In the present work, the multiplicity of process variable spaces is analyzed for modern industrial processes where a large number of process variables may be collected from different sources. Each process space is composed of different variables, revealing different underlying characteristics. The multi-space version of total projection to latent structures algorithm (MsT-PLS) is thus developed. By the proposed algorithm, the relationship across multiple process spaces is studied from the quality-concerned viewpoint. In this way, comprehensive information decomposition is obtained in each process space, where four systematic parts can be separated, revealing cross-space common and specific process variability. Process monitoring strategy is developed based on the MsT-PLS subspace decomposition result and illustrated on the Tennessee Eastman process in comparison with the other methods.
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