Sobol Method Research Articles

A Bayesian Belief Network Model for the Risk Assessment and Management of Premature Screen-Out during Hydraulic Fracturing

Hydraulic fracturing is a well completion technique for Oil and Gas production enhancement in both conventional and unconventional reservoirs. However, it can result in the unfavorable consequence of the premature screen-out, which occurs due to the proppant bridging across the perforations or similar restricted flow areas.The objective of this work is to propose a novel framework of analysis that enables to quantify the risk of screen-out occurrence, to identify the riskiest scenarios and to determine the best risk mitigation strategies. The premature screen-out problem is addressed within a Risk Management and Control Process, wherein the qualitative and quantitative assessments of the early screen-out risk are performed by a Features, Events and Processes Analysis structured with a Bayesian Belief Network. The BBN probabilities are subject to a thorough uncertainty and sensitivity analysis. Sensitivity analysis is performed by the Sobol's variance decomposition method and the identified most influential probabilities of the BBN are re-estimated in order to reduce the output uncertainty.Finally, risk mitigation plans are formulated using risk importance measures to identify the riskiest scenarios and cost-benefit analysis to determine the optimal risk reduction actionsThe developed framework has been applied to a case study of vertical wells.

Temperature Distribution Simulation, Prediction and Sensitivity Analysis of Orthogonal Cutting of Cortical Bone.

Bone cutting plays an important role in spine surgical operations. The power devices with high speed employing in bone cutting usually leads to high cutting temperature of the bone tissue. This high temperature control is important in improving cutting surface quality and optimizing the cutting parameters. In this paper, the bone-cutting model was appropriately simplified for finite element (FE) based modeling of 2D orthogonal cutting to discuss the change law of cutting temperature of cortical bones for cervical vertebra, and to study the orthogonal cutting mechanism of the anisotropic cortical bone, a 3D FE simulation model had been also established in which longitudinal, vertical, and transversal cutting types were accomplished to investigate the effect of osteons orientation. Secondly, this response surface method was used to regress the simulation results, and establishes the prediction model of maximum temperature on cutting depth, cutting speed, and feed speed. Then, the Sobol method was used to analyze the sensitivity of the milling temperature prediction mathematical model parameters, in order to clarify and quantitatively analyze the influence of input milling parameters on the output milling temperature. Finally, the cutting temperatures obtained with the simulations were compared with the corresponding experimental results obtained from the bone milling tests. This study verifies the influence of key variables and the cutting parameters on thermo mechanical behavior of the bone cutting. The obtained cutting temperature distribution for the bone surfaces could be employed to establish a theoretical foundation for research on thermal damage control of bone tissues.

An integrated framework for criticality evaluation of oil & gas pipelines based on fuzzy logic inference and machine learning

Oil & gas transportation pipeline is susceptible to failure because of the influence of external complex environment and internal aggressive medium. It is necessary to accurately evaluate the failure criticality of the pipeline for developing reasonable protective measures. However, due to the complexity and uncertainty of the failure scenarios of the oil & gas pipeline, direct quantitative evaluation of the failure criticality is very difficult. Therefore, this paper proposed a novel evaluation framework based on an integration of fuzzy logic inference and machine learning approaches. In this framework, transportation interruption effect, safety/health effect, environment/ecological effect, and equipment maintenance effect are set as the influencing factors on failure criticality of pipelines. Fuzzy logic inference was applied to generate the mapping relationship of the influencing factors to criticality index and establish the prediction model for criticality index evaluation of oil & gas pipelines. For facilitating the evaluation process, three machine learning approaches (i.e., multilayer perceptron, support vector regression and random forest) were employed to fit the relationship so as to construct an additional, easy-to-use prediction model. Furthermore, the sensitivity of each influencing factor was discussed by Sobol method. The results show that the random forest model has better prediction capability in comparison of the other two models, and safety/health effect and environment/ecological effect have the biggest impact on criticality. Finally, an application example of natural gas pipeline was conducted by using the proposed framework, which verified its practicability and flexibility.

Spatio-temporal feature fusion for real-time prediction of TBM operating parameters: A deep learning approach

This research provides a spatio-temporal approach to perform real-time forecasting for the tunnel boring machine (TBM) operating parameters. By extracting the real-time TBM operational data from the data acquisition system, a Long Short-Term Memory (LSTM) based deep learning model is trained for accurate prediction. A global sensitivity analysis (GSA) by adopting the Sobol method is performed for the model to quantify the contribution of input variables. The developed methodology can be a useful tool for TBM performance improvement and it enhances the state of knowledge on underground excavation. The result from the case study indicates that: (1) The proposed spatio-temporal method provides reliable real-time forecasting with mean absolute error (MAE) and root mean squared error (RMSE) of 1.261 mm and 1.955 mm, respectively, and (2) GSA results indicate that TBM's thrust and CHD torque are the 2 most influential spatial factors, while the historical data of penetration rate is critical for accurate forecasting. Further studies could focus on backward optimization to improve TBM's performance based on the prediction.

Modeling and Sensitivity Analysis of Concrete Creep with Machine Learning Methods

Although machine learning algorithms to predict the mechanical properties of concrete have been studied extensively, most of the research focused on the prediction of the strength of concrete and only a few studies have focused on concrete creep. This paper analyzed the maximum information correlation (MIC) between concrete creep influence parameters based on the updated Infrastructure Technology Institute of Northwestern University (NU-ITI) database, and the parameters in the database were adopted in the classical creep prediction models for calculation. Three machine learning algorithms (MLAs)—back-propagation artificial neural network (BPANN), support vector regression (SVR), and extreme learning machine (ELM)—were trained with the NU-ITI database to model concrete creep. The SVR-based model achieved high predictive accuracy. Sensitivity analysis of the parameters and feature selection of concrete creep were carried out based on the SVR and the Sobol method. By retraining the SVR model after feature selection, it was demonstrated that low-sensitivity and strongly correlated parameters will increase the robustness of machine learning models.

Global sensitivity analysis for uncertainty quantification in fire spread models

Environmental models involve inherent uncertainties, the understanding of which is required for use by practitioners. One method of uncertainty quantification is global sensitivity analysis (GSA), which has been extensively used in environmental modeling. The suitability of GSA methods depends on the model, implementation, and computational complexity. Thus, we present a comparative analysis of different GSA methods (Morris, Sobol, FAST, and PAWN) applied to empirical fire spread models (Dry Eucalypt and Rothermel) and explain their implications. GSA methods such as PAWN, may not be able to explain all the interactions whereas methods such as Sobol can result in high computational costs for models with several parameters. We found that the Morris or the PAWN method should be prioritized over the Sobol and the FAST methods for a balanced trade-off between convergence and robustness under computational constraints. Additionally, the Sobol method should be chosen for more detailed sensitivity information.

A New Approach for Optimizing a Bipolar Charge Transport Model for Dielectric Materials: Theoretical Framework

A bipolar charge transport model with two levels of traps (shallow and deep traps) is employed to describe and investigate the dynamic behavior of the space charge in low-density polyethylene (LDPE). This kind of model requires some initial experimental conditions alongside a set of parameters. An optimization method is used in order to provide the best precision for model parameters. Furthermore, the sensitivity of these parameters has been analyzed using an approach based on Sobol's method. In essence, this paper proposes a specific protocol that contributes to producing a global set of parameters able to provide the best approximate fit between experimental and simulated results. Net charge density is measured by the pulse electro-acoustic method (PEA) along with what is known as external charging current measurements. The simulated data are obtained by a bipolar charge transport model, which is developed for low-sensity polyethylene.

The trade-off between mobility and vaccination for COVID-19 control: a metapopulation modelling approach.

November 2020 received a string of encouraging results from leading vaccine developers raising hopes for the imminent availability of an effective and safe vaccine against the SARS-CoV-2. In the present work, we discuss the theoretical impact of introducing a vaccine across a range of scenarios. In particular, we investigate how vaccination coverage, efficacy and delivery time affect the control of the transmission dynamics in comparison to mobility restrictions. The analysis is based on a metapopulation epidemic model structured by risk. We perform a global sensitivity analysis using the Sobol method. Our analysis suggest that the reduction of mobility among patches plays a significant role in the mitigation of the disease close to the effect of immunization coverage of 30% achieved in four months. Moreover, for an immunization coverage between 20% and 50% achieved in the first half of 2021 with a vaccine efficacy between 70% and 95%, the percentage reduction in the total number of SARS-CoV-2 infections is between 30% and 50% by the end of 2021 in comparison with the no vaccination scenario.

Multi-Criteria Evaluation and Sensitivity Analysis for the Optimal Location of Constructed Wetlands (METland) at Oceanic and Mediterranean Areas.

METland is a new variety of Constructed Wetland (CW) for treating wastewater where gravel is replaced by a biocompatible electroconductive material to stimulate the metabolism of electroactive bacteria. The system requires a remarkably low land footprint (0.4 m2/pe) compared to conventional CW, due to the high pollutant removal rate exhibited by such microorganisms. In order to predict the optimal locations for METland, a methodology based on Multi-Criteria Evaluation (MCE) techniques applied to Geographical Information Systems (GIS) has been proposed. Seven criteria were evaluated and weighted in the context of Analytical Hierarchy Process (AHP). Finally, a Global Sensitivity Analysis (GSA) was performed using the Sobol method for resource optimization. The model was tested in two locations, oceanic and Mediterranean, to prove its feasibility in different geographical, demographic and climate conditions. The GSA revealed as conclusion the most influential factors in the model: (i) land use, (ii) distance to population centers, and (iii) distance to river beds. Interestingly, the model could predict best suitable locations by reducing the number of analyzed factors to just such three key factors (responsible for 78% of the output variance). The proposed methodology will help decision-making stakeholders in implementing nature-based solutions, including constructed wetlands, for treating wastewater in rural areas.

Inverse Modeling of Thermal Decomposition of Flame-Retardant PET Fiber with Model-Free Coupled with Particle Swarm Optimization Algorithm.

The thermal decomposition model of flame-retardant polyethylene terephthalate (FRPET) fiber is essential for predicting its fire behavior and do relevant fire simulation. In this work, the thermal decomposition character of FRPET is investigated via thermogravimetric analysis at four heating rates. Two kinetic schemes are proposed based on the analysis of experimental data and model-free methods. The model-free methods (Friedman and advanced Vyazovkin methods) are employed to determine possible search range for particle swarm optimization algorithm with constriction factor (CFPSO). Thus, this coupled method could evaluate the kinetic parameters for two proposed schemes without initial guess. Both models could reasonably predict the experimental data with obtained parameters, and the second two-step consecutive model shows better performance. The performance of CFPSO on the second model is further compared with improved generalized simulated annealing algorithm, and CFPSO was found to be more effective. Furthermore, global sensitivity analysis was conducted via the Sobol method to investigate the influence of kinetic parameters for the second model on predicted results. The most influential parameters are ln A and Eα of the second reaction and reaction order n of the third reaction.

Variance Based Sensitivity Analysis of FLake Lake Model for Global Land Surface Modeling

AbstractGiven the ever increasing spatial resolution of climate models and the significant role of lakes on the regional climate, it becomes important to represent water bodies in climate models. Such developments have started in the IPSL (Institut Pierre Simon Laplace) climate model and its land surface component, ORganizing Carbon and Hydrology In Dynamic Ecosystems (ORCHIDEE), with the Freshwater Lake model, FLake. To answer the questions raised by these new developments, such as the lake differentiation and related model parameters, we analyze spatial distributions of lake characteristics in the whole world to perform a global sensitivity analysis of the FLake parameters. As a result, three different climates and four lake depth configurations were selected as test cases. The Sobol method as sensitivity analysis based on variance decomposition was chosen to rank parameters impact on the model output, that is, lake surface water temperature, latent and sensible heat fluxes. We focus on the 11 parameters of the FLake model, which are the lake depth, the albedo and light extinction coefficient of water, snow, and ice respectively, the fetch, and the relaxation coefficient of the thermocline shape factor. The results show different sensitivity features according to the lake type and climate. The dominant role and time varying contribution of the lake depth, radiative parameters (albedo, light extinction coefficient) and thermocline relaxation coefficient linked to the atmospheric conditions, were clearly highlighted. These findings will lead us to distinguish between different lake categories in each grid cell of ORCHIDEE in the future implementation.

Reliability and reproducibility in computational science: implementing validation, verification and uncertainty quantification in silico.

Reliability and reproducibility in computational science: implementing validation, verification and uncertainty quantification in silico.

Parameter sensitivity and dynamic characteristic analysis of bulb hydro generating unit with shaft crack fault

The shaft crack fault of hydro generating unit (HGU) has a serious threat to the reliability and security of the hydropower station. However, the parameter sensitivity, operation stability and dynamic characteristics of HGU considering the shaft crack fault are rarely studied. In view of this, taking the bulb hydro generating unit (BHGU) as the research object, a nonlinear dynamic model of the BHGU under the shaft crack fault is firstly established here. And Newmark-Newton-Raphson method is used to solve this high-DOF model. Furthermore, the proposed model is also verified by comparing with existing models. Then, the parameter sensitivity of the BHGU with the shaft crack fault is analyzed via Sobol method. Meanwhile, ranks of parameter sensitivity for the vibration displacement and unbalanced forces are respectively obtained. Finally, based on sensitivity analyses, effects of some typical sensitivity parameters on dynamic characteristics of the BHGU are discussed in detail including parameters related to the shaft crack, unbalanced magnetic pull, mass eccentricity and unbalanced hydraulic force. And some stability ranges and dynamic evolution characteristics of the unit are gotten. More importantly, proposed dynamic models and analysis results can provide a guidance for the operation and maintenance of the BHGU with the shaft crack fault.

Statistical Modeling, Optimization and Sensitivity Analysis of Tool’s Geometrical Parameters on Process Force in Automatic Cortical Bone Drilling Process

One of the most prevalent machining processes in medical treatments is bone drilling process. During bone drilling, excessive process force can cause breakage, crack initiation and severe damage to bone tissue. In this paper, a systematic study with simultaneous use of response surface method, sensitivity analysis based on Sobol method and regression analysis is performed for investigation the effect of helix angle and point angle of the tool as the most important geometrical parameters on imposed force to the bone during drilling process. Initially, using design of experiments and response surface method, imposed force to the bone is modeled and the governing second order linear regression equation is derived and verified. Then, using Sobol sensitivity analysis, with ability to quantify the sensitivity, it is attempted to investigate the effect of input parameters on drilling force. Finally, optimization of the process inputs is followed to find the best combination which yields the desired drilling force. The minimum drilling force, within the range of input parameters, coincides with point angle of 90 and helix angle of 18. This minimal force is lower than the force in surgery and standard tools. The results showed that an increasing in point angle leads to an increase in drilling force. Also, it is concluded that there is an optimum value for using the helix angle in bone drilling process with minimum imposed force.

Method for Potential Evaluation and Parameter Optimization for CO2-WAG in Low Permeability Reservoirs based on Machine Learning

The CO2 water-alternating-gas flooding (CO2-WAG) is a key technology to improve the oil recovery of low permeability reservoirs. The effect of CO2 flooding to enhance the oil recovery is affected by geological conditions and production systems. The effect of CO2 flooding parameters on the enhanced recovery factor should be clarified to optimize the production system. In this paper, the machine learning algorithms are used to carry out the study and establish a set of procedures for optimizing CO2 flooding parameters based on the artificial neural network (ANN) and the particle swarm optimization (PSO) algorithm. Firstly, large amounts of basic data are generated by the Monte Carlo sampling method. Then, the recovery factor by the water flooding and the CO2-WAG and the enhanced recovery factor by CO2-WAG in different models are calculated in the reservoir numerical simulator. Moreover, the machine learning method is used to establish a neural network model, and analysis of the sensitivity of parameters of the enhanced oil recovery (EOR) is carried out by combining with the Sobol method. Finally, the neural network model and the particle swarm algorithm are combined to optimize the parameters of CO2-WAG flooding. The results show that the established model has a good prediction accuracy (97.6%), thus it could be used to predict the enhanced recovery factor by CO2-WAG, and it is applicable in potential evaluation of enhancing the oil recovery and optimization for parameters in the CO2-WAG well group.

CMSRAS: A Novel Chaotic Multi-Specular Reflection Optimization Algorithm Considering Shared Nodes

Specular reflection algorithm (SRA) was a single population meta-heuristic algorithm inspired by the physical function of mirror. However, similar to most of meta-heuristic algorithms, it had the disadvantages of weak population diversity, stagnation in local optimal and low convergence rate. In order to overcome these shortcomings, a chaotic multi-specular reflection optimization algorithm considering shared nodes (CMSRAS) was proposed by the combination of population strategy with shared node, improved Tent chaos strategy and Gaussian mutation strategy. Initially, a single population SRA was extended to the multi-population with shared node and the population was initialized by improved Tent chaos sequence to improve the quality of the initial solution and the population diversity, and to enhance the global search ability. Meanwhile, to strengthen the local search ability and the convergence accuracy, the Gaussian mutation and improved Tent chaotic disturbance strategy were introduced into SRA. And then the influence law and sensitivity analysis of the CMSRAS algorithm between the initial setting parameters were obtained based on the response surface method and the Sobol's method. Finally, compared with both 12 state-of-the-art algorithms and 8 well-known advanced algorithms, the performance of CMSRAS was evaluated on a comprehensive set of 32 benchmark problems. In addition, CMSRAS was applied to solve the complex optimization problems of engineering structure. The results demonstrated that proposed CMSRAS algorithm outperformed most competitive algorithms and efficiently solve the real-life global optimization problems.

Uncertainty Quantification for the Flow of Nanofluids in Converging/Diverging Channels

In mathematical models, parameters are one of the most important input factors that affect the model outputs. In this work, the effects of parameters in complementing their interaction effects on nanofluids' output variables in converging and diverging channels have been studied. The mathematical model is solved numerically by using Matlab's built-in solver bvp4c. Global sensitivity analysis (Sobol's method) quantifies the effects of input parameters and their interactions on model outputs. The results showed that the channel opening (α) is the most influential model parameter for the velocity profile. Simultaneously, Eckert number (Ec) becomes the most influential parameter for temperature distribution in diverging and converging channels. The least sensitive parameters and interaction effects of involved parameters are identified on velocity and temperature profiles in converging and diverging channels.

A Trade-Off Between Explorations and Repetitions for Estimators of Two Global Sensitivity Indices in Stochastic Models Induced by Probability Measures

Sobol sensitivity indices assess how the output of a given mathematical model is sensitive to its inputs. If the model is stochastic then it cannot be represented as a function of the inputs, thus raising questions as how to do a sensitivity analysis in those models. Practitioners have been using an approach that exploits the availability of methods for deterministic models. For each input, the stochastic model is repeated and the outputs are averaged. These averages are seen as if they came from a deterministic model and hence Sobol's method can be used. We show that the estimator so obtained is asymptotically biased if the number of repetitions goes to infinity too slowly. With limited computational resources, the number of repetitions of the stochastic model and the number of explorations of the input space cannot be large together and hence some balance must be found. We find the pair of numbers that minimizes a bound on some rank-based error criterion, penalizing bad rankings of the inputs' sensitivities. Also, under minimal distributional assumptions, we derive a functional relationship between the output, the input and some random noise; the Sobol-Hoeffding decomposition can be applied to it to define a new sensitivity index, which asymptotically is estimated without bias even though the number of repetitions remains fixed. The theory is illustrated on numerical experiments.

Global sensitivity analysis of a single-cell HBV model for viral dynamics in the liver.

The predictive accuracy of mathematical models representing anything ranging from the meteorological to the biological system profoundly depends on the quality of model parameters derived from experimental data. Hence, robust sensitivity analysis (SA) of these critical model parameters aids in sifting the influential from the negligible out of typically vast parameter regimes, thus illuminating key components of the system under study. We here move beyond traditional local sensitivity analysis to the adoption of global SA techniques. Partial rank correlation coefficient (PRCC) based on Latin hypercube sampling is compared with the variance-based Sobol method. We selected for this SA investigation an infection model for the hepatitis-B virus (HBV) that describes infection dynamics and clearance of HBV in the liver [Murray & Goyal, 2015]. The model tracks viral particles such as the tenacious and nearly ineradicable covalently closed circular DNA (cccDNA) embedded in infected nuclei and an HBV protein known as p36. Our application of these SA methods to the HBV model illuminates, especially over time, the quantitative relationships between cccDNA synthesis rate and p36 synthesis and export. Our results reinforce previous observations that the viral protein, p36, is by far the most influential factor for cccDNA replication. Moreover, both methods are capable of finding crucial parameters of the model. Though the Sobol method is independent of model structure (e.g., linearity and monotonicity) and well suited for SA, our results ensure that LHS-PRCC suffices for SA of a non-linear model if it is monotonic.

Comparison of global sensitivity analysis techniques based on a process-based model CROBAS.

Constructions of process or mechanistic models are limited by physiological parameters, due to difficulty in direct and precise measurement. Global sensitivity analysis could evaluate the response of model outputs to changes in physiological parameters, and provide information for improving model structure, data collection, and parameter calibration. Based on a process model CROBAS, 10 parameters related to tree structure of Pinus armandii were selected to compare three widely used global sensitivity analysis methods (the Morris screening method, the variance-based Sobol indices, and the Extended Fourier Amplitude Sensitivity Test (EFAST)), with the objective function formulated by the Nash-Sutcliffe Efficiency (NSE) of tree height and biomass. The results showed that the sensitivity order of parameters slightly varied across different methods, which considerably changed with different objective functions. Both the Morris method and the EFAST method outperformed the Sobol method in terms of time consuming and convergence efficiency. All outputs were sensitive to the maximum rate of canopy photosynthesis per unit area, the specific leaf area, and the extinction coefficient. The light interception of tree canopy played a key role in the simulation of tree growth with CROBAS, suggesting that the module of photosynthetic carbon fixation took priority over any other modules for data collection and model validation during module calibration and tree growth simulation for CROBAS. The calculation and validation of foliage biomass module were crucial when applying carbon balance theory to biomass simulations. In conclusion, for the sensitivity analysis of a complex process-based model, the Morris method was suitable for qualitative studies, while the EFAST method was recommended for quantitative studies.