大数据时代，随着计算机性能的进步和人工智能的不断发展，数据科学快速兴起。近年来，数据驱动的统计学习方法在许多工程学科中越来越受欢迎。传热领域涉及许多复杂的非线性问题，依据传统的热力学方法是难以解决的，统计学习方法逐渐成为研究人员和工程师更好地理解基本传热现象和优化系统设计的新工具。

再入飞行器的高温热防护是一类引起广泛关注的传热问题。随着航天工程的进一步发展，热防护材料性能的提升已是迫在眉睫，利用统计学习方法优化材料结构进而提升材料性能是一个值得探索的研究方向。本文研究了材料结构与性能之间的量化关系，主要成果概括如下：

建立了基于反向前馈神经网络的烧蚀传热模型。首先，提出了基于能量守 恒、质量守恒和阿伦尼乌斯方程等数学传热模型的数值模拟方法，对硅基复合材料H41N 的高温传热过程进行了模拟。模拟结果与实验数据吻合较好，最大偏差不超过 11.01%。其次，基于此数值模拟方法构建数据集，并采用反向前馈神经网络对孔隙率的分段式分布与冷壁面温度之间的相关关系进行量化。结果表明，反向前馈神经网络模型表现出非常好的性能，在不同段数下 R² 均可达到 0.999 以上，这也说明使用统计学习方法对材料结构与性能之间的关系进行量化十分有效。

基于非线性规划方法优化了材料的热防护性能。首先，以孔隙总量相同为前提，使用非线性规划方法求得优化的孔隙率分布。然后，将具有优化分布的烧蚀器与传统的均质烧蚀器及两个孔隙度分布呈递增和递减等差数列的对照组烧蚀器进行比较。结果表明，优化烧蚀器的热防护性能获得较大提升。使用统计学习方法合理优化孔隙率分布可以进一步提高材料利用率，从而提高复合材料的热防护性能。

本文的研究成果对于再入飞行器热防护系统的量化设计具有一定的指导意义。

In the era of big data, with the progress of computer performance and the continuous development of artificial intelligence, data science is rising rapidly. In recent years, data-driven statistical learning methods have become increasingly popular in many engineering disciplines. The field of heat transfer involves many complex nonlinear problems that are difficult to solve based on traditional thermodynamic methods. Statistical learning methods are gradually becoming a new tool for researchers and engineers to better understand the basic heat transfer phenomena and optimize system design.

The high temperature thermal protection of reentry vehicle is a kind of heat transfer problem which has attracted wide attention. With the further development of aerospace engineering, it is imminent to improve the performance of thermal protection materials. It is the general trend to use statistical learning methods to optimize the structure and improve the performance of materials. This paper studies the quantitative relationship between material structure and properties. The main achievements are summarized as follows:

An ablative heat transfer model based on back propagation neural network was established. Firstly, a numerical simulation method based on energy conservation, mass conservation and Arrhenius equation was proposed to model the heat transfer process of silicon matrix composites. The simulation results are in good agreement with the experimental da- ta, and the maximum deviation is less than 11.01%. Secondly, a simulated data set was constructed, and the relationship between the piecewise porosity distribution and bondline temperature was quantified by using the back propagation neural network. The results show that the back propagation neural network model shows very good performance, R² can reach 0.999 under different number of segments, which also indicates that the use of statistical learning method to quantify the relationship between material structure and performance is very effective.

The thermal protection performance of the material was optimized based on nonlinear programming method. Firstly, on the premise of the same total pore, the optimized porosity distribution was obtained by using nonlinear programming method. Then, for the purpose of evaluating the thermal protection performance of the optimized scheme, two additional ablators distributed in arithmetic sequences and one traditional homogeneous ablator was compared with the optimized ablator. The results show that the thermal protection performance of the optimized ablator is greatly improved. Thus adopting statistical learning method to optimize the porosity distribution can further improve the utilization rate of materials and the thermal protection performance of composites.

The research results of this paper have certain guiding significance for the quantitative design of thermal protection system of reentry vehicles.