Majdi Mansouri

Multiscale Kernel PLS-Based Exponentially Weighted-GLRT and Its Application to Fault Detection

In this paper, we develop an improved statistical technique in order to enhance monitoring of biological processes. To improve the performance of monitoring, a detection statistic that exploits the advantages of the generalized likelihood ratio test (GLRT) statistic with those of the exponentially weighted moving average filter, kernel partial least square (KPLS) model, and multiscale representation is developed. The advantages of multiscale (MS) KPLS-based exponentially weighted GLRT (EW-GLRT) are threefold: First, the developed EW-GLRT statistic takes into account the information given by the current and previous data by giving high importance to the more recent data; second, the dynamical multiscale representation is proposed to extract accurate deterministic features and decorrelate autocorrelated measurements; third, the MSKPLS model evaluates the KPLS of the wavelet coefficients at each scale. Due to its multiscale nature, MSKPLS is appropriate for modeling of data that contain contributions from events whose behavior changes over time and frequency. The detection performance is studied using Cad System in E. coli model and genomic copy number data for detecting small and moderate shifts. MSKPLS-based EW-GLRT is used to enhance fault detection of the Cad System in E. coli model through monitoring some of the key variables involved in this model, such as enzymes, lysine, and cadaverine. The proposed technique is also applied to detect diseases using genomic copy number data through better detection of aberrations in the genetic information of patients, which can help medical doctors make more accurate diagnosis of diseases.

Process Monitoring Using Data-Based Fault Detection Techniques: Comparative Studies

Data based monitoring methods are often utilized to carry out fault detection (FD) when process models may not necessarily be available. The partial least square (PLS) and principle component analysis (PCA) are two basic types of multivariate FD methods, however, both of them can only be used to monitor linear processes. Among these extended data based methods, the kernel PCA (KPCA) and kernel PLS (KPLS) are the most well-known and widely adopted. KPCA and KPLS models have several advantages, since, they do not require nonlinear optimization, and only the solution of an eigenvalue problem is required. Also, they provide a better understanding of what kind of nonlinear features are extracted: the number of the principal components (PCs) in a feature space is fixed a priori by selecting the appropriate kernel function. Therefore, the objective of this work is to use KPCA and KPLS techniques to monitor nonlinear data. The improved FD performance of KPCA and KPLS is illustrated through two simulated examples, one using synthetic data and the other using simulated continuously stirred tank reactor (CSTR) data. The results demonstrate that both KPCA and KPLS methods are able to provide better detection compared to the linear versions.

Predicting biomass and grain protein content using Bayesian methods

This paper deals with the problem of predicting biomass and grain protein content using improved particle filtering (IPF) based on minimizing the Kullback–Leibler divergence. The performances of IPF are compared with those of the conventional particle filtering (PF) in two comparative studies. In the first one, we apply IPF and PF at a simple dynamic crop model with the aim to predict a single state variable, namely the winter wheat biomass, and to estimate several model parameters. In the second study, the proposed IPF and the PF are applied to a complex crop model (AZODYN) to predict a winter-wheat quality criterion, namely the grain protein content. The results of both comparative studies reveal that the IPF method provides a better estimation accuracy than the PF method. The benefit of the IPF method lies in its ability to provide accuracy related advantages over the PF method since, unlike the PF which depends on the choice of the sampling distribution used to estimate the posterior distribution, the IPF yields an optimum choice of this sampling distribution, which also utilizes the observed data. The performance of the proposed method is evaluated in terms of estimation accuracy, root mean square error, mean absolute error and execution times.

An improved particle filtering for time-varying nonlinear prediction of biomass and grain protein content

Propose to use the improved particle filter for nonlinear states and parameters estimation.Apply the improved particle filter for time-varying nonlinear prediction of biomass and grain protein content.Investigate the effects of practical challenges on the estimation performances.Comparative performance analysis of various state-of-the-art estimation techniques. This paper addresses the problem of time-varying nonlinear prediction of biomass and grain protein content. The objectives of this paper are threefold. The first objective is to use an improved particle filter with better proposal distribution for nonlinear prediction. The second objective is to extend the state and parameter estimation techniques (i.e., particle filter (PF) and improved particle filter (IPF)) to better handle nonlinear and non-Gaussian processes without a priori state information, by utilizing a time-varying assumption of statistical parameters. The third objective is to apply the state estimation techniques PF and IPF for predicting and modeling biomass and grain protein content. In a first step, we present an application of PF and IPF to a simple dynamic crop model with the aim to predict a single state variable, namely winter wheat biomass. In a second step, we apply PF and IPF for updating predictions of complex nonlinear crop models in order to predict protein grain content.The comparative analysis is conducted to study the effects of two practical challenges (measurement noise, and the number of states and parameters to be estimated) on the estimation performances of PF, and IPF. To study the effect of measurement noise on the estimation performances, several measurement noise contributions are considered. Then, the estimation performances of PF and IPF are compared for different noise levels. Similarly, to investigate the effect of the number of states and parameters to be estimated on the estimation performances of PF and IPF, the estimation performance is analyzed for different numbers of estimated states and parameters.The simulation results of both comparative studies show that the IPF provides a significant improvement over the PF. This is because, unlike the PF which depends on the choice of sampling distribution used to estimate the posterior distribution, the IPF yields an optimum choice of this distribution, which also utilizes the observed data. The results of the comparative studies show also that, for all the techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The performance of the proposed method is evaluated on a synthetic example in terms of estimation accuracy, root mean square error and execution times.

Nonlinear State and Parameter Estimation Using Iterated Sigma Point Kalman Filter: Comparative Studies

In this chapter, iterated sigma‐point Kalman filter (ISPKF) methods are used for nonlinear state variable and model parameter estimation. Different conventional state estimation methods, namely the unscented Kalman filter (UKF), the central difference Kalman filter (CDKF), the square‐root unscented Kalman filter (SRUKF), the square‐ root central difference Kalman filter (SRCDKF), the iterated unscented Kalman filter (IUKF), the iterated central difference Kalman filter (ICDKF), the iterated square‐root unscented Kalman filter (ISRUKF) and the iterated square‐root central difference Kalman filter (ISRCDKF) are evaluated through a simulation example with two comparative studies in terms of state accuracies, estimation errors and convergence. The state variables are estimated in the first comparative study, from noisy measure‐ ments with the several estimation methods. Then, in the next comparative study, both of states and parameters are estimated, and are compared by calculating the estimation root mean square error (RMSE) with the noise‐free data. The impacts of the practical challenges (measurement noise and number of estimated states/ parameters) on the performances of the estimation techniques are investigated. The results of both comparative studies reveal that the ISRCDKF method provides better estimation accuracy than the IUKF, ICDKF and ISRUKF. Also the previous methods provide better accuracy than the UKF, CDKF, SRUKF and SRCDKF techniques. The ISRCDKF method provides accuracy over the other different estimation techniques; by iterating maximum a posteriori estimate around the updated state, it re‐linearizes the measurement equation instead of depending on the predicted state. The results also represent that estimating more parameters impacts the estimation accuracy as well as the convergence of the estimated parameters and states. The ISRCDKF provides improved state accuracies than the other techniques even with abrupt changes in estimated states.

Prediction of non-linear time-variant dynamic crop model using Bayesian methods

This work addresses the problem of predicting a non-linear time-variant leaf area index and soil moisture model (LSM) using state estimation. These techniques include the extended Kalman filter (EKF), particle filter (PF) and the more recently developed technique, variational filter (VF). In the comparative study, the state variables (the leaf-area index LAI, the volumetric water content of the layer 1, HUR1 and the volumetric water content of the layer 2, HUR2) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error with respect to the noise-free data. The results show that VF provides a significant improvement over EKF and PF.