Theoretical studies of the cockpit systems thermophysical parameters using stochastic differential equations Free

A distinctive feature of the aviation technology development in recent years is the quantitative and qualitative complication of on-board equipment, which increases the problem of the cockpit thermal condition. The need to reduce sharply increased volumes of full-scale work related to the assessment and assurance of the cockpit thermal state caused an increase in the role of the cockpit systems thermophysical parameters estimation, which include air flow rates in air conditioning and ventilation systems, the characteristics of electrothermal and jet protection against fogging of the cockpit window, as well as the thickness of the insulation in the cockpit. In this work, a mathematical simulation of the thermal state of a pressurized thermally insulated compartment with honeycomb structures was proposed when solving direct and inverse problems of heat exchange. To solve the direct problem, the Galerkin method with the use of a piecewise linear basis, a second-order approximation Rosenbrock-type numerical scheme for non-autonomous systems, a combined walk-on-the-spheres method, and the Euler method were used. The inverse heat transfer problem solution is carried out by the quasi-Newton method of Broyden – Fletcher – Goldfarb – Shanno in combination with the Newton method. Confidence intervals of parametric identification estimates are determined using the covariance matrix of parameters estimate errors and quantile χ2 - probability distribution 1-α. The evaluation of required values of the air flow in the air conditioning and ventilation systems, the characteristics of the electrothermal and jet protection against fogging of the cockpit window, as well as the thickness of the insulation in the cockpit of a passenger aircraft was carried out.