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Performance of soft sensors based on stochastic configuration networks with nonnegative garrote

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Abstract

In this study, stochastic configuration networks (SCNs) and nonnegative garrote (NNG) algorithm are employed to develop a soft-sensing technique that infers difficult-to-measure variables with easy-to-measure variables in industrial processes. The proposed method consists of two stages, that is, performing industrial data modeling with SCNs and applying NNG algorithm for shrinking input weights and removing some redundant input variables from the well-trained leaner model. Cross-validation and the Akaike information criterion are employed to determine the optimal shrinkage parameter for the NNG. A numerical example and real industrial data are used to validate the performance of the proposed algorithm. Several state-of-the-art feature selection schemes for neural networks are tested. Comparative results demonstrate that the proposed soft-sensor outperforms others in terms of the prediction accuracy.

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Acknowledgements

The authors would like to thank the editors and reviewers for the time and effort they spent reviewing this paper as well as for their detailed and constructive comments for the paper improvement in terms of presentation and quality.

Funding

This work is funded in part by the Shandong Provincial Natural Science Foundation under grant ZR2021MF022, in part by the Key Research and Development Program of Shandong Province under Grant 2019GGX104037, and in part by the National Key Research and Development Program of China under Grant 2018AAA0100304.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Qilu University of Technology(Shandong Academy of Sciences), Jinan, 250353, China

    Pengxin Tian & Kai Sun

  2. Artificial Intelligence Research Institute, China University of Mining and Technology, Xuzhou, 221116, China

    Dianhui Wang

  3. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China

    Dianhui Wang

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  1. Pengxin Tian
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  2. Kai Sun
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  3. Dianhui Wang
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Correspondence to Kai Sun or Dianhui Wang.

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Appendix

Appendix

Tables

Table 5 Parameters configuration of the artificial dataset
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5 and

Table 6 Parameters configuration of the CDQ dataset
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6 showed the settings of the important parameters of algorithms in the experiments based on the artificial dataset and the CDQ dataset, respectively. Para.1 is the number of bins when calculating the probability density function by histogram. During the calculation, samples were sorted into Para.1 equally spaced bins. Para.2 and Para.3 are the weights of the regular terms when LASSO is applied to the input and hidden layers, respectively. Para.4 is the garrote parameter s of NNG.

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Tian, P., Sun, K. & Wang, D. Performance of soft sensors based on stochastic configuration networks with nonnegative garrote. Neural Comput & Applic 34, 16061–16071 (2022). https://doi.org/10.1007/s00521-022-07254-w

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  • DOI: https://doi.org/10.1007/s00521-022-07254-w

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