基于ARMA和ANN的碳纳米管参数化建模及非局域常数估计

摘要

Nonlocal continuum mechanics is a popular growing theory for investigating the dynamic behavior of Carbon nanotubes (CNTs). Estimating the nonlocal constant is a crucial step in mathematical modeling of CNTs vibration behavior based on this theory. Accordingly, in this study a vibration-based nonlocal parameter estimation technique, which can be competitive because of its lower instrumentation and data analysis costs, is proposed. To this end, the nonlocal models of the CNT by using the linear and nonlinear theories are established. Then, time response of the CNT to impulsive force is derived by solving the governing equations numerically. By using these time responses the parametric model of the CNT is constructed via the autoregressive moving average (ARMA) method. The appropriate ARMA parameters, which are chosen by an introduced feature reduction technique, are considered features to identify the value of the nonlocal constant. In this regard, a multi-layer perceptron (MLP) network has been trained to construct the complex relation between the ARMA parameters and the nonlocal constant. After training the MLP, based on the assumed linear and nonlinear models, the ability of the proposed method is evaluated and it is shown that the nonlocal parameter can be estimated with high accuracy in the presence/absence of nonlinearity.%非局域连续介质力学是研究碳纳米管(CNTs)动态行为的一种新兴理论.在基于该理论的碳纳米管振动行为数学建模中,非局域常数的估计是一个关键步骤.因此,本文提出一种基于振动的非局部参数估计技术,该技术具有较低的仪器和数据分析成本,具有很强的竞争力.为此,利用线性理论和非线性理论建立了碳纳米管的非局域模型.然后,通过数值求解控制方程,得到了 CNT 在脉冲力作用下的时间响应.利用这些时间响应,采用自回归滑动平均(ARMA)方法建立了CNT的参数模型.引入特征约简技术选择合适的 ARMA 参数作为识别非局部常数值的特征.在此基础上,通过训练多层感知器(MLP)网络,建立ARMA参数与非局部常数之间的关系.在训练MLP后,基于假设的线性模型和非线性模型,对该方法的性能进行评估.结果表明,在非线性存在或不存在的情况下,该方法都能够以较高的精度估计出非局部参数.