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考虑铰链间隙和杆件尺寸误差的不确定性并通过概率统计方法对其进行研究,提出了一种基于单变量降维算法(UDRM)和等效杆长模型的可展结构精度分析方法。利用UDRM将可展结构的精度性能函数解耦为多个杆件尺寸误差的独立作用形式,建立精度分析模型。引入等效杆长模型,等效杆件替代原杆件进行精度计算。将铰链间隙与原始杆件尺寸误差合并到等效杆件的尺寸误差中,同时证明了等效杆长尺寸误差近似服从正态分布。以某卫星可展开天线为算例,结合高斯求积公式求解展开状态下精度指标的分布期望和方差。通过与蒙特卡罗模拟(MCS)和一次二阶矩(FOSM)法计算结果的对比验证了本文精度分析方法的正确性和高效性。
Considering the uncertainty of the hinge clearance and the dimension error of the bar, the paper studies the probabilistic statistical method, and presents an expandable structure accuracy analysis method based on univariate dimensionality reduction (UDRM) and equivalent rod length model. UDRM is used to decouple the precision performance function of the expandable structure into the independent action form of multiple rod dimensional errors and establish the precision analysis model. The equivalent rod length model is introduced, and the equivalent rod is replaced by the original rod to calculate the precision. The error between the hinge clearance and the original rod size is incorporated into the dimensional error of the equivalent rod. At the same time, it is proved that the equivalent length error of the rod approximately obeys the normal distribution. Taking an example of a deployable satellite, the Gaussian quadrature formula was used to solve the distribution expectation and variance of the accuracy index in the unfolded state. The accuracy and efficiency of the proposed method are verified by comparison with Monte Carlo simulation (MCS) and first-order second-order moments (FOSM).