由于数据驱动的过程监测方法具有普遍性，且不依赖反应机理，其已经成为复杂工业系统过程监测的主流。然而，大多数数据驱动的过程监测方法均假设历史训练数据和在线测试数据遵循相同的分布。事实上，由于工业系统恶劣的环境，从实际工业过程中收集的数据总是受到许多因素的影响，如多变的操作环境、原材料的变化和生产指标的修改。这些因素通常会使在线监测数据和历史训练数据分布不同，从而导致过程监测任务中的模型失配。因此，当将从训练数据中学习的模型应用于实际的在线监测时，很难实现精确的过程监测。为了解决操作环境变化导致的历史训练数据和在线测试数据之间的分布差异问题，提出了一种鲁棒的迁移字典学习（RTDL）算法用于工业过程监测。RTDL是表示学习和域自适应迁移学习的协同方法。该方法将历史训练数据和在线测试数据分别作为迁移学习问题的源域和目标域。然后将最大均值差异正则化和线性判别分析正则化引入字典学习框架，可以减少源域和目标域之间的分布差异。这样，即使源域和目标域的特征在实际变化的操作环境的干扰下明显不同，仍可以学习鲁棒的字典。这样的字典可以有效地提高过程监测和模态识别的性能。通过数值仿真和两个工业系统的实验验证了该方法的有效性和优越性。

Data-driven process-monitoring methods have been the mainstream for complex industrial systems due to their universality and the reduced need for reaction mechanisms and first-principles knowledge. However, most data-driven process-monitoring methods assume that historical training data and online testing data follow the same distribution. In fact, due to the harsh environment of industrial systems, the
collected data from real industrial processes are always affected by many factors, such as the changeable operating environment, variation in the raw materials, and production indexes. These factors often cause the distributions of online monitoring data and historical training data to differ, which induces a model mismatch in the process-monitoring task. Thus, it is difficult to achieve accurate process monitoring when a model learned from training data is applied to actual online monitoring. In order to resolve the problem of the distribution divergence between historical training data and online testing data that is induced by changeable operation environments, a robust transfer dictionary learning (RTDL) algorithm is proposed in this paper for industrial process monitoring. The RTDL is a synergy of representative learning and domain adaptive transfer learning. The proposed method regards historical training data and online testing data as the source domain and the target domain, respectively, in the transfer learning problem. Maximum mean discrepancy regularization and linear discriminant analysis-like regularization are then incorporated into the dictionary learning framework, which can reduce the distribution divergence between the source domain and target domain. In this way, a robust dictionary can be learned even if the characteristics of the source domain and target domain are evidently different under the interference of a realistic and changeable operation environment. Such a dictionary can effectively improve the performance of process monitoring and mode classification. Extensive experiments including a numerical simulation and two industrial systems are conducted to verify the efficiency and superiority of the proposed method.