Estimation of wave spectral shapes using ANN

Representation of surface spectral density against various frequencies of ocean waves has applications in structural design, laboratory wave simulations and coastal wave modeling. Estimation of such a wave spectrum is currently made with the help of empirical relations, like, Pierson–Muskowitz and JONSWAP. These relationships were proposed using statistical curve fitting to observed data. This paper attempts to provide an alternative to such empirical theoretical spectra in the form of neural networks. Networks were developed in order to estimate shapes of the wave spectra out of the given values of representative wave height, period, spectral width and peakedeness parameter. The data collected by wave rider buoys, deployed at stations off the US as well as the Indian coast have been analyzed. The neural network-based spectral estimations were found to be more close to the ‘true’ spectra than the traditional empirical ones. It is argued that they may be used instead as substitute.     

Spectral element solutions for the PN neutron transport equations

This paper discusses the application of the Legendre spectral element method to the steady one-velocity P_N equations describing neutron transport in a one-dimensional heterogeneous slab. Emphasis is put on the implementation of the method. Some key elements related to its efficiency are analyzed to prepare further developments in higher dimensions to evaluate benchmark solutions to the simplified P_N equations.     

Computationally efficient estimation of wave propagation functions from 1-D wave experiments on viscoelastic materials

Least-squares based non-parametric estimation of the wave propagation functions of a viscoelastic material is considered in this paper. Widely used nonlinear least-squares-based algorithms are often computationally expensive and suffer from numerical problems. In this paper, we propose a class of subspace estimators which assume equidistant sensor configuration. The proposed estimator is computationally economical and numerically robust. Analytical expressions for the estimation accuracy have been derived. It is also shown that the subspace estimator achieves the optimal accuracy under the optimal weighting. The algorithm is employed on simulated data as well as on real experimental data. The results therefrom are shown to confirm the analytical results.     

Scalar multivariate subdivision schemes and box splines

We study scalar d-variate subdivision schemes, with dilation matrix 2I, satisfying the sum rules of order k. Using the results of Möller and Sauer, stated for general expanding dilation matrices, we characterize the structure of the mask symbols of such schemes by showing that they must be linear combinations of shifted box spline generators of some polynomial ideal. The directions of the corresponding box splines are columns of certain unimodular matrices. The ideal is determined by the given order of the sum rules or, equivalently, by the order of the zero conditions.The results presented in this paper open a way to a systematic study of subdivision schemes, since box spline subdivisions turn out to be the building blocks of any reasonable multivariate subdivision scheme.As in the univariate case, the characterization we give is the proper way of matching the smoothness of the box spline building blocks with the order of polynomial reproduction of the corresponding subdivision scheme. However, due to the interaction of the building blocks, convergence and smoothness properties may change, if several convergent schemes are combined.The results are illustrated with several examples.     

A weighted ENO-flux limiter scheme for hyperbolic conservation laws

We present a new scheme that combines essentially non-oscillatory (ENO) reconstructions together with monotone upwind schemes for scalar conservation laws interpolants. We modify a second-order ENO polynomial by choosing an additional point inside the stencil in order to obtain the highest accuracy when combined with the Harten–Osher reconstruction-evolution method limiter. Numerical experiments are done in order to compare a weighted version of the hybrid scheme to weighted essentially non-oscillatory (WENO) schemes with constant Courant–Friedrichs–Lewy number under relaxed step size restrictions. Our results show that the new scheme reduces smearing near shocks and corners, and in some cases it is more accurate near discontinuities compared with higher-order WENO schemes. The hybrid scheme avoids spurious oscillations while using a simple componentwise extension for solving hyperbolic systems. The new scheme is less damped than WENO schemes of comparable accuracy and less oscillatory than higher-order WENO schemes. Further experiments are done on multi-dimensional problems to show that our scheme remains non-oscillatory while giving good resolution of discontinuities.     

The multisymplectic numerical method for Gross-Pitaevskii equation

For a Bose-Einstein Condensate placed in a rotating trap and confined in the z-axis, a multisymplectic difference scheme was constructed to investigate the evolution of vortices in this paper. First, we look for a steady state solution of the imaginary time G-P equation. Then, we numerically study the vortices's development in real time, starting with the solution in imaginary time as initial value.     

A time integration scheme with energy–momentum conservation for a shell formulation with arbitrary geometric and material non-linearities

The paper is concerned with a time integration scheme which conserves energy, momentum and angular momentum for shells exhibiting arbitrary non-linearities in the strain–displacement relations together with a possible non-linear constitutive behaviour and displacement-dependent loading. The formulation is general and can apply to any shell formulation. However, we derive the equations for the specific case of the so-called seven-parametric shell theory which is characterized by a quadratic displacement field over the shell thickness. Numerical examples of large overall motion of shells are provided showing the main features of the algorithm.     

Hybrid parallel computing of minimum action method

In this work, we report a hybrid (MPI/OpenMP) parallelization strategy for the minimum action method recently proposed in [17]. For nonlinear dynamical systems, the minimum action method is a useful numerical tool to study the transition behavior induced by small noise and the structure of the phase space. The crucial part of the minimum action method is to minimize the Freidlin–Wentzell action functional. Due to the fact that the corresponding Euler–Lagrange equation is, in general, highly nonlinear and of high order, we solve the optimization problem directly instead of discretizing the Euler–Lagrange equation to provide a general but equivalent numerical framework. To enhance the efficiency of the minimum action method for general dynamical systems we consider parallel computing. In particular, we present a hybrid parallelization strategy based on MPI and OpenMP. Numerical results are presented to demonstrate the efficiency of the proposed parallelization strategy.     

Chebyshev pseudospectral method for wave equation with absorbing boundary conditions that does not use a first order hyperbolic system

The analysis and solution of wave equations with absorbing boundary conditions by using a related first order hyperbolic system has become increasingly popular in recent years. At variance with several methods which rely on this transformation, we propose an alternative method in which such hyperbolic system is not used. The method consists of approximation of spatial derivatives by the Chebyshev pseudospectral collocation method coupled with integration in time by the Runge-Kutta method. Stability limits on the timestep for arbitrary speed are calculated and verified numerically. Furthermore, theoretical properties of two methods by Jackiewicz and Renaut are derived, including, in particular, a result that corrects some conclusions of these authors. Numerical results that verify the theory and illustrate the effectiveness of the proposed approach are reported.     

基于动作模板匹配的弱监督动作定位

为解决视频中的动作定位问题，提出一种基于模板匹配的弱监督动作定位方法。首先在视频的每一帧上给出若干个动作主体位置的候选框，按时间顺序连接这些候选框形成动作提名；然后利用训练集视频的部分帧得到动作模板；最后利用动作提名与动作模板训练模型，找到最优的模型参数。在UCF-sports数据集上进行实验，结果显示，与TLSVM方法相比，所提方法的动作分类准确率提升了0.3个百分点；当重叠度阈值取0.2时，与CRANE方法相比，所提方法的动作定位准确率提升了28.21个百分点。实验结果表明，所提方法不但能够减少数据集标注的工作量，而且动作分类和动作定位的准确率均得到提升。     

On the Stability and Accuracy of the Spectral Difference Method

In this article, it is shown that under certain conditions, the spectral difference (SD) method is independent of the position of the solution points. This greatly simplifies the design of such schemes, and it also offers the possibility of a significant increase in the efficiency of the method. Furthermore, an accuracy and stability study, based on wave propagation analysis, is presented for several 1D and 2D SD schemes. It was found that higher than second-order 1D SD schemes using the Chebyshev–Gauss–Lobatto nodes as the flux points have a weak instability. New flux points were identified which produce accurate and stable SD schemes. In addition, a weak instability was also found in 2D third- and fourth-order SD schemes on triangular grids. Several numerical tests were performed to verify the analysis.     

Automatic code generator for higher order integrators

Some explicit algorithms for higher order symplectic integration of a large class of Hamilton’s equations have recently been discussed by Mushtaq et al. Here we present a Python program for automatic numerical implementation of these algorithms for a given Hamiltonian, both for double precision and multiprecision computations. We provide examples of how to use this program, and illustrate behavior of both the code generator and the generated solver module(s).     

A parallel compact-TVD method for compressible fluid dynamics employing shared and distributed-memory paradigms

A novel multi-block compact-TVD finite difference method for the simulation of compressible flows is presented. The method combines distributed and shared-memory paradigms to take advantage of the configuration of modern supercomputers that host many cores per shared-memory node. In our approach a domain decomposition technique is applied to a compact scheme using explicit flux formulas at block interfaces. This method offers great improvement in performance over earlier parallel compact methods that rely on the parallel solution of a linear system. A test case is presented to assess the accuracy and parallel performance of the new method.     

Dispersion,group velocity,and multisymplectic discretizations

This paper examines the dispersive properties of multisymplectic discretizations of linear and nonlinear PDEs. We focus on a leapfrog in space and time scheme and the Preissman box scheme. We find that the numerical dispersion relations are monotonic and determine the relationship between the group velocities of the different numerical schemes. The group velocity dispersion is used to explain the qualitative differences in the numerical solutions obtained with the different schemes. Furthermore, the numerical dispersion relation is found to be relevant when determining the ability of the discretizations to resolve nonlinear dynamics.     

Empowering wave energy with control technology: Possibilities and pitfalls

With an increasing focus on climate action and energy security, an appropriate mix of renewable energy technologies is imperative. Despite having considerable global potential, wave energy has still not reached a state of maturity or economic competitiveness to have made an impact. Challenges include the high capital and operational costs associated with deployment in the harsh ocean environment, so it is imperative that the full energy harnessing capacity of wave energy devices, and arrays of devices in farms, is realised. To this end, control technology has an important role to play in maximising power capture, while ensuring that physical system constraints are respected, and control actions do not adversely affect device lifetime. Within the gamut of control technology, a variety of tools can be brought to bear on the wave energy control problem, including various control strategies (optimal, robust, nonlinear, etc.), data-based model identification, estimation, and forecasting. However, the wave energy problem displays a number of unique features which challenge the traditional application of these techniques, while also presenting a number of control ‘paradoxes’. This review articulates the important control-related characteristics of the wave energy control problem, provides a survey of currently applied control and control-related techniques, and gives some perspectives on the outstanding challenges and future possibilities. The emerging area of control co-design, which is especially relevant to the relatively immature area of wave energy system design, is also covered.     

Dispersion free wave splittings for structural elements

Wave splittings are derived for three types of structural elements: membranes, Timoshenko beams, and Mindlin plates. The Timoshenko beam equation and the Mindlin plate equation are inherently dispersive, as is each Fourier component of the membrane equation in an angular decomposition of the field. The distinctive feature of the wave splittings derived in the present paper is that, in homogeneous regions, they transform the dispersive wave equations into simple one-way wave equations without dispersion. Such splittings have uses both for radial scattering problems in the 2D cases and for scattering problems in dispersive media. As an example of how the splittings may be applied, a direct scattering problem is solved for a membrane with radially varying density. The imbedding method is utilized, and agreement is obtained with an FE simulation.     

Feedback noncausal model predictive control of wave energy converters

In this paper, a novel feedback noncausal model predictive control (MPC) strategy for sea wave energy converters (WECs) is proposed, where the wave prediction information can be explicitly incorporated into the MPC strategy to improve the WEC control performance. The main novelties of the MPC strategy proposed in this paper include: (i) the recursive feasibility and robust constraints satisfaction are guaranteed without a significant increase in the computational burden; (ii) the information of short-term wave prediction is incorporated into the feedback noncausal MPC method to maximise the potential energy output; (iii) the sea condition for the WEC to safely operate in can be explicitly calculated. The proposed feedback noncausal MPC algorithm can also be extended to a wide class of control design problems, especially to the energy maximisation problems with constraints to be satisfied and subject to persistent but predictable disturbances. Numerical simulations are provided to show the efficacy of the proposed feedback noncausal MPC.     

Penalty,Semi-Recursive and Hybrid Methods for MBS Real-Time Dynamics in the Context of Structural Integrators

In a previous work, the authors presented a new real-time formulation for the dynamics of multibody systems, which encompasses high ranks of efficiency, accuracy, robustness and easiness of implementation. The new method, called hybrid, was obtained as a combination of a topological semi-recursive formulation based on velocities transformation, and a global penalty formulation for closed-loops consideration. It was proven to be more robust and efficient that its predecessors for large problems. For the three methods compared, the implicit, single-step trapezoidal rule was used as numerical integrator. In this paper, the influence of the integration scheme on the performance of the three mentioned methods is studied. Since the hybrid formulation becomes competitive for large multibody systems, a rather demanding simulation of the full model of a car vehicle is selected as benchmark problem. Computer codes implementing the three dynamic formulations in combination with different structural integrators, like Newmark, HHT and Generalized- algorithms, are used to run the simulation, so that the performance of each couple dynamic-formulation/numerical-integrator can be appraised. The example is also analyzed through a commercial tool, so as to provide the readers with a well-known reference for comparison.     

Human action recognition using boosted EigenActions

This paper proposes a boosting EigenActions algorithm for human action recognition. A spatio-temporal Information Saliency Map (ISM) is calculated from a video sequence by estimating pixel density function. A continuous human action is segmented into a set of primitive periodic motion cycles from information saliency curve. Each cycle of motion is represented by a Salient Action Unit (SAU), which is used to determine the EigenAction using principle component analysis. A human action classifier is developed using multi-class Adaboost algorithm with Bayesian hypothesis as the weak classifier. Given a human action video sequence, the proposed method effectively locates the SAUs in the video, and recognizes the human actions by categorizing the SAUs. Two publicly available human action databases, namely KTH and Weizmann, are selected for evaluation. The average recognition accuracy are 81.5% and 98.3% for KTH and Weizmann databases, respectively. Comparative results with two recent methods and robustness test results are also reported.     

Hessian distances and their applications in the complexity analysis of interior-point methods

For interior points in convex cones, we introduce the Hessian distance function, and show that it is convenient for complexity analysis of polynomial-time interior-point methods (IPMs). As an example of its application, we develop new infeasible-start IPM for the linear conic optimization problem. In our setting, the primal and dual cones need not to be self-dual. We can start from any primal–dual point in the interior of the cones. Then, the damped Newton's method can be used for obtaining an approximate solution for the strictly feasible case, or for detecting primal/dual infeasibility. The complexity of these cases depends on the Hessian distance between the starting point and the feasibility/infeasibility certificates. We also present some numerical results.