Explicit Filtering Research Articles

Coupling Fully Staggered Grids via Numerical Filtering for Wave Propagation Simulation

The fully staggered grid (FSG) combines multiple standard staggered grids (SSGs) to simulate seismic wave propagation in anisotropic elastic media. However, its accuracy is contingent upon the wavefield’s consistency and continuity across multiple sets of SSGs. In isotropic or weakly anisotropic media, decoupling or weak coupling between the SSGs can lead to wavefield discontinuities at adjacent grid points in the diagonal direction. Issues such as inconsistent source activation, medium parameter discontinuities, and different numerical treatments of boundary conditions over multiple sets of SSGs can exacerbate these problems. While previous methods, such as FD-consistent point source technique and equivalent medium parameterization methods, have partially addressed these issues, they do not completely solve the problem. This study, drawing inspiration from numerical damping techniques used in collocated-grid finite-difference schemes to eliminate odd-even oscillations, introduces an explicit filter operator along the diagonal direction of the FSG. This approach ensures wavefield consistency and continuity across multiple SSGs, improving the accuracy of the FSG scheme. Although this method increases computational costs, it is essential for reliable seismic modeling in anisotropic media.

Modal analysis of turbulent flows simulated with spectral element method

Leveraging the high-order nature of spectral element methods, this work introduces a methodology that enables instantaneous, local analysis of turbulent flows through a transformation to a modal space. It also introduces a dynamic explicit modal filter (DEMF) for removing the excess energy in large-eddy simulation of turbulent flows. The transformation is achieved through the application of the discrete Chebyshev transform to nodal solution values, and the resulting modes are employed to characterize and distinguish different turbulent flow properties. Implementing direct numerical simulation (DNS), a qualitative explanation of how modes can assess flow directionality and turbulence properties is provided by considering the modal representation at different locations for different turbulent flows. Additionally, reducing the resolution from DNS, it is shown how modes can qualitatively assess local flow resolvedness. A quantitative assessment of local flow resolvedness is conducted by calculating sequential energy levels from the modes and then comparing them between DNS and under-resolved cases. These energy levels correspond to different scales of motion and their behavior changes as turbulence intensifies and decays. It is observed that flow under-resolvedness manifests itself in the increased magnitudes of higher energy levels corresponding to small scales of motion. Finally, the new DEMF is discussed, which is triggered locally by comparing the local Kolmogorov length scale and the average grid spacing. The filter removes the excess energy in the detected under-resolved regions by selectively removing the energy of the modes that contribute to higher energy levels.

Novel mixed approximate deconvolution subgrid-scale models for large-eddy simulation

Approximate deconvolution (AD) has emerged as a promising closure for large-eddy simulation in complex multi-physics flows, where the conventional pure dynamic eddy-viscosity (DEV) models experience issues. In this research, we propose novel improved mixed hard-deconvolution or secondary-regularization models and compare their performance with the existing standard mixed AD-DEV and penalty-term regularizations. For this aim, five consistency criteria, based on the properties of the modeled sub-filter-scale stress in limiting conditions, are introduced for the first time. It is proved that the conventional hard-deconvolution models do not adhere to a couple of important primary criteria. Furthermore, through a priori and a posteriori analyses of Burgers turbulence and turbulent channel flow, it is manifested that the inconsistency with the primary criteria can result in larger modeling errors, the over-prediction and pileup of kinetic energy in eddies of a length scale between the explicit filter width and grid size, and even the solution instability. On the other hand, the favorable characteristics of the new mixed models, in terms of the consistency criteria, significantly improve the accuracy of the predictions, the solution stability, and even the computational cost, particularly for one of the new models called mixed alternative-DEV (A-DEV).

TRAM: A new non‐hydrostatic fully compressible numerical model suited for all kinds of regional atmospheric predictions

AbstractA new limited‐area numerical model (TRAM, for Triangle‐based Regional Atmospheric Model) has been built using a non‐hydrostatic and fully compressible version of the Navier–Stokes equations. Advection terms are solved using a Reconstruct–Evolve–Average (REA) strategy over the computational cells. These cells consist of equilateral triangles in the horizontal. The classical z‐coordinate is used in the vertical, allowing arbitrary stretching (e.g., higher resolution in the Planetary Boundary Layer, PBL). Proper treatment of terrain slopes in the bottom boundary conditions allows for accurately representing the orographic forcing. To gain computational efficiency, time splitting is used to integrate fast and slow terms separately and acoustic modes in the vertical are solved implicitly. For real cases on the globe, the Lambert map projection is applied, and all Coriolis and curvature terms are retained. No explicit filters are needed. The first part of the manuscript describes the dynamical core of the model and provides its thorough validation using a variety of benchmark tests (mostly in two dimensions) in the context of a dry‐adiabatic atmosphere. In the second part, TRAM is reformulated for a moist atmosphere and is completed with a proper set of physical parametrizations of cloud microphysics, cumulus convection, short and long‐wave radiation, PBL processes and surface fluxes. Various examples of the great versatility offered by this full version will be presented, with special emphasis on Mediterranean case studies. In summary, TRAM performs as well as state‐of‐the‐art numerical models and is suitable for simulating circulations ranging from small‐scale thermal bubbles (≈100 m scale) to synoptic‐scale baroclinic cyclones (>1000 km size), including orographic circulations, thermally driven flows, squall lines, supercells, all kinds of precipitation systems and medicanes. Besides opening a myriad of academic and research applications, TRAM regional forecasts at different resolutions are being disseminated in the web (see https://meteo.uib.es/tram).

Non-intrusive Speech Intelligibility Prediction Method for Reverberant Speech Using Neural Network-Based Frequency Segmentation and Masking Front-end

In conventional non-intrusive speech intelligibility estimation, reverberation is extracted from the time-frequency representation of the input by explicit filter bank processing or spectral masking. However, these filter banks and masking processes are not always optimal. We replaced these processes with convolutional neural networks using rectangular kernels restricted to the frequency direction and masking such as a self-attention mechanism. We believe that this will enable feature extraction that is optimal for intelligibility estimation and will enable its estimation with high accuracy that generalizes well to input under various conditions. We further applied this front-end CNN to a previously proposed prediction model using speech enhancement. As a result, the estimation accuracy was improved compared to conventional front-ends using fixed filter banks, and this prediction showed a correlation coefficient with the subjective evaluation of 0.84 compared to 0.80 with the fixed filter bank.

Yawing stability and manipulative approach design for maglev car based on active disturbance rejection control

AbstractIn the present work, to realize the stable static suspension of a new type of electrodynamic wheel (EDW) magnetic levitation (maglev) car without track constraints on the conductor plate. Design and analysis of the active disturbance rejection control and explicit complementary filter (ADRC‐ECF) have been presented to solve the maglev car's yaw angle disturbance rejection under low lateral damping characteristics. Simple and efficient ECF helps to filter the high and low frequency noise generated by EDWs when rotating at high speed, to obtain accurate data in real‐time. Design and build the hardware control system for maglev car, and conduct experimental comparisons with PID controller to verify the effectiveness of suppressing yaw angle disturbances. Based on simulation and experimental results, it is shown that both PID and ADRC‐ECF can improve the stable yaw angle convergence of maglev car under external disturbances. However, ADRC performs better in resisting disturbances than PID and can achieve more accurate fixed angle steering. This paper is the first attempt to control maglev car on a trackless conductor plate for precise steering and anti‐disturbance, which is anticipated to have some reference significance in this field.

Grid resolution requirement of chemical explosive mode analysis for large eddy simulations of premixed turbulent combustion

The grid resolution requirement for trustworthy Chemical Explosive Mode Analysis (CEMA) in Large Eddy Simulation (LES) of premixed turbulent combustion is proposed. Explicit filtering, to emulate the effect of the LES filter, is applied to one-dimensional laminar flame and three-dimensional planar turbulent flames across a wide range of Karlovitz numbers . The identification of the flame front by CEMA is found relatively insensitive to the cell size (Δ), while the combustion mode identification shows more significant sensitivity. Specifically, increasing Δ falsely enhances the auto-ignition and local extinction modes and suppresses the diffusion-assisted mode. Limited dependence of the CEMA performance on the turbulent combustion regime (Karlovitz number) is observed. A simple grid size criterion for reliable CEMA mode identification in LES is proposed as ; The criterion can be relaxed to in the laminar flame limit. Furthermore, theoretical analysis is conducted on an idealised chemistry-diffusion system. The effects of the filtering process and turbulence on the local combustion mode are demonstrated, which is consistent with the numerical observations. By incorporating turbulent combustion models in CEMA, potential improvement in identifying local combustion modes can be expected.

Tensor product decomposed multi‐material isogeometric topology optimization with explicit NURBS element stiffness computation

AbstractBased on the explicit stiffness computation formula of NURBS (non‐uniform rational B‐splines) element and tensor product decomposed explicit filter, a novel multi‐material isogeometric topology optimization (MMITO) method is put forward to generate multi‐material structures efficiently. The explicit NURBS element stiffness computation formula is: derived from the Bėzier extraction operator under the combination of scaled and rotational geometric transformations between NURBS elements, and the stiffness matrices of NURBS elements can be computed by the stiffness matrix of a Bėzier element without resorting to the time‐consuming integral procedure. As the presented MMITO is a nested optimization framework, we apply the explicit filtering technique to update the multi‐phase design variables efficiently in combination with the tensor product decomposition method. With the decomposed weight matrices of the filter and the explicit form of the NURBS stiffness matrix, we obtain the equivalent but much simplified preprocessing procedure and sensitivity analysis for the MMITO method. A comprehensive set of multi‐material numerical examples are optimized to verify that, while improving the preprocessing efficiency and reducing the memory overhead, the present MMITO scheme is able to generate semblable two‐dimensional and three‐dimensional multi‐material structures with identical structural performance to the traditional scheme. Therefore, the proposed MMITO method is a promising approach to optimizing multi‐material structures.

Exploring Stroke-Level Modifications for Scene Text Editing

Scene text editing (STE) aims to replace text with the desired one while preserving background and styles of the original text. However, due to the complicated background textures and various text styles, existing methods fall short in generating clear and legible edited text images. In this study, we attribute the poor editing performance to two problems: 1) Implicit decoupling structure. Previous methods of editing the whole image have to learn different translation rules of background and text regions simultaneously. 2) Domain gap. Due to the lack of edited real scene text images, the network can only be well trained on synthetic pairs and performs poorly on real-world images. To handle the above problems, we propose a novel network by MOdifying Scene Text image at strokE Level (MOSTEL). Firstly, we generate stroke guidance maps to explicitly indicate regions to be edited. Different from the implicit one by directly modifying all the pixels at image level, such explicit instructions filter out the distractions from background and guide the network to focus on editing rules of text regions. Secondly, we propose a Semi-supervised Hybrid Learning to train the network with both labeled synthetic images and unpaired real scene text images. Thus, the STE model is adapted to real-world datasets distributions. Moreover, two new datasets (Tamper-Syn2k and Tamper-Scene) are proposed to fill the blank of public evaluation datasets. Extensive experiments demonstrate that our MOSTEL outperforms previous methods both qualitatively and quantitatively. Datasets and code will be available at https://github.com/qqqyd/MOSTEL.

The implicit bulk-surface filtering method for node-based shape optimization and a comparison of explicit and implicit filtering techniques

This work studies shape filtering techniques, namely the convolution-based (explicit) and the PDE-based (implicit), and introduces the implicit bulk-surface filtering method to control the boundary smoothness and preserve the internal mesh quality simultaneously in the course of bulk (solid) shape optimization. To that end, the volumetric mesh is governed by the pseudo-solid smoothing equations, which are stiffened by the mesh-Jacobian and endowed with the Robin boundary condition, which involves the Laplace-Beltrami operator on the mesh boundaries. Its superior performance from the non-simultaneous (sequential) treatment of boundary and internal meshes is demonstrated for the shape optimization of complex solid structures. Well-established explicit filters, namely Gaussian and linear, and the Helmholtz/Sobolev-based (implicit) filter are critically examined for shell optimization in terms of consistency (rigid-body-movement production), geometric characteristics, and computational cost. It is demonstrated that implicit filtering is more numerically efficient and robustly enforces fixed boundaries compared to explicit filtering. Supported by numerical experiments, a regularized Green’s function is introduced as an equivalent explicit form of the Helmholtz/Sobolev filter. Furthermore, we give special attention to deriving mesh-independent filtered sensitivities for node-based shape optimization with non-uniform meshes. It is shown that mesh-independent filtering can be achieved by scaling discrete sensitivities with the inverse of the mesh mass matrix.

An optimisation framework for the development of explicit discrete forward and inverse filters

Discrete filters are used in numerous digital signal processing applications and numerical simulations, for anti-aliasing, de-noising, and post-processing. Our specific interest is for application in large-eddy simulations. In this work, we investigate analytically the reconstruction properties of different filters, and how their discrete approximations using different rules affect the convergence and accuracy of the reconstructed signal. Following this analysis, a constrained and adaptive optimisation framework is proposed for the automated calculation of explicit forward but also direct-inverse discrete filter coefficients for a given filter transfer function. The optimised forward filters are shown to perform well with stable reconstruction using classic van Cittert iterations. The optimised direct-inverse filters eliminate the need to apply any iterations thereby substantially reducing the computational cost required for reconstruction which is one of the main challenges associated with deconvolution-based modelling in large-eddy simulations.

Characterization of measurement and instrument noise in areal surface topography measurements by the Allan deviation

Measurement and instrument noise as proposed in ISO 25178-600 and defined in ISO 25178-700 are assumed to be both stationary and randomly distributed. This paper presents the temporal and lateral Allan deviation as useful tools for deeper noise analysis in surface topography measurements. The temporal Allan deviation may be used to identify and qualify drift and spikes in the mean topography, which makes averaging over longer times no longer beneficial to reduce measurement noise. The lateral Allan deviation may reveal the application of implicit and/or explicit filtering or other correlations on surface topography measurements.

Conservative low-pass filter with compact stencils for hierarchical Cartesian mesh

A conservative low-pass explicit filter with compact stencils for hierarchical Cartesian mesh is proposed. The proposed filter has two key features; the primary conservation of the conservative variables (i.e., mass, momentum, and total energy) are satisfied even at non-conforming block boundaries where grid refinement level change, and the compact stencils are achieved by employing the explicit filter while the low-pass characteristic is enhanced by properly controlling the transfer function. The proposed filter is the flux-based filter and introduces the filter flux that satisfies the conservation of the conservative variables at the non-conforming block boundaries, and the appropriate control of the transfer function is achieved by controlling the filter flux. The proposed filter is coupled with the stable and non-dissipative kinetic energy and entropy preserving (KEEP) scheme for the hierarchical Cartesian mesh (Kuya and Kawai 2020) and applied to the numerical experiments of the inviscid vortex advection, Taylor–Green vortex, and turbulent wake behind a sphere. The numerical experiments demonstrate that the proposed filter conserves the conservative variables on the non-conforming mesh and successfully removes the high-wavenumber spurious oscillations while not showing any major detrimental effects on the well-resolved flows.

Large eddy simulation on unstructured grids using explicit differential filtering: A case study of Taylor-Green vortex

The application of an approximate deconvolution model was extended for large eddy simulation (LES) on unstructured grids by further developing a three dimensional explicit differential filter. Decaying isotropic homogeneous turbulence at a Reynolds number 3,400 was modeled on both structured and unstructured grids. Results were compared to a reference direct numerical simulation and other results reported in the literature. A Taylor-Green vortex at a Reynolds number of 1,600 was also studied as it is a canonical problem for laminar to turbulent transitional flow. Investigative studies on the ADM order and under-relaxation coefficient, the degree of anisotropy of the grid, and the grid resolution were performed to benchmark the filter performance in conjunction with ADM. Finally, a large eddy simulation on a fully unstructured grid was performed to demonstrate the range of applications of the proposed filter. All numerical results showed strong LES numerical stability when the explicit differential filter was used.

Convergence of Finite Memory Q Learning for POMDPs and Near Optimality of Learned Policies Under Filter Stability

In this paper, for partially observed Markov decision problems (POMDPs), we provide the convergence of a Q learning algorithm for control policies using a finite history of past observations and control actions, and consequentially, we establish near optimality of such limit Q functions under explicit filter stability conditions. We present explicit error bounds relating the approximation error to the length of the finite history window. We establish the convergence of such Q learning iterations under mild ergodicity assumptions on the state process during the exploration phase. We further show that the limit fixed point equation gives an optimal solution for an approximate belief Markov decision problem (MDP). We then provide bounds on the performance of the policy obtained using the limit Q values compared with the performance of the optimal policy for the POMDP, in which we also present explicit conditions using recent results on filter stability in controlled POMDPs. Whereas there exist many experimental results, (i) the rigorous asymptotic convergence (to an approximate MDP value function) for such finite memory Q learning algorithms and (ii) the near optimality with an explicit rate of convergence (in the memory size) under filter stability are results that are new to the literature to our knowledge. Funding: This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

Whom do we learn from? The impact of global networks and political regime types on e-government development

This study investigates the impact of global networks on e-government development and the role of political regime types in e-government diffusion through international networks. We built a unique social network dataset that covers 148 countries for the years between 2003 and 2014. Our network dataset is rooted in two assumptions: 1) international organizations serve as peak organizations for international policy networks, 2) public managers who participate in international e-government conferences held by the UN and OECD work as boundary spanners. Our empirical evidence suggests that countries well embedded in global e-government networks receive ideas for public sector innovation from international conferences and show a high level of e-government development. However, political regime types serve as implicit and explicit filters of ideas for boundary-spanning activities. Ties between countries with the same political regime improve e-participation and ties between autocracies have a positive impact on online service delivery. However, ties between countries with different political regimes have no impact on e-participation and a negative influence on online service delivery. Thus, we debunk the democratic advantage perspective by demonstrating that democracies and autocracies have different ideas of and purposes for e-government.

On transport tensor of dynamically unresolved oceanic mesoscale eddies

Parameterizing mesoscale eddies in ocean circulation models remains an open problem due to the ambiguity with separating the eddies from large-scale flow, so that their interplay is consistent with the resolving skill of the employed non-eddy-resolving model. One way to address the issue is by using recently formulated dynamically filtered eddies. These eddies are obtained as the field errors of fitting some given reference ocean circulation into the employed coarse-grid ocean model. The main strengths are (i) no explicit spatio-temporal filter is needed for separating the large-scale and eddy flow components, (ii) the eddies are dynamically translated into the error-correcting forcing that perfectly augments the coarse-grid model towards reproducing the reference circulation. We uncovered physical properties of the eddies by interpreting involved nonlinear eddy/large-scale interactions via the classical flux-gradient relation. We described the eddies in terms of their full, space–time dependent transport tensor, which was made unique by constraining it to be the same for the potential vorticity, momentum and buoyancy fluxes. Both diffusive and advective parts of the transport tensor were found to be significant. The diffusive tensor component is characterised by polar eigenvalues and is further decomposed into isotropic and filamentation components. The latter component completely dominates, therefore, it should be taken into account by eddy parameterizations, which is not yet the case. We also showed that spatial inhomogeneities of the transport tensor components are important. Comparing these properties with those obtained for more common, locally filtered eddies revealed that they are distinctly different.

A machine learning framework for LES closure terms

In the present work, we explore the capability of artificial neural networks (ANN) to predict the closure terms for large eddy simulations (LES) solely from coarse-scale data. To this end, we derive a consistent framework for LES closure models, with special emphasis laid upon the incorporation of implicit discretization-based filters and numerical approximation errors. We investigate implicit filter types that are inspired by the solution representation of discontinuous Galerkin and finite volume schemes and mimic the behavior of the discretization operator, and a global Fourier cutoff filter as a representative of a typical explicit LES filter. Within the perfect LES framework, we compute the exact closure terms for the different LES filter functions from direct numerical simulation results of decaying homogeneous isotropic turbulence. Multiple ANN with a multilayer perceptron (MLP) or a gated recurrent unit (GRU) architecture are trained to predict the computed closure terms solely from coarse-scale input data. For the given application, the GRU architecture clearly outperforms the MLP networks in terms of accuracy, whilst reaching up to 99.9% correlation between the networks' predictions and the exact closure terms for all considered filter functions. The GRU networks are also shown to generalize well across different LES filters and resolutions. The present study can thus be seen as a starting point for the investigation of data-based modeling approaches for LES, which not only include the physical closure terms, but account for the discretization effects in implicitly filtered LES as well.

A Low-Noise Instrumentation Amplifier With Built-in Anti-Aliasing for Hall Sensors

We present a compact, versatile Hall readout system with digital output, fully integrated in 180nm technology. The core of the system is an instrumentation amplifier architecture that provides inherent anti-aliasing filtering, where the anti-aliasing characteristic is locked into a shape that maximally prevents aliasing to low frequencies. The efficiency for blocking out-of-band white noise is comparable to that of a second-order filter, eliminating the need for an explicit anti-aliasing filter before the ADC. Chopping/spinning is applied for up-modulating offset and 1/f noise to just beyond the signal band. A mostly-digital ripple reduction loop (RRL) is added for mitigating offset-related dynamic range limitations. In this, a bilinear integrator is introduced for eliminating the impact of the RRL on the system's DC gain. Moreover, the resolution of the DAC generating the analog offset compensation is reduced significantly, and the effect thereof is eliminated by digital noise cancellation logic. The one-step amplification and the simple, low-resolution DAC for offset compensation both aid in keeping the area footprint low: the analog circuits (including DAC and ADC) only occupy 0.21mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Notable performance characteristics are an input-referred noise floor of 55nT/ √{Hz} within a 410kHz bandwidth, a current consumption of only 5.1mA, and a 47dB dynamic range. The amplifier architecture can be easily applied as an analog preconditioning circuit in other sensor readout situations as well.

Dynamic iterative approximate deconvolution models for large-eddy simulation of turbulence

Dynamic iterative approximate deconvolution (DIAD) models with Galilean invariance are developed for subgrid-scale (SGS) stress in the large-eddy simulation (LES) of turbulence. The DIAD models recover the unfiltered variables using the filtered variables at neighboring points and iteratively update model coefficients without any a priori knowledge of direct numerical simulation (DNS) data. The a priori analysis indicates that the DIAD models reconstruct the unclosed SGS stress much better than the classical velocity gradient model and approximate deconvolution model with different filter scales ranging from viscous to inertial regions. We also propose a small-scale eddy viscosity (SSEV) model as an artificial dissipation to suppress the numerical instability based on a scale-similarity-based dynamic method without affecting large-scale flow structures. The SSEV model can predict a velocity spectrum very close to that of DNS data, similar to the traditional implicit large-eddy simulation. In the a posteriori testing, the SSEV-enhanced DIAD model is superior to the SSEV model, dynamic Smagorinsky model, and dynamic mixed model, which predicts a variety of statistics and instantaneous spatial structures of turbulence much closer to those of filtered DNS data without significantly increasing the computational cost. The types of explicit filters, local spatial averaging methods, and initial conditions do not significantly affect the accuracy of DIAD models. We further successfully apply DIAD models to the homogeneous shear turbulence. These results illustrate that the current SSEV-enhanced DIAD approach is promising in the development of advanced SGS models in the LES of turbulence.