The assessment of variability of the concentration of chromium in soils with the application of neural networks
Various ways of approaching the horizontal distribution trend (tendency) of Chromium (Cr) in soil, where pollution by this element is high, were analyzed. Interpolation algorithms: triangular irregular network (TIN), kriging, regularized spline with tension (RST), and artificial neural networks; radial basis function network (RBF), probabilistic neural network (PNN), generalized regression neural network (GRNN) and mixture density network (MDN) were applied. Data from field experiments, carried out in the area of the chemical plant in Alwernia, were used. The soil pollution spatial distribution examinations lead to the conclusion that in the first place was the information precision determination, and also the limit of error, through the pollution evaluation acceptance, whereas in the second place was the indication or standing out the regularity connected with the emission effect mechanism. It seems that the chromium concentration in soils variation, noticed even on short distances, makes the acceptance of interpolation method difficult, as a method of contamination distribution evaluation. On the other hand the considerable nonlinearity makes difficult the acceptance of regression model. In these circumstances, the possibility which is worth consideration is the modelling with the application of neuron networks, that is also hybrid solution application (for instance MDN), which gives the possibility of Cr concentration in soil variation deeper analysis (e. g. calculation local probability distribution, local variance, etc.).
- 1. NOWICKA E., OPRYSZEK Z. Ground observations methods assessment, aiming the heavy metals concentration determination.(In Polish) Master's thesis, AGH-University of Science and Technology, Cracow, June 2000.
- 2. TRAFAS M. Technology of Running Research and Cartographic Processing of Data Concerning the Contamination of Soils in Mining and Industrial Areas.(In Polish) Technical Report KBN 8 T 12E 007 20, AGH-University of Science and Technology, Cracow 2004.
- 3. MITASOVA H., MITAS L. Interpolation by regularized spline with tension: I. theory and implementation, 1993. URL citeseer.ist.psu.edu/mitasova93interpolation.html.
- 4. MASTERS T. Practical neural networks recipies in C++.(In Polish) Wydawnictwa Naukowo-Techniczne, Warsaw, 1996.
- 5. HECHT-NIELSEN R. Neurocomputing. Reading: AddisonWesley Pub. Co., Reading, 1990. ISBN 0-201-09355-3.
- 6. TADEUSIEWICZ R. Neural networks. (In Polish) Problemy Współczesnej Nauki i Techniki. Informatyka. Akademicka Oficyna Wydawnicza RM, Warsaw, 1993.
- 7. ŻURADA J., BARSKI M., JĘDRUCH W. Artificial neural networks. (In Polish) Wydawnictwo Naukowe PWN, Warszawa, 1996.
- 8. DUCH W., JANKOWSKI N. Survey of neural transfer functions, 1999. URL citeseer.ist.psu.edu/ duch99survey.html.
- 9. BISHOP C. Improving the generalization properties of radial basis function neural networks. Neural Computation, 3, (4), 579, 1991.
- 10. PARZEN E. On the estimation of a probability density function and mode. Annals of Mathematical Statistics, 33, 1065, 1962. URL citeseer.ist.psu.edu/ parzen62estimation.html.
- 11. SPECHT D. F. A generalized regression neural network. IEEE Transactions on Neural Networks, 2, 568, November 1991.
- 12. BISHOP C. M. Mixture density networks. Technical Report NCRG/94/004, Neural Computing Research Grup, Aston University, Birmingham B4 7ET, February 1994. URL http://www.ncrg.aston.ac.uk.
- 13. GOLDBERG P. W., WILLIAMS C. K. I , BISHOP C. M. Regression with input-dependent noise: A gaussian process treatment. In Michael I. Jordan, Michael J. Kearns, and Sara A. Solla, editors, Advances in Neural Information Processing Systems, volume 10. The MIT Press, 1998. URL citeseer.ist.psu.edu/article/goldberg98regression.html.
- 14. CORNFORD D., NABNEY I. T., BISHOP C. M. Neural network based wind vector retrieval from satellite scaterrometer data. Neural Computing and Application, 8, 206, 1999.
- 15. EVANS D. J. Mixture density network training by computation in parameter space. Technical Report NCRG/98/016, Neural Computing Research Grup, Aston University, Birmingham B4 7ET, August 1998. URL http://www.ncrg.aston.ac.uk.
- 16. LARK R. M. Designing sampling grids from imprecise information on soil variability, an approach based on the fuzzy kriging variance. Geoderma, 98, 35, April 2000.
- 17. MITASOVA H., BROWN W. M., HOFIERKA J. Multidimensional dynamic cartography. URL citeseer.ist.psu.edu/ mitasova95multidimensional.html.