Nonlinear Dynamic Identification of Beams Resting on Nonlinear Viscoelastic Foundations Based on the Time-Delayed Transfer Entropy and Improved Surrogate Data Algorithm

Abstract

In this work, the transfer entropy and surrogate data algorithm were introduced to identify the nonlinearity level of the system by using a numerical solution of nonlinear response of beams. A homogeneous Euler-Bernoulli beam was subjected to a time-varying concentrated load and resting on a nonlinear foundation. The Galerkin method was applied to discretize the dimensionless differential governing equation of the forced vibration, and then the fourth-order Runge-Kutta method was used to obtain the time-history response of the lateral displacement. In order to simulate different nonlinearity levels, different ratios between nonlinear parameters and linear parameters of foundation, as well as different Young’s moduli, were used. A nonlinearity index was proposed. In the case of different nonlinearity levels, the nonlinearity index was used to analyze the difference between the transfer entropy calculated from the original data and the transfer entropy calculated from the surrogate data. By comparing and analyzing the nonlinearity index values under different ratios, it was found that the nonlinearity index values generally increased with the increase of the ratio and the sum of nonlinearity index values had a positive correlation with the ratio. By comparing the nonlinearity index values of the transfer entropy results of beams with different Young's moduli, it was found that the sum of the nonlinearity index values generally decreased with the increase of Young's modulus. The numerical results demonstrate that the present approach could effectively quantify the nonlinearity in the response of a beam resting on a nonlinear foundation.

Parallelism Strategies for Big Data Delayed Transfer Entropy Evaluation

“…A derivation of TE metric called Delayed TE (DTE) is explored in Kirst et al [32] to extract topology in complex networks, where they mentioned an ad hoc complex network example. Liu et al [33] make inferences in nonlinear systems with this tool; in addition, Berger et al [34] use DTE to estimate externally applied forces to a robot using low-cost sensors. However, DTE calculation requires a high demanding processing power [35,36], which is aggravated with large datasets as those found in big data.…”

Stochastic P-Bifurcation of a Bistable Viscoelastic Beam with Fractional Constitutive Relation under Gaussian White Noise

“…In recent years, many scholars have done a lot of work and achieved fruitful results in this field: Li and Tang studied the nonlinear parametric vibration of an axially moving string made by rubber-like materials, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton's second law, the Euler beam theory, and the Lagrangian strain, and the principal parametric resonance is analytically investigated via applying the direct multiscale method [12]. Liu et al introduced a transfer entropy and surrogate data algorithm to identify the nonlinearity level of the system by using a numerical solution of nonlinear response of beams, the Galerkin method was applied to discretize the dimensionless differential governing equation of the forced vibration, and then the fourth-order Runge-Kutta method was used to obtain the time history response of the lateral displacement [13]. Liu et al investigated the stochastic stability of coupled viscoelastic system with nonviscously damping driven by white noise through moment Lyapunov exponents and Lyapunov exponents, obtained the coupled Itô stochastic differential equations of the norm of the response and angles process by using the coordinate transformation, and discussed the effects of various physical quantities of stochastic coupled system on the stochastic stability [14].…”