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A multivariate normal boundary intersection PCA-based approach to reduce dimensionality in optimization problems for LBM process

机译：基于多元法向边界交点的基于PCA的方法来减少LBM过程的优化问题中的维数

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摘要

Laser beam machining (LBM) is a promising manufacturing process that exhibits several desirable quality characteristics. Given a large number of objective functions, the level of complexity increases in an optimization problem. Therefore, this study presents a multivariate application of the normal boundary intersection (NBI) method to reduce dimensionality in optimization problems of the LBM process. Such an approach is capable of exploring the entire solution space with only a small number of Pareto points, and generating equispaced frontiers based on the objective functions written in terms of principal component scores. Hence, a design of experiment with three input parameters and six quality characteristics was undertaken to appropriately model the process requirements applied to AISI 314S steel. The results indicate that the proposed methodology is capable of achieving optimal values for interest characteristics. In addition, this approach shows a reduction in computational effort of approximately 91.89% (from 259 to 21 subproblems) in obtaining the best solution for rough operation.
机译：激光束加工（LBM）是一种有前途的制造工艺，具有几个理想的质量特性。给定大量的目标函数，在优化问题中复杂度会增加。因此，本研究提出了法向边界相交（NBI）方法的多变量应用，以减少LBM过程的优化问题中的维数。这种方法能够仅使用少量的Pareto点来探索整个解决方案空间，并能够根据以主成分分数表示的目标函数生成等距的边界。因此，进行了具有三个输入参数和六个质量特征的实验设计，以适当地模拟应用于AISI 314S钢的工艺要求。结果表明，所提出的方法能够实现利益特征的最优值。此外，这种方法在为粗操作获得最佳解决方案方面显示出将计算工作量减少了约91.89％（从259个子问题减少到21个子问题）。

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