基于线性代数和正则化方法的驻留时间算法

Dwell time algorithm based on matrix algebra and regularization method

将加工的数学模型由去除函数与驻留时间的卷积过程转变为去除矩阵与驻留时间向量的乘积过程,从而将驻留时间的计算变为线性方程的求解。因测量误差而引入的噪声导致了方程的病态,传统的数值计算方法失效,因此,用Tik-honov正则化对建立的模型进行求解。采用了无须任何先验知识的自适应方法选取正则化参数。对同一组数据采用其他的驻留时间算法进行计算并对比,精度提高了30%以上。最后对一组面形数据使用实际参数进行了模拟加工,加工后的PV、RMS的收敛比率分别达到0.48,0.62,满足实际驻留时间的求解要求。该方法稳定收敛,精度高,设置灵活,是一种较实用的驻留时间算法。

A novel algorithm to solve dwell time based on linear algebra (matrix-based algorithm) is discussed, in which math model changes the fabrication process from convolution to matrix product, so that the calculation of the dwell time becomes a solution to linear equations. Traditional factorization methods such as Gaussian elimination and total least squares can not be used because the linear equations are severely ill condition. So, the Tikhonov regularization is used to solve the ill-posed problem caused by meterage error, and the regularization parameter is determined adaptive method without any prior knowledge. By comparing with different algorithms, the advantages of the matrix-based algorithm are obviously with the precision enhancing 30%. In the end, an error data is solved with actual parameters using the matrix-based algorithm. The simulation results show that the convergence rates of the PV and RMS values can reach up to 0.48 and 0.62, respectively. The matrix-based algorithm can satisfy the requirement of fabrication very well.