components, and inherited features, which were compared quantitatively. For the curtain wall building , the absolute mean (sensitivity indices) input factors were up to 2.3 for energy indicators and 3.0 for structural indicators. The precast concrete panel wall building exhibited the absolute mean of input factors up to 2.8 for energy indicators and 2.4 for structural indicators. Overall, the results indicate this new framework, methodology, and sensitivity analysis can be used for commercial hybrid building energy-structure performance analysis. • Introduced a novel sensitivity framework based on a multi-physics simulation. • Proposed a systematic sensitivity analysis for energy-structure performance. • Proposed a Scaled Morris Method for global sensitivity analysis. • Performed a case study to quantify the building energy-structure indicators.

A framework for uncertainty and sensitivity analysis of district energy systems considering different parameter types

A variety of renewable energy sources, demand side loads, and other factors bring a lot of uncertainties to the operation of district energy systems. However, there is no strict standard for the selection of uncertainty factors. Too much uncertainty, or not enough of it, is not appropriate for the system optimization. In this paper, a method of uncertainty and sensitivity analysis for district energy system is proposed to identify the important uncertainties in the system optimization process. Firstly, the mathematical model of the system is established and the uncertain parameters are screened from technological, economic, environmental and demand-side perspectives. In addition, the selected parameters are divided into two categories according to whether they are time-related, and two methods are adopted to collect samples. Further, a global sensitivity analysis technique is introduced to calculate the sensitivity index of each parameter simultaneously. Case study is performed for a classic district energy system in a typical day of transition season. The sensitivity indexes under different objective functions are also discussed on this basis. The results show that the proposed framework can effectively analyze the uncertain parameters of the system, which can further contribute to the optimal operation decision.

An analytical framework for local and global system kinematic reliability sensitivity of robotic manipulators

This paper develops a novel analytical framework for system kinematic reliability sensitivity analysis of robotic manipulators, which can provide the analytical results of local and global reliability sensitivity defined on the pose and position errors. First, uncertainty analysis of the pose error of the end-effector is accomplished by virtue of the second-order closed-form error propagation formula on motion groups. Then, the system kinematic reliability, namely the probability of the system kinematic error located within the prescribed safe boundary, is analytically calculated. Specifically, the non-central chi-square approximation and expectation propagation technique are employed to compute the system kinematic reliability defined on the position and pose errors, respectively. On this basis, the local and global system kinematic reliability sensitivity of robotic manipulators are analytically obtained. Finally, the effectiveness of the proposed method is validated by comparison with the Monte Carlo simulation and Kriging modeling method. The results indicate the proposed method has good efficacy and efficiency in system kinematic reliability sensitivity analysis for robotic manipulators.

A framework for the resilience analysis of complex natural gas pipeline networks from a cyber-physical system perspective

The vulnerability of gas pipeline networks to physical and cyber-attacks calls for a resilience analysis based on models, capable of quantifying the network robustness and recovery from failures.This work proposes an original resilience analysis framework for a complex gas pipeline transmission network, considering the cybernetic interdependence of the physical gas pipeline network with the SCADA system. The maximum flow algorithm computes the gas network supply capacity and when a failure occurs, the pressure of the network nodes and the gas supply capacity change, leading to dissatisfaction of customer demands. The framework allows quantifing the value of resilience through specific performance metrics.The SCADA communication network, implemented in Network Simulator®, provides the necessary information regarding the delay of data packets coming from the sensors located along the pipelines. The packet delay value allows to evaluate the actual time at which the SCADA system blocks the remote control valves, ready to keep the pipelines under pressure when a failure occurs.Important insights on the resilience model are obtained through a systematic sensitivity analysis (SA) framework, customized for gas pipeline transmission networks. Specifically, we investigate the influence of model inputs to the network robustness and recovery uncertainty. The effects of individual parameters and groups formed by inputs with similar functionalities provide useful information, such as to what extent the supervisory SCADA system interconnection affects the degradation and the recovery process of the physical gas pipeline network.The results of the case study confirm, as expected, that gas transmission networks are vulnerable to both cyber and physical failures, pointing at the need for systemic methods of analysis for managing the system resilience.

SMIM: A unified framework of survival sensitivity analysis using multiple imputation and martingale.

Censored survival data are common in clinical trial studies. We propose a unified framework for sensitivity analysis to censoring at random in survival data using multiple imputation and martingale, called SMIM. The proposed framework adopts the δ-adjusted and control-based models, indexed by the sensitivity parameter, entailing censoring at random and a wide collection of censoring not at random assumptions. Also, it targets a broad class of treatment effect estimands defined as functionals of treatment-specific survival functions, taking into account missing data due to censoring. Multiple imputation facilitates the use of simple full-sample estimation; however, the standard Rubin's combining rule may overestimate the variance for inference in the sensitivity analysis framework. We decompose the multiple imputation estimator into a martingale series based on the sequential construction of the estimator and propose the wild bootstrap inference by resampling the martingale series. The new bootstrap inference has a theoretical guarantee for consistency and is computationally efficient compared to the nonparametric bootstrap counterpart. We evaluate the finite-sample performance of the proposed SMIM through simulation and an application on an HIV clinicaltrial.

An integrated framework of global sensitivity analysis and calibration for spatially explicit agent‐based models

AbstractCalibration of agent‐based models (ABMs) is a major challenge due to the complex nature of the systems being modeled, the heterogeneous nature of geographical regions, the varying effects of model inputs on the outputs, and computational intensity. Nevertheless, ABMs need to be carefully tuned to achieve the desirable goal of simulating spatiotemporal phenomena of interest, and a well‐calibrated model is expected to achieve an improved understanding of the phenomena. To address some of the above challenges, this article proposes an integrated framework of global sensitivity analysis (GSA) and calibration, called GSA‐CAL. Specifically, variance‐based GSA is applied to identify input parameters with less influence on differences between simulated outputs and observations. By dropping these less influential input parameters in the calibration process, this research reduces the computational intensity of calibration. Since GSA requires many simulation runs, due to ABMs' stochasticity, we leverage the high‐performance computing power provided by the advanced cyberinfrastructure. A spatially explicit ABM of influenza transmission is used as the case study to demonstrate the utility of the framework. Leveraging GSA, we were able to exclude less influential parameters in the model calibration process and demonstrate the importance of revising local settings for an epidemic pattern in an outbreak.