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Article Excerpt
1. Introduction
In general, a complex system consists of multiple embedded operations. Although the separate measurement of individual operation responses can provide explicit diagnostic information for system monitoring, it is often not possible or economic to install individual sensors at each operation. In practice, a commonly used method is to measure the combined response of embedded operations, this combined response is called an aggregated signal. Therefore, it is desirable to know whether it is possible to monitor the performance of individual operations based on available aggregated signals.
For example, in a transfer/progressive stamping or forging process, strain gage sensors are usually installed on press machines to measure the total press tonnage force (i.e., an aggregated signal), which is comprised of the forces of all embedded operations. In contrast, in-die sensors, which are installed inside the dies of individual operations to measure their respective forces, are very rarely used in real-world production, because of the extra costs for purchasing, installing, inspecting, and replacing the sensors, as well as the accompanying complexity of die changes. Similarly, in a computer network, a border router is usually available to collect aggregated packet traffic data (i.e., an aggregated signal) corresponding to the total number of queries from all relevant nodes in the network, while the number of queries from individual nodes is not separately measurable. A third example is a transportation network in an urban area, where traffic flow is usually measured at certain main intersections (i.e., an aggregated signal), but not along each branch road whose traffic flow passes through the intersection and which contributes to its overall traffic flow. In these three examples, it is highly desirable to have the ability to use aggregated signals to monitor and detect abnormalities in individual manufacturing operations, network nodes and branch road traffic flows, for the purpose of quality assurance in stamping and forging, computer network intrusion detection and better route planning and traffic control, respectively. There is a substantial need for research on how to map features of system-level aggregated signals to the responses of embedded operations. The advantage of using such mapping features is improved diagnostic capabilities for system monitoring, which can be shown in two ways: first, when there is a one-to-one mapping between a feature and an individual operation; this feature can be used to monitor the operation exclusively. Second, even for some operations lacking dedicated features, an explicit mapping between a feature and some of the operations, rather than all of the embedded operations, can expedite the search for the specific failures in operations.
In this research, we focus on systems consisting of multiple embedded operations, each of which generates a localized "time-frequency" response. In other words, in order to allow multiple embedded operations to be monitored separately based on the aggregated signals, these operations must engage in the system at different time segments (i.e., possibly overlapping but not identical time periods) and/or have their energy concentrated within overlapping but not identical frequency bands. This characteristic is shared by the systems in the previous three examples. Specifically, past research in stamping and forging process control (Jin, 2004; Jin and Shi, 2005) has found that the actual working range of each individual operation only occupies a limited, mostly different, portion of the entire time cycle of the aggregated signal, and each embedded operation has its energy concentrated in mostly different frequency bands. Likewise, the number of queries from the individual nodes of a computer network also forms localized time-frequency signals due to the differences among the individual nodes in the network in terms of usage time and usage patterns (Barford et al., 2002). Similar phenomena can be observed in the traffic flow passing through an intersection from branch roads (Guo and Jin, 2006).
An extensive literature exists on the analysis of signal profiles and the extraction of features for system monitoring and diagnoses (Woodall et al., 2004). Generally, multivariate statistical methods, such as Principle Component Analysis (PCA) (Johnson and Wichern, 2002), PCA-based pattern recognition (Ceglarek and Shi, 1996), factor analysis (Apley and Shi, 2001; Johnson and Wichern, 2002), variance component analysis (Rao and Kleffe, 1988; Zhou et al., 2003) and signature metrics approaches (Kibarian and Strojwas, 1991; Gardner et al, 1997), focus on analyzing signals in the time domain. Fourier transforms (Bracewell, 2000) decompose signals in the frequency domain, but these are applicable only to stationary signals and not to localized time-frequency non-stationary signals. Short-time Fourier transforms can be used to analyze localized time-frequency signals but at a fixed resolution (or scale) in both the time and frequency domains. In contrast, wavelet analysis (Mallat, 1989) is able to decompose a signal at multiscale time-frequency domains, and the resulting wavelet coefficients capture localized signal features at different time segments and different frequency bands.
Most past research on the application of wavelet analysis to system monitoring and diagnosis resides in the general field of profile or functional data monitoring, which aims to develop control charts for different types of profiles, including linear (Stover and Brill, 1998; Kang and Albin, 2000; Kim et al, 2003; Mahmoud and Woodall, 2004; Mahmoud et al., 2007) or non-linear profiles (Young et al., 1999; Walker and Wright, 2002; Ding et al., 2006), profiles that can be represented in a parametric (Stover and Brill, 1998; Kang and Albin, 2000; Kim et al., 2003; Mahmoud and Woodall, 2004; Mahmoud et al., 2007) or non-parametric (Winistorfer et al., 1996; Gardner et al., 1997; Fan and Lin, 1998) forms, and complex waveform profiles that have rich information in a localized time domain (Jin, 2004), or in both localized time and frequency domains (Jin and Shi, 1999, 2001; Lada et al., 2002). In this area of research, wavelet analysis is often used for signal denoising, profile fitting or feature-preserving data compression (Jin and Shi, 1999). Very little research, however, has been published on the application of wavelet analysis to the profile analysis of aggregated signals for embedded operation monitoring. This opens a new research area on how to map features (i.e., the wavelet coefficients) of the aggregated signals to the embedded individual operations.
This paper uses a multistage progressive stamping process to illustrate the development of a data analysis method for exacting features of aggregated signals that can be mapped to the corresponding embedded operations. In the literature of stamping signal analysis, the Discrete Wavelet Transform (DWT) approach has been successfully used for multiscale feature extraction (Jin and Shi, 1999). Therefore, this paper will also apply the DWT approach to the aggregated stamping force signals in the first step of data analysis. Then, the extraction of mapping features is performed by...
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