Abstract
In order to guarantee and improve the product quality, the data-driven fault detection technique has been widely used in industry. For three-way datasets of batch process in industry process (i.e., batch × variable × time), a novel method named functional local kernel principal component analysis (FLKPCA) is proposed. Since the variables' trajectories often show functional nature and can be considered as smooth functions rather than just vectors. Firstly, the variables' trajectory is expressed as the combination of smooth basis functions using functional data analysis (FDA), which means that the datasets of batches process would be transformed from the three-ways array into two-ways function matrix. Then, kernel locality preserving projections (LKPCA) is used to perform dimensionality reduction on two-way function matrix directly. Different from kernel principal component analysis (KPCA). LKPCA aims at preserving the both local and global structure of the data in a new optimization objective. Consequently, FLKPCA could more effectively seek the potential information that hidden in the three-ways datasets. Lastly, the effectiveness of the proposed approach is illustrated by the benchmark of fed-batch penicillin fermentation process and the hot strip rolling process.
Highlights
With the development of industry process, the customers put forward higher demands for production quality, so the fault detection of the industrial process has been research hotspot
AND DISCUSSION the fault detection procedure of functional local kernel principal component analysis (FLKPCA) is demonstrated by following actual cases, including the Fed-batch penicillin fermentation process and head width shrinkage of hot rolled strip process
local KPCA (LKPCA) based on functional matrixes which integrates the local structure analysis with kernel principal component analysis is proposed to build the fault detection model
Summary
With the development of industry process, the customers put forward higher demands for production quality, so the fault detection of the industrial process has been research hotspot. The shortcoming of single variable monitoring promotes the rapid development of the multivariate statistical process monitoring (MSPM) technique, and many famous data-driven fault diagnosis methods have been proposed including principal component analysis (PCA), canonical variate analysis (CVA), independent component analysis (ICA) and partial least squares (PLS) [4]–[9]. The trilinear methods that the three-way data is dealt directly with tensor decomposition, including parallel factor analysis (PARAFAC), tensor locality preserving projections (TLPP), trilinear decomposition (TLD), GTucker and Tucker decomposition [26]–[30] Both the bilinear and trilinear methods require the original dataset at the same sampling duration for each batch and same sampling rate for each variable, but these constraints are often not satisfied in the actual production process. In order to obtain local-global structure information and deal with nonlinear features in the data, LKPCA based on the functional matrix is used to build the process monitoring model.
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