Yuncheng Du

Comparison of stochastic fault detection and classification algorithms for nonlinear chemical processes

Abstract This paper presents a comparative study of two methods to identify and classify intermittent stochastic faults occurring in a dynamic nonlinear chemical process. The methods are based on two popular stochastic modelling techniques, i.e., generalized polynomial chaos expansion (gPC) and Gaussian Process (GP). The goal is to assess which method is more efficient for fault detection and diagnosis (FDD) when using models with parametric uncertainty, and to show the capabilities and drawbacks of each method. The first method is based on a first-principle model combined with a gPC expansion to represent the uncertainty. Resulting statistics such as probability density functions (PDFs) of the measured variables is further used to infer the intermittent faults. For the second method, a GP model is used to project multiple inputs into a univariate model response from which the fault can be identified based on a minimum distance criterion. The performance of the proposed FDD algorithms is illustrated through two examples: (i) a chemical process involving two continuous, stirred tank reactors (CSTRs) and a flash tank separator, and (ii) the Tennessee Eastman benchmark problem.

Wavelet based soft threshold denoising for vortex flowmeter

The vortex flowmeter is widely used due to its unique advantages, but the acquirement and measurement of vortex flowmeter signal in low velocity have not been resolved yet. Wavelet transform is gaining great popularity for denoising and has been proven to be an effective method to extract signal from noise. Based on multi-resolution analysis (MRA) and vortex flowmeter signal, a modified soft threshold filtering method was proposed to realize denoising for vortex flowmeter signal. Daubechies wavelets (dbN) and single branch reconstruction algorithm (SBRA) were adopted in this experiment. Analysis and simulations show that the modified soft threshold algorithm is powerful to separate the vortex flowmeter signal from noise when the output of vortex flowmeter is in low velocity.

Propagation of parametric uncertainty for the K+ channel model in mouse ventricular myocytes

Cardiac potassium (K+) channel plays an important role in cardiac electrical signaling. Mathematical models have been widely used to investigate the effects of K+ channels on cardiac functions. However, the model of K+ channel involves parametric uncertainties, which can be induced by fitting the models parameters that best capture experimental data. Since the prediction of cardiac functions are highly parameter-dependent, it is critical to quantify the influence of parametric uncertainty on the model responses to provide the more reliable predictions. This paper presents a new method to efficiently propagate the uncertainty on the models parameters of K+ channel to the gating variables as well as the current density. In this way, we can estimate the model predictions and their corresponding confidence intervals simultaneously. A generalized polynomial chaos (gPC) expansion approximating the parametric uncertainty is used in combination with the physical models to quantify and propagate the parametric uncertainties onto the modeled predictions of steady state activation and steady state inactivation of the K+ channel. Using Galerkin projection, the variation (i.e., confidence interval) of the gating variables resulting from the uncertainty of model parameters can then be estimated in a computationally efficient fashion. As compared with the Monte Carlo (MC) simulations, the proposed methodology shows its advantageous in terms of computational efficiency and accuracy, thus demonstrating the potential for dealing with more complicated cardiac models.Cardiac potassium (K+) channel plays an important role in cardiac electrical signaling. Mathematical models have been widely used to investigate the effects of K+ channels on cardiac functions. However, the model of K+ channel involves parametric uncertainties, which can be induced by fitting the models parameters that best capture experimental data. Since the prediction of cardiac functions are highly parameter-dependent, it is critical to quantify the influence of parametric uncertainty on the model responses to provide the more reliable predictions. This paper presents a new method to efficiently propagate the uncertainty on the models parameters of K+ channel to the gating variables as well as the current density. In this way, we can estimate the model predictions and their corresponding confidence intervals simultaneously. A generalized polynomial chaos (gPC) expansion approximating the parametric uncertainty is used in combination with the physical models to quantify and propagate the parametric uncertainties onto the modeled predictions of steady state activation and steady state inactivation of the K+ channel. Using Galerkin projection, the variation (i.e., confidence interval) of the gating variables resulting from the uncertainty of model parameters can then be estimated in a computationally efficient fashion. As compared with the Monte Carlo (MC) simulations, the proposed methodology shows its advantageous in terms of computational efficiency and accuracy, thus demonstrating the potential for dealing with more complicated cardiac models.

Fault detection and diagnosis using empirical mode decomposition based principal component analysis

Abstract This paper presents a new algorithm to identify and diagnose stochastic faults in Tennessee Eastman (TE) process. The algorithm combines Ensemble Empirical Mode Decomposition (EEMD) with Principal Component Analysis (PCA) and Cumulative Sum (CUSUM) to diagnose a group of faults that could not be properly detected and/or diagnosed with previously reported techniques. This algorithm includes three steps: measurements pre-filtering, fault detection, and fault diagnosis. Measured variables are first decomposed into different scales using the EEMD-based PCA, from which fault signatures can be extracted for fault detection and diagnosis (FDD). The T2 and Q statistics-based CUSUMs are further applied to improve fault detection, where a set of PCA models are developed from historical data to characterize anomalous fingerprints that are correlated with each fault for accurate fault diagnosis. The algorithm developed in this paper can successfully identify and diagnose both individual and simultaneous occurrences of stochastic faults.

Global sensitivity analysis for developing biological models: Application to K+ channel model in mouse ventricular myocytes

Mathematical models of cardiac myocytes are highly nonlinear and involve a large number of model parameters. The parameters are estimated using experimental data, which are often corrupted by noise and uncertainty. Such uncertainty can be propagated onto model parameters during model calibration, which further affects model reliability and credibility. In order to improve model accuracy, it is important to quantify and reduce the uncertainty in model response resulting from parametric uncertainty. Sensitivity analysis is a key technique to investigate the significance of parametric uncertainty and its effect on model responses. This can identify and rank most sensitive parameters, and evaluate the effect of uncertainty on model outputs. In this work, a global sensitivity analysis is developed to determine the significance of parametric uncertainty on model responses using Sobol indices. This method is applied to nonlinear K+ channel models of mouse ventricular myocytes to demonstrate the efficacy of the developed algorithm.Mathematical models of cardiac myocytes are highly nonlinear and involve a large number of model parameters. The parameters are estimated using experimental data, which are often corrupted by noise and uncertainty. Such uncertainty can be propagated onto model parameters during model calibration, which further affects model reliability and credibility. In order to improve model accuracy, it is important to quantify and reduce the uncertainty in model response resulting from parametric uncertainty. Sensitivity analysis is a key technique to investigate the significance of parametric uncertainty and its effect on model responses. This can identify and rank most sensitive parameters, and evaluate the effect of uncertainty on model outputs. In this work, a global sensitivity analysis is developed to determine the significance of parametric uncertainty on model responses using Sobol indices. This method is applied to nonlinear K+ channel models of mouse ventricular myocytes to demonstrate the efficacy of the developed algorithm.

Detection of the propagating direction of electrical wavefront in atrial fibrillation

Atrial Fibrillation (AF) is one of the most common sustained arrhythmia, which can increase the risk of heart failure and stroke. Understanding the complex electrical dynamics of AF and correctly targeting AF sources for ablation therapies remain challenging in clinical practice. This is due to the incapability to reconstruct the electrical dynamic of AF, and lack of efficient approach for AF source identification. This paper builds a multi-sale framework for modeling of the abnormal electrical propagation in AF initiated by triggers from Pulmonary Veins (PVs). A new algorithm is developed to detect the propagating direction of electrical wavefronts. The detection algorithm is further validated using modeling results. The developed multi-scale framework and the detection algorithm will contribute to AF diagnosis and potentially improve the treatment outcomes of AF ablations.Atrial Fibrillation (AF) is one of the most common sustained arrhythmia, which can increase the risk of heart failure and stroke. Understanding the complex electrical dynamics of AF and correctly targeting AF sources for ablation therapies remain challenging in clinical practice. This is due to the incapability to reconstruct the electrical dynamic of AF, and lack of efficient approach for AF source identification. This paper builds a multi-sale framework for modeling of the abnormal electrical propagation in AF initiated by triggers from Pulmonary Veins (PVs). A new algorithm is developed to detect the propagating direction of electrical wavefronts. The detection algorithm is further validated using modeling results. The developed multi-scale framework and the detection algorithm will contribute to AF diagnosis and potentially improve the treatment outcomes of AF ablations.

Nonperiodic cycle detection and application in gas liquid two-phase flow

Nonperiodic cycle detection methods for gas/liquid two phase flow system were discussed. Cycle detection methods, such as Hurst analysis, the V statistic and the P statistic were briefly reviewed; in addition, a modified P statistic method was introduced. Two types of time series, i.e. mathematically sine wave time series and experimental electrical capacitance tomography time series of plug flow and slug flow under different flow conditions were investigated to verify the effectiveness of different cycle detection methods. The sine wave time series and sine wave time series under gauss noise were used to validate different cycle detection methods. For the electrical capacitance tomography time series of different flow regime, discrete wavelet transform (DWT) was adopted to decompose the original signal into approximate signal and detail signals, and then different cycle detection methods were mainly applied to realize cyclic characterization analysis of detail signals for plug flow and slug flow. The results show that the nonperiodic cycle characteristic analysis can reflect the property of different flow regimes.