(245t) A Semi-Parametric Independent Component Analysis Method for Multivariate Process Monitoring

Independent Component Analysis (ICA) is a method of decomposing a multivariate signal into statistically independent components. In contrast to its simplistic counterpart, principle component analysis, ICA is particularly useful when the signal components have non-Gaussian probability distributions. ICA is based on two major assumptions of non-Gaussian distribution and statistical independence of the components, and it involves minimizing mutual information or maximizing non-Gaussianity of the components [1].

In recent years, ICA has found applications in process monitoring and control. In multivariate process monitoring, ICA can be used to analyze sensor measurements to find statistically-independent source components that have generated the sensor data. These components can be processed further for use in monitoring and diagnosis [2] and in process control systems [3]. These applications have motivated the development of a variety of ICA methods [4, 5, 6].  In most ICA methods, probability distributions are assumed to be describable by a few leading moments of the distributions. As in practice variables can have any probability distribution, the use of a few leading moments to capture dependence structures can lead to poor predictions [7].

In this work, we propose an alternative ICA method that is based on capturing the dependence structure of variables using a semi-parametric approach. This approach combines parametric copulas with non-parametrically-estimated marginal distributions. The approach allows for modeling non-elliptical and highly nonlinear dependence structures and offers a flexible framework to represent non-Gaussian marginal distributions. The proposed ICA method offers an alternative way to efficiently calculate rotation matrices for complicated interactions that cannot be described by a few leading moments. The application and performance of the method will be shown using examples. 

References

[1].  Hyvärinen, A., & Oja, E. (2000). Independent component analysis: algorithms and applications. Neural networks, 13(4), 411-430.

[2].  Stefatos, G., & Hamza, A. B. (2010). Dynamic independent component analysis approach for fault detection and diagnosis. Expert Systems with Applications, 37(12), 8606-8617.

[3].  Kano, M., Hasebe, S., Hashimoto, I., & Ohno, H. (2004). Evolution of multivariate statistical process control: application of independent component analysis and external analysis. Computers & chemical engineering, 28(6), 1157-1166.

[4].  Favero, J. L., Silva, L. F. L., & Lage, P. L. (2014). Comparison of methods for multivariate moment inversion—Introducing the independent component analysis. Computers & Chemical Engineering, 60, 41-56.

[5].  Rashid, M. M., & Yu, J. (2012). A new dissimilarity method integrating multidimensional mutual information and independent component analysis for non-Gaussian dynamic process monitoring. Chemometrics and Intelligent Laboratory Systems, 115, 44-58.

[6].  Albazzaz, H., & Wang, X. Z. (2006). Multivariate statistical batch process monitoring using dynamic independent component analysis. Computer aided chemical engineering, 21, 1341-1346.

[7].  Stone, J. V. (2004). Independent Component Analysis: A Tutorial Introduction. Cambridge, Mass.: MIT Press.