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Traditional industrial production processes, such as nonferrous metallurgy, are mostly based on complex, cascading, large-scale equipment. Many soft sensing approaches are rendered inapplicable due to the particularity of this physical structure, which involves uncertain time delay and extreme imbalance between the input and output dimensions. To alleviate this problem, this article first proposes a time-delay analysis strategy to preliminarily reduce the input dimensions of the process variables. Then, a new orthogonal self-attention (OSA) mechanism is proposed to capture nonlinear features related to quality variables along both spatial and temporal dimensions, thus solving the problem of uncertainty of the time delays of process variables affecting quality variables. In addition, a new long short-term memory (LSTM) structure called differential-cross LSTM is proposed, which is incorporated in a cascading manner differential-cross cascade LSTM (DCCLSTM) to emulate the physical structure of the industrial process. Therefore, the soft-sensor framework called OSA-DCCLSTM is constructed, where data from each major equipment undergo the time-delay analysis strategy and the OSA computation and is subsequently input into the corresponding differential-cross LSTM module. Extensive experiments on a real-world alumina evaporation process datasets show the effectiveness of the proposed framework. Compared with some existing state-of-the-art methods, the root-mean-squared error and mean absolute error are on average decreased by 0.3742 and 0.2234, while the correlation coefficient is on average increased by 0.1389.
Yue et al. (Tue,) studied this question.