Search results for "Nonlinear system"

showing 10 items of 1446 documents

Non-linear systems under delta correlated processes handled by perturbation theory

1998

Statistical responses in terms of moment and correlation functions of non-linear systems driven by non-normal delta correlated external pulses are derived. The procedure takes full advantage of the perturbation theory approach. Then, by means of a proper coordinate transformation, the system is replaced by a quasi-linear system for which the statistical quantities can be exactly found.

Mechanical EngineeringDirect methodNumerical analysisCoordinate systemAerospace EngineeringDuffing equationOcean EngineeringStatistical and Nonlinear PhysicsCondensed Matter PhysicsMoment (mathematics)Nonlinear systemClassical mechanicsNuclear Energy and EngineeringRandom vibrationStatistical physicsPerturbation theoryCivil and Structural EngineeringMathematics
researchProduct

Spectral Approach to Equivalent Statistical Quadratization and Cubicization Methods for Nonlinear Oscillators

2003

Random vibrations of nonlinear systems subjected to Gaussian input are investigated by a technique based on statistical quadratization, and cubicization. In this context, and depending on the nature of the given nonlinearity, statistics of the stationary response are obtained via an equivalent system with a polynomial nonlinearity of either quadratic or cubic order, which can be solved by the Volterra series method. The Volterra series response is expanded in a trigonometric Fourier series over an adequately long interval T, and exact expressions are derived for the Fourier coefficients of the second- and third-order response in terms of the Fourier coefficients of the first-order, Gaussian…

Mechanical EngineeringGaussianMathematical analysisVolterra seriesTrigonometric seriessymbols.namesakeNonlinear systemMechanics of MaterialsFrequency domainsymbolsRandom vibrationFourier seriesGaussian processMathematicsJournal of Engineering Mechanics
researchProduct

Identification of linear parameter varying models

2002

We consider identification of a certain class of discrete-time nonlinear systems known as linear parameter varying system. We assume that inputs, outputs and the scheduling parameters are directly measured, and a form of the functional dependence of the system coefficients on the parameters is known. We show how this identification problem can be reduced to a linear regression, and provide compact formulae for the corresponding least mean square and recursive least-squares algorithms. We derive conditions on persistency of excitation in terms of the inputs and scheduling parameter trajectories when the functional dependence is of polynomial type. These conditions have a natural polynomial i…

Mechanical EngineeringGeneral Chemical EngineeringBiomedical EngineeringAerospace EngineeringIndustrial and Manufacturing EngineeringPolynomial interpolationScheduling (computing)Parameter identification problemLeast mean squares filterNonlinear systemControl and Systems EngineeringControl theoryLinear regressionApplied mathematicsElectrical and Electronic EngineeringMathematicsInternational Journal of Robust and Nonlinear Control
researchProduct

Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution

2008

An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac's deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.

Mechanical EngineeringInfinitesimalMathematical analysisMonte Carlo methodAerospace EngineeringWhite noisePoisson distributionPoisson White Noise Kolmogorov-Feller equation Path integral solution.Nonlinear systemsymbols.namesakeDistribution (mathematics)Mechanics of MaterialsAutomotive EngineeringPath integral formulationsymbolsGeneral Materials ScienceLimit (mathematics)Settore ICAR/08 - Scienza Delle CostruzioniMathematicsJournal of Vibration and Control
researchProduct

Higher order statistics of the response of MDOF linear systems under polynomials of filtered normal white noises

1997

This paper exploits the work presented in the companion paper in order to evaluate the higher order statistics of the response of linear systems excited by polynomials of filtered normal processes. In fact, by means of a variable transformation, the original system is replaced by a linear one excited by external and linearly parametric white noise excitations. The transition matrix of the new enlarged system is obtained simply once the transition matrices of the original system and of the filter are evaluated. The method is then applied in order to evaluate the higher order statistics of the approximate response of nonlinear systems to which the pseudo-force method is applied.

Mechanical EngineeringLinear systemStochastic matrixAerospace EngineeringOrder (ring theory)Ocean EngineeringStatistical and Nonlinear PhysicsHigher-order statisticsWhite noiseFilter (signal processing)Condensed Matter PhysicsNonlinear systemNuclear Energy and EngineeringControl theoryApplied mathematicsCivil and Structural EngineeringMathematicsParametric statisticsProbabilistic Engineering Mechanics
researchProduct

Path Integral Method for Nonlinear Systems Under Levy White Noise

2017

In this paper, the probabilistic response of nonlinear systems driven by alpha-stable Lévy white noises is considered. The path integral solution is adopted for determining the evolution of the probability density function of nonlinear oscillators. Specifically, based on the properties of alpha-stable random variables and processes, the path integral solution is extended to deal with Lévy white noises input with any value of the stability index alpha. It is shown that at the limit when the time increments tend to zero, the Einstein–Smoluchowsky equation, governing the evolution of the response probability density function, is fully restored. Application to linear and nonlinear systems under…

Mechanical EngineeringMathematical analysisShot noise020101 civil engineering02 engineering and technologyWhite noiseLevy white noiseStability (probability)Stochastic Response0201 civil engineeringPath Integral SolutionNonlinear systemsymbols.namesake020303 mechanical engineering & transportsAdditive white Gaussian noise0203 mechanical engineeringGaussian noisePath integral formulationsymbolsSafety Risk Reliability and QualitySafety ResearchMathematics
researchProduct

Stochastic dynamics of nonlinear systems driven by non-normal delta-correlated processes

1993

In this paper, nonlinear systems subjected to external and parametric non-normal delta-correlated stochastic excitations are treated. A new interpretation of the stochastic differential calculus allows first a full explanation of the presence of the Wong-Zakai or Stratonovich correction terms in the Itoˆ’s differential rule. Then this rule is extended to take into account the non-normality of the input. The validity of this formulation is confirmed by experimental results obtained by Monte Carlo simulations.

Mechanical EngineeringMonte Carlo methodDifferential calculusCondensed Matter PhysicsInterpretation (model theory)Nonlinear systemClassical mechanicsMechanics of MaterialsRandom vibrationStatistical physicsDifferential (mathematics)ExcitationMathematicsParametric statistics
researchProduct

Approximate solution of the Fokker-Planck-Kolmogorov equation

2002

The aim of this paper is to present a thorough investigation of approximate techniques for estimating the stationary and non-stationary probability density function (PDF) of the response of nonlinear systems subjected to (additive and/or multiplicative) Gaussian white noise excitations. Attention is focused on the general scheme of weighted residuals for the approximate solution of the Fokker-Planck-Kolmogorov (FPK) equation. It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF). The criteria for selecting the set of weighting functions i…

Mechanical EngineeringMultiplicative functionAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionWhite noiseCondensed Matter PhysicsMultiplicative noiseWeightingNonlinear systemsymbols.namesakeNuclear Energy and EngineeringGaussian noiseProbability density functionsymbolsApplied mathematicsFokker–Planck equationWeighted residuals methodSafety Risk Reliability and QualityCivil and Structural EngineeringMathematical physicsMathematicsFokker-Planck-Kolmogorov equation
researchProduct

Direct evaluation of jumps for nonlinear systems under external and multiplicative impulses

2015

In this paper the problem of the response evaluation of nonlinear systems under multiplicative impulsive input is treated. Such systems exhibit a jump at each impulse occurrence, whose value cannot be predicted through the classical differential calculus. In this context here the correct jump evaluation of nonlinear systems is obtained in closed form for two general classes of nonlinear multiplicative functions. Analysis has been performed to show the different typical behaviors of the response, which in some cases could diverge or converge to zero instantaneously, depending on the amplitude of the Dirac's delta.

Mechanical EngineeringMultiplicative functionMathematical analysisAerospace Engineering020101 civil engineeringDifferential calculus02 engineering and technologyImpulse (physics)0201 civil engineeringNonlinear system020303 mechanical engineering & transportsAmplitude0203 mechanical engineeringMechanics of MaterialsControl theoryAutomotive EngineeringNonlinear systemJumpGeneral Materials ScienceDirac's deltaDirect evaluationSettore ICAR/08 - Scienza Delle Costruzionimultiplicative impulsive inputMathematicsJournal of Vibration and Control
researchProduct

An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems

2015

The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF…

Mechanical EngineeringReliability (computer networking)Monte Carlo methodnonlinear systemCondensed Matter PhysicsDisplacement (vector)Nonlinear systemStochastic dynamicsOrders of magnitude (time)Variational formulationMechanics of MaterialsControl theorystochastic dynamicPath integral formulationBoundary value problemWiener path integralMathematics
researchProduct