Continuous advances of sensor technology and real-time computational capability is leading to data rich environments to improve industrial automation and machine intelligence. When multiple signals are acquired from different sources (i.e., multi-channel signal data), two main issues must be faced: i) reduce data dimensionality, to make the overall signal analysis system efficient and actually implementable in industrial environment, and ii) fuse together all the sensor outputs to achieve a better comprehension of the process. In this frame, Multi-way Principal Component Analysis (PCA) represents a multivariate technique to perform both the tasks. The paper investigates two main multi-way extensions of the traditional PCA to deal with multi-channel signals, one based on unfolding the original datasets, and one based on multi-linear analysis of data in their tensorial form. The approaches proposed for data modelling are combined with appropriate control charting to achieve multi-channel profile data monitoring.The developed methodologies are demonstrated with both simulated and real data.
IntroductionThe development of low-cost, non-intrusive and smart sensors on one hand, and the continuous improvement of real-time computational capability on the other hand, make a large amount of data potentially available in industry. In this frame, sensor signals acquired during the process provide a suitable source of information to develop an inprocess quality control and to allow a faster implementation of corrective actions. In several applications, the acquired signals present cyclically repeating patterns; in those cases the suite of profile monitoring techniques (Woodall et al., 2004;Williams et al., 2007) provides the natural framework to evaluate the stability over time of processquality. An overview of parametric and nonparametric approaches for profile data as well as application domains investigated at this time can be found in the recent book edited by Noorossana et al. (2012).This paper focuses on the specific case of monitoring profiles that are signal data.On this topic, the first seminal paper on signal profile monitoring is due to Jin and Shi (1999), who suggested using wavelet analysis to monitor tonnage signals in stamping The largest portion of profile monitoring literature focuses on single signal analysis, regardless the strong industrial interest for multi-signal applications. Data-rich environments in industry, in fact, are leading to an increasing demand for multi-sensor data fusion methods to solve quality-related problems. The most widely studied applications in literature include stability analysis and chatter detection (Kuljanic et al., 2009;Inasaki, 1999) and tool condition monitoring (Cho et al., 2010;Wang et al., 2007;Chen and Jen, 2000;Bahr et al., 1997;Bhattacharyya and Sengupta, 2009;Lezanski, 2001;Shi and Gindy, 2007;Aliustaoglu et al. 2009). However, only few authors studied profile monitoring approaches in the field of sensor fusion. Among them, Kim et al. In this study, we co...