EFP尺寸优化数学方法和爆轰成型过程探讨

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摘要: 结合优化设计的若干方法，从结构尺寸优化角度对爆炸成型侵彻体（Explosively Formed Penetrators ---简称EFP）的尺寸实现优化，在优化分析的基础上，对EFP的药型罩在爆炸成型过程中的几个典型瞬态进行了理论分析，探讨了可以描述EFP爆炸成型效果的估计模型。本文的主要研究内容包括：62943

（1）结合灰色系统中灰关联度理论，通过几何建模，运用变尺度二次规划算法对在两个正交截面内均有尺度变化的药型罩优化。对整个EFP系统构造了一个包含二重分辨系数的优化函数Z，实现对药型罩、外壳、炸药的同步优化，避免只对药型罩、外壳、炸药单独优化并直接组合优化结果产生的系统耦合误差。提出了折算等效关联度概念，在计算分辨系数时从统计角度对灰关联度矩阵的元素实行严格的归一化处理。

（2）利用整体近似方法，结合卡尔曼滤波技术对EFP优化设计模型进行了分析。从尺寸优化的角度构建了EFP卡尔曼滤波模型的预测方程，用曲线拟合的方法构建了对应的观测方程，建立了EFP卡尔曼滤波模型的迭代方程。实验结果表明人为构建的预测方程只能起到较好的迭代作用，而不具有较好的滤波作用。

（3）将GM（n.h）模型融入到卡尔曼滤波方法中，对EFP仿真得到的具有非负性、递增性的历史数据列进行卡尔曼滤波建模。结果表明，结合灰色GM（n,h）模型建立的卡尔曼滤波模型对历史数据具有很好的拟合效果，在历史数据的有限递增数据段，该模型对EFP的设计变量有很好的优化效果。

（4）从爆轰成型的角度分析了EFP在爆炸成型过程的若干瞬态过程。将已成型的EFP分成头部、中段密实部、尾段开裂部三个部分，通过几何建模和力学建模模拟了EFP从爆轰初时到翻转再到金属流动、拉伸闭合最后形成成型侵彻体这一系列过程。借助EFP上各点的速度模型和各点的爆轰驱动泰勒角模型估算了EFP头部的长度，借助流体刚性壁冲击模型估算了EFP中段密实部分长度和直径，借助材料应变模型估计了尾部的开裂效果。

毕业论文关键词：爆炸成型侵彻体，瞬态过程，灰色系统，耦合误差，归一化，整体近似，卡尔曼滤波，灰色GM（n,h）模型，微分方程，爆轰驱动

Abstract:

This paper realized EFP (Explosively Formed Penetrators) optimization by using several methods of optimizing design from structural and size perspective. Finally, based on optimization work, this paper gives more analysis on the EFP liner collapse process during the detonation by deep study of several typical transient processes. The followings are the main contents of this dissertation:

(1)Combined with the theory of grey correlation degree, this paper designed variable scale quadratic programming algorithm and successfully applied it to the optimization of a new kind of EFP liner which has scale changes in all two orthogonal cross sections. An optimization function Z was constructed with a double resolution coefficient in it so as to realize synchronization optimization in only single one objective function for the liner, shell cover and explosive. To avoid system coupling error caused by directly combinatorial optimization results from single optimization for each component. This paper puts forward the concept of translation equivalent relation without directly take the grey correlation matrix elements as the resolution coefficient. In the calculation of resolution coefficient, normalization processing was strictly implemented for the grey correlation matrix elements.

(2)By means of global approximation method, Calman filtering technology has been used to analyze the EFP optimization design model. This paper constructs a prediction equation from the optimization point of view and an observation equation by curve fitting method. And experimental results show that the artificially constructed prediction equation has better function of iteration but inefficiency in filtering. And the results may not have practical significance beyond the scope of the simulation of historical data range.