Resonances and resonant frequencies for a class of nonlinear systems

Resonant phenomena for a class of nonlinear systems, which can be described by a SDOF model with a polynomial type nonlinear stiffness, are investigated using Nonlinear Output Frequency Response Functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for the first time for a class of nonlinear systems. The effects of damping on the resonances and resonant frequencies are also analyzed. These results produce a novel interpretation of energy transfer phenomena in this class of nonlinear systems and show how the damping effect influences the system resonant frequencies and amplitudes. The results are important for the design and fault diagnosis of mechanical systems and structures which can be described by the SDOF nonlinear model

Algorithmic Verification of Continuous and Hybrid Systems

We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Level Set Methods for Stochastic Discontinuity Detection in Nonlinear Problems

Stochastic physical problems governed by nonlinear conservation laws are challenging due to solution discontinuities in stochastic and physical space. In this paper, we present a level set method to track discontinuities in stochastic space by solving a Hamilton-Jacobi equation. By introducing a speed function that vanishes at discontinuities, the iso-zero of the level set problem coincide with the discontinuities of the conservation law. The level set problem is solved on a sequence of successively finer grids in stochastic space. The method is adaptive in the sense that costly evaluations of the conservation law of interest are only performed in the vicinity of the discontinuities during the refinement stage. In regions of stochastic space where the solution is smooth, a surrogate method replaces expensive evaluations of the conservation law. The proposed method is tested in conjunction with different sets of localized orthogonal basis functions on simplex elements, as well as frames based on piecewise polynomials conforming to the level set function. The performance of the proposed method is compared to existing adaptive multi-element generalized polynomial chaos methods

Identification of Nonlinear Parameter-Dependent Common-Structured models to accommodate varying experimental conditions and design parameter properties

This study considers the identification problem for a class of nonlinear parameter-varying systems associated with the following scenario: the system behaviour depends on some specifically prescribed parameter properties, which are adjustable. To understand the effect of the varying parameters, several different experiments, corresponding to different parameter properties, are carried out and different data sets are collected. The objective is to find, from the available data sets, a common parameter-dependent model structure that best fits the adjustable parameter properties for the underlying system. An efficient common model structure selection (CMSS) algorithm, called the extended forward orthogonal regression (EFOR) algorithm, is proposed to select such a common model structure. Several examples are presented to illustrate the application and the effectiveness of the new identification approach

Accurate robot simulation through system identification

Robot simulators are useful tools for developing robot behaviours. They provide a fast and efficient means to test robot control code at the convenience of the office desk. In all but the simplest cases though, due to the complexities of the physical systems modelled in the simulator, there are considerable differences between the behaviour of the robot in the simulator and that in the real world environment. In this paper we present a novel method to create a robot simulator using real sensor data. Logged sensor data is used to construct a mathematically explicit model(in the form of a NARMAX polynomial) of the robot’s environment. The advantage of such a transparent model — in contrast to opaque modelling methods such as artificial neural networks — is that it can be analysed to characterise the modelled system, using established mathematical methods In this paper we compare the behaviour of the robot running a particular task in both the simulator and the real-world using qualitative and quantitative measures including statistical methods to investigate the faithfulness of the simulator

Piecewise-polynomial associated transform macromodeling algorithm for fast nonlinear circuit simulation

We present a piecewise-polynomial based associated transform algorithm (PWPAT) for macromodeling nonlinear circuits in system-level circuit design. The generated reduced model can provide both global and local accuracies with the most compact dimension. Numerical examples compare it with existing algorithms and verify its superior accuracy in higher order harmonics simulation over traditional Trajectory Piecewise-Linear (TPWL) approach. © 2013 IEEE.published_or_final_versio