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Currently, it is challenging to investigate aneurismal hemodynamics based on current in vivo data such as Magnetic Resonance Imaging or Computed Tomography due to the limitations in both spatial and temporal resolutions. In this work, we investigate the use of modal analysis at various resolutions to examine its usefulness for analyzing blood flows in brain aneurysms. Two variants of Dynamic Mode Decomposition (DMD): (i) Hankel-DMD; and (ii) Optimized-DMD, are used to extract the time-dependent dynamics of blood flows during one cardiac cycle. First, high-resolution hemodynamic data in patient-specific aneurysms are obtained using Computational Fluid Dynamics. Second, the dynamics modes, along with their spatial amplitudes and temporal magnitudes are calculated using the DMD analysis. Third, an examination of DMD analyses using a range of spatial and temporal resolutions of hemodynamic data to validate the applicability of DMD for low-resolution data, similar to ones in clinical practices. Our results show that DMD is able to characterize the inflow jet dynamics by separating large-scale structures and flow instabilities even at low spatial and temporal resolutions. Its robustness in quantifying the flow dynamics using the energy spectrum is demonstrated across different resolutions in all aneurysms in our study population. Our work indicates that DMD can be used for analyzing blood flow patterns of brain aneurysms and is a promising tool to be explored in in vivo. 

Modeling corrosion growth for complex systems such as the oil refinery system is a major challenge since the corrosion process of oil and gas pipelines are inherently stochastic and depends on many factors including exposures to environmental conditions, operating conditions, and electrochemical reactions. Moreover, the number of sensors is usually limited, and sensor data are incomplete and scattering, which hinders the capability of capturing the corrosion growth behaviors. Therefore, this paper proposes Multi-sensor Corrosion Growth Model with Latent Variables to predict the corrosion growth process in oil refinery piping. The proposed model is a combination of the hierarchical clustering algorithm and the vector autoregression (VAR) model. The clustering algorithm aims to find the hidden (i.e., latent) data clusters of the measured time series data, from which the time series from the same cluster will be included in the VAR model to predict the corrosion depth from multiple sensors. The model can capture the relationship between sensor time series data and identify latent variables. A real case study of an oil refinery system, in which in-line inspection (ILI) data were collected, was utilized to validate model. Regarding corrosion growth prediction, the paper compared the prediction accuracy of VAR model with other three forms of power law model, which is widely accepted to expect the time-dependent depth of corrosion such as power function (PF), PF with initiation time of corrosion (PFIT), and PF with initiation time of corrosion and covariates (PFCOV). The results showed that VAR model has the lowest prediction error based on the mean absolute percentage error (MAPE) evaluation for test data. Finally, the proposed model is believed to be useful for dealing with a complex system that has a variety of corrosion growth behaviors, such as the oil refinery system, as well as it can be applied in other real-time applications.