Reinitialization Scheme Research Articles

Multi-objective topology optimization of heat transfer surface using level-set method and adaptive mesh refinement in OpenFOAM

The present study proposes a new efficient and robust algorithm for multi-objectives topology optimization of heat transfer surfaces to achieve heat transfer enhancement with a less pressure drop penalty based on a continuous adjoint approach. It is achieved with a customized OpenFOAM solver, which is based on a volume penalization method for solving a steady and laminar flow around iso-thermal solid objects with arbitrary geometries. The fluid-solid interface is captured by a level-set function combined with a newly proposed robust reinitialization scheme ensuring that the interface diffusion is always kept within a single local grid spacing. Adaptive mesh refinement is applied in near-wall regions automatically detected by the level-set function to keep high resolution locally, thereby reduces the overall computational cost for the forward and adjoint analyses. The developed solver is first validated in a drag reduction problem of a flow around a two-dimensional cylinder at the Reynolds numbers of 10 and 40 by comparing reference data. Then, the proposed scheme is extended to heat transfer problems in a two-dimensional flow at the Prandtl number of 0.7 and 6.9. Finally, three-dimensional topology optimization for multi-objective problems is considered for cost functionals with different weights for the total drag and heat transfer. Among various solutions obtained on the Pareto front, 4.0% of heat transfer enhancement with 12.6% drag reduction is achieved at the Reynolds number of 10 and the Prandtl number of 6.9. Moreover, the optimization of a staggered pin-fin array demonstrates that the optimal shapes and arrangement of the fins strongly depend on the number of rows from the inlet. Specifically, the pin-fins in the first and third rows extended in the upstream direction further enhance heat transfer, while the fins in the second row vanish to reduce pressure loss.

Generalized and efficient wall boundary condition treatment in GPU-accelerated smoothed particle hydrodynamics

This paper presents a generalized and efficient wall boundary treatment in the smoothed particle hydrodynamics (SPH) method for 3-D complex and arbitrary geometries with single- and multi-phase flows to be executed on graphics processing units (GPUs). Using a force balance between the wall and fluid particles with a novel penalty method, a pressure boundary condition is applied on the wall dummy particles which effectively prevents non-physical particle penetration into the wall also in highly violent impacts and multi-phase flows with high density ratios. A new density reinitialization scheme is also presented to enhance the accuracy and robustness. The proposed method is simple in comparison with previous wall boundary formulations on GPUs and enforces no additional memory caching and thus is well suited for massively parallel architecture of GPUs. The method is validated in various test cases involving inviscid violent single- and multi-phase flows, demonstrating very good robustness, accuracy and performance. The new wall boundary treatment is able to improve the high accuracy of its previous version by Adami et al. [1] also in 3-D and multi-phase problems, while it is efficiently executable on GPUs. Therefore, the method can be a reliable solution for the long-lasting wall boundary condition challenge in SPH for a broad range of problems.

An Effective Cooperative Co-Evolutionary Algorithm for Distributed Flowshop Group Scheduling Problems.

This article addresses a novel scheduling problem, a distributed flowshop group scheduling problem, which has important applications in modern manufacturing systems. The problem considers how to arrange a variety of jobs subject to group constraints at a number of identical manufacturing cellulars, each one with a flowshop structure, with the objective of minimizing makespan. We explore the problem-specific knowledge and present a mixed-integer linear programming model, a counterintuitive paradox, and two suites of accelerations to save computational efforts. Due to the complexity of the problem, we consider a decomposition strategy and propose a cooperative co-evolutionary algorithm (CCEA) with a novel collaboration model and a reinitialization scheme. A comprehensive and thorough computational and statistical campaign is carried out. The results show that the proposed collaboration model and reinitialization scheme are very effective. The proposed CCEA outperforms a number of metaheuristics adapted from closely related scheduling problems in the literature by a significantly considerable margin.

Finite Difference and Reinitialization Methods with Level Set to Interfacial Area Transport Equations for Gas–Liquid Two-Phase Flows

For the direct simulation of liquid atomization processes affected by surface tension, the level-set method was suitable, owing to the ease of estimating normal vectors and interface curvatures. However, the mass is not conserved in the original method because of errors in the interfacial advection evaluation. Therefore, previous studies have developed the interfacial advection equation and the interfacial evaluation method for reinitialization. The reinitialization method can be organized in terms of control parameters. Therefore, we modified and optimized the control parameters of the high-order constrained reinitialization scheme developed previously. Furthermore, the difference method in the convection term was adapted to the interfacial advection equation to evaluate the best method for simulating the droplet atomization process. Consequently, the fifth-order accuracy weighted essentially non-oscillatory scheme was observed to provide the best mass conservation for both the reinitialization and the advection equations.

Nonisometric Surface Registration via Conformal Laplace–Beltrami Basis Pursuit

Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are nearly isometric. However, it is much more challenging to compute correspondence between surfaces which are intrinsically less similar. In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations. This method enables us to compute geometrically meaningful point-to-point maps between non-isometric shapes. Our model is based on a novel basis pursuit scheme whereby we simultaneously compute a conformal deformation of a ’target shape’ and its deformed LB eigensystem. We solve the model using a proximal alternating minimization algorithm hybridized with the augmented Lagrangian method which produces accurate correspondences given only a few landmark points. We also propose a re-initialization scheme to overcome some of the difficulties caused by the non-convexity of the variational problem. Intensive numerical experiments illustrate the effectiveness and robustness of the proposed method to handle non-isometric surfaces with large deformation with respect to both noises on the underlying manifolds and errors within the given landmarks or feature functions.

An isogeometrical level set topology optimization for plate structures

This study presents topology optimization of plate structures by employing isogeometrical level set method. For structural analysis of plates, the IsoGeometric Analysis (IGA) approach is applied and Non-Uniform Rational B-Splines (NURBS) basis functions are used for approximation of the design domain geometry as well as the unknown deformation field. In this paper, the level set function is parametrized with Radial Basis Functions (RBFs), which is more efficient than the conventional level set method. This approach along with an approximate re-initialization scheme can maintain a smooth level set function during the optimization process and has less dependency on initial designs because of its ability to nucleate new holes inside the design domain. Due to capability of IGA method in modeling complex design domains while maintaining high accuracy in analysis, combination of IGA with RBFs level set method provides a very useful and effective technique for topology optimization problems. Several numerical examples are prepared to demonstrate the efficiency and accuracy of the method and obtained optimum topologies are compared with the results of other methods in literature.

A gene selection algorithm using simplified swarm optimization with multi-filter ensemble technique

Gene expression data has been successfully applied to various purposes, especially for cancer classification. The challenges confronted by the development of effective classifiers for expression data are the curse of dimensionality and over-fitting. Gene selection is an efficient and effective method for overcoming the above difficulties and enhancing the predictive accuracy of a classifier. This work presents a hybrid gene selection method based on a novel multi-filter ensemble technique and simplified swarm optimization (SSO). This proposed method was comprised of two phases. In the first phase, the ensemble technique was developed via VIKOR to integrate the outcomes of multiple filters to preselect the most informative gene subset from the original dataset. In the second phase, SSO was tailored with a new gene pruning strategy, re-initialization scheme, and support vector machine as a wrapper to further search the optimal gene subset on the space of the candidate genes selected in the first phase. As evidence of the performance of the proposed method, extensive experiments on nineteen microarray datasets were carried out. The computational results compared favorably with well-known methods in the literature. Statistical analysis indicated that the proposed method was highly competitive and could be an effective tool for microarray analysis.

A new detailed long-term hydrometeorological dataset: first results of extreme characteristics estimations for the Russian Arctic seas

A detailed long-term hydrometeorological dataset for Russian Arctic seas has been created using hydrodynamic modelling via a regional nonhydrostatic atmospheric model, COSMO-CLM, for 1980-2016. This paper presents evaluation techniques of long-term experiments and a preliminary analysis of the dataset. The experiments are conducted for a model domain including the Barents, Kara, and Laptev Seas, with a 12 km grid. Many test experiments have been evaluated to determine the best model configuration, which includes a new model version 5.06, a “spectral nudging” technique, and an ERA-Interim reanalysis as forcing data. A reinitialization scheme of additional “assimilation” of soil properties reanalysis data is suggested to avoid possible errors, particularly due to soil draining in the model. The primary assessment has shown that a wind speed climatology based on COSMO-CLM experiments is very close to the ERA-Interim pattern, besides many details of wind speed distributions in different Arctic regions. At the same time, the high wind speed frequencies based on the COSMO-CLM data are increased compared to the ERA-Interim, especially over the Barents Sea, the Arctic islands (Novaya Zemlya), and some seacoasts and mainland areas. Regional details are manifested in a wind speed increase up to 0.5 – 1 m/s and marked well for large lakes, orography, as well as over the polar region. At the same time, there is a mesoscale wind speed decrease compared to the ERA-Interim data for the Pechora and Laptev Sea coasts and the New Siberian islands. Comparison of two periods (1980 – 1990 and 2010 – 2016) has shown that the spatial distributions of high wind speed frequencies are very similar, but there are some detailed differences. The wind speed frequencies above 17.2 and 20.8 m/s decreased in the last decade over Novaya Zemlya, southwest of Svalbard, Northern Atlantic, and the middle Siberia continent; at the same time, it increased between Franz Josef Land and Severnaya Zemlya and in the polar regions. The preliminary assessment of the results has revealed that the dataset is promising for analysis of regional wind speed regimes and estimation of severe wind speed risks. The next step of this work is to run simulations on a 3-km grid and collaborate with the scientific community to sufficiently use this dataset.

High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic anchoring formulation ensures that the location of the actual interface is preserved, leading to better mass conservation property. It also provides high order accurate algebraic constraint for solving the Eikonal equation on a finite difference grid. Geometric properties of the interface such as surface normal and curvature are subsequently computed from the reinitialized distance function. Various analytical functions for modeling distortion in level set field are considered and accuracy of reinitialization is evaluated using first and second order anchoring schemes. It is also shown that accurate computation of interface curvature requires a high order anchor in addition to a high order fast sweeping method. Mass conservation property of reinitialization is also analyzed by considering test problems from literature including the classic Rider–Kothe single vortex problem. The formulation is suitable for efficient parallelization for both distributed memory and on-node shared memory parallel systems. Scalability and performance of the reinitialization scheme on multiple architectures are demonstrated.

A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids

We developed a novel conservative model for simulating incompressible multiphase flows on collocated unstructured grids. In conventional schemes, the divergence-free condition is enforced by the numerical approximations based on the least-square approach which inherently cannot guarantee its conservative property for volume integrated average (VIA) of velocity. In this study, point values (PVs) at cell vertices are defined in addition to its VIAs for the pressure variable and a novel discretized formulation is devised for the pressure Poisson equation so as to enforce the VIA of velocity to satisfy the divergence-free condition. Considering the large density ratios in the vicinity of fluid interface, we have also put forward a non-oscillatory and less dissipative reconstruction scheme to improve the resolvability of discontinuous solutions. For the surface-tension dominated flow problems, a novel reinitialization scheme is proposed to transform the abruptly-varying volume fractions into a smooth-varying level-set function which significantly improves the solution accuracy of curvature estimation so as to suppress the spurious currents in presence of the unphysical oscillation. The resulting multiphase model that combines above numerical methods and techniques, therefore adequately assures divergence-free condition to preserve mass conservation, effectively controls the numerical oscillations and dissipations in the vicinity of moving interface and accurately resolves surface tension force with substantially suppressed spurious currents. Various numerical examples have been presented which demonstrate the excellent performance of the newly developed model to predict both fluid dynamics and interfacial deformations with high-fidelity.

A consistent and balanced-force model for incompressible multiphase flows on polyhedral unstructured grids

This paper presents a consistent and balanced-force model with level-set and volume-of-fluid function (CBLSVOF) to simulate incompressible multiphase flows. The model is constructed by combining FVMS3 (Finite Volume method based on Merged Stencil with 3rd-order reconstruction) and THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature) scheme which are newly developed on polyhedral unstructured grids. The key principles of this model are characterized by the consistent treatment of mass and momentum transport equation and balanced-force formulation based on LS and VOF methods. The former is realized by approximating the convective fluxes of volume fraction and momentum with identical discrete schemes while the latter is achieved by discretizing the surface tension and gravity forces in the same formulation as the pressure gradient. In addition, a novel algebraic re-initialization scheme is proposed to construct the smooth-varying LS function for curvature estimation which significantly improves the surface tension. The resulting model integrates the advantages of rigorous mass conservation of VOF scheme and of accurate curvature estimation of LS method without loss of simplicity. As verified by numerous benchmark tests, the present model demonstrates remarkable capability to handle large topological changes of interface and high density ratios in complex geometries which is of great importance for practical applications.

Fully-automated tongue detection in ultrasound images

Tracking the tongue in ultrasound images provides information about its shape and kinematics during speech. Current methods for detecting/tracking the tongue require manual initialization or training using large amounts of labeled images. In this article, we propose a solution to convert a semi-automatic tongue contour tracking system to a fully-automatic one. This work introduces a new method for extracting tongue contours in ultrasound images that requires no training nor manual intervention. The method consists in an image enhancement step based on phase symmetry, followed by skeletonization and clustering steps, leading to a set of candidate points that can be used to fit an active contour to the image and subsequently initialize a tracking algorithm. Two novel quality measures were also developed that predict the reliability of the segmentation result so that an image with a reliable contour can be chosen to confidently initialize fully automated tongue tracking. This is achieved by automatically generating and choosing a set of points that can replace the manually segmented points for a semi-automated tracking approach. This paper also improves the accuracy of tracking by incorporating two criteria to reset the tracking algorithm from time to time. Experiments show that fully automated and semi-automated methods result in very similar mean sum of distances errors, respectively, indicating that the proposed automatic initialization does not significantly alter accuracy. Moreover, further results show that tracking accuracy is improved when using the new segmentation technique within the proposed re-initialization scheme.

A regularization scheme for explicit level-set XFEM topology optimization

Regularization of the level-set (LS) field is a critical part of LS-based topology optimization (TO) approaches. Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme. This approach, however, may limit the maximum step size and introduces discontinuities in the design process. Alternatively, energy functionals and intermediate LS value penalizations have been proposed. This paper introduces a novel LS regularization approach based on a signed distance field (SDF) which is applicable to explicit LS-based TO. The SDF is obtained using the heat method (HM) and is reconstructed for every design in the optimization process. The governing equations of the HM, as well as the ones describing the physical response of the system of interest, are discretized by the extended finite element method (XFEM). Numerical examples for problems modeled by linear elasticity, nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.

Design of shell-infill structures by a multiscale level set topology optimization method

Shell-infill structures are widely used in additive manufacturing (AM) to retain the external appearance and reduce the printing costs. However, shell-infill structures are generally designed by a mono-scale topology optimization method. In this case, these shell-infill structures are not optimal designs due to their incompatible shell and infill layouts. In order to obtain the optimized shell and infill simultaneously, this paper presents a multiscale level set topology optimization method for designing shell-infill structures. In macroscale optimization, two distinct level sets of a single level set function (LSF) are used to represent the interface of the shell and the infill, respectively. The thickness of the shell is assumed to be uniform, which is guaranteed by a level set reinitialization scheme. In microscale optimization, the pattern of the microstructure is optimized to achieve the optimal macro structural performance. The numerical homogenization method is applied to evaluate the effective elasticity matrix of the microstructural infill. The shell-coated macro structure and the micro infill are optimized concurrently to achieve the optimal shell-infill design with prescribed volume fractions. Both 2D and 3D examples are investigated to demonstrate the effectiveness of the presented method.

Fully-automated tongue detection in ultrasound images

Tracking the tongue in ultrasound images provides information about its shape and kinematics during speech. Current methods for detecting/tracking the tongue require manual initialization or training using large amounts of labeled images. In this article, we propose a solution to convert a semi-automatic tongue contour tracking system to a fully-automatic one. This work introduces a new method for extracting tongue contours in ultrasound images that requires no training nor manual intervention. The method consists in an image enhancement step based on phase symmetry, followed by skeletonization and clustering steps, leading to a set of candidate points that can be used to fit an active contour to the image and subsequently initialize a tracking algorithm. Two novel quality measures were also developed that predict the reliability of the segmentation result so that an image with a reliable contour can be chosen to confidently initialize fully automated tongue tracking. This is achieved by automatically generating and choosing a set of points that can replace the manually segmented points for a semi-automated tracking approach. This paper also improves the accuracy of tracking by incorporating two criteria to reset the tracking algorithm from time to time. Experiments show that fully automated and semi-automated methods result in very similar mean sum of distances errors, respectively, indicating that the proposed automatic initialization does not significantly alter accuracy. Moreover, further results show that tracking accuracy is improved when using the new segmentation technique within the proposed re-initialization scheme.

An advection velocity correction scheme for interface tracking using the level-set method

We present an advection velocity correction (AVC) scheme for interface tracking using the level-set method in this paper. The key idea is to apply a correction to the interface advection velocity at points adjacent to the zero level-set, so as to enforce the preservation of the signed distance function property at these points. As such, the AVC scheme eliminates the need for explicit sub-cell fix approaches as reinitialization at points adjacent to the zero level-set is not needed. This approach of correcting the advection velocity field near the interface and computing the signed distance function; SDF to a high order of accuracy near the interface, rather than applying an explicit sub-cell fix during the reinitialization step represents the key novel aspect of the AVC scheme. We present results from using the AVC scheme along with advection and reinitialization schemes using upwind finite differencing on uniform meshes in this paper. These results are determined for four canonical test problems: slotted disk rotation, deforming sphere, interacting circles and vortex in a box. We compare these results with corresponding results determined using a recently proposed explicit sub-cell fix based reinitialization scheme (CR2). These comparisons show that the AVC scheme yields significantly improved conservation of enclosed volume/area within the interface. Note, the present AVC scheme achieves this by only modifying velocity field values at mesh points. Therefore, the AVC algorithm can in principle be used within the framework of nearly any numerical scheme used to compute interface evolution using the level-set method, even on non-uniform and unstructured meshes, in order to achieve improvements in solution quality.

An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions

This paper presents a compact and efficient 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (RBFs), which is applied to minimize the compliance of a two-dimensional linear elastic structure. This parameterized level set method using radial basis functions can maintain a relatively smooth level set function with an approximate re-initialization scheme during the optimization process. It also has less dependency on initial designs due to its capability in nucleation of new holes inside the material domain. The MATLAB code and simple modifications are explained in detail with numerical examples. The 88-line code included in the appendix is intended for educational purposes.

Global-best brain storm optimization algorithm

Abstract Brain storm optimization (BSO) is a population-based metaheuristic algorithm that was recently developed to mimic the brainstorming process in humans. It has been successfully applied to many real-world engineering applications involving non-linear continuous optimization. In this work, we propose improving the performance of BSO by introducing a global-best version combined with per-variable updates and fitness-based grouping. In addition, the proposed algorithm incorporates a re-initialization scheme that is triggered by the current state of the population. The introduced Global-best BSO (GBSO) is compared against other BSO variants on a wide range of benchmark functions. Comparisons are based on final solutions and convergence characteristics. In addition, GBSO is compared against global-best versions of other meta-heuristics on recent benchmark libraries. Results prove that the proposed GBSO outperform previous BSO variants on a wide range of classical functions and different problem sizes. Moreover, GBSO outperforms other global-best meta-heuristic algorithms on the well-known CEC05 and CEC14 benchmarks.

Parametric structural shape & topology optimization with a variational distance-regularized level set method

The signed distance function (SDF) gives the shortest distance from a given point to the boundary, and the sign indicates whether this point is inside or outside the closed boundary or enclosed region. The SDF property is highly preferred in classical level set methods to maintain the numerical stability during the topology optimization process and provide a metric for the distance-based interpolation of different material properties. In conventional level set methods, a common way of achieving a level set function with the signed distance property is to periodically implement the so-called reinitialization scheme by solving an additional Hamilton–Jacobi partial differential equation. However, such reinitialization scheme is implemented outside the optimization loop with the optimization process suspended, which may shift the optimization result and bring convergence issues. In this paper, a double-well potential functional is employed for distance regularization inside the topology optimization loop, which can enforce the signed distance property of the level set function in a narrow band along the design boundaries while keeping the level set function flat in the rest area of the computational domain. The radial basis function (RBF) based parameterization technique is combined with mathematical programming to improve the performance of the proposed distance-regularized topology optimization method in handling problems with non-convex objective functions and multiple constraints. The flatness of the level set function in the material region also enables easy creation of new holes to the design in the topology optimization process. Both 2D and 3D benchmark examples are employed to demonstrate the validity of the proposed method.

Temporal weighted learning model for background estimation with an automatic re-initialization stage and adaptive parameters update

Abstarct Background initialization and background update are two important stages considered in the design of most background modeling algorithms. Commonly, these algorithms implement strategies in which their parameters have a very high adaptability in the background initialization stage in order to learn all the variations of the background. Contrary, in the background update phase, these parameters adapt slowly, in most cases with an exponential decay. This paper presents the BE-AAPSA method which automatically determines if the background initialization and the background update need to be re–initialized. Re -initialization is triggered if the video scene presents high variations, allowing the background to be defined more accurately. BE-AAPSA is based on a previously developed system, where two adaptive background models based on weight arrays with temporal learning mechanism identify dynamic objects within a video scene. The system implements four independent modules to treat the different factors that affect a correct definition of the dynamic object. In BE-AAPSA, the objective is to create a robust background estimation model where the learning rates for each pixel are calculated according to the results of the two adaptive weight arrays and the module where the video is classified. This approach allows handling different strategies to update learning rates at a pixel resolution. BE-AAPSA is validated with the SBI and SBMnet video databases and with a video created by concatenating scenes of the video categories presented in the CDnet 2014 database. According to the findings, BE-AAPSA produced highly accurate results with SBI and SBMnet and surpassed state-of-the-art methods with the CDnet video. These results demonstrate the importance of using an automatic re-initialization scheme in the background initialization and background update stages when the video scene presents a major change or involves jittering. Furthermore, it shows the benefits of handling in separate modules the analysis of the background estimation results.