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Fault Detection and Diagnosis (II)

Fault Detection and Diagnosis (II). Qualitative Model-based Methods. Qualitative Model-based. Causal Models. Abstraction Hierarchy. Diagraphs. Qualitative Physics. Fault trees. Structural. Functional. Input. Process. Output. Diagraph.

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Fault Detection and Diagnosis (II)

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  1. Fault Detection and Diagnosis(II)

  2. Qualitative Model-based Methods Qualitative Model-based Causal Models Abstraction Hierarchy Diagraphs Qualitative Physics Fault trees Structural Functional

  3. Input Process Output Diagraph • Signed diagraph (SDG): representing cause-effect • Nodes: • Input: • Process: • Output:

  4. Tank Example F1 Z F2

  5. Model • SDG F1 dZ F2 Z

  6. Fault Tree • Definition: a logical tree that propagates primary events (faults) to top level event or fault • Fault tree analysis • System definition • Fault tree construction • Qualitative evaluation • Quantitative evaluation

  7. Fault Tree • Work from top level event down to primary event • Find the cause (a lower level event) of each event • Use OR, AND and XOR

  8. Fault Tree Example C D B A

  9. Qualitative Physics • Common sense • Qualitative (confluence) eqs from ODEs • Causal ordering • Precedence ordering: information flow • Qualitative behavior from ODEs • Qualitative simulation (QSIM) • Dynamic, require constraints and IC • Qualitative process theory (QPT) • Processobjectsstates parameters (quantity)

  10. Abstraction Hierarchy • Decompose the system into units • Construct the input-output relationship • Structural: connectivity • Functional: outputs=f(inputs)

  11. Search Methods • Topographic: • use template of normal operation • No assumption for fault required • Symptomatic: • look for symptoms for direction • Information economy

  12. Topographic Search • Structural decomposition • Identify the information flow path,include all the subcomponents within the path of fault • Select subpaths to localize the fault • Functional decomposition • Search in terms of functionality

  13. Symptomatic Search • Require defined symptoms, difficult to detect multiple faults • Require complete knowledge of symptoms, difficult to detect novel faults • Approaches • Look-up table: fault template • Hypothesis and test search: on-line generated hypothesis

  14. Process History Based Methods • Qualitative • Expert systems • Trend modeling • Quantitative • Statistical • PCA,PLS, Statistical pattern classifiers • Non-statistical • Neural network

  15. Process History-Based Qualitative Quantitative QTA Statistical Non-Statistical Expert Systems PCA/PLS Statistical classifiers Neural Network

  16. Expert System • Rule-based feature extraction • Components • Knowledge acquisition • Choice of knowledge representation • Coding • Development of inference procedures • Development of input-output interface

  17. Expert System • Advantages • Easy to develop • Transparent reasoning • Able to reason under uncertainty • Able to provide explanation • Disadvantages • System-specific • Difficult to update

  18. Qualitative Trend Analysis • Predict future events • Filters needed • Detect a fault from a distinct trend • May confuse transit with fault

  19. Quantitative Feature Extraction • Statistical • Measurements are considered statistical time series • Fault changes the underlying distribution (μ and σ) • Stop region • Test statistic • Statistic process control chart: Shewhart

  20. Quantitative Feature Extraction • Multivariate Statistical • Principle Components Analysis (PCA) • Transform related variables to lower dimension uncorrelated variables • Partial Least Squares (PLS) • Reduce process/product quality variables

  21. PCA • X and covariance

  22. PLS • PLS model – X: Predictor matrix (process variables) • Y: Predicted matrix (product quality) • Find regression X->Y that maximizes covariance between X and Y • First few latent variables explain the covariance

  23. Y h<δ? N C1 C2 Statistical Classifier

  24. Comparison of Approaches • Quantitative model-based • Advantages • Fault diagnosis is well defined if complete knowledge is available • Provide design schemes to minimize disturbance effect • Disadvantages • Limited to linear and few nonlinear models • Modeling cost may be prohibitive

  25. Comparison of Approaches • Qualitative model-based approaches • Advantage • When quantitative models are not available and fundamentals are understood • Provide explanation of path of the propagation of fault • Disadvantage • Resolution from ambiguity

  26. Comparison of Approaches • Process history based methods • Advantages • No model needed • Robust to noise • Meet isolability requirement • Disadvantage • Performance limited by training data

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