贝叶斯正则化Bayesian BP Regulation

APPLICATION OF BAYESIAN REGULARIZED BP NEURAL

NETWORK MODEL FOR TREND ANALYSIS,ACIDITY AND

CHEMICAL COMPOSITION OF PRECIPITATION IN NORTH

CAROLINA

MIN XU1,GUANGMING ZENG1,2,∗,XINYI XU1,GUOHE HUANG1,2,RU JIANG1

and WEI SUN2

1College of Environmental Science and Engineering,Hunan University,Changsha410082,China;

2Sino-Canadian Center of Energy and Environment Research,University of Regina,

Regina,SK,S4S0A2,Canada

(∗author for correspondence,e-mail:zgming@,ykxumin@,

Tel.:86–731-882-2754,Fax:86-731-882-3701)

(Received1August2005;accepted12December2005)

Abstract.Bayesian regularized back-propagation neural network(BRBPNN)was developed for trend analysis,acidity and chemical composition of precipitation in North Carolina using precipitation chemistry data in NADP.This study included two BRBPNN application problems:(i)the relationship between precipitation acidity(pH)and other ions(NH+4,NO−3,SO2−4,Ca2+,Mg2+,K+,Cl−and Na+) was performed by BRBPNN and the achieved optimal network structure was8-15-1.Then the relative importance index,obtained through the sum of square weights between each input neuron and the hidden layer of BRBPNN(8-15-1),indicated that the ions’contribution to the acidity declined in the order of NH+4>SO2−4>NO−3;and(ii)investigations were also carried out using BRBPNN with respect to temporal variation of monthly mean NH+4,SO2−4and NO3−concentrations and their optimal architectures for the1990–2003data were4-6-1,4-6-1and4-4-1,respectively.All the estimated results of the optimal BRBPNNs showed that the relationship between the acidity and other ions or that between NH+4,SO2−4,NO−3concentrations with regard to precipitation amount and time variable was obviously nonlinear,since in contrast to multiple linear regression(MLR),BRBPNN was clearly better with less error in prediction and of higher correlation coefficients.Meanwhile,results also exhibited that BRBPNN was of automated regularization parameter selection capability and may ensure the excellentfitting and robustness.Thus,this study laid the foundation for the application of BRBPNN in the analysis of acid precipitation.

Keywords:Bayesian regularized back-propagation neural network(BRBPNN),precipitation,chem-ical composition,temporal trend,the sum of square weights

1.Introduction

Characterization of the chemical nature of precipitation is currently under con-siderable investigations due to the increasing concern about man’s atmospheric inputs of substances and their effects on land,surface waters,vegetation and mate-rials.Particularly,temporal trend and chemical composition has been the subject of extensive research in North America,Canada and Japan in the past30years(Zeng Water,Air,and Soil Pollution(2006)172:167–184

DOI:10.1007/s11270-005-9068-8C Springer2006