In this paper, we consider the online regularized pairwise learning (ORPL) algorithm with least squares loss function for non-independently and identically distribution (non-i.i.d.) observations. We first establish new Bennett’s inequalities for [Formula: see text]-mixing sequence, geometrically [Formula: see text]-mixing sequence, [Formula: see text]-geometrically ergodic Markov chain and uniformly ergodic Markov chain. Then we establish the convergence rates for the last iterate of the ORPL algorithm with the polynomially decaying step sizes and varying regularization parameters for non-i.i.d. observations. These established results in this paper extend the previously known results of ORPL from i.i.d. observations to the case of non-i.i.d. observations, and the established result of ORPL for [Formula: see text]-mixing can be nearly optimal rate of ORPL for i.i.d. observations with [Formula: see text]-norm.

The thermal structure characteristic of the Solid Rocket Motor (SRM) nozzle component under thermal and flow field is investigated by finite element method (FEM). The sensitivity of contact parameter of friction coefficient between multi-layer structures on thermo-structure coupled simulation is priority analyzed and the individual test of the friction coefficient between real material of carbon/carbon material and molded asbestos/phenolic material with temperature under real work condition is also designed. The numerical results and the experimental conclusions can provide some important value to the reliability design of nozzle thermal structure.

AbstractͶWhen the nozzle is working, there is large amount of hot gas at the interface of the carbon-carbon(C/C) exit-cone because of the pyrolysis of insulator. The hot gas may cause high pressure which may impact the reliability of the joint structure. So the high temperature and pressure measurement were developed to measure the temperature and pressure at the interface of the C/C exit-cone and the insulator. The result shows that the hot gas makes pressure at the interface of the C/C exitcone. Different exit-cone materials, pressures are different. The higher the density of the C/C material, the higher is the pressure. The effect of the pyrolysis hot gas to the reliability of the joint structure was also analyzed.