Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter

Kulikov, G. Yu.; Kulikova, Maria V.

doi:10.1109/tac.2013.2272136

Cited by 122 publications

(68 citation statements)

References 16 publications

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“…Thus, the continuousdiscrete stochastic state-space model (1), (2) is best suited for state estimation in chemical systems and widely used in chemistry research and industrial applications (see, for instance, Wilson et al (1998); Soroush (1998); Dochain (2003); Rawlings (2002, 2005); Jørgensen (2007); Rawlings and Bakshi (2006); Romanenko and Castro (2004); ). Concerning state estimation algorithms, we have to remark that, at present, there exist a great variety of different methods starting from a rigorous probabilistic approach solving Kolmogorov's (Fokker-Planck's) forward equation (as discussed, for instance, in Jazwinski (1970); Maybeck (1982)) till approximate approaches including various nonlinear modifications and implementations of the well-known Kalman filter (see Lewis (1986); Singer (2002Singer ( , 2006; Julier et al (2000); Julier and Uhlmann (2004); Ito and Xiong (2000); Nørgaard et al (2000); Haykin (2008, 2009); Arasaratnam et al (2010); Frogerais et al (2012); Jørgensen et al (2007); Kulikov and Kulikova (2014); Rawlings and Bakshi (2006); Romanenko and Castro (2004); ; Schneider and Georgakis (2013)) as well as optimization based approaches usually referred to as the moving horizon estimation (studied by Jang et al (1986); Rao et al (2001); Rawlings (2002, 2005); Rawlings and Bakshi (2006) and so on). Undoubtedly, the extended Kalman filter (EKF) still remains among the most popular and widely used numerical techniques for practical state estimation in nonlinear stochastic systems because of its implementation simplicity and good performance.…”

Section: Dx(t) = F X(t) U(t) Dt + G X(t) U(t) Dw(t)mentioning

confidence: 99%

“…If the control interval is increased to match the availability of measurements then control performance deteriorates significantly." Recently, Kulikov and Kulikova (2014) presented a way to resolve some cases of the "EKF failure" by means of adaptive ODE solvers with automatic error control. Therefore, the task of searching for the most appropriate ODE solver in the frame of EKF technology has arisen.…”

Section: Dx(t) = F X(t) U(t) Dt + G X(t) U(t) Dw(t)mentioning

confidence: 99%

“…It is worthwhile to remark that our NIRK6(4)M2 method distinguishes from what was used and published earlier in Kulikov and Kulikova (2014). First, the embedded NIRK pair of orders 2 and 4 with the global error control from Kulikov (2013) was applied for the simultaneous solution of the state mean and error covariance equations in the earlier published research.…”

Section: Dx(t) = F X(t) U(t) Dt + G X(t) U(t) Dw(t)mentioning

confidence: 99%

“…All this reduces the cost of NIRK6(4)M2 in comparison to the earlier published state estimator. Second, Kulikov and Kulikova (2014) studied the standard continuous-discrete EKF technology whereas the present paper deals with a more stable square-root implementation of the EKF, as explained in Section 2.3.…”

Section: Dx(t) = F X(t) U(t) Dt + G X(t) U(t) Dw(t)mentioning

confidence: 99%

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High-order accurate continuous-discrete extended Kalman filter for chemical engineering

Kulikov

Kulikova

2015

European Journal of Control

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Section: Dx(t) = F X(t) U(t) Dt + G X(t) U(t) Dw(t)mentioning

confidence: 99%

Section: Dx(t) = F X(t) U(t) Dt + G X(t) U(t) Dw(t)mentioning

confidence: 99%

Section: Dx(t) = F X(t) U(t) Dt + G X(t) U(t) Dw(t)mentioning

confidence: 99%

Section: Dx(t) = F X(t) U(t) Dt + G X(t) U(t) Dw(t)mentioning

confidence: 99%

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High-order accurate continuous-discrete extended Kalman filter for chemical engineering

Kulikov

Kulikova

2015

European Journal of Control

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“…The study shows satisfactory performance in the estimated speed over the entire speed-control range. A recently published paper by Kulikov and Kulikova [200] [202] used frequency tracking algorithm based on EKF on non-stationary systems with success.…”

Section: Extended Kalman Filteringmentioning

confidence: 99%

Multi-Sensor Condition Monitoring of Bearings Using Support Vector Machines

Kan¹

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Keywords AbstractBearings are one of the most commonly-used and crucial components in the majority of rotating machines in industrial applications. Failure of this component is common and can lead to machine breakdown. If it is not detected in time, bearing faults can even lead to catastrophic failures. An effective diagnostic system provides early warning and fault identification such that any machine breakdown can be avoided. Condition monitoring can benefit plant operators resulting in shorter downtimes, higher operation reliability, reduced operations and maintenance cost, and more effective maintenance and logistics planning.However, machines and associated systems today are increasingly complex, while diagnostic techniques have been mainly applied to relatively simple rotating machines. Therefore, there is a need for research on condition monitoring techniques that can be applied to complex systems in variable operating conditions. This thesis presents a study on bearing condition monitoring under variable operating condition using Support Vector Machines. Data collected from multiple sensors including accelerometers, acoustic emission sensors and tachometers are used for the studies presented in this thesis. Support Vector Machines are an efficient method for classification and prediction, and shows outstanding performance in modelling and generalization.The study begins with collecting bearing condition monitoring data. Vibration analysis is a well-established technique, while acoustic emission is gaining an increasing amount of attention especially on its capability to detect bearing incipient fault such as subsurface cracks. Existing studies so far have not demonstrated AE's diagnostic capabilities using naturally-damaged bearing, and only a very few studies adopt envelope and cyclostationary analysis on bearing fault diagnosis with this sensor technology. Due to the second-order cyclostationary nature of bearing signals and the success of envelope analysis in analysing bearing signals, the diagnostic and prognostic studies presented in this thesis make use of both envelope analysis and cyclostationary analysis to analyse vibration and acoustic emission bearing signals that will be collected from bearing diagnostics and run-to-failure prognostic experiments through a bearing diagnostic test-rig and a bearing prognostic test-rig.Using the collected data, the effectiveness and diagnostic capability of cyclostationary analysis will first be assessed using feature analysis with support vector machine. A diagnostic study is then conducted, investigating the diagnostic effectiveness of acoustic emission and its superiority to vibration, especially in the detection of bearing subsurface cracks. Through comparison of AE with vibration signals, this study confirms AE's superiority in detecting subsurface cracks in bearings and the absence of vibration symptoms of subsurface cracks.This diagnostic study has also shown the crucial ability of the cyclic logarithmic envelope iii spectrum in separating different cyc...

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Online estimation for catalyst activity of acetylene hydrogenation reactor

Xie

Zhang

et al. 2020

Asia-Pacific J Chem Eng

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In the ethylene industry, the high purity of the ethylene product depends on hydrogenation in acetylene hydrogenation reactor. Because the catalyst deactivation leads to the moving of the operating point, the operation scheme must be adjusted continually according to the catalyst activity. It is necessary to estimate the catalyst activity online. Based on the discrete dynamic model of the acetylene hydrogenation reactor, the extended Kalman filter (EKF) is used to build the soft sensor for catalyst activity. Considering that EKF involves the large computation costs, we propose a method that estimates the parameters of the time‐varying deactivation kinetics model for the tradeoff of accuracy and complexity. The method is effective to reduce computation complexity of estimation, and simultaneously, the accuracy satisfies the process requirement.

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Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter

Cited by 122 publications

References 16 publications

High-order accurate continuous-discrete extended Kalman filter for chemical engineering

High-order accurate continuous-discrete extended Kalman filter for chemical engineering

Multi-Sensor Condition Monitoring of Bearings Using Support Vector Machines

Online estimation for catalyst activity of acetylene hydrogenation reactor

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