航天器单层板结构弹道极限的支持向量机预测模型

提出了一种基于非线性不可分支持向量机（SVM）方法的航天器单层板结构弹道极限预测模型。利用实验数据对SVM进行训练，建立穿透点和未穿透点的分隔面，进而预测新结构弹道极限特性。SVM的训练问题是以实验点分类正确性为约束，预测置信度最大化为目标的二次规划问题，用Lagrange对偶方法有效求解了该训练问题，并通过附加Lagrange乘子的上限约束处理不可分数据集。引入二次核函数将线性SVM推广到非线性，有效实现了实验点的分类。利用超高速碰撞实验数据对SVM弹道极限预测模型进行了验证，计算对比表明SVM方法有效预测了弹道极限，并且精度高于NASA JSC单层板弹道极限方程。对分离面方程分离变量，建立了基于SVM的弹道极限方程显式表达式。

Support Vector Machine Model for Spacecraft Single Wall Ballistic Limit Prediction

An approach for spacecraft single wall ballistic limit prediction is proposed based on nonlinear nonseparable support vector machine (SVM). The test data are used to train the SVM, and the separation plane of both penetration and non\|penetration points is built. The trained SVM can be used for new case predictions. The training problem of SVM is a quadratic programming problem. The constraint of the optimization is the correctness of the test data classification and the aim of the optimization is maximizing the confidence of the classification. The Lagrangian dual theory is introduced to solve the training problem. With adding the upper boundary to the Lagrangian multipliers, the nonseparable data set is handled. Quadratic kernel function is introduced to extend the SVM approach to nonlinear problem. The test data are effectively classified with the quadratic kernel function SVM. The hypervelocity impact test data are used for the SVM prediction model verification. The results show that the SVM approach is feasible, and the accuracy is higher than NASA JSC single wall ballistic limit equation. By separating the variable of projectile diameter from the classifier equation, the SVM ballistic limit equation is built.