Continuous stirred tank reactor fault detection using higher degree Cubature Kalman filter

Continuous Stirred Tank Reactor (CSTR) plays a major role in chemical industries, it ensures the process of mixing reactants according to the attended specification to produce a specific output. It is a complex process that usually represent with nonlinear model for benchmarking. Any abnormality, disturbance and unusual condition can easily interrupt the operations, especially fault. And this problem need to detect and rectify as soon as possible. A good knowledge based fault detection using available model require a good error residual between the measurement and the estimated state. Kalman filter is an example of a good estimator, and has been exploited in many researches to detect fault. In this paper, Higher degree Cubature Kalman Filter (HDCKF) is proposed as a method for fault detection by estimation the current state. Cubature Kalman filter (CKF) is an extension of the Kalman filter with the main purpose is to estimate process and measurement state with high nonlinearities. It is based on spherical radial integration to estimate current state by generating cubature points with specific value. Conventional CKF use 3rd degree spherical and 3rd degree radial, here we implement Higher Degree CKF (HDCKF) to have better accuracy as compared to conventional CKF. High accuracy is required to ensure no false alarm is detected and furthermore good computational cost will improve its detection. Finally, a numerical example of CSTR fault detection using HDCKF is presented. Implementation of HDCKF for fault detection is compared with other filter to show effective results

The Sparse-grid based Nonlinear Filter: Theory and Applications

Filtering or estimation is of great importance to virtually all disciplines of engineering and science that need inference, learning, information fusion, and knowledge discovery of dynamical systems. The filtering problem is to recursively determine the states and/or parameters of a dynamical system from a sequence of noisy measurements made on the system. The theory and practice of optimal estimation of linear Gaussian dynamical systems have been well established and successful, but optimal estimation of nonlinear and non-Gaussian dynamical systems is much more challenging and in general requires solving partial differential equations and intractable high-dimensional integrations. Hence, Gaussian approximation filters are widely used. In this dissertation, three innovative point-based Gaussian approximation filters including sparse Gauss-Hermite quadrature filter, sparse-grid quadrature filter, and the anisotropic sparse-grid quadrature filter are proposed. The relationship between the proposed filters and conventional Gaussian approximation filters is analyzed. In particular, it is proven that the popular unscented Kalman filter and the cubature Kalman filter are subset of the proposed sparse-grid filters. The sparse-grid filters are employed in three aerospace applications including spacecraft attitude estimation, orbit determination, and relative navigation. The results show that the proposed filters can achieve better estimation accuracy than the conventional Gaussian approximation filters, such as the extended Kalman filter, the cubature Kalman filter, the unscented Kalman filter, and is computationally more efficient than the Gauss-Hermite quadrature filter

Strong Tracking Filter for Nonlinear Systems with Randomly Delayed Measurements and Correlated Noises

This paper proposes a novel strong tracking filter (STF), which is suitable for dealing with the filtering problem of nonlinear systems when the following cases occur: that is, the constructed model does not match the actual system, the measurements have the one-step random delay, and the process and measurement noises are correlated at the same epoch. Firstly, a framework of decoupling filter (DF) based on equivalent model transformation is derived. Further, according to the framework of DF, a new extended Kalman filtering (EKF) algorithm via using first-order linearization approximation is developed. Secondly, the computational process of the suboptimal fading factor is derived on the basis of the extended orthogonality principle (EOP). Thirdly, the ultimate form of the proposed STF is obtained by introducing the suboptimal fading factor into the above EKF algorithm. The proposed STF can automatically tune the suboptimal fading factor on the basis of the residuals between available and predicted measurements and further the gain matrices of the proposed STF tune online to improve the filtering performance. Finally, the effectiveness of the proposed STF has been proved through numerical simulation experiments

State Estimation Fusion for Linear Microgrids over an Unreliable Network

Microgrids should be continuously monitored in order to maintain suitable voltages over time. Microgrids are mainly monitored remotely, and their measurement data transmitted through lossy communication networks are vulnerable to cyberattacks and packet loss. The current study leverages the idea of data fusion to address this problem. Hence, this paper investigates the effects of estimation fusion using various machine-learning (ML) regression methods as data fusion methods by aggregating the distributed Kalman filter (KF)-based state estimates of a linear smart microgrid in order to achieve more accurate and reliable state estimates. This unreliability in measurements is because they are received through a lossy communication network that incorporates packet loss and cyberattacks. In addition to ML regression methods, multi-layer perceptron (MLP) and dependent ordered weighted averaging (DOWA) operators are also employed for further comparisons. The results of simulation on the IEEE 4-bus model validate the effectiveness of the employed ML regression methods through the RMSE, MAE and R-squared indices under the condition of missing and manipulated measurements. In general, the results obtained by the Random Forest regression method were more accurate than those of other methods.This research was partially funded by public research projects of Spanish Ministry of Science and Innovation, references PID2020-118249RB-C22 and PDC2021-121567-C22 - AEI/10.13039/ 501100011033, and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors, reference EPUC3M17

Regularized EM algorithm for sparse parameter estimation in nonlinear dynamic systems with application to gene regulatory network inference

Parameter estimation in dynamic systems finds applications in various disciplines, including system biology. The well-known expectation-maximization (EM) algorithm is a popular method and has been widely used to solve system identification and parameter estimation problems. However, the conventional EM algorithm cannot exploit the sparsity. On the other hand, in gene regulatory network inference problems, the parameters to be estimated often exhibit sparse structure. In this paper, a regularized expectation-maximization (rEM) algorithm for sparse parameter estimation in nonlinear dynamic systems is proposed that is based on the maximum a posteriori (MAP) estimation and can incorporate the sparse prior. The expectation step involves the forward Gaussian approximation filtering and the backward Gaussian approximation smoothing. The maximization step employs a re-weighted iterative thresholding method. The proposed algorithm is then applied to gene regulatory network inference. Results based on both synthetic and real data show the effectiveness of the proposed algorithm

Nonlinear State Estimation Using Optimal Gaussian Sampling with Applications to Tracking

This thesis is concerned with the ubiquitous problem of estimating the hidden state of a discrete-time stochastic nonlinear dynamic system. The focus is on the derivation of new Gaussian state estimators and the improvement of existing approaches. Also the challenging task of distributed state estimation is addressed by proposing a sample-based fusion of local state estimates. The proposed estimation techniques are applied to extended object tracking