基于降维算法和等效杆长的可展结构精度分析

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。

Precision analysis of deployable structures based on dimension reduction method and effective link length

The uncertainties of joint clearances and link length errors are studied by the method of probability and statistics.A precision analysis method for deployable structure is proposed based on Univariate Dimension Reduction Method (UDRM) and effective link length model.Using the UDRM,the precision function for the deployable structure is decoupled into a combination of independent effects of multiple link length errors to establish the precision analysis model for the structure.The effective link length model is applied to replace the original link length for precision calculation.The effective model converts the joint clearances and link length errors into effective link length errors,which are proved to follow normal distributions.An example of deployable antenna is given to calculate the means and variances in the deployable state with the Gauss quadrature based on the error distributions of link lengths and joint clearances.The correctness and effectiveness of the precision analysis method is verified by comparing the results of Monte Carlo Simulation (MCS) and First Order Second Moment (FOSM) method.