The aircraft hydraulic system units and pipelines heat exchange parameters study

A method of mathematical simulation of the aircraft hydraulic system thermal state is proposed. The mathematical model is a system of partial differential equations for carbon-fiber composite thermal insulation and ordinary differential equations for hydraulic system elements that describe their heat exchange with the air and surrounding surfaces. To solve the direct problem of the hydraulic system elements thermal state, that is, to solve stiff ordinary differential equations, a Rosenbrock-type second order approximation numerical scheme for non-autonomous systems and the solution of a system of partial differential equations, the Monte Carlo method based on a probabilistic representation of the solution in the form of a diffusion process functional expectation were used. The inverse problem of the hydraulic system elements thermal state is solved by the composition of the steepest descent method, the Newton method and the quasi-Newton method of Broyden-Fletcher-Goldfarb-Shanno. A thermal state mathematical model of the hydraulic system unit in an aircraft unpressurized compartment has been developed and the confidence intervals of each of the required model coefficients have been estimated using χ 1 − α 2   at a confidence probability β  = 0.95.