Nonlinear models for lateral dynamics of railway vehicles on bridges subject to wind action

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require threedimensional coupled vehicle-bridge models, wheree consideration of wheel to rail contact is a key aspect. Furthermore, an adequate evaluation of safety of rail traffic requires nonlinear models. A nonlinear coupled model is proposed here for vehicle-structure vertical and lateral dynamics. Vehicles are considered as fully three-dimensional multibody systems including gyroscopic terms and large rotation effects. The bridge structure is modeled by means of finite elements which may be of beam, shell or continuum type and may include geometric or material nonlinearities. The track geometry includes distributed track alignment irregularities. Both subsystems (bridge and vehicles) are described with coordinates in absolute reference frames, as opposed to alternative approaches which describe the multibody system with coordinates relative to the base bridge motion. The wheelrail contact employed is a semi-Hertzian model based on realistic wheel-rail profiles. It allows a detailed geometrical description of the contact patch under each wheel including multiple-point contact, flange contact and uplift. Normal and tangential stresses in each contact are integrated at each time-step to obtain the resultant contact forces. The models have been implemented within an existing finite element analysis software with multibody capabilities, Abaqus (Simulia Ltd., 2010). Further details of the model are presented in Antolín et al. (2012). Representative applications are presented for railway vehicles under lateral wind action on laterally compliant viaducts, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

A simple torsion-free nonlinear beam element for multibody dynamics

We propose in this work a very simple torsion-free beam element capable of capturing geometrical nonlinearities. The simple formulation is objective and unconditionally con- vergent for geometrically nonlinear models with large displacements, in the traditional sense that guarantees more precise numerical solutions for finer discretizations. The formulation does not employ rotational degrees of freedom, can be applied to two and three-dimensional problems, and it is computationally very efficient.

Damping models in the truncated derivative nonlinear Schrödinger equation

Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schrödinger equation, has been analyzed; wave 1 is linearly unstable with growth rate , and waves 2 and 3 are stable with damping 2 and 3, respectively. The dependence of gross dynamical features on the damping model as characterized by the relation between damping and wave-vector ratios, 2 /3, k2 /k3, and the polarization of the waves, is discussed; two damping models, Landau k and resistive k2, are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist as against flow contraction just requiring.In the case of right-hand RH polarization, point P may exist for all models other than Landau damping; for the resistive model, P may exist for RH polarization only if 2+3/2.

Hybrid analysis of nonlinear circuits: DAE models with indices zero and one

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices.

On nonlinearity in neural encoding models applied to the primary visual cortex

Within the regression framework, we show how different levels of nonlinearity influence the instantaneous firing rate prediction of single neurons. Nonlinearity can be achieved in several ways. In particular, we can enrich the predictor set with basis expansions of the input variables (enlarging the number of inputs) or train a simple but different model for each area of the data domain. Spline-based models are popular within the first category. Kernel smoothing methods fall into the second category. Whereas the first choice is useful for globally characterizing complex functions, the second is very handy for temporal data and is able to include inner-state subject variations. Also, interactions among stimuli are considered. We compare state-of-the-art firing rate prediction methods with some more sophisticated spline-based nonlinear methods: multivariate adaptive regression splines and sparse additive models. We also study the impact of kernel smoothing. Finally, we explore the combination of various local models in an incremental learning procedure. Our goal is to demonstrate that appropriate nonlinearity treatment can greatly improve the results. We test our hypothesis on both synthetic data and real neuronal recordings in cat primary visual cortex, giving a plausible explanation of the results from a biological perspective.

Models for Lateral Dynamic Interaction of High-Speed Trains and Bridges

In this work a methodology for analysing the lateral coupled behavior of large viaducts and high-speed trains is proposed. The finite element method is used for the structure, multibody techniques are applied for vehicles and the interaction between them is established introducing wheel-rail nonlinear contact forces. This methodology is applied for the analysis of the railway viaduct of the R´ıo Barbantino, which is a very long and tall bridge in the north-west spanish high-speed line.

Turbulence models of gravitational clustering.

Large-scale structure formation can be modeled as a nonlinear process that transfers energy from the largest scales to successively smaller scales until it is dissipated, in analogy with Kolmogorov’s cascade model of incompressible turbulence. However, cosmic turbulence is very compressible, and vorticity plays a secondary role in it. The simplest model of cosmic turbulence is the adhesion model, which can be studied perturbatively or adapting to it Kolmogorov’s non-perturbative approach to incompressible turbulence. This approach leads to observationally testable predictions, e.g., to the power-law exponent of the matter density two-point correlation function.

Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude.

Improving automatic detection of obstructive sleep apnea through nonlinear analysis of sustained speech

We present a novel approach for the detection of severe obstructive sleep apnea (OSA) based on patients' voices introducing nonlinear measures to describe sustained speech dynamics. Nonlinear features were combined with state-of-the-art speech recognition systems using statistical modeling techniques (Gaussian mixture models, GMMs) over cepstral parameterization (MFCC) for both continuous and sustained speech. Tests were performed on a database including speech records from both severe OSA and control speakers. A 10 % relative reduction in classification error was obtained for sustained speech when combining MFCC-GMM and nonlinear features, and 33 % when fusing nonlinear features with both sustained and continuous MFCC-GMM. Accuracy reached 88.5 % allowing the system to be used in OSA early detection. Tests showed that nonlinear features and MFCCs are lightly correlated on sustained speech, but uncorrelated on continuous speech. Results also suggest the existence of nonlinear effects in OSA patients' voices, which should be found in continuous speech.

A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution

In this paper we present a continuum theory for large strain anisotropic elastoplasticity based on a decomposition of the modified plastic velocity gradient into energetic and dissipative parts. The theory includes the Armstrong and Frederick hardening rule as well as multilayer models as special cases even for large strain anisotropic elastoplasticity. Texture evolution may also be modelled by the formulation, which allows for a meaningful interpretation of the terms of the dissipation equation

Analysis of lateral dynamics of railway vehicles on viaducts with coupled models

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require 3D coupled vehicle-bridge models, and consideration of wheel to rail contact, a phenomenon which is complex and costly to model in detail. We describe here a fully nonlinear coupled model, described in absolute coordinates and incorporated into a commercial finite element framework. Two applications are presented, firstly to a vehicle subject to a strong wind gust traversing a br idge, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle. The second application is to a real viaduct in a high-speed line, with a long continuous deck and tall piers with high lateral compliance. The results show the safety of the traffic as well as the relevance of considering the wind action and the nonlinear response.

Coupled models for the dynamics of bridges under high-speed rail traffic

The dynamic effects of high-speed trains on viaducts are important issues for the design of the structures, as well as for determining safe running conditions of trains. In this work we start by reviewing the relevance of some basic moving load models for the dynamic action of vertical traffic loads. The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require 3D coupled vehicle-bridge models and consideration of wheel to rail contact. We describe here a fully nonlinear coupled model, formulated in absolute coordinates and incorporated into a commercial finite element framework. An application example is presented for a vehicle subject to a strong wind gust traversing a bridge, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

Asymptotic Description of Flutter Amplitude Saturation by Nonlinear Friction Forces

The computation of the non-linear vibration dynamics of an aerodynamically unstable bladed-disk is a formidable numerical task, even for the simplified case of aerodynamic forces assumed to be linear. The nonlinear friction forces effectively couple dif- ferent travelling waves modes and, in order to properly elucidate the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is basically a superposition of the linear aeroelastic un- stable travelling waves, which exhibit a slow time modulation that is much longer than the elastic oscillation period. This slow time modulation is due to both, the small aerodynamic effects and the small nonlinear friction forces, and it is crucial to deter- mine the final amplitude of the flutter vibration. In this presenta- tion we apply asymptotic techniques to obtain a new simplified model that captures the slow time dynamics of the amplitudes of the travelling waves. The resulting asymptotic model is very re- duced and extremely cheap to simulate, and it has the advantage that it gives precise information about the characteristics of the nonlinear friction models that actually play a role in the satura- tion of the vibration amplitude.

Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate.

First order mem-circuits: modeling, nonlinear oscillations and bifurcations

This paper presents a theoretical framework intended to accommodate circuit devices described by characteristics involving more than two fundamental variables. This framework is motivated by the recent appearance of a variety of so-called mem-devices in circuit theory, and makes it possible to model the coexistence of memory effects of different nature in a single device. With a compact formalism, this setting accounts for classical devices and also for circuit elements which do not admit a two-variable description. Fully nonlinear characteristics are allowed for all devices, driving the analysis beyond the framework of Chua and Di Ventra We classify these fully nonlinear circuit elements in terms of the variables involved in their constitutive relations and the notions of the differential- and the state-order of a device. We extend the notion of a topologically degenerate configuration to this broader context, and characterize the differential-algebraic index of nodal models of such circuits. Additionally, we explore certain dynamical features of mem-circuits involving manifolds of non-isolated equilibria. Related bifurcation phenomena are explored for a family of nonlinear oscillators based on mem-devices.