PPT-Status of Nonlinear Model Reduction

Framework in Py A Da Ronch University of L iverpool UK Liverpool 16 March 2012 Target Nonlinear models for flexible aircraft hierarchy Nonlinear model reduction. Nonlinear Model Problem Let us consider the nonlinear model problem 87228711 f in 8486 1a 0 on 8486 1b where is a given positive function depending on the unknown solution As usual is a given source function which we for simplicity assume not to Di64256erentiating 8706S 8706f Setting the partial derivatives to 0 produces estimating equations for the regression coe64259cients Because these equations are in general nonlinear they require solution by numerical optimization As in a linear model The o64260ine phase of the method builds the local red ucedorder bases using an unsupervised learning algorithm In the online phase of the method the choice of the local basis is based on the current state of the system Inexp ensive rankone updates Formulation of the nonlinear transient hydro dynamic model Lagrangian based dynamic equation of 2D ship manoeuvring motin in the horizontal plane Oxyz Oxz Oxyz GG brPage 4br Oxyz Oz Oxyz Ox Oxyz Xmuvrxr Ymvurxr zG NIrmxvur mg mgL uvrxr gx vurxr gy z Viscoelastic Material Analysis. Objectives. The objective of this module is to provide an introduction to the theory and methods used in the analysis of components containing materials described by viscoelastic material models.. . . . . N.D.Tantaroudas. . . K.J.Badcock,A.Da. . Ronch. University . for . Liquid-Rocket . Transverse Combustion Instability. by W. A. Sirignano and P. Popov. Mechanical and Aerospace Engineering. University of California, Irvine. Supported by Air Force Office of Scientific Research . A. . Da . Ronch. , K. J. . Badcock. University of. . L. iverpool, Liverpool, U.K.. Y. Wang, A. Wynn, and R. Palacios. Imperial College, London, U.K.. AIAA Paper 2012-. 4404. Minneapolis, 13 August 2012. A. . Da . Ronch, N.D. . Tantaroudas. , . S.Timme. and K.J. Badcock. University of Liverpool, U.K.. AIAA Paper 2013-. 1942. Boston, MA, 08 April 2013. email:. K.J.Badcock@liverpool.ac.uk. Shape Optimisation. Final report. Ville-Pietari Louhiala . Status of the project . Main problem of the project is solved. The statistics of the stochastic nonlinear combustion engine model in question can be calculated with Extended . RMG Study Group Presentation. Kehang Han. Apr. 28, 2015. Outline. Why we need model reduction. Two levels of model reduction. Most recent methods. Personal opinion. High CPU time . in predictive . combustion. w. hich are not generally available. Experience has shown that the simplest model for molecules. w. ith . permanent dipole moments . requires a minimum of two states, the ground state and one. excited state. In fact, such a two level model has been effective in predicting nonlinearities in. Introduction. In many complex optimization problems, the objective and/or the constraints are . nonlinear functions . of the decision variables. Such optimization problems are called . nonlinear programming . Introduction. In many complex optimization problems, the objective and/or the constraints are . nonlinear functions . of the decision variables. Such optimization problems are called . nonlinear programming .