Lag Structure in Dynamic Principal Component Analysis

• Purpose of this PresentationAutomatic data collection schemes and abundant availability of multivariate data increase the need for latent variable methods in statistical process control (SPC) such as SPC based on principal component analysis (PCA). However, process dynamics combined with high-frequency sampling will often cause successive observations to be autocorrelated which can have a negative impact on PCA-based SPC, see Vanhatalo and Kulahci (2015).Dynamic PCA (DPCA) proposed by Ku et al. (1995) has been suggested as the remedy ‘converting’ dynamic correlation into static correlation by adding the time-lagged variables into the original data before performing PCA. Hence an important issue in DPCA is deciding on the number of time-lagged variables to add in augmenting the data matrix; addressed by Ku et al. (1995) and Rato and Reis (2013). However, we argue that the available methods are rather complicated and lack intuitive appeal.The purpose of this presentation is to illustrate a new and simple method to determine the maximum number of lags to add in DPCA based on the structure in the original data. FindingsWe illustrate how the maximum number of lags can be determined from time-trends in the eigenvalues of the estimated lagged autocorrelation matrices of the original data. We also show the impact of the system dynamics on the number of lags to be considered through vector autoregressive (VAR) and vector moving average (VMA) processes. The proposed method is compared with currently available methods using simulated data.Research Limitations / Implications (if applicable)The method assumes that the same numbers of lags are added for all variables. Future research will focus on adapting our proposed method to accommodate the identification of individual time-lags for each variable. Practical Implications (if applicable)The visualization possibility of the proposed method will be useful for DPCA practitioners.Originality/Value of PresentationThe proposed method provides a tool to determine the number of lags in DPCA that works in a manner similar to the autocorrelation function (ACF) in the identification of univariate time series models and does not require several rounds of PCA. Design/Methodology/ApproachThe results are based on Monte Carlo simulations in R statistics software and in the Tennessee Eastman Process simulator (Matlab).

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TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Tillförlitlighets- och kvalitetsteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Reliability and Maintenance (hsv//eng)

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Kvalitetsteknik

Quality Technology and Management

Intelligent industrial processes (AERI)

Intelligenta industriella processer (FOI)

Effektiv innovation och organisation (FOI)

Effective innovation and organisation (AERI)

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