IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3837-d944800.html
   My bibliography  Save this article

Development of a Robust Data-Driven Soft Sensor for Multivariate Industrial Processes with Non-Gaussian Noise and Outliers

Author

Listed:
  • Yongshi Liu

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

  • Xiaodong Yu

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

  • Jianjun Zhao

    (State Key Laboratory of Process Automation in Mining & Metallurgy, Beijing 100160, China
    Beijing Key Laboratory of Process Automation in Mining & Metallurgy, Beijing 100160, China)

  • Changchun Pan

    (Laboratory of Navigation and Location Based Services, Shanghai Jiao Tong University, Shanghai 200240, China)

  • Kai Sun

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

Abstract

Industrial processes are often nonlinear and multivariate and suffer from non-Gaussian noise and outliers in the process data, which cause significant challenges in data-driven modelling. To address these issues, a robust soft-sensing algorithm that integrates Huber’s M-estimation and adaptive regularisations with multilayer perceptron (MLP) is proposed in this paper. The proposed algorithm, called RAdLASSO-MLP, starts with an initially well-trained MLP for nonlinear data-driven modelling. Subsequently, the residuals of the proposed model are robustified with Huber’s M-estimation to improve the resistance to non-Gaussian noise and outliers. Moreover, a double L1-regularisation mechanism is introduced to minimise redundancies in the input and hidden layers of MLP. In addition, the maximal information coefficient (MIC) index is investigated and used to design the adaptive operator for the L1-regularisation of the input neurons to improve biased estimations with L1-regularisation. Including shrinkage parameters and Huber’s M-estimation parameter, the hyperparameters are determined via grid search and cross-validation. To evaluate the proposed algorithm, simulations were conducted with both an artificial dataset and an industrial dataset from a practical gasoline treatment process. The results indicate that the proposed algorithm is superior in terms of predictive accuracy and robustness to the classic MLP and the regularised soft-sensing approaches LASSO-MLP and dLASSO-MLP.

Suggested Citation

  • Yongshi Liu & Xiaodong Yu & Jianjun Zhao & Changchun Pan & Kai Sun, 2022. "Development of a Robust Data-Driven Soft Sensor for Multivariate Industrial Processes with Non-Gaussian Noise and Outliers," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3837-:d:944800
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3837/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3837/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chien-Chih Wang & Hsin-Tzu Chang & Chun-Hua Chien, 2022. "Hybrid LSTM-ARMA Demand-Forecasting Model Based on Error Compensation for Integrated Circuit Tray Manufacturing," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    2. Hongxun Wang & Lin Sui & Mengyan Zhang & Fangfang Zhang & Fengying Ma & Kai Sun, 2021. "A Novel Input Variable Selection and Structure Optimization Algorithm for Multilayer Perceptron-Based Soft Sensors," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-10, May.
    3. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July.
    4. Song, Xiao & Han, Daolin & Sun, Jinghan & Zhang, Zenghui, 2018. "A data-driven neural network approach to simulate pedestrian movement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 827-844.
    5. Gijbels, I. & Vrinssen, I., 2015. "Robust nonnegative garrote variable selection in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 1-22.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    2. Smucler, Ezequiel & Yohai, Victor J., 2017. "Robust and sparse estimators for linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 116-130.
    3. Mingqiu Wang & Guo-Liang Tian, 2016. "Robust group non-convex estimations for high-dimensional partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 49-67, March.
    4. Kepplinger, David, 2023. "Robust variable selection and estimation via adaptive elastic net S-estimators for linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).
    5. Nahapetyan Yervand, 2019. "The benefits of the Velvet Revolution in Armenia: Estimation of the short-term economic gains using deep neural networks," Central European Economic Journal, Sciendo, vol. 53(6), pages 286-303, January.
    6. Zhu Wang, 2022. "MM for penalized estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 54-75, March.
    7. Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.
    8. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.
    9. Casado Yusta, Silvia & Nœ–ez Letamendía, Laura & Pacheco Bonrostro, Joaqu’n Antonio, 2018. "Predicting Corporate Failure: The GRASP-LOGIT Model || Predicci—n de la quiebra empresarial: el modelo GRASP-LOGIT," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 26(1), pages 294-314, Diciembre.
    10. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    11. Jiang, Rong & Qian, Weimin & Zhou, Zhangong, 2012. "Variable selection and coefficient estimation via composite quantile regression with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 308-317.
    12. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.
    13. Barrera, Carlos, 2010. "¿Respuesta asimétrica de precios domésticos de combustibles ante choques en el WTI?," Working Papers 2010-016, Banco Central de Reserva del Perú.
    14. Sophie Lambert-Lacroix & Laurent Zwald, 2016. "The adaptive BerHu penalty in robust regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 487-514, September.
    15. Florian Ziel, 2015. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes," Papers 1502.06557, arXiv.org, revised Dec 2015.
    16. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    17. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    18. Carlos R. Barrera Chaupis, 2018. "Inventory Adjustments to Demand Shocks under Flexible Specifications," Monetaria, Centro de Estudios Monetarios Latinoamericanos, CEMLA, vol. 0(1), pages 149-201, january-j.
    19. T. Cai & J. Huang & L. Tian, 2009. "Regularized Estimation for the Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 65(2), pages 394-404, June.
    20. Junlong Zhao & Chao Liu & Lu Niu & Chenlei Leng, 2019. "Multiple influential point detection in high dimensional regression spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 385-408, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3837-:d:944800. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.