Probabilistic description of extreme events in intermittently unstable systems excited by correlated stochastic processes

In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and give rise to heavy-tailed probability distributions. By making appropriate assumptions on the form of these instabilities, which are valid for a broad range of systems, we formulate a method for the analytical approximation of the probability distribution function (pdf) of the system response (both the main probability mass and the heavy-tail structure). In particular, this method relies on conditioning the probability density of the response on the occurrence of an instability and the separate analysis of the two states of the system, the unstable and stable state. In the stable regime we employ steady state assumptions, which lead to the derivation of the conditional response pdf using standard methods for random dynamical systems. The unstable regime is inherently transient and in order to analyze this regime we characterize the statistics under the assumption of an exponential growth phase and a subsequent decay phase until the system is brought back to the stable attractor. The method we present allows us to capture the statistics associated with the dynamics that give rise to heavy-tails in the system response and the analytical approximations compare favorably with direct Monte Carlo simulations, which we illustrate for two prototype intermittent systems: an intermittently unstable mechanical oscillator excited by correlated multiplicative noise and a complex mode in a turbulent signal with fixed frequency, where multiplicative stochastic damping and additive noise model interactions between various modes.Comment: 29 pages, 15 figure

A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems

We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the 'next-best' data point (set of parameters) that when evaluated results in improved estimates of the probability density function (pdf) for a scalar quantity of interest. The approach utilizes Gaussian process regression to perform Bayesian inference on the parameter-to-observation map describing the quantity of interest. We then approximate the desired pdf along with uncertainty bounds utilizing the posterior distribution of the inferred map. The 'next-best' design point is sequentially determined through an optimization procedure that selects the point in parameter space that maximally reduces uncertainty between the estimated bounds of the pdf prediction. Since the optimization process utilizes only information from the inferred map it has minimal computational cost. Moreover, the special form of the metric emphasizes the tails of the pdf. The method is practical for systems where the dimensionality of the parameter space is of moderate size, i.e. order O(10). We apply the method to estimate the extreme event statistics for a very high-dimensional system with millions of degrees of freedom: an offshore platform subjected to three-dimensional irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using limited number of samples

Switchable filtering in vivaldi antenna

Presented is a new frequency switchable Vivaldi antenna that has a capability to operate in a wideband mode (1-3 GHz) and reconfigure to six different subbands of operations. The reconfiguration is realised by coupling and changing the effective electrical length of ring slots inserted in the structure by means of pin diode switches. To examine antenna performances, simulated and measured results are presented. Good impedance matches and radiation patterns have been achieved. The proposed antenna is suitable for wideband and multimode radio applications

IMPLEMENTASI COMPUTER BASED INSTRUCTION MODEL INSTRUCTIONAL GAMES PADA PEMBELAJARAN INTERAKTIF

Teknologi komunikasi dan informasi telah berkembang seiring dengan globalisasi. Hal ini menuntut adanya perkembangan sumber daya manusia dan pendidikan adalah salah satu hal penting dalam pengembangan sumber daya manusia. Bagi tenaga pengajar mengintegrasikan teknologi komputer dalam sistem pembelajaran merupakan tantangan, sehingga pembelajaran dapat lebih berkualitas dan menyenangkan. Terkait dengan peningkatan mutu pembelajaran secara garis besar komputer dapat dimanfaatkan dalam bentuk pembelajaran berbasis komputer atau Computer Based Instruction (CBI). CBI model Instructional games bertujuan untuk menyediakan pengalaman belajar melalui bentuk permainan yang mendidik dan tantangan yang menyenangkan bagi siswa. Tujuan akhir dari pembuatan Instructional games ini adalah memberikan siswa sebuah alternatif dalam belajar, sehingga dapat memudahkan siswa menerima dan mengaplikasikan materi yang disajikan. Penelitian ini diimplementasikan menggunakan perangkat lunak Adobe Flash CS6 serta perangkat lunak tambahan untuk menghasilkan instructional games yang interaktif untuk digunakan dalam pembelajaran

Reduced-order Description of Transient Instabilities and Computation of Finite-Time Lyapunov Exponents

High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g. long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy--Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples