Rough Model Research Articles

Modeling and experimental study of surface roughness in smart MR fluid-based finishing process

Ball-end magnetorheological finishing (BEMRF) is a high-efficiency nano-finishing technology based on smart magnetorheological fluid to polish complex materials precisely. The surface roughness can be linked with the experimental data to understand the finishing mechanism based on advancements in manufacturing automation and the prediction of material removal. This study proposes a mathematical model to predict surface roughness, helping to understand the effects of various process parameters on surface quality during the BEMRF process. This study adds value to practitioners by providing a mathematical model to predict the optimum parameters for attaining the desired surface finish in BEMRF polishing.

Numerical Investigation of Stratified Slope Failure Containing Rough Non-Persistent Joints Based on Distinct Element Method

To address the critical issue of slope stability in jointed rock masses with complex and rough structural planes, a rough joint network model using the Fourier transform was proposed and applied to the Shilu open pit mine. The on-site structural plane survey results were combined with MATLAB and PFC2D to establish numerical models for slope stability analysis considering both linear-jointed and rough-jointed rock slopes. By comparing the slip body and fracture distribution, it was found that the rough-jointed slope was stabler than the linear-jointed slope. In addition, the fracture patterns and slip displacement were significantly influenced by the inclination and undulation of the bedding planes. Slip failure patterns occurred when the angle of inclination was set at 60°. The joints played a crucial role in inducing the shear strength of slope rock masses, and the slide area was mainly observed in the shallow slope surface for inclination angles of 0° and 45°, and in the middle deep area for 60° and 90°. These results demonstrated the importance of considering rough non-persistent fractures when developing a new numerical model for slope failure modes.

Slip flow and thermal characteristics in gas thrust bearings with rough surfaces

PurposeThis study aims to investigate the rarefaction effects on flow and thermal performances of an equivalent sand-grain roughness model for aerodynamic thrust bearing.Design/methodology/approachIn this study, a model of gas lubrication thrust bearing was established by modifying the wall roughness and considering rarefaction effect. The flow and lubrication characteristics of gas film were discussed based on the equivalent sand roughness model and rarefaction effect.FindingsThe boundary slip and the surface roughness effect lead to a decrease in gas film pressure and temperature, with a maximum decrease of 39.2% and 8.4%, respectively. The vortex effect present in the gas film is closely linked to the gas film’s pressure. Slip flow decreases the vortex effect, and an increase in roughness results in the development of slip flow. The increase of roughness leads to a decrease for the static and thermal characteristics.Originality/valueThis work uses the rarefaction effect and the equivalent sand roughness model to investigate the lubrication characteristics of gas thrust bearing. The results help to guide the selection of the surface roughness of rotor and bearing, so as to fully control the rarefaction effect and make use of it.

Functional central limit theorems for rough volatility

The non-Markovian nature of rough volatility makes Monte Carlo methods challenging, and it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide an efficient one for stochastic Volterra processes, based on an extension of Donsker’s approximation of Brownian motion to the fractional Brownian case with arbitrary Hurst exponent H∈(0,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$H \\in (0,1)$\\end{document}. Some of the most relevant consequences of this ‘rough Donsker (rDonsker) theorem’ are functional weak convergence results in Skorokhod space for discrete approximations of a large class of rough stochastic volatility models. This justifies the validity of simple and easy-to-implement Monte Carlo methods, for which we provide detailed numerical recipes. We test these against the current benchmark hybrid scheme and find remarkable agreement (for a large range of values of H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$H$\\end{document}). Our rDonsker theorem further provides a weak convergence proof for the hybrid scheme itself and allows constructing binomial trees for rough volatility models, the first available scheme (in the rough volatility context) for early exercise options such as American or Bermudan options.

Deep calibration with random grids

We propose a neural network-based approach to calibrating stochastic volatility models, which combines the pioneering grid approach by Horvath et al. [Deep learning volatility: A deep neural network perspective on pricing and calibration in (rough) volatility models. Quant. Finance, 2021, 21(1), 11–27]. with the pointwise two-stage calibration of Bayer and Stemper [Deep calibration of rough stochastic volatility models. Working Paper, arXiv:1810.03399, 2018] and Liu et al. [A neural network-based framework for financial model calibration. J. Math. Ind., 2019, 9(1), 1–28]. Our methodology inherits robustness from the former while not suffering from the need for interpolation/extrapolation techniques, a clear advantage ensured by the pointwise approach. The crucial point to the entire procedure is the generation of implied volatility surfaces on random grids, which one dispenses to the network in the training phase. We support the validity of our calibration technique with several empirical and Monte Carlo experiments for the rough Bergomi and Heston models under a simple but effective parametrization of the forward variance curve. The approach paves the way for valuable applications in financial engineering—for instance, pricing under local stochastic volatility models—and extensions to the fast-growing field of path-dependent volatility models.

Numerical modelling of contact adhesion in a random assembly of elastic–plastic particles

The prediction of tensile strength properties of powder compacts remains an important industrial issue. In particular, one of the main problems of the powder compaction process is the failure of compacts. Indeed, some powder compacts exhibit cracks which appear during compaction. Such defects occur due to localised tensile or shear stresses, for example close to geometrical singularities. They are also related to the ability of a powder to create enough adhesion at contacts between particles to withstand tensile stresses. Therefore, cracks are a consequence of phenomena occurring at the particle scale and below, down to the molecular scale. To help understanding this mechanism, a particle-scale, numerical method called the multi-particle finite-element method was developed using the finite-element software suite Abaqus (Abaqus 6.14 Documentation, 2016). Such a method allowed to explicitly model the microstructure of a granular media idealised as an assembly of elastic–plastic spheres. The particles were meshed such that their deformations were fully taken into account, using a continuum-mechanics-based material model. The interactions between particles were managed using finite-element contact formulations. A multi-scale, adhesive contact model was developed based on the literature and implemented into the multi-particle finite-element code. The contact model was based on a surface energy formulation weighted by the roughness model developed by Pullen and Williamson (1972). It introduced a novel aspect, the development of adhesion under the effect of external mechanical loads, which is consistent with the cold compaction process. This model was then applied to predict the mesoscopic properties of a packing of spheres, i.e. its response to mechanical stresses of any type, in particular strongly deviatoric stress paths. Such a method intends to be a help toward the development of an efficient continuum model for the modelling of the powder compaction process.

Changeable environment visual detection of grinding surface roughness based on lightweight network

ABSTRACT The texture features of the grinding surface are not obvious, when the light source environment and shooting angle change, the prediction model of grinding surface roughness based on the deep learning method is greatly affected. Moreover, when applied to the mobile end or the embedded end, the model requires smaller size and faster inference time. This paper proposes a surface roughness detection model for grinding based on lightweight network MoCoViT, which can be applied to changeable imaging environments. This model uses the advantages of Transformer and mobile convolutional networks to improve performance and efficiency, so as to complete the recognition of grinding surface roughness in a transformable image environment. For different angles and different light sources, three experiments are designed to test the recognition effect of the model under unknown angles and unknown lighting conditions. The experimental results show that the grinding surface roughness detection model based on MoCoViT network has the highest accuracy in the test set. It proves that MoCoViT model has good robustness to the grinding surface roughness detection in the image changeable environment, which lays a foundation for the industrial application of online visual detection of grinding surface roughness.

Correlation between the sound speed ratio and physical properties of seafloor sediments in the northwestern shelf of the south China sea

Based on a substantial number of seabed sediment samples and corresponding acoustic characteristic and physical property test data collected in the continental shelf area of the northwestern South China Sea, this study employed a sound speed ratio correction model to analyze the correlation between the sound speed ratio of seabed sediments and parameters such as porosity, density, mean grain size, and water content. This study resulted in the development of both single-parameter and double-parameter empirical formulas for the sound speed ratio of seabed sediments in this marine region. The determination coefficients (r2) for the single-parameter empirical formulas based on physical properties, excluding the mean grain size (r2 ≤ 0.75), were all above 0.78, indicating a strong correlation. Additionally, the fitting curve at 100 kHz was slightly greater than that at 50 kHz, consistent with the acoustic dispersion characteristics of sediments. To assess the applicability of the empirical formulas to different maritime areas, the formulas derived from the South Yellow Sea, East China Sea, and South China Sea were compared with those of the study area. The results indicated that the empirical formulas for the sound speed ratio established in this study have general applicability, especially for sediments with low porosity, high density, and low mean grain size. In addition, the determination coefficient of the dual-parameter empirical formula for the sound speed ratio–porosity–mean grain size is superior to that of the single-parameter empirical formula for the sound speed ratio–mean grain size. Through comparative studies with other marine areas, it was found that there are certain differences in the relationships between porosity and mean grain size established in different marine areas. Therefore, based on the rough sphere model, this study transforms the GS model into a single-parameter model built on either porosity or mean grain size. The error analysis results indicate that the single-parameter GS model has a smaller error than the measured data. However, the GS model controlled by a single parameter performs poorly compared to the predicted curves of the sound speed ratio–porosity and the sound speed ratio–mean grain size fitted in this study. This discrepancy may be attributed to the fact that the input parameters of the GS model are reference values, emphasizing the need for further research to determine suitable input parameters for the GS model in this marine area.

Simplified Formulation for Bush, Gibson, and Thomas Model

Abstract The random process model, also known as the multi-asperity contact model or statistical model, is one of the dominant methodologies for analyzing the contact between nominally flat rough surfaces. In 1975, Bush, Gibson, and Thomas developed a complete random process model (known as the BGT model) assuming that solid–solid contacts occur on the summits of the asperities, which are semi-ellipsoids uniquely described by three random variables (the asperity height and two principal peak curvatures). The Hertzian elliptic contact theory states that the contact area and normal load are implicit functions of the random variables, which results in an original BGT model with a complex formulation. In this study, we used an adapted Hertzian elliptic contact theory to simplify the formulation of the BGT model. The relative contact area to normal load relation predicted by the simplified BGT model perfectly agrees with that of the original formulation. It is anticipated that rough surface contact models with complex asperity interactions can be effectively built under the framework of this simplified BGT model.

Four types of grey [formula omitted]-covering models and their applications

To handle the limitations of a fuzzy β-neighbourhood, many researchers apply this notion to different structures to allow them to make a suitable decision in some real problems. In this article, we introduce the notions of grey β-neighbourhood and grey complementary β-neighbourhood, and then we establish the grey β-covering approximation space (GβCAS). The relevant characteristics are also examined. Furthermore, we construct two new GβCAS models to combine the definitions of a grey β-neighbourhood and a grey complementary β-neighbourhood and explain their relations. In addition, employing grey β-neighbourhoods, we investigate four types of β-neighbourhoods and use them to build four rough approximation models. Hence, in order to give a new approach to MADM in grey β-covering approximation space, we establish a novel methodology based on GCβAS models called multi-attribute grey decision making (MAGDM). Finally, with comparisons to current studies, a numerical example is given to demonstrate the feasibility and usefulness of our suggested methodologies.

Adaptive neighborhood rough set model for hybrid data processing: a case study on Parkinson’s disease behavioral analysis

Extracting knowledge from hybrid data, comprising both categorical and numerical data, poses significant challenges due to the inherent difficulty in preserving information and practical meanings during the conversion process. To address this challenge, hybrid data processing methods, combining complementary rough sets, have emerged as a promising approach for handling uncertainty. However, selecting an appropriate model and effectively utilizing it in data mining requires a thorough qualitative and quantitative comparison of existing hybrid data processing models. This research aims to contribute to the analysis of hybrid data processing models based on neighborhood rough sets by investigating the inherent relationships among these models. We propose a generic neighborhood rough set-based hybrid model specifically designed for processing hybrid data, thereby enhancing the efficacy of the data mining process without resorting to discretization and avoiding information loss or practical meaning degradation in datasets. The proposed scheme dynamically adapts the threshold value for the neighborhood approximation space according to the characteristics of the given datasets, ensuring optimal performance without sacrificing accuracy. To evaluate the effectiveness of the proposed scheme, we develop a testbed tailored for Parkinson’s patients, a domain where hybrid data processing is particularly relevant. The experimental results demonstrate that the proposed scheme consistently outperforms existing schemes in adaptively handling both numerical and categorical data, achieving an impressive accuracy of 95% on the Parkinson’s dataset. Overall, this research contributes to advancing hybrid data processing techniques by providing a robust and adaptive solution that addresses the challenges associated with handling hybrid data, particularly in the context of Parkinson’s disease analysis.

Intelligent prediction using AI-based modeling and optimization of surface roughness in Al7049 end milling with coconut oil under minimum quantity lubrication

Intelligent prediction using AI-based modeling and optimization of surface roughness in Al7049 end milling with coconut oil under minimum quantity lubrication

Influence of surface roughness on the fluid flow in microchannel

Surface roughness is a crucial factor of fluid flow in microfluidic channels. Most of the existing studies focus on the effect of regular microstructured surfaces on fluid flow, while researchs about the impact of random rough surfaces on fluid flow remains limited. Therefore, in this study, a random rough surface model and two microstructured surface models were established, and the effects surface roughness on the fluid flow at Wenzel state and Cassie-Baxter state were studied using COMSOL multi-physics simulation software. Our findings reveal that both the flow velocity and the fluid flow rate at the microchannel outlet decreases with the surface roughness increases. Notably, the flow rate and velocity of the fluid flow at Cassie-Baxter state is higher than that of fluid flow at Wenzel state.

Effect of Surface Roughness on Aerodynamic Loads of Bluff Body in Vicinity of Smoothed Moving Wall

This paper contributes to a new Lagrangian vortex method for the statistical control of turbulence in two-dimensional flow configurations around a rough circular cylinder in ground effect when considering higher subcritical Reynolds numbers, namely 3 × 104 ≤ Re ≤ 2 × 105. A smoothed moving wall (active control technique) is used to include the blockage effect in association with the variation in cylinder surface roughness (passive control technique), characterizing a hybrid approach. In contrast with the previous approaches of our research group, the rough cylinder surface is here geometrically constructed, and a new momentum source term is introduced and calculated for the investigated problem. The methodology is structured by coupling the random Discrete Vortex Method, the Lagrangian Dynamic Roughness Model, and the Large Eddy Simulation with turbulence closure using the truncated Second-Order Velocity Structure Function model. This methodological option has the advantage of dispensing with the use of both a refined near-wall mesh and wall functions. The disadvantage of costly processing is readily solved with Open Multi-Processing. The results reveal that intermediate and high roughness values are most efficient for Reynolds numbers on the orders of 105 and 104, respectively. In employing a moving wall, the transition from the large-gap to the intermediate-gap regime is satisfactorily characterized. For the conditions studied with the hybrid technique, it was concluded that the effect of roughness is preponderant and acts to anticipate the characteristics of a lower gap-to-diameter ratio regime, especially with regard to intermittency.

Towards enhanced surface roughness modeling in machining: an analysis of data transformation techniques

Data transformation methods are utilized to convert datasets into non-integer formats, potentially altering their distribution patterns. This implies that the variance and standard deviation of the dataset may be altered after the dataset undergoes data transformation operations. Improving model accuracy is a primary application of these methods. This study compares the efficacy of three data transformation techniques: square root transformation, logarithmic transformation, and inverse transformation. The comparison is conducted within the context of developing a surface roughness model for a turning process. Eighteen experiments are performed using the Box-Behnken method, with surface roughness chosen as the response variable. The surface roughness dataset undergoes transformation using the mentioned methods. Four surface roughness regression models are then built: one without transformation, one with square root transformation, one with logarithmic transformation, and one with inverse transformation. Evaluation metrics include coefficient of determination (R-Sq), adjusted coefficient of determination (R-Sq(adj)), Mean Absolute Error (%MAE), and Mean Squared Error (%MSE). Results indicate logarithmic transformation as the most effective, followed by square root transformation, in enhancing model accuracy. The surface roughness model utilizing data transformation exhibits high R-Sq and R-Sq(adj) values, at 0.8792 and 0.7434 respectively. On the other hand, this model has %MAE and %MSE values of only 10.33 and 2.05 respectively. Conversely, inverse transformation exhibits the least effectiveness among the three methods

An improved B-L model for dynamic stall prediction of rough-surface airfoils

The Beddoes-Leishman (B-L) semi-empirical model is a classical method for predicting the dynamic stall of wind turbine airfoils. However, the model performs poorly for rough-surface airfoils due to the premature entry of turbulence and stall condition under the roughness effect. In this study, an improved dynamic stall model is developed for rough-surface airfoils. Two corrections are involved in the modifications. First, the calculation of flow separation points is corrected considering the difference between the normal and tangential separation points, and then an attenuation coefficient is introduced for the effective angle of attack to account for the rough-surface effect. Subsequently, the proposed model is extensively verified by experimental data of S-series airfoils with rough surfaces. Results show that the proposed model can well predict the dynamic stall characteristics of rough-surface airfoils with a higher accuracy than that of the original B-L model under various mean angle of attacks, oscillating amplitudes and reduced frequencies. At last, the model is utilized to predict the operating loads of a wind turbine using the Blade-Element Momentum theory. Significant difference between the dynamic loads predicted by smooth and rough models is observed. This indicates that the roughness effect on the dynamic stall model as well as the prediction of the operating loads on wind turbines cannot be ignored.

Predicting Surface Roughness in Turning Complex-Structured Workpieces Using Vibration-Signal-Based Gaussian Process Regression.

Surface roughness prediction is a pivotal aspect of the manufacturing industry, as it directly influences product quality and process optimization. This study introduces a predictive model for surface roughness in the turning of complex-structured workpieces utilizing Gaussian Process Regression (GPR) informed by vibration signals. The model captures parameters from both the time and frequency domains of the turning tool, encompassing the mean, median, standard deviation (STD), and root mean square (RMS) values. The signal is from the time to frequency domain and it is executed using Welch's method complemented by time-frequency domain analysis employing three levels of Daubechies Wavelet Packet Transform (WPT). The selected features are then utilized as inputs for the GPR model to forecast surface roughness. Empirical evidence indicates that the GPR model can accurately predict the surface roughness of turned complex-structured workpieces. This predictive strategy has the potential to improve product quality, streamline manufacturing processes, and minimize waste within the industry.

Continuous-time Markov chain approximation for pricing Asian options under rough stochastic local volatility models

We propose a general framework for pricing both discretely and continuously monitored arithmetic average Asian options whose underlying asset price satisfies the rough stochastic local volatility model. We use a semimartingale approximation approach for the rough stochastic local volatility model to obtain its Markovian representation. For each type of Asian options, we use the double-layer continuous-time Markov chain to approximate the transformed underlying asset price, and derive the double transform of the Asian option price in terms of the unique bounded solution to a related functional equation. We invert the analytical double transforms of Asian option prices under the approximate continuous-time Markov chain numerically to obtain the approximations for Asian option prices. Monte Carlo simulation demonstrates the accuracy and efficiency of the proposed method for Asian option pricing.

ANFIS prediction modeling of surface roughness and cutting force of titanium alloy ground with carbon nanotube grinding wheel

ANFIS prediction modeling of surface roughness and cutting force of titanium alloy ground with carbon nanotube grinding wheel

PEMFC sealing modeling relating to fractal characteristics of gasket-BPP interface based on micro-contact

The interface leaking of the gasket-BPP sealing structure affects the efficiency, safety, and reliability of PEMFCs. Aiming to reveal the basic cause of interface leaking and predict the leakage rate, the contact behavior at the micro-scale had been researched by FEM with the fractal multi-scale method, which could eliminate the negative influence of a single observation scale on the gasket-BPP rough interface modeling. Furthermore, in order to relate the contacting behavior at the micro-scale to the leakage rate at the macro-scale of PEMFCs, the mapping model had been established to analyze the sealing performance of the entire interface through the self-affine and self-similar characteristics of the fractal multi-scale contacting model of the gasket-BPP. Not only macroscopic properties of gasket rubber materials are considered in this model, but also microscopic morphologies are taken in to investigate the interface leakage rate, which had not been studied in traditional macroscopic research. By comparing the compression curves and interface leakage rates of the flange sealing device in testing and calculating approaches, the accuracy and reliability of the mapping model had been verified, leading to the analysis and the prediction of the PEMFC interface leakage rate rapidly.