Recently, data-driven soft sensor has been a popular research focus in the field of process system engineering. Modern industrial processes tend to be large scale, highly complicated, and nonlinear. As a result, process data gradually become high-dimensional. Therefore, it is difficult to achieve acceptable modeling accuracy using basic data-driven methods. To handle this limitation, a novel data-driven model using improved whale optimization and regularization-based functional link neural network (FLNN) is proposed. In the proposed model, regularization is first used to overcome the problems of structure risk and overfitting during the training phase of FLNN, thereby improving its ability to deal with the complex process data; to simplify the calculation, a radial basis function (RBF)-based kernel is selected to reconstruct the expanded inputs; meanwhile, an improved whale optimization algorithm (WOA) is utilized to optimize the parameters of the regularization and RBF kernel. Finally, novel regularized FLNN based on WOA and RBF kernel (WOA-RBFRFLNN) can be developed. To verify the modeling performance of WOA-RBFRFLNN, a case study on the purified terephthalic acid (PTA) industrial process is conducted. Simulation results show that the presented WOA-RBFRFLNN model can achieve high accuracy, indicating that the feasibility and effectiveness of the proposed WOA-RBFRFLNN are confirmed.

中文翻译：

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使用改进的鲸鱼优化和基于正则化的功能链接神经网络进行软传感器开发

近年来，数据驱动的软传感器已成为过程系统工程领域的热门研究重点。现代工业过程倾向于大规模，高度复杂和非线性。结果，过程数据逐渐变为高维。因此，使用基本的数据驱动方法很难达到可接受的建模精度。为了解决这个限制，提出了一种使用改进的鲸鱼优化和基于正则化的功能链接神经网络（FLNN）的新型数据驱动模型。在提出的模型中，首先使用正则化来克服FLNN训练阶段的结构风险和过拟合问题，从而提高了其处理复杂过程数据的能力。为了简化计算，选择了基于径向基函数（RBF）的内核来重构扩展的输入。同时，采用改进的鲸鱼优化算法（WOA）对正则化和RBF内核参数进行优化。最后，可以开发基于WOA和RBF核的新型正则化FLNN（WOA-RBFRFLNN）。为了验证WOA-RBFRFLNN的建模性能，以精制对苯二甲酸（PTA）工业流程为例进行了研究。仿真结果表明，所提出的WOA-RBFRFLNN模型可以达到较高的精度，表明所提出的WOA-RBFRFLNN模型具有可行性和有效性。以精对苯二甲酸（PTA）工业过程为例进行了研究。仿真结果表明，所提出的WOA-RBFRFLNN模型可以达到较高的精度，表明所提出的WOA-RBFRFLNN模型具有可行性和有效性。以精对苯二甲酸（PTA）工业过程为例进行了研究。仿真结果表明，所提出的WOA-RBFRFLNN模型可以达到较高的精度，表明所提出的WOA-RBFRFLNN模型具有可行性和有效性。