Orsino Renato Maia Matarazzo
Offshore Mechanics Laboratory, Mechanical Engineering Department, Escola Politécnica, University of São Paulo, São Paulo, Brazil.
Proc Math Phys Eng Sci. 2017 Aug;473(2204):20160891. doi: 10.1098/rspa.2016.0891. Epub 2017 Aug 30.
This paper proposes a novel approach to the modelling of lumped-parameter dynamic systems, based on representing them by hierarchies of mathematical models of increasing complexity instead of a single (complex) model. Exploring the multilevel modularity that these systems typically exhibit, a general recursive modelling methodology is proposed, in order to conciliate the use of the already existing modelling techniques. The general algorithm is based on a fundamental theorem that states the conditions for computing projection operators recursively. Three procedures for these computations are discussed: orthonormalization, use of orthogonal complements and use of generalized inverses. The novel methodology is also applied for the development of a recursive algorithm based on the Udwadia-Kalaba equation, which proves to be identical to the one of a Kalman filter for estimating the state of a static process, given a sequence of noiseless measurements representing the constraints that must be satisfied by the system.
本文提出了一种对集总参数动态系统进行建模的新方法，该方法基于用复杂度不断增加的数学模型层次结构来表示这些系统，而非单个（复杂的）模型。通过探索这些系统通常表现出的多级模块化，提出了一种通用的递归建模方法，以协调现有建模技术的使用。通用算法基于一个基本定理，该定理阐述了递归计算投影算子的条件。讨论了三种进行这些计算的方法：正交归一化、使用正交补和使用广义逆。这种新方法还被应用于开发一种基于乌德瓦迪亚－卡拉巴方程的递归算法，结果证明，对于给定的表示系统必须满足的约束的无噪声测量序列，该算法与用于估计静态过程状态的卡尔曼滤波器算法相同。
