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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NIMIA 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

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

NIMIA 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

NIMIA 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

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

NIMIA 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)

NIMIA 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)

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

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

NIMIA 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)

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

NIMIA 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

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

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

NIMIA 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

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

NIMIA 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)

NIMIA 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

NIMIA 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

NIMIA 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