Gaussian Weighting Function Research Articles

Phase-field formulated meshless simulation of axisymmetric Rayleigh-Taylor instability problem

A formulation of the immiscible Newtonian two-liquid system with different densities and influenced by gravity is based on the Phase-Field Method (PFM) approach. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in all the terms. The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in Cartesian and axisymmetric coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. This solution procedure has improved stability compared to Chorin's pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the authors’ previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris, Open-source Field Operation and Manipulation (OpenFOAM®) code and previously existing results.

Tool State Recognition Based on POGNN-GRU under Unbalanced Data.

Accurate recognition of tool state is important for maximizing tool life. However, the tool sensor data collected in real-life scenarios has unbalanced characteristics. Additionally, although graph neural networks (GNNs) show excellent performance in feature extraction in the spatial dimension of data, it is difficult to extract features in the temporal dimension efficiently. Therefore, we propose a tool state recognition method based on the Pruned Optimized Graph Neural Network-Gated Recurrent Unit (POGNN-GRU) under unbalanced data. Firstly, design the Improved-Majority Weighted Minority Oversampling Technique (IMWMOTE) by introducing an adaptive noise removal strategy and improving the MWMOTE to alleviate the unbalanced problem of data. Subsequently, propose a POG graph data construction method based on a multi-scale multi-metric basis and a Gaussian kernel weight function to solve the problem of one-sided description of graph data under a single metric basis. Then, construct the POGNN-GRU model to deeply mine the spatial and temporal features of the data to better identify the state of the tool. Finally, validation and ablation experiments on the PHM 2010 and HMoTP datasets show that the proposed method outperforms the other models in terms of identification, and the highest accuracy improves by 1.62% and 1.86% compared with the corresponding optimal baseline model.

Railroad Catenary Insulator Fault Detection Based on Improved Faster R-CNN

Background:: The railroad catenary insulator, which is a crucial component of the catenary system and is situated between the pillar and wrist arm, is crucial for electrical conductor isolation, electrical equipment insulation, mechanical load bearing, anti-fouling, and anti-leakage. The catenary insulators will experience tarnished flash, breakage, insulation strength deterioration, and other issues as a result of the long-term outside unfavorable working circumstances. The train electrical system's ability to operate normally is greatly hampered by these problems. Although there are many patents and articles related to insulator fault detection, the precision is not high enough. Therefore, it is crucial to improve the precision of catenary insulator fault detection. Objective:: An improved region-based convolutional neural networks (Faster R-CNN)-based fault detection method for railway catenary insulators is proposed in response to the long detection time of the conventional railroad catenary insulator fault, the low precision of the catenary insulator fault detection for occlusion and truncation, the poor performance of multi-scale object detection, and the processing of class unbalance problem. Methods:: The Faster R-CNN is optimized from four perspectives: feature extraction, feature fusion, candidate box screening, and loss function, in accordance with the properties of the catenary insulator. First, to solve the problem of multi-scale catenary insulator fault detection, convolutional block attention module (CBAM) and feature pyramid network (FPN) are used to fuse the deep feature and shallow features of the image. This results in a feature map with more critical semantic information and higher resolution. After that, the weighted non-maximum suppression (WNMS) algorithm improved by distance-intersection over union (DIOU) and Gaussian weighting function is used instead of the traditional NMS algorithm, which effectively introduces the overlap of detection frames into the confidence level and makes full use of the effective information of the detection frames. Finally, the improved Focal loss is used as the classification loss, and the focusing parameter and the balance factor of the Focal Loss are adjusted dynamically to solve the problem of sample imbalance and difficult sample identification in the model better. Results:: The effects of SSD, YOLOV3, traditional Faster R-CNN and improved Faster R-CNN models are tested on the contact network insulator fault detection dataset constructed in this paper, and the experimental results show that the improved Faster R-CNN has higher precision, recall, and mAP compared to the other detection models, which reach 94.31%, 96.68% and 95.22%, respectively. Conclusion:: The results of the experiments demonstrate that this method may successfully detect the faults in different scale catenary insulators. It can effectively detect truncated, obscured faulty catenary insulators. It has higher precision and recall and provides a reliable reference for maintaining faulty insulators in railway catenary.

Phase-field formulated meshless simulation of Rayleigh-Taylor instability problem

The interface between two immiscible Newtonian liquids with different densities and the same viscosity, influenced by gravity, is based on the Phase-Field Method (PFM) formulation. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in the inertial and buoyancy terms (non-Boussinesq formulation). The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in two-dimensional Cartesian coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. Implicit time discretisation is performed for the NS and CH equations in the momentum predictor and Phase-Field (PF) variable corrector steps of PISO, while the momentum corrector steps solve the NS equation explicitly. This solution procedure has improved stability compared to Chorin’s pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the author’s previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris.

Research on ultrasonic defect imaging based on a neural network with Gaussian weight function fusion model

Ultrasonic testing is widely used in the industrial field because of its high sensitivity, safety and low-cost, which plays an increasingly important role in detecting defects on industrial. However, at present, defect detection only stays in scanning surface defects and classifying the internal defects of the specimen. The accuracy of quantitative imaging of the morphology of the internal defects of the specimen is still an issue to be improved. In this paper, the simple defects in several specimens are detected by ultrasound based on finite element simulation software and the accuracy of the signal can be verified by ultrasonic experiment. Then, the features can be extracted by signal processing method. The neural network imagines the inversion results with the Gaussian weight function fusion model. Finally, this paper uses the signals of simple shape defects as the training set to detect the shapes of complex defects and obtain the corresponding imaging results.

Elastoplastic Analysis of Metallic Parts Employing a Meshless Method.

The use of finite element method-based approaches has been popular in studying the elastoplastic behavior of metal parts. However, there has been a growing demand for meshless methods. In response, researchers have developed a meshless solution for 2D elastoplastic evaluation of metal components. This approach obtains the locally symmetric weak form of the governing elastoplastic integral equations at each node throughout the problem area and boundary. The elastoplastic constitutive relationships consider a small deformation rate independent associative flow theory applicable to isotropic hardening materials. The proposed solution algorithm can handle loading, unloading, and reverse loading. Numerical results were computed using Gaussian and spline weight functions, and the presented meshless solution proved to be robust and accurate for conducting the elastoplastic investigation of metallic parts. Furthermore, the Gaussian weight function was found to be more robust than the spline weight function. In conclusion, this paper presents a reliable meshless solution for elastoplastic analysis and highlights the advantages of using Gaussian weight functions.

Measuring spatial availability of children for older adults with disability

BackgroundHaving an adult child living with or nearby may prevent parents with disability from moving to nursing homes and reduce the use of paid care services. Despite the profound implications for care resources and utilization among older adults, there is no measure summarizing the spatial availability of all adult children for an older adult. Our study aims to develop a holistic measure of adult children's spatial availability to assess potential family care resources for older adults with disability. MethodsData were obtained from the population-based, longitudinal study in the U.S., the Health and Retirement Study (HRS). We selected a nationally representative sample of older adults 55+ years with disability. Using multivariable two-part regression models, we developed a care-weighted child spatial availability for caregiving (CSAC) index, which summarizes the spatial dispersion of all adult children accounting for potential caregiving associated with distance. We also constructed a reference index of child spatial proximity (CSP) focusing only on spatial distance by employing Gaussian kernel weighting functions. ResultsCSAC index highlights the great importance of having an adult child in the same household (vs. nearby or far) for receiving care among older adults with disability, compared to the CSP index, showing relatively a gradual decline over the spatial distance. Both indices vary substantially by older adults’ sociodemographic attributes. ConclusionsThe holistic indices of adult child spatial availability will contribute to assessing care resources for older adults, albeit future development is needed to extend the utility of the indices tailored for specific care needs.

Hankel determinant and orthogonal polynomials for a perturbed Gaussian weight: From finite n to large n asymptotics

We study the monic polynomials Pn(x; t), orthogonal with respect to a symmetric perturbed Gaussian weight function w(x)=w(x;t)≔e−x21+tx2λ,x∈R, with t>0,λ∈R. This problem is related to single-user multiple-input multiple-output systems in information theory. It is shown that the recurrence coefficient βn(t) is related to a particular Painlevé V transcendent, and the sub-leading coefficient p(n, t) of Pn(x; t) (Pn(x; t) = xn + p(n, t)xn−2 + ⋯) satisfies the Jimbo–Miwa–Okamoto σ-form of the Painlevé V equation. Furthermore, we derive the second-order difference equations satisfied by βn(t) and p(n, t), respectively. This enables us to obtain the large n full asymptotic expansions for βn(t) and p(n, t) with the aid of Dyson’s Coulomb fluid approach in the one-cut case [i.e., λt ≤ 1 (t > 0)]. We also consider the Hankel determinant Dn(t), generated by the perturbed Gaussian weight. It is found that Φn(t), a quantity allied to the logarithmic derivative of Dn(t) via Φn(t)=2t2ddtlnDn(t)−2nλt, can be expressed in terms of βn(t) and p(n, t). Based on this result, we obtain the large n asymptotic expansion of Φn(t) and then that of the Hankel determinant Dn(t) in the one-cut case.

The Potential of the Wavelength-integrated Scattering Polarization of the Hydrogen Lyα Line for Probing the Solar Chromosphere

The intensity and the linear scattering polarization profiles of the hydrogen Lyα line encode valuable information on the thermodynamic and magnetic structure of the upper layers of the solar chromosphere. The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) sounding rocket experiment provided unprecedented spectropolarimetric data of this line, as well as two-dimensional broadband images in intensity and linear polarization. We theoretically investigate the potential of the Lyα broadband polarimetric signals for probing the solar chromosphere and its magnetic fields. We analyze the synthetic Stokes profiles obtained from a series of radiative transfer (RT) calculations out of local thermodynamic equilibrium, considering semi-empirical one-dimensional models of the solar atmosphere. The wavelength-integrated linear polarization signal is found to be dominated by the contribution from the wings when considering a Gaussian weighting function with a FWHM that corresponds to the CLASP slit-jaw broadband filter. These broadband linear polarization signals are strongly sensitive to magnetic fields of strengths on the order of 50 G, via the action of magneto-optical (MO) effects, and are expected to encode information on the middle–upper chromosphere. The two-dimensional broadband intensity and linear polarization images observed by CLASP can be suitably mimicked using synthetic wavelength-integrated signals obtained considering atmospheric models and magnetic fields that are representative of solar regions with different levels of activity, provided that the impact of MO effects is taken into account. Despite the limitations of a one-dimensional RT modeling, this work illustrates the diagnostic potential of filter-polarimetric Lyα signals for probing the solar chromosphere and its magnetism.

Video representation learning for temporal action detection using global-local attention

Video representation is of significant importance for temporal action detection. The two sub-tasks of temporal action detection, i.e., action classification and action localization, have different requirements for video representation. Specifically, action classification requires video representations to be highly discriminative, so that action features and background features are as dissimilar as possible. For action localization, it is crucial to obtain information about the action itself and the surrounding context for accurate prediction of action boundaries. However, the previous methods failed to extract the optimal representations for the two sub-tasks, whose representations for both sub-tasks are obtained in a similar way. In this paper, a Global-Local Attention (GLA) mechanism is proposed to produce a more powerful video representation for temporal action detection without introducing additional parameters. The global attention mechanism predicts each action category by integrating features in the entire video that are similar to the action while suppressing other features, thus enhancing the discriminability of video representation during the training process. The local attention mechanism uses a Gaussian weighting function to integrate each action and its surrounding contextual information, thereby enabling precise localization of the action. The effectiveness of GLA is demonstrated on THUMOS’14 and ActivityNet-1.3 with a simple one-stage action detection network, achieving state-of-the-art performance among the methods using only RGB images as input. The inference speed of the proposed model reaches 1373 FPS on a single Nvidia Titan Xp GPU. The generalizability of GLA to other detection architectures is verified using R-C3D and Decouple-SSAD, both of which achieve consistent improvements. The experimental results demonstrate that designing representations with different properties for the two sub-tasks leads to better performance for temporal action detection compared to the representations obtained in a similar way.

A novel rotated sigmoid weight function for higher performance in heterogeneous deformation measurement with digital image correlation

Conventional digital image correlation (C-DIC) combined with a rotated Gaussian weight (RGW) function for subset has demonstrated attractive ability in resolving heterogeneous deformation parameters. To further improve the performance, the selection of an optimum weight function becomes the key issue. In this paper, a novel rotated sigmoid weight (RSW) function is proposed. RSW function aims to get a more uniform weight distribution near the subset center, and to realize the continuous change of the equivalent subset size as well. The performance of the RSW function is compared with the Gaussian weight (GW) function, RGW function, the rotated inverse distance weight (RIDW) function and the inverse distance square weight (RIDSW) function through Star 5 image set from the DIC challenge 2.0 and the simulated image set. A total of six methods with different weight functions and rotated weights are systematically compared. The experiment results clearly show that DIC combined with RSW function (i.e. RSW-DIC) has the best spatial resolution without sacrificing much measurement resolution. The spatial resolution of RSW-DIC is only about half of the other methods for both first- and second-order shape functions when a big initial subset size is adopted.

A meshless solution of the compressible viscous flow in axisymmetric tubes with varying cross-sections

The meshless Diffuse Approximate Method (DAM) is for the first time formulated and applied to simulate the compressible Newtonian flow of an ideal gas in an axisymmetric tube with varying cross-sections. The problem is structured by coupled partial differential equations for conservation of mass, momentum and energy, and the equation of state closure. These equations are solved in primitive variables and strong form. DAM is formulated on irregular node arrangement by using the second and third-order polynomial shape functions and Gaussian weights, leading to weighted least squares approximation on overlapping local subdomains. Pressure-velocity coupling is performed by the Pressure Implicit with Splitting of Operators (PISO) scheme. The solution of the represented novel application of DAM is verified by matching the meshless results with the fine-mesh finite-volume method results. The characteristics of meshless DAM for this kind of problem are systematically assessed by a detailed investigation of the varying node density, shape function order, Gaussian weight's shape, and the number of nodes in a local subdomain. The sensitivity study of DAM parameters shows that for the tested problems, the most suitable values of the Gaussian weight function and the number of nodes in a local subdomain are 5.0 and 13, respectively. Third-order convergence rate with better results is observed while using third-order polynomial shape functions.

A Decision-Making Machine Learning Approach in Hermite Spectral Approximations of Partial Differential Equations

The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains are strongly affected by the amplitude of the Gaussian weight function employed to describe the approximation space. This is particularly true if the problem is under-resolved, i.e., there are no enough degrees of freedom. The issue becomes even more crucial when the equation under study is time-dependent, forcing in this way the choice of Hermite functions where the corresponding weight depends on time. In order to adapt dynamically the approximation space, it is here proposed an automatic decision-making process that relies on machine learning techniques, such as deep neural networks and support vector machines. The algorithm is numerically tested with success on a simple 1D problem, but the main goal is its exportability in the context of more serious applications. As a matter of fact we also show at the end an application in the framework of plasma physics.

Fast Registration of Terrestrial LiDAR Point Clouds Based on Gaussian-Weighting Projected Image Matching

Terrestrial point cloud registration plays an important role in 3D reconstruction, heritage restoration and topographic mapping, etc. Unfortunately, current research studies heavily rely on matching the 3D features of overlapped areas between point clouds, which is error-prone and time-consuming. To this end, we propose an automatic point cloud registration method based on Gaussian-weighting projected image matching, which can quickly and robustly register multi-station terrestrial point clouds. Firstly, the point cloud is regularized into a 2D grid, and the point density of each cell in the grid is normalized by our Gaussian-weighting function. A grayscale image is subsequently generated by shifting and scaling the x-y coordinates of the grid to the image coordinates. Secondly, the scale-invariant features (SIFT) algorithm is used to perform image matching, and a line segment endpoint verification method is proposed to filter out negative matches. Thirdly, the transformation matrix between point clouds from two adjacent stations is calculated based on reliable image matching. Finally, a global least-square optimization is conducted to align multi-station point clouds and then obtain a complete model. To test the performance of our framework, we carry out the experiment on six datasets. Compared to previous work, our method achieves the state-of-the-art performance on both efficiency and accuracy. In terms of efficiency, our method is comparable to an existing projection-based methods and 4 times faster on the indoor datasets and 10 times faster on the outdoor datasets than 4PCS-based methods. In terms of accuracy, our framework is ~2 times better than the existing projection-based method and 6 times better than 4PCS-based methods.

Research on Roundness Error Evaluation of Connecting Rod Journal in Crankshaft Journal Synchronous Measurement

The crankshaft is the core part of an automobile engine, and the accuracy requirements of various shape and position errors are very high. On the basis of a synchronous measurement system, the connecting rod journal is deeply studied, including data processing and roundness evaluation. Firstly, according to the measuring processes of connecting rod journals, the real sampling angle distribution function was established, and the corresponding Gaussian weight function of each sampling angle was calculated. The weight function and the collected data corresponding to the angle were subjected to discrete cyclic convolution operation in the spatial domain to obtain the filtered effective circular contour data. Secondly, the particle swarm optimization algorithm was improved, and its inertia weight was set to decrease nonlinearly to speed up the convergence. A calculation process suitable for the evaluation of journal errors was designed. Then, the improved particle swarm optimization algorithm was used to evaluate the roundness of the corrected rod journal contour data. At last, through multiple measurement experiments, the feasibility and effectiveness of the synchronous measurement scheme and data processing method proposed in this paper are verified.

Parameterization of Outer-scale on DECam Point-spread Function

Abstract A method to better parameterize the Outer-Scale (L 0) of the Point-Spread Function (PSF) in Dark Energy Camera is described. The PSF characterizes the atmospheric turbulence and diffraction in astronomical images. In particular, the Outer-Scale describes the maximum coherence length in the turbulent atmosphere and leads to a maximum value of the turbulence structure function. We model the PSF by computing a pattern of star features, which are used to fit our PSF model. For each star, we apply a weight function which maximizes the signal-to-noise ratio. We find difficulty in parameterizing L 0, thus, we propose to change the current Gaussian weight function to the von Kaŕmań weight function which extends to larger radii. We find that by changing to the von Kaŕmań, we double our total sensitivity but lose 1st order sensitivity to L 0. Therefore, ulterior methods need to be explored to parameterize L 0.

Development and verification of meshless diffuse approximate method for simulation of compressible flow between parallel plates

A meshless numerical model is developed to simulate single-phase, Newtonian, compressible flow in the Cartesian coordinate system. The coupled set of partial differential equations, i.e., mass conservation, momentum conservation, energy conservation, and equation of state is solved by using Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO) pressure correction algorithm on an irregular node arrangement. DAM is structured by using the second-order polynomial basis functions and the Gaussian weight function, leading to the weighted least squares approximation on overlapping sub-domains. Implicit time discretization is performed for the predictor step of PISO, while in the corrector steps the equations are discretized explicitly. The numerical model is validated for flow between parallel plates with helium obeying ideal gas law. The solver’s accuracy is assessed by investigating the shape of the Gaussian weight and the number of the nodes in the local subdomains. The calculated velocity, temperature and pressure fields are compared with the Finite Volume Method (FVM) results obtained by OpenFOAM software and show a reasonably good agreement.

Nonlocal plastic softening algorithm and numerical investigation based on the Drucker–Prager criterion

Strain softening in geotechnical materials often leads to the ill condition of boundary value problems. That is, the regional governing equations or partial differential equations are no longer applicable under the original fixed solution conditions, and the over non-localization theory is used to solve the finite element equations to ensure the possibilities of the governing equations. Based on the Drucker–Prager (D–P) criterion, a nonlocal elastoplastic constitutive model and its numerical algorithm for geomaterials are established while considering the softening plasticity. Strain localization leads to high strain gradients and severe deformations in the zone. The introduction of characteristic lengths establishes the relationship between microstructure and macroscopic deformation. Accordingly, the surroundings will affect a certain point of a damaged rock material. When a Gaussian weight function is introduced, and the characterization is concerned on the damage point, the influence gradually decreases, and the characteristic length controls the influence range as the distance increases. When using the closest point projection method to calculate the stress regression of the D–P criterion, the plastic multiplier is weighted and averaged by the Gaussian weight function, and the local plastic multiplier is converted into a nonlocal plastic multiplier for numerical analysis. The results show that with the introduction of the weight function and the feature length, the localized zone width no longer depends on the grid size, that is, the grid sensitivity is overcome, and the result is more in line with the physical nature.

Application of Intelligent Fuzzy Decision Tree Algorithm in English Teaching Model Improvement

As the number of students in universities continues to grow, the university academic management system has a large amount of data on student performance. However, the utilization of these data is only limited to simple query and statistical work, and there is no precedent of using these data for improving English teaching mode. With the application of fuzzy theory in machine learning and artificial intelligence, the fuzzy decision tree algorithm was born by integrating fuzzy set theory with decision tree algorithm. In this paper, we propose a way to obtain the centroids of continuous attribute clustering by K-means algorithm and combine the triangular fuzzy number to fuzzy the continuous data. In addition, this paper analyzes the influence of nearest neighbor distance on classification, introduces Gaussian weight function, gives different voting weights to the neighborhood according to the distance, and establishes a weighted K-nearest neighbor classification algorithm. To address the problem of low classification efficiency of K-nearest neighbor algorithm when the dataset is large, this paper further improves the algorithm and establishes the partitioned weighted K-nearest neighbor algorithm. The classification time was shortened from 11.39 seconds to 5.22 seconds, and the classification efficiency greatly improved.

Meshless simulation of a lid-driven cavity problem with a non-Newtonian fluid

The purpose of the present paper is to solve the lid-driven cavity problem for a non-Newtonian power-law shear thinning and shear thickening fluid by a meshless method. Results are presented for Re=100 and Re=1000, where different levels of shear thinning and thickening are considered. Furthermore, the lid-driven cavity case is made geometrically more complex by adding several circular-shaped obstacles in the geometry. The Navier-Stokes equations are solved with the local meshless diffuse approximate method. The weighted least squares approximation is structured by using the second-order polynomial basis vector and the Gaussian weight function. The explicit Euler scheme is used to perform the artificial time stepping. The non-incremental pressure correction scheme is used to couple the pressure and the velocity fields. Results are presented in terms of viscosity contours, stream function, velocity vectors, mid-plane velocity and viscosity profiles for the steady state. The numerical method is verified by a comparison with the results obtained from the literature, which are computed with the least squares finite element formulation. Furthermore, an investigation of the node density and node distribution type is performed. A near perfect match with the reference solution and between the structured and unstructured node distribution is found.