Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known to only provide approximated results, is omnipresent in this activity. In order to validate the behaviors of numerical simulations using abstract interpretation-based static analysis, we present, theoretically and with experiments, a new partially relational abstract domain dedicated to floating-point variables. It comes from interval expansion of non-linear functions using slopes and it is able to mimic all the behaviors of the floating-point arithmetic. Hence it is adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems

Fast recursive filters for simulating nonlinear dynamic systems

A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters and static nonlinearities. The parameters of these filters and nonlinearities may depend on system variables, and the topology of the system may be complex, including feedback. Several examples taken from neuroscience are given: phototransduction, photopigment bleaching, and spike generation according to the Hodgkin-Huxley equations. The scheme uses two slightly different forms of autoregressive filters, with an implicit delay of zero for feedforward control and an implicit delay of half a sample distance for feedback control. On a fairly complex model of the macaque retinal horizontal cell it computes, for a given level of accuracy, 1-2 orders of magnitude faster than 4th-order Runge-Kutta. The computational scheme has minimal memory requirements, and is also suited for computation on a stream processor, such as a GPU (Graphical Processing Unit).Comment: 20 pages, 8 figures, 1 table. A comparison with 4th-order Runge-Kutta integration shows that the new algorithm is 1-2 orders of magnitude faster. The paper is in press now at Neural Computatio

Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics

This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provide

Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects

Abstract—This paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index Terms—Finite difference methods, time-domain analysis, transmission lines, wavelet transforms. I

Meshless Local Petrov-Galerkin (MLPG) Method with Orthogonal Polynomials for Euler-Bernoulli Beam Problems

In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods

Seasonal Correction of Offshore Wind Energy Potential due to Air Density: Case of the Iberian Peninsula

A constant value of air density based on its annual average value at a given location is commonly used for the computation of the annual energy production in wind industry. Thus, the correction required in the estimation of daily, monthly or seasonal wind energy production, due to the use of air density, is ordinarily omitted in existing literature. The general method, based on the implementation of the wind speed’s Weibull distribution over the power curve of the turbine, omits it if the power curve is not corrected according to the air density of the site. In this study, the seasonal variation of air density was shown to be highly relevant for the computation of offshore wind energy potential around the Iberian Peninsula. If the temperature, pressure, and moisture are taken into account, the wind power density and turbine capacity factor corrections derived from these variations are also significant. In order to demonstrate this, the advanced Weather Research and Forecasting mesoscale Model (WRF) using data assimilation was executed in the study area to obtain a spatial representation of these corrections. According to the results, the wind power density, estimated by taking into account the air density correction, exhibits a difference of 8% between summer and winter, compared with that estimated without the density correction. This implies that seasonal capacity factor estimation corrections of up to 1% in percentage points are necessary for wind turbines mainly for summer and winter, due to air density changes.This work has been funded by the Spanish Government’s MINECO project CGL2016-76561-R (AEI/FEDER EU) and the University of the Basque Country (UPV/EHU funded project GIU17/02). The ECMWF ERA-Interim data used in this study have been obtained from the ECMWF-MARS Data Server. The authors wish to express their gratitude to the Spanish Port Authorities (Puertos del Estado) for being kind enough to provide data for this study. The computational resources used in the project were provided by I2BASQUE. The authors thank the creators of the WRF/ARW and WRFDA systems for making them freely available to the community. NOAA_OI_SST_V2 data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, through their web-site at http://www.esrl.noaa.gov/psd/ were used in this paper. National Centres for Environmental Prediction/National Weather Service/NOAA/U.S. Department of Commerce. 2008, updated daily. NCEP ADP Global Upper Air and Surface Weather Observations (PREPBUFR format), May 1997—continuing. Research Data Archive at the National Centre for Atmospheric Research, Computational and Information Systems Laboratory. http://rda.ucar.edu/datasets/ds337.0/ were used. All the calculations have been carried out in the framework of R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org

New computer-based search strategies for extreme functions of the Gomory--Johnson infinite group problem

We describe new computer-based search strategies for extreme functions for the Gomory--Johnson infinite group problem. They lead to the discovery of new extreme functions, whose existence settles several open questions.Comment: 54 pages, many figure