Fault Detection of Complex Processes Using nonlinear Mean Function Based Gaussian Process Regression: Application to the
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RESEARCH ARTICLE-CHEMICAL ENGINEERING
Fault Detection of Complex Processes Using nonlinear Mean Function Based Gaussian Process Regression: Application to the Tennessee Eastman Process Avinash Maran Beena1 · Ajaya Kumar Pani1 Received: 5 June 2020 / Accepted: 20 October 2020 © King Fahd University of Petroleum & Minerals 2020
Abstract Process monitoring or fault detection and diagnosis have gained tremendous attention over the past decade in order to achieve better product quality, minimise downtime and maximise profit in process industries. Among various process monitoring techniques, data-based machine learning approaches have become immensely popular in the past decade. However, a promising machine learning technique Gaussian process regression has not yet received adequate attention for process monitoring. In this work, Gaussian process regression (GPR)-based process monitoring approach is applied to the benchmark Tennessee Eastman challenge problem. Effect of various GPR hyper-parameters on monitoring efficiency is also thoroughly investigated. The results of GPR model is found to be better than many other techniques which is reported in a comparative study in this work. Keywords Fault detection · Gaussian process regression · Process monitoring · Tennessee Eastman (TE) process
List of Symbols
N o
Notations abs a, b, B, c, d cov D D E(.) f ∗ , g∗ f¯∗ , g¯ GP I k k∗ K l m m(x)
B 1
Absolute value Weights assigned Predicted covariance Dataset Number of variables Expectations Gaussian process posterior prediction Predicted mean Gaussian process Identity matrix Covariance function for a single case Covariance function for single test case Covariance (gram) matrix Length scale Number of samples Mean function
Ajaya Kumar Pani [email protected]
p V x X X∗ y
Normal distribution function Value associated with (1 − α)% confidence interval Probability density Variance of a sample Sample vector Matrix of training input Matrix of testing input Output training vector
Greek Letters β β¯ δ pq σ σ 2f σn2
Gaussian prior Constant Kronecker delta Gaussian noise Variance associated with the predicted output Signal variance Noise variance
Department of Chemical Engineering, Birla Institute of Technology and Science, Pilani 333031, India
123
Arabian Journal for Science and Engineering
Abbreviations BICSPE
Bayesian Inference-Based Criterion Squared Prediction Error Bayesian inference-based probability in BIPS state space BIP Bayesian inference-based probability BSPCA Bayesian strategy PCA CCA-ERD Canonical correlation analysis-based explicit relation discovery D Dissimilarity index DiPCA Distributed PCA DR Distance from the hypersphere DTL Determining whether it is tight or loose EICA Ensemble ICA FA Factor analysis FA-ICA Factor analysis-ICA Statistic to monitor the factor space GT 2 GLSA Global local structure analysis GMM Gaussian mixture models JIR-PCA-SVDD Just in time response-PCA-SVDD KGLPP Kernel global local preserving projections KICA Kernel independent component analysis KLPP Kernel local p
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