An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems
An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems
复制标题
嵌入式系统反问题实时求解的代数框架
DOI：
10.1109/hpcc-css-icess.2015.50
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
G. Rath
中科院分区：
文献类型：
--
作者：
C. Gugg;M. Harker;P. O’Leary;G. Rath
本文提出了一种新的平台无关的方法来实时求解嵌入式系统中的反问题。所处理的这类问题对应于具有广义线性约束的常微分方程组(ODE)，由此来自传感器阵列的数据形成强迫函数。问题的代数离散化使得微分方程组能够一对一地映射到它的离散等价线性微分算子，以及表示约束的附加矩阵方程。该方程的解被表示为具有线性约束的最小二乘问题。LS方法使该方法适用于强迫函数受噪声扰动的反问题的显式求解。代数计算被划分为初始准备步骤和循环运行时计算，前者预先计算运行时计算所需的矩阵，后者随着传感器数据的每次采集而重复。循环计算由单个矩阵-向量乘法组成，以这种方式，计算复杂度是先验已知的，满足实时计算的定义。该方案采用基于模型的设计，只使用基本的线性代数，因此，该方法支持自动生成代码以部署在嵌入式系统上。通过软件和处理器在环验证来测试目标概念。该方法在实验室样机上进行了测试，并获得了柔性结构的实际监测数据。测量装置由一个嵌入式系统组成，链上连接了14个测斜仪传感器，另外两个节点总共实施了四个约束。所解决的问题是：从测量的梯度实时重建曲线的过约束。这样的系统在结构和/或地面下沉的监测中经常遇到。
This article presents a new platform independent approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the data from an array of sensors forms the forcing function. The algebraic discretization of the problem enables an one-to-one mapping of the ODE to its discrete equivalent linear differential operator, together with an additional matrix equation representing the constraints. The solution of the equation is formulated as a least squares (LS) problem with linear constraints. The LS approach makes the method suitable for the explicit solution of inverse problems where the forcing function is perturbed by noise. The algebraic computation is partitioned into an initial preparatory step, which precomputes the matrices required for the run-time computation, and the cyclic run-time computation, which is repeated with each acquisition of sensor data. The cyclic computation consists of a single matrix-vector multiplication, in this manner computation complexity is known a-priori, fulfilling the definition of a real-time computation. The solution is implemented with model based design and uses only fundamental linear algebra, consequently, this approach supports automatic code generation for deployment on embedded systems. The targeting concept was tested via software-and processor-in-the-loop verification. The method was tested on a laboratory prototype with real measurement data for the monitoring of flexible structures. The measurement arrangement consists of an embedded system with a chain of 14 inclinometer sensors connected to it, two additional nodes implement a total of four constraints. The problem solved is: the real-time overconstrained reconstruction of a curve from measured gradients. Such systems are commonly encountered in the monitoring of structures and/or ground subsidence.