Dual Faceted Linearization of Nonlinear Dynamical Systems Based on Physical Modeling Theory
Dual Faceted Linearization of Nonlinear Dynamical Systems Based on Physical Modeling Theory
复制标题
基于物理建模理论的非线性动力系统的双面线性化
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Filippos E. Sotiropoulos
中科院分区：
文献类型：
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作者：
H. Asada;Filippos E. Sotiropoulos
基于物理建模理论和数据驱动的统计方法，提出了一种新的非线性集中参数系统的建模和线性化方法。在由独立状态变量和与状态变量非线性相关的辅助变量组成的增广空间中，非线性动力系统用两组微分方程组表示。结果表明，如果用所有非线性元素的输出变量作为辅助变量来扩充空间，则具有积分因果关系的键合图模型的非线性动力系统的状态方程是线性的。将辅助变量的动态变化作为第二组微分方程组进行研究，并用统计线性化方法对其进行线性化。结果表明，辅助变量的线性微分方程组反映了原始非线性系统的行为，而仅靠第一组状态方程是不能表示的。基于这两组线性状态方程的线性化被称为双面线性化(DFL)，它可以捕捉到非线性动力学的不同方面，从而提供了更丰富的非线性系统表示。这两个状态方程也被集成到一个由所有重要模式组成的不共线的潜在模型中。最后，数值算例验证了该方法的有效性。
A new approach to modeling and linearization of nonlinear lumped-parameter systems based on physical modeling theory and a data-driven statistical method is presented. A nonlinear dynamical system is represented with two sets of differential equations in an augmented space consisting of independent state variables and auxiliary variables that are nonlinearly related to the state variables. It is shown that the state equation of a nonlinear dynamical system having a bond graph model of integral causality is linear, if the space is augmented by using the output variables of all the nonlinear elements as auxiliary variables. The dynamic transition of the auxiliary variables is investigated as the second set of differential equations, which is linearized by using statistical linearization. It is shown that the linear differential equations of the auxiliary variables inform behaviors of the original nonlinear system that the first set of state equations alone cannot represent. The linearization based on the two sets of linear state equations, termed dual faceted linearization (DFL), can capture diverse facets of the nonlinear dynamics and, thereby, provide a richer representation of the nonlinear system. The two state equations are also integrated into a single latent model consisting of all significant modes with no collinearity. Finally, numerical examples verify and demonstrate the effectiveness of the new methodology.