Regional Sensitivity Analysis Research Articles

Energy Consumption Modeling in Presence of Uncertainty

This paper studies the behavior of an energy consumption model for electric vehicles in presence of input uncertainty, that is under heterogeneous driving behaviors and traffic conditions, or at varied performances of technology and operating scenarios. In fact, these sources of uncertainty are often neglected in customary applications, i.e. the model is evaluated only around nominal conditions, thus inhibiting the model’s ability to capture the intrinsic variability of energy consumptions observed in real driving. Therefore, a general framework to perform global and regionalized sensitivity analysis on energy consumption models is here formulated and applied to identify which model inputs contribute the most to the variance of simulated energy consumption and recovery, and which input values lead to average or extreme model outputs. Results proved that driving behaviors and traffic flow dynamics have the greatest impact on simulated consumption and show strong interaction effects with the parameters of the regenerative braking strategy with respect to the recovered energy. While the vehicle weight and the auxiliary systems have an increasing impact at lower speeds, the technology performances and the vehicle characteristics were proved to be non-influential at all. Ultimately, the model was validated against its ability to reproduce the variability of consumptions observed in field experiments. Results show a tendency to over-estimating average consumption and underestimating average recovery, i.e. the model predictions are conservative. In addition, evidence shows that there are un-modeled details of the regenerative braking strategy to be further investigated via future experimental analyses.

Forward-reverse switch between density-based and regional sensitivity analysis

Global sensitivity analysis is a widely used tool for uncertainty apportionment and is very useful for decision making, risk assessment, model simplification, optimal design of experiments, etc. Density-based sensitivity analysis and regional sensitivity analysis are two widely used approaches. Both of them can work with a given sample set of model input-output pairs. One significant difference between them is that density-based sensitivity analysis analyzes output distributions conditional on input values (forward), while regional sensitivity analysis analyzes input distributions conditional on output values (reverse). In this paper, we study the relationship between these two approaches and show that regional sensitivity analysis (reverse), when focusing on probability density functions of input, converges towards density-based sensitivity analysis (forward) as the number of classes for conditioning model outputs in the reverse method increases. Similar to the existing general form of forward sensitivity indices, we derive a general form of the reverse sensitivity indices and provide the corresponding reverse given-data method. Due to the shown equivalence, the reverse given-data method provides an efficient way to approximate density-based sensitivity indices. Two test examples are used to verify this connection and compare the results. Finally, we use the reverse given-data method to perform sensitivity analysis in a carbon dioxide storage benchmark problem with multiple outputs, where forward analysis of density-based indices would be impossible due to the high-dimensionality of its model outputs.

Uncertainty and Sensitivity Analysis of Phosphorus Model Parameters in Large Shallow Lakes

Lake Taihu was chosen as a typical large shallow lake, and a diagenesis model of phosphorus was established based on environmental fluid dynamic code (EFDC). The uncertainty of the simulation results and the sensitivity of 16 parameters related to phosphorus migration and transformation in the diagenesis model were analyzed using Latin hypercube sampling (LHS), generalized likelihood uncertainty estimation (GLUE), and regionalized sensitivity analysis (RSA). The results showed that the temporal and spatial distribution of phosphate and total phosphorus in Lake Taihu was extremely uneven. Furthermore, the uncertainty of the diagenesis model had a strong influence on the simulation of phosphate and total phosphorus. For phosphate in the overlying, wind and wave disturbance at the 'sediment-water' interface was stronger in shallower water regions. The circulation of water in the bay area, where the dissolved oxygen content was low, was poor, which was conducive to the release of dissolved phosphorus in the sediment. For total phosphorus in the overlying water, the granular phosphorus and dissolved organic phosphorus contents in the central lake area were greatly affected by parameter uncertainties in the diagenesis model. The sensitive parameters mainly consisted of two kinds related to oxygen and dynamic characteristics, respectively. For large shallow lakes, the importance of parameter sensitivity in diagenesis models is no less than for hydrodynamic and water quality models. For large shallow lakes, the calibration of sensitive parameters should, therefore, be given attention when simulating the phosphorus content of areas with complicated water quality and sediment distributions.

Sensitivity analysis of the critical speed in a railway bogie system with uncertain parameters

An extended Dichotomy method is proposed for an accurate determination of the critical speed of railway vehicles. The high-dimensional Hermite orthogonal polynomial (HOP) based on the independent and normal distribution parameters is derived. Both the Monte Carlo (MC) method based on a Latin hypercube sampling (LHS) and the HOP expansion method using different collocation methods are compared to investigate the statistical characteristics of the critical speed of a Chinese railway bogie. After that, the relation between the critical speed and the random input parameters is approximately constructed. The relation is then used to conduct a relative local sensitivity analysis (LSA), a global sensitivity analysis (GSA) and a regional sensitivity analysis (RSA) of the bogie. It is indicated that RSA is a good method for sensitivity analysis of the critical speed due to its good efficiency and trusty precision. The results also show that the secondary lateral damper is the most important parameter to the critical speed for this bogie. By increasing its values and reducing its variation range, the critical speed can be increased and the variation is decreased. It may offer some instructions and practical values for vehicle design, operation, and comprehensive evaluation of the stability of railway vehicles.

Failure probability-based global and regional sensitivity analysis using copula

In risk and reliability assessment, the failure probability-based global sensitivity analysis (GSA) and the failure probability-based regional sensitivity analysis (RSA) have attracted much interest. In this article, we deduce the relationship of the failure probability-based GSA importance measure and copula, and point out that the failure probability-based GSA importance measure can be interpreted as the dependence measure between the failure probability and the input variables from copula viewpoint. To calculate the importance measure, the least square fitting copula (LSFC) method is proposed subsequently. The method decouples the double-loop estimating of the conditional failure probability. Additionally, to analyze and identify the effects of the different regions of the input variables on failure probability, a RSA importance measure is proposed, its properties are investigated and proved. At last, an engineering example is employed to demonstrate and validate the effectiveness of the LSFC method and the proposed RSA importance measure.

Identifying a Suitable Model for Low-Flow Simulation in Watersheds of South-Central Chile: A Study Based on a Sensitivity Analysis

Choosing a model that suitably represents the characteristics of a watershed to simulate low flows is crucial, especially in watersheds whose main source of baseflow generation depends on groundwater storage and release. The goal of this investigation is to study the performance and representativeness of storage-release process modeling, considering aspects such as the topography and geology of the modeled watershed through regional sensitivity analysis, in order to improve low-flow prediction. To this end, four groundwater storage-release structures in various watersheds with different geological (fractured and sedimentary rock) and topographic domains (steep and gentle slopes) were analyzed. The results suggest that the two-reservoir structure with three runoff responses is suitable (better) for simulating low flows in watersheds with fractured geological characteristics and rugged or steep topography. The results also indicate that a one-reservoir model can be adequate for predicting low flows in watersheds with a sedimentary influence or flat topography.

Practical Experience of Sensitivity Analysis: Comparing Six Methods, on Three Hydrological Models, with Three Performance Criteria

Currently, practically no modeling study is expected to be carried out without some form of Sensitivity Analysis (SA). At the same time, there is a large number of various methods and it is not always easy for practitioners to choose one. The aim of this paper is to briefly review main classes of SA methods, and to present the results of the practical comparative analysis of applying them. Six different global SA methods: Sobol, eFAST (extended Fourier Amplitude Sensitivity Test), Morris, LH-OAT, RSA (Regionalized Sensitivity Analysis), and PAWN are tested on three conceptual rainfall-runoff models with varying complexity: (GR4J, Hymod, and HBV) applied to the case study of Bagmati basin (Nepal). The methods are compared with respect to effectiveness, efficiency, and convergence. A practical framework of selecting and using the SA methods is presented. The result shows that, first of all, all the six SA methods are effective. Morris and LH-OAT methods are the most efficient methods in computing SI and ranking. eFAST performs better than Sobol, and thus it can be seen as its viable alternative for Sobol. PAWN and RSA methods have issues of instability, which we think are due to the ways Cumulative Distribution Functions (CDFs) are built, and using Kolmogorov–Smirnov statistics to compute Sensitivity Indices. All the methods require sufficient number of runs to reach convergence. Difference in efficiency of different methods is an inevitable consequence of the differences in the underlying principles. For SA of hydrological models, it is recommended to apply the presented practical framework assuming the use of several methods, and to explicitly take into account the constraints of effectiveness, efficiency (including convergence), ease of use, and availability of software.

Parameter Estimation and Uncertainty Analysis: A Comparison between Continuous and Event-Based Modeling of Streamflow Based on the Hydrological Simulation Program–Fortran (HSPF) Model

Hydrologic modeling is usually applied to two scenarios: continuous and event-based modeling, between which hydrologists often neglect the significant differences in model application. In this study, a comparison-based procedure concerning parameter estimation and uncertainty analysis is presented based on the Hydrological Simulation Program–Fortran (HSPF) model. Calibrated parameters related to base flow and moisture distribution showed marked differences between the continuous and event-based modeling. Results of the regionalized sensitivity analysis identified event-dependent parameters and showed that gravity drainage and storage outflow were the primary runoff generation processes for both scenarios. The overall performance of the event-based simulation was better than that of the daily simulation for streamflow based on the generalized likelihood uncertainty estimation (GLUE). The GLUE analysis also indicated that the performance of the continuous model was limited by several extreme events and low flows. In the event-based scenario, the HSPF model performances decreased as the precipitation became intense in the event-based modeling. The structure error of the HSFP model was recognized at the initial phase of the rainfall-event period. This study presents a valuable opportunity to understand dominant controls in different hydrologic scenario and guide the application of the HSPF model.

Inverse uncertainty characteristics of pollution source identification for river chemical spill incidents by stochastic analysis

Identifying source information after river chemical spill occurrences is critical for emergency responses. However, the inverse uncertainty characteristics of this kind of pollution source inversion problem have not yet been clearly elucidated. To fill this gap, stochastic analysis approaches, including a regional sensitivity analysis method, identifiability plot and perturbation methods, were employed to conduct an empirical investigation on generic inverse uncertainty characteristics under a well-accepted uncertainty analysis framework. Case studies based on field tracer experiments and synthetic numerical tracer experiments revealed several new rules. For example, the release load can be most easily inverted, and the source location is responsible for the largest uncertainty among the source parameters. The diffusion and convection processes are more sensitive than the dilution and pollutant attenuation processes to the optimization of objective functions in terms of structural uncertainty. The differences among the different objective functions are smaller for instantaneous release than for continuous release cases. Small monitoring errors affect the inversion results only slightly, which can be ignored in practice. Interestingly, the estimated values of the release location and time negatively deviate from the real values, and the extent is positively correlated with the relative size of the mixing zone to the objective river reach. These new findings improve decision making in emergency responses to sudden water pollution and guide the monitoring network design.

APEXSENSUN: An Open‐Source Package in R for Sensitivity Analysis and Model Performance Evaluation of APEX

AbstractThe Agricultural Policy/Environmental eXtender (APEX) model is used to evaluate the impact of different land management strategies associated with water availability, soil and water quality, plant growth, and economics. This article presents APEXSENSUN, an open‐source software package that automates global sensitivity analysis and assists with calibration of the APEX model. APEXSENSUN was developed in R programming language and includes regression‐based, derivative‐based, and variance‐based methods, as well as a regional sensitivity analysis method. Evapotranspiration data measured at a research field located at the United States Department of Agriculture‐Agricultural Research Service Conservation and Production Research Laboratory in Bushland, Texas were utilized to illustrate the main features of APEXSENSUN, which are to identify important parameters and assist with calibration. The results from variance‐based methods were in agreement regarding the ranking of top five sensitive parameters including the soil evaporation‐plant factor, root growth‐soil strength, and the coefficient for adjusting the microbial activity function in the top soil layer. The Fourier amplitude sensitivity testing method required the least number of simulations for calculation of the total‐effect sensitivity indices. The Monte Carlo‐based calibration feature of the package was also tested for calculating the posterior parameter distributions and prediction intervals with a desired level of confidence for output predictions.

Identifying advantages and drawbacks of two hydrological models based on a sensitivity analysis: a study in two Chilean watersheds

ABSTRACTHydrological modelling has undergone constant growth with the increase in information processing capabilities. Hydrological models have traditionally been used to study the effects of climate change on management and land-use changes and for water resources planning, among other purposes. The aim of this study was to determine and analyse the advantages of the HBV and HYMOD models, which are commonly used in hydrology on daily and monthly time scales. A regional sensitivity analysis was used to compare the processes that take on greater importance at different time scales in the two models. As a result, it was found that quick precipitation–runoff processes prove to be better represented in the HBV model, while slow, time-aggregated processes are better represented by the HYMOD model. This study confirms that both models are adequate for rain-dominated basins, such as those of the study area. Additionally, the HBV model proved to be more robust in comparison to HYMOD.

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

The application of reliability sensitivity analysis (RSA) to the high voltage direct current (HVDC) transmission systems is one of the hot topics in the future. A regional RSA method, the contribution to failure probability (CFP) plot, is investigated in this paper. This CFP plot contains both aleatory and epistemic uncertain variables modeled as random variables by probability theory and interval variables by evidence theory, respectively. A surrogate model of second-level limit state function needs to be established for each joint focal element (JFE), which is a time-consuming process. Additionally, an excessive number of Monte Carlo simulations (MCS) and optimizations may exceed the computing power of modern computers. In order to deal with the above problems and further decrease the computational cost, a more effective CFP calculation method under the framework of random-evidence hybrid reliability analysis is proposed. Three important improvements in the proposed method make the calculation of CFP more efficient and easy to implement. Firstly, an active learning kriging (ALK) based on the symbol prediction idea is employed to directly establish a surrogate model rather than a second-level limit state function with fewer function calls, which greatly simplifies construction of the model. Secondly, a random set-based Monte Carlo simulation (RS-MCS) is used to handle the issue of oversized optimization caused by too many JFEs. Thirdly, for further reducing the size of optimizations and improving the efficiency of the CFP calculation, a Karush-Kuhn-Tucker-based optimization (KKTO) method is recommended in the proposed method to solve the extreme value of performance function. A numerical example and an engineering example were studied to verify the accuracy, effectiveness and practicality of the proposed method. It can be seen from the results that regardless of whether it is modeling or computational efficiency, the proposed method is better than the original method.

The Sensitivity of a Water Distribution System to Regional State Parameter Variations

The sensitivity of a pressurised water distribution system (WDS) to state parameter variations is studied. A novel local regional sensitivity analysis (LRSA) approach is introduced which applies the same change to a collection of parameters, called a region. For example, sensitivity to suburbs can be studied. General analytical (using algebraic methods) results are derived. They show how sensible conclusions arise from LRSA and state this dependence of the WDS on regions for the first time. For most cases, the WDS is 1.852–2 times more sensitive to pipe roughness coefficients than to pipe lengths. In most cases, when certain pipes do not have minor losses, the WDS is 4.871–5.333 times more sensitive to pipe diameters than to pipe lengths. Hence, the WDS is the most sensitive to pipe diameters, medium sensitive to pipe roughness coefficients, and least sensitive to pipe lengths. For most cases, when all reservoir and tank elevations (and heads) remain the same, changes of other elevations do not change flow rates and change the pressures in a simple additive way. In most cases, when all the reservoir water surface elevations are changed together, the flow rates remain unchanged, and the pressures change in a simple additive way.

A Regional Sensitivity Analysis-based Expert System for safety margins control

Thermal-Hydraulic (TH) codes are used to simulate the response of nuclear safety systems under transient and accident conditions. The outcomes of the simulations are used to verify the safety margins required for safe operation and make decisions on how to maintain them.In this work, a novel Expert System (ES) based on Regional Sensitivity Analysis (RSA) is developed to guide a system undergoing an accident scenario towards the safest conditions in the optimal number of operation. The ES proceeds by firstly identifying the (uncertain) system controllable variables (i.e., control rods position, feed-water flow rate, void fraction inside the steam generator, etc.) that most affect the system response by RSA; then, the limit-state function is calibrated on a dataset of outcomes of TH code runs and the system failure boundary (i.e., the limit surface) is defined on the set of (uncertain) TH input variables.Application of the ES is firstly shown with respect to an analytical case study that artificially simulates the response of a NPP to an accident scenario and, then, to a practical case study concerning the response of the pressurizer of a Pressurized Water Reactor (PWR).

Sensitivity Analysis for the Inverted Siphon in a Long Distance Water Transfer Project: An Integrated System Modeling Perspective

Long distance water diversion projects are developed to alleviate the conflicts between supply and demand of water resources across different watersheds. However, the significant scale water diversion projects bring new challenges for the water supply security. This paper presents the flood risk of inverted siphon structure which is used for crossing transversally in the water diversion project through sensitivity analysis. Soboĺ and regionalized sensitivity analysis are used to investigate the sensitive parameters of the integrated model and the sensitive range of the parameters, respectively. The integrated system model consists of the hydrologic model, the sediment transport model and the siphon hydraulic model to determine the flood overtopping duration and volume, which are used to quantify flood risk in this study. The flood overtopping duration and volume indicators are used to quantify flood risk in the sensitivity analysis. The South to North Water Diversion Project in China is used as a case study. The results show the mean rainfall and roughness coefficient of the pipe are the most sensitive parameters in the integrated models, while the sensitive range of these two parameters are distinct. The sensitivity analysis of the inverted siphon provides an insight into the significant contributions to the flood risk. The analysis can provide the guidance for the system operation security.

Application of Monte Carlo filtering method in regional sensitivity analysis of AASHTOWare Pavement ME design

Abstract Since AASHTO released the Mechanistic-Empirical Pavement Design Guide (MEPDG) for public review in 2004, many highway research agencies have performed sensitivity analyses using the prototype MEPDG design software. The information provided by the sensitivity analysis is essential for design engineers to better understand the MEPDG design models and to identify important input parameters for pavement design. In literature, different studies have been carried out based on either local or global sensitivity analysis methods, and sensitivity indices have been proposed for ranking the importance of the input parameters. In this paper, a regional sensitivity analysis method, Monte Carlo filtering (MCF), is presented. The MCF method maintains many advantages of the global sensitivity analysis, while focusing on the regional sensitivity of the MEPDG model near the design criteria rather than the entire problem domain. It is shown that the information obtained from the MCF method is more helpful and accurate in guiding design engineers in pavement design practices. To demonstrate the proposed regional sensitivity method, a typical three-layer flexible pavement structure was analyzed at input level 3. A detailed procedure to generate Monte Carlo runs using the AASHTOWare Pavement ME Design software was provided. The results in the example show that the sensitivity ranking of the input parameters in this study reasonably matches with that in a previous study under a global sensitivity analysis. Based on the analysis results, the strengths, practical issues, and applications of the MCF method were further discussed.

Identification of the dominant hydrological process and appropriate model structure of a karst catchment through stepwise simplification of a complex conceptual model

Conceptual models often suffer from the over-parameterization problem due to limited available data for the calibration. This leads to the problem of parameter nonuniqueness and equifinality, which may bring much uncertainty of the simulation result. How to find out the appropriate model structure supported by the available data to simulate the catchment is still a big challenge in the hydrological research. In this paper, we adopt a multi-model framework to identify the dominant hydrological process and appropriate model structure of a karst spring, located in Guilin city, China. For this catchment, the spring discharge is the only available data for the model calibration. This framework starts with a relative complex conceptual model according to the perception of the catchment and then this complex is simplified into several different models by gradually removing the model component. The multi-objective approach is used to compare the performance of these different models and the regional sensitivity analysis (RSA) is used to investigate the parameter identifiability. The results show this karst spring is mainly controlled by two different hydrological processes and one of the processes is threshold-driven which is consistent with the fieldwork investigation. However, the appropriate model structure to simulate the discharge of this spring is much simpler than the actual aquifer structure and hydrological processes understanding from the fieldwork investigation. A simple linear reservoir with two different outlets is enough to simulate this spring discharge. The detail runoff process in the catchment is not needed in the conceptual model to simulate the spring discharge. More complex model should need more other additional data to avoid serious deterioration of model predictions.

Global sensitivity analysis applied to traffic rescheduling in case of power shortage

The present work addresses traffic rescheduling in case of electric infrastructure failure. The power available for train traction is restricted and the traffic must be reorganized according to this constraint. The system behaviour is computed using a dynamic multi-physics railway simulator which gives physi- cal quantities such as the train speed profiles, voltage along the catenary lines and temperatures. The rescheduling problem relies on this non-linear model, with a large number of continuous and discrete variables, constraints on dynamic outputs (typically voltage limits) and a high computation cost. We propose a rescheduling process based on sensitivity analysis in order to analyse the behaviour of this complex system and obtain information about the adjustment operations needed in order to reschedule the traffic in an optimal way. Our approach is based on statistics, with predefined variation ranges of the input parameters. In a first stage, variance decomposition-based sensitivity analysis (generalized Sobol indexes) is used for prioritization and fixing factors; then regional sensitivity analysis is used for factor mapping. The proposed approach has been tested on a simple case, with a nominal traffic running on a single-track line. The considered incident is the loss of a feeding power substation. The variables to be adjusted are the time interval between departure times and speed reduction in the vicinity of the faulty substation. The results show that increasing the time interval between trains is the most influential vari- able. Pareto-optimal fronts are also built in order to perform multi-criteria analysis according to travel- ling time, train delays and traction energy.

DGSA: A Matlab toolbox for distance-based generalized sensitivity analysis of geoscientific computer experiments

Sensitivity analysis plays an important role in geoscientific computer experiments, whether for forecasting, data assimilation or model calibration. In this paper we focus on an extension of a method of regionalized sensitivity analysis (RSA) to applications typical in the Earth Sciences. Such applications involve the building of large complex spatial models, the application of computationally extensive forward modeling codes and the integration of heterogeneous sources of model uncertainty. The aim of this paper is to be practical: 1) provide a Matlab code, 2) provide novel visualization methods to aid users in getting a better understanding in the sensitivity 3) provide a method based on kernel principal component analysis (KPCA) and self-organizing maps (SOM) to account for spatial uncertainty typical in Earth Science applications and 4) provide an illustration on a real field case where the above mentioned complexities present themselves. We present methods that extend the original RSA method in several ways. First we present the calculation of conditional effects, defined as the sensitivity of a parameter given a level of another parameters. Second, we show how this conditional effect can be used to choose nominal values or ranges to fix insensitive parameters aiming to minimally affect uncertainty in the response. Third, we develop a method based on KPCA and SOM to assign a rank to spatial models in order to calculate the sensitivity on spatial variability in the models. A large oil/gas reservoir case is used as illustration of these ideas.

Satellite detection of soil moisture related water stress impacts on ecosystem productivity using the MODIS-based photochemical reflectance index

Abstract Satellite remote sensing provides continuous observations of vegetation properties that can be used to estimate global terrestrial ecosystem gross primary production (GPP). The Photochemical Reflectance Index (PRI) has been shown to be sensitive to vegetation photosynthetic light use efficiency (LUE), GPP and canopy water-stress. Here, we use the NASA EOS MODIS (Moderate Resolution Imaging Spectroradiometer) based PRI with eddy covariance CO2 flux measurements and meteorological observations from 20 tower sites representing major plant functional type (PFT) classes within the continental USA (CONUS) to assess GPP sensitivity to soil moisture related water stress. The sPRI (scaled PRI) metric derived using MODIS band 13 as a reference channel (sPRI13) shows generally higher correspondence with tower GPP estimates than other potential MODIS reference bands. The sPRI13 observations were used as a proxy for soil moisture related water supply constraints to LUE within a satellite data driven terrestrial carbon flux model to estimate GPP (GPPPRI). The GPPPRI calculations show generally favorable correspondence with tower GPP estimates (0.457 ≤ R2 ≤ 0.818), except for lower GPPPRI performance over evergreen needleleaf forest (ENF) sites. A regional model sensitivity analysis using the sPRI13 as a water supply proxy indicated that water restrictions limit GPP over more than 21% of the CONUS domain, particularly in drier climate areas where atmospheric moisture deficits (VPD) alone are insufficient to represent both atmosphere demand and water supply controls affecting productivity. Our results indicate strong potential of the MODIS sPRI13 to represent soil moisture related water supply controls influencing photosynthesis, with enhanced (1-km resolution) delineation of these processes closer to the scale of in situ tower observations. These observations may provide an effective tool for characterizing sub-grid spatial heterogeneity in soil moisture related controls that inform coarser scale observations and estimates determined from other satellite observations and earth system models.