Human Pose Estimation using Global and Local Normalization

In this paper, we address the problem of estimating the positions of human joints, i.e., articulated pose estimation. Recent state-of-the-art solutions model two key issues, joint detection and spatial configuration refinement, together using convolutional neural networks. Our work mainly focuses on spatial configuration refinement by reducing variations of human poses statistically, which is motivated by the observation that the scattered distribution of the relative locations of joints e.g., the left wrist is distributed nearly uniformly in a circular area around the left shoulder) makes the learning of convolutional spatial models hard. We present a two-stage normalization scheme, human body normalization and limb normalization, to make the distribution of the relative joint locations compact, resulting in easier learning of convolutional spatial models and more accurate pose estimation. In addition, our empirical results show that incorporating multi-scale supervision and multi-scale fusion into the joint detection network is beneficial. Experiment results demonstrate that our method consistently outperforms state-of-the-art methods on the benchmarks.Comment: ICCV201

Kernel Free Boundary Integral Method for 3D Stokes and Navier Equations on Irregular Domains

A second-order accurate kernel-free boundary integral method is presented for Stokes and Navier boundary value problems on three-dimensional irregular domains. It solves equations in the framework of boundary integral equations, whose corresponding discrete forms are well-conditioned and solved by the GMRES method. A notable feature of this approach is that the boundary or volume integrals encountered in BIEs are indirectly evaluated by a Cartesian grid-based method, which includes discretizing corresponding simple interface problems with a MAC scheme, correcting discrete linear systems to reduce large local truncation errors near the interface, solving the modified system by a CG method together with an FFT-based Poisson solver. No extra work or special quadratures are required to deal with singular or hyper-singular boundary integrals and the dependence on the analytical expressions of Green's functions for the integral kernels is completely eliminated. Numerical results are given to demonstrate the efficiency and accuracy of the Cartesian grid-based method

Partial discharge pulse propagation in power cable and partial discharge monitoring system

Partial discharge (PD) based condition monitoring has been widely applied to power cables. However, difficulties in interpretation of measurement results (location and criticality) remain to be tackled. This paper aims to develop further knowledge in PD signal propagation in power cables and attenuation by the PD monitoring system devices to address the localization and criticality issues. As on-line or in-service PD monitoring sensors commonly comprise of a high frequency current transformer (HFCT) and a high-pass filter, the characteristics of detected PD pulses depend on the attenuation of the cable, the HFCT used and the filter applied. Simulation of pulse propagation in a cable and PD monitoring system are performed, based on analyses in the frequency domain using the concept of transfer functions. Results have been verified by laboratory experiments and using on-site PD measurements. The knowledge gained from the research on the change in pulse characteristics propagating in a cable and through a PD detection system can be very useful to PD denoising and for development of a PD localization technique

Kernel-free boundary integral method for two-phase Stokes equations with discontinuous viscosity on staggered grids

A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the difficulties, a kernel free boundary integral (KFBI) method combined with a modified marker-and-cell (MAC) scheme is developed to solve the two-phase Stokes problems with discontinuous viscosity. The main idea is to reformulate the two-phase Stokes problem into a single-fluid Stokes problem by using boundary integral equations and then evaluate the boundary integrals indirectly through a Cartesian grid-based method. Since the jump conditions of the single-fluid Stokes problems can be easily decoupled, the modified MAC scheme is adopted here and the existing fast solver can be applicable for the resulting linear saddle system. The computed numerical solutions are second order accurate in discrete $\ell^2$-norm for velocity and pressure as well as the gradient of velocity, and also second order accurate in maximum norm for both velocity and its gradient, even in the case of high contrast viscosity coefficient, which is demonstrated in numerical tests

Modelling of advection-dominated transport in fluid-saturated porous media

The modelling of contaminant transport in porous media is an important topic to geosciences and geo-environmental engineering. An accurate assessment of the spatial and temporal distribution of a contaminant is an important step in the environmental decision-making process. Contaminant transport in porous media usually involves complex non-linear processes that result from the interaction of the migrating chemical species with the geological medium. The study of practical problems in contaminant transport therefore usually requires the development of computational procedures that can accurately examine the non-linear coupling processes involved. However, the computational modelling of the advection-dominated transport process is particularly sensitive to situations where the concentration profiles can exhibit high gradients and/or discontinuities. This thesis focuses on the development of an accurate computational methodology that can examine the contaminant transport problem in porous media where the advective process dominates.The development of the computational method for the advection-dominated transport problem is based on a Fourier analysis on stabilized semi-discrete Eulerian finite element methods for the advection equation. The Fourier analysis shows that under the Courant number condition of Cr=1, certain stabilized finite element scheme can give an oscillation-free and non-diffusive solution for the advection equation. Based on this observation, a time-adaptive scheme is developed for the accurate solution of the one-dimensional advection-dominated transport problem with the transient flow velocity. The time-adaptive scheme is validated with an experimental modelling of the advection-dominated transport problem involving the migration of a chemical solution in a porous column. A colour visualization-based image processing method is developed in the experimental modelling to quantitatively determinate the chemical concentration on the porous column in a non-invasive way. A mesh-refining adaptive scheme is developed for the optimal solution of the multi-dimensional advective transport problem with a time- and space-dependent flow field. Such mesh-refining adaptive procedure is quantitative in the sense that the size of the refined mesh is determined by the Courant number criterion. Finally, the thesis also presents a brief study of a numerical model that is capable to capture coupling Hydro-Mechanical-Chemical processes during the advection-dominated transport of a contaminant in a porous medium

Second order convergence of a modified MAC scheme for Stokes interface problems

Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution study, the rigorous convergence proofs are usually limited to particular reformulations and boundary conditions. In this paper, a rigorous error analysis of the marker and cell (MAC) scheme for Stokes interface problems with constant viscosity in the framework of the finite difference method is presented. Without reformulating the problem into elliptic PDEs, the main idea is to use a discrete Ladyzenskaja-Babuska-Brezzi (LBB) condition and construct auxiliary functions, which satisfy discretized Stokes equations and possess at least second order accuracy in the neighborhood of the moving interface. In particular, the method, for the first time, enables one to prove second order convergence of the velocity gradient in the discrete $\ell^2$-norm, in addition to the velocity and pressure fields. Numerical experiments verify the desired properties of the methods and the expected order of accuracy for both two-dimensional and three-dimensional examples

Accelerating Atmospheric Gravity Wave Simulations using Machine Learning: Kelvin-Helmholtz Instability and Mountain Wave Sources Driving Gravity Wave Breaking and Secondary Gravity Wave Generation

Gravity waves (GWs) and their associated multi-scale dynamics are known to play fundamental roles in energy and momentum transport and deposition processes throughout the atmosphere. We describe an initial, two-dimensional (2-D), machine learning model – the Compressible Atmosphere Model Network (CAMNet) - intended as a first step toward a more general, three-dimensional, highly-efficient, model for applications to nonlinear GW dynamics description. CAMNet employs a physics-informed neural operator to dramatically accelerate GW and secondary GW (SGW) simulations applied to two GW sources to date. CAMNet is trained on high-resolution simulations by the state-of-the-art model Complex Geometry Compressible Atmosphere Model (CGCAM). Two initial applications to a Kelvin-Helmholtz instability source and mountain wave generation, propagation, breaking, and SGW generation in two wind environments are described here. Results show that CAMNet can capture the key 2-D dynamics modeled by CGCAM with high precision. Spectral characteristics of primary and SGWs estimated by CAMNet agree well with those from CGCAM. Our results show that CAMNet can achieve a several order-of-magnitude acceleration relative to CGCAM without sacrificing accuracy and suggests a potential for machine learning to enable efficient and accurate descriptions of primary and secondary GWs in global atmospheric models