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NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy NEURAL NETWORKS FOR SENSORS AND MEASUREMENT SYSTEMS Part IV Vincenzo.

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Presentation on theme: "NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy NEURAL NETWORKS FOR SENSORS AND MEASUREMENT SYSTEMS Part IV Vincenzo."— Presentation transcript:

1 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy NEURAL NETWORKS FOR SENSORS AND MEASUREMENT SYSTEMS Part IV Vincenzo Piuri University of Milan, Italy

2 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy OUTLINE Calibration Static and dynamic calibration Calibration enhancement by ANNs

3 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy SENSOR CALIBRATION Calibration operations that establish under given conditions the relationship between values produced by an instrument and the known values of the measurand

4 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy AN EXAMPLE (1) - 1 mW HeNe LASER (2) - Measuring fiber (3) - Reference fiber (4) - Bifurcated fiber bundle (5) - Bidirectional coupler (6) - Optical power meter (7) - Switching system (8) - Multimeter (9) - IC temperature sensor (10)- Temperature sensor signal conditioning Distance Measurement

5 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy CALIBRATED SENSOR OUTPUT

6 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Newton interpolation F(x) = F[x 0 ]+ F[x 1,x 0 ] (x- x 0 )+…+F[x n x n-1,…,x 0 ] (x- x 0 ) (x- x 1 )… (x- x n ) F[x i,x j,x k ] = (F[x i,x j ]-F[x j,x k ])/(x i -x k ) GLOBAL INTERPOLATION (1)

7 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Lagrange interpolation F(x) =  k=0..n L k (x) y k L k (x) =  i=0..n,i<>k (x-x i )/(x k -x i ) GLOBAL INTERPOLATION (2)

8 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Splines F k (x) =  i=0..n a k,i x i LOCAL INTERPOLATION

9 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Least Mean Squares F(x) =  i=0..p a i x i REGRESSION (1)

10 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Feedforward Neural Networks F(x) = F N (W N *(F N-1 (… F 2 (W 2 * F 1 (W 1 * x i +B 1 ) +B 2 )… +B N-1 ) +B N ) single hidden layer with sigmoidal neurons + linear output neuron is a universal approximator under mild conditions REGRESSION (2)

11 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy COMPARISON OF SENSOR CALIBRATION

12 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Static calibration Dynamic calibration Difficult function specification High accuracy Robust calibration Generalization ability: less calibration samples Less computational intensive Calibration with dependence from other parameters Calibration of multi-sensor systems SENSOR CALIBRATION WITH ANNS

13 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy STATIC EFFICIENT CALIBRATION Toxin measurement by biosensor accuracycomplexity spline RBF NN calibration reconstruction

14 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy STATIC MULTI-SENSOR CALIBRATION Feedforward NN spline Pressure measurement

15 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy DYNAMIC CALIBRATION Pressure measurement by piezoelectric quartz crystal oscillators No correctionStatic regression NN with feedbacks

16 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy SENSOR DIAGNOSIS Validation of correct sensor operation by analysis of sensor behavior

17 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Multi-sensor fusion with sensors for the same physical quantity Sensor redundancy Sensor inference SENSOR DIAGNOSIS (2)

18 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy SENSOR DIAGNOSIS (3) Multi-sensor fusion with sensors for different physical quantities Sensor redundancy Sensor inference

19 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Sensor prediction and comparison with actual sensor output No sensor redundancy SENSOR DIAGNOSIS (4) sensor predictor sensor z -1 z -2 … comparatorcomparator errorerror

20 NIMIA 2001- 9 October 2001, Crema, Italy - Vincenzo Piuri, University of Milan, Italy Error compensation: aircraft gyroscope hard error: no compensation SENSOR DIAGNOSIS (5) hard error: NN compensation soft error: NN compensation

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