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.

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.

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.

A surrogate model for uncertainty quantification and global sensitivity analysis of nonlinear large-scale dome structures

Full-scale dome structures intrinsically have numerous sources of irreducible aleatoric uncertainties.A large-scale numerical simulation of the dome structure is required to quantify the effects of these sources on the dynamic performance of the structure using the finite element method(FEM).To reduce the heavy computational burden,a surrogate model of a dome structure was constructed to solve this problem.The dynamic global sensitivity of elastic and elastoplastic structures was analyzed in the uncertainty quantification framework using fully quantitative variance-and distribution-based methods through the surrogate model.The model considered the predominant sources of uncertainty that have a significant influence on the performance of the dome structure.The effects of the variables on the structural performance indicators were quantified using the sensitivity index values of the different performance states.Finally,the effects of the sample size and correlation function on the accuracy of the surrogate model as well as the effects of the surrogate accuracy and failure probability on the sensitivity index values are discussed.The results show that surrogate modeling has high computational efficiency and acceptable accuracy in the uncertainty quantification of large-scale structures subjected to earthquakes in comparison to the conventional FEM.

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.

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 and uncertainty analysis of the VIP ecosystem model with an expanded soil nitrogen module for winter wheat-summer maize rotation system in the North China Plain

Accurately simulating the soil nitrogen(N)cycle is crucial for assessing food security and resource utilization efficiency.The accuracy of model predictions relies heavily on model parameterization.The sensitivity and uncertainty of the simulations of soil N cycle of winter wheat-summer maize rotation system in the North China Plain(NCP)to the parameters were analyzed.First,the N module in the Vegetation Interface Processes(VIP)model was expanded to capture the dynamics of soil N cycle calibrated with field measurements in three ecological stations from 2000 to 2015.Second,the Morris and Sobol algorithms were adopted to identify the sensitive parameters that impact soil nitrate stock,denitrification rate,and ammonia volatilization rate.Finally,the shuffled complex evolution developed at the University of Arizona(SCE-UA)algorithm was used to optimize the selected sensitive parameters to improve prediction accuracy.The results showed that the sensitive parameters related to soil nitrate stock included the potential nitrification rate,Michaelis constant,microbial C/N ratio,and slow humus C/N ratio,the sensitive parameters related to denitrification rate were the potential denitrification rate,Michaelis constant,and N2 O production rate,and the sensitive parameters related to ammonia volatilization rate included the coefficient of ammonia volatilization exchange and potential nitrification rate.Based on the optimized parameters,prediction efficiency was notably increased with the highest coefficient of determination being approximately 0.8.Moreover,the average relative interval length at the 95% confidence level for soil nitrate stock,denitrification rate,and ammonia volatilization rate were 11.92,0.008,and 4.26,respectively,and the percentages of coverage of the measured values in the 95% confidence interval were 68%,86%,and 92%,respectively.By identifying sensitive parameters related to soil N,the expanded VIP model optimized by the SCE-UA algorithm can effectively simulate the dynamics of soil nitrate stock,denitrification rate,and ammonia volatilization rate in the NCP.

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.

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.

Jackknife based generalized resampling reliability approach for rock slopes and tunnels stability analyses with limited data:Theory and applications

An efficient resampling reliability approach was developed to consider the effect of statistical uncertainties in input properties arising due to insufficient data when estimating the reliability of rock slopes and tunnels.This approach considers the effect of uncertainties in both distribution parameters(mean and standard deviation)and types of input properties.Further,the approach was generalized to make it capable of analyzing complex problems with explicit/implicit performance functions(PFs),single/multiple PFs,and correlated/non-correlated input properties.It couples resampling statistical tool,i.e.jackknife,with advanced reliability tools like Latin hypercube sampling(LHS),Sobol’s global sensitivity,moving least square-response surface method(MLS-RSM),and Nataf’s transformation.The developed approach was demonstrated for four cases encompassing different types.Results were compared with a recently developed bootstrap-based resampling reliability approach.The results show that the approach is accurate and significantly efficient compared with the bootstrap-based approach.The proposed approach reflects the effect of statistical uncertainties of input properties by estimating distributions/confidence intervals of reliability index/probability of failure(s)instead of their fixed-point estimates.Further,sufficiently accurate results were obtained by considering uncertainties in distribution parameters only and ignoring those in distribution types.

An experiment evaluating how the tiny mass eccentricities in spinstabilized projectiles affect the position of impact points

This study investigates and quantifies some possible sources affecting the position of impact points of small caliber spin-stabilized projectiles(such as 12.7 mm bullets).A comparative experiment utilizing the control variable method was designed to figure out the influence of tiny eccentric centroids on the projectiles.The study critically analyzes data obtained from characteristic parameter measurements and precision trials.It also combines Sobol’s algorithm with an artificial intelligence algorithmdAdaptive Neuro-Fuzzy Inference Systems(ANFIS)ein order to conduct global sensitivity analysis and determine which parameters were most influential.The results indicate that the impact points of projectiles with an entry angle of 0°deflected to the left to that of projectiles with an entry angle of 90°.The difference of the mean coordinates of impact points was about 12.61 cm at a target range of 200 m.Variance analysis indicated that the entry angleei.e.the initial position of mass eccentricityehad a notable influence.After global sensitivity analysis,the significance of the effect of mass eccentricity was confirmed again and the most influential factors were determined to be the axial moment and transverse moment of inertia(Izz Iyy),the mass of a projectile(m),the distance between nose and center of mass along the symmetry axis for a projectile(Lm),and the eccentric distance of the centroid(Lr).The results imply that the control scheme by means of modifying mass center(moving mass or mass eccentricity)is promising for designing small-caliber spin-stabilized projectiles.

Bi-objective path optimization of flapping airfoils based on a surrogate model

A bi-objective optimization problem for flapping airfoils is solved to maximize the time-averaged thrust coefficient and the propulsive efficiency. Design variables include the plunging amplitude, the pitching amplitude and the phase shift angle. A well defined Kriging model is used to substitute the time-consuming high fidelity model, and a multi-objective genetic algorithm is employed as the search algorithm. The optimization results show that the propulsive efficiency can be improved by reducing the plunging amplitude and the phase shift angle in a proper way. The results of global sensitivity analysis using the Sobol’s method show that both of the time-averaged thrust coefficient and the propulsive efficiency are most sensitive to the plunging amplitude, and second most sensitive to the pitching amplitude. It is also observed that the phase shift angle has an un-negligible influence on the propulsive efficiency, and has little effect on the time-averaged thrust coefficient.

Robust Design Optimization and Improvement by Metamodel

The robust design optimization(RDO)is an effective method to improve product performance with uncertainty factors.The robust optimal solution should be not only satisfied the probabilistic constraints but also less sensitive to the variation of design variables.There are some important issues in RDO,such as how to judge robustness,deal with multi-objective problem and black-box situation.In this paper,two criteria are proposed to judge the deterministic optimal solution whether satisfies robustness requirment.The robustness measure based on maximum entropy is proposed.Weighted sum method is improved to deal with the objective function,and the basic framework of metamodel assisted robust optimization is also provided for improving the efficiency.Finally,several engineering examples are used to verify the advantages.

Multi-perspective analysis on rainfall-induced spatial response of soil suction in a vegetated soil

In this study, an intelligent monitoring platform is established for continuous quantification of soil,vegetation, and atmosphere parameters (e.g. soil suction, rainfall, tree canopy, air temperature, and windspeed) to provide an efficient dataset for modeling suction response through machine learning. Twocharacteristic parameters representing suction response during wetting processes, i.e. response time andmean reduction rate of suction, are formulated through multi-gene genetic programming (MGGP) usingeight selected influential parameters including depth, initial soil suction, vegetation- and atmosphererelated parameters. An error standardebased performance evaluation indicated that MGGP has appreciable potential for model development when working with even fewer than 100 data. Global sensitivityanalysis revealed the importance of tree canopy and mean wind speed to estimation of response timeand indicated that initial soil suction and rainfall amount have an important effect on the estimatedsuction reduction rate during a wetting process. Uncertainty assessment indicated that the two MGGPmodels describing suction response after rainfall are reliable and robust under uncertain conditions. Indepth analysis of spatial variations in suction response validated the robustness of two obtained MGGPmodels in prediction of suction variation characteristics under natural conditions.

Variable Importance Measure System Based on Advanced Random Forest

The variable importance measure(VIM)can be implemented to rank or select important variables,which can effectively reduce the variable dimension and shorten the computational time.Random forest(RF)is an ensemble learning method by constructing multiple decision trees.In order to improve the prediction accuracy of random forest,advanced random forest is presented by using Kriging models as the models of leaf nodes in all the decision trees.Referring to the Mean Decrease Accuracy(MDA)index based on Out-of-Bag(OOB)data,the single variable,group variables and correlated variables importance measures are proposed to establish a complete VIM system on the basis of advanced random forest.The link of MDA and variance-based sensitivity total index is explored,and then the corresponding relationship of proposed VIM indices and variance-based global sensitivity indices are constructed,which gives a novel way to solve variance-based global sensitivity.Finally,several numerical and engineering examples are given to verify the effectiveness of proposed VIM system and the validity of the established relationship.

Ranking parameters in urban energy models for various building forms and climates using sensitivity analysis

Urban Building Energy Modelling(UBEM)allows us to simulate buildings’energy performances at a larger scale.However,creating a reliable urban-scale energy model of new or existing urban areas can be difficult since the model requires overly detailed input data,which is not necessarily publicly unavailable.Model calibration is a necessary step to reduce the uncertainties and simulation results in order to develop a reliable and accurate UBEM.Due to the concerns over computational resources and the time needed for calibration,a sensitivity analysis is often required to identify the key parameters with the most substantial impact before the calibration is deployed in UBEM.Here,we study the sensitivity of uncertain input parameters that affect the annual heating and cooling energy demand by employing an urban-scale energy model,CitySim.Our goal is to determine the relative influence of each set of input parameters and their interactions on heating and cooling loads for various building forms under different climates.First,we conduct a global sensitivity analysis for annual cooling and heating consumption under different climate conditions.Building upon this,we investigate the changes in input sensitivity to different building forms,focusing on the indices with the largest Total-order sensitivity.Finally,we determine First-order indices and Total-order effects of each input parameter included in the urban building energy model.We also provide tables,showing the important parameters on the annual cooling and heating demand for each climate and each building form.We find that if the desired calibration process require to decrease the number of the inputs to save the computational time and cost,calibrating 5 parameters;temperature set-point,infiltration rate,floor U-value,avg.walls U-value and roof U-value would impact the results over 55%for any climate and any building form.

Influence of yaw damper layouts on locomotive lateral dynamics performance:Pareto optimization and parameter analysis

High-speed locomotives are prone to carbody or bogie hunting when the wheel-rail contact conicity is excessively low or high.This can cause negative impacts on vehicle dynamics performance.This study presents four types of typical yaw damper layouts for a high-speed locomotive(Bo-Bo)and compares,by using the multi-objective optimization method,the influences of those layouts on the lateral dynamics performance of the locomotive;the linear stability indexes under lowconicity and high-conicity conditions are selected as optimization objectives.Furthermore,the radial basis function-based highdimensional model representation(RBF-HDMR)method is used to conduct a global sensitivity analysis(GSA)between key suspension parameters and the lateral dynamics performance of the locomotive,including the lateral ride comfort on straight tracks under the low-conicity condition,and also the operational safety on curved tracks.It is concluded that the layout of yaw dampers has a considerable impact on low-conicity stability and lateral ride comfort but has little influence on curving performance.There is also an important finding that only when the locomotive adopts the layout with opening outward,the difference in lateral ride comfort between the front and rear ends of the carbody can be eliminated by adjusting the lateral installation angle of the yaw dampers.Finally,force analysis and modal analysis methods are adopted to explain the influence mechanism of yaw damper layouts on the lateral stability and differences in lateral ride comfort between the front and rear ends of the carbody.

Radiative transfer models(RTMs)for field phenotyping inversion of rice based on UAV hyperspectral remote sensing

The nondestructive and rapid acquisition of rice field phenotyping information is very important for the precision management of the rice growth process.In this research,the phenotyping information LAI(leaf area index),leaf chlorophyll content(C_(ab)),canopy water content(C_(w)),and dry matter content(C_(dm))of rice was inversed based on the hyperspectral remote sensing technology of an unmanned aerial vehicle(UAV).The improved Sobol global sensitivity analysis(GSA)method was used to analyze the input parameters of the PROSAIL model in the spectral band range of 400-1100 nm,which was obtained by hyperspectral remote sensing by the UAV.The results show that C_(ab) mainly affects the spectrum on 400-780 nm band,C_(dm) on 760-1000 nm band,C_(w) on 900-1100 nm band,and LAI on the entire band.The hyperspectral data of the 400-1100 nm band of the rice canopy were acquired by using the M600 UAV remote sensing platform,and the radiance calibration was converted to the canopy emission rate.In combination with the PROSAIL model,the particle swarm optimization algorithm was used to retrieve rice phenotyping information by constructing the cost function.The results showed the following:(1)an accuracy of R^(2)=0.833 and RMSE=0.0969,where RMSE denotes root-mean-square error,was obtained for C_(ab) retrieval;R^(2)=0.816 and RMSE=0.1012 for LAI inversion;R^(2)=0.793 and RMSE=0.1084 for C_(dm);and R^(2)=0.665 and RMSE=0.1325 for C_(w).The C_(w) inversion accuracy was not particularly high.(2)The same band will be affected by multiple parameters at the same time.(3)This study adopted the rice phenotyping information inversion method to expand the rice hyperspectral information acquisition field of a UAV based on the phenotypic information retrieval accuracy using a high level of field spectral radiometric accuracy.The inversion method featured a good mechanism,high universality,and easy implementation,which can provide a reference for nondestructive and rapid inversion of rice biochemical parameters using UAV hyperspectral remote sensing.