Variance-based Sensitivity Analysis Method Research Articles

Prediction of the Waviness Error in Ultra-Precision Fly Cutting Using the Direct Integration Method

Abstract Fly cutting is widely used in manufacturing of large-scale, high-precision optical components. However, the discontinuity of fly cutting machining leads to significant relative vibrations between the tool and the workpiece. The cutting process generates periodic waves along the cutting direction, which will deteriorate the wavefront characteristics of optical components. Based on the machining dynamics, this paper proposes a direct integration method to predict the waviness error of the machined surface. The cutting force model of fly cutting is established. The multi-mode characteristics of the spindle-tool system are measured by the experimental method. Then, the influence of uncertainties on the calculation results is analyzed by the variance-based sensitivity analysis method. Finally, the plane cutting experiment verifies that the direct integration method effectively predicts the waviness error and its variation trend, and the waviness prediction research is important for optimization of the machining parameters.

Torsional Vibration and Sensitivity Analysis of Microcantilever in Liquid

Development of microsystems and ever-increasing advances of nanotechnology have resulted in growing applications of microcantilevers (MCs), including Atomic Force Microscopy (AFM). In AFM, transverse vibration of microfiber from a liquid medium results in resonance of unwanted hydrodynamic and electrostatic forces, which can be minimized by torsional mode. In the present study, the differential equation of the vibrational motion is extracted by acquiring the hydrodynamic force applied to MCs aiming to investigate the torsional vibration behavior of MCs in a liquid medium; and the extracted equation is solved to study the behavior of MCs in a liquid medium. Considering the significant effect of MC geometry on its torsional vibrations in a liquid medium, Sobol's variance-based sensitivity analysis method was utilized to investigate the effectiveness of MC geometry on torsional vibration. The sensitivity analysis results show that length and width have the most significant effects on the quality factor and the resonance frequency of MCs.

Machine learning method for shale gas adsorption capacity prediction and key influencing factors evaluation

Shale gas plays a pivotal role in the global energy landscape, emphasizing the need for accurate shale gas-in-place (GIP) prediction to facilitate effective production planning. Adsorbed gas in shale, the primary form of gas storage under reservoir conditions, is a critical aspect of this prediction. In this study, a machine learning Gaussian process regression (GPR) model for methane adsorption prediction was established and validated using published experimental data. Five typical variables, i.e., total organic carbon (TOC), clay minerals, temperature, pressure, and moisture were considered, which were derived from the Marine shale of the Longmaxi formation in the Sichuan Basin through correlation analysis. The performance of the GPR model was compared with the widely used an extreme gradient boosting model. It turned out that our GPR model had better accuracy for predicting methane adsorption in shale with an average relative error of less than 3%. Furthermore, a variance-based sensitivity analysis method in conjunction with kernel density estimation theory was employed to conduct a global sensitivity analysis, quantifying the nonlinear influence of each variable methane adsorption. The findings indicate that TOC is the most significant factor affecting methane adsorption, while clay minerals have a limited direct impact but can enhance their influence through interactions with other influencing factors. Finally, based on the GPR model, a GIP prediction method was proposed that eliminates the need for calculating the density of the adsorbed phase. These findings are expected to extend the shale gas reserve assessment methodologies and offer valuable insight for further exploring the adsorption mechanisms of shale gas.

Measuring the β-decay Properties of Neutron-rich Exotic Pm, Sm, Eu, and Gd Isotopes to Constrain the Nucleosynthesis Yields in the Rare-earth Region

The β-delayed neutron-emission probabilities of 28 exotic neutron-rich isotopes of Pm, Sm, Eu, and Gd were measured for the first time at RIKEN Nishina Center using the Advanced Implantation Detector Array (AIDA) and the BRIKEN neutron detector array. The existing β-decay half-life (T 1/2) database was significantly increased toward more neutron-rich isotopes, and uncertainties for previously measured values were decreased. The new data not only constrain the theoretical predictions of half-lives and β-delayed neutron-emission probabilities, but also allow for probing the mechanisms of formation of the high-mass wing of the rare-earth peak located at A ≈ 160 in the r-process abundance distribution through astrophysical reaction network calculations. An uncertainty quantification of the calculated abundance patterns with the new data shows a reduction of the uncertainty in the rare-earth peak region. The newly introduced variance-based sensitivity analysis method offers valuable insight into the influence of important nuclear physics inputs on the calculated abundance patterns. The analysis has identified the half-lives of 168Sm and of several gadolinium isotopes as some of the key variables among the current experimental data to understand the remaining abundance uncertainty at A = 167–172.

Global Sensitivity Analysis of Economic Model Predictive Longitudinal Motion Control of a Battery Electric Vehicle

Global warming forces the automotive industry to reduce real driving emissions and thus, its CO2 footprint. Besides maximizing the individual efficiency of powertrain components, there is also energy-saving potential in the choice of driving strategy. Many research works have noted the potential of model predictive control (MPC) methods to reduce energy consumption. However, this results in a complex control system with many parameters that affect the energy efficiency. Thus, an important question remains: how do these partially uncertain (system or controller) parameters influence the energy efficiency? In this article, a global variance-based sensitivity analysis method is used to answer this question. Therefore, a detailed powertrain model controlled by a longitudinal nonlinear MPC (NMPC) is developed and parameterized. Afterwards, a qualitative Morris screening is performed on this model, in order to reduce the parameter set. Subsequently, the remaining parameters are quantified using Generalized Sobol Indices, in order to take the time dependence of physical processes into account. This analysis reveals that the variations in vehicle mass, battery temperature, rolling resistance and auxiliary consumers have the greatest influence on the energy consumption. In contrast, the parameters of the NMPC only account for a maximum of 5% of the output variance.

Variance-based sensitivity analysis for the influence of residual stress on machining deformation

Sensitivity analysis is widely used in engineering design to illustrate the effect of the variations of input variables on the output response of a system efficiently. The current study proposes a novel method of variance-based sensitivity analysis to evaluate the effects of initial residual stress (IRS) and surface residual stress (SRS) on the uncertainty of machining deformation. This analysis introduced the variance as the uncertainty evaluation index and the variance contribution to reflect the effects of residual stress on machining deformation. The variance contributions were divided into two components: (1) independent contributions due to the variations from the independent portion of a variable and (2) correlated contributions due to the variations from the portion of a variable correlated with other variables. Uncertainty characteristics (variance σ 2 ) of residual stress were extracted and an analytical model for the relationship between residual stress and the bending moment was established. An importance measure matrix consisted of variance contribution of each residual stress variable was constructed. Concerning correlated residual stress variables, the effects of variances and correlation coefficients of residual stress on the variance of machining deformation were studied. Experimental work on a sidewall structure showed that the variance contribution of IRS at the surface layer was 5.3 to 17.8 times greater than SRS. Furthermore, the sensitivity analysis for correlated residual stress variables indicated that decreasing the variances of IRS and SRS (especially IRS) and keeping the values of correlation coefficients between −0.5 to 0.5 are beneficial to reduce the uncertainty of machining deformation. • A variance-based sensitivity analysis method for machining deformation was proposed. • Variance contribution reflected the effects of RS on the machining deformation. • An analytical model between bending moment and RS was proposed. • Standard deviations and correlation coefficients of RS were studied.

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

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

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.

Uncertainty quantification of grain morphology in laser direct metal deposition

Uncertainty quantification (UQ) has an important role to play in the quality control of additively manufactured products. With a focus on laser direct metal deposition (LDMD), this work presents a systematic UQ framework to quantify the uncertainty of grain morphology due to various sources of uncertainty in the LDMD simulation process. The LDMD process is simulated by a coupled analysis consisting of a macroscale finite element model for the melt pool and a microscale cellular automata model for solidification to predict the microstructure. UQ is carried out using singular value decomposition-based Kriging surrogate of the expensive simulation model. The effectiveness of the proposed approach is demonstrated by identifying several major sources of uncertainty and studying their contributions to the uncertainty in the grain size distribution using a variance-based sensitivity analysis method.

Projection and uncertainty of precipitation extremes in the CMIP5 multimodel ensembles over nine major basins in China

This study presented an analysis of projection and uncertainty of precipitation extremes over 9 river basins in China based on the outputs of 18 global climate models (GCMs) with 3 Representative Concentration Pathways (RCPs) from the Coupled Model Inter-comparison Project Phase 5 (CMIP5). The temporal and spatial changes in precipitation extremes for the period 2020–2100 were analyzed using the climate indices defined by the Expert Team on Climate Detection and Indices (ETCCDI). Uncertainty of GCMs and RCPs in the projections of precipitation extremes was quantified using the variance-based sensitivity analysis method. The model simulations generally predict a consistent intensification of precipitation extremes during the 21st century with respect to different RCPs scenarios: the higher emission scenarios (e.g., RCP8.5), the larger intensity and frequency of precipitation extremes. The projected changes in precipitation extremes exhibit a large spatial variation across China. The high-latitude and high elevation regions of China (e.g., Continental and Southwest basins) are projected to respond more strongly to the increase in precipitation amount and intensity (e.g., RCPTOT, RX1day and RX5day), while southeastern and southern China (e.g., Southeast and Pearl River basins) tend to be more sensitive to the increase in the frequency of precipitation extreme (e.g., R10mm and R20mm). Consecutive dry days (CDD) is projected to decrease in northern China (e.g., Continental basin) but increase in southern China (e.g., Southeast, Pearl River, and Yangtze River basins). Uncertainty analysis shows that variation of GCMs contributes >90% uncertainty of precipitation extremes projections for the whole China, with larger uncertainty range under the higher emission scenarios (e.g., RCP8.5). The uncertainty from RCPs is generally limited (contribution <10%) in comparison with GCMs, and slightly increases with the long-term projections of precipitation extremes.

Application of variance-based uncertainty and sensitivity analysis to biological modeling in carbon ion treatment plans.

In ion beam therapy, biological models to estimate the relative biological effectiveness (RBE) and subsequently the RBE-weighted dose (RWD) are needed in treatment planning and plan evaluation. The required biological parameters as well as their dependency on ion species and ion energy can typically not be determined directly in experiments for invivo situations. For that reason they are often derived from invitro data and biological modeling and subject to large uncertainties. We present a model-independent Monte Carlo (variance-) based uncertainty and Sensitivity Analysis (SA) approach to quantify the impact of different input uncertainties on a simulated carbon ion treatment plan. The influences of different input uncertainties are examined by variance-based SA methods. In this Monte Carlo approach, a function is evaluated 103 -105 times. For each of those runs, all inputs are changed simultaneously, using random numbers according to their associated uncertainties. Variance-based statistic formalisms then rank the input parameter/uncertainty pairs according to their impact on the result of the function. The method of SA includes an uncertainty analysis and was applied to a two-field spot scanning carbon ion treatment plan for two commonly used biological models and two representative tissue parameter sets. Based on an exemplary patient case, the application of variance-based SA for biological measures, relevant in (carbon) ion therapy, is demonstrated. A voxel-wise calculation for 2.9·105 voxels takes ~6h. A structure-based SA, which adds an uncertainty band to a RWD-volume histogram (RW-DVH) and shows how to decrease the uncertainty in the most effective way, can be calculated in 0.1-1.5h (depending on the size of the structure). The uncertainties in RBE, RWD or RW-DVH are broken down to the impact of different uncertainties in the (biological) model input. Biological uncertainties have a higher impact on the resulting RBE and RWD than uncertainties in the physical dose. Excluding the physical dose from the SA only slightly decreased the overall uncertainty, emphasizing the necessity to include biological uncertainties into treatment plan evaluation. Variance-based SA is a powerful tool to evaluate the impact of uncertainties in (carbon) ion therapy. The number of input parameters that can be examined at once is only limited by computation time. A Monte Carlo-derived, comprehensive uncertainty quantification and a corresponding sensitivity analysis are implemented and provide new information for treatment plan evaluation. A possible future application is a SA-based biologically robust treatment plan optimization using the additional uncertainty information as presented here.

Extending the global reliability sensitivity analysis to the systems under double-stochastic uncertainty

Systems with random variables and random excitations exist widely in various engineering problems. Extending the traditional global reliability sensitivity to this double-stochastic system has important guiding significance for its design optimization. However, because there is a certain coupling between the randomness of variables and the randomness of excitation, this coupling mechanism is difficult to determine in practical projects. Therefore, it is difficult to extend the traditional reliability sensitivity analysis method to this double-stochastic system. In this research, it is assumed that there is no correlation between variables and excitations. Then, combining the first-passage method–based dynamic strength formula and the variance-based sensitivity analysis method, an approximate global reliability sensitivity analysis method for this double-stochastic system is proposed. In order to improve the computational efficiency, a nested loop method based on seven-point estimation is proposed for reliability sensitivity analysis. In order to verify the accuracy and efficiency of the proposed method, a Monte Carlo simulation is given as a reference. Three examples are studied and discussed to illustrate the practicality and feasibility of the proposed method.

Sensitivity analysis of building energy performance: A simulation-based approach using OFAT and variance-based sensitivity analysis methods

In this research, one-factor-at-a-time (OFAT) and variance-based sensitivity analysis methods integrate with EnergyPlus through MATLAB to define predominant variables affecting the energy efficiency of buildings in the early phase of building design. To explore the capabilities of the developed method, it is tested on a typical room model; and the impacts of the design variables, including building orientation, window size, overhang system, and the glazing and walls specifications on the building energy demands are studied in four main weather conditions of Iran. The local and global sensitivity analysis of the annual cooling, heating, lighting and total building electricity are carried out. The results show that for our typical case study, the window size is the prevailing parameter on the annual cooling, heating and total building energy electricity while the glazing visible transmittance has the greatest influence on the annual lighting one in all weather conditions. The developed simulation-based sensitivity analysis method demonstrates a useful tool that aids building energy engineers and decision-makers to concentrate on the most important parameters in the initial stages of planning and promote the building energy efficiency.

Sensitivity analysis using a variance-based method for a three-axis diamond turning machine

It is of great interest to determine which of the numerous sources of error in an ultra-precision diamond turning machine has the greatest influence on the machining inaccuracy. Global sensitivity analysis is a well-known mathematical technique that is able to quantify the contribution of each error source to the machining inaccuracy. The present study employs a variance-based sensitivity analysis method to comprehensively investigate the influence of each error source in a three-axis diamond turning machine on the machining inaccuracy. The procedure for establishing a volumetric error model based on multi-body system theory in conjunction with a homogeneous transformation matrix is first described in detail. The basic working principle and relevant estimation process of the Sobol method is then explained, and the Sobol method is employed to quantify the sensitivity index of each error source based on the volumetric error model. Finally, simulation testing is conducted to comprehensively investigate the main geometric error sources contributing to machining errors along the X, Y, and Z directions, and with respect to comprehensive volumetric errors. After the main geometric error sources are identified, some measures are taken to improve the identified error sources, and a flat surface cutting experiment is conducted to verify the effectiveness of the proposed sensitivity method. The results show that the proposed sensitivity method is effective for identifying the most crucial geometric errors, the form error of flat surface is improved by approximately 50% after modifying parts of these errors, and these errors should then be the subjects of careful scrutiny in the precision design, error compensation, and precision processing stages. The method is of significant guidance for on-machine and real-time online error compensation.

The improvement of a variance-based sensitivity analysis method and its application to a ship hull optimization model

Increasingly, more parameters to express and modify ship hull forms are used as variables to identify better designs; however, such proliferation of parameters may result in inefficient and impractical optimization. Dimension reduction by sensitivity analysis (SA) is a feasible way to alleviate this problem. The widely applied variance-based SA is able to determine uninfluential variables for the descending dimension. Sobol and kriging model-based tensor-product basis function (TPBF) methods are studied as representatives of the classical and metamodeling approach of variance-based SA, respectively. The Sobol method is improved by new integrals with less variance and quasi-random numbers with lower star discrepancy for increasing SA accuracy. New integrals reduce the variance of estimation for conditional variance, which results in higher accuracy as demonstrated from the perspective of the Monte Carlo method. More uniform quasi-random numbers generated by uniform design instead of a conventional Sobol sequence potentially improve the accuracy of the quasi Monte Carlo method. A function indicates that both measures can effectively increase the accuracy of SA. The kriging model-based TPBF method is extended from the original ordinary kriging model to linear and quadratic kriging models to extend its application in hull form optimization. A numerical example demonstrates that the accuracy of the kriging model-based TPBF method is higher than that of the improved Sobol method. Nevertheless, it is vulnerable to ill-conditioned correlation matrices. Finally, both methods are implemented in a ship hull form optimization model, and an uninfluential variable for dimension reduction is determined. Both methods should be applied simultaneously if possible due to the higher accuracy of the kriging model-based TPBF method and better robustness of the improved Sobol method.

Assessment of parameter uncertainty in hydrological model using a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis method

Summary Without a realistic assessment of parameter uncertainty, decision makers may encounter difficulties in accurately describing hydrologic processes and assessing relationships between model parameters and watershed characteristics. In this study, a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis (MCMC-MFA) method is developed, which can not only generate samples of parameters from a well constructed Markov chain and assess parameter uncertainties with straightforward Bayesian inference, but also investigate the individual and interactive effects of multiple parameters on model output through measuring the specific variations of hydrological responses. A case study is conducted for addressing parameter uncertainties in the Kaidu watershed of northwest China. Effects of multiple parameters and their interactions are quantitatively investigated using the MCMC-MFA with a three-level factorial experiment (totally 81 runs). A variance-based sensitivity analysis method is used to validate the results of parameters’ effects. Results disclose that (i) soil conservation service runoff curve number for moisture condition II (CN2) and fraction of snow volume corresponding to 50% snow cover (SNO50COV) are the most significant factors to hydrological responses, implying that infiltration-excess overland flow and snow water equivalent represent important water input to the hydrological system of the Kaidu watershed; (ii) saturate hydraulic conductivity (SOL_K) and soil evaporation compensation factor (ESCO) have obvious effects on hydrological responses; this implies that the processes of percolation and evaporation would impact hydrological process in this watershed; (iii) the interactions of ESCO and SNO50COV as well as CN2 and SNO50COV have an obvious effect, implying that snow cover can impact the generation of runoff on land surface and the extraction of soil evaporative demand in lower soil layers. These findings can help enhance the hydrological model’s capability for simulating/predicting water resources.

RelapManager: A Safety Analysis Automation Framework and Software for RELAP5-3D

Evaluation methodologies are under development at BWX Technologies (BWXT) to support licensure of the BWXT small modular reactor. In these evaluation methodologies, RELAP5-3D is being used as the computation engine for reactor coolant system performance. To facilitate analyses, the RelapManager code was developed as a Windows-based graphical user interface for RELAP5-3D. It is used to edit RELAP5-3D input models and develop simulation suites with unique attention to the preparation of Quality Program records required per 10 CFR 50 Appendix B. The software has been created with Visual Studio employing the .NET integrated development environment. The programming focal point for RelapManager is an XML schema that captures the modeling rules inherent in RELAP5-3D. It transforms an existing input model into XML, which, through a large library of functions created to support XML file types, provides a rich user experience capable of improving productivity and quality.RelapManager includes specialized features for the preparation of uncertainty and sensitivity/importance analyses, execution on a remote server, plotting, and data checking against the modeling rules. As a demonstration of these features, an uncertainty and importance analysis has been prepared using the “Typical PWR” test problem provided with the nominal RELAP5-3D release package. RelapManager takes as input uncertainty models characterizing the expected domain of model parameter variability. Subsequently, a calculation suite derived from sampling the uncertainty domain is described, and a run script is prepared by RelapManager. Figure of merit results are gathered by RelapManager and analyzed using a variance-based sensitivity analysis method.

Understanding hydrological flow paths in conceptual catchment models using uncertainty and sensitivity analysis

Increasing pressures on water quality due to intensification of agriculture have raised demands for environmental modeling to accurately simulate the movement of diffuse (nonpoint) nutrients in catchments. As hydrological flows drive the movement and attenuation of nutrients, individual hydrological processes in models should be adequately represented for water quality simulations to be meaningful. In particular, the relative contribution of groundwater and surface runoff to rivers is of interest, as increasing nitrate concentrations are linked to higher groundwater discharges. These requirements for hydrological modeling of groundwater contribution to rivers initiated this assessment of internal flow path partitioning in conceptual hydrological models.In this study, a variance based sensitivity analysis method was used to investigate parameter sensitivities and flow partitioning of three conceptual hydrological models simulating 31 Irish catchments. We compared two established conceptual hydrological models (NAM and SMARG) and a new model (SMART), produced especially for water quality modeling. In addition to the criteria that assess streamflow simulations, a ratio of average groundwater contribution to total streamflow was calculated for all simulations over the 16 year study period. As observations time-series of groundwater contributions to streamflow are not available at catchment scale, the groundwater ratios were evaluated against average annual indices of base flow and deep groundwater flow for each catchment. The exploration of sensitivities of internal flow path partitioning was a specific focus to assist in evaluating model performances. Results highlight that model structure has a strong impact on simulated groundwater flow paths. Sensitivity to the internal pathways in the models are not reflected in the performance criteria results. This demonstrates that simulated groundwater contribution should be constrained by independent data to ensure results within realistic bounds if such models are to be used in the broader environmental sustainability decision making context.

Personalization of models with many model parameters: an efficient sensitivity analysis approach.

Uncertainty quantification and global sensitivity analysis are indispensable for patient-specific applications of models that enhance diagnosis or aid decision-making. Variance-based sensitivity analysis methods, which apportion each fraction of the output uncertainty (variance) to the effects of individual input parameters or their interactions, are considered the gold standard. The variance portions are called the Sobol sensitivity indices and can be estimated by a Monte Carlo (MC) approach (e.g., Saltelli's method [1]) or by employing a metamodel (e.g., the (generalized) polynomial chaos expansion (gPCE) [2, 3]). All these methods require a large number of model evaluations when estimating the Sobol sensitivity indices for models with many parameters [4]. To reduce the computational cost, we introduce a two-step approach. In the first step, a subset of important parameters is identified for each output of interest using the screening method of Morris [5]. In the second step, a quantitative variance-based sensitivity analysis is performed using gPCE. Efficient sampling strategies are introduced to minimize the number of model runs required to obtain the sensitivity indices for models considering multiple outputs. The approach is tested using a model that was developed for predicting post-operative flows after creation of a vascular access for renal failure patients. We compare the sensitivity indices obtained with the novel two-step approach with those obtained from a reference analysis that applies Saltelli's MC method. The two-step approach was found to yield accurate estimates of the sensitivity indices at two orders of magnitude lower computational cost.

Identifying the key water levels in reservoir operation on ecological objectives

This paper investigates the influences of reservoir water level variations of the operation rule curves on different objectives, especially on ecological objectives. Five representative ecological objectives are selected besides industrial and domestic (I&amp;D) and agricultural water supply objectives. They can reflect the impacts of reservoir operation on different attributes of ecological flow regime in the Biliuhe Reservoir case study, Northeastern China. Sensitivities of water supply and ecological objectives caused by water level variations of I&amp;D and agricultural operation rule curves are analyzed by using a variance-based sensitivity analysis method – Sobol's method. Results show that impacts of individual water levels and their interactions on ecological objectives are very different. Also the ecological objectives do not always conflict with water supply objectives. This study provides new insights for reservoir managers to improve downstream aquatic ecosystem by adjusting water levels not only at individual time periods but also at some interacting time periods. Furthermore, it helps us better understand the influence mechanism of water level changes on different objectives, and provides guidance for the development of reservoir operation rules.