In the study, multivariate statistical methods including factor, principal component and cluster analysis were applied to analyze surface water quality data sets obtained from Xiangjiang watershed, and generated during 7 years (1994-2000) monitoring of 12 parameters at 34 different profiles. Hierarchical cluster analysis grouped 34 sampling sites into three clusters, including relatively less polluted (LP), medium polluted (MP) and highly polluted (HP) sites, and based on the similarity of water quality characteristics, the watershed was divided into three zones. Factor analysis/principal component analysis, applied to analyze the data sets of the three different groups obtained from cluster analysis, resulted in four latent factors accounting for 71.62%, 71.77% and 72.01% of the total variance in water quality data sets of LP, MP and HP areas, respectively. The PCs obtained from factor analysis indicate that the parameters for water quality variations are mainly related to dissolve heavy metals. Thus, these methods are believed to be valuable to help water resources managers understand complex nature of water quality issues and determine the priorities to improve water quality.
We consider the fully parity-time (PT) symmetric nonlocal (2 + 1)-dimensional nonlinear Schrödinger (NLS) equation with respect to x and y. By using Hirota's bilinear method, we derive the N-soliton solutions of the nonlocal NLS equation. By using the resulting N-soliton solutions and employing long wave limit method, we derive its nonsingular rational solutions and semi-rational solutions. The rational solutions act as the line rogue waves. The semi-rational solutions mean different types of combinations in rogue waves, breathers, and periodic line waves. Furthermore, in order to easily understand the dynamic behaviors of the nonlocal NLS equation, we display some graphics to analyze the characteristics of these solutions.
KEYWORDSrational wave, semi-rational wave, soliton wave, the nonlocal (2 + 1)-dimensional NLS equation
MSC CLASSIFICATION
35C08; 35Q51; 35Q55Math Meth Appl Sci. 2019;42:6865-6877.wileyonlinelibrary.com/journal/mma
In this paper, the load time-series measured from 2016 to 2018 in Qingdao is investigated in order to make a prediction more accurately by using an artificial neural network model combined with some regular and irregular features. The results of spectral analysis show that several periodic variations in diurnal, semidiurnal and weekly frequencies are prominent, and considered as critical parts of predictior variables of the training and test sets in this forecasting model. However, a significant decline of load happens during the national statutory festivals in China, and is more obvious with the longer holidays, which should be taken into account as abnormal conditions. Moreover, both temperatuer and hummity filtered out by mutual information method are also added as two essential weather factors to improve the prediction accuracy, especially in the hot summer. Finally, the comparative results of five different experiments in term of mean absolute percent error show that the forecasting model combined with all periodic and non-periodic factors outperforms the others with one single or a few of factors. This multifactorial model, taking fully account of internal charateristics of load data and external important influences, is proved more suitable to predict the load trend in Qingdao. INDEX TERMS Short-term load forcasting, artificial neural network, periodic and non-periodic factors, mean absolute percent error.
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