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  • 1. Deosthale, Eeshan
    et al.
    Jung, Daniel
    Ahmed, Qadeer
    Sensor Selection for Fault Detection and Isolation in Structurally Reconfigurable Systems2018In: 2018 Annual American Control Conference (ACC), 2018, p. 5807-5812Conference paper (Refereed)
    Abstract [en]

    Fault diagnosis of structurally re-configurable systems is complicated as the system structure changes when the system operates in different modes. It is important that faults can be detected and isolated in each operating mode. In model-based diagnosis, faults are detected and isolated by detecting inconsistencies between model predictions and sensor data. Thus, determining where to mount sensors is an important task to be able to detect and isolate faults, especially when faults can result in unexpected system re-configuration. For structurally re-configurable systems this means selecting a set of sensors that fulfills requirements in multiple models describing the different system modes. A sensor selection algorithm is proposed for structurally re-configurable systems which computes minimal sensor sets that make faults in all modes detectable and isolable. As a case study, the sensor selection algorithm is applied to determine sensor locations in an eight-speed automatic transmission.

  • 2.
    Eriksson, Daniel
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Diagnosability analysis and FDI system design for uncertain systems2013Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Our society depends on advanced and complex technical systems and machines, for example, cars for transportation, industrial robots in production lines, satellites for communication, and power plants for energy production. Consequences of a fault in such a system can be severe and result in human casualties, environmentally harmful emissions, high repair costs, or economical losses caused by unexpected stops in production lines. Thus, a diagnosis system is important, and in some applications also required by legislations, to monitor the system health in order to take appropriate preventive actions when a fault occurs. Important properties of diagnosis systems are their capability of detecting and identifying faults, i.e., their fault detectability and isolability performance.

    This thesis deals with quantitative analysis of fault detectability and isolability performance when taking model uncertainties and measurement noise into consideration. The goal is to analyze diagnosability performance given a mathematical model of the system to be monitored before a diagnosis system is developed. A measure of fault diagnosability performance, called distinguishability, is proposed based on the Kullback-Leibler divergence. For linear descriptor models with Gaussian noise, distinguishability gives an upper limit for the fault to noise ratio of any linear residual generator. Distinguishability is used to analyze fault detectability and isolability performance of a non-linear mean value engine model of gas flows in a heavy duty diesel engine by linearizing the model around different operating points.

    It is also shown how distinguishability is used for determine sensor placement, i.e, where sensors should be placed in a system to achieve a required fault diagnosability performance. The sensor placement problem is formulated as an optimization problem, where minimum required diagnosability performance is used as a constraint. Results show that the required diagnosability performance greatly affects which sensors to use, which is not captured if not model uncertainties and measurement noise are taken into consideration.

    Another problem considered here is the on-line sequential test selection problem. Distinguishability is used to quantify the performance of the different test quantities. The set of test quantities is changed on-line, depending on the output of the diagnosis system. Instead of using all test quantities the whole time, changing the set of active test quantities can be used to maintain a required diagnosability performance while reducing the computational cost of the diagnosis system. Results show that the number of used test quantities can be greatly reduced while maintaining a good fault isolability performance.

    A quantitative diagnosability analysis has been used during the design of an engine misfire detection algorithm based on the estimated torque at the flywheel. Decisions during the development of the misfire detection algorithm are motivated using quantitative analysis of the misfire detectability performance. Related to the misfire detection problem, a flywheel angular velocity model for misfire simulation is presented. An evaluation of the misfire detection algorithm show results of good detection performance as well as low false alarm rate.

    List of papers
    1. A method for quantitative fault diagnosability analysis of stochastic linear descriptor models
    Open this publication in new window or tab >>A method for quantitative fault diagnosability analysis of stochastic linear descriptor models
    2013 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 6, p. 1591-1600Article in journal (Refereed) Published
    Abstract [en]

    Analyzing fault diagnosability performance for a given model, before developing a diagnosis algorithm, can be used to answer questions like “How difficult is it to detect a fault fi?” or “How difficult is it to isolate a fault fi from a fault fj?”. The main contributions are the derivation of a measure, distinguishability, and a method for analyzing fault diagnosability performance of discrete-time descriptor models. The method, based on the Kullback–Leibler divergence, utilizes a stochastic characterization of the different fault modes to quantify diagnosability performance. Another contribution is the relation between distinguishability and the fault to noise ratio of residual generators. It is also shown how to design residual generators with maximum fault to noise ratio if the noise is assumed to be i.i.d. Gaussian signals. Finally, the method is applied to a heavy duty diesel engine model to exemplify how to analyze diagnosability performance of non-linear dynamic models.

    Place, publisher, year, edition, pages
    Elsevier, 2013
    Keywords
    Fault diagnosability analysis; Fault detection and isolation; Model-based diagnosis
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-89941 (URN)10.1016/j.automatica.2013.02.045 (DOI)000319540500007 ()
    Available from: 2013-03-11 Created: 2013-03-11 Last updated: 2017-12-06Bibliographically approved
    2. Using quantitative diagnosability analysis for optimal sensor placement
    Open this publication in new window or tab >>Using quantitative diagnosability analysis for optimal sensor placement
    2012 (English)In: Proceedings of the 8th IFAC Safe Process, Mexico City, Mexico / [ed] Carlos Manuel Astorga-Zaragoza, Arturo Molina Gutierrez and Adriana Aguilera-Gonzalez, Curran Associates, Inc., 2012, p. 940-945Conference paper, Published paper (Refereed)
    Abstract [en]

    A good placement of sensors is crucial to get good performance in detecting and isolating faults. Here, the sensor placement problem is cast as a minimal cost optimization problem. Previous works have considered this problem with qualitative detectability and isolability specifications. A key contribution here is that quantified detectability and isolability performance is considered in the optimization formulation. The search space for the posed optimization problem is exponential in size, and to handle complexity a greedy optimization algorithm that compute optimal sensor positions is proposed. Two examples illustrate how the optimal solution depends on the required quantified diagnosability performance and the results are compared to the solutions using a deterministic method.

    Place, publisher, year, edition, pages
    Curran Associates, Inc., 2012
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-89942 (URN)10.3182/20120829-3-MX-2028.00196 (DOI)978-390282309-0 (ISBN)
    Conference
    8th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS 2012; Mexico City; Mexico
    Available from: 2013-03-11 Created: 2013-03-11 Last updated: 2014-11-13Bibliographically approved
    3. A sequential test selection algorithm for fault isolation
    Open this publication in new window or tab >>A sequential test selection algorithm for fault isolation
    2012 (English)In: Proceedings of the 10th European Workshop on Advanced Control and Diagnosis, ACD 2012, Copenhagen, Denmark, 2012Conference paper, Published paper (Refereed)
    Abstract [en]

    A sequential test selection algorithm is proposed which updates the set of active test quantities depending on the present minimal candidates. By sequentially updating the set of active test quantities, computational time and memory usage can be reduced. If test quantities are generated on-line, a sequential test selection algorithm gives information about which test quantities that should be created. The test selection problem is defined as an optimization problem where a set of active test quantities is chosen such that the cost is minimized while the set fulfills a required minimum detectability and isolability performance. A quantitative diagnosability measure, distinguishability, is used to quantify diagnosability performance of test quantities. The proposed test selection algorithm is applied to a DC-circuit where the diagnosis algorithm generates residuals on-line. Experiments show that the sequential test selection algorithm can significantly reduce the number of active test quantities during a scenario and still be able to identify the true faults.

    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-89943 (URN)
    Conference
    10th European Workshop on Advanced Control and Diagnosis, ACD 2012, November 8-9, Copenhagen, Denmark
    Available from: 2013-03-11 Created: 2013-03-11 Last updated: 2013-03-12Bibliographically approved
    4. Flywheel angular velocity model for misfire simulation
    Open this publication in new window or tab >>Flywheel angular velocity model for misfire simulation
    2013 (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    A flywheel angular velocity model for misfire and disturbance simulation is presented. Applications of the model are, for example, initial parameter calibration or robustness analysis of misfire detection algorithms. An analytical model of cylinder pressure is used to model cylinder torque and a multi-body model is used to model crankshaft and driveline oscillations. Different types of disturbances, such as cylinder variations, changes in auxiliary load, and flywheel manufacturing errors can be injected in the model. A qualitative validation of the model shows that simulated angular velocity captures the amplitude and oscillatory behavior of real measurements and the effects of different types of disturbances, e.g. misfire and flywheel manufacturing errors.

    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-89944 (URN)
    Available from: 2013-03-12 Created: 2013-03-12 Last updated: 2018-01-30
    5. Analysis and optimization with the Kullback-Leibler divergence for misfire detection using estimated torque
    Open this publication in new window or tab >>Analysis and optimization with the Kullback-Leibler divergence for misfire detection using estimated torque
    2013 (English)Report (Other academic)
    Abstract [en]

    Engine misfire detection is an important part of the On-Board Diagnostics (OBDII) legislations to reduce exhaust emissions and avoid damage to the catalytic converters. The flywheel angular velocity signal is analyzed, investigating how to use the signal in order to best detect misfires. An algorithm for engine misfire detection is proposed based on the flywheel angular velocity signal. The flywheel signal is used to estimate the torque at the flywheel and a test quantity is designed by weighting and thresholding the samples of estimated torque related to one combustion. During the development process, the Kullback-Leibler divergence is used to analyze the ability to detect a misfire given a test quantity and how the misfire detectability performance varies depending on, e.g., load and speed. The Kullback-Leibler divergence is also used for parameter optimization to maximize the difference between misfire data and fault-free data. Evaluation shows that the proposed misfire detection algorithm is able to have a low probability of false alarms while having a low probability of missed detections.

    Place, publisher, year, edition, pages
    Linköping: Linköping University Electronic Press, 2013. p. 36
    Series
    LiTH-ISY-R, ISSN 1400-3902 ; 3057
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-89946 (URN)LiTH-ISY-R-3057 (ISRN)
    Available from: 2013-03-12 Created: 2013-03-12 Last updated: 2018-01-30Bibliographically approved
  • 3.
    Eriksson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Eriksson, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Analysis and optimization with the Kullback-Leibler divergence for misfire detection using estimated torque2013Report (Other academic)
    Abstract [en]

    Engine misfire detection is an important part of the On-Board Diagnostics (OBDII) legislations to reduce exhaust emissions and avoid damage to the catalytic converters. The flywheel angular velocity signal is analyzed, investigating how to use the signal in order to best detect misfires. An algorithm for engine misfire detection is proposed based on the flywheel angular velocity signal. The flywheel signal is used to estimate the torque at the flywheel and a test quantity is designed by weighting and thresholding the samples of estimated torque related to one combustion. During the development process, the Kullback-Leibler divergence is used to analyze the ability to detect a misfire given a test quantity and how the misfire detectability performance varies depending on, e.g., load and speed. The Kullback-Leibler divergence is also used for parameter optimization to maximize the difference between misfire data and fault-free data. Evaluation shows that the proposed misfire detection algorithm is able to have a low probability of false alarms while having a low probability of missed detections.

  • 4.
    Eriksson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Eriksson, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Flywheel angular velocity model for misfire and driveline disturbance simulation2013In: Proceedings of the 7th IFAC Symposium on Advances in Automotive Control, The International Federation of Automatic Control, Elsevier, 2013, Vol. 46, no 21, p. 570-575Conference paper (Refereed)
    Abstract [en]

    A flywheel angular velocity model for misfire and disturbance simulation is presented. Applications of the model are, for example, initial parameter calibration and robustness analysis of misfire detection algorithms. An analytical cylinder pressure model is used to model cylinder torque and a multi-body model with torsional flexibilities is used to model crankshaft and driveline oscillations. Misfires, cylinder variations, changes in auxiliary load, and flywheel manufacturing errors can be injected in the model and the resulting speed variations can be simulated. A qualitative validation of the model shows that simulated angular velocity captures the amplitude and oscillatory behavior of measurement data and the effects of different phenomena, such as misfire and flywheel manufacturing errors.

  • 5.
    Eriksson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Eriksson, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Flywheel angular velocity model for misfire simulation2013Manuscript (preprint) (Other academic)
    Abstract [en]

    A flywheel angular velocity model for misfire and disturbance simulation is presented. Applications of the model are, for example, initial parameter calibration or robustness analysis of misfire detection algorithms. An analytical model of cylinder pressure is used to model cylinder torque and a multi-body model is used to model crankshaft and driveline oscillations. Different types of disturbances, such as cylinder variations, changes in auxiliary load, and flywheel manufacturing errors can be injected in the model. A qualitative validation of the model shows that simulated angular velocity captures the amplitude and oscillatory behavior of real measurements and the effects of different types of disturbances, e.g. misfire and flywheel manufacturing errors.

  • 6.
    Eriksson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    A method for quantitative fault diagnosability analysis of stochastic linear descriptor models2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 6, p. 1591-1600Article in journal (Refereed)
    Abstract [en]

    Analyzing fault diagnosability performance for a given model, before developing a diagnosis algorithm, can be used to answer questions like “How difficult is it to detect a fault fi?” or “How difficult is it to isolate a fault fi from a fault fj?”. The main contributions are the derivation of a measure, distinguishability, and a method for analyzing fault diagnosability performance of discrete-time descriptor models. The method, based on the Kullback–Leibler divergence, utilizes a stochastic characterization of the different fault modes to quantify diagnosability performance. Another contribution is the relation between distinguishability and the fault to noise ratio of residual generators. It is also shown how to design residual generators with maximum fault to noise ratio if the noise is assumed to be i.i.d. Gaussian signals. Finally, the method is applied to a heavy duty diesel engine model to exemplify how to analyze diagnosability performance of non-linear dynamic models.

  • 7.
    Eriksson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    A sequential test selection algorithm for fault isolation2012In: Proceedings of the 10th European Workshop on Advanced Control and Diagnosis, ACD 2012, Copenhagen, Denmark, 2012Conference paper (Refereed)
    Abstract [en]

    A sequential test selection algorithm is proposed which updates the set of active test quantities depending on the present minimal candidates. By sequentially updating the set of active test quantities, computational time and memory usage can be reduced. If test quantities are generated on-line, a sequential test selection algorithm gives information about which test quantities that should be created. The test selection problem is defined as an optimization problem where a set of active test quantities is chosen such that the cost is minimized while the set fulfills a required minimum detectability and isolability performance. A quantitative diagnosability measure, distinguishability, is used to quantify diagnosability performance of test quantities. The proposed test selection algorithm is applied to a DC-circuit where the diagnosis algorithm generates residuals on-line. Experiments show that the sequential test selection algorithm can significantly reduce the number of active test quantities during a scenario and still be able to identify the true faults.

  • 8.
    Eriksson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Quantitative Fault Diagnosability Performance of Linear Dynamic Descriptor Models2011Conference paper (Refereed)
    Abstract [en]

    A theory is developed for quantifying fault detectability and fault isolability properties of time discrete linear dynamic models. Based on the model, a stochastic characterization of system behavior in different fault modes is defined and a general measure, called distinguishability, based on the Kullback-Leibler information, is used to quantify the difference between the modes. An analysis of distinguishability as a function of the number of observations is discussed. This measure is also shown to be closely related to the fault to noise ratios in residual generators. Further, the distinguishability of the model is shown to give upper limits of the fault to noise ratios of residual generators.

  • 9.
    Eriksson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Quantitative Stochastic Fault Diagnosability Analysis2011In: 2011 50th IEEE Conference on Decision and Control andEuropean Control Conference (CDC-ECC)Orlando, FL, USA, December 12-15, 2011, Institute of Electrical and Electronics Engineers (IEEE), 2011, p. 1563-1569Conference paper (Refereed)
    Abstract [en]

    A theory is developed for quantifying fault detectability and fault isolability properties of static linear stochastic models. Based on the model, a stochastic characterization of system behavior in different fault modes is defined and a general measure, based on the Kullback-Leibler information, is proposed to quantify the difference between the modes. This measure, called distinguishability, of the model is shown to give sharp upper limits of the fault to noise ratios of residual generators. Finally, a case-study of a diesel engine model shows how the general framework can be applied to a dynamic and nonlinear model.

  • 10.
    Eriksson, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Using quantitative diagnosability analysis for optimal sensor placement2012In: Proceedings of the 8th IFAC Safe Process, Mexico City, Mexico / [ed] Carlos Manuel Astorga-Zaragoza, Arturo Molina Gutierrez and Adriana Aguilera-Gonzalez, Curran Associates, Inc., 2012, p. 940-945Conference paper (Refereed)
    Abstract [en]

    A good placement of sensors is crucial to get good performance in detecting and isolating faults. Here, the sensor placement problem is cast as a minimal cost optimization problem. Previous works have considered this problem with qualitative detectability and isolability specifications. A key contribution here is that quantified detectability and isolability performance is considered in the optimization formulation. The search space for the posed optimization problem is exponential in size, and to handle complexity a greedy optimization algorithm that compute optimal sensor positions is proposed. Two examples illustrate how the optimal solution depends on the required quantified diagnosability performance and the results are compared to the solutions using a deterministic method.

  • 11.
    Jung, Daniel
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Diagnosability performance analysis of models and fault detectors2015Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Model-based diagnosis compares observations from a system with predictions using a mathematical model to detect and isolate faulty components. Analyzing which faults that can be detected and isolated given the model gives useful information when designing a diagnosis system. This information can be used, for example, to determine which residual generators can be generated or to select a sufficient set of sensors that can be used to detect and isolate the faults. With more information about the system taken into consideration during such an analysis, more accurate estimations can be computed of how good fault detectability and isolability that can be achieved.

    Model uncertainties and measurement noise are the main reasons for reduced fault detection and isolation performance and can make it difficult to design a diagnosis system that fulfills given performance requirements. By taking information about different uncertainties into consideration early in the development process of a diagnosis system, it is possible to predict how good performance can be achieved by a diagnosis system and avoid bad design choices. This thesis deals with quantitative analysis of fault detectability and isolability performance when taking model uncertainties and measurement noise into consideration. The goal is to analyze fault detectability and isolability performance given a mathematical model of the monitored system before a diagnosis system is developed.

    A quantitative measure of fault detectability and isolability performance for a given model, called distinguishability, is proposed based on the Kullback-Leibler divergence. The distinguishability measure answers questions like "How difficult is it to isolate a fault fi from another fault fj?. Different properties of the distinguishability measure are analyzed. It is shown for example, that for linear descriptor models with Gaussian noise, distinguishability gives an upper limit for the fault to noise ratio of any linear residual generator. The proposed measure is used for quantitative analysis of a nonlinear mean value model of gas flows in a heavy-duty diesel engine to analyze how fault diagnosability performance varies for different operating points. It is also used to formulate the sensor selection problem, i.e., to find a cheapest set of available sensors that should be used in a system to achieve required fault diagnosability performance.

    As a case study, quantitative fault diagnosability analysis is used during the design of an engine misfire detection algorithm based on the crankshaft angular velocity measured at the flywheel. Decisions during the development of the misfire detection algorithm are motivated using quantitative analysis of the misfire detectability performance showing, for example, varying detection performance at different operating points and for different cylinders to identify when it is more difficult to detect misfires.

    This thesis presents a framework for quantitative fault detectability and isolability analysis that is a useful tool during the design of a diagnosis system. The different applications show examples of how quantitate analysis can be applied during a design process either as feedback to an engineer or when formulating different design steps as optimization problems to assure that required performance can be achieved.

    List of papers
    1. A method for quantitative fault diagnosability analysis of stochastic linear descriptor models
    Open this publication in new window or tab >>A method for quantitative fault diagnosability analysis of stochastic linear descriptor models
    2013 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 6, p. 1591-1600Article in journal (Refereed) Published
    Abstract [en]

    Analyzing fault diagnosability performance for a given model, before developing a diagnosis algorithm, can be used to answer questions like “How difficult is it to detect a fault fi?” or “How difficult is it to isolate a fault fi from a fault fj?”. The main contributions are the derivation of a measure, distinguishability, and a method for analyzing fault diagnosability performance of discrete-time descriptor models. The method, based on the Kullback–Leibler divergence, utilizes a stochastic characterization of the different fault modes to quantify diagnosability performance. Another contribution is the relation between distinguishability and the fault to noise ratio of residual generators. It is also shown how to design residual generators with maximum fault to noise ratio if the noise is assumed to be i.i.d. Gaussian signals. Finally, the method is applied to a heavy duty diesel engine model to exemplify how to analyze diagnosability performance of non-linear dynamic models.

    Place, publisher, year, edition, pages
    Elsevier, 2013
    Keywords
    Fault diagnosability analysis; Fault detection and isolation; Model-based diagnosis
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-89941 (URN)10.1016/j.automatica.2013.02.045 (DOI)000319540500007 ()
    Available from: 2013-03-11 Created: 2013-03-11 Last updated: 2017-12-06Bibliographically approved
    2. Asymptotic behavior of fault diagnosis performance
    Open this publication in new window or tab >>Asymptotic behavior of fault diagnosis performance
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    Fault detection and fault isolation performance of a model based diagnosis system mainly depends on the level of model uncertainty and the time allowed for detection. The longer time for detection that can be accepted, the more certain detection can be achieved and the main objective of this paper is to show how the window length relates to diagnosis performance. A key result is an explicit expression for asymptotic performance with respect to window length. A key property of the approach is that the model is analyzed directly, which makes the approach independent of detection filter design. It is shown that there exists a linear asymptote as the window length tends to infinity and it is also shown how this linear asymptote can be computed as well as higher order approximations.

    National Category
    Electrical Engineering, Electronic Engineering, Information Engineering
    Identifiers
    urn:nbn:se:liu:diva-117174 (URN)
    Available from: 2015-04-21 Created: 2015-04-21 Last updated: 2015-04-21Bibliographically approved
    3. Quantitative isolability analysis of different fault modes
    Open this publication in new window or tab >>Quantitative isolability analysis of different fault modes
    2015 (English)In: 9th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes SAFEPROCESS 2015 – Paris, 2–4 September 2015: Proceedings / [ed] Didier Maquin, Elsevier, 2015, Vol. 48(21), p. 1275-1282Conference paper, Published paper (Refereed)
    Abstract [en]

    To be able to evaluate quantitative fault diagnosability performance in model-based diagnosis is useful during the design of a diagnosis system. Different fault realizations are more or less likely to occur and the fault diagnosis problem is complicated by model uncertainties and noise. Thus, it is not obvious how to evaluate performance when all of this information is taken into consideration. Four candidates for quantifying fault diagnosability performance between fault modes are discussed. The proposed measure is called expected distinguishability and is based of the previous distinguishability measure and two methods to compute expected distinguishability are presented.

    Place, publisher, year, edition, pages
    Elsevier, 2015
    Series
    IFAC-PapersOnLine, ISSN 2405-8963
    Keywords
    Fault detection and isolation, quantitative diagnosability analysis, Kullback-Leibler divergence
    National Category
    Electrical Engineering, Electronic Engineering, Information Engineering Computer Engineering
    Identifiers
    urn:nbn:se:liu:diva-117175 (URN)10.1016/j.ifacol.2015.09.701 (DOI)
    Conference
    9th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes SAFEPROCESS 2015 – Paris, France, 2–4 September 2015
    Note

    At the time for thesis presentation publication was in status: Manuscript

    Available from: 2015-04-21 Created: 2015-04-21 Last updated: 2018-09-18Bibliographically approved
    4. Sensor selection for fault diagnosis in uncertain systems
    Open this publication in new window or tab >>Sensor selection for fault diagnosis in uncertain systems
    Show others...
    2018 (English)In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, p. 1-11Article in journal (Refereed) Epub ahead of print
    Abstract [en]

    Finding the cheapest, or smallest, set of sensors such that a specified level of diagnosis performance is maintained is important to decrease cost while controlling performance. Algorithms have been developed to find sets of sensors that make faults detectable and isolable under ideal circumstances. However, due to model uncertainties and measurement noise, different sets of sensors result in different achievable diagnosability performance in practice. In this paper, the sensor selection problem is formulated to ensure that the set of sensors fulfils required performance specifications when model uncertainties and measurement noise are taken into consideration. However, the algorithms for finding the guaranteed global optimal solution are intractable without exhaustive search. To overcome this problem, a greedy stochastic search algorithm is proposed to solve the sensor selection problem. A case study demonstrates the effectiveness of the greedy stochastic search in finding sets close to the global optimum in short computational time.

    Place, publisher, year, edition, pages
    Taylor & Francis, 2018
    Keywords
    Fault diagnosis, fault detection and isolation, sensor selection
    National Category
    Electrical Engineering, Electronic Engineering, Information Engineering Computer Engineering
    Identifiers
    urn:nbn:se:liu:diva-117176 (URN)10.1080/00207179.2018.1484171 (DOI)
    Note

    The previous status of this article was Manuscript.

    Available from: 2015-04-21 Created: 2015-04-21 Last updated: 2018-07-14Bibliographically approved
    5. Development of misfire detection algorithm using quantitative FDI performance analysis
    Open this publication in new window or tab >>Development of misfire detection algorithm using quantitative FDI performance analysis
    2015 (English)In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 34, p. 49-60Article in journal (Refereed) Published
    Abstract [en]

    A model-based misfire detection algorithm is proposed. The algorithm is able to detect misfires and identify the failing cylinder during different conditions, such as cylinder-to-cylinder variations, cold starts, and different engine behavior in different operating points. Also, a method is proposed for automatic tuning of the algorithm based on training data. The misfire detection algorithm is evaluated using data from several vehicles on the road and the results show that a low misclassification rate is achieved even during difficult conditions. (C) 2014 Elsevier Ltd. All rights reserved.

    Place, publisher, year, edition, pages
    Elsevier, 2015
    Keywords
    Misfire detection; Fault diagnosis; Fault detection and isolation; Kullback-Leibler divergence; Pattern recognition
    National Category
    Electrical Engineering, Electronic Engineering, Information Engineering
    Identifiers
    urn:nbn:se:liu:diva-114011 (URN)10.1016/j.conengprac.2014.10.001 (DOI)000347599500005 ()
    Note

    Funding Agencies|Volvo Car Corporation; Swedish Research Council within the Linnaeus Center CADICS

    Available from: 2015-02-06 Created: 2015-02-05 Last updated: 2018-01-30
    6. A flywheel error compensation algorithm for engine misfire detection
    Open this publication in new window or tab >>A flywheel error compensation algorithm for engine misfire detection
    2016 (English)In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 47, p. 37-47Article in journal (Refereed) Published
    Abstract [en]

    A commonly used signal for engine misfire detection is the crankshaft angular velocity measured at the flywheel. However, flywheel manufacturing errors result in vehicle-to-vehicle variations in the measurements and have a negative impact on the misfire detection performance, where the negative impact is quantified for a number of vehicles. A misfire detection algorithm is proposed with flywheel error adaptation in order to increase robustness and reduce the number of mis-classifications. Since the available computational power is limited in a vehicle, a filter with low computational load, a Constant Gain Extended Kalman Filter, is proposed to estimate the flywheel errors. Evaluations using measurements from vehicles on the road show that the number of mis-classifications is significantly reduced when taking the estimated flywheel errors into consideration.

    National Category
    Electrical Engineering, Electronic Engineering, Information Engineering Computer Engineering
    Identifiers
    urn:nbn:se:liu:diva-117177 (URN)10.1016/j.conengprac.2015.12.009 (DOI)000370091900004 ()
    Note

    Funding agencies:The work is partially supported by the Swedish Research Council within the Linnaeus Center CADICS.

    Vid tiden för disputation förelåg publikationen endast som manuskript

    Available from: 2015-04-21 Created: 2015-04-21 Last updated: 2018-09-17Bibliographically approved
  • 12. Jung, Daniel
    et al.
    Ahmed, Qadeer
    Rizzoni, Giorgio
    Design Space Exploration for Powertrain Electrification using Gaussian Processes2018In: 2018 Annual American Control Conference (ACC), 2018, p. 846-851Conference paper (Refereed)
    Abstract [en]

    Design space exploration of hybrid electric vehicles is an important multi-objective global optimization problem. One of the main objectives is to minimize fuel consumption while maintaining satisfactory driveability performance and vehicle cost. The design problem often includes multiple design options, including different driveline architectures and component sizes, where different candidates have various trade-offs between different, in many cases contradictory, performance requirements. Thus, there is no global optimum but a set of Pareto-optimal solutions to be explored. The objective functions can be expensive to evaluate, due to time-consuming simulations, which requires careful selection of which candidates to evaluate. A design space exploration algorithm is proposed for finding the set of Pareto-optimal solutions when the design search space includes multiple design options. As a case study, powertrain optimization is performed for a medium-sized series hybrid electric delivery truck.

  • 13. Jung, Daniel
    et al.
    Ahmed, Qadeer
    Zhang, Xieyuan
    Rizzoni, Giorgio
    Mission-based Design Space Exploration for Powertrain Electrification of Series Plugin Hybrid Electric Delivery Truck2018In: WCX World Congress Experience, SAE International , 2018Conference paper (Refereed)
    Abstract [en]

    Hybrid electric vehicles (HEV) are essential for reducing fuel consumption and emissions. However, when analyzing different segments of the transportation industry, for example, public transportation or different sizes of delivery trucks and how the HEV are used, it is clear that one powertrain may not be optimal in all situations. Choosing a hybrid powertrain architecture and proper component sizes for different applications is an important task to find the optimal trade-off between fuel economy, drivability, and vehicle cost. However, exploring and evaluating all possible architectures and component sizes is a time-consuming task. A search algorithm, using Gaussian Processes, is proposed that simultaneously explores multiple architecture options, to identify the Pareto-optimal solutions. The search algorithm is designed to carefully select the candidate in each iteration which is most likely to be Pareto-optimal, based on the results from previous candidates, to reduce computational time. The powertrain of a medium-sized series plugin hybrid electric delivery truck with a range extender is optimized for different driving missions. Three different powertrain architectures are included in the design space exploration and the fuel economy is evaluated using a simulation model of the powertrain and Dynamic Programming. Results from the analysis show which ranges of powertrain component sizes are recommended for the different types of driving scenarios.

  • 14.
    Jung, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Dong, Yi
    Institute for Software Integrated Systems, Vanderbilt University, Nashville, USA.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, The Institute of Technology.
    Biswas, Gautam
    Institute for Software Integrated Systems, Vanderbilt University, Nashville, USA.
    Sensor selection for fault diagnosis in uncertain systems2018In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, p. 1-11Article in journal (Refereed)
    Abstract [en]

    Finding the cheapest, or smallest, set of sensors such that a specified level of diagnosis performance is maintained is important to decrease cost while controlling performance. Algorithms have been developed to find sets of sensors that make faults detectable and isolable under ideal circumstances. However, due to model uncertainties and measurement noise, different sets of sensors result in different achievable diagnosability performance in practice. In this paper, the sensor selection problem is formulated to ensure that the set of sensors fulfils required performance specifications when model uncertainties and measurement noise are taken into consideration. However, the algorithms for finding the guaranteed global optimal solution are intractable without exhaustive search. To overcome this problem, a greedy stochastic search algorithm is proposed to solve the sensor selection problem. A case study demonstrates the effectiveness of the greedy stochastic search in finding sets close to the global optimum in short computational time.

  • 15.
    Jung, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Eriksson, Lars
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, The Institute of Technology.
    Development of misfire detection algorithm using quantitative FDI performance analysis2015In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 34, p. 49-60Article in journal (Refereed)
    Abstract [en]

    A model-based misfire detection algorithm is proposed. The algorithm is able to detect misfires and identify the failing cylinder during different conditions, such as cylinder-to-cylinder variations, cold starts, and different engine behavior in different operating points. Also, a method is proposed for automatic tuning of the algorithm based on training data. The misfire detection algorithm is evaluated using data from several vehicles on the road and the results show that a low misclassification rate is achieved even during difficult conditions. (C) 2014 Elsevier Ltd. All rights reserved.

  • 16.
    Jung, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering. The Ohio State University, Columbus, OH, USA.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Residual selection for fault detection and isolation using convex optimization2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 97, p. 143-149Article in journal (Refereed)
    Abstract [en]

    In model-based diagnosis there are often more candidate residual generators than what is needed and residual selection is therefore an important step in the design of model-based diagnosis systems. The availability of computer-aided tools for automatic generation of residual generators have made it easier to generate a large set of candidate residual generators for fault detection and isolation. Fault detection performance varies significantly between different candidates due to the impact of model uncertainties and measurement noise. Thus, to achieve satisfactory fault detection and isolation performance, these factors must be taken into consideration when formulating the residual selection problem. Here, a convex optimization problem is formulated as a residual selection approach, utilizing both structural information about the different residuals and training data from different fault scenarios. The optimal solution corresponds to a minimal set of residual generators with guaranteed performance. Measurement data and residual generators from an internal combustion engine test-bed is used as a case study to illustrate the usefulness of the proposed method.

    The full text will be freely available from 2020-08-18 11:24
  • 17.
    Jung, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, The Institute of Technology.
    A flywheel error compensation algorithm for engine misfire detection2016In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 47, p. 37-47Article in journal (Refereed)
    Abstract [en]

    A commonly used signal for engine misfire detection is the crankshaft angular velocity measured at the flywheel. However, flywheel manufacturing errors result in vehicle-to-vehicle variations in the measurements and have a negative impact on the misfire detection performance, where the negative impact is quantified for a number of vehicles. A misfire detection algorithm is proposed with flywheel error adaptation in order to increase robustness and reduce the number of mis-classifications. Since the available computational power is limited in a vehicle, a filter with low computational load, a Constant Gain Extended Kalman Filter, is proposed to estimate the flywheel errors. Evaluations using measurements from vehicles on the road show that the number of mis-classifications is significantly reduced when taking the estimated flywheel errors into consideration.

  • 18.
    Jung, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, The Institute of Technology.
    Quantitative isolability analysis of different fault modes2015In: 9th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes SAFEPROCESS 2015 – Paris, 2–4 September 2015: Proceedings / [ed] Didier Maquin, Elsevier, 2015, Vol. 48(21), p. 1275-1282Conference paper (Refereed)
    Abstract [en]

    To be able to evaluate quantitative fault diagnosability performance in model-based diagnosis is useful during the design of a diagnosis system. Different fault realizations are more or less likely to occur and the fault diagnosis problem is complicated by model uncertainties and noise. Thus, it is not obvious how to evaluate performance when all of this information is taken into consideration. Four candidates for quantifying fault diagnosability performance between fault modes are discussed. The proposed measure is called expected distinguishability and is based of the previous distinguishability measure and two methods to compute expected distinguishability are presented.

  • 19.
    Jung, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Khorasgani, Hamed
    Inst. of Software-integrated Systems, Vanderbilt Univ., USA.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Krysander, Mattias
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Biswas, Gautam
    Inst. of Software-integrated Systems, Vanderbilt Univ., USA.
    Analysis of fault isolation assumptions when comparing model-based design approaches of diagnosis systems2015In: Proceedings of the 9th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes Safeprocess'15, Elsevier, 2015, Vol. 48, no 21, p. 1289-1296Conference paper (Refereed)
    Abstract [en]

    Most model-based diagnosis approaches reported in the literature adopt a generic architecture and approach. However, the fault hypotheses generated by these methods may differ. This is not only due to the methods, but also on the basic assumptions made by different diagnostic algorithms on fault manifestation and evolution. While comparing different diagnosis approaches, the assumptions made in each case will have a significant effect on fault diagnosability performance and must therefore also be taken into consideration. Thus, to make a fair comparison, the different approaches should be designed based on the same assumptions. This paper studies the relation between a set of commonly made assumptions and fault isolability performance in order to compare different diagnosis approaches. As a case study, five developed diagnosis systems for a wind turbine benchmark problem are evaluated to analyze the type of assumptions that are applied in the different designs.

  • 20.
    Jung, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Sundström, Christofer
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    A Combined Data-Driven and Model-Based Residual Selection Algorithm for Fault Detection and Isolation2019In: IEEE Transactions on Control Systems Technology, ISSN 1063-6536, E-ISSN 1558-0865, Vol. 27, no 2, p. 616-630Article in journal (Refereed)
    Abstract [en]

    Selecting residual generators for detecting and isolating faults in a system is an important step when designing model-based diagnosis systems. However, finding a suitable set of residual generators to fulfill performance requirements is complicated by model uncertainties and measurement noise that have negative impact on fault detection performance. The main contribution is an algorithm for residual selection that combines model-based and data-driven methods to find a set of residual generators that maximizes fault detection and isolation performance. Based on the solution from the residual selection algorithm, a generalized diagnosis system design is proposed where test quantities are designed using multivariate residual information to improve detection performance. To illustrate the usefulness of the proposed residual selection algorithm, it is applied to find a set of residual generators to monitor the air path through an internal combustion engine.

  • 21. Khorasgani, Hamed
    et al.
    Jung, Daniel
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, Faculty of Science & Engineering.
    Biswas, Gautam
    Structural approach for distributed fault detection and isolation2015Conference paper (Refereed)
    Abstract [en]

    This paper presents a framework for distributed fault detection and isolation in dynamic systems. Our approach uses the dynamic model of each subsystem to derive a set of independent, local diagnosers. If needed, the subsystem model is extended to include measurements and model equations from its immediate neighbors to compute its diagnosis. Our approach is designed to ensure that each subsystem diagnoser provides the correct results, therefore, a local diagnosis result is equivalent to the results that would be produced by a global system diagnoser. We discuss the distribute diagnosis algorithm, and illustrate its application using a multi-tank system.

  • 22. Oruganti, Pradeep Sharma
    et al.
    Ahmed, Qadeer
    Jung, Daniel
    Effects of Thermal and Auxiliary Dynamics on a Fuel Cell Based Range Extender2018In: SAE Technical Paper, SAE International , 2018Conference paper (Refereed)
    Abstract [en]

    Batteries are useful in Fuel Cell Hybrid Electric Vehicles (FCHEV) to fulfill transient demands and for regenerative braking. Efficient energy management strategies paired with optimal powertrain design further improves the efficiency. In this paper, a new methodology to simultaneously size the propulsive elements and optimize the power-split strategy of a Range Extended Battery Electric Vehicle (REBEV), using a Polymer Electron Membrane Fuel Cell (PEMFC), is proposed and preliminary studies on the effects of the driving mission profile and the auxiliary power loads on the sizing and optimal performance of the powertrain design are carried out. Dynamic Programming is used to compute the optimal energy management strategy for a given driving mission profile, providing a global optimal solution. The component sizing problem is performed using a machine learning based, guided design space exploration to find the set of Pareto-optimal solutions that give the best trade-offs between the different objectives. The powertrain model includes the dynamic behavior of the fuel cell system compressor and a battery lumped parameter thermal model along with the quasi-static semi-empirical model of the fuel cell and a zero-order battery model. Initial results indicate an increase in the Pareto-optimal sizes with the inclusion of thermal management.

  • 23. Tamilarasan, Santhosh
    et al.
    Jung, Daniel
    Guvenc, Levent
    Drive Scenario Generation Based on Metrics for Evaluating an Autonomous Vehicle Controller2018In: SAE Technical Paper, SAE International , 2018Conference paper (Refereed)
    Abstract [en]

    An important part of automotive driving assistance systems and autonomous vehicles is speed optimization and traffic flow adaptation. Vehicle sensors and wireless communication with surrounding vehicles and road infrastructure allow for predictive control strategies taking near-future road and traffic information into consideration to improve fuel economy. For the development of autonomous vehicle speed control algorithms, it is imperative that the controller can be evaluated under different realistic driving and traffic conditions. Evaluation in real-life traffic situations is difficult and experimental methods are necessary where similar driving conditions can be reproduced to compare different control strategies. A traditional approach for evaluating vehicle performance, for example fuel consumption, is to use predefined driving cycles including a speed profile the vehicle should follow. However, if the vehicle speed is part of the vehicle control output, a different vehicle evaluation framework is necessary. Here, speed constraints are defined based on route and traffic conditions, such as speed limits, traffic signs and signals, and the locations of surrounding vehicles. Hence, route generation is an important task for evaluating speed control algorithms. A route is a distance-based description of the road conditions and locations of traffic signs and signals. A driving scenario is defined as a route which also includes information about traffic density and the location of surrounding traffic as function of time. It is discussed how driving scenarios can be used to evaluate and compare different speed control algorithms. The generation of driving scenarios is performed in two steps, route generation and traffic data generation. First, two approaches are discussed for generating the route conditions, such as varying speed limits and locations of traffic signals, either using real road map data or to recreate from vehicle speed data. In a second step, traffic conditions are simulated using the software SUMO to generate speed profiles of surrounding vehicles on the road. To assure that the selected driving scenarios represent varying driving conditions, a set of metrics is selected and used for driving scenario selection.

  • 24.
    Åslund, Jan
    et al.
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Frisk, Erik
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Jung, Daniel
    Linköping University, Department of Electrical Engineering, Vehicular Systems. Linköping University, The Institute of Technology.
    Asymptotic behavior of fault diagnosis performanceManuscript (preprint) (Other academic)
    Abstract [en]

    Fault detection and fault isolation performance of a model based diagnosis system mainly depends on the level of model uncertainty and the time allowed for detection. The longer time for detection that can be accepted, the more certain detection can be achieved and the main objective of this paper is to show how the window length relates to diagnosis performance. A key result is an explicit expression for asymptotic performance with respect to window length. A key property of the approach is that the model is analyzed directly, which makes the approach independent of detection filter design. It is shown that there exists a linear asymptote as the window length tends to infinity and it is also shown how this linear asymptote can be computed as well as higher order approximations.

1 - 24 of 24
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