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Probabilistic Slow Feature Regression for Dynamic Soft Sensing

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Dynamic Modeling of Complex Industrial Processes: Data-driven Methods and Application Research

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Latent variable (LV) models provide explicit representations of underlying driving forces of process variations and retain the dominant information of process data. In this chapter, we develop a new soft sensor model called probabilistic slow feature regression (PSFR). Slow features as temporally correlated LVs are first derived using probabilistic slow feature analysis (PSFA). Probabilistic slow features that evolve in a state-space form effectively represent nominal variations of processes, some of which may be potentially correlated to quality variables and hence help improving the prediction performance of soft sensors when used as inputs. An efficient expectation maximization algorithm is proposed to estimate parameters of the PSFA model, and two alternative criteria are put forward to select quality-relevant SFs in the PSFR model. The validity and advantages of the proposed method are demonstrated via two case studies.

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Notes

  1. 1.

    For general LDS, it is quite difficult to define \(\mathbf {F}^{t_k - t_k^-}\) for an arbitrary matrix \(\mathbf {F}\). For PSFA, however, such generalization is unique because \(\mathbf {F}\) is diagonal, which particularly applies to this unideal case.

  2. 2.

    Available at http://www.springer.com/gp/book/9781846284793.

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Authors and Affiliations

  1. Department of Automation, Tsinghua University, Beijing, China

    Chao Shang

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  1. Chao Shang
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Correspondence to Chao Shang .

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Shang, C. (2018). Probabilistic Slow Feature Regression for Dynamic Soft Sensing. In: Dynamic Modeling of Complex Industrial Processes: Data-driven Methods and Application Research. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6677-1_5

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  • DOI: https://doi.org/10.1007/978-981-10-6677-1_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6676-4

  • Online ISBN: 978-981-10-6677-1

  • eBook Packages: EngineeringEngineering (R0)

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