Program Predicts Temperatures at Nodes of a Thermal Network

Node Prediction for Thermal Networks (NOPTHER) is a computer program that predicts steady-state temperatures at un- observed nodes of a thermal network, given noisy values of the temperatures measured at observed nodes. The program is based partly on modeling of the heat fluxes among nodes as sums of external heat loads, conduction terms (products of conduction coefficients and differences among nodal temperatures), and radiation terms (products of radiation coefficients and differences among the fourth powers of nodal temperatures). The temperature-prediction problem is formulated as an optimization problem — more specifically as a nonlinear least-squares minimization problem with a single quadratic constraint imposed by the measured temperatures. The problem is solved by the method of Lagrange multipliers. NOPTHER incorporates algorithms that find local minima of a cost functional through Newton iteration. What distinguishes these algorithms from other such algorithms is that they exploit specific characteristics of the temperature-prediction problem that enable the use of a fast and memory-efficient computational method. The algorithms have been shown to be at least an order of magnitude faster than are prior algorithms used for the same purpose.