计算机控制光学抛光驻留时间求解中两类优化算法的分析
Analysis of dwell time algorithm based on optimization theory for computer controlled optical surfacing
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摘要: 建立了基于矩阵计算的驻留时间计算模型，根据实际加工要求建立了最小二乘和最佳一致逼近最优化求解数学模型，总结了两类优化问题的求解方法。根据自研数学解法器，利用数值计算分析了这两类算法的计算特点。仿真结果显示，两种自研算法具有较高的计算精度，最小二乘逼近算法计算效率有待提高，对外界扰动和计算模型等误差不敏感,最佳一致逼近算法计算效率较高，但对误差比较敏感。实际加工时，如果面形精度已经比较高时，建议多采用最小二乘逼近算法。
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关键词:
- 计算机控制光学表面成形技术 /
- 驻留时间 /
- 优化算法 /
- 最小二乘法 /
- 最佳一致逼近
Abstract: A mathematical model of the dwell time algorithm based on the optimization theory and matrix equation was established, which aims to minimize the 2-norm or -norm of the residual surface error. In the theory, the dwell time solution meets almost all the requirements of precise computer numerical control (CNC) without any need for extra data processing. Several practical methods were discussed on how to solve the optimization model and obtain an optimal solution. Also analyses of the two algorithms were performed in this paper. The simulations show that both of the two algorithms have high precision. The computation efficiency is crucial for least squares algorithms because it is lower for large computation models. The least squares algorithm is numerically robust, whi -
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