Application of ANN Model

Application of ANN Model4.0. Introduction In this chapter, the results of ANN pretendingling argon discussed through and through performance parameters, time series plotting and presentation through tables. Before the occupation of ANN impersonate, statistical analytic thinking of data ar d iodine. It is discussed earlier that the selection of admit commentary combination from the available data is the crucial step of the pose development process. Five different types of input changeable selection (IVS) techniques were utilized and twenty six input combinations were prep bed base on the IVS techniques which be discussed in section 4.2. Fin all toldy, results of four ANN exemplifications argon discussed sensation by unrivaled. Firstly, the fly the coop forward neural network model were picked to predict fade out atomic number 8 of Surma River with all twenty six input combinations and compared with one a nonher. Secondly, the sensitivity abstract was done by chang ing the quantify of various(prenominal) input variants in a certain percentage. Thirdly, six crush input combinations were selected based on their performances and rest of the trine ANN models were utilized with those selected six input combinations. Finally, three best models from each ANN model were picked to compare with each otherwise. The results of statistical data summary, results of IVS, and results of ANN models leave be discussed in this chapter chronologically.4.1. Statistical Analysis of Data Statistical parameters are very important components to understand the variability of a data coterie which is prerequisite of any modeling works.This study used some elemental statistical parameters i.e. minimum, maximum, dream up, standard going away (SD) and coefficient of variability (CV) as defined to a lower placeWhere, N is the total number of samples, is the irrigate feeling data, is the arithmetic mean of that particular data series. The summary of analysis is represented in remit 4.1. Standard Deviation (SD) steers the variation in data set, where littler time value represents the data is close together, while larger value denotes wide public exposure of data set. The SD of dependent variable ( variant) showed relatively small value with deference to other parameters. But sometimes its difficult to understand variability tho by SD value. Thus, coefficient of variability (CV) was used in this study for clear accord of variability. Value of CV for BOD displayed larger variation (75%) that represents huge quantities of untreated waste piss was dumping from various point and nonpoint sources into this river during sample collection. All case-by-case variables (remaining 14 parameters) also showed an enormous variation in CV value (8% to 144%). Such variability might be happened due to geographic variations in climate and seasonal inuences in the study region. pH showed lowest variation and it whitethorn happen due to the buffering capacity of the river. hold over 4. 1 Basic Statistics i.e. minimum (min), maximum (max), mean (M), standard deviation (SD) and coefficient of variation (CV) of the measured water type variables for a period of three years (January, 2010-December, 2012) in Surma River, Sylhet, Bangladesh.VariableMinMaxMeanStd.CV (%)Phosphate (mg/l)0.013.790.530.70132Nitrates (mg/l)0.184.01.531.0569 carbon dioxide (mg/l)8.012732.6620.9964Alkalinity (mg/l)2119559.3430.5651TS (mg/l)55947292.2165.6957TDS (mg/l)10522142.3102.1572pH5.78.256.920.558Hardness (mg/l)452621194336SO4-3 (mg/l)2.033.1010.686.8264BOD (mg/l)0.617.33.792.8675turbidness (NTU)4.1842.6211.847.3762K (mg/l)1.4735.225.455.75106Zinc (mg/l)0.10.520.190.0947Iron (mg/l)0.096.090.480.69144DO (mg/l)1.917.305.402.45454.2 Results of input variable selection It is mentioned earlier that selection of allow input variables is one of the most crucial steps in the development of schmaltzy neural network models. The selection of high number of input variables may contain some irrelevant, redundant, and noisy variables might be included in the data set (Noori et al., 2010). However, on that point could be some meaningful variables which may provide important information. Therefore, reduction of input variables or selection of admit input variables is needed. There are so many IVS techniques available much(prenominal) as genetic algorithm, Akaike information criteria, partial mutual information, Gamma mental test (GT), factor analysis, principal component analysis, forward selection, backward selection, wholeness variable regression, part ostentation factor, Pearsons correlation and so on. In this research, five IVS techniques much(prenominal) as factor analysis, disagreement inflation factors, and hit(a) variable -ANN, item-by-item variable regression, and Pearsons correlation (PC) are utilized to reclaim break through appropriate input combinations. The explanation of five selected IVS techniques are explained wi th the respective input combinations.4.2.1. factor in Analysis cypher analysis is a order used to symbolise the mutation of a large dataset of inter correlated variables with a smaller set of independent variables. At the initial stage, the feasibility study was carried out for the input variables used in this study was done by KMO indicant and correlation parameter matrix. The data are suitable for factor analysis if KMO index is greater than 0.5 and correlation coefficient is higher than 0.3. According to turn off 4.1, the data are feasible for factor analysis as the KMO index of all data is plant as 0.720 (greater than 0.5) and a null hypothesis (p=0.000) indicates a significant correlation amid the variables. Moreover, from shelve 4.2, many of the correlation coefficient (Pearsons) between water quality parameters are greater than 0.3 which also confirms the feasibility of water quality parameters for factor analysis. Table 4.3 describes the eigenvalues for the factor analysis with percent variance and cumulative variance. To find out the number of efficient factor, factors with Eigen values 1.5 are considered for ANN model. The scree plot of Eigenvalues are illustrated in Figure 4.2. As find in Figure 4.1, the Eigen values are in descending rear and a drop after 2nd factor confirms the existence of at least two main factors.Table 4.2 Coefficient of KMO and Bartlett test resultsKaiser-Meyer-Olkin quantity of Sampling Adequacy0.720Bartletts Test of SphericityApprox. Chi-Square533.3Df.78.00Sig.0.000Normally, factors having steeper slope are good for analysis whereas factors with low slope have less clash on the analysis. The first two factors cover 64.607% of total variance (Table 4.4). The results of rotate factor loading apply Varimax method are tabulated in Table 4.5. The results indicated that the first factor is carbon dioxide, Alkalinity and K+, which are the most influential water quality parameter for Surma River. However, hardness, total solid (TS), Fe and total dissolved solid (TDS) are grouped in the second factor.Figure 4.1 astragal plot of eigenvalues of the Surma RiverTable 4.4 Individual eigenvalues and the cumulative variance of water quality observations in the Surma RiverFactorsEigen Values% sectionCumulative Variance %13.80029.22729.22721.83914.14743.37431.55311.94755.32141.2079.28664.60750.9977.66872.27560.8026.17278.44770.6454.96583.41280.6394.91488.32690.4423.40091.727100.3312.54894.275110.3042.34196.615Table 4.5 Rotated factors loading for water quality observations in the Surma River using a Vartimax method120.2411.85598.470130.1991.530100.000FactorNO3pH carbon dioxideAlk.Hard.TSBODTur.K+FeTDSPO4-301.070.173.791.876.238.273-.178.443.859-.038.079.17902.133-.22-.004.143.702.797.007.141.176.621.787.16503.789-.41-.050-.13.107-.25.152-.526-.010.114-.135.61304.156.737-.199-.057-.283.117.613.287-.079.416-.162.170Phosphate and process are grouped in factor 3 whereas pH, BOD, Fe are grouped in factor 4. In this research, the variables in the first, second, third and twenty-five percent factor are named as the M16, M17, M18 and M19 respectively. All the model names on with their respective variables are tabulated in Table 4.6.Table 4.6 results of factor analysis with their respective inputsModelInput VariablesFA Icarbonic acid gas+ Alkalinity + K+FA IIHardness + TS + Fe + TDSFA IIINO3+ PO4 -3FA IVpH + BOD4.2.2. Variance Inflation FactorThe variance inflation factor (VIF) is a method which measure the multi-collinearity in a regression analysis. In this study, variance inflation factors (VIF) were utilized to find appropriate inputs for the proposed model. The performances of VIF are tabulated in Table 4.7. It is found that, the VIF value is not that much satisfactory for all the variables. However, alkalinity, potassium, total solids and inorganic phosphate show quite a good result. To prepare some effective input combination for the ANN model, alkalinity was preferred for th e model first and all the variables were added one by one. Moreover, only alkalinity is individually not considered in the model as the SV-ANN shows a weak performance for alkalinity (Table 22222). Eleven input combinations were prepared based on the VIF value which is shown in Table 4.8.Table 4.7 Result of variance inflation factor for individual variablesInput CombinationVIFAlkalinity (mg/l)3.180K+ (mg/l)2.847TS (mg/l)2.628PO43- (mg/l)2.070CO2 (mg/l)2.036TDS (mg/l)1.997pH1.898Hardness (mg/l)1.820turbidness (NTU)1.696Fe (mg/l)1.290BOD (mg/l)1.177NO3 (mg/l)1.175Table 4.8 Results of variance inflation factor (VIF) with their respective inputsModelInput CombinationsVIF-IAlkalinity + K+VIF-IIAlkalinity + K+ TSVIF-IIIAlkalinity + K+ TS+ PO4-3VIF-IVAlkalinity + K+ TS+ PO4-3+ CO2VIF-VAlkalinity + K+ TS+ PO4-3+ CO2+TDSVIF-VIAlkalinity + K+ TS+ PO4-3+ CO2+TDS+ pHVIF-VIIAlkalinity + K+ TS+ PO4-3+ CO2+TDS+ pH+ HardVIF-VIIIAlkalinity + K+ TS+ PO4-3+ CO2+TDS+ pH+ Hard+ Tur.VIF-IXAlkalinity + K+ TS+ PO4-3+ CO2+TDS+ pH+ Hard + Tur. + FeVIF-XAlkalinity + K+ TS+ PO4-3+ CO2 +TDS+ pH+ Hard + Tur. + Fe + BODVIF-XIAlkalinity +K+TS+PO4-3+CO2+TDS+pH+Hard+Tur. +Fe + BOD + NO34.2.3. Pearsons correlation coefficientIt is not always true that all the variables should contribute to simulate the value of other parameters. Some variables can have a very good human relationship with other, some may have weak connection. Pearson correlation is an effective plectron to understand the relationship with one variable to another. While modelling DO value for the Surma River, it is important to select the variables to have positive relationship with one another. For this reason, a Pearson correlation was prepared which is tabulated in Table 4.3. It is found that there are 4 different types of data combinations which have positive and significant relationship with each other as tabulated in Table 4.9.Table 4.9 Input combinations using Pearson correlationModelInput CombinationsPC IAlkalinity + TD S+ PO4-3+CO2+K+PC IIpH + Hardness + TurbidityPC IIIAlkalinity + Hardness+ TS+CO2+K+PC IVHardness+ TS+ K+ TurbidityPC VHardness+ TS+ Fe +TDSPC VITS + Turbidity + Fe +TDS + K+4.2.4. SV-ANNThe performance of single variable artificial neural network was also done to find out appropriate input variables for the proposed model. All the individual variables are singly trained, tested and validated. During utilization of SV-ANN, only correlation coefficient (R) is considered to select the appropriate variables. The performances of SV-ANN are tabulated in Table 4.10 for testing, training and validation array. From the analysis, it is found that the individual variables show a weak performance. Only TS and BOD perform better study with other variables. The SV-ANN with TS shows a correlation coefficient of 0.596, 0.600 and 0.700 for testing, training, and validation phases respectively. Moreover, the respective correlation coefficient (R) for SV-ANN model with BOD are found as 0.578, 0.574 and 0.652 for testing, training and validation. However, turbidity, carbon di oxide, phosphate and nitrate have quite good relations with DO. As individual variables did not provide significant result, the variables are not considered in the ANN model individually. BOD and TS have quite wellTable 4.10 the correlation coefficient (R) for single variable ANN and single variable MLRVariablesPhaseSV-ANNSV-MLRRRPO43- (mg/l) test0.4390.115Training0.549 ecesis0.440NO3 (mg/l) testing0.2110.148Training0.311 brass0.112pHexamination0.2340.087Training0.201Validation0.432CO2 (mg/l) test0.3910.057Training0.453Validation0.514Alkalinity (mg/l)Testing0.2220.200Training0.211Validation0.099Hardness (mg/l)Testing0.1390.089Training0.649Validation0.155TS (mg/l)Testing0.5960.199Training0.600Validation0.700BOD (mg/l)Testing0.5780.100Training0.574Validation0.652Turbidity (NTU)Testing0.4310.183Training0.583Validation0.398K+ (mg/l)Testing0.1110.046Training0.543Validation0.219Fe (mg/l)Testing0.2170.002Training 0.210Validation0.306TDS (mg/l)Testing0.2220.084Training0.345Validation0.245relations with DO so they are grouped in one model (SV-ANN I) and turbidity, carbon di oxide, phosphate and nitrate are grouped in another one (SV-ANN II). The input variables utilizing SV-ANN is tabulated in Table 4.11.4.3.5. SV-MLRLike the performances of single variable ANN model, SV-MLR with all the input individual variables show weak performance. Moreover, variables comparable alkalinity, nitrates, total solid and turbidity show good result comparatively. The performances of SV-MLR are tabulated in Table 4.10. It is found that, alkalinity and TS show quite good results compare with other variables and hence they are grouped together (SV-MLR I). Another model (SV-MLR II) was prepared using all the variables with correlation coefficient more than 0.200. The input variables using SV-MLR model are tabulated in table 4.12.Table 4.11 results of single variable artificial neural network with their respective inputsModelInput VariablesSV-ANN-ITS + BODSV-ANN-IITS + BOD+ PO4-3+ CO2+TurbidityTable 4.12 results of single variable aggregate linear regression with their respective inputsModelInput VariablesSV- MLR IAlkalinity + TSSV-MLR IIAlkalinity + TS + Turbidity + NO3ModelIVS TypeInput VariablesM1PC IAlkalinity + TDS+ PO4-3+ CO2 +K+M2P