TY - GEN

T1 - An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems

AU - Gugg, Christoph

AU - Harker, Matthew

AU - O'Leary, Paul

AU - Rath, Gerhard

PY - 2015/8/26

Y1 - 2015/8/26

N2 - 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.

AB - 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.

UR - http://10.1109/HPCC-CSS-ICESS.2015.50

M3 - Conference contribution

SP - 1097

EP - 1102

BT - 12th IEEE International Conference on Embedded Software and Systems

PB - Institute of Electrical and Electronics Engineers

T2 - 12th IEEE International Conference on Embedded Software and Systems

Y2 - 24 August 2015 through 26 August 2015

ER -