Improved Statistical Fault Detection Technique and Application to Biological Phenomena Modeled by S-Systems.

In our previous work, we have demonstrated the effectiveness of the linear multiscale principal component analysis (PCA)-based moving window (MW)-generalized likelihood ratio test (GLRT) technique over the classical PCA and multiscale principal component analysis (MSPCA)-based GLRT methods. The developed fault detection algorithm provided optimal properties by maximizing the detection probability for a particular false alarm rate (FAR) with different values of windows, and however, most real systems are nonlinear, which make the linear PCA method not able to tackle the issue of non-linearity to a great extent. Thus, in this paper, first, we apply a nonlinear PCA to obtain an accurate principal component of a set of data and handle a wide range of nonlinearities using the kernel principal component analysis (KPCA) model. The KPCA is among the most popular nonlinear statistical methods. Second, we extend the MW-GLRT technique to one that utilizes exponential weights to residuals in the moving window (instead of equal weightage) as it might be able to further improve fault detection performance by reducing the FAR using exponentially weighed moving average (EWMA). The developed detection method, which is called EWMA-GLRT, provides improved properties, such as smaller missed detection and FARs and smaller average run length. The idea behind the developed EWMA-GLRT is to compute a new GLRT statistic that integrates current and previous data information in a decreasing exponential fashion giving more weight to the more recent data. This provides a more accurate estimation of the GLRT statistic and provides a stronger memory that will enable better decision making with respect to fault detection. Therefore, in this paper, a KPCA-based EWMA-GLRT method is developed and utilized in practice to improve fault detection in biological phenomena modeled by S-systems and to enhance monitoring process mean. The idea behind a KPCA-based EWMA-GLRT fault detection algorithm is to combine the advantages brought forward by the proposed EWMA-GLRT fault detection chart with the KPCA model. Thus, it 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, transport proteins, regulatory proteins, lysine, and cadaverine. The results demonstrate the effectiveness of the proposed KPCA-based EWMA-GLRT method over Q , GLRT, EWMA, Shewhart, and moving window-GLRT methods. The detection performance is assessed and evaluated in terms of FAR, missed detection rates, and average run length (ARL1) values.

Modeling of nonlinear biological phenomena modeled by S-systems.

A central challenge in computational modeling of biological systems is the determination of the model parameters. In such cases, estimating these variables or parameters from other easily obtained measurements can be extremely useful. For example, time-series dynamic genomic data can be used to develop models representing dynamic genetic regulatory networks, which can be used to design intervention strategies to cure major diseases and to better understand the behavior of biological systems. Unfortunately, biological measurements are usually highly infected by errors that hide the important characteristics in the data. Therefore, these noisy measurements need to be filtered to enhance their usefulness in practice. This paper addresses the problem of state and parameter estimation of biological phenomena modeled by S-systems using Bayesian approaches, where the nonlinear observed system is assumed to progress according to a probabilistic state space model. The performances of various conventional and state-of-the-art state estimation techniques are compared. These techniques include the extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), and the developed variational Bayesian filter (VBF). Specifically, two comparative studies are performed. In the first comparative study, the state variables (the enzyme CadA, the model cadBA, the cadaverine Cadav and the lysine Lys for a model of the Cad System in Escherichia coli (CSEC)) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error (RMSE) with respect to the noise-free data. In the second comparative study, the state variables as well as the model parameters are simultaneously estimated. In this case, in addition to comparing the performances of the various state estimation techniques, the effect of the number of estimated model parameters on the accuracy and convergence of these techniques is also assessed. The results of both comparative studies show that the UKF provides a higher accuracy than the EKF due to the limited ability of EKF to accurately estimate the mean and covariance matrix of the estimated states through lineralization of the nonlinear process model. The results also show that the VBF provides a relative improvement over PF. This is because, unlike the PF which depends on the choice of sampling distribution used to estimate the posterior distribution, the VBF yields an optimum choice of the sampling distribution, which also utilizes the observed data. The results of the second comparative study show that, for all techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. The VBF, however, still provides advantages over other methods with respect to estimation accuracy as well convergence.

Fuzzy intervention in biological phenomena.

An important objective of modeling biological phenomena is to develop therapeutic intervention strategies to move an undesirable state of a diseased network toward a more desirable one. Such transitions can be achieved by the use of drugs to act on some genes/metabolites that affect the undesirable behavior. Due to the fact that biological phenomena are complex processes with nonlinear dynamics that are impossible to perfectly represent with a mathematical model, the need for model-free nonlinear intervention strategies that are capable of guiding the target variables to their desired values often arises. In many applications, fuzzy systems have been found to be very useful for parameter estimation, model development and control design of nonlinear processes. In this paper, a model-free fuzzy intervention strategy (that does not require a mathematical model of the biological phenomenon) is proposed to guide the target variables of biological systems to their desired values. The proposed fuzzy intervention strategy is applied to three different biological models: a glycolytic-glycogenolytic pathway model, a purine metabolism pathway model, and a generic pathway model. The simulation results for all models demonstrate the effectiveness of the proposed scheme.