Thresholded scalogram and its applications in process fault detection

Abstract

SUMMARYScalograms provide measures of signal energy at various frequency bands and are commonly used in decision making in many fields including signal and image processing, astronomy and metrology. This article extends the scalogram's ability for handling noisy and possibly massive data. The proposed thresholded scalogram is built on the fast wavelet transform, which can capture non-stationary changes in data patterns effectively and efficiently. The asymptotic distribution of the thresholded scalogram is derived. This leads to large sample confidence intervals that are useful in detecting process faults statistically, based on scalogram signatures. Application of the scalogram-based data mining procedure (mainly, classification and regression trees) demonstrates the potential of the proposed methods for analysing complicated signals for making engineering decisions.

Multiscale Monitoring Using Machine Learning Methods: New Methodology and an Industrial Application to a Photovoltaic System

“…To solve the eigen-value problem given in (10), as well as projecting the input space towards the kernel PCA space by employing (13), performing the nonlinear mappings can be evaded. In addition, both dot products can be computed in the feature space by bringing a kernel function as k(x, y) = ∅(x i ), ∅ x j [31,32].…”

“…This method allows us to detect errors in each of the scales and then to reconstruct the signals by keeping the significant scales (where the detection took place). A comparative analysis was performed between different approaches [30], which are: dissimilarity measure [31], multi-scale PCA [32], and moving PCA [33]. Implemented on the Tennessee Eastman process, the work showed that the multiscale PCA is superior to conventional methods in some cases and equivalent to them in others.…”

Data reduction for multiple functional data with class information

“…The automated extraction of features from time-dependent complex QMS waveforms will ultimately lead to better process characterization and reduction of run-to-run process variability (Jeong et al 2003). By incorporating wavelets for process control, we obtain the following benefits: (1) dimensionality reduction through feature extraction of real-time QMS data, (2) automated detection of run-to-run incipient equipment faults to minimize variability, and (3) utilization of the wavelet transform's inherent time-localization properties for improved modeling of complex time-varying QMS waveforms.…”

“…For example, functional data such as the rapid thermal chemical vapor deposition (RTCVD) signal, as presented in figure 2, are useful in process monitoring and improvement. Various other studies of functional data in fields such as semiconductor fabrication (Gardner et al 1997, Ganesan et al 2003, Jeong et al 2003, chemical manufacturing (Bakshi 1999), sheet-metal stamping (Jin and Shi 1999), and rotating machinery applications (Mori et al 1996, Urmanov et al 2002 demonstrate the utility of functional data.…”