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12 nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011 Dry Wet Figure 7 Class errors for two categories Dry and Wet. For the Random Forest, the two Wet classes were merged to one. DISCUSSION In general, our results indicate that all algorithms are able to successfully identify dry and wet periods based on MWL signals. In Figure 7 we compare the online algorithms S1a, S1b and S2 to RF4, which is based on similar attributes. For the factor graphs, only an offline algorithm was available. We found that the quantization had a great influence and therefore provide separate bars for the MWL with fine (bold) and coarse (shaded) quantization (Figure 7). In general, it can be seen that S2 shows smaller type II errors than S1a or S1b and out of the type II errors, less correspond to heavy rains ( Figure 5, right). However, we also notice that the cost of fewer type II errors lies in higher misclassification rates for dry periods. Based on our results, we find that the choice of one specific algorithm strongly depends on the user’s preferences and the available resources. First, the absolute performance can be adjusted according to the user’s preference by varying the respective tuning parameters. For the original (S1) and extended (S2) moving window algorithms, the fraction of wet periods is a physically-based parameter and should therefore not necessarily be changed. For the random forests, the composition of the training set and the weights assigned to each class can be can be tuned. For the Factor graph, the threshold parameter could be further adjusted to lower the misclassification rate for the wet classes, which would automatically lead to an increased D misclassification. Second, such parameters could be optimized by introducing a cost or preference function. Ideally, this should be defined by the user of the algorithms and will be different for online and offline algorithms as the user is probably interested in different kind of rainfall data (e.g., real-time information to control waster water infrastructure vs. generated time series for the dimensioning of waste water infrastructure). This should also consider the absolute deviation from observed rainfall volumes. CONCLUSIONS In this study, our goal was to develop an appropriate offline and online algorithm for the preprocessing of MWL data to support urban drainage applications. We compared novel algorithms based on moving windows, random forests and factor graphs, which is a rather novel technique from signal processing to those reported in literature. Our results show that an appropriate online and offline algorithm strongly depends on the quantization and temporal resolution of the MWL data, which greatly depends on the deployed instruments. With regard Page 8 of 12
12 nd International Conference on Urban Drainage, Porto Alegre/Brazil, 10-15 September 2011 to the individual algorithms we conclude that i) the improved moving window algorithm is easy to implement and provides an instant prediction of the baseline and the rain-induced attenuation. The method performs unsatisfactory with a low temporal or power resolution, ii) the power of the random forest algorithm is its flexibility, because it can readily consider various types of information. However, this supervised learning method requires a comprehensive ground truth and, to cope with seasonal variations, ideally a whole year of data should already be available. In our case study, offline and online algorithms performed similarly and results were more robust to a coarse quantization than the moving window algorithm, iii) the Factor graph is a very elegant solution, as it decomposes the observed signals by means of stochastic state-space estimation. Although it performed well, even without intensive tuning, a post processing step is suggested for MWL with a coarse quantization to avoid the prediction of too many small rain rates. This is the preferred method for low temporal resolution data, because of its underlying dynamic system model. ACKNOWLEDGEMENTS We thank Michal Piotrowski and Johannes Graf, ORANGE SA and Maciej Rudnicki from Alcatel-Lucent for kind provision of the MWL data and ERZ for rainfall information. Dr. Marcel Dettling provided valuable advice regarding statistical classification using random forests. We are most grateful to Prof. Loeliger, Christoph Reller, Juan Pablo Marín Díaz from the Signal and Information Processing Laboratory (ISI) of ETH for developing and implementing the novel factor graph algorithm. REFERENCES Atkinson, E. J., et al. (2000) An Introduction to Recursive Partitioning Using the RPART Routines. Mayo Clinic Division for Biostatistics, Berne, A. and Uijlenhoet, R. (2007) Path-averaged rainfall estimation using microwave links: Uncertainty due to spatial rainfall variability. Geophysical Research Letters, 34 (7). Breiman, Friedman, Olshen and Stone. (1984). “Classification and Regression Trees”. Chapman and Hall/CRC. 978-0412048418 Breiman, L. (2001) Random forests. Machine Learning, 45 (1),5-32. Brussaard, G. and Watson, P. A. (1994). “Atmospheric Modelling And Millimetre Wave Propagation”. Springer-Verlag, New York. Germann, U., Galli, G., Boscacci, M. and Bolliger, M. (2006) Radar precipitation measurement in a mountainous region. Q. J. Roy. Meteor. Soc., 132 (618),1669-1692. Gini, C. (1921) Measurement of inequality of incomes. Economic Journal 31 124–126. Krämer, S., Verworn, H. R. and Redder, A. (2005) Improvement of X-band radar rainfall estimates using a microwave link. Atmospheric Research, 77 (1-4 SPEC. ISS.),278-299. Leijnse, H., Uijlenhoet, R. and Stricker, J. N. M. (2007) Hydrometeorological application of a microwave link. Part II: precipitation. Water Resour. Res., 43 (4),W04417. Loeliger, H. A., Bolliger, L., Reller, C. and Korl, S. (2009) Localizing, forgetting, and likelihood filtering in state-space models. In “Information Theory and Applications Workshop, ITA 2009”, pp. 184- 186. Loeliger, H. A., Dauwels, J., Hu, J., Korl, S., Ping, L. and Kschischang, F. R. (2007) The factor graph approach to model-based signal processing. Proceedings of the IEEE, 95 (6),1295-1322. Messer, H., Zinevich, A. and Alpert, P. (2006) Environmental monitoring by wireless communication networks. Science, 312 713. Reller, C., Marín Díaz, J. P. and Loeliger, H. A. (2011) A model for quasi-periodic signals with application to rain estimation from microwave link gain. In “19th European Signal Processing Conference (EUSIPCO 2011) , August 29-September 2, 2011”, Barcelona, Spain. Rieckermann, J., Lüscher, R. and Krämer, S. (2009) Assessing urban precipitatoin using radio signals from a commercial communication network. In “8th International Workshop on Precipitation in Urban Areas 10-13 December, 2009, St. Moritz, Switzerland”. Schleiss, M. and Berne, A. (2010) Identification of dry and rainy periods using telecommunciation microwave links. IEEE Geosci. Remote Sens. Lett. Upton, G. J. G, Holt, A. R., Cummings, R. J., Rahimi, A. R. and Goddard, J. W. F. (2005) Microwave links: the future for urban rainfall measurements? Atmos. Res., 77 (1-4),300-312. Zinevich, A., Alpert, P. and Messer, H. (2008) Estimation of rainfall fields using commercial microwave communication networks of variable density. Adv. Water Resour., 31 (11),1470-1480. Page 9 of 12
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