A Bayesian multi-model inference methodology for imprecise momentindependent global sensitivity analysis of rock structures

Traditional global sensitivity analysis(GSA)neglects the epistemic uncertainties associated with the probabilistic characteristics(i.e.type of distribution type and its parameters)of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response.This paper proposes an augmented Bayesian multi-model inference(BMMI)coupled with GSA methodology(BMMI-GSA)to address this issue by estimating the imprecision in the momentindependent sensitivity indices of rock structures arising from the small size of input data.The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties.The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo’s indices by employing a reweighting approach on candidate probabilistic models.The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India.The proposed methodology was superior to the conventional GSA(neglects all epistemic uncertainties)and Bayesian coupled GSA(B-GSA)(neglects model uncertainty)due to its capability to incorporate the uncertainties in both model type and parameters of properties.Imprecise Borgonovo’s indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates,which makes the user more informed in the data collection efforts.Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes.The accurate importance ranking of properties was only possible via samples of large sizes.Further,the impact of the prior knowledge in terms of prior ranges and distributions was significant;hence,any related assumption should be made carefully.

Numerical modeling and parametric sensitivity analysis of heat transfer and two-phase oil and water flow characteristics in horizontal and inclined flowlines using OpenFOAM

Estimating the oil-water temperatures in flowlines is challenging especially in deepwater and ultra-deepwater offshore applications where issues of flow assurance and dramatic heat transfer are likely to occur due to the temperature difference between the fluids and the surroundings. Heat transfer analysis is very important for the prediction and prevention of deposits in oil and water flowlines, which could impede the flow and give rise to huge financial losses. Therefore, a 3D mathematical model of oil-water Newtonian flow under non-isothermal conditions is established to explore the complex mechanisms of the two-phase oil-water transportation and heat transfer in different flowline inclinations. In this work, a non-isothermal two-phase flow model is first modified and then implemented in the InterFoam solver by introducing the energy equation using OpenFOAM® code. The Low Reynolds Number (LRN) k-ε turbulence model is utilized to resolve the turbulence phenomena within the oil and water mixtures. The flow patterns and the local heat transfer coefficients (HTC) for two-phase oil-water flow at different flowlines inclinations (0°, +4°, +7°) are validated by the experimental literature results and the relative errors are also compared. Global sensitivity analysis is then conducted to determine the effect of the different parameters on the performance of the produced two-phase hydrocarbon systems for effective subsea fluid transportation. Thereafter, HTC and flow patterns for oil-water flows at downward inclinations of 4°, and 7° can be predicted by the models. The velocity distribution, pressure gradient, liquid holdup, and temperature variation at the flowline cross-sections are simulated and analyzed in detail. Consequently, the numerical model can be generally applied to compute the global properties of the fluid and other operating parameters that are beneficial in the management of two-phase oil-water transportation.

Global sensitivity analysis of wheat grain yield and quality and the related process variables from the DSSAT-CERES model based on the extended Fourier Amplitude Sensitivity Test method

A crop growth model,integrating genotype,environment,and management factor,was developed to serve as an analytical tool to study the influence of these factors on crop growth,production,and agricultural planning.A major challenge of model application is the optimization and calibration of a considerable number of parameters.Sensitivity analysis(SA) has become an effective method to identify the importance of various parameters.In this study,the extended Fourier Amplitude Sensitivity Test(EFAST) approach was used to evaluate the sensitivity of the DSSAT-CERES model output responses of interest to 39 crop genotype parameters and six soil parameters.The outputs for the SA included grain yield and quality(take grain protein content(GPC) as an indicator) at maturity stage,as well as leaf area index,aboveground biomass,and aboveground nitrogen accumulation at the critical process variables.The key results showed that:(1) the influence of parameter bounds on the sensitivity results was slight and less than the impacts from the significance of the parameters themselves;(2) the sensitivity parameters of grain yield and GPC were different,and the sensitivity of the interactions between parameters to GPC was greater than those between the parameters to grain yield;and(3) the sensitivity analyses of some process variables,including leaf area index,aboveground biomass,and aboveground nitrogen accumulation,should be performed differently.Finally,some parameters,which improve the model’s structure and the accuracy of the process simulation,should not be ignored when maturity output as an objective variable is studied.

Global analysis of sensitivity of bioretention cell design elements to hydrologic performance

Analysis of sensitivity of bioretention cell design elements to their hydrologic performances is meaningful in offering theoretical guidelines for proper design. Hydrologic performance of bioretention cells was facilitated with consideration of four metrics： the overflow ratio, groundwater recharge ratio, ponding time, and runoff coefficients. The storm water management model （SWMM） and the bioretention infiltration model RECARGA were applied to generating runoff and outflow time series for calculation of hydrologic performance metrics. Using a parking lot to build a bioretention cell, as an example, the Morris method was used to conduct global sensitivity analysis for two groups of bioretention samples, one without underdrain and the other with underdrain. Results show that the surface area is the most sensitive element to most of the hydrologic metrics, while the gravel depth is the least sensitive element whether bioretention cells are installed with underdrain or not. The saturated infiltration rate of planting soil and the saturated infiltration rate of native soil are the other two most sensitive elements for bioretention cells without underdrain, while the saturated infiltration rate of native soil and underdrain size are the two most sensitive design elements for bioretention cells with underdrain.

Parameter identification and global sensitivity analysis of Xin'anjiang model using meta-modeling approach

Parameter identification, model calibration, and uncertainty quantification are important steps in the model-building process, and are necessary for obtaining credible results and valuable information. Sensitivity analysis of hydrological model is a key step in model uncertainty quantification, which can identify the dominant parameters, reduce the model calibration uncertainty, and enhance the model optimization efficiency. There are, however, some shortcomings in classical approaches, including the long duration of time and high computation cost required to quantitatively assess the sensitivity of a multiple-parameter hydrological model. For this reason, a two-step statistical evaluation framework using global techniques is presented. It is based on （1） a screening method （Morris） for qualitative ranking of parameters, and （2） a variance-based method integrated with a meta-model for quantitative sensitivity analysis, i.e., the Sobol method integrated with the response surface model （RSMSobol）. First, the Morris screening method was used to qualitatively identify the parameters＇ sensitivity, and then ten parameters were selected to quantify the sensitivity indices. Subsequently, the RSMSobol method was used to quantify the sensitivity, i.e., the first-order and total sensitivity indices based on the response surface model （RSM） were calculated. The RSMSobol method can not only quantify the sensitivity, but also reduce the computational cost, with good accuracy compared to the classical approaches. This approach will be effective and reliable in the global sensitivity analysis of a complex large-scale distributed hydrological model.

Moment-independence global sensitivity analysis for the system with fuzzy failure state and its Kriging method

For the system with the fuzzy failure state, the effects of the input random variables and the fuzzy failure state on the fuzzy probability of failure for the structural system are studied, and the moment-independence global sensitivity analysis（GSA） model is proposed to quantitatively measure these effects. According to the fuzzy random theory, the fuzzy failure state is transformed into an equivalent new random variable for the system, and the complementary function of the membership function of the fuzzy failure state is defined as the cumulative distribution function（CDF） of the new random variable. After introducing the new random variable, the equivalent performance function of the original problem is built. The difference between the unconditional fuzzy probability of failure and conditional fuzzy probability of failure is defined as the moment-independent GSA index. In order to solve the proposed GSA index efficiently, the Kriging-based algorithm is developed to estimate the defined moment-independence GSA index. Two engineering examples are employed to verify the feasibility and rationality of the presented GSA model, and the advantages of the developed Kriging method are also illustrated.

A Processor Performance Prediction Method Based on Interpretable Hierarchical Belief Rule Base and Sensitivity Analysis

The prediction of processor performance has important referencesignificance for future processors. Both the accuracy and rationality of theprediction results are required. The hierarchical belief rule base (HBRB)can initially provide a solution to low prediction accuracy. However, theinterpretability of the model and the traceability of the results still warrantfurther investigation. Therefore, a processor performance prediction methodbased on interpretable hierarchical belief rule base (HBRB-I) and globalsensitivity analysis (GSA) is proposed. The method can yield more reliableprediction results. Evidence reasoning (ER) is firstly used to evaluate thehistorical data of the processor, followed by a performance prediction modelwith interpretability constraints that is constructed based on HBRB-I. Then,the whale optimization algorithm (WOA) is used to optimize the parameters.Furthermore, to test the interpretability of the performance predictionprocess, GSA is used to analyze the relationship between the input and thepredicted output indicators. Finally, based on the UCI database processordataset, the effectiveness and superiority of the method are verified. Accordingto our experiments, our prediction method generates more reliable andaccurate estimations than traditional models.

Global Mission Sensitivity Study for Phased MissionSystem with Analysis of Variance Method

A comprehensive mission sensitivity analysis index based on Sobol's index called global mission sensitivity( GMS) was proposed in this paper which focused on analyzing the mission sensitivity of components of phased mission systems( PMS). The simulation strategy of GMS based on a Petri net and Monte Carlo method was presented which had broad applicability. Finally,the GMS and Birnbaum's sensitivity of components in a PMS example were compared. The GMS of component is demonstrated to be more adaptable to reflect the component mission sensitivity when the rated reliability parameters of components cannot be obtained, and components have state dependency or the system is subjected to common cause failure.

Global sensitivity analysis based on high-dimensional sparse surrogate construction

Surrogate models are usually used to perform global sensitivity analysis （GSA） by avoiding a large ensemble of deterministic simulations of the Monte Carlo method to provide a reliable estimate of GSA indices. However, most surrogate models such as polynomial chaos （PC） expansions suffer from the curse of dimensionality due to the high-dimensional input space. Thus, sparse surrogate models have been proposed to alleviate the curse of dimensionality. In this paper, three techniques of sparse reconstruc- tion are used to construct sparse PC expansions that are easily applicable to computing variance-based sensitivity indices （Sobol indices）. These are orthogonal matching pursuit （OMP）, spectral projected gradient for L1 minimization （SPGL1）, and Bayesian compressive sensing with Laplace priors. By computing Sobol indices for several benchmark response models including the Sobol function, the Morris function, and the Sod shock tube problem, effective implementations of high-dimensional sparse surrogate construction are exhibited for GSA.

Global Comprehensive Sensitivity Analysis of Arch Dam Construction Parameters Based on Orthogonal Experiment

The construction of arch dams exhibits high uncertainty. Sensitivity analysis of construction parameters is important for the design and optimization of dam construction duration. However, current research cannot fully consider the combined influences of multiple parameters on the total construction. To effectively analyze the duration of arch dam construction, this study proposes a global comprehensive sensitivity analysis method in view of the whole process of arch dam construction based on an orthogonal experiment. This method could comprehensively consider the influence of the construction parameters that may lead to the uncertainty of construction duration. In addition, this method is able to identify the key parameters that may have a significant effect on duration uncertainty and sums up the general rules of combined parameters’ interaction effect, which provides a scientific basis for reasonable optimization of the duration of dam construction. © 2017, Tianjin University and Springer-Verlag GmbH Germany.

Global Bounded Solutions for the Keller-Segel Chemotaxis System with Singular Sensitivity

In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity (0.1) is considered in a bounded domain with smooth boundary, Ω ⊂Rn (n ≥ 1), where d1 > 0, d2 > 0 with parameter χ ∈ R. When d1 = d2 + χ, satisfying for all initial data 0 ≤ n0 ∈ C0 and 0 < v0∈ W1,∞ (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).

Global Sensitivity Analysis in Physiological Systems

Pharmacokinetic models are mathematical models which provide insights into the interaction of chemicals with biological processes. During recent decades, these models have become central of attention in industry that caused to do a lot of efforts to make them more accurate. Current work studies the process of drug and nanoparticle (NPs) distribution throughout the body which consists of a system of ordinary differential equations. We use a tri-compartmental model to study the perfusion of NPs in tissues and a six-compartmental model to study drug distribution in different body organs. We have performed global sensitivity analysis by LHS Monte Carlo method using PRCC. We identify the key parameters that contribute most significantly to the absorption and distribution of drugs and NPs in different organs in body.

Rational Drug Delineation: A Global Sensitivity Approach Based on Therapeutic Tolerability to Deviations in Execution

Noncompliance to therapeutic regimen is a real public health problem with tremendous socioeconomic consequences. Instead of direct intervention to patients, which can add extra burden to the already overloaded health system, alternative strategies oriented to drugs’ own properties turns to be more appealing. The aim of this study was establish a rational way to delineate drugs in terms of their “forgiveness”, based on drugs PK/PD properties. A global sensitivity analysis has been performed to identify the most sensitive parameters to dose omissions. A Comparative Drug Forgiveness Index (CDFI), to rank the drugs in terms of their tolerability to non compliance, has been proposed. The index was applied to a number of calcium channel blockers, namely benidipine, nivaldipine, manidipine and felodipine. Using the calculation, benedipine and manidipine showed the best performance among those considered. This result is in accordance with what has been previously reported. The classification method developed here proved to be a powerful quantitative way to delineate drugs in terms of their forgiveness and provides a complementary decision rule for clinical and experimental studies.

Global sensitivity analysis for choosing the main soil parameters of a crop model to be determined

The use of a crop model like STICS for appropriate management decision support requires a good knowledge of all the parameters of the model. Among them, the soil parameters are difficult to know at each point of interest and costly techniques may be used to measure them. It is therefore important to know which soil parameters need to be determined. It can be stated that those which affect significantly the output variable deserve an accurate determination while those which slightly affect the model output variable do not. This paper demonstrates how a global sensitivity analysis method based on variance decomposition can be applied on soil parameters in order to divide them in the two categories. The Extended FAST method applied to the crop model STICS and a set of 13 soil parameters first allows to calculate the part of variance explained by each soil parameter (giving global sensitivity indices of the soil parameters) and the coefficient of variation of the output variables (measuring the effect of the parameter uncertainty on each variable). These metrics are therefore used for deciding on the importance of the parameter value measurement. Different output variables (Leaf Area Index and chlorophyll content) are evaluated at different stages of interest while others (crop yield, grain protein content, soil mineral nitrogen) are evaluated at harvest. The analysis is applied on two different annual crops (wheat and sugar beet), two contrasted weather and two types of soil depth. When the uncertainty of the output generated by the soil parameters is large (coefficient of variation > 1/3), only the parameters having a significant global sensitivity indices (higher than 10%) are retained. The results show that the number of soil parameters which deserve an accurate determination can be significantly reduced by the use of this relevant method for appropriate management decision support.

Multi-parameter Sensitivity Analysis and Application Research in the Robust Optimization Design for Complex Nonlinear System

The current research of complex nonlinear system robust optimization mainly focuses on the features of design parameters, such as probability density functions, boundary conditions, etc. After parameters study, high-dimensional curve or robust control design is used to find an accurate robust solution. However, there may exist complex interaction between parameters and practical engineering system. With the increase of the number of parameters, it is getting hard to determine high-dimensional curves and robust control methods, thus it＇s difficult to get the robust design solutions. In this paper, a method of global sensitivity analysis based on divided variables in groups is proposed. By making relevant variables in one group and keeping each other independent among sets of variables, global sensitivity analysis is conducted in grouped variables and the importance of parameters is evaluated by calculating the contribution value of each parameter to the total variance of system response. By ranking the importance of input parameters, relatively important parameters are chosen to conduct robust design analysis of the system. By applying this method to the robust optimization design of a real complex nonlinear system-a vehicle occupant restraint system with multi-parameter, good solution is gained and the response variance of the objective function is reduced to 0.01, which indicates that the robustness of the occupant restraint system is improved in a great degree and the method is effective and valuable for the robust design of complex nonlinear system. This research proposes a new method which can be used to obtain solutions for complex nonlinear system robust design.

Simulation of phytoplankton biomass in Quanzhou Bay using a back propagation network model and sensitivity analysis for environmental variables

Prediction and sensitivity models,to elucidate the response of phytoplankton biomass to environmental factors in Quanzhou Bay,Fujian,China,were developed using a back propagation(BP) network.The environmental indicators of coastal phytoplankton biomass were determined and monitoring data for the bay from 2008 was used to train,test and build a three-layer BP artificial neural network with multi-input and single-output.Ten water quality parameters were used to forecast phytoplankton biomass(measured as chlorophyll-a concentration).Correlation coefficient between biomass values predicted by the model and those observed was 0.964,whilst the average relative error of the network was-3.46% and average absolute error was 10.53%.The model thus has high level of accuracy and is suitable for analysis of the influence of aquatic environmental factors on phytoplankton biomass.A global sensitivity analysis was performed to determine the influence of different environmental indicators on phytoplankton biomass.Indicators were classified according to the sensitivity of response and its risk degree.The results indicate that the parameters most relevant to phytoplankton biomass are estuary-related and include pH,sea surface temperature,sea surface salinity,chemical oxygen demand and ammonium.

Unrealistic treatment of detrained water substance in FGOALS-s2 and its influence on the model's climate sensitivity

Based on a series of aqua-planet and air–sea coupled experiments,the influence of unrealistic treatment of water substance in the Flexible Global Ocean–Atmosphere–Land System Model,spectral version 2（FGOALS-s2）,on the model＇s climate sensitivity is investigated in this paper.Because the model does not adopt an explicit microphysics scheme,the detrained water substance from the convection scheme is converted back to the humidity.This procedure could lead to an additional increase of water vapor in the atmosphere,which could strengthen the model＇s climate sensitivity.Further sensitivity experiments confirm this deduction.After removing the water vapor converted from the detrained water substance,the water vapor reduced significantly in the upper troposphere and the high clouds also reduced.Quantitative calculations show that the water vapor reduced almost 10% of the total water vapor,and 50% at 150 h Pa,when the detrained water substance was removed,contributing to the 30% atmospheric surface temperature increase.This study calls for an explicit microphysics scheme to be introduced into the model in order to handle the detrained water vapor and thus improve the model＇s simulation skill.

Sensitivity of the Indian Monsoon to Human Activities

In this paper the authors perform an extensive sensitivity analysis of the Indian summer monsoon rainfall to changes in parameters and boundary conditions which are influenced by human activities. For this study the authors use a box model of the Indian monsoon which reproduces key features of the observed monsoon dynamics such as the annual course of precipitation and the transitions between winter and summer regimes. Because of its transparency and computational efficiency, this model is highly suitable for exploring the effects of anthropogenic perturbations such as emissions of greenhouse gases and sulfur dioxide, and land cover changes, on the Indian monsoon. Results of a systematic sensitivity analysis indicate that changes in those parameters which are related to emissions of greenhouse gases lead to an increase in Indian summer rainfall. In contrast, all parameters related to higher atmospheric aerosol concentrations lead to a decrease in Indian rainfall. Similarly, changes in parameters which can be related to forest conversion or desertifieation, act to decrease the summer precipitation. The results indicate that the sign of precipitation changes over India will be dependent on the direction and relative magnitude of different human perturbations.

Method Based on Time Randomization to Resist Fault Sensitivity Analysis

A fault sensitivity analysis（FSA）-resistance model based on time randomization is proposed.The randomization unit is composed of two parts,namely the configurable register array（R-A）and the decoder（chiefly random number generator,RNG）.In this way,registers chosen can be either valid or invalid depending on the configuration information generated by the decoder.Thus,the fault sensitivity information can be confusing.Meanwhile,based on this model,a defensive scheme is designed to resist both fault sensitivity analysis（FSA）and differential power analysis（DPA）.This scheme is verified with our experiments.

Sensitivity Analysis on the Negative Degree of Difficulty Geometric Programming Problem

The range of optimal values in cost optimization models provides management with options for decision making. However, it can be quite challenging to achieve feasible range of optimality in Geometric programming (Gp) models having negative degrees of difficulty. In this paper, we conduct sensitivity analysis on the optimal solution of Geometric programming problem with negative degree of difficulty. Using imprest data, we determine the optimal objective function, dual decision variables, primal decision variables;the range of values, the cost coefficient and RHS constraint must lie for the solution to stay optimal. From the analysis, we established that incremental sensitivity analysis has the functional form .