Kalman Filtering With Inequality Constraints For Turbofan Engine Health Estimation
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| Author | : |
| Publisher | : |
| Total Pages | : 38 |
| Release | : 2003 |
| Genre | : |
| ISBN | : |
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satis- fied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estima- tion accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model con- tains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
| Author | : National Aeronautics and Space Adm Nasa |
| Publisher | : Independently Published |
| Total Pages | : 38 |
| Release | : 2018-09-15 |
| Genre | : Science |
| ISBN | : 9781723734168 |
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.Simon, Dan and Simon, Donald L.Glenn Research CenterTURBOFAN ENGINES; AIRCRAFT ENGINES; KALMAN FILTERS; QUADRATIC PROGRAMMING; SYSTEMS HEALTH MONITORING; GAS TURBINE ENGINES; ALGORITHMS; ESTIMATES; INEQUALITIES; SIMULATION
| Author | : |
| Publisher | : |
| Total Pages | : 16 |
| Release | : 2003 |
| Genre | : |
| ISBN | : |
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
| Author | : National Aeronautics and Space Administration (NASA) |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 28 |
| Release | : 2018-06-20 |
| Genre | : |
| ISBN | : 9781721590476 |
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering. Simon, Dan and Simon, Donald L. Glenn Research Center NASA/TM-2003-212528, ARL-TR-2956, GT2003-38584, E-14090, NAS 1.15:212528
| Author | : National Aeronautics and Space Adm Nasa |
| Publisher | : Independently Published |
| Total Pages | : 28 |
| Release | : 2018-09-28 |
| Genre | : |
| ISBN | : 9781724120250 |
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering. Simon, Dan and Simon, Donald L. Glenn Research Center NASA/TM-2003-212528, ARL-TR-2956, GT2003-38584, E-14090, NAS 1.15:212528...
| Author | : National Aeronaut Administration (Nasa) |
| Publisher | : |
| Total Pages | : 36 |
| Release | : 2020-08-05 |
| Genre | : |
| ISBN | : |
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health. Simon, Dan and Simon, Donald L. Glenn Research Center NASA/TM-2005-213962, ARL-MR-621, E-15278 TURBOFAN ENGINES; KALMAN FILTERS; ESTIMATES; HEURISTIC METHODS; RISK; SIMULATION; INEQUALITIES
| Author | : National Aeronautics and Space Administration (NASA) |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 28 |
| Release | : 2018-05-29 |
| Genre | : |
| ISBN | : 9781720451761 |
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the PDF (probability density function) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. The turbofan engine model contains 3 state variables, 11 measurements, and 10 component health parameters. It is also shown that the truncated Kalman filter may be a more accurate way of incorporating inequality constraints than other constrained filters (e.g., the projection approach to constrained filtering).Simon, Dan and Simon, Donald L.Glenn Research CenterTURBOFAN ENGINES; PROBABILITY THEORY; KALMAN FILTERS; AIRCRAFT ENGINES; FLIGHT SAFETY; INEQUALITIES; SIMULATION
| Author | : Ginalber Luiz Serra |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 315 |
| Release | : 2018-02-21 |
| Genre | : Mathematics |
| ISBN | : 9535138278 |
This book presents recent issues on theory and practice of Kalman filters, with a comprehensive treatment of a selected number of concepts, techniques, and advanced applications. From an interdisciplinary point of view, the contents from each chapter bring together an international scientific community to discuss the state of the art on Kalman filter-based methodologies for adaptive/distributed filtering, optimal estimation, dynamic prediction, nonstationarity, robot navigation, global navigation satellite systems, moving object tracking, optical communication systems, and active power filters, among others. The theoretical and methodological foundations combined with extensive experimental explanation make this book a reference suitable for students, practicing engineers, and researchers in sciences and engineering.
| Author | : Meriem Gharbi |
| Publisher | : Logos Verlag Berlin GmbH |
| Total Pages | : 174 |
| Release | : 2022-04-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3832554564 |
In this thesis, we develop and analyze a novel framework for moving horizon estimation (MHE) of linear and nonlinear constrained discrete-time systems, which we refer to as proximity moving horizon estimation. The conceptual idea of the proposed framework is to employ a stabilizing a priori solution in order to ensure stability of MHE and to combine it with an online convex optimization in order to obtain an improved performance without jeopardizing stability. The goal of this thesis is to provide proximity-based MHE approaches with desirable theoretical properties and for which reliable and numerically efficient algorithms allow the estimator to be applied in real-time applications. In more detail, we present constructive and simple MHE design procedures which are tailored to the considered class of dynamical systems in order to guarantee important properties of the resulting estimation error dynamics. Furthermore, we develop computationally efficient MHE algorithms in which a suboptimal state estimate is computed at each time instant after an arbitrary and limited number of optimization algorithm iterations. In particular, we introduce a novel class of anytime MHE algorithms which ensure desirable stability and performance properties of the estimator for any number of optimization algorithm iterations, including the case of a single iteration per time instant. In addition to the obtained theoretical results, we discuss the tuning of the performance criteria in proximity MHE given prior knowledge on the system disturbances and illustrate the theoretical properties and practical benefits of the proposed approaches with various numerical examples from the literature.
| Author | : |
| Publisher | : DEStech Publications, Inc |
| Total Pages | : 740 |
| Release | : 2014-09-02 |
| Genre | : Technology & Engineering |
| ISBN | : 1605951838 |
The aim of MSCE 2014 is to provide a platform for researchers, engineers, and academicians, as well as industrial professionals, to present their research results and development activities in mechanism science and control engineering. It provides opportunities for the delegates to exchange new ideas and application experiences, to establish business or research relations and to find global partners for future collaboration. MSCE2014 is conducted to all the researchers, engineers, industrial professionals and academicians, who are broadly welcomed to present their latest research results, academic developments or theory practice. Topics of interest include but are not limited to Mechanism theory and Application, Mechanical control and Automation Engineering, Mechanical Dynamics, Materials Processing and Control, Instruments and Vibration Control. It is of great pleasure to see the delegates exchanging ideas and establishing sound relationships on the conference.
