Aluminum electrolysis cells are characterized by harsh environments where several measurements have to be done manually. Due to the operational costs related to manual sampling, the sampling rates of these measurements are low. Therefore, the information in the data can be limited, making it challenging to develop robust data-driven methods for aluminum electrolysis process. A broad array of physics-based models have been developed throughout the years to provide excellent system knowledge about the dynamics in the aluminum electrolysis cells. However, due to highly complex and interrelated sub-processes, the state-of-the-art physics-based models are insufficient to accurately express the dynamics in the cell. The combination of inadequate prediction models and low sampling rates makes estimating process variables in the aluminum electrolysis process less accurate than what is desired for optimal and safe operation of the cells. In this paper, a novel hybrid modeling approach that addresses insufficient prediction models and low sampling rates is suggested. The novel hybrid modeling approach involves manipulating a measured signal with a first principle model estimate. This manipulation, which consists of subtracting the first principle model estimate from the measurements of the signal, produces a residual that represents the unmodeled dynamics in the signal. Since the unmodeled dynamics of the measured signal is much sparser than the measured signal itself, this manipulation enables utilizing a powerful technique for estimating sparse signals from only a few measurements. The technique is called compressed sensing. The manipulated data is used as input data in a compressed sensing algorithm which produces a high fidelity estimate of the unmodeled dynamics in the original signal. Thus, the novelty in this article is two-fold. First, compressed sensing is introduced to the field of aluminum electrolysis. Second, the novel technique of sparsifying a measured signal with a first principle model in order to utilize compressed sensing on the measured data is introduced. The signal estimate of the unmodeled dynamics is integrated into an Extended Kalman filter as a pseudo measurement to improve the estimation of the system states. The novel method applies to signals with stationary periodical unmodeled dynamics. The case study in this article is conducted on simulated data of a sub-process describing the mass balance in an aluminum electrolysis cell.

铝电解槽的特点是环境恶劣，必须手动进行多次测量。由于与手动采样相关的运营成本，这些测量的采样率很低。因此，数据中的信息可能是有限的，这使得为铝电解过程开发稳健的数据驱动方法具有挑战性。多年来，已经开发了大量基于物理的模型，以提供有关铝电解槽动力学的出色系统知识。然而，由于高度复杂和相互关联的子过程，最先进的基于物理的模型不足以准确表达细胞中的动力学。不适当的预测模型和低采样率的结合使得铝电解过程中的过程变量估计不如电解槽最佳和安全运行所需的准确。在本文中，提出了一种新颖的混合建模方法，可以解决预测模型不足和采样率低的问题。新颖的混合建模方法涉及使用第一原理模型估计来处理测量信号。这种操作包括从信号的测量中减去第一原理模型估计，产生代表信号中未建模动态的残差。由于被测信号的未建模动态比被测信号本身稀疏得多，这种操作能够利用一种强大的技术来仅从几个测量中估计稀疏信号。该技术称为压缩感知。处理后的数据用作压缩感知算法中的输入数据，该算法可对原始信号中的未建模动态进行高保真估计。因此，本文的新颖性有两个方面。首先，将压缩传感引入铝电解领域。其次，介绍了使用第一原理模型对测量信号进行稀疏化以便对测量数据利用压缩感知的新技术。未建模动力学的信号估计被集成到扩展卡尔曼滤波器中作为伪测量，以改进系统状态的估计。新方法适用于具有平稳周期性未建模动态的信号。本文中的案例研究是根据描述铝电解槽质量平衡的子过程的模拟数据进行的。