The development of low-cost sounding rockets is considered highly significant for the accurate acquisition of in-situ atmospheric data in near-space environments and the enhancement of the strike accuracy of medium- to long-range missile weapons. However, sounding rockets are often designed as uncontrolled, self-stabilizing rockets, which may be affected by atmospheric wind fields, design flaws, and manufacturing errors during flight missions. This can result in rocket instability or flight altitudes that do not meet design specifications. Therefore, a quantitative uncertainty analysis of the flight performance parameters of sounding rockets is conducted. The impact of different flight environments and rocket parameter deviations on the actual flight performance of sounding rockets is calculated. An evaluation is conducted to determine whether the flight performance parameters, such as the maximum trajectory height, maximum angle of attack, sideslip angle, and maximum dynamic pressure, meet the design requirements under the influence of uncertainties during actual flight. This analysis is used to provide reliable references for actual flight missions.

In this study, the coupling relationships among various rocket disciplines were analyzed, and a multi-disciplinary integrated simulation process for low-cost sounding rockets was established, enabling efficient computation of flight performance. The uncertainty propagation analysis problem of flight performance was addressed by conducting research based on dynamic augmented sampling and surrogate modeling. A bounded sequential augmented Latin hypercube experimental design scheme was proposed, facilitating efficient acquisition of training data for different random variables. An improved augmented radial basis hybrid approximate model was developed and applied to uncertainty propagation analysis. Through dynamic augmented sampling, an uncertainty bias model was established, and the improved hybrid approximate model was used to predict the characteristic parameters of rocket flight performance. Finally, the precision of the predictions was compared with the results obtained from the traditional MCS method to validate the effectiveness of the proposed approach.

In this study, an augmented radial basis function approximate model, based on 200 sample points, was used to predict the flight performance of sounding rockets. The statistical values of the predictions were found to be close to those obtained from 5,000 flight simulations using the MCS method. From the experimental data comparison, it was observed that the prediction accuracy of the statistical mean of the flight performance parameters could reach levels of 1% or even 0.1‰ and the prediction accuracy of the standard deviation could be controlled within 10%. This indicates that an approximate model built using 200 flight simulation samples can achieve high-precision predictions of the statistical values of the flight performance parameters of sounding rockets, with accuracy comparable to that obtained from 5,000 Monte Carlo simulations. Additionally, as the number of samples increases, the ARBF approximate model can be dynamically updated using the BRELHD method, facilitating the assessment of the feasibility of the prediction results.

In this study, the problem of uncertainty propagation analysis for the flight performance of sounding rockets was addressed by investigating a method based on dynamic augmented sampling and surrogate modeling. A bounded sequential augmented Latin hypercube experimental design scheme was proposed for uniform sampling of different distribution random variables, enabling efficient acquisition of training data for different random variables. To enhance the generalization performance of the approximate model, the advantages of both PCE and RBF models were leveraged to establish an improved augmented radial basis hybrid approximate model, which was applied to the uncertainty propagation analysis of sounding rockets. Through dynamic augmented sampling, an uncertainty bias model was established, and the improved hybrid approximate model was used to predict the characteristic parameters of the rocket's flight performance. Finally, the algorithm's accuracy was compared with the results obtained from the traditional MCS method, demonstrating the effectiveness of the uncertainty propagation method for the flight performance of sounding rockets developed in this research.

In the complex engineering design problems represented by aircraft design, in order to improve the design performance, reduce the development cost and shorten the design cycle, it is usually necessary to optimize the product performance, cost and other design indexes. At the same time, in order to improve the credibility of simulation results, high time-consumption simulation models are more and more widely used in actual engineering design, while the improvement of model simulation accuracy leads to an exponential increase in simulation time, resulting in an increase in computational cost and a decrease in optimization efficiency. Therefore, surrogate-based optimization methods are introduced to achieve the goal of reducing design, analysis and computational consumption. In practical engineering problems, it is necessary to combine with constraint handling methods to obtain the optimal feasible solution that satisfies the constraints. After the introduction of constraints, complex factors such as the type of constraints, the number of different constraints, the size of the feasible domain, the number of valid constraints, etc. can lead to problems such as reduced efficiency of the optimization algorithm and difficulty in searching for the globally optimal solution. Therefore it is necessary to conduct research for constraint handling methods.

The feasibility rule method is easy to implement and does not require tedious parameter tuning, but ignores the ability of high-quality infeasible solutions to explore the boundary of the feasible domain. Especially for the surrogate models optimization problem, it is difficult to get a more accurate solution at the early stage of optimization, and the high-quality infeasible solutions near the feasible domain can improve the accuracy of the models on the constraint boundaries and enhance the algorithm's ability to explore the boundary of the feasible domain. Therefore, the idea of ε-constraint holding is proposed, where the feasible domain is enlarged at the early stage of optimization, and as the algorithm iterates, the feasible domain shrinks until it coincides with the real feasible domain. As the infeasible solutions with smaller constraint conflicts are added to the sample set constructed by the surrogate models in the pre-optimization stage, the accuracy of the constraint boundary surrogate models is improved, which can better support the algorithm to explore the boundary of the feasible domain.

When performing the test algorithms, more than 25 independent runs are performed for each of the algorithms to ensure the stability of the results. The optimization results are compared with the Chaotic grey wolf optimization method, The extended balanced ranking method and Modified global best artificial bee colony method published in recent years. The proposed CDRAO (constraints dynamic relaxation approximate optimization) algorithm is a constrained optimization algorithm with superior performance and possesses the potential for complex engineering constrained optimization applications. The CDRAO method is used to optimize the solid rocket motor charge design, the optimization objective is the stability of the combustion surface during the combustion process of the pillars, and the constraints are the mass of the pillars of the motor, and the results also verify the effectiveness of the algorithm.

In order to address the problem of optimal design of high time-consuming models, the adaptive sampling phase of surrogate models is investigated. Considering various types of constraints on the objective function, a multi-constraint adaptive sampling method is proposed, and the proposed method is verified by mathematical and engineering examples.