光辐射是核爆能量组成的重要部分,研究其对特种防护材料的损伤具有重要意义。为方便评估特种防护材料在空中核爆光辐射下的损伤情况,基于多种材料激光损伤试验数据和在核爆下的真实损伤数据,结合小子样问题常用的Bootstrap理论,提出基于Bootstrap-TRF混合优化的分段拟合法,拟合出核爆与激光之间对材料损伤的等效关系函数。算法拟合优度R²=0.458 8,测试集平均相对误差仅为26.45%,在高能段(x=5.49×10⁶ J/m²)的预测误差为1.92%,计算时间为18.69 s。对比已有基于Bootstrap理论的3次B-样条插值法和最小二乘支持向量机(LS-SVM)法用于小子样问题研究,算法在拟合优度、误差情况、外推能力及计算效率等方面均具有良好的表现,展示出在光辐射与激光对特种防护材料损伤等效关系函数拟合的有效性和适用性。

Light radiation is an important component of nuclear explosion energy, and studying its impact on special protective materials is of significant importance. To facilitate the assessment of the damage to special protective materials under the light radiation from an airborne nuclear explosion, a hybrid optimization approach based on Bootstrap-TRF segmentation fitting method is proposed. This method is derived from experimental data on laser damage for various materials and real-world damage data from nuclear explosions, combined with the Bootstrap theory commonly used in small sample problems. The algorithm achieves a fitting goodness of R² = 0.458 8, with an average relative error of only 26.45% in the test set. In the high-energy segment (x= 5.49 × 10⁶ J/m²), the prediction error is as low as 1.92%, with a computation time of 18.69 seconds. Compared to existing studies on small sample problems, such as the 3rd-order B-spline interpolation method based on Bootstrap theory and the the LS-SVM (least squares xxxxxxx) method, the proposed algorithm demonstrates strong performance in fitting goodness, error reduction, extrapolation ability, and computational efficiency. It shows significant effectiveness and applicability in fitting the equivalent relationship function of material damage between light radiation and laser.