Some remarks on the determination of unknown parameters in large nonlinear systems- a problem in spacecraft thermal test evaluation

Abstract

As a special case of large nonlinear systems with many imprecisely known parameters, this paper considers the thermal behaviour of a spacecraft. It is simu lated in the steady state by a mathematical model consisting of a system of nonlinear equations and in the transient state by a system of nonlinear differ ential equations. The system contains a large number of parameters, many of which cannot be calculated or measured directly with satisfactory precision. The estimated parameters of the initial mathematical model can be improved by analysing the results of thermal tests performed on the spacecraft itself. The objective is to minimize the differences between measured and calculated temperatures. Since the temperatures are nonlinear functions of many para meters, the minimization is a difficult task. Methods which transform the nonlinear functions into linear ones may not result in the minimization of the temperature deviations. The major disadvantage of linearizing methods is the restriction of the validity of the first-order terms to the vicinity of the point about which the linearization was made. Therefore there cannot be a universal, straightfor ward procedure to evaluate a great number of unknown parameters in complex nonlinear systems. Engineering methods for special solutions need to be developed and made as general as ingenuity can make them.