Search results for "Aerospace Engineering"

showing 10 items of 378 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

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 excited by linearly parametric white noises and external excitations

1997

The aim of this paper is the evaluation of higher order statistics of the response of linear systems subjected to external excitations and to linearly parametric white noise. The external excitations considered are deterministic or filtered white noise processes. The procedure implies the knowledge of the transition matrix connected to the linear system; this, however, has already been evaluated for obtaining the statistics at single times. The method, which avoids making further integrations for the evaluation of the higher order statistics, is very advantageous from a computational point of view.

Mechanical EngineeringLinear systemStochastic matrixAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsHigher-order statisticsWhite noiseCondensed Matter PhysicsNuclear Energy and EngineeringControl theoryExcited statePoint (geometry)Statistical physicsCivil and Structural EngineeringMathematicsParametric statistics
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 solution handled by Fast Gauss Transform

2009

Abstract The path integral solution method is an effective tool for evaluating the response of non-linear systems under Normal White Noise, in terms of probability density function (PDF). In this paper it has been observed that, using short-time Gaussian approximation, the PDF at a given time instant is the Gauss Transform of the PDF at an earlier close time instant. Taking full advantage of the so-called Fast Gauss Transform a new integration method is proposed. In order to overcome some unsatisfactory trends of the classical Fast Gauss Transform, a new version termed as Symmetric Fast Gauss Transform is also proposed. Moreover, extensions to the two Fast Gauss Transform to MDOF systems ar…

Mechanical EngineeringMathematical analysisMathematicsofComputing_NUMERICALANALYSISAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionWhite noiseCondensed Matter Physicssymbols.namesakeNuclear Energy and EngineeringKronecker deltaComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONPath integral formulationsymbolsTwo-sided Laplace transformApplied mathematicsGauss–Seidel methodSettore ICAR/08 - Scienza Delle CostruzioniPath integral solution Fast Gauss Transform Symmetric Fast Gauss Transform Fokker-Planck equation Ito calculusS transformGaussian processCivil and Structural EngineeringMathematicsProbabilistic Engineering Mechanics
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

Higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses

1999

The higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses are evaluated by means of knowledge of the first order statistics and without any further integration. This is made possible by a coordinate transformation which replaces the original system by a quasi-linear one with parametric Poisson delta-correlated input; and, for these systems, a simple relationship between first order and higher order statistics is found in which the transition matrix of the dynamical new system, incremented by the correction terms necessary to apply the Ito calculus, appears.

Mechanical EngineeringOrder statisticCoordinate systemMathematical analysisLinear systemStochastic matrixAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsHigher-order statisticsCondensed Matter PhysicsPoisson distributionCombinatoricssymbols.namesakeNuclear Energy and EngineeringsymbolsRandom vibrationCivil and Structural EngineeringParametric statisticsMathematics
researchProduct

Probabilistic characterization of nonlinear systems under Poisson white noise via complex fractional moments

2014

In this paper, the probabilistic characterization of a nonlinear system enforced by Poissonian white noise in terms of complex fractional moments (CFMs) is presented. The main advantage in using such quantities, instead of the integer moments, relies on the fact that, through the CFMs the probability density function (PDF) is restituted in the whole domain. In fact, the inverse Mellin transform returns the PDF by performing integration along the imaginary axis of the Mellin transform, while the real part remains fixed. This ensures that the PDF is restituted in the whole range with exception of the value in zero, in which singularities appear. It is shown that using Mellin transform theorem…

Mellin transformApplied MathematicsMechanical EngineeringMonte Carlo methodMathematical analysisProbabilistic logicAerospace EngineeringOcean EngineeringProbability density functionWhite noiseComplex fractional moment Kolmogorov-Feller Mellin transform Poisson white noise Probability density functionNonlinear systemLinear differential equationControl and Systems EngineeringMellin inversion theoremElectrical and Electronic EngineeringMathematics
researchProduct