6 research outputs found
Resilient dynamic state estimation for power system using Cauchy-kernel-based maximum correntropy cubature Kalman filter
Accurate estimation of dynamic states is the key to monitoring power system operating conditions and controlling transient stability. The inevitable non-Gaussian noise and randomly occurring denial-of-service (DoS) attacks may, however, deteriorate the performance of standard filters seriously. To deal with these issues, a novel resilient cubature Kalman filter based on the Cauchy kernel maximum correntropy (CKMC) optimal criterion approach (termed CKMC-CKF) is developed, in which the Cauchy kernel function is used to describe the distance between vectors. Specifically, the errors of state and measurement in the cost function are unified by a statistical linearization technique, and the optimal estimated state is acquired by the fixed-point iteration method. Because of the salient thick-tailed feature and the insensitivity to the kernel bandwidth (KB) of Cauchy kernel function, the proposed CKMC-CKF can effectively mitigate the adverse effect of non-Gaussian noise and DoS attacks with better numerical stability. Finally, the efficacy of the proposed method is demonstrated on the standard IEEE 39-bus system under various abnormal conditions. Compared with standard cubature Kalman filter (CKF) and maximum correntropy criterion CKF (MCC-CKF), the proposed algorithm reveals better estimation accuracy and stronger resilience
Novel Computational Methods for State Space Filtering
The state-space formulation for time-dependent models has been long used invarious applications in science and engineering. While the classical Kalman filter(KF) provides optimal posterior estimation under linear Gaussian models, filteringin nonlinear and non-Gaussian environments remains challenging.Based on the Monte Carlo approximation, the classical particle filter (PF) can providemore precise estimation under nonlinear non-Gaussian models. However, it suffers fromparticle degeneracy. Drawing from optimal transport theory, the stochastic map filter(SMF) accommodates a solution to this problem, but its performance is influenced bythe limited flexibility of nonlinear map parameterisation. To account for these issues,a hybrid particle-stochastic map filter (PSMF) is first proposed in this thesis, wherethe two parts of the split likelihood are assimilated by the PF and SMF, respectively.Systematic resampling and smoothing are employed to alleviate the particle degeneracycaused by the PF. Furthermore, two PSMF variants based on the linear and nonlinearmaps (PSMF-L and PSMF-NL) are proposed, and their filtering performance is comparedwith various benchmark filters under different nonlinear non-Gaussian models.Although achieving accurate filtering results, the particle-based filters require expensive computations because of the large number of samples involved. Instead, robustKalman filters (RKFs) provide efficient solutions for the linear models with heavy-tailednoise, by adopting the recursive estimation framework of the KF. To exploit the stochasticcharacteristics of the noise, the use of heavy-tailed distributions which can fit variouspractical noises constitutes a viable solution. Hence, this thesis also introduces a novelRKF framework, RKF-SGαS, where the signal noise is assumed to be Gaussian and theheavy-tailed measurement noise is modelled by the sub-Gaussian α-stable (SGαS) distribution. The corresponding joint posterior distribution of the state vector and auxiliaryrandom variables is estimated by the variational Bayesian (VB) approach. Four differentminimum mean square error (MMSE) estimators of the scale function are presented.Besides, the RKF-SGαS is compared with the state-of-the-art RKFs under three kinds ofheavy-tailed measurement noises, and the simulation results demonstrate its estimationaccuracy and efficiency.One notable limitation of the proposed RKF-SGαS is its reliance on precise modelparameters, and substantial model errors can potentially impede its filtering performance. Therefore, this thesis also introduces a data-driven RKF method, referred to asRKFnet, which combines the conventional RKF framework with a deep learning technique. An unsupervised scheduled sampling technique (USS) is proposed to improve theistability of the training process. Furthermore, the advantages of the proposed RKFnetare quantified with respect to various traditional RKFs
Resilient dynamic state estimation for multi-machine power system with partial missing measurements
Accurate tracking the dynamics of power system plays a significant role in its reliability, resilience and security. To achieve the reliable and precise estimation results, many advanced estimation methods have been developed. However, most of them are aiming at filtering the measurement noise, while the adverse affect of partial measurement missing is rarely taken into account. To deal with this issue, a discrete distribution in the interval [0,1] is introduced to depict mechanism of partial measurement data loss that caused by the sensor failure. Then, a resilient fault tolerant extended Kalman filter (FTEKF) is designed in the recursive filter framework. Eventually, extensive simulations are carried on the different scale test systems. Numerical experimental results illustrate that the resilience and robustness of the proposed fault tolerant EKF method against partial measurement data loss
Novel Methodologies in State Estimation for Constrained Nonlinear Systems under Non-Gaussian Measurement Noise & Process Uncertainty
Chemical processes often involve scheduled/unscheduled changes in the operating conditions that may
lead to non-zero mean non-Gaussian (e.g., uniform, multimodal) process uncertainties and
measurement noises. Moreover, the distribution of the variables of a system subjected to process
constraints may not often follow Gaussian distributions. It is essential that the state estimation schemes
can properly capture the non-Gaussianity in the system to successfully monitor and control chemical
plants. Kalman Filter (KF) and its extension, i.e., Extended Kalman Filter (EKF), are well-known
model-driven state estimation schemes for unconstrained applications. The present thesis initially
performed state estimation using this approach for an unconstrained large-scale gasifier that supports
the efficiency and accuracy offered by KF. However, the underlying assumption considered in KF/EKF
is that all state variables, input variables, process uncertainties, and measurement noises follow
Gaussian distributions. The existing EKF-based approaches that consider constraints on the states
and/or non-Gaussian uncertainties and noises require significantly larger computational costs than
those observed in EKF applications. The current research aims to introduce an efficient EKF-based
scheme, referred to as constrained Abridged Gaussian Sum Extended Kalman Filter (constrained AGS EKF), that can generalize EKF to perform state estimation for constrained nonlinear applications
featuring non-zero mean non-Gaussian distributions. Constrained AGS-EFK uses Gaussian mixture
models to approximate the non-Gaussian distributions of the constrained states, process uncertainties,
and measurement noises. In the present abridged Gaussian sum framework, the main characteristics of
the overall Gaussian mixture models are used to represent the distributions of the corresponding non-Gaussian variable. Constrained AGS-EKF includes new modifications in both prior and posterior
estimation steps of the standard EKF to capture the non-zero mean distribution of the process
uncertainties and measurement noises, respectively. These modified prior and posterior steps require
the same computational costs as in EKF. Moreover, an intermediate step is considered in the
constrained AGS-EKF framework that explicitly applies the constraints on the priori estimation of the
distributions of the states. The additional computational costs to perform this intermediate step is
relatively small when compared to the conventional approaches such as Gaussian Sum Filter (GSF).
Note that the constrained AGS-EKF performs the modified EKF (consists of modified prior,
intermediate, and posterior estimation steps) only once and thus, avoids additional computational costs
and biased estimations often observed in GSFs.
Moving Horizon Estimation (MHE) is an optimization-based state estimation approach that provides
the optimal estimations of the states. Although MHE increases the required computation costs when
compared to EKF, MHE is best known for the constrained applications as it can take into account all
the process constraints. This PhD thesis initially provided an error analysis that shows that EKF can
provide accurate estimates if it is constantly initialized by a constrained estimation scheme such as
MHE (even though EKF is unconstrained state estimator). Despite the benefits provided by MHE for
constrained applications, this framework assumes that the distributions the process uncertainties and
measurement noises are zero-mean Gaussian, known a priori, and remain unchanged throughout the
operation, i.e., known time-independent distributions, which may not be accurate set of assumptions
for the real-world applications. Performing a set of MHEs (one MHE per each Gaussian component in
the mixture model) more likely become computationally taxing and hence, is discouraged. Instead, the
abridged Gaussian sum approach introduced in this thesis for AGS-EKF framework can be used to
improve the MHE performance for the applications involving non-Gaussian random noises and
uncertainties. Thus, a new extended version of MHE, i.e., referred to as Extended Moving Horizon
Estimation (EMHE), is presented that makes use of the Gaussian mixture models to capture the known
time-dependent non-Gaussian distributions of the process uncertainties and measurement noises use of
the abridged Gaussian sum approach. This framework updates the Gaussian mixture models to
represent the new characteristics of the known time-dependent distribution of noises/uncertainties upon
scheduled changes in the process operation. These updates require a relatively small additional CPU
time; thus making it an attractive estimation scheme for online applications in chemical engineering.
Similar to the standard MHE and despite the accuracy and efficiency offered by the EMHE scheme,
the application of EMHE is limited to the scenarios where the changes in the distribution of noises and
uncertainties are known a priori. However, the knowledge of the distributions of measurement noises
or process uncertainties may not be available a priori if any unscheduled operating changes occur
during the plant operation. Motivated by this aspect, a novel robust version of MHE, referred to as
Robust Moving Horizon Estimation (RMHE), is introduced that improves the robustness and accuracy
of the estimation by modelling online the unknown distributions of the measurement noises or process
uncertainties. The RMHE problem involves additional constraints and decision variables than the
standard MHE and EMHE problems to provide optimal Gaussian mixture models that represent the
unknown distributions of the random noises or uncertainties along with the optimal estimated states.
The additional constraints in the RMHE problem do not considerably increase the required
computational costs than that needed in the standard MHE and consequently, both the present RMHE and the standard MHE require somewhat similar CPU time on average to provide the point estimates.
The methodologies developed through this PhD thesis offers efficient MHE-based and EKF-based
frameworks that significantly improve the performance of these state estimation schemes for practical
chemical engineering applications
Self-aware reliable monitoring
Cyber-Physical Systems (CPSs) can be found in almost all technical areas where they constitute a key enabler for anticipated autonomous machines and devices. They are used in a wide range of applications such as autonomous driving, traffic control, manufacturing plants, telecommunication systems, smart grids, and portable health monitoring systems. CPSs are facing steadily increasing requirements such as autonomy, adaptability, reliability, robustness, efficiency, and performance.
A CPS necessitates comprehensive knowledge about itself and its environment to meet these requirements as well as make rational, well-informed decisions, manage its objectives in a sophisticated way, and adapt to a possibly changing environment. To gain such comprehensive knowledge, a CPS must monitor itself and its environment. However, the data obtained during this process comes from physical properties measured by sensors and may differ from the ground truth. Sensors are neither completely accurate nor precise. Even if they were, they could still be used incorrectly or break while operating. Besides, it is possible that not all characteristics of physical quantities in the environment are entirely known. Furthermore, some input data may be meaningless as long as they are not transferred to a domain understandable to the CPS. Regardless of the reason, whether erroneous data, incomplete knowledge or unintelligibility of data, such circumstances can result in a CPS that has an incomplete or inaccurate picture of itself and its environment, which can lead to wrong decisions with possible negative consequences.
Therefore, a CPS must know the obtained data’s reliability and may need to abstract information of it to fulfill its tasks. Besides, a CPS should base its decisions on a measure that reflects its confidence about certain circumstances. Computational Self-Awareness (CSA) is a promising solution for providing a CPS with a monitoring ability that is reliable and robust — even in the presence of erroneous data. This dissertation proves that CSA, especially the properties abstraction, data reliability, and confidence, can improve a system’s monitoring capabilities regarding its robustness and reliability. The extensive experiments conducted are based on two case studies from different fields: the health- and industrial sectors