On Equivalent Linearization Using Wavelet Transform

1999 ◽  
Vol 121 (4) ◽  
pp. 429-432 ◽  
Author(s):  
B. Basu ◽  
V. K. Gupta
Keyword(s):  
Wavelet Transform ◽  
Duffing Oscillator ◽  
Time Dependent ◽  
Equivalent Linearization ◽  
Equivalent System ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
The Mean ◽  
The Given

This paper proposes a wavelet-based formulation for linearizing a base-excited single-degree-of-freedom nonlinear system to a time-variant linear (TVL) system. The given system is assumed to be nonlinear in stiffness, and the time-dependent natural frequency of the equivalent system is proposed to he estimated through instantaneous minimization of the mean-square error. A duffing oscillator has been considered to illustrate the performance of the proposed TVL system.

scholarly journals Financial Time Series Image Algorithm Based on Wavelet Analysis and Data Fusion

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Wuwei Liu ◽  
Jingdong Yan
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Mean Square Error ◽  
Financial Time Series ◽  
Prediction Method ◽  
Mean Square ◽  
Rbf Network ◽  
Network Prediction ◽  
The Mean ◽  
Hidden Layer

In recent years, people are more and more interested in time series modeling and its application in prediction. This paper mainly discusses a financial time series image algorithm based on wavelet analysis and data fusion. In this research, we conducted an in-depth study on the scale decomposition sequence and wavelet transform sequence in different scale domains of wavelet transform according to the scale change rule based on wavelet transform. We use wavelet neural network with different input neurons and hidden neurons to predict, respectively. Finally, the prediction results are integrated into the final prediction results based on the original time series by using wavelet reconstruction technology. Using RBF algorithm in neural network and SPSS Clementine, the wavelet transform sequences on five scales are modeled. Each network model has three layers: one input layer, one hidden layer, and one output layer, and each output layer has only one output element. In order to compare the prediction effect of the model proposed in this study, the ordinary RBF network is used to model and predict the log yield itself. When the input sample is 5, the minimum mean square error is obtained when the hidden layer is 6, and the mean square error is 1.6349. The mean square error of the training phase is 0.0209, and the validation error is 1.6141. The results show that the prediction results of the wavelet prediction method combined with the RBF network prediction method are better than those of wavelet prediction or RBF network prediction.

The Research on Hysteretic Energy in the Equivalent System Schemes between Multi Degree of Freedom System and Single Degree of Freedom System

2012 ◽  
Vol 166-169 ◽  
pp. 2177-2181
Author(s):  
Ming Qiang Sheng ◽  
Ying Liu
Keyword(s):  
Seismic Design ◽  
Seismic Waves ◽  
Good Alternative ◽  
Cumulative Damage ◽  
Degree Of Freedom ◽  
Equivalent System ◽  
Single Degree Of Freedom ◽  
Hysteretic Energy ◽  
Single Degree ◽  
Comparison And Analysis

The cumulative damage produced by severe earthquake is significant to the structural dilapidation and collapse. Most design methods based on force or displacement can’t reflect the effect of cumulative damage. Energy-based seismic design is known as a good alternative design. At present the research on the hysteretic energy of single-degree of freedom system(SDOF) is abundant, but real buildings can only be simplified as multi-degree of freedom systems(MDOF) mostly. Therefore how to acquire suitable equivalent single-degree of freedom system(ESDOF) is a key program. In this paper 12 equivalent system schemes(ESS) have been put forward, then the ratio of hysteretic energy(RH) of 6-floors framework was calculated with 30 typical seismic waves. Based on the comparison and analysis between calculations of 3 typical ESS, by the way of envelope fitting, the expression of RH related to earthquake characteristic value a/v was established.

Linearization Equations for Vibration Induced by Oscillatory Flow

1979 ◽  
Vol 46 (4) ◽  
pp. 946-948 ◽  
Author(s):  
P-T. D. Spanos ◽  
T. W. Chen
Keyword(s):  
Linear System ◽  
Oscillatory Flow ◽  
Degree Of Freedom ◽  
Approximate Determination ◽  
Equivalent Linearization ◽  
Mean Velocity ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Nonzero Mean

Equations are presented for the approximate determination through equivalent linearization of the response of a single-degree-of-freedom linear system to excitation induced by oscillatory flow with nonzero mean velocity. The reliability of the proposed methodology is examined.

PD Control Strategy Design and Simulation of Magnetic Bearing with Single Freedom of Degree

2013 ◽  
Vol 760-762 ◽  
pp. 1207-1211 ◽  
Author(s):  
Guang Yang ◽  
Jian Min Zhang
Keyword(s):  
Control Strategy ◽  
Magnetic Bearing ◽  
Degree Of Freedom ◽  
Pd Control ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Unstable Plant ◽  
Strategy Design ◽  
The Given ◽  
Bearing System

Based on the analysis of the model of the Single-Degree-of-Freedom (SDF) magnetic bearing system, the issue of design and simulation of PD control strategy in the system is investigated. First, the plant model of the AMB (Active Magnetic Bearings) with Single-Degree-of-Freedom (SDF) is found out to be unstable plant. Then, based on the root locus theory and Routh stability criteria, the necessity of derivation action in the controller is analyzed.In addition, the PD control strategy for a particular plant is designed, the effectiveness of which is validated by the given simulation examples. The proposed approach can provide an important reference for the practical application of PD control strategy in the magnetic bearing system.

Mean-Square Response of Simple Mechanical Systems to Nonstationary Random Excitation

1969 ◽  
Vol 36 (2) ◽  
pp. 221-227 ◽  
Author(s):  
R. L. Barnoski ◽  
J. R. Maurer
Keyword(s):  
White Noise ◽  
Random Noise ◽  
Random Excitation ◽  
Correlated Noise ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Step Functions ◽  
Unit Step ◽  
Mean Square Response ◽  
The Mean

This paper concerns the mean-square response of a single-degree-of-freedom system to amplitude modulated random noise. The formulation is developed in terms of the frequency-response function of the system and generalized spectra of the nonstationary random excitation. Both the unit step and rectangular step functions are used for the amplitude modulation, and both white noise and noise with an exponentially decaying harmonic correlation function are considered. The time-varying mean-square response is shown not to exceed its stationary value for white noise. For correlated noise, however, it is shown that the system mean-square response may exceed its stationary value.

A Computationally Efficient Numerical Algorithm for the Transient Response of High-Speed Elastic Linkages

1979 ◽  
Vol 101 (1) ◽  
pp. 138-148 ◽  
Author(s):  
A. Midha ◽  
A. G. Erdman ◽  
D. A. Frohrib
Keyword(s):  
Transient Response ◽  
Numerical Algorithm ◽  
High Speed ◽  
Relative Size ◽  
Degree Of Freedom ◽  
Time Dependent ◽  
Computationally Efficient ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Forcing Function

A new numerical algorithm, easily adaptable for computer simulation, is developed to approximate the transient response of a single degree-of-freedom vibrating system; governing differential equation is linear and second order with time-dependent and periodic coefficients. This is accomplished by first solving the classical linear single degree-of-freedom problem with constant coefficients. The system is excited by a periodic forcing function possessing a certain degree of smoothness. The integration terms in the solution are systematically expanded into two groups of terms: one consists of non-integral terms while the other contains only integral terms. The final integral terms are bounded. For certain combinations of frequency and damping, within the sub-resonant frequency range, the relative size of the integral terms are demonstrated to be small. The algebraic expansion (non-integral) terms then approximate the solution. The solution to a single degree-of-freedom system with time-dependent and periodic parameters is made possible by discretizing the forcing period into a number of intervals and assuming the system parameters as constant over each interval. The numerical algorithm is then employed to solve an elastic linkage problem via modal superposition. Convergence of the solution is verified by refining the number of intervals of discretization.

Optimization of Mechanism Timing Using Noncircular Gearing

1992 ◽  
Author(s):  
Judd Bernard
Keyword(s):  
Input Function ◽  
Linear Displacement ◽  
Degree Of Freedom ◽  
Output Link ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Noncircular Gears ◽  
The Given ◽  
Crank Mechanism

Abstract A single degree of freedom mechanism whose input link is a crank driven through continuous revolutions will generate output motions dependent upon the inherent mechanism geometry. For example, the slider of a slider-crank mechanism has a linear displacement (the output motion) as a function of the crank rotation (input). Only within the realm of link proportioning can the slider crank output-input function be altered. In this investigation, the continuously rotating crank of a mechanism is rigidly attached to a gear which is one of a pair of externally meshing noncircular gears. By using noncircular gears, it will be shown that the output motion of the given mechanism can be correlated to the rotation of the mating gear to which the crank is not attached. In this fashion, the output link can then be made to execute its motion according to any prescribed law. The above technique has been implemented for the cases of a crank and rocker mechanism and a slider-crank mechanism.

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