Stochastic Parameters Research Articles

A novel exponential degradation approach for predicting the remaining useful life of roadheader bearings

Based on the optimized exponential-degradation model (OEDM), a novel approach for predicting the remaining useful life(RUL) of roadheader bearings under different working conditions is proposed in this study. Specifically, the exponential process is used to construct the degradation process from a single performance characteristic under variable operating conditions, the generalized expectation maximization is employed to estimate model parameters, and the proposed degradation model is updated after new data is available. In the traditional exponential degradation method, the hyperparameters are only optimized, which leads to low calculation accuracy under severe working conditions. In the proposed method, the Bayesian algorithm and the Drift Brownian motion algorithm were respectively employed to optimize hyperparameters and stochastic parameters to ensure the high accuracy of the prediction results. In addition, degradation characteristics combined with sensory data acquired through condition monitoring were used to continuously update the RUL in the proposed degradation model. Finally, the effectiveness of the proposed model is verified by a simulation case and a case study. The results show that compared with the linear degradation model and the general exponential degradation model, the proposed OEDM performs well in practical applications and has a higher prediction accuracy. This study provides a reference for predictive maintenance of critical parts of tunneling machinery and cost reduction of tunneling.

A coupling analysis method of foundation soil dynamic responses induced by metro train based on PDEM and stochastic field theory

Foundation soil is an important medium for vibration wave propagation in the running of metro train. The spatial variability of soil properties has an important influence on vibration response. The parameters of foundation soil are often determined. Based on the probability density evolution method (PDEM) and stochastic field theory, a coupling model of the metro train-track-shield tunnel-foundation soil is established. The stochastic field is expressed by the series of stochastic variables and deterministic space functions by the Karhunen-Loeve Expansion (KLE) method. The stochastic parameters of the cross-section of tunnel-foundation soil are specified to simulate the stochastic field of foundation soil. Based on PDEM, the environmental vibration caused by metro trains in shield tunnels is studied. The results of ground surface vibration displacement under different metro train speeds are analyzed, and the upper and lower limits and probability density information of ground surface vibration displacement are obtained. The results show that the probability density distribution of ground vibration displacement at each time is approximately normal due to the stochastic field of foundation soil. The peak and valley of the vibration displacement curve at the inverted arch of the tunnel are caused by the wheel distance of the metro train. The probability density distribution of velocity and acceleration is more sensitive to the stochastic field of velocity foundation soil and the change in metro train speed. The maximum Z vibration level results under different metro train speeds all meet the requirements of vibration allowable limits in the specification.

Modeling Stochastic Data Using Copulas for Applications in the Validation of Autonomous Driving

The verification and validation processes of fully automated vehicles are linked to an almost intractable challenge of reflecting the real world with all its interactions in a virtual environment. Influential stochastic parameters need to be extracted from real-world measurements and real-time data, capturing all interdependencies, for an accurate simulation of reality. A copula is a probability model that represents a multivariate distribution, examining the dependence between the underlying variables. This model is used on drone measurement data from a roundabout containing dependent stochastic parameters. With the help of the copula model, samples are generated that reflect the real-time data. The resulting applications and possible extensions are discussed and explored.

Stochastic inverse modeling of transient laboratory-scale three-dimensional two-phase core flooding scenarios

We develop a comprehensive and efficient workflow for a stochastic assessment of key parameters governing two-phase flow conditions associated with core-scale experiments. We rely on original and detailed datasets collected on a Berea sandstone sample. These capture the temporal evolution of pressure drop across the core and three-dimensional maps of phase saturations (determined via X-ray CT) in oil- and brine-displacement flooding scenarios characterized by diverse brine/oil viscosity contrasts. Such experiments are used as a test-bed for the proposed stochastic model calibration strategy. The latter is structured across three main steps: (i) a preliminary calibration, aimed at identifying a behavioral region of the model parameter space; (ii) a Global Sensitivity Analysis (GSA), geared towards identification of the relative importance of model parameters on observed model outputs and assessment of non-influential parameters to reduce dimensionality of the parameter space; and (iii) a stochastic inverse modeling procedure. The latter is based on a differential-evolution genetic algorithm to efficiently explore the reduced parameter space stemming from the GSA. It enables one to obtain a probabilistic description of the relevant model parameters through their frequency distributions conditional on the detailed type of information collected. Coupling GSA with a stochastic parameter estimation approach based on a genetic algorithm of the type we consider enables streamlining the procedure and effectively cope with the considerable computational efforts linked to the two-phase scenario considered. Results show a remarkable agreement with experimental data and imbue us with confidence on the potential of the approach to embed the type of rich datasets considered towards model parameter estimation fully including uncertainty.

SVR-based weighted processing method for electrical imaging logging in oil-based mud

Electrical imaging logging in high-resistivity oil-based mud (OBM) has been one of the hotspots in petroleum exploration and development recently. Compared with the traditional electrical imaging logging in water-based mud (WBM), the core issue restricting the application of electrical imaging logging in OBM is that the mud-layer with high impedance prevents the emitted current from flowing into the formation and seriously disturbs the measurement of formation properties. Here, a SVR (support vector machine regression)-based weighted processing method is proposed to resolve the intractable problem and three key parameters are obtained simultaneously. First, the equivalent circuit model of electrical imaging logging in OBM is established and the drawback especially occurring in low-resistivity formation is analyzed. Then, a weighted coefficient applied to the mud-layer impedance is introduced for the quantitative calculation of formation resistivity, and the change of relative formation permittivity and mud-layer thickness can also be depicted with weighted processing. Next, a SVR model is established to inverse the weighted coefficient and then figure out the inversed parameters including the formation resistivity, the relative formation permittivity, and the mud-layer thickness. A stochastic parameter model is adopted to verify the validity of SVR model. Finally, two deviated formation models further test the advantage and robustness of SVR model. The results demonstrate that the SVR-based weighted processing method possesses a terrific performance and all the three parameters can be calculated simultaneously regardless of the borehole wall condition. This study will provide a new approach to the data processing and interpretation of electrical imaging logging in OBM.

Numerical conservation issues for the stochastic Korteweg–de Vries equation

In this paper, we focus on structure-preserving issues for the numerical solution of the stochastic Korteweg–de Vries equation, via stochastic ϑ-methods. It is well-known that the aforementioned model exhibits invariant laws along its exact dynamics. Here, our goal is to analyze whether such invariant laws are also reproduced along the numerical dynamics provided by stochastic ϑ-methods. Furthermore, we are also interested in rigorously studying the characterization of such invariant laws along numerical solutions of this model, with respect to the growth of the stochasticity parameter ɛ. At this purpose, the so-called ɛ-expansion of the exact solution to the aforementioned equation will be performed. Numerical results confirming the effectiveness of our analysis are also provided.

Micro-scale deterministic asperity contact FEM simulation

There are numerous stochastic approaches to indirectly couple solid asperity contact with the fluid hydrodynamics in the region of boundary or mixed lubrication. In contrast, deterministic approaches for calculating solid contact pressure curves offer advantages in terms of flexibility and accuracy. This contribution aims at providing a publicly available, automated method to derive solid asperity contact pressure curves for given surfaces, implemented in commercial software based upon Finite Element Method (FEM). Solid asperity pressure curves were calculated and compared to various established stochastic models for artificially generated surfaces and surfaces measured via laser scanning microscopy. Thereby, it was shown that the usage of artificially generated surfaces based on stochastic parameters only allowed an approximate representation of real measured surfaces as well as to lower calculated pressures, so that 3D measurement data is preferred to calculate the contact pressure. Moreover, the values of the FEM model were in a similar region but slightly below the stochastic models over a wide range of gap distances and the asperity pressure graphs were more curved/convex. At very small gap height values, the pressure in the FEM model reached values similar to the stochastic models. This was attributed to the fact that real surface topographies were considered, also allowing for peak-to-valley pairings instead of merely asperity-to-asperity contacts, as well as to the fact that the roughness and mean planes were re-calculated in each simulation step, while most stochastic approaches neglect the elastic deformation of asperities when determining the distances between the rough surfaces.

Вычислительный фантом для дозиметрии красного костного мозга новорожденного ребенка от инкорпорированных бета-излучателей

Active (red) bone marrow (AM) exposure due to ingested bone-seeking radionuclides can lead to grave medical consequences. For example, a radioactive contamination of the Techa River in the 1950s caused exposure to AM for riverside residents and led to chronic radioactive exposure syndrome in some of them, with higher risk of leukemia. The main sources of the marrow exposure were the bone-seeking beta emitters 89,90Sr. Improving the dosimetry of AM internal exposure is an important step in clarifying the risks of chronic radiation exposure for riverside residents. To evaluate the energy absorbed by AM from incorporated 90Sr it is customary to use computational phantoms where radiation transport can be emulated. A phantom is a representative digital representation of skeletal bone geometry and AM The goal of this work was to develop a computational phantom of a newborn skeleton for dosimetry of AM from incorporated 90Sr. The researchers have used the Stochastic Parametric Skeletal Dosimetry method (SPSD), where hematopoietic sites were modeled as a set of phantoms of simple geometric shape describing individual skeletal bone areas. The AM content in the skeleton as well as the phantom parameters were evaluated on the basis of published measurements of real bones. As a result, a computational phantom of the main skeletal hematopoietic sites was generated for a newborn baby, including 34 phantoms of bone areas. The simulated phantom simulates the bone structure as well as the variability of skeletal parameters within the population and corresponds well to measurements of real bones.

Sensitivity Analysis of Random Parameters for Earthquake Response of Hakka Tulou in Fujian

The seismic response analysis of the Fujian tulou structure considers the influence of six input random variables of the tulou structure. It obtains the seismic response of the apex displacement, the maximum inter-story displacement angle, and the base shear force of the tulou structure. An analysis method based on moment-independent importance measure is proposed and applied to the stochastic parameter sensitivity (importance measure) analysis of structural seismic response. The results show that the importance metric analysis method of the seismic response of the structure based on the moment-independent importance measure analysis method generates consistent outcomes with the importance measure method of the variance. However, the method in this study can better reflect the actual earthquake response of the tulou structure, and it is also an efficient method.

A three-layer joint distributionally robust chance-constrained framework for optimal day-ahead scheduling of e-mobility ecosystem

A high number of electric vehicles (EVs) in the transportation sector necessitates an advanced scheduling framework for e-mobility ecosystem operation to overcome range anxiety and create a viable business model for charging stations (CSs). The framework must account for the stochastic nature of all stakeholders’ operations, including EV drivers, CSs, and retailers and their mutual interactions. In this paper, a three-layer joint distributionally robust chance-constrained (DRCC) model is proposed to plan day-ahead grid-to-vehicle (G2V) and vehicle-to-grid (V2G) operations for e-mobility ecosystems. The proposed three-layer joint DRCC framework formulates the interactions of the stochastic behaviour of the stakeholders in an uncertain environment with unknown probability distributions. The proposed stochastic model does not rely on a specific probability distribution for stochastic parameters. An iterative process is proposed to solve the problem using joint DRCC formulation. To achieve computational tractability, the second-order cone programming reformulation is implemented for double-sided and single-sided chance constraints (CCs). Furthermore, the impact of the temporal correlation of uncertain PV generation on CSs operation is considered in the formulation. A simulation study is carried out for an ecosystem of three retailers, nine CSs, and 600 EVs based on real data from San Francisco, USA. The simulation results show the necessity and applicability of such a scheduling framework for the e-mobility ecosystem in an uncertain environment, e.g., by reducing the number of unique EVs that failed to reach their destination from 272 to 61. In addition, the choice of confidence level significantly affects the cost and revenue of the stakeholders as well as the accuracy of the schedules in real-time operation, e.g., for a low-risk case study, the total net cost of EVs increased by 247.3% compared to a high-risk case study. Also, the total net revenue of CSs and retailers decreased by 26.6% and 10.6%, respectively.

A cost-efficient Based Cooperative Model for Relible Energy Management Of Networked Microgrids Within a Smart Island

This paper mainly focuses on investigating a stochastic energy management approach to enhance reliability of the networked microgrids within a smart island. In this regard, a networked microgrid is considered in the smart island, which is integrated with a multi-energy hub (multi-EH) system aiming to simultaneously support the electrical, thermal, and water demands of the island, isolated from the main grid. The objective function is organized as the cost of operation and reliability of the networked microgrid and is solved using a modified bat algorithm. The uncertainty of stochastic parameters is modelled using the 2-m point estimate method, which has notable advantages in terms of accuracy and simplicity of implementation. Different scenarios are considered both in critical and normal conditions to evaluate the performance of the studied model. Both GAMS and MATLAB software’s were employed to study the proposed model. The proposed model improved the reliability of the networked microgrid system and results reveal that the proposed cooperative approach could decrease total operation and investment cost of the networked microgrid by 13%.

Safety risk assessment method for thermal abuse of lithium-ion battery pack based on multiphysics simulation and improved bisection method

The thermal safety of lithium-ion (Li-ion) batteries is of great importance for their further development and application. The accurate evaluation of the thermal safety boundary has always been the key issue. Due to the coupling effect of the internal, external, and randomness factors, the risk probability is difficult to evaluate using existing deterministic analyses. Therefore, a safety risk assessment method for the thermal abuse of Li-ion battery packs is proposed, and an improved bisection-method-based analysis algorithm for the thermal safety boundary is established. Moreover, a multiphysics model is developed considering an equivalent circuit, thermal abuse, and a fluid dynamics model. Furthermore, stochastic models of the battery parameters and loading are constructed to describe the randomness. The temperature and power stress–strength interference models are integrated to evaluate the thermal safety risk of the battery pack. Then, the models are validated by the temperature and analyzing the stochastic parameters. Finally, several case studies are implemented, including the analyses of thermal safety boundary, effect of stochastic parameters, safety risk probability, and thermal runaway propagation in different scenarios. The results denote that the effect of internal resistance dispersion is dominant and that the risk probability will increase with degradation.

Insights into the micromechanical response of adhesive joint with stochastic surface micro-roughness

Micro-roughness at adhesion surface yields significant influences on the structural behaviour of adhesive joints. Investigations into the micromechanical mechanism are extremely limited. This works developed a novel particle-based model of joints with stochastic microstructural features of roughness, which can capture refined multi-scale responses as first of this kind. Aluminium adherends with mechanical surface treatments were firstly scanned using 3D laser scanning microscope. The statistical features and reconstruction method of micro-roughness profiles were determined. Single lap shear tests on joints made of epoxy adhesive (Loctite EA 9497) and treated aluminium adherends were performed to provide testing data and observations on failure modes. The refined numerical models were subsequently developed to examine the influences of the actual micro-roughness on the micromechanical behaviors and failure mechanism. The mechanical interlocking, mitigation on crack propagation due to the irregular roughness were investigated. It is followed by introducing the reconstructed roughness of various magnitudes and further numerically examining the micromechanical responses by key stochastic parameters such as root mean square roughness and correlation length. The results indicate that the mechanical interlocking contribute more to enhancing the joint strength than the increase of adhesion area by micro-roughness. A rougher surface in either horizontal or vertical directions does not exhibit a consistent improvement of joint strength, which also depends on the threshold of roughness and the surface skewness triggering the transition of failure modes.

Ensemble quantification of short-term predictability of the ocean dynamics at a kilometric-scale resolution: a Western Mediterranean test case

Abstract. We investigate the predictability properties of the ocean dynamics using an ensemble of short-term numerical regional ocean simulations forced by prescribed atmospheric conditions. In that purpose, we developed a kilometric-scale, regional model for the Western Mediterranean sea (MEDWEST60, at 1/60∘ horizontal resolution). A probabilistic approach is then followed, where a stochastic parameterization of model uncertainties is introduced in this setup to initialize ensemble predictability experiments. A set of three ensemble experiments (20 members and 2 months) are performed, one with the deterministic model initiated with perturbed initial conditions and two with the stochastic model, for two different amplitudes of stochastic model perturbations. In all three experiments, the spread of the ensemble is shown to emerge from the smallest scales (kilometric scale) and progressively upscales to the largest structures. After 2 months, the ensemble variance saturates over most of the spectrum, and the small scales (<100 km) have become fully decorrelated across the ensemble members. These ensemble simulations can provide a statistical description of the dependence between initial accuracy and forecast accuracy for time lags between 1 and 20 d. The predictability properties are assessed using a cross-validation algorithm (i.e., using alternatively each ensemble member as the reference truth and the remaining 19 members as the ensemble forecast) together with a given statistical score to characterize the initial and forecast accuracy. From the joint distribution of initial and final scores, it is then possible to quantify the probability distribution of the forecast score given the initial score or reciprocally to derive conditions on the initial accuracy to obtain a target forecast accuracy. The misfit between ensemble members is quantified in terms of overall accuracy (CRPS score), geographical position of the ocean structures (location score) and spatial spectral decorrelation of the sea surface height 2-D fields (decorrelation score). With this approach, we estimate for example that, in the region and period of interest, the initial location accuracy required (necessary condition) with a perfect model (no model uncertainty) to obtain a location accuracy of the forecast of 10 km with a 95 % confidence is about 8 km for a 1 d forecast, 4 km for a 5 d forecast and 1.5 km for a 10 d forecast, and this requirement cannot be met with a 15 d or longer forecast.

The Stochastic Ice-Sheet and Sea-Level System Model v1.0 (StISSM v1.0)

Abstract. We introduce the first version of the Stochastic Ice-sheet and Sea-level System Model (StISSM v1.0), which adds stochastic parameterizations within a state-of-the-art large-scale ice sheet model. In StISSM v1.0, stochastic parameterizations target climatic fields with internal variability, as well as glaciological processes exhibiting variability that cannot be resolved at the spatiotemporal resolution of ice sheet models: calving and subglacial hydrology. Because both climate and unresolved glaciological processes include internal variability, stochastic parameterizations allow StISSM v1.0 to account for the impacts of their high-frequency variability on ice dynamics and on the long-term evolution of modeled glaciers and ice sheets. StISSM v1.0 additionally includes statistical models to represent surface mass balance and oceanic forcing as autoregressive processes. Such models, once appropriately calibrated, allow users to sample irreducible uncertainty in climate prediction without the need for computationally expensive ensembles from climate models. When combined together, these novel features of StISSM v1.0 enable quantification of irreducible uncertainty in ice sheet model simulations and of ice sheet sensitivity to noisy forcings. We detail the implementation strategy of StISSM v1.0, evaluate its capabilities in idealized model experiments, demonstrate its applicability at the scale of a Greenland ice sheet simulation, and highlight priorities for future developments. Results from our test experiments demonstrate the complexity of ice sheet response to variability, such as asymmetric and/or non-zero mean responses to symmetric, zero-mean imposed variability. They also show differing levels of projection uncertainty for stochastic variability in different processes. These features are in line with results from stochastic experiments in climate and ocean models, as well as with the theoretical expected behavior of noise-forced non-linear systems.

A multi-element non-intrusive Polynomial Chaos method using agglomerative clustering based on the derivatives to study irregular and discontinuous Quantities of Interest

A non-intrusive method to get a multi-element Polynomial Chaos model is developed. This method is called ME-ACD, for Multi-Element based on Agglomerative Clustering on Derivatives. It aims at approximating a Quantity of Interest which presents discontinuities or irregularities making it difficult to be accurately approximated by standard Polynomial Chaos models. The method permits to efficiently split the parameter space and to train local polynomial models of lower degrees on every element where the local pieces of the Quantity of Interest are smoother. The algorithm is based on agglomerative clustering of the observations in a well-chosen abstract space taking into account the value of the Quantity of Interest and of its derivatives with respect to the stochastic input parameters. The same observations are used for both partitioning the space and training the local models. Several partitions of the parameter space are tested, and the one leading to local models minimising a cross-validation error is selected. Once the training observations are labelled with a class number indicating the element they are located in, a neural network classifier is trained to determine which local model to use for further evaluations. The method has proven to efficiently split the parameter space for a set of applications of moderate dimension. The piecewise chaos model is compared with the ones of a standard Polynomial Chaos non-intrusive method and of a Gradient Boosted Trees method in terms of accuracy.

Improving real-time energy decision-making model with an actor-critic agent in modern microgrids with energy storage devices

The hereby study combines a reinforcement learning machine and a myopic optimization model to improve the real-time energy decisions in microgrids with renewable sources and energy storage devices. The reinforcement learning-based agent is built as an actor-critic agent making the aggregated near-optimal charging/discharging energy decisions of the microgrid energy storage devices from a discrete action space relying on a reward related to the microgrid online optimal objective function value. The next step time energy levels of storage devices are then computed and provided to the myopic optimization-based decision-making model as parameters which optimally find the incurred power flow within the microgrid minimizing the real-time microgrid energy cost. The real-time measurement of stochastic parameters of the microgrid coupled with the current energy levels of electrical and heat storage are input to the artificially intelligent machine as observations states. The actor-critic agent approximators are modeled as deep neural networks optimized using the Adam gradient descent algorithm with a gradient threshold. Although the proposed model with a 2-kWh increment of the charging/discharging energy training is time-consuming, it has been able at 100% to optimally make microgrid energy decisions and improve online energy decisions by 90.98% compared to the myopic model alone.

Electric Vehicles and Vehicle–Grid Interaction in the Turkish Electricity System

Electric vehicles and energy storage systems are technologies in the stage of intensive development. One of the innovative ways to use electric cars is the Vehicle to Grid (V2G) concept. V2G charging points are characterized by the ability of bidirectional energy flow while charging EV/BEV (Electric Vehicles/Battery Electric Vehicles). In periods of low energy consumption and the presence of the highest shares of renewable sources, the cleanest electricity is drawn from the grid at the lowest prices and stored in a “mobile warehouse”, which is an electric car. During the reported peaks in electricity demand and the presence of high tariffs, the previously stored energy may be sold back to the distribution network operator. Thanks to this application, the technology determines the highest profitability of the system and assigns EV/BEV the ability to manage electricity flows, while improving the energy balance of the economy. The prospects for the spread of V2G have increased along with the growing requirements for domestic economies, closely related to the significant share of renewable energy sources. The vision of connecting EV/BEV with the power grid creates completely new ways of managing energy and makes it possible to build smart agglomerations in line with the Smartcity idea. Especially since Turkey is one of the countries promoting this idea. The scientific aim of the study is to maximize the aggregator’s profits for V2G by creating a coalition with renewable energy producers and combining the capacities of many EVs and offering their total capacities to the electricity markets. The subject of the research was to obtain extensive knowledge about the vehicle–grid interactions taking place in the Turkish power system. For this purpose, an analysis is conducted to determine the optimal preferred operating points and the amount of regulation proposals that maximize the profit of the EV users while satisfying the constraints of each stochastic parameter. The results show the system benefits from the implementation of the algorithms are significant to optimal bidirectional V2G impacts on distribution systems with high penetration of EVs. The research can find practical applications in assessing the role of electric vehicles and their integration in the vehicle–grid system in power systems. At the same time, pointing to the benefits related to the implementation of such solutions for Turkey and other countries in the field of electromobility, stability of energy systems, and energy independence through the possibility of achieving the desired synergy effect.

Three Strikes and You�re Out

Suggests a new methodology for approximating barrier option prices in stochastic local volatility models. For touch options the method only requires the input of the level, slope and curvature around the barrier in addition to the stochastic volatility parameters. Three strikes are enough.

Sensitivity-based Parameter Calibration of Single- and Dual-continuum Coreflooding Simulation Models

Our study is keyed to the development of a viable framework for the stochastic characterization of coreflooding simulation models under two- and three-phase flow conditions taking place within a core sample in the presence of preferential flow of the kind that can be associated with the presence of a system of fractures. We do so considering various modeling strategies based on (spatially homogeneous or heterogeneous) single- and dual-continuum formulations of black-oil computational models and relying on a global sensitivity-driven stochastic parameter calibration. The latter is constrained through a set of data collected under a water alternating gas scenario implemented in laboratory-scale coreflooding experiments. We set up a collection of Monte Carlo (MC) numerical simulations while considering uncertainty encompassing (a) rock attributes (i.e., porosity and absolute permeability), as well as (b) fluid–fluid/ fluid–solid interactions, as reflected through characteristic parameters of relative permeability and capillary pressure formulations. Modern moment-based global sensitivity indices are evaluated on the basis of the MC model responses, with the aim of (i) quantifying sensitivity of the coreflooding simulation results to variations of the input uncertain model parameters and (ii) assessing the possibility of reducing the dimensionality of model parameter spaces. We then rest on a stochastic inverse modeling approach grounded on the acceptance–rejection sampling (ARS) algorithm to obtain probability distributions of the key model parameters (as identified through our global sensitivity analyses) conditional to the available experimental observations. The relative skill of the various candidate models to represent the system behavior is quantified upon relying on the deviance information criterion. Our findings reveal that amongst all tested models, a dual-continuum formulation provides the best performance considering the experimental observations available. Only a few of the parameters embedded in the dual-continuum formulation are identified as major elements significantly affecting the prediction (and associated uncertainty) of model outputs, petrophysical attributes and relative permeability model parameters having a stronger effect than parameters related to capillary pressure.