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Published byAlexina Arnold Modified over 9 years ago
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Soft Sensor for Faulty Measurements Detection and Reconstruction in Urban Traffic Department of Adaptive systems, Institute of Information Theory and Automation, June 2010, Prague
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Outline Problem description Soft sensors Gaussian Process models Soft sensor for faulty measurement detection and reconstruction Conclusions
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Outline Problem description Soft sensors Gaussian Process models Soft sensor for faulty measurement detection and reconstruction Conclusions
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Problem description Traffic crossroad - count of vehicles Inductive loop is a popular choice Devastating for traffic control system Failure detection and recovery of sensor signal
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Example of controlled network (Zličin shopping centre, Prague) Sensors on crossroads Failure: control system has no means to react Possible solution: soft sensor for failure detection and signal reconstruction
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Soft sensors Models that provide estimation of another variable `Soft sensor’: process engineering mainly Applications in various engineering fields Model-driven, data-driven soft sensors Issues: missing data, data outliers, drifting data, data co-linearity, different sampling rates, measurement delays.
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Outline Problem description Soft sensors Gaussian Process models Soft sensor for faulty measurement detection and reconstruction Conclusions
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Probabilistic (Bayes) nonparametric model. GP model determined by: Input/output data (data points, not signals) (learning data – identification data): Covariance matrix: GP model
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Covariance function: functional part and noise part stationary/unstationary, periodic/nonperiodic, etc. Expreses prior knowledge about system properties, frequently: Gaussian covariance function »smooth function »stationary function Covariance function
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Identification of GP model = optimisation of covariance function parameters Cost function: maximum likelihood of data for learning Hyperparameters
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GP model prediction Prediction of the output based on similarity test input – training inputs Output: normal distribution Predicted mean Prediction variance
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Static illustrative example Static example: 9 learning points: Prediction Rare data density increased variance (higher uncertainty). -1.5-0.500.511.52 -4 -2 0 2 4 6 8 x y Nonlinear function to be modelled from learning points y=f(x) Learning points -1.5-0.500.511.52 -6 -4 -2 0 2 4 6 8 10 x y Nonlinear fuction and GP model -1.5-0.500.511.52 0 2 4 6 x e Prediction error and double standard deviation of prediction 2 |e| Learning points 2 f(x)
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GP model attributes (vs. e.g. ANN) Smaller number of parameters Measure of confidence in prediction, depending on data Data smoothing Incorporation of prior knowledge * Easy to use (engineering practice) Computational cost increases with amount of data Recent method, still in development Nonparametrical model * (also possible in some other models)
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Outline Problem description Soft sensors Gaussian Process models Soft sensor for faulty measurement detection and reconstruction Conclusions
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The profile of vehicle arrival data
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Modelling One working day for estimation data Different working day for validation data Validation based regressor selection the fourth order AR model (four delayed output values as regressors) Gaussian+constant covariance function Residuals of predictions with 3 band
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Estimation
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Validation
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Proposed algorithm for detecting irregularities and for reconstruction the data with prediction Sensor fault: longer lasting outliers.
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The comparison of MRSE for k-step- ahead predictions Purposiveness of the obtained model (the measure of measurement validity, close-enough prediction, fast calculation, model robustness)
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Soft sensor applied on faulty data
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Conclusions Soft sensors: promising for FD and signal reconstruction. GP models: excessive noise, outliers, no delay in prediction, measure of prediction confidence. The excessive noise limits the possibility to develop better predictor. Traffic sensor problem successfully solved for working days.
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