Confidence Intervals for Identification Parameters of Heat Exchange Processes in Aircraft Instrument Compartments

Uncertainty of estimating the parameters of the aircraft compartments heat exchange mathematical model requires the use of a joint confidence region for estimating the model parameters. The joint confidence regions of parameter estimates describe in the model parameter space the r- dimensional ellipsoid with the center in the vector of the model parameters actual values, where $r$ is the number of model parameters. In the case of a large dimension of the parameter vector, the use of the joint confidence region is associated with computational difficulties. Therefore, conditional joint confidence intervals of each required parameters are introduced in the form of projections of the joint confidence region on the corresponding coordinate axes of the parameter space, which is equivalent to replacing the elliptical region by the parallelepiped circumscribed around it. In recent two or three decades, with the emergence of a powerful supercomputer technology, new possibilities for the numerical solution of the time-consuming tasks, including multidimensional ones, have opened up. Due to the fact that the Monte-Carlo methods are parallelized with a good measure of effectiveness and compared with other methods they are far less sensitive by labor intensity to the dimension of problems increase, they become more competitive. In particular, multi-dimensional problems for parabolic equations on the basis of probabilistic concepts of their decisions can be solved by the method of statistical modeling. Among other things, it is possible to solve inverse problems of the thermal state of the aircraft fuselage honeycomb core and grid constructions using the parabolic boundary value problem with discontinuous coefficients basing on the numerical solution of stochastic differential equations with the use of derivatives assessments on the expected functional parameters of the diffusion processes.