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Design of a Limit Cycle Controller for the Nonlinear Wheel-Railsystem
Published in A.H. Wickens, The Dynamics of Vehicles on roads and on tracks, 2018
The nonlinear force F is developed into a fourier polynomial of k harmonics and inserted into (7). Nonlinear damping and stiffness matrices build up and quasilinear differential equations expand. They are transformed into a set of 2n x k algebraic equations for the periodic part and n algebraic equations for the quasistatic equilibrium. These (2n × k)+ n equations are solved simultaneously by the hybrid method of Powell /14/. Powell’s method uses function values only and does not need user-supplied gradient information.
Optimization
Published in P. P. J. van den Bosch, A. C. van der Klauw, Modeling, Identification and Simulation of Dynamical Systems, 2020
P. P. J. van den Bosch, A. C. van der Klauw
Consequently, each iteration consists of n + 1 line searches in the directions di, where the last direction is calculated on the basis of the results obtained. Powell’s method adapts its search directions to the shape of the cost function J(θ). Its convergence is much better than the convergence of perpendicular search. Powell’s method is one of the best known nonlinear optimization methods in cases where no gradient information is available.
Optimization in Product Design – Synthesis
Published in S. Ratnajeevan H. Hoole, Yovahn Yesuraiyan R. Hoole, Finite Elements-based Optimization, 2019
S. Ratnajeevan H. Hoole, Yovahn Yesuraiyan R. Hoole
Powell’s method is one such method employing the univariate search to reduce searching for the minimum in a multi-dimensional space to a sequence of one-dimensional univariate searches. It may be shown to be a zeroth-order approximation of a first-order method but that need not detain us here (Vanderplaats, 1984).
Comprehensive model for predicting surface roughness of ground workpieces considering the plowing effect
Published in Machining Science and Technology, 2018
Jianliang Guo, Chenggang Liu, Jun Chi, Lianqing Chen
In this work, the improved Powell method was adopted for implement the prediction of surface roughness. Powell method is one of the direct methods with a rapid convergence rate based on conjugate directions, which allows us to reach the minimum within finite steps without calculating the gradient of the objective function. The basic idea is to choose a set of conjugate directions and then perform the first round of search for the minimum. With the minimum of the previous round as the new original point, repeat the searching process until getting a satisfactory solution.
Anatomy aware-based 2.5D bronchoscope tracking for image-guided bronchoscopic navigation
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2023
Cheng Wang, Masahiro Oda, Yuichiro Hayashi, Takayuki Kitasaka, Hayato Itoh, Hirotoshi Honma, Hirotsugu Takebatake, Masaki Mori, Hiroshi Natori, Kensaku Mori
The optimisation procedure is performed by using Powell’s method (Powell 1964). This method uses the camera pose of the previous frame as the initial pose of the current frame and finds the optimised camera pose by minimising the Eq. 1.