Search results for "Nonlinear systems"

Identification of Nonlinear Systems Described by Hammerstein Models

2004

This paper deals with a method for identification of nonlinear systems suitable to be described by Hammerstein models consisting of a static nonlinearity followed by an ARX linear model. The estimation of the static nonlinearity is carried out supplying the system with a sequence of step signals of various amplitude and determining the corresponding steady-state responses. The estimation of the parameters of the ARX linear system is carried out by means of a least square estimator using data generated supplying the system with a Pseudorandom Binary Sequence (PRBS). The method in question is able to identify static nonlinearities of general type, also with hysteresis and/or discontinuities. …

Probabilistic response of nonlinear systems via PI: normal, Poissonian and combined white noises

2009

Galerkin Scheme-Based Determination of Survival Probability of Oscillators With Fractional Derivative Elements

2016

In this paper, an approximate semi-analytical approach is developed for determining the first-passage probability of randomly excited linear and lightly nonlinear oscillators endowed with fractional derivative elements. The amplitude of the system response is modeled as one-dimensional Markovian process by employing a combination of the stochastic averaging and the statistical linearization techniques. This leads to a backward Kolmogorov equation which governs the evolution of the survival probability of the oscillator. Next, an approximate solution of this equation is sought by resorting to a Galerkin scheme. Specifically, a convenient set of confluent hypergeometric functions, related to …

Scaling and data collapse for the mean exit time of asset prices

2005

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model …

Experimental Analysis of Passive Intermodulation at Waveguide Flange Bolted Connections

2007

[EN] In this paper, the generation of passive intermodulation at rectangular waveguide flange bolted connections is investigated. An exhaustive series of tests has been performed in order to provide understanding on the physics lying behind such a phenomenon. In particular, the intermodulation response of the system has been studied as a function of the applied torque to the flange screws. It has been found that, in some situations, the intermodulation response differs from its expected behavior. An interpretation of such discrepancies is given, and practical guidelines for the design of waveguide flanges free of passive intermodulation are provided as well.

A numerical study of postshock oscillations in slowly moving shock waves

2003

Abstract Godunov-type methods and other shock capturing schemes can display pathological behavior in certain flow situations. This paper discusses the numerical anomaly associated to slowly moving shocks. We present a series of numerical experiments that illustrate the formation and propagation of this pathology, and allows us to establish some conclusions and question some previous conjectures for the source of the numerical noise. A simple diagnosis on an explicit Steger-Warming scheme shows that some intermediate states in the first time steps deviate from the true direction and contaminate the flow structure. A remedy is presented in the form of a new flux split method with an entropy i…

Two optimizing procedures for the solution of complex systems of equations: a powerful tool for modelling and simulation of metabolism

2000

Introduction Standard calculations for the evaluation of indirect calorimetry (IC) are based on two-dimensional nonlinear systems of equations. For a more sophisticated evaluation metabolic models can be used, which are described by complex systems of equations. Since the solutions are multidimensional, a concrete result must be selected by means of constraints, using optimizing procedures. These multidimensional optimizations are critical concerning processing time and reproducibility of minimum detection. Methods In order to simulate the status of metabolism of ICU patients on the basis of IC data, a complex model of metabolism was developed. The model was described by a system of equatio…

Control of a nonlinear continuous bioreactor with bifurcation by a type-2 fuzzy logic controller

2008

The object of this paper is the application of a type-2 fuzzy logic controller to a nonlinear system that presents bifurcations. A bifurcation can cause instability in the system or can create new working conditions which, although stable, are unacceptable. The only practical solution for an efficient control is the use of high performance controllers that take into account the uncertainties of the process. A type-2 fuzzy logic controller is tested by simulation on a nonlinear bioreactor system that is characterized by a transcritical bifurcation. Simulation results show the validity of the proposed controllers in preventing the system from reaching bifurcation and instable or undesirable s…

Stability measures in metastable states with Gaussian colored noise

2009

We present a study of the escape time from a metastable state of an overdamped Brownian particle, in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity. We observe the noise enhanced stability effect for all the initial unstable states used, and for all values of the correlation time $\tau_c$ investigated. We can distinguish two dynamical regimes characterized by weak and strong correlated noise respectively, depending on the value of $\tau_c$ with respect to …

Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments

2015

Abstract The probability density function of the response of a nonlinear system under external α -stable Levy white noise is ruled by the so called Fractional Fokker–Planck equation. In such equation the diffusive term is the Riesz fractional derivative of the probability density function of the response. The paper deals with the solution of such equation by using the complex fractional moments. The analysis is performed in terms of probability density for a linear and a non-linear half oscillator forced by Levy white noise with different stability indexes α . Numerical results are reported for a wide range of non-linearity of the mechanical system and stability index of the Levy white nois…