Optimization methods are widely used to improve industrial processes and enhance the quality characteristics of product, where process costs are directly linked. Given this assumption, this study aims to present a multivariate proposal of the Taguchi loss function, to model and optimize manufacturing processes, searching to establish values that prioritize quality and provide the minimum loss in view of the process costs. For this, design of experiments techniques will be used to model the process and the calculated loss functions. The strategy of principal components analysis is used to minimize the data dimension, considering the structure of variance–covariance. Then, the normal boundary intersection method is used to find the Pareto frontier. Based on the values, the method also proposes a total loss function equation, which is characterized as an approach to choose the optimal point based on the sum of the loss functions for the Pareto frontier through the process cost. To demonstrate the behavior of the method, the flux-cored arc welding of stainless-steel cladding process was applied. In view of the results, the method provided an optimal value at the Pareto frontier, contemplating an appropriate balance between minimal loss and higher quality, which were compared with other studies in the literature. The method also provided a reduction in computational effort of approximately 90% (from 210 to 21 subproblems), obtaining the best solution and contemplating the multivariate nature of the data.

中文翻译：

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基于主成分分析和正态边界交叉的多元田口损失函数优化

优化方法被广泛用于改进工业过程和增强产品的质量特性，其中过程成本直接相关。鉴于这一假设，本研究旨在提出田口损失函数的多变量建议，对制造过程进行建模和优化，寻找建立优先质量的值，并鉴于过程成本提供最小的损失。为此，将使用实验设计技术对过程和计算的损失函数进行建模。考虑到方差-协方差的结构，使用主成分分析的策略来最小化数据维度。然后，使用法线边界相交方法来寻找帕累托边界。基于这些值，该方法还提出了一个总损失函数方程，它的特点是通过过程成本，根据帕累托边界的损失函数的总和来选择最佳点的方法。为了证明该方法的行为，应用了不锈钢包覆工艺的药芯电弧焊。鉴于结果，该方法在帕累托边界提供了一个最佳值，考虑了最小损失和更高质量之间的适当平衡，并将其与文献中的其他研究进行了比较。该方法还将计算工作量减少了大约 90%（从 210 个子问题减少到 21 个子问题），从而获得了最佳解决方案并考虑了数据的多元性质。为了证明该方法的行为，应用了不锈钢包覆工艺的药芯电弧焊。鉴于结果，该方法在帕累托边界提供了一个最佳值，考虑了最小损失和更高质量之间的适当平衡，并将其与文献中的其他研究进行了比较。该方法还将计算工作量减少了大约 90%（从 210 个子问题减少到 21 个子问题），从而获得了最佳解决方案并考虑了数据的多元性质。为了证明该方法的行为，应用了不锈钢包覆工艺的药芯电弧焊。鉴于结果，该方法在帕累托边界提供了一个最佳值，考虑了最小损失和更高质量之间的适当平衡，并将其与文献中的其他研究进行了比较。该方法还将计算工作量减少了大约 90%（从 210 个子问题减少到 21 个子问题），从而获得了最佳解决方案并考虑了数据的多元性质。