in this paper, the unified power flow controller (upfc) is enhanced with a chaotic particle swarm optimization (cpso) damping controller in order to mitigate the low frequency oscillations (lfo) in a single machine infinite bus (smib) power system. the designed damping controller is an optimized lead-lag controller, which extracts the speed deviation of the generator rotor and generates the out...

Volterra and Wiener theories provide the concepts of linear, bilinear, tri-linear, etc., kernels, which upon convolution with the excitation force, can be employed to represent the response of a nonlinear system. Based on these theories, higher-order frequency response functions (FRFs) are employed to estimate the nonlinear stiffness of rolling element bearings, supporting a rigid rotor. The ro...

A mathematical model is introduced for weakly nonlinear wave phenomena in molecular systems like DNA and protein molecules that includes thermal effects: exchange of heat energy with the surrounding aqueous medium. The resulting equation is a stochastic discrete nonlinear Schrödinger equation with focusing cubic nonlinearity and “Thermal” terms modeling heat input and loss: PDSDNLS. New numeric...

A horizontal axis wind turbine blade in steady rotation endures cyclic transverse loading due to wind shear, tower shadowing and gravity, and a cyclic gravitational axial loading at the same fundamental frequency. These direct and parametric excitations motivate the consideration of a forced Mathieu equation with cubic nonlinearity to model its dynamic behavior. This equation is analyzed for re...

This paper shows how periodic covariance functions in Gaussian process regression can be reformulated as state space models, which can be solved with classical Kalman filtering theory. This reduces the problematic cubic complexity of Gaussian process regression in the number of time steps into linear time complexity. The representation is based on expanding periodic covariance functions into a ...

Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actua-tors. Donnell-Mushtari equations, modiied to include Kelvin-Voigt damping, are used to model the system dynamics. Basis functio...

The damping ratio of chassis suspension is a key parameter for damping matching of in-wheel motor vehicles (IWMVs). Because the motor is attached to the driving wheel, the initial design method of the damping ratio for traditional cars is not entirely suitable for IWMVs. This paper proposes an innovative initial design method of the damping ratio for IWMVs. Firstly, a traveling vibration model ...

A central issue in contemporary applied mathematics is the development of simpler dynamical models for a reduced subset of variables in complex high dimensional dynamical systems with many spatio-temporal scales. Recently, ad hoc quadratic multi-level regression models have been proposed to provide suitable reduced nonlinear models directly from data. The main results developed here are rigorou...

The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear osc...

Recent experimental and theoretical studies show that the switching behavior of magnetic nanoparticles can be well controlled by external time-dependent magnetic fields. In this work, we inspect theoretically the influence of the temperature and the magnetic anisotropy on the spin-dynamics and the switching properties of single domain magnetic nanoparticles (Stoner-particles). Our theoretical t...