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.

Sensitivity analysis of factors affecting gravity dam anti-sliding stability along a foundation surface using Sobol method

The anti-sliding stability of a gravity dam along its foundation surface is a key problem in the design of gravity dams.In this study,a sensitivity analysis framework was proposed for investigating the factors affecting gravity dam anti-sliding stability along the foundation surface.According to the design specifications,the loads and factors affecting the stability of a gravity dam were comprehensively selected.Afterwards,the sensitivity of the factors was preliminarily analyzed using the Sobol method with Latin hypercube sampling.Then,the results of the sensitivity analysis were verified with those obtained using the Garson method.Finally,the effects of different sampling methods,probability distribution types of factor samples,and ranges of factor values on the analysis results were evaluated.A case study of a typical gravity dam in Yunnan Province of China showed that the dominant factors affecting the gravity dam anti-sliding stability were the anti-shear cohesion,upstream and downstream water levels,anti-shear friction coefficient,uplift pressure reduction coefficient,concrete density,and silt height.Choice of sampling methods showed no significant effect,but the probability distribution type and the range of factor values greatly affected the analysis results.Therefore,these two elements should be sufficiently considered to improve the reliability of the dam anti-sliding stability analysis.

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.

Parameter sensitivity analysis for a biochemically-based photosynthesis model

A challenge for the development of Land Surface Models(LSMs) is improving transpiration of water exchange and photosynthesis of carbon exchange between terrestrial plants and the atmosphere, both of which are governed by stoma in leaves. In the photosynthesis module of these LSMs, variations of parameters arising from diversity in plant functional types(PFTs) and climate remain unclear. Identifying sensitive parameters among all photosynthetic parameters before parameter estimation can not only reduce operation cost, but also improve the usability of photosynthesis models worldwide. Here, we analyzed 13 parameters of a biochemically-based photosynthesis model(FvCB), implemented in many LSMs, using two sensitivity analysis(SA) methods(i.e., the Sobol’ method and the Morris method) for setting up the parameter ensemble. Three different model performance metrics, i.e.,Root Mean Squared Error(RMSE), Nash Sutcliffe efficiency(NSE), and Standard Deviation(STDEV) were introduced for model assessment and sensitive parameters identification. The results showed that among all photosynthetic parameters only a small portion of parameters were sensitive, and the sensitive parameters were different across plant functional types: maximum rate of Rubisco activity(Vcmax25), maximum electron transport rate(Jmax25), triose phosphate use rate(TPU) and dark respiration in light(Rd) were sensitive in broad leafevergreen trees(BET), broad leaf-deciduous trees(BDT) and needle leaf-evergreen trees(NET), while only Vcmax25and TPU are sensitive in short vegetation(SV), dwarf trees and shrubs(DTS), and agriculture and grassland(AG). The two sensitivity analysis methods suggested a strong SA coherence;in contrast, different model performance metrics led to different SA results. This misfit suggests that more accurate values of sensitive parameters, specifically, species specific and seasonal variable parameters, are required to improve the performance of the FvCB model.

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 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.

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.

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.

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 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.

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.

Sensitivity Analysis for Epistemic Uncertain System Based on Sobol' Method

Considering the characteristics of sensitivity analysis in epistemic uncertain system,a new sensitivity analysis index based on Sobol' method was proposed. Then the index calculation method with single cycle Monte-Carlo sampling was studied, and an application was developed. Numerical examples show that,the new method could solve the system sensitivity analysis problem with mixed aleotory and epistemic uncertainties. In this method,aleotory uncertain parameters could be sampled randomly according their distributions, and need not be translated to evidence bodies.Epistemic uncertain parameters were sampled randomly based on evidence theory. Therefore the loss of information in the sampling process was small,and the shortcomings of the existing methods were overcome.

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.

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 .

基于FAST和Sobol指数法的雷达系统效能敏感性分析

为了以较小的代价快速提升对空探测雷达系统的综合效能,首先搭建了对空探测雷达系统综合效能的评估指标体系,在此基础上完成了综合效能评估模型的建立。选择两种基于方差原理的全局敏感性分析方法,即傅里叶幅度敏感性测试(Fourier amplitudes sensitivity test,FAST)和Sobol指数法,分别从频域和时域对建立的评估模型进行敏感性分析。在基于FAST进行敏感性分析时,提出了21维输入指标所对应的特征频率集的选取方法;在基于Sobol指数法进行敏感性分析时,考虑了二阶及高阶敏感性指数的影响。对比FAST和Sobol指数法的分析结果,两种方法获得的敏感性分析结果具有较好的一致性。其中,功率和频率为对空探测雷达系统的主要影响指标,为雷达系统的研发和升级提供了可靠性依据。

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.