combining signal processing and machine learning techniques for real time measurement of raindrops

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 50, NO. 6, DECEMBER 2001 1717

Combining Signal Processing and Machine LearningTechniques for Real Time Measurement of Raindrops

Bruce Denby, Senior Member, IEEE, Jean-Christophe Prévotet, Member, IEEE, Patrick Garda, Member, IEEE,Bertrand Granado, Laurent Barthes, Peter Golé, Jacques Lavergnat, and Jean-Yves Delahaye

Abstract—The data acquisition system for a new type of opticaldisdrometer is presented. As the device must measure sizes andvelocities of raindrops as small as 0.1 mm diameter in real time inthe presence of high noise and a variable baseline, algorithm designhas been a challenge. The combining of standard signal processingtechniques and machine learning methods (in this case, a neuralnetwork) has been essential to obtaining good performance.

Index Terms—Machine learning, meteorology, neural networks,optical disdrometer, real time instrumentation, telecommunica-tions.

I. INTRODUCTION

T HE MEASUREMENT of individual droplet sizes andvelocities in rainfall is of interest in meteorology as well

as for predicting attenuation in microwave telecommunicationslinks. Many techniques exist (see [1]–[5] and referencestherein), including early blotting paper methods, the electro-mechanical Joss–Waldvogel device, video imaging of droplets,Doppler radar scattering, and the optical extinction disdrometerwhich has now come into widespread use. Comparative studies[2], [3] indicate roughly comparable performance of thedifferent methods for droplets down to about 0.2 millimetersradius, below which the low signal to noise ratio makesmeasurement very difficult. In the case of optical extinctiondevices, fluctuations in the air refractive index are the majornoise source.

At the Centre d’Etudes des Environnements Terrestre etPlanétaires (CETP), Vélizy, France, a new type of opticaldisdrometer has been developed which should be able toprovide diameters and velocities of raindrops of 0.1 mm inradius or even smaller. The device functions by measuringthe variations in photodiode current (sampled at 10 kHz) asdroplets pass through a pair of collimated infrared beams as inFig. 1(a). The passage of a droplet through the device produces

Manuscript received April 18, 2001; revised September 10, 2001. This workwas supported in part by the French Centre National d’Etudes de Télécommu-nications (now France Telecom R&D).

B. Denby is with the Université de Versailles St. Quentin en Yvelines, Labo-ratoire des Instruments et Systèmes, Paris Cedex 05, France and he is also withthe Centre d’Etude des Environnements Terrestre et Planétaires, Vélizy, France(e-mail: [email protected]).

J.-C. Prévotet, P. Garda, and B. Granado are with the Université Pierre etMarie Curie, Laboratoire des Instruments et Systèmes, Paris Cedex 05, France(e-mail: [email protected]; [email protected];[email protected]).

L. Barthes, P. Golé, J. Lavergnat, and J.-Y. Delahaye are with the Centred’Etude des Environnements Terrestre et Planétaires, Vélizy, France (e-mail:[email protected]; [email protected]; [email protected]; [email protected]).

Publisher Item Identifier S 0018-9456(01)10944-7.

(a)

(b)

Fig. 1. (a) Optical layout of dual beam disdrometer. (b) Schematicrepresentation of (inverted) diode signal pulses produced by the passage of araindrop. As the spacing between beams is equal to the beam thicknesses, allthree time intervals indicated by the double arrows must be equal for a dropletfalling at constant velocity. The active volume of the device has been chosen toensure that simultaneous occupancy of the beams by multiple droplets (whichcannot be analyzed) will be negligible.

a roughly rectangular pulse [Fig. 1(b)] which, in a sphericaldroplet approximation, allows radii to be calculated from pulseheights and velocities from the widths and separations of thepulses. A straightforward data processing scheme could thus,in principle, be based on measuring plateau heights and thepositions of rising and falling edges in the two beams.

II. NOISE ANALYSIS

In practice, the situation is complicated by the fact that fluc-tuations in the current baseline are quite large compared to thedroplet signals of interest, as seen in Fig. 2, where a 500 sampleseries from one of the beams is presented. The peak containedin the rightmost circle in the figure corresponds to a 0.15 mmradius simulated droplet pulse which has been superimposed onthe real noise signal. The left circle contains a noise peak whichcould easily be confused with a droplet of similar size. In sucha situation, the definitions of features such as leading edges andplateaus can be ambiguous, and false alarm rejection is difficult.

The power spectral density of the system noise is shown inFig. 3 for two types of conditions: 1) disdrometer in the labora-tory (lower curve); and 2) disdrometer outdoors in clear weather

0018–9456/01$10.00 © 2001 IEEE

1718 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 50, NO. 6, DECEMBER 2001

Fig. 2. Fifty milliseconds of raw signal samples (voltage relative to average) with an added simulated droplet. Baseline fluctuations make it difficult for thealgorithms to distinguish a “false” droplet (leftmost circle) from a true 0.15 mm radius one (right circle).

Fig. 3. Noise power spectral density for clear weather (upper curve) and laboratory measurements (lower curve) taken on two different dates. Peaks atlineharmonics and switching frequencies are apparent. The dashed line shows thef behavior expected from fluctuations in the local index of refraction. Therolloff after 120 Hz is due to the device size.

(upper curve). For the outdoor measurements, the data is reason-ably well modeled by the well known dependence of airrefractive index fluctuations coupled with a gradual turnoff be-yond a cutoff frequency, in this case about 120 Hz, dictated bythe device size. In normal operation, these index fluctuations arethe dominant source of noise in the disdrometer system.

Fig. 4 shows the normalized noise amplitude distributiontaken for two different sets of outdoor conditions, DAY 1, clearwith mild temperatures, and DAY 2, with clear and hot condi-tions. It is evident that the distribution of system noise varieswith time and tends toward a bimodal shape when refractive

index fluctuations are largest. Also, the noise distributions ofthe two beams are in general different from each other.

III. CHOICE OFALGORITHMS

As the system noise characteristic appears to be rather diffi-cult, and to undergo strong changes according to meteorolog-ical conditions, droplet detection algorithms were drawn fromad-hocsignal processing techniques and machine learning ap-proaches for which explicit models of underlying noise distribu-tions are not necessary. A straightforward possibility, given the

DENBY et al.: COMBINING SIGNAL PROCESSING AND MACHINE LEARNING TECHNIQUES 1719

Fig. 4. Normalized noise distributions for the upper (gray curve) and lower(black curve) beams of the disdrometer. The top set of curves is for a clear, mildday, and the bottom set for a clear, hot day. The distributions for the two daysare substantially different and tend toward bimodality in the case of the hotterconditions.

parallel beam signals and characteristic droplet shape, wouldbe an intercorrelation of the two beam signals. Initial tests ofsuch a method, however, were not promising, as accidental noisecorrelations gave rise to multiple peaks in the intercorrelationproduct, and the number of calculations involved appeared to betoo high for a real-time implementation. It could nonetheless beinteresting to investigate various methods of filtering the photo-diode data before calculating the intercorrelation, as suggestedin [6]. The signal processing and machine learning algorithmsfinally retained are described in the following two sections. Asshall be seen, the most successful method incorporated elementsof both approaches.

IV. SIGNAL PROCESSINGAPPROACH—THE SLOPEALGORITHM

The signal processing algorithm adopted, called the “slope”algorithm, is presented in Fig. 5. The procedure is carried out inthree stages, the first two being identical for both beams:

1) Slope Calculation and Edge Detection. Raw voltagesamples are replaced by instantaneous slope values

at each sampling instantusing a linear regressionalgorithm applied to windows of width eight samples.

is then thresholded to produce lists of rising andfalling edges and for upper and lowerbeams at instants and . The THRESHOLD valuewas determined empirically and adjusted for best overallresults.

2) Droplet finding within the individual beams. For eachrising edge, a falling edge with similar slope is soughtat a relative delay of WIDTH samples, where WIDTHis less than a fixed samples. Confirmedrising/falling edge pairs are added to droplet candidatelists for the upper and lower beams.

3) Cross-validation of candidates. For each candidate fromthe upper beam, a corresponding candidate in the lowerbeam is sought with similar rising and falling edge slopesand satisfying the pulse width criterion described in thecaption of Fig. 1(b). For confirmed candidates, the dropletparameters (diameter and velocity) and a quality flag cannow be computed under a spherical droplet approxima-tion, which is realistic.

The quality flag is a sort ofad hocchi-squared measuring thedegree of agreement of the three widths illustrated in Fig. 1(b),plus an additional term favoring droplets with a high value ofthe average of the four slope measurements. Droplets having aquality flag greater than 50 are rejected.

V. MACHINE LEARNING APPROACH—THE TDNN ALGORITHM

The machine learning algorithm retained is based upon timedelay neural networks. TDNNs are a standard technique in pat-tern recognition problems (optical character recognition, imageanalysis, etc., see for example [7], [8]), and are invoked whencharacteristic features—edges or plateaus for instance—can ap-pear anywhere in the input stream. As shown in Fig. 6, fea-tures extracted by regularly spaced MLPs (multilayer percep-tions) with shared (i.e., identical) weights can be combined todetect more complex structures—droplets for example—usinga second, higher-level MLP.

Two distinct TDNN assemblies were used in the presentwork, one to detect droplets and a second to measure theparameters of droplets detected. The MLP extractors used inthe TDNNs examined ten sample-wide input windows andoutput one, or two, features, for the case of droplet detectionand parameter assemblies, respectively. Both TDNNs inputfive extractors from the upper beam—sufficient to contain eventhe slowest droplets (i.e., longest pulses)—and 15 from thelower beam in order to account for thea priori unknown delayof the second pulse relative to the first one (Fig. 6). The inputto a TDNN was thus 10 (15 5) 200 samples. Twentyhidden units were used in both TDNNs, and two outputs wereproduced. For the droplet detection TDNN, these were flagsindicating the presence of a droplet in upper and/or lowerbeams, whereas for the parameter measurement assembly, theoutputs were continuous and coded the diameter and velocityof the droplet. The overall architecture of the higher-levelMLPs was thus 20-20-2 (droplet detection TDNN) or 40-20-2(parameter TDNN). In normal operation, the detection TDNNadvances along the sample stream in steps of five samples (halfa window), in order to reduce calculation time as compared to a


Fig. 5. Three-stage “slope” algorithm. Instantaneous slope values are first thresholded to yield rising and falling edge lists. In the second stage,droplet candidatesare defined as slope-matched rising/falling edge pairs with separations corresponding to valid droplet sizes. In the final stage, candidates are cross-validated betweenthe two beams, and droplet parameters and a quality flag are calculated.

standard sliding window. When the detection assembly signalsa droplet in both beams, the second TDNN, applied to the same200 inputs, calculates the droplet parameters.

The training set was constructed by superimposing 500simulated spherical droplets upon real noise measurementstaken during clear weather. In order to favor detection of thesmallest possible droplets, only radii in the range 0.04 mm to0.2 mm were used. The data were segmented into 5000 patternsfor presentation to the network, some of which contained fullor partial droplets, others, only noise. All of the patterns wereused in the training of the droplet detection TDNN, whereasonly those actually containing a droplet were used to train theparameter TDNN. As is usual, network inputs were normalizedto lie between 1 and 1. A statistically independent trainingset of 500 additional droplets was also created for validatingthe networks.

In previous work using simulated noise distributions[9]–[11], good results were obtained with standard backprop-agation by training the MLP extractors to find edges andplateaus, fixing those weights, and then training the higher levelMLP independently to detect droplets. When real data becameavailable, however, this approach no longer worked due to themany droplet-like structures caused by turbulence within thenoise. To remedy the situation, a new training strategy wasemployed in which the shared weights of the MLP extractorswere allowed to evolve at the same time as the weights of thehigher-level MLP. In essence, the extractors thus learned thebest features necessary to solve the problem, which no longer

strictly representeda priori determined characteristics such asedges or plateaus. With this modification, the TDNN approachagain became viable.

Neural network training packages handling shared weightsfor arbitrary architectures are difficult to find and often expen-sive. For the present work, a project-specific shared-weightbackpropagation program was written from scratch. The timefor a typical training session was about 12 h on a Sun Ultra5workstation. After each epoch, the current weights weretested on the test set, and training was terminated when themean-squared error on the test set began to increase. A numberof tests with differing numbers of hidden units were madebefore settling upon the final network architectures describedabove.

Before proceeding to the detailed comparison of the algo-rithms, it should be mentioned that when raw voltages wereused as inputs to the TDNNs, their performance was typicallyno better than that obtained with the slope algorithm. For thisreason, a number of experiments for preprocessing the raw datawere undertaken. The best performance was obtained when thedifferences between successive current samples were used asnetwork inputs. It is interesting to note that this correspondsin essence to thea priori observation in the signal processingalgorithm that slope information should be a salient variable;furthermore, the machine learning approach was apparently notable to deduce this information on its own. All of the compar-isons in the following section are based upon TDNNs using thisdifferential preprocessing.


Fig. 6. Overall structure of the TDNN assemblies. A bank of 20 MLPs (five from the upper beam, 15 from the lower) operating on windows of ten samplescalculates features useful for droplet detection or parameter determination. A higher level MLP then combines these features into droplet detection flags or variablescoding for droplet radius and velocity.

Fig. 7. Droplet detection efficiencies (%) as a function of radius (mm) for the TDNN method and the slope method.

VI. COMPARISON OFSLOPE AND TDNN ALGORITHMS

The comparison was performed using the same 500 droptraining set for both slope and TDNN algorithms, using ascriteria: 1) the droplet detection efficiency as a function ofradius, 2) the percentage of false droplet detections;, and 3) theaccuracy with which the radii and the velocities are determined.

Fig. 7 compares the detection efficiency for the two methods.While both methods achieve nearly 100% identification in theirplateaus, the TDNN efficiency extends down to about 0.06 mm,while for the SP method, it has fallen to only 70% already at 0.08

mm. For the set of parameters used in the figures, the false alarmrate was 2.43% for the TDNN and 8.9% for the slope method.

Fig. 8 compares the accuracy of the radius measurement forthe two methods. As compared to the TDNN method, the slopemethod presents three drawbacks:

• a lack of efficiency below 0.08 mm as already observed;• a tendency to underestimate small radii and overestimate

large ones (compare to the diagonal line);• a larger spread in radius values. This last point is con-

firmed by a comparison of the standard deviation of thedistributions of actual radius minus estimated radius for


(a)

(b)

Fig. 8. Comparison of droplet radius estimation for (a) the TDNN method and(b) the slope method.

the two methods: 0.002 mm for the TDNN versus 0.005mm for the slope method.

(a)

(b)

Fig. 9. Droplet velocities measured by the (a) TDNN method and (b) slopemethod. In (c) TDNN velocities for droplets having slope-determined velocitiesof less than 1.2 m/s.

In Fig. 9, the performance on velocity measurements is pre-sented. The following remarks can be made:

• The TDNN method gives smaller errors on high velocities.For lower velocities, the slope method appears to have a


smaller error, but this is in fact a consequence of the low ef-ficiency of the slope method for small droplets, which tendto have lower velocities [12]. To prove this, TDNN-de-termined velocities were plotted for droplets determinedby the slope algorithm to have velocities below 1.2 m/s.This is shown in Fig. 9(c). The figure demonstrates that theslope method gave the appearance of a superior error per-formance at low velocities by reporting only those caseswhich were “easier” to measure. The standard deviationsof the distributions of actual minus estimated velocities inFig. 9(a) and (b) are 0.08 m/s and 0.03 m/s, respectively.

• The slope method tends to underestimate small velocities.• The slope method exhibits a band structure not present in

the TDNN method. This is due to a discretization of edgepositions and could in principle be eliminated.

VII. REAL TIME CONSIDERATIONS

As the algorithm chosen must be executable in real time, it isimportant to examine the calculation times of the two methods.Measurements were made of the time taken by the two algo-rithms presented here as measured on an Intel PII running at400 MHz and operating on 110 000 samples from each beam.The total time for the slope method, including normalization,slope calculation, and output of results was about 810 ms. Forthe TDNN, including computing the derivative of the originalsignal, normalization, and execution of the neural net, thecorresponding number was 1040 ms. These measurements arenot to be considered as exact, but the indication is that thetwo algorithms are comparable from a time standpoint, and,as 110 000 samples corresponds to 11 seconds at the samplingrate, that either would be appropriate for a real-time application.The TDNN times are quoted here for a scenario in which theTDNN is moved by uniform steps of 5 samples across the data;the calculation time could likely be significantly reduced bytaking a larger step when no drops are detected in a section ofthe data.

VIII. D ISCUSSION ANDCONCLUSION: COMPLEMENTARITY

OF APPROACHES

Two data processing algorithms for an optical disdrometerare presented: a signal processing one based upon slope as asalient feature for edge detection, and a machine learning ap-proach using TDNNs. Though the TDNN algorithm ultimatelygave the best performance, its results were only equivalent tothe slope method until the networks were furnished with differ-entiated current inputs, corresponding, in essence, to the slopeinformation used in the signal processing algorithm. This is pre-sumably because with raw data as input, the backpropagationlearning was penalized by the difference in scale (factor 50)of the baseline fluctuations as compared to pulse heights of thesmaller droplets, particularly since the neural net inputs werenormalized between1 and 1, effectively restricting the numberof bits available to the training algorithm. The use of slope infor-mation essentially eliminates the more slowly varying baseline.

Crucial to the good performance of the TDNN algorithm wasa training procedure in which the shared weights of the featureextraction MLPs were allowed to evolve at the same time as

those of the higher-order MLP. This allows the extractors to“learn” the best features to solve the problem and gives supe-rior performance over a scheme in which features are fixed ac-cording to ana priori model.

Although the TDNN method gave better performance, bothalgorithms meet target specifications for real-time dropletdetection and precision of radius and velocity measurements.As development of the final algorithm is still underway, thecomplementarity between signal processing and machinelearning approaches will likely continue to play an importantrole in the final choice, which will be based upon tests usingreal data, where nonspherical droplets, nonuniformities in theoptical system, and long-term variations in the character of thenoise may prove to be important factors.

ACKNOWLEDGMENT

The authors are indebted to the reviewers for numeroushelpful suggestions.

REFERENCES

[1] J. Joss and A. Waldvogel, “A spectrograph for the automatic analysisof raindrops” (in German),Pure Appl. Geophys., vol. 68, pp. 240–246,1967.

[2] E. Campos and I. Zawadzki, “Instrumental uncertainties in Z-R rela-tions,” J. Appl. Meteorol., vol. 39, pp. 1088–1102, 2000.

[3] M. Löffler-Mang and J. Moss, “An optical disdrometer for measuringsize and velocity of hydrometeors,”J. Atmos. Ocean. Technol., vol. 17,pp. 130–139, Feb. 2000.

[4] D. Hauser, P. Amayenc, B. Nutten, and P. Waldteufel, “1984: A newoptical instrument for simultaneous measurement of raindrop diameterand fall speed distribution,”J. Atmos. Ocean. Technol., vol. 1, no. 3, pp.256–245.

[5] M. Grossklaus, K. Uhlig, and L. Hasse, “An optical disdrometer foruse in high wind speeds,”J. Atmos. Oceanic Technol., vol. 15, pp.1051–1059, Aug. 1998.

[6] C. H. Knapp and G. C. Carter, “The generalized correlation method forestimation of time delay,”IEEE Trans. Acoustics, Speech, Signal Pro-cessing, vol. 24, pp. 320–327, Aug. 1976.

[7] J. Principe and N. Euliano. ([ISBN: 0 471 351 679], copyright 2000)Neural and Adaptive Systems: Fundamentals Through Simulations.Wiley, New York. [Online]. Available: http://www.nd.com/products/ns-book.htm

[8] S. Haykin, Neural Networks, A Comprehensive Founda-tion. Englewood Cliffs, NJ: Prentice Hall, 1994.

[9] B. Denby, P. Golé, A. Sartori, and G. Tecchiolli, “Real time readoutdata acquisition techniques in meteorological applications,”IEEE Trans.Nucl. Sci., vol. 45, pp. 1840–1844, Aug. 1998.

[10] B. Denby, P. Golé, and J. Tarniewicz, “Structured neural network ap-proach for measuring raindrop sizes and velocities,” inProc. 1998 IEEESignal Processing Soc. Workshop Neural Networks Signal Processing,Constantinides, Kung, Niranjan, and Wilson, Eds. Piscataway, NJ:IEEE Press.

[11] , “TDNN approach to measuring raindrop sizes and velocities,”in Proc. Int. Conf. Artificial Neural Networks, Niklasson, Boden, andZiemke, Eds. London, Skovde, Sweden: Springer-Verlag, Sept. 2–4,1998.

[12] D. Atlas and C. Ulbrich, “Path- and area-integrated rainfall measure-ments by microwave attenuation in 1–3 cm band,”J. Appl. Meteor., vol.16, pp. 1622–1631, 1997.

Bruce Denby(SM’99) earned the B.S. degree from California Institute of Tech-nology, Pasadena, the M.S. degree from Rutgers University, New Brunswick,NJ, and the Ph.D. from the University of California, Santa Barbara.

He is currently Professor of electronics and signal processing at the Universitéde Versailles St. Quentin en Yvelines, Paris, France, and a Research Scientist atthe Laboratoire des Instruments et Systèmes Ile de France, Paris. After working20 years in experimental high energy physics, his current research interests in-clude electronic instrumentation, machine learning, and telecommunications.


Jean-Christophe Prévotet(M’01) was born in Paris, France, in 1975. He re-ceived the M.S. degree in electronic engineering from the Université Pierre etMarie Curie, Paris, in 1999. He is currently pursuing the Ph.D. degree in theimplementation of neural networks in fast dedicated hardware for real time ap-plications.

In 1999, he joined the Laboratoire des Instruments et Systèmes Ile de France,Paris, where he began working on instrumentation and applications of neuralsystems.

Patrick Garda (M’01) has been a Professor at the Université Pierre et MarieCurie, Paris, France, since 1995. He was Director of the Laboratoire des Instru-ments et Systèmes from 1997 to 2000 and is currently Head of the ElectronicSystems Research Group. His current research interests include real-time andembedded architectures, systems on a chip, neural networks and image pro-cessing, as well as their applications in the automotive and telecommunicationsfields.

Bertrand Granado received the Ph.D. degree in computer science from theUniversité de Paris XI, Orsay, France, in 1998.

He is an Associate Professor of electronics at the Université Pierre et MarieCurie, Paris, where his research interests focus on architectural techniques forhigh performance in neural network simulation and electronic integration ofsuch systems.

Laurent Barthes was born in Paris, France. He received the Ph.D. degree fromthe Université de Paris XI, Paris, in 1993.

He is currently working at the Centre d’étude des Environnements Terrestre etPlanétaires (CETP), Vélizy, France, a joint CNRS and Université de Versailleslaboratory which is also part of the Institut Pierre Simon Laplace. He is currentlyworking on propagation disturbances due to atmospheric hydrometeors in theKaband. He has used artificial neural network models in his research since 1996.

Peter Goléreceived the Ph.D. degree in physics from the Université de Nice,Nice, France in 1981, treating the propagation of microwaves through snow andrain.

He is presently working on the measurement of size of raindrops, and theireffects on the propagation of microwaves on satellite-earth links, at the Centred’etude des Environnements Terrestre et Planétaires, Vélizy, France, a jointCNRS and Université de Versailles laboratory which is part of the Institut PierreSimon Laplace.

Jacques Lavergnatwas born in Paris, France, in 1944. He received the M.S.degree in elecrtrical engineering from Ecole Nationale Supérieure des Télécom-munications, Paris, France, in 1966, and the D.Sc. from the Université Paris XI,Orsay, France, in 1976.

He is currently Professor at the Université de Versailles St. Quentin enYvelines, Paris, France, and Research Director at the Centre d’étude desEnvironnements Terrestres et Planétaires, Vélizy, France. His specific interestsinclude microwave propagation in the atmosphere, remote sensing, and signalprocessing.

Jean-Yves Delahaye received the engineering degree from the EcoleSupérieure d’Electricité de Malakoff-Gif, Malakoff-Gif, France, in 1969 andthe Docteur Ingénieur degree in electronics, instrumentation, and metrologyfrom the Université de Paris VI, Paris, France, in 1981.

He is currently working with the Centre d’etude des Environnements Terrestreet Planétaires, Vélizy, France, a joint CNRS and Université de Versailles labo-ratory and member of the Institut Pierre Simon Laplace. His current researchinterests include remote sensing and meteorological sensor development.

combining signal processing and machine learning techniques for real time measurement of raindrops

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