A Dynamic Model for Ordinal Time Series: An Application to Consumers’ Perceptions of Inflation

The dynamic model of a planar free-floating flexible redundant space manipulator with three joints is derived by the assumed modes method, Lagrange principle, and momentum conservation. According to minimal joint torque’s optimization (MJTO), the state equations of the dynamic model for the free-floating redundant space manipulator are described. The PD control using the tracking position error and velocity error in the manipulator is introduced. Then, the chaotic dynamic behavior of the manipulator is analyzed by chaotic numerical methods, in which time series, phase plane portrait, Poincaré map, and Lyapunov exponents are used to analyze the chaotic behavior of the manipulator. Under certain conditions for the joint torque optimization and initial values, chaotic vibration motion of the space manipulator can be observed. The chaotic time series prediction scheme for the space manipulator is presented based on the theory of phase space reconstruction under Takens’ embedding theorem. The trajectories of phase space can be reconstructed in embedding space, which are equivalent to the original space manipulator in dynamics. The one-step prediction model for the chaotic time series and the chaotic vibration was established by using support vector regression (SVR) prediction model with RBF kernel function. It has been proved that the SVR prediction model has a good performance of prediction. The experimental results show the effectiveness of the presented method.

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Steady-State Responses of Pulley-Belt Systems With a One-Way Clutch and Belt Bending Stiffness

Journal of Vibration and Acoustics ◽

10.1115/1.4027456 ◽

2014 ◽

Vol 136 (4) ◽

Cited By ~ 46

Author(s):

Hu Ding ◽

Jean W. Zu

Keyword(s):

Time Series ◽

Steady State ◽

Differential Equations ◽

Dynamic Model ◽

Time Discretization ◽

Bending Stiffness ◽

Response Curves ◽

Axially Moving ◽

The One ◽

Belt System

A nonlinear hybrid discrete-continuous dynamic model is established to analyze the steady-state response of a pulley-belt system with a one-way clutch and belt bending stiffness. For the first time, the translating belt spans in pulley-belt systems coupled with one-way clutches are modeled as axially moving viscoelastic beams. Moreover, the model considers the rotations of the driving pulley, the driven pulley, and the accessory. The differential quadrature and integral quadrature methods are developed for space discretization of the nonlinear integropartial-differential equations in the dynamic model. Furthermore, the four-stage Runge–Kutta algorithm is employed for time discretization of the nonlinear piecewise ordinary differential equations. The time series are numerically calculated for the driven pulley, the accessory, and the translating belt spans. Based on the time series, the fast Fourier transform is used for obtaining the natural frequencies of the nonlinear vibration. The torque-transmitting directional behavior of the one-way clutch is revealed by the steady-state of the clutch torque in the primary resonances. The frequency-response curves of the translating belt, the driven pulley, and the accessory show that the one-way clutch reduces the resonance of the pulley-belt system. Furthermore, the belt cross section's aspect ratio significantly affects the dynamic response.

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The Use of Ordinal Time-Series Analysis In Assessing Policy Inputs and Impacts

The Journal of Applied Behavioral Science ◽

10.1177/002188638602200111 ◽

1986 ◽

Vol 22 (1) ◽

pp. 77-93 ◽

Cited By ~ 3

Author(s):

Diana M. Dinitto ◽

Reuben R. Mcdaniel ◽

Timothy W. Ruefli ◽

James B. Thomas

Keyword(s):

Time Series ◽

Time Series Analysis ◽

Series Analysis ◽

Ordinal Time Series

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Validation of Dynamic Models by Image Distances in the Time-Scale Domain

ASME 2009 Dynamic Systems and Control Conference, Volume 1 ◽

10.1115/dscc2009-2565 ◽

2009 ◽

Author(s):

Kourosh Danai ◽

James R. McCusker ◽

Todd Currier ◽

David O. Kazmer

Keyword(s):

Time Series ◽

Dynamic Model ◽

Model Validation ◽

Time Scale ◽

Prediction Error ◽

Dynamic Models ◽

Traditional Approaches

Model validation is the procedure whereby the fidelity of a model is evaluated. The traditional approaches to dynamic model validation either rely on the magnitude of the prediction error between the process observations and model outputs or consider the observations and model outputs as time series and use their similarity to assess the closeness of the model to the process. Here, we propose transforming these time series into the time-scale domain, to enhance their delineation, and using image distances between these transformed time series to assess the closeness of the model to the process. It is shown that the image distances provide a more consistent measure of model closeness than available from the magnitude of the prediction error.

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