This paper has proposed a parameter estimation method for a laser welding process inherently highly nonlinear as a result of the highly nonlinear inputs and outputs of the system. Hence, a nonlinear system identification method was developed for the laser welding process using the wavelet network nonlinear autoregressive exogenous (ARX) model. The advantage of ARX over the standard nonlinear models is that it not only considers the delayed input and output regressors but also uses nonlinear functions for mapping, thus making ARX a better candidate for the prediction of nonlinear behaviors. In total, nine available datasets for the training and test phases at pulse durations, pulse frequencies, focal lengths, currents, and welding speeds were considered. Five inputs including pulse duration, pulse frequency, focal length, current and welding speed, and temperature as one output were considered. The first eight datasets were utilized for the training phase and one was used for the testing phase. The results showed that the ARX model had an acceptable performance in training and test phases, and it was capable of identifying the nonlinear and time-variant phenomenon of the laser welding process examined in this paper. For instance, most fitness values for austenitic and ferritic steel samples in the training time histories were 97.13 and 97.95, respectively.

中文翻译：

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AISI 304和AISI 420异种激光焊接熔合区温度分布预测：小波网络非线性ARX模型

由于系统的高度非线性输入和输出，本文提出了一种用于激光焊接过程固有高度非线性的参数估计方法。因此，使用小波网络非线性自回归外生 (ARX) 模型为激光焊接过程开发了一种非线性系统识别方法。ARX 相对于标准非线性模型的优势在于它不仅考虑了延迟输入和输出回归量，而且还使用非线性函数进行映射，从而使 ARX 成为预测非线性行为的更好候选者。总共考虑了脉冲持续时间、脉冲频率、焦距、电流和焊接速度的训练和测试阶段的九个可用数据集。五个输入，包括脉冲持续时间、脉冲频率、焦距、电流和焊接速度，和温度作为一种输出被考虑。前八个数据集用于训练阶段，一个用于测试阶段。结果表明，ARX 模型在训练和测试阶段具有可接受的性能，并且能够识别本文研究的激光焊接过程的非线性和时变现象。例如，训练时间历史中奥氏体和铁素体钢样品的大多数适应度值分别为 97.13 和 97.95。它能够识别本文研究的激光焊接过程的非线性和时变现象。例如，训练时间历史中奥氏体和铁素体钢样品的大多数适应度值分别为 97.13 和 97.95。它能够识别本文研究的激光焊接过程的非线性和时变现象。例如，训练时间历史中奥氏体和铁素体钢样品的大多数适应度值分别为 97.13 和 97.95。