Nodal Temperature Estimation Algorithms for Nonlinear Thermal Network Models

Algorithms for estimating temperatures at arbitrary nodes of steady-state thermal network models, given noisy measured values of a subset of the nodes of the network, are described. Applications where temperature estimation is desired include correlation of test and analysis results, thermal-stress estimation, and others. An optimization problem is formulated to recover the temperatures at the unobservable nodes. This problem is an example of nonlinear, least-squares minimization with a single quadratic constraint (imposed by the measured data) and is solved with the method of Lagrange multipliers. New algorithms are developed that find local minima of the cost functional through a Newton-type iteration procedure. At each iteration a least-squares problem with a quadratic inequality is solved with a fast and memory-efficient method. The proposed algorithms are shown to be at least an order of magnitude faster than standard algorithms. Their accuracy and speed are examined through a series of tests on thermal models from ongoing NASA missions