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  1. Uncertainty is a common feature in first-principles models that are widely used in various engineering problems. Uncertainty quantification (UQ) has become an essential procedure to improve the accuracy and reliability of model predictions. Polynomial chaos expansion (PCE) has been used as an efficient approach for UQ by approximating uncertainty with orthogonal polynomial basis functions of standard distributions (e.g., normal) chosen from the Askey scheme. However, uncertainty in practice may not be represented well by standard distributions. In this case, the convergence rate and accuracy of the PCE-based UQ cannot be guaranteed. Further, when models involve non-polynomial forms, the PCE-based UQ can be computationally impractical in the presence of many parametric uncertainties. To address these issues, the Gram–Schmidt (GS) orthogonalization and generalized dimension reduction method (gDRM) are integrated with the PCE in this work to deal with many parametric uncertainties that follow arbitrary distributions. The performance of the proposed method is demonstrated with three benchmark cases including two chemical engineering problems in terms of UQ accuracy and computational efficiency by comparison with available algorithms (e.g., non-intrusive PCE).
  2. Uncertainty quantification (UQ) is an important part of mathematical modeling and simulations, which quantifies the impact of parametric uncertainty on model predictions. This paper presents an efficient approach for polynomial chaos expansion (PCE) based UQ method in biological systems. For PCE, the key step is the stochastic Galerkin (SG) projection, which yields a family of deterministic models of PCE coefficients to describe the original stochastic system. When dealing with systems that involve nonpolynomial terms and many uncertainties, the SG-based PCE is computationally prohibitive because it often involves high-dimensional integrals. To address this, a generalized dimension reduction method (gDRM) is coupled with quadrature rules to convert a high-dimensional integral in the SG into a few lower dimensional ones that can be rapidly solved. The performance of the algorithm is validated with two examples describing the dynamic behavior of cells. Compared to other UQ techniques (e.g., nonintrusive PCE), the results show the potential of the algorithm to tackle UQ in more complicated biological systems.
  3. Left ventricular assist devices (LVADs) have been used for end-stage heart failure patients as a therapeutic option. The aortic valve plays a critical role in heart failure and its treatment with a LVAD. The cardiovascular-LVAD model is often used to investigate the physiological demands required by patients and predict the hemodynamic of the native heart supported with a LVAD. As it is a “ bridge-to-recovery ” treatment, it is important to maintain appropriate and active dynamics of the aortic valve and the cardiac output of the native heart, which requires that the LVAD pump be adjusted so that a proper balance between the blood contributed through the aortic valve and the pump is maintained. In this paper, we investigate how the pump power of the LVAD pump can affect the dynamic behaviors of the aortic valve for different levels of activity and different severities of heart failure. Our objective is to identify a critical value of the pump power (i.e., breakpoint ) to ensure that the LVAD pump does not take over the pumping function in the cardiovascular-pump system and share the ejected blood with the left ventricle to help the heart to recover. In addition, the hemodynamic often involvesmore »variability due to patients’ heterogeneity and the stochastic nature of the cardiovascular system. The variability poses significant challenges to understanding dynamic behaviors of the aortic valve and cardiac output. A generalized polynomial chaos (gPC) expansion is used in this work to develop a stochastic cardiovascular-pump model for efficient uncertainty propagation, from which it is possible to rapidly calculate the variance in the aortic valve opening duration and the cardiac output in the presence of variability. The simulation results show that the gPC-based cardiovascular-pump model is a reliable platform that can provide useful information to understand the effect of the LVAD pump on the hemodynamic of the heart.« less
  4. The Lithium-ion battery (Li-ion) has become the dominant energy storage solution in many applications, such as hybrid electric and electric vehicles, due to its higher energy density and longer life cycle. For these applications, the battery should perform reliably and pose no safety threats. However, the performance of Li-ion batteries can be affected by abnormal thermal behaviors, defined as faults. It is essential to develop a reliable thermal management system to accurately predict and monitor thermal behavior of a Li-ion battery. Using the first-principle models of batteries, this work presents a stochastic fault detection and diagnosis (FDD) algorithm to identify two particular faults in Li-ion battery cells, using easily measured quantities such as temperatures. In addition, models used for FDD are typically derived from the underlying physical phenomena. To make a model tractable and useful, it is common to make simplifications during the development of the model, which may consequently introduce a mismatch between models and battery cells. Further, FDD algorithms can be affected by uncertainty, which may originate from either intrinsic time varying phenomena or model calibration with noisy data. A two-step FDD algorithm is developed in this work to correct a model of Li-ion battery cells and tomore »identify faulty operations in a normal operating condition. An iterative optimization problem is proposed to correct the model by incorporating the errors between the measured quantities and model predictions, which is followed by an optimization-based FDD to provide a probabilistic description of the occurrence of possible faults, while taking the uncertainty into account. The two-step stochastic FDD algorithm is shown to be efficient in terms of the fault detection rate for both individual and simultaneous faults in Li-ion batteries, as compared to Monte Carlo (MC) simulations.« less