International Conference in Inductive Modelling ICIM' 2013 Perceptron Model of System Environmental Assessment of Water Quality in River Basins P.I. Kovalchuk, A.V. Gerus, V.P. Kovalchuk Institute of Water Problems and Land Reclamation NAAS [email protected] Abstract. Perceptron model for system environmental assessment of water quality in river basins was formalized. The model was tested in basins of Desna river. Keywords: Perceptron model, water quality, river basins. 1 Problem statement Data analysis of monitoring observations requires formal their submission for objective spatial assessment of water quality and system decision-making [1]. The existing methods of water quality ecological assessment [2] is characterized by the hierarchical nature of gradual complication from simple to complex integrated assessments, but adapted to only one observation point. To implement the basin management principle it is stated a problem to develop a systematic approach which is to select an interconnected set of points in the river basin. The observation points are elements of the system. To formalize the system model of decision making a perceptron model is the most appropriate [3,4], the feature of which is an ensemble of perceptron type neurons that interact at the basin level. Therefore, the objective of the work is to develop a perceptron model and software package for the automated ecosystem spatial-temporal analysis of water quality, to compare the changes in individual and integrated parameters at different levels of hierarchy of criterion functions. 2 Formalizing the problem of water system classification Formalizing the perceptron model is developing an operation algorithm for formal neurons of perceptron type and their interaction at the level of condition parameters of the river basin. Formal neuron is an elementary perceptron, i.e. a solving system at a separate point, that consists of several layers, which are formed respectively by the elements of three types: sensory elements, i.e. receptors (S-elements), that record hydrochemical parameters concentration at a given point; associative elements (A-elements) that carry out a threshold selection; R-elements of decision-making, that implement integrated assessments of water quality (numerical, graphical, logical and linguistic) by the hierarchy levels. The block diagram of such a perceptron as to the water quality assessment is shown in Figure 1. Fig. 1 Hierarchy chart of decision-making for the environmental assessment of water quality at the observation point: 279 International Conference in Inductive Modelling ICIM' 2013 Hierarchy level I-classes and categories of certain parameters by the concentrations Sk ; Hierarchy level II - environmental assessment of water quality by the groups of parameters (salt content, tropho- saprobiotic (sanitation and epidemiological) and toxic and radioactive agents content); Hierarchy level III - generalized index of water quality. At the first hierarchy level of the hydrochemical parameters are presented as a vector of their concentrations: for the salt block parameters (SSS,, ); for the tropho-saprobiotic block parameters (SSS,... , ); for the 11 12 13 21 2,n2− 1 2, n2 parameters block of water pollution by specific toxic and radioactive agents (SSS,... , ). 31 3,n3− 1 3, n3 At the A-level elements numerical, graphical and logical-linguistic assessments are made using the average and worst values (for some period of time) of sensory elements. Using some discretization indices of the signal Sij the numerical value of water quality of Lj class and l j category is determined by using the following equation: ⎧ j j k−1 k ⎪L, l then Pij ≤ Sij ≤ P ij ; ()Sij =⎨ (1) ⎩⎪i=1,2,3; j ∈ [1;3] ∪ [1; n1 ] ∪ [1; n2 ]. The output signals of A-elements are used at the second level of the hierarchy to calculate the integral indices using three blocks of parameters for the average values and for the values of parameters that characterize the worst conditions. The calculation is made by using the following formulas: nk nk nk nk j j QR,сер = ∑ aj L/, ∑ aj qz,сер = ∑ aj l/; ∑ a j j=1 j=1 j=1 j=1 j j QR,max =max L qz,max = maxl (2) j=1,2,... nk j=1,2,... nk . where QQR, averp , R ,max - average and worst index values of every blocks to determine the classes; qz, averp, q z,max - average and worst index values to determine the categories; a j - weighting coefficients: ⎧ ,1 if the parameters is known; a j = ⎨ ⎩ ,0 if the parametrs is unknown, іnformations is not aviable. R, r - current indices by the parameters of three blocks (R= A , b , C ; r= a , b , c ). Block indices sampling by the intervals similarly (1) allows to determine the classes and categories of water quality at the second level of the hierarchy. The values of block indices can be fractional . This allows to differentiate the water quality assessment, make it more accurate for determining the subcategory of water quality as well as to characterize verbally water quality. The last line consists of a single R-element. At the third level of the hierarchy the integral index (,)II EEaverp max of integrated environmental assessment is calculated using the formulas: 3 3 I= q;3/ I= q .3/ (3) Eaverp ∑ r, averp Emax ∑ r,max r =1 r =1 Threshold selection by the intervals of subcategories of the integrated environmental assessment allows to determine classes, categories and subcategories of water quality at the sampling point of hydrochemical parameters. The system ecological assessment of water quality in the basin or in the part of the basin as well as lengthways the river channel (Fig. 2) is made using the ensemble of relevant neurons. A schematic map of the basin is generated with plotting on the map the sampling points as a visualization element of the environmental assessment. The feature of the system model (Fig. 2) is the possibility of making the complete environmental assessment that takes into account interim evaluations of output values of the neural network ensemble at all levels of hierarchy (Fig. 2) Thus, the matrix S, composed of the sensor elements of each sampling points, determines the matrix of the neural network A (S) for S- A transformation relations in the matrix of classes and categories. 280 International Conference in Inductive Modelling ICIM' 2013 Fig. 2. Chart of basin environment assessments of water quality by the ensemble of perceptron neurons. ,11 ... SS 1 N ,21 ... SS 2 N S = , = + + nnm ;3 ........., 21 S ... S m 1 , m N At the level of response elements R )1( the block indices matrixes are formed as well as the matrixes of classes and categories for three blocks of water quality parameters as a result of the threshold selection. The pooled environmental assessment (level R )1( ) is presented by the integrated assessments vector and the vectors of subcategories, categories and classes of water quality. The system spatially-temporal analysis of water quality using the ensemble of perceptron neurons makes it possible to identify the most promising directions of decision making to improve water quality in river basins. 3. The results of system environmental assessment of water quality (the case of the Desna river) For the ecosystem assessments the schematic map (Fig. 3) of the spatial location of water quality observation points along the Desna river was generated. Processing the data from the Ministry of Environment and Natural Resources [5] of Ukraine for the period of three years (2009- 2011) enabled to make the spatially-temporal assessments by the average and worst values. 1.Litky village on the border with the Kyiv region; 2. Krekhayiv village of Kozeletsky district; 3. downstream the mouth of the Oster river; 4. upstream the mouth of the Oster river; 5. near Shestovytsya village; 6. Chernigiv city, 0.5 km upstream the mouth of the Bilous river; 7. downstream the mouth of the Bilous river; 8. Bobrovytsi village, upstream Chernigiv city; 9. Brusyliv village, 0.1 km downstream the mouth of the Snov river; 10. Brusyliv village, 0.1 km upstream the mouth of the Snov river; 11. V. Ustya village, downstream the mouth of the Seym river; 12. Pekariv village, upstream the mouth of the Seym river; 13. 0.1 km downstream the mouth of the Shostka river; 14. Pyrogivka village, 0.2 km upstream the mouth of the Shostka river; 15. 0,1 km downstream Novgorod-Siversky town; 16. 0,1 km upstream Novgorod-Siversky town; 17. Muravyi village, 0.5 km upstream the Sudost river. Fig.3. 281 International Conference in Inductive Modelling ICIM' 2013 Thus, the assessment according to the first block (parameters - sum of ions, chlorides and sulfates amounts) and calculation using the indices of salt composition ( I ,1 averp , I max,1 ,) showed that the water at the Desna river station by the average and worst values of І1 is in the range (1,0 ≤ I1 ≤ 2,0) and belongs to the first class of the first category, and in some cases to the second class of the second category respectively. Water is described as "excellent" and "very clean" by I ,1 averp and "very good" and "clean" by I max,1 . Fig. 4. Classification of water quality according to the classes and categories at the sampling points by ammonium nitrogen parameters (2011) According to the water quality parameters the most unfavorable is the block of tropho-saprobiotic parameters. According to the classification [2] the water of the Desna river almost at all observation points is of the third class, which specifies it as eutrophic, transient by the quality from "good", "quite clean" to "satisfactory" and "slightly polluted." The worst values