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 ana...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.展开更多
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. Howev...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.展开更多
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...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.展开更多
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 du...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.展开更多
In the field of rail transit,the UK Department of Transport stated that it will realize a comprehensive transformation of UK railways by 2050,abandoning traditional diesel trains and upgrading them to new environmenta...In the field of rail transit,the UK Department of Transport stated that it will realize a comprehensive transformation of UK railways by 2050,abandoning traditional diesel trains and upgrading them to new environmentally friendly trains.The current mainstream upgrade methods are electrification and hydrogen fuel cells.Comprehensive upgrades are costly,and choosing the optimal upgrade method for trams and mainline railways is critical.Without a sensitivity analysis,it is difficult for us to determine the influence relationship between each parameter and cost,resulting in a waste of cost when choosing a line reconstruction method.In addition,by analyzing the sensitivity of different parameters to the cost,the primary optimization direction can be determined to reduce the cost.Global higher-order sensitivity analysis enables quantification of parameter interactions,showing non-additive effects between parameters.This paper selects the main parameters that affect the retrofit cost and analyzes the retrofit cost of the two upgrade methods in the case of trams and mainline railways through local and global sensitivity analysis methods.The results of the analysis show that,given the current UK rail system,it is more economical to choose electric trams and hydrogen mainline trains.For trams,the speed at which the train travels has the greatest impact on the final cost.Through the sensitivity analysis,this paper provides an effective data reference for the current railway upgrading and reconstruction plan and provides a theoretical basis for the next step of train parameter optimization.展开更多
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 facili...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.展开更多
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 th...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.展开更多
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-d...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.展开更多
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 ...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.展开更多
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 indicato...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.展开更多
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 i...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.展开更多
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 typ...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.展开更多
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) t...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.展开更多
The key to achieving the optimal design of towed cables,maintaining numerical simulation accuracy,and achieving precise control of the towed body lies in sensitivity analysis.However,the traditional global sensitivity...The key to achieving the optimal design of towed cables,maintaining numerical simulation accuracy,and achieving precise control of the towed body lies in sensitivity analysis.However,the traditional global sensitivity analysis method presents challenges such as high calculation costs and low accuracy.To ad-dress these issues,this paper introduces polynomial chaos expansion(PCE)to quantitatively analyze the impact of uncertainties in physical and environmental parameters on the position and attitude of the towed cable.Latin hypercube sampling is employed to obtain sample sets of input parameters,and these samples are applied to the lumped mass method to calculate the end position coordinates of the towed cable,which serves as the output response.PCE is utilized to quantitatively compute the Sobol global sensitivity index of the towed cable parameters.The accuracy of the PCE model is verified,and the op-timal degree of basis functions is selected using the bias-variance trade-off.The advantages of PCE are demonstrated by comparing it with the Monte Carlo and Morris methods.The results indicate that PCE accurately calculates the global sensitivity index of towed cable parameters even with a limited sample size.Under the condition of a fixed cable length,the position and attitude of the towed cable are sensi-tive to the current rate,liquid density,cable diameter,normal drag coefficient,and specific gravity.The feasibility and efficiency of PCE applied to the sensitivity analysis of towed cable parameters is verified,and recommendations for the engineering application of towed cables are summarized.展开更多
Fault diagnosis of fuel cells often focuses on single faults,leading to lower accuracy in diagnosing simultaneous faults.This paper researches a data-driven diagnostic method for both single and simultaneous faults,ai...Fault diagnosis of fuel cells often focuses on single faults,leading to lower accuracy in diagnosing simultaneous faults.This paper researches a data-driven diagnostic method for both single and simultaneous faults,aiming to establish an efficient online fault diagnosis approach.Firstly,a theoretical model of a proton exchange membrane fuel cell(PEMFC)system is established.Based on this,a radial basis function(RBF)neural network surrogate model is designed to improve computational efficiency.The average relative error across all features between the surrogate model and the theoretical model is below 1%.Subsequently,Sobol's global sensitivity analysis is used to analyse the relationship between PEMFC system faults and various characteristic parameters during real-time operation.The sensitive feature set related to different faults in the PEMFC system is then identified.Finally,an adaptive diagnostic strategy is proposed,and a sensitivity-based diagnostic algorithm is established.Compared with other common single-label and multi-label diagnostic methods,the sensitivity-based diagnostic algorithm achieves an F1_Score of 99.1%on single-fault data,cutting training time by more than 80%.In scenarios with simultaneous faults and sparse data,the method achieves an accuracy of 92.5%,which is 7.5%higher than that achieved by the best multi-label method.展开更多
Turning performance represents a critical indicator of underwater vehicle maneuverability and correlates strongly with motion parameters such as rudder angle and propeller speed.This investigation examines the influen...Turning performance represents a critical indicator of underwater vehicle maneuverability and correlates strongly with motion parameters such as rudder angle and propeller speed.This investigation examines the influence of rudder angle and propeller speed on underwater vehicle turning performance.A fully coupled CFD-based hull-propellerrudder model enables high-accuracy computation of turning performance.The propeller modeling utilizes the body force method,while the overlapping mesh technique addresses the relative motion between rudder and hull.To optimize computational efficiency,an optimal Latin hypercube sampling method generates combinations of rudder angle and propeller speed,and a Kriging surrogate model substitutes for resource-intensive CFD simulations.Through application of the improved Sobol’s method,global sensitivity analysis quantitatively evaluates the contributions of rudder angle and propeller speed to turning performance.The analysis reveals that rudder angle substantially impacts turning performance,whereas propeller speed demonstrates comparatively limited influence.展开更多
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 th...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.展开更多
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 amplitu...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.展开更多
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 se...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.展开更多
Cardiac modeling entails the epistemic uncertainty of the input parameters,such as bundles and chambers geometry,electrical conductivities and cell parameters,thus calling for an uncertainty quantification(UQ)analysis...Cardiac modeling entails the epistemic uncertainty of the input parameters,such as bundles and chambers geometry,electrical conductivities and cell parameters,thus calling for an uncertainty quantification(UQ)analysis.Since the cardiac activation and the subsequent muscular contraction is provided by a complex electrophysiology system made of interconnected conductive media,we focus here on the fast conductivity structures of the atria(internodal pathways)with the aim of identifying which of the uncertain inputs mostly influence the propagation of the depolarization front.Firstly,the distributions of the input parameters are calibrated using data available from the literature taking into account gender differences.The output quantities of interest(Qols)of medical relevance are defined and a set of metamodels(one for each Qol)is then trained according to a polynomial chaos expansion(PCE)in order to run a global sensitivity analysis with non-linear variance-based SoboF indices with confidence intervals evaluated through the bootstrap method.The most sensitive parameters on each Qol are then identified for both genders showing the same order of importance of the model inputs on the electrical activation.Lastly,the probability distributions of the Qols are obtained through a forward sensitivity analysis using the same trained metamodels.It results that several input parameters-including the position of the internodal pathways and the electrical impulse applied at the sinoatrial node一have a little influence on the Qols studied.Vice-versa the electrical activation of the atrial fast conduction system is sensitive on the bundles geometry and electrical conductivities that need to be carefully measured or calibrated in order for the electrophysiology model to be accurate and predictive.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 41271003)the National Basic Research Program of China (Grants No. 2010CB428403 and 2010CB951103)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Nos.11172049 and11472060)the Science Foundation of China Academy of Engineering Physics(Nos.2015B0201037and 2013A0101004)
文摘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.
基金supported by the National Natural Science Foundation of China(11702281)the Science Challenge Project(TZ2018007)the Technology Foundation Project of State Administration of Science,Technology and Industry for National Defence,PRC(JSZL2017212A001)
文摘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.
文摘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.
文摘In the field of rail transit,the UK Department of Transport stated that it will realize a comprehensive transformation of UK railways by 2050,abandoning traditional diesel trains and upgrading them to new environmentally friendly trains.The current mainstream upgrade methods are electrification and hydrogen fuel cells.Comprehensive upgrades are costly,and choosing the optimal upgrade method for trams and mainline railways is critical.Without a sensitivity analysis,it is difficult for us to determine the influence relationship between each parameter and cost,resulting in a waste of cost when choosing a line reconstruction method.In addition,by analyzing the sensitivity of different parameters to the cost,the primary optimization direction can be determined to reduce the cost.Global higher-order sensitivity analysis enables quantification of parameter interactions,showing non-additive effects between parameters.This paper selects the main parameters that affect the retrofit cost and analyzes the retrofit cost of the two upgrade methods in the case of trams and mainline railways through local and global sensitivity analysis methods.The results of the analysis show that,given the current UK rail system,it is more economical to choose electric trams and hydrogen mainline trains.For trams,the speed at which the train travels has the greatest impact on the final cost.Through the sensitivity analysis,this paper provides an effective data reference for the current railway upgrading and reconstruction plan and provides a theoretical basis for the next step of train parameter optimization.
文摘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.
基金the Key Project of the Natural Science Foundation of Tianjin City(No.19JCZDJC39300)is acknowledged.
文摘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.
基金Supported by National Natural Science Foundation of China(Grant No.51275164)
文摘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.
文摘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.
基金Supported by the Ocean Public Welfare Scientific Research Project,State Oceanic Administration of China(No.200705029)the National Special Fund for Basic Science and Technology of China(No.2012FY112500)the National Non-profit Institute Basic Research Fund(No.FIO2011T06)
文摘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.
基金This work is supported in part by the Postdoctoral Science Foundation of China under Grant No.2020M683736in part by the Teaching reform project of higher education in Heilongjiang Province under Grant No.SJGY20210456in part by the Natural Science Foundation of Heilongjiang Province of China under Grant No.LH2021F038.
文摘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.
基金supported by the National Railway Group Science and Technology Program(Nos.N2020J026 and N2021J028)the Independent Research and Development Project of State Key Laboratory of Traction Power,China(No.2022TPL_Q02)。
文摘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.
基金the financial support funded by the Science and Technology Development Fund of Macao SAR (Grant Nos. 0026/2020/AFJ and SKL-IOTSC(UM)-2021-2023)the Funds for University of Macao (Grant No. MYRG2018-00173-FST)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.52071215)ponsored by the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University(project number SL2022MS003).
文摘The key to achieving the optimal design of towed cables,maintaining numerical simulation accuracy,and achieving precise control of the towed body lies in sensitivity analysis.However,the traditional global sensitivity analysis method presents challenges such as high calculation costs and low accuracy.To ad-dress these issues,this paper introduces polynomial chaos expansion(PCE)to quantitatively analyze the impact of uncertainties in physical and environmental parameters on the position and attitude of the towed cable.Latin hypercube sampling is employed to obtain sample sets of input parameters,and these samples are applied to the lumped mass method to calculate the end position coordinates of the towed cable,which serves as the output response.PCE is utilized to quantitatively compute the Sobol global sensitivity index of the towed cable parameters.The accuracy of the PCE model is verified,and the op-timal degree of basis functions is selected using the bias-variance trade-off.The advantages of PCE are demonstrated by comparing it with the Monte Carlo and Morris methods.The results indicate that PCE accurately calculates the global sensitivity index of towed cable parameters even with a limited sample size.Under the condition of a fixed cable length,the position and attitude of the towed cable are sensi-tive to the current rate,liquid density,cable diameter,normal drag coefficient,and specific gravity.The feasibility and efficiency of PCE applied to the sensitivity analysis of towed cable parameters is verified,and recommendations for the engineering application of towed cables are summarized.
基金supported by the National Natural Science Foundation of China(Grant No.51905217)the Carbon Peak and Carbon Neutral Technology Innovation Fund Project of Jiangsu Province(Grant No.BE2023091-1)+1 种基金the International Postdoctoral Exchange Fellowship Program from China Postdoctoral Council(Grant No.PC2021032)the State Scholarship Fund from the China Scholarship Council。
文摘Fault diagnosis of fuel cells often focuses on single faults,leading to lower accuracy in diagnosing simultaneous faults.This paper researches a data-driven diagnostic method for both single and simultaneous faults,aiming to establish an efficient online fault diagnosis approach.Firstly,a theoretical model of a proton exchange membrane fuel cell(PEMFC)system is established.Based on this,a radial basis function(RBF)neural network surrogate model is designed to improve computational efficiency.The average relative error across all features between the surrogate model and the theoretical model is below 1%.Subsequently,Sobol's global sensitivity analysis is used to analyse the relationship between PEMFC system faults and various characteristic parameters during real-time operation.The sensitive feature set related to different faults in the PEMFC system is then identified.Finally,an adaptive diagnostic strategy is proposed,and a sensitivity-based diagnostic algorithm is established.Compared with other common single-label and multi-label diagnostic methods,the sensitivity-based diagnostic algorithm achieves an F1_Score of 99.1%on single-fault data,cutting training time by more than 80%.In scenarios with simultaneous faults and sparse data,the method achieves an accuracy of 92.5%,which is 7.5%higher than that achieved by the best multi-label method.
基金financially supported by the National Natural Science Foundation of China(Grant No.52372356)Zhenjiang City Science and Technology Program Project(Grant No.JC2024015)the“Qinglan Project”of Jiangsu Higher Education.
文摘Turning performance represents a critical indicator of underwater vehicle maneuverability and correlates strongly with motion parameters such as rudder angle and propeller speed.This investigation examines the influence of rudder angle and propeller speed on underwater vehicle turning performance.A fully coupled CFD-based hull-propellerrudder model enables high-accuracy computation of turning performance.The propeller modeling utilizes the body force method,while the overlapping mesh technique addresses the relative motion between rudder and hull.To optimize computational efficiency,an optimal Latin hypercube sampling method generates combinations of rudder angle and propeller speed,and a Kriging surrogate model substitutes for resource-intensive CFD simulations.Through application of the improved Sobol’s method,global sensitivity analysis quantitatively evaluates the contributions of rudder angle and propeller speed to turning performance.The analysis reveals that rudder angle substantially impacts turning performance,whereas propeller speed demonstrates comparatively limited influence.
文摘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.
基金Supported by the National Science Foundation for Post-doctoral Scientists of China (20090460216 )the National Defense Fundamental Research Foundation of China(B222006060)
文摘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.
基金The study is supported by the National Numerical Wind tunnel project(No.2019ZT2-A05)the Nature Science Foundation of China(No.11902254).
文摘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.
基金This study has been performed with support of the'Fluid dynamics of hearts at risk of failure:towards methods for the prediction of disease progressions’funded by the Italian Ministry of Education and University(Grant 2017A889FP).
文摘Cardiac modeling entails the epistemic uncertainty of the input parameters,such as bundles and chambers geometry,electrical conductivities and cell parameters,thus calling for an uncertainty quantification(UQ)analysis.Since the cardiac activation and the subsequent muscular contraction is provided by a complex electrophysiology system made of interconnected conductive media,we focus here on the fast conductivity structures of the atria(internodal pathways)with the aim of identifying which of the uncertain inputs mostly influence the propagation of the depolarization front.Firstly,the distributions of the input parameters are calibrated using data available from the literature taking into account gender differences.The output quantities of interest(Qols)of medical relevance are defined and a set of metamodels(one for each Qol)is then trained according to a polynomial chaos expansion(PCE)in order to run a global sensitivity analysis with non-linear variance-based SoboF indices with confidence intervals evaluated through the bootstrap method.The most sensitive parameters on each Qol are then identified for both genders showing the same order of importance of the model inputs on the electrical activation.Lastly,the probability distributions of the Qols are obtained through a forward sensitivity analysis using the same trained metamodels.It results that several input parameters-including the position of the internodal pathways and the electrical impulse applied at the sinoatrial node一have a little influence on the Qols studied.Vice-versa the electrical activation of the atrial fast conduction system is sensitive on the bundles geometry and electrical conductivities that need to be carefully measured or calibrated in order for the electrophysiology model to be accurate and predictive.
