Nonlinear State Estimation Technique Research Articles

Challenges and Opportunities on Nonlinear State Estimation of Chemical and Biochemical Processes

This paper provides an overview of nonlinear state estimation techniques along with a discussion on the challenges and opportunities for future work in the field. Emphasis is given on Bayesian methods such as moving horizon estimation (MHE) and extended Kalman filter (EKF). A discussion on Bayesian, deterministic, and hybrid methods is provided and examples of each of these methods are listed. An approach for nonlinear state estimation design is included to guide the selection of the nonlinear estimator by the user/practitioner. Some of the current challenges in the field are discussed involving covariance estimation, uncertainty quantification, time-scale multiplicity, bioprocess monitoring, and online implementation. A case study in which MHE and EKF are applied to a batch reactor system is addressed to highlight the challenges of these technologies in terms of performance and computational time. This case study is followed by some possible opportunities for state estimation in the future including the incorporation of more efficient optimization techniques and development of heuristics to streamline the further adoption of MHE.

Batch and Moving Horizon Estimation for Systems subjected to Non-additive Stochastic Disturbances

Abstract Nonlinear state estimation techniques for state dynamics involving additive discrete zero mean white noise have received considerable attention in the past. The probabilistic formulation of the conventional moving horizon estimation (MHE) is also developed under this simplifying assumption. In reality, the unmeasured disturbances affect the states and measurements in much more complex way and thus can not be treated in additive manner. In current work, we formally introduce a probabilistic formulation of MHE which can handle such nonlinear uncertainties in the state dynamics. The efficacy of the proposed MHE has been demonstrated by conducting stochastic simulation studies on a benchmark continuous stirred tank reactor (CSTR) system. It is found that the estimation performance of the proposed MHE formulation is comparable to estimation performance of a sampling based Bayesian estimator (unscented Kalman filter or UKF), which deals with non-additive disturbances systematically, and significantly better than the extended Kalman filter (EKF) that deals with non-additive disturbances through successive linearisation.

Secure State Estimation and Control for Cyber Security of the Nonlinear Power Systems

We focus on securely estimating the state of a nonlinear dynamical system from a set of corrupted measurements for two classes of nonlinear systems, and propose a technique that enables us to perform secure state estimation for those systems. We then illustrate how the proposed nonlinear secure state estimation technique can be used to perform estimation in the cyber layer of interconnected power systems under cyber-physical attacks and communication failures. In particular, we focus on an interconnected power system comprised of several synchronous generators, transmission lines, loads, and energy storage units, and propose a secure estimator that allows us to securely estimate the dynamic states of the power network. Finally, we numerically demonstrate the effectiveness of the proposed secure estimation algorithm, and show that the algorithm enables the cyber layer to accurately reconstruct the attack signals.

A Nonlinear Dynamics-Based Estimator for Functional Electrical Stimulation: Preliminary Results From Lower-Leg Extension Experiments

Miniature inertial measurement units (IMUs) are wearable sensors that measure limb segment or joint angles during dynamic movements. However, IMUs are generally prone to drift, external magnetic interference, and measurement noise. This paper presents a new class of nonlinear state estimation technique called state-dependent coefficient (SDC) estimation to accurately predict joint angles from IMU measurements. The SDC estimation method uses limb dynamics, instead of limb kinematics, to estimate the limb state. Importantly, the nonlinear limb dynamic model is formulated into state-dependent matrices that facilitate the estimator design without performing a Jacobian linearization. The estimation method is experimentally demonstrated to predict knee joint angle measurements during functional electrical stimulation of the quadriceps muscle. The nonlinear knee musculoskeletal model was identified through a series of experiments. The SDC estimator was then compared with an extended kalman filter (EKF), which uses a Jacobian linearization and a rotation matrix method, which uses a kinematic model instead of the dynamic model. Each estimator's performance was evaluated against the true value of the joint angle, which was measured through a rotary encoder. The experimental results showed that the SDC estimator, the rotation matrix method, and EKF had root mean square errors of 2.70°, 2.86°, and 4.42°, respectively. Our preliminary experimental results show the new estimator's advantage over the EKF method but a slight advantage over the rotation matrix method. However, the information from the dynamic model allows the SDC method to use only one IMU to measure the knee angle compared with the rotation matrix method that uses two IMUs to estimate the angle.

A Comparison of Advanced Non-linear State Estimation Techniques for Ground Vehicles

This paper presents a comparative examination of state-of-the-art non-linear state estimation techniques. First, the Sigma- Point (SPKF) stochastic estimators are investigated on the basis of the Unscented Transformation. This is followed by the technique of non-linear symmetry-preserving observers for non-linear dynamics on the basis of symmetrical LIE groups. The variety of the deterministic and stochastic state estimation algorithms is studied the kinematics of ground vehicles. Two cases are described that deal with the reliability of path tracking, the convergence and speed of off-line calibration.

Robust on-line fault detection diagnosis for HVAC components based on nonlinear state estimation techniques

This work presents a robust and computationally efficient algorithm for both whole-building and component-level energy fault detection and diagnosis (FDD). The algorithm is able to provide reliable estimation of multiple and simultaneous fault conditions, even in the presence of noisy and sometimes erroneous sensor data, and to provide uncertainty estimation. The algorithm can be used to provide such outputs as the probability of a fault, the likely cause(s), and the expected consequences of the fault(s) on energy use. The approach is based on an advanced Bayesian nonlinear state estimation technique called Unscented Kalman Filtering, but with our addition of a back-smoothing method that provides fast and robust FDD for common building use cases. The approach is presented and demonstrated for detecting energy and hydraulic faults in a chiller plant. The model of the chiller plant is a subsystem of an actual chiller plant, calibrated to real data. The algorithm can detect common faults, such as (1) energy faults (e.g., the chiller is not working properly, or far from its nominal condition), (2) functional faults caused by issues in the compressor and (3) occlusions in the valves that may reduce the water flow rate through the condenser and evaporator water loop. It is also shown that estimates of uncertainty are consistent with the error in the synthetic data, and can be updated as new data stream in from sensors.

Supervisory control and data acquisition data‐based non‐linear state estimation technique for wind turbine gearbox condition monitoring

Offshore wind energy is catching increasing worldwide interest. However, access and maintenance offshore can be difficult and will be more costly than onshore, and hence, availability is correspondingly lower. As a result, there is a growing interest in wind turbine condition monitoring with condition-based rather than responsive and scheduled maintenance. A non-linear state estimation technique (NSET) model is presented here to model a healthy wind turbine gearbox using stored historical data. These data capture the inter-relationship between the model input and output parameters. The state vectors comprising the data should cover as much as turbine operational range, including the extreme conditions in order to obtain an accurate model performance. A model so constructed can be applied to assess the operational data. Welch's t-test is employed in the fault detection algorithm, together with suitable time series filtering, to identify incipient anomalies in the turbine gearbox before they develop into catastrophic faults. Two case studies based on 10-minute supervisory control and data acquisition data from a commercial wind farm are presented to demonstrate the model's effectiveness. Comparison is made with neural network modelling, and the NSET approach is demonstrated to be superior.

Wind Turbine Tower Vibration Modeling and Monitoring by the Nonlinear State Estimation Technique (NSET)

With appropriate vibration modeling and analysis the incipient failure of key components such as the tower, drive train and rotor of a large wind turbine can be detected. In this paper, the Nonlinear State Estimation Technique (NSET) has been applied to model turbine tower vibration to good effect, providing an understanding of the tower vibration dynamic characteristics and the main factors influencing these. The developed tower vibration model comprises two different parts: a sub-model used for below rated wind speed; and another for above rated wind speed. Supervisory control and data acquisition system (SCADA) data from a single wind turbine collected from March to April 2006 is used in the modeling. Model validation has been subsequently undertaken and is presented. This research has demonstrated the effectiveness of the NSET approach to tower vibration; in particular its conceptual simplicity, clear physical interpretation and high accuracy. The developed and validated tower vibration model was then used to successfully detect blade angle asymmetry that is a common fault that should be remedied promptly to improve turbine performance and limit fatigue damage. The work also shows that condition monitoring is improved significantly if the information from the vibration signals is complemented by analysis of other relevant SCADA data such as power performance, wind speed, and rotor loads.

Ensemble-Kalman-Filter-Based Power System Harmonic Estimation

The growing use of power-electronics-based components and nonlinear loads is increasing the presence of harmonics in power system signals. In this scenario, proper estimation of such harmonics is intended to maintain power quality and improved operation of the system. It is also desirable that the estimation technique should be computationally efficient while being accurate. From this viewpoint, this paper proposes a nonlinear state estimation technique based on ensemble Kalman filtering for estimation of harmonics, interharmonics, and subharmonics, all using a single framework and at a time, from distorted power system signal. The proposed technique is computationally efficient compared to conventional Kalman filtering leading to less computational cost and hardware requirement. It is observed from both simulation and experimental studies that the proposed ensemble Kalman filter (KF) approach to estimation of harmonics, interharmonics, and subharmonics in a distorted power system signal exhibits superior estimation performance in terms of tracking time and accuracy as compared to performances of some of the existing techniques such as recursive least square, recursive least mean square, and KF algorithms. The proposed technique is also found to be robust and gives accurate estimates even in the presence of amplitude variations in the measured signal.

A co-processor design to accelerate sequential monocular SLAM EKF process

Extended Kalman Filter (EKF) is a non-linear state estimation technique which is used to produce values that close to the true value when given with measurement containing noise and other inaccuracies. In Monocular Simultaneous Localization and Mapping (SLAM), EKF is used to estimate position and motion information. In this paper, Monocular SLAM software implementation on a general purpose computer is studied to find the most time consuming part of the estimation program. The analysis concentrates on the Monocular SLAM EKF estimation process which involves prediction, measurement prediction, matching and update. For this purpose, a form of dynamic programming analysis tool called software profiling is utilized to determine which section of the estimation program demands the highest processing time. Based on the analysis, it is found that EKF “matching” process contribute to the highest computation time. The reason behind the time-consuming process is because for every predicted feature in the matching stage, the acceptance region and their cross correlation have to be calculated. In a typical general purpose computer software implementation, the processing is limited to sequences of operations (i.e. sequential processing). Such implementation will delay the next process until the prior process completed. However, further analysis conducted in this paper shows that each feature does not depend on the prior process and can be processed individually. This would allow several features to be processed simultaneously to improve the execution speed. Therefore, an FPGA pipelined and parallel processing architecture is proposed.

Single Pan and Tilt Camera Indoor Positioning and Tracking System

An inexpensive single pan and tilt camera based indoor positioning and tracking system is proposed, supported on a functional architecture where three main modules can be identified: one related to the interface with the camera, tackled with parameter estimation techniques; other, responsible for isolating and identifying the target, based on advanced image processing techniques, and a third, that resorting to nonlinear dynamic system suboptimal state estimation techniques, performs the tracking of the target and estimates its position, and linear and angular velocities. The contributions of this work are fourfold: i) a new indoor positioning and tracking system architecture; ii) a new lens distortion calibration method, that preserves generic straight lines in images; iii) suboptimal nonlinear multiple-model adaptive estimation techniques, for the adopted target model, to tackle the positioning and trackingtasks, andiv) theimplementationandvalidationin real time of a complex tracking system, based on a low cost single camera. To assess the performance of the proposed system, a series of indoor experimental tests for a range of operation of up to ten meter were carried out. Acentimetric accuracy was obtained under realistic conditions.

A fast and versatile technique for constrained state estimation

In situ adaptive tabulation or ISAT based moving horizon estimation (MHE) is suggested as a fast and robust approach for state estimation. Computational issues with a moving horizon constrained state estimation technique like MHE are discussed. Implementation of storage and retrieval approach of ISAT for state estimation is proposed to maintain the accuracy and robustness of MHE, while generating the estimates at a reduced computational cost (∼300 times faster). Comparison with the widely used nonlinear state estimation technique of extended Kalman filtering (EKF) shows better performance using ISAT–MHE. Case studies with nonlinear discrete-time and continuous-time systems are carried out using ISAT, which is tailored for solving the optimal estimation problem.

Comparison of unconstrained nonlinear state estimation techniques on a MMA polymer reactor

Estimation theory finds a wide variety of applications in process engineering. Most chemical processes exhibit highly nonlinear dynamics, and the extended Kalman filter (EKF) has been widely used to solve the estimation problem in chemical processes. However, it is claimed that the EKF performs poorly when the noise sequences are non-Gaussian (NG). Owing to high nonlinearity of chemical process dynamics, it is likely that innovation sequences are non-Gaussian. Nonlinear estimators such as the unscented Kalman filter (UKF) and particle filters (PF) have been developed to address the theoretical limitations of the EKF. In this paper, we study the effect of filter assumptions on their practical performance. Different estimation algorithms are applied onto a methyl methacrylate (MMA) continuous stirred tank reactor (CSTR) under different scenarios of state and measurement noise and plant-model mismatch.

SOFT SENSING AND STATE ESTIMATION: REVIEW AND RECENT TRENDS

AbstractProcess monitoring and control requires estimation of quality variables, which are often not measurable directly. A cost effective approach to monitor these variables in real time is to employ model based soft sensing and state estimation techniques. Dynamic model based state estimation is a rich and highly active area of research and many novel approaches have emerged over last over last few years. In this paper, we review recent developments in the area of recursive linear and nonlinear Bayesian state estimation techniques.

CURRENT OUTPUT FILTER FOR STATE ESTIMATION OF SCALAR NONLINEAR SYSTEMS WITH APPLICATION TO CHAOTIC COMMUNICATION

A novel nonlinear state estimation technique called Current Output Filter is proposed in this paper. By taking two successive measurements into account and optimizing the coefficients of the proposed filter structure, an unbiased minimum variance state estimation algorithm with guaranteed estimation error performance is derived for scalar nonlinear systems. The performance of this filter is shown to be superior to the Extended Kalman Filter (EKF) in simulations. An application to a chaotic communication scheme is also presented in this work.

APPLICATION OF EXTENDED KALMAN FILTER TO A BATCH COOLING CRYSTALLIZER

The application of the extended Kalman filter (EKF) to a batch cooling crystallization process is presented. The simulation results point out that the feasibility of the on-line application of this nonlinear state estimation technique to a noisy nonlinear system heavily depends on the accurate measurement of the crystallizer temperature and the dissolved solute concentration. The EKF can reduce the effect of significant amounts of random noise in the measurements.