Discrete Model Research Articles

Designing employee benefits to optimize turnover: A prescriptive analytics approach

Employee turnover significantly impacts organizations, particularly those with substantial investments in training their workforce. To mitigate these effects, we propose a Prescriptive Human Resources Analytics approach that optimizes employee benefits to minimize total costs, focusing on turnover management The methodology models employee decision-making using a discrete choice model, with parameters estimated through maximum likelihood. We solve the resulting nonlinear optimization problem with a heuristic tailored to the problem’s complexity. We applied this methodology to a hospital case study, which was used to enhance the transportation system as an employee benefit, considering the associated turnover costs. The results demonstrate that our approach can reduce total costs, optimize the usage level of the designed benefits, and increase employee satisfaction. This research provides a robust framework for data-driven decision-making in HR, offering practical tools for improving employee retention strategies.

Consumer preference and willingness-to-pay for formal recycling of electric vehicle batteries: a discrete choice experiment study

The burgeoning electric vehicle (EV) market poses a substantial challenge to battery recycling systems, yet understanding EV battery recycling behavior from the demand side remains limited. Previous studies have analyzed perceptual or attitudinal factors, neglecting the observable attributes of EV battery recycling. To this end, we proposed a discrete choice model to investigate the differences between formal and informal recycling behaviors, identifying consumer preferences and willingness to pay. By analyzing 1190 sample data collected from Chongqing, China, we find that: (1) The formal recycling market exhibits greater sensitivity to prices compared to the informal recycling market. (2) The formal recycling market favors recycling by EV battery producers, whereas the informal recycling market shows the least preference for recycling by automobile producers. (3) Door-to-door recycling services are the most effective in facilitating the transition from informal to formal recycling markets for EV batteries. (4) Capacity subsidy policies outperform one-time fixed subsidy policies in incentivizing formal recycling. (5) The formal recycling market for EV batteries necessitates "traceability to the recycling outlet", as opposed to being untraceable. (6) The high-awareness group exhibits greater sensitivity to government policies compared to those with lower environmental concerns and less knowledge of EV battery recycling.

A hybrid multiscale model for fluid flow in fractured rocks using homogenization method with discrete fracture networks

Fluid flow in subsurface tight reservoirs containing pores, microcracks and macrocracks is notably influenced by the characteristics of macro/micro-cracks. A novel hybrid multiscale model is proposed to address the response of macrocracks and pores/microcracks in different spatial scales. Specifically, an equivalent macroscopic model (EMM) deduced from locally periodic representative element volume (REV) is developed using the asymptotic homogenization method to represent the poroelastic behavior of porous medium with microcracks. Simultaneously, the macrocracks are modeled explicitly using the discrete fracture model (DFM), where the hydraulic properties of cracks influenced by fluid pressure gradient is represented by the nonlinear opening/closure behavior. The obtained hybrid model takes into account the heterogeneous nature of fractured rock masses containing pores, micro/macro-cracks, which is fundamental to describe fluid flow behavior in fracture-matrix system. Specialized finite elements, regular meshing technique and adaptive time stepping algorithm are adopted to improve the computational efficiency. The hybrid multiscale model is firstly validated step by step to demonstrate the accuracy and then used to simulate fluid flow in fractured rock reservoir, shedding light on the underlying mechanisms of the enhanced flow capacity resulting from microcrack distribution, connectivity, and macrocrack stimulation.

Building credibility for human systems integration in model‐based systems engineering

AbstractRobust and trusted digital human representations are necessary to successfully account for human considerations in model‐based systems engineering (MBSE). Multiple domains and modeling frameworks leverage verification, validation, and accreditation (VV&A) processes to characterize when and under what conditions a model is valid to establish credibility. A literature review was completed on mathematical, physics‐based, software development, discrete event simulation, agent‐based, system dynamics, and MBSE models with the goal of proposing a process for performing VV&A on digital engineering (DE) and MBSE models for sociotechnical systems. However, this research also revealed the need for a broader framework to characterize the risk associated with using these models for making high‐consequence decisions. While accomplishing the literature review, another approach to building credibility was identified that is used heavily in the financial industry, namely model risk management (MRM). This process is extended by leveraging MRM approaches from within the financial community to propose a framework for sociotechnical model users to characterize the risk of using MBSE models to make programmatic decisions. The primary contribution of this work is to document a meta‐analysis of model VV&A while proposing an alternative approach to characterizing and communicating credibility that was discovered during this analysis. This approach could be a viable option for ensuring the credibility of human systems integration in MBSE models.

Refracturing Time Optimization Considering the Effect of Induced Stress by Pressure Depletion in the Shale Reservoir

Refracturing is an important technology for tapping remaining oil and gas areas and enhancing recovery in old oilfields. However, a complete and detailed refracturing timing optimization scheme has not yet been proposed. In this paper, based on the finite volume method and the embedded discrete fracture model, a new coupled fluid flow/geomechanics pore-elastic-fractured reservoir model is developed. The COMSOL 3.5 commercial software was used to verify the accuracy of our model, and by studying the influence of matrix permeability, initial stress difference, cluster spacing, and fracture half-length on the orientation of maximum horizontal stress, a timing optimization method for refracturing is proposed. The results of this paper show that the principle of optimizing the refracturing timing is to avoid the time window where the percentage of Type I (Type I indicates that stress inversion has occurred, 0∘≤α≤20∘; Type II indicates that the turning degree is strong, 20∘<α≤70∘; and Type III indicates less stress reorientation, 70∘<α≤90∘) stress reorientation area is relatively large, so that the fractures can extend perpendicular to the horizontal wellbore. At the same time, the simulation results show that with the increase in production time, the percentage of Type I and Type II increases first and then decreases, while the percentage of Type III decreases first and then increases. When the reservoir permeability, stress difference, and cluster spacing are larger, the two types of refracturing measures can be implemented earlier. But, with the increase in fracture half-length, the timing of refracturing Method I is earlier, and the timing of refracturing Method II is later. The research results of this paper are of great significance to the perfection of the refracturing theory and the optimization of refracturing design.

A 3D DEM modeling of soil-rock mixture considering spatial distribution orientation of blocks

Spatial distribution orientations of blocks can cause significant errors in the discrete element model (DEM) calculation of soil-rock mixture (SRM). To avoid this error, spherical harmonic (SH) series whose harmonization degrees fixed at 15 were proposed for block reconstruction. This research refers to the case-history of a deep excavation rift valley spanning from the Mabian to Zhaojue section of the Leshan-Xichang Expressway, mainly containing moderately-weathered silty mudstone, in the Leshan City, Sichuan Province, China. The appropriate degree of finite-term SH series is selected by the volume, surface area. 100 blocks were scanned on site, and sphericity and angularity of the blocks were calculated. The sphericity and angularity of 50 reconstructed blocks were considered for the error analysis of SH method. Moreover, stochastic polyhedron method was considered for comparing different block reconstructions. The maximum block placement angle was defined to control the spatial distribution orientations of the blocks. Large scale direct tests were carried. Numerical simulations of large-scale direct shear tests were conducted to study the influence of the spatial distribution orientations of the blocks on the mechanical properties of the SRMs. The results revealed that the finite-term SH series fixed at 15 accurately reflected the shape characteristics and mechanical behaviors of actual blocks. The spatial distribution orientations of the blocks had a minimal impact on the friction angle and cohesion of SRM constructed through the SH method. The SRMs developed via the SH method exhibited marginal variations in contact force and anisotropy index of contact across diverse block placement strategies. The evolution of coordination number was closer when employing the SH method under varied block placement methods. Blocks reconstructed by the SH method, could mitigate errors in DEM calculation caused by the spatial distribution orientations of the blocks.

Efficient probabilistic inference in biochemical networks

Biochemical networks are usually modeled by ordinary differential equations that describe the time evolution of the concentrations of the interacting (biochemical) species for specific initial concentrations and certain values of the interaction rates. They consist, in general, of many variables and parameters. Parameter estimation of such systems using standard optimization algorithms is computationally expensive since a large number of numerical simulations must be performed for numerous values of initial conditions and parameters, making these approaches either inefficient or inaccurate. In this paper, we explain how biochemical networks can be approximated by dynamic Bayesian networks, a class of discrete probabilistic models. This type of approximation enables the use of Bayesian inference for performing tasks such as parameter estimation. We explain how to make this type of approximations and the subsequent parameter estimation task as accurate and computationally efficient as possible. Our approach is applied on concrete examples such as the EGF-NGF cellular signaling pathway.

An optimization DEM modelling method for soil-fibre undrained cyclic loading tests model based on the influence range of fibre

The computational cost of discrete element modelling is high owing to the limitations of particle size and contact in fibre modelling. This paper proposes an optimised discrete element method (DEM) for a hybrid model of soil and fibres based on the fibre influence range. First, a relative velocity state function is established based on the relative motion state between the fibres and soil particles under undrained cyclic loading. Subsequently, the influence range of the fibres is determined using the relative velocity function based on the first few cycles of the undrained cyclic loading numerical tests. Cluster and clump models of the fibre are then generated based on the influence range of the fibre. Finally, a symmetrical shape of the optimised model is developed by extracting the distribution length of the edge curve of the influence range along the vertical direction of the axis. In this study, the proposed optimised DEM was validated through a series of undrained cyclic loading numerical tests on fibre-reinforced soil. The results of the optimised model were highly consistent with those of the traditional model, and the computational time was significantly reduced. The cyclic loading timing for determining the range of influence of the fibre was analysed. The optimised model based on the influence range of the 15th cycles not only restored almost the same results but also saved the calculation cost by nearly eight times. The optimised model established based on the influence range after the 15th cycles had a slight influence on the results. In addition, the applicability of the optimised model is discussed. This paper provides new insights into the establishment of a hybrid model of soil and fibres.

Evaluating overhanging slope failure mechanisms and rockfall trajectories through integrated UAV imagery and discrete element modeling

AbstractTo evaluate the threat of rockfall from an overhanging slope above a bridge, this study proposes a comprehensive analysis procedure to assess the failure mechanisms of the slope and the associated rockfall trajectories. The analysis utilizes high-resolution point cloud data obtained through integrated UAV-based imagery technology, enabling a detailed evaluation of joint configurations and slope stability. The geometric reconstruction of unstable rock blocks, combined with stereographic projections, provides an in-depth analysis of potential failure modes. Discrete element modeling (DEM) is employed to simulate the failure processes and predict rockfall trajectories, with particular emphasis on the potential risks to the underlying bridge. The results indicate that rockfall events near the bridge are primarily driven by wedge-shaped failures, a finding confirmed by both the proposed inverted three-dimensional projection method and DEM simulations. The analysis identifies critical rock blocks near the bridge, underscoring the need for targeted mitigation strategies. This case study demonstrates the effectiveness of integrating UAV-derived data with DEM for assessing overhanging slope failures and managing rockfall risks in similar geological settings.

The effect of particle size distribution on the collapse of wet polydisperse granular materials

Low-saturation liquid-containing granular materials are commonly encountered in both natural and industrial settings, where interstitial liquids significantly affect the motion of particles, while particle size polydispersity plays a crucial role in determining the level of system cohesion. In this study, the collapse of wet polydisperse granular columns is numerically investigated based on the developed discrete element model, with corresponding dam-break experiments performed to validate our numerical model and methodology. The dependence of the dynamics and flow mobility on particle size distribution is primarily examined, and the underlying mechanisms are also explored by analyzing particle path lengths and average fidelity. Building upon the effective Bond number proposed using the mixing theory, a macroscopic cohesion parameter at the material scale is defined by considering the dependence of the collapse on the system size effect. The relevance of this cohesion parameter in describing different wet polydisperse granular collapses is further validated based on our designed experimental tests and DEM simulations. The approach of constructing the cohesion parameters at different scales can be extended to characterize cohesion effects in more complex wet polydisperse granular flows and describe their associated rheological behaviors.

Computational Modeling of Cough Droplet Behavior in the Human Upper Respiratory Airway

Abstract This study investigated the interaction of cough droplets with airflow in a realistic human airway. The ultimate aim was to understand the behavior of cough droplets inside the airway and to assess the potential of droplets to be retained in the airway or transmitted to the lungs. A computational fluid dynamics (CFD) model, based on the Euler–Lagrangian framework, was employed to predict the two-phase, droplet-laden transient cough flow in a realistic three-dimensional (3D) human airway. The airway geometry was reconstructed from patient computed tomography (CT) scan dataset. The discrete phase model was used to track the motion of the droplets in the air flow. Two distinct cough profiles—a strong cough and a weak cough—acquired experimentally from human subjects, were used as input to simulate normal and disordered cough functions. The effects of cough strength and droplet size on droplet retention and aspiration in the airway were investigated. It was found that droplet retention was significantly higher for a weak cough compared to a strong cough. For a weak cough, the highest droplet retention percentage exceeded 60%, while for a strong cough, it was less than 20%. Larger sized droplets were more likely to be aspirated into the lungs, especially under weak cough conditions. In the case of weak cough, more than 5% of the 200 μm sized droplets were aspirated into the lungs, whereas for strong cough, aspiration was less than 2%.

Dynamic simulation of cargo transport along cislunar suspension tether by single node coupling model

A cislunar suspension tether (CST) is a kind of ultra-long tether anchored to the lunar surface and extends to the vicinity of the Earth, looks like hanging to the Moon, could be used as cislunar pathway for interstellar freightage easier. Its feasibility on material mechanics and dynamics has been verified by the authors. This paper focuses on the process of the cargo transport along the CST. A single coupling model is established, which couples the cargo with one single node of the discrete CST model. Merely the interactive force between the coupled node and cargo is considered, with a proper definition description of the cargo's velocity along the CST. The description defines the direction of the cargo's velocity to the next one node on the CST all the time. The dynamic equations of the whole system are established based on afore stipulations. Several examples will be simulated and presented, their results will prove the effectiveness of the single coupling model, while, reflect some interesting phenomena of the CST's work. This paper also explains the advantage of the model by contrasting to some other models with multi nodes actions to the cargo.

Calibration of discrete meta-parameters of bamboo flour based on magnitude analysis and BP neural network.

In the research and development of technology and equipment for bamboo products deep processing, such as filling, drying, and medicinal use of bamboo flour (BF), the poor compaction and fluidity of BF materials entails the need for accurate discrete element model (DEM) and BF parameters to provide a reference for the simulation of BF processing operationsand the development of related equipment. The average particle size of the 5 types of BFs ranges from 0.136 mm to 0.293 mm, and the small particle size of BF particles causes to the number of BF particles in bamboo processing equipment to reach tens of millions or even billions. When conventional methods are used for simulation, ordinary computers cannot provide the required computing power. To address the aforementioned challenges, this paper proposes a calibration method for the discrete element contact parameters of BFs based on dimensional analysis and a back propagation (BP) neural network. Using particle scaling theory and dimensional analysis methods, the average particle size of the BF was increased to 1 mm, and the main discrete element contact parameters of the five types of BF to be tested were used as input layers. The injection method and sidewall collapse method were used to obtain the angle of repose (AR) as the output layer. Fifty groups were randomly selected using MATLAB for EDEM simulation, and the simulation results were trained using the BP neural network algorithm; an ideal neural network model was obtained, the discrete element parameters of different BFs were predicted, and physical experiments were performed to verify two types of AR and mold hole compression under calibrated parameters. The relative error between the simulated AR obtained through calibration parameters and the physical experimental values is less than 2.3%. Through BF parameter validity verification, the simulated maximum compression displacement and compression ratio after stabilization were 34.81 mm and 0.477, which were close to the actual experimental results of 34.77 mm and 0.461, respectively, verifying the accuracy of the neural network prediction model. The research results provide a reference for the simulation of BF processing operations and the development of related equipment.

Adaptive control of magnetic levitation system based on fuzzy inversion

A novel adaptive tracking controller for magnetic levitation systems (MLS) is developed. The controller is based on a special adaptive control scheme incorporating fuzzy model of electromagnetic acceleration enabling fast and accurate fuzzy inversion. The controller ensures accurate tracking of any smooth desired position signal, despite unknown MLS parameters. The closed-loop system stability, in the sense of uniform ultimate boundedness (UUB) of error trajectories, is proved using Lyapunov approach. The closed-loop system performance is investigated during numerical experiments. Finally the proposed controller is verified by successful implementation on a DSP board controlling a typical magnetic levitation ball system. Performed tests and experiments demonstrate that the proposed control technique is robust against discretization and unknown MLS model parameters, provides high tracking accuracy, is easily implementable, and simple to tune.

Uncertainty propagation of initial conditions in thermal models

The operation of machine tools often demands a highly accurate knowledge of the tool center point’s (TCP) position. The displacement of the TCP over time can be inferred from coupled thermal models, which comprise a set of geometrically coupled heat equations. Each of these equations represents the temperature in part of the machine, and they are often formulated on complicated geometries. The accuracy of the TCP prediction depends highly on the accuracy of the model parameters, such as heat exchange parameters, and the initial temperature. Thus it is of utmost interest to determine the influence of these parameters on the TCP displacement prediction. In turn, the accuracy of the parameter estimate is essentially determined by the measurement accuracy and the sensor placement. Determining the accuracy of a given sensor configuration is a key prerequisite of optimal sensor placement. In this paper, we develop a thermal model for the discretization of realistic machine tool. On top of this model we propose two numerical algorithms to evaluate any given thermal sensor configuration with respect to its accuracy. We compute the posterior variances from the posterior covariance matrix with respect to an uncertain initial temperature field. The full matrix is dense and potentially very large, depending on the size of the discretized model. We first present a way to compute this approximation, which relies on the computation of the model sensitivities with respect to the initial values. Additionally, we present a low-rank tensor method which exploits the underlying system structure. We compare the efficiency of both algorithms with respect to runtime and memory requirements and discuss their respective advantages with regard to optimal sensor placement problems.

Accessing Elastic Properties of Porous Solid Oxide Fuel Cell Electrodes Using 2D Image-Based Discrete Element Modeling and Deep Learning

Accessing Elastic Properties of Porous Solid Oxide Fuel Cell Electrodes Using 2D Image-Based Discrete Element Modeling and Deep Learning

Deep learning surrogate for predicting hydraulic conductivity tensors from stochastic discrete fracture-matrix models

Deep learning surrogate for predicting hydraulic conductivity tensors from stochastic discrete fracture-matrix models

High-Fugacity Expansion and Crystallization in Non-sliding Hard-Core Lattice Particle Models Without a Tiling Constraint

In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in dimension d≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\ge 2$$\\end{document}. We consider only models featuring a single species of particles, which in particular forbids the particles from rotation and reflection, and establish a criterion under which crystallization occurs at sufficiently high densities. The criterion is more general than that in Jauslin and Lebowitz (Commun Math Phys 364:655–682, 2018), as it allows models in which particles do not tile the space in the close-packing configurations, such as discrete hard-disk models. To prove crystallization, we prove that the pressure is analytic in the inverse of the fugacity for large enough complex fugacities, using Pirogov–Sinai theory. One of the main new tools used for this result is the definition of a local density, based on a discrete generalization of Voronoi cells. We illustrate the criterion by proving that it applies to three examples: staircase models and the radius 2.5 hard-disk model on Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb Z^{2}$$\\end{document}, and a heptacube model on Z3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb Z^{3}$$\\end{document}.

Performance of Monotonic Pile Penetration in Sand: Model Test and DEM Simulation

By integrating laboratory tests and three-dimensional discrete element methods, this research extensively explores the macroscopic and microscopic mechanisms of static pile penetration in standard sand. Initially, the mesoscopic parameters of standard sand were established via flexible triaxial compression tests, and a three-dimensional discrete element model was created using the particle size magnification technique. The study results confirm the rationality of parameter selection and numerical modeling by comparing penetration resistance and displacement obtained from laboratory model tests and discrete element simulations. Initially, penetration resistance swiftly increases, then stabilizes progressively with increasing depth. The lateral friction resistance grows with penetration depth, especially peaking near the cone tip. Moreover, horizontal stress quickly rises during pile penetration, mainly caused by the pile foundation compressing the adjacent soil particles. Displacement of the foundation particles is primarily focused around the pile side and cone tip, affecting an area roughly twice the pile diameter. Soil particle displacement exhibits a pronounced vertical downward movement, primarily driven by lateral friction. The distribution of force chains among foundation particles indicates that the primary stressed areas are at the pile ends, highlighting stress concentration features. This research offers significant insights into the mechanical behaviors and soil responses during pile foundation penetration.

Landslide Hazard Prediction Based on UAV Remote Sensing and Discrete Element Model Simulation—Case from the Zhuangguoyu Landslide in Northern China

Rainfall-triggered landslides generally pose a high risk due to their sudden initiation, massive impact force, and energy. It is, therefore, necessary to perform accurate and timely hazard prediction for these landslides. Most studies have focused on the hazard assessment and verification of landslides that have occurred, which were essentially back-analyses rather than predictions. To overcome this drawback, a framework aimed at forecasting landslide hazards by combining UAV remote sensing and numerical simulation was proposed in this study. A slow-moving landslide identified by SBAS-InSAR in Tianjin city of northern China was taken as a case study to clarify its application. A UAV with laser scanning techniques was utilized to obtain high-resolution topography data. Then, extreme rainfall with a given return period was determined based on the Gumbel distribution. The Particle Flow Code (PFC), a discrete element model, was also applied to simulate the runout process after slope failure under rainfall and earthquake scenarios. The results showed that the extreme rainfall for three continuous days in the study area was 151.5 mm (P = 5%), 184.6 mm (P = 2%), and 209.3 mm (P = 1%), respectively. Both extreme rainfall and earthquake scenarios could induce slope failure, and the failure probabilities revealed by a seepage–mechanic interaction simulation in Geostudio reached 82.9% (earthquake scenario) and 92.5% (extreme rainfall). The landslide hazard under a given scenario was assessed by kinetic indicators during the PFC simulation. The landslide runout analysis indicated that the landslide had a velocity of max 23.4 m/s under rainfall scenarios, whereas this reached 19.8 m/s under earthquake scenarios. In addition, a comparison regarding particle displacement also showed that the landslide hazard under rainfall scenarios was worse than that under earthquake scenarios. The modeling strategy incorporated spatial and temporal probabilities and runout hazard analyses, even though landslide hazard mapping was not actually achieved. The present framework can predict the areas threatened by landslides under specific scenarios, and holds substantial scientific reference value for effective landslide prevention and control strategies.