Efficient control and optimization of processes require fast-rate measurements of process variables. However, certain variables can only be measured at a slow rate due to technical or economic limitations. Video cameras are commonly available in process industry. Taking images regularly may provide valuable insights into the process dynamics. In this paper, a vision model is proposed to provide a fast-rate prediction for the slow-rate measured variables. However, since images are susceptible to various deteriorating factors including environmental sources, an autoencoder-based image inpainting method is used to retrieve the true images. Then, a predictive multirate auto-regressive with eXogenous input (ARX) model is developed using image features and slow-rate measurements. Unknown parameters are estimated using the expectation–maximization (EM) algorithm. A Kalman filter and Rauch–Tung–Striebel smoother are used to determine the posterior distribution of states. The proposed vision model demonstrates promising performance in providing fast-rate predictions of the interface level in a laboratory-scale primary separation cell.

过程的有效控制和优化需要对过程变量进行快速测量。然而，由于技术或经济限制，某些变量只能以缓慢的速度测量。摄像机在过程工业中很常见。定期拍摄图像可以为过程动态提供有价值的见解。在本文中，提出了一种视觉模型来为慢速测量变量提供快速预测。然而，由于图像容易受到包括环境源在内的各种恶化因素的影响，因此使用基于自动编码器的图像修复方法来检索真实图像。然后，使用图像特征和慢速测量开发了具有外源输入（ARX）的预测多速率自回归模型。使用期望最大化 (EM) 算法估计未知参数。卡尔曼滤波器和 Rauch-Tung-Striebel 平滑器用于确定状态的后验分布。所提出的视觉模型在实验室规模的初级分离单元中提供界面水平的快速预测方面表现出良好的性能。