In this study, the characteristics of different intelligent algorithms, from the simulated annealing algorithm (SA) and genetic algorithm to the quantum genetic algorithm, are analyzed. By utilizing the variety of the population and the rapidity of the convergence of the real double-chain coding objective gradient quantum genetic algorithm, this algorithm is fused with SA; the resulting real double-chain coding objective gradient quantum genetic simulated annealing algorithm is proposed. As the performance of the least squares support vector regression (LSSVR) is very sensitive to its key parameters, the proposed algorithm is applied to optimize these parameters to improve the generalization ability of LSSVR. Following that, a new hybrid nonparametric regression prediction model is put forward. The health monitoring of a liquid-fuel rocket engine is a very important topic, and all types of sensors are used to monitor the factors that can affect the engine thrust from different aspects. The relationship between the thrust and these factors is nonlinear and difficult to express using some formulas. The proposed model is used in the fault prediction of liquid-fuel rocket engine thrust, and the simulation results show that the average relative error is determined to be 0.37% using LSSVR and 0.2977% using the proposed model. Thus, this model is applicable to small samples, nonlinearity, and high dimensions of failure prediction, and is worth promoting to a certain extent.