CHAPTER 8 ARTIFICIAL NEURAL NETWORKS

Transcription

1 247 CHAPTER 8 ARTIFICIAL NEURAL NETWORKS 8.1 GENERAL Artificial neural networks are biologically inspired and they are composed of elements that perform in a manner that is analogous to the most elementary functions of the biological neuron. These elements are then organized in a way that they may be related to the anatomy of the human brain. Despite this superficial resemblance, artificial neural networks exhibit a surprising number of the brain s characteristics. For example, they learn from experience, generalize from previous examples to new ones and abstract essential characteristics from inputs containing irrelevant data. Each neuron collects inputs from multiple sources and produces an output after the weighted combined inputs are processed by an activation function. Once a network is trained, it can be used to predict the output for given set of input values. Neural Networks are especially powerful for identifying patterns, trends and internal relationships. The typical biological neorn is shown in Figure 8.1. Figure 8.1 A sketch of a biological neuron (Fausett 1994)

2 248 The neuron has three major components as shown in Figure The dendrites (constituting a vastly multi-branching tree-like structure which collects inputs from other cells). 2. The cell body (the processing part, called the soma). 3. The axon (which carries electrical pulses to other cells) Biological neurons and ANN The concepts of biological neurons and human brain system can be explained with the following points and it can be represented diagrammatically as shown in Figure The inputs are the activity of collecting data from the relevant sources. 2. The weights control the effects of inputs on the neuron. In other words, an ANN saves its information over its links and each link is considered as a weight. These weights are constantly varied while trying to optimize the relation between input and output. 3. Summation function is to calculate net input readings from the processing elements. 4. Transfer (activation) function determines the output of the neuron by accepting the net input provided by the summation function. Depending on the nature of the problem, the determination of transfer and the summation functions are made.

3 249 Figure 8.2 Artificial representation of biological neuron Transfer function generally consists of algebraic equations of linear or nonlinear form. A commonly used function is sigmoid function, because it is self-limiting and has a simple derivative. Outputs accept the results of the transfer function and present them to the relevant processing element. An ANN may be regarded as a directed graph containing summation function, transfer function, its structure and the learning rule used in it. The processing elements have links in between them forming a layer of networks. Neural networks consist of three layers. They are input layer, hidden layer and output layer. The net input to a node i in layer k+1 is n i k+1 = (j=1) w ij k+1 o j k + b j k+1 The out put of node i will be, O i k+1 = f k+1 + (n i k+1 ) Where f is the activation function, For a sigmoid activation function O i = 1 / (1 + e (neti+ i)/ 0 ).

4 NEED FOR ANN MODEL Artificial Neural Network (ANN) model has been extensively used in groundwater quality modeling for predicting the groundwater chemical and physical parameters. Groundwater quality can be affected by composition and solubility of rock materials in the soil or aquifer, water temperature, partial pressure of carbon dioxide, acid-base reactions, oxidation-reduction reactions, loss or gain of constituents as water percolates through clay layers and mixing of ground water from adjacent strata. The extent of each effect will vary with respect to the residence time of the water within the different environments. In general, the groundwater quality is the function of solubility of rocks and resident time of water within the subsurface. And the solubility of rocks depends on the type of rock and the quantity of percolating water. The groundwater quality is also deteriorated by surface influences. But the dominant mechanism controlling the groundwater chemistry of the study area is the rock interaction with the groundwater. TDS is a hydro chemical parameter which represents the wholesome quality of groundwater. Hence, the prediction of amount of TDS content will assist to assess the water quality of any locality. The nature of various surface and subsurface factors of a locality may provide necessary information to predict TDS content at that locality. Since, the formulation of mathematical relation between surface and subsurface parameters are non-linear and very tedious, the use of any high level software working on the concept of artificial intelligence may be an apt approach at this moment. The software ANN is selected and attempted in this work to predict the quantum of TDS from geological and meteorological parameters.

5 DEVELOPMENT OF ANN MODEL TDS has been considered as the output after processing various input variables. The various factors considered here as input/ independent variable are listed below. They are, 1. Conductivity of top soil 2. Depth of top soil 3. Geomorphologic type 4. Depth of each layer of sub stratum 5. Conductivity of each layer of sub stratum 6. Land cover 7. Rainfall 8. Water level The values of input variables or inputs are found out from thematic maps, processed satellite imagery and hydro metereologic data of a selected location. The accuracy of the input data is very important as the neural network processes are very sensitive Index assigned to the parameters The mathematical relation for any physical or chemical phenomenon requires coefficients and algebraic relations of physical or chemical parameters. But the neural network functions based on the concept of pattern or type recognition. Hence, various indices are assigned to the governing parameters of TDS to feed as inputs. The indices assigned here are numerical identities to facilitate the software ANN to process different string parameters. The different units in each theme are assigned a knowledge-based hierarchy of ranking from 1 to 10. These are assigned on the basis of their significance with reference to their influence on rainfall infiltration. The various indices assigned to the conductivity of the substratum layers and land covers are summarized in Table 8.1.

6 252 Table 8.1 Indices assigned to the parameters Parameters Types Index assigned Black soil 1 Top Soil Brown soil 2 Red soil 3 Alluvial soil 4 Geomorphology Plateau 1 Composite slope 2 Shallow pediment 3 Bazada zone 4 Flood plain 5 Lithology Jointed granite gneiss 1 Weathered granite gneiss 2 Fresh charnockite 3 Weathered charnockite 4 Weathered pyroxenite 5 Fresh gneiss 6 Jointed gneiss 7 Weathered gneiss 8 Land cover Builtup Land 1 Barren Rocky 2 Fallow land 3 Land without Scrub 4 Land With Scrub 5 Forest Blank 6 Crop Land 7 Open Forest 8 Dence Forest 9 Water Bodies 10

7 Network architecture In the ANN model, NF tool has been chosen due to its high accuracy in similar function approximation which contains large number of input data set. Neural networks consist of three layers. They are input layer, hidden layer and output layer. In this work, 60 hidden neurons have been assigned to train the model. The train ratio assigned is 90%. Both the validity and test ratio are assigned 5 %. The final network structure is chosen after the observation of regression terms and mean square error terms. The procedures followed to train the network and to optimize the network size are explained in Appendix I. Figure 8.3 shows the structure of ANN model developed to predict the value of TDS. Figure 8.3 Structure of ANN model for the prediction of TDS

8 PERFORMANCE OF ANN MODEL The ANN models have been developed for both pre-monsoon and postmonsoon seasons. The various steps followed in developing the model are illustrated here. The software MATLAB R2009b version is used here to develop ANN model. The software is user friendly and it has many applications Input The surface and sub-surface parameters are given as input. The noicy data are removed. The final input data set is a 12 x 59 matrix. It contains 12 parameters from 59 sample locations. The input contains thickness of top four layers with its respective hydraulic conductivity, land cover, geomorphology, annual rain fall and water table. The input values of any location in the study area can be arrived using the software ArcView3.2a. The land cover details of any location can be arrived from satellite images. A new M-file is created for the input data and it is saved with txt extension. Each column of the input matrix represents hydrogeological data of each sample location Targeted output The TDS values of 59 locations which are found out from water quality analysis is present in a matrix of 1 x 59 size and saved in a new M-file with txt extension. This new M-file is the targeted output and the ANN model has to be trained to obtain this targeted output. The validity of the model is justified by comparing the TDS values of the water quality results of the respective locations and the results of the targeted output. These two values should be equal or the difference between these two values should be very less.

9 Neural fitting tool Neural fitting tool (NFT) solves an input output fitting problem with a two layer feed forward neural network. In fitting problems, neural network maps between dataset of numeric input and data set of numeric targets. NFT evaluates the performance of neural networks using mean square error and regression analysis. A two layer feed forward network with sigmoid hidden neurons and linear output neurons (new fit) can fit multi-dimensional mapping problems well with given consistent data and enough neurons in its hidden layers. The network will be trained with Levenberg-Marquardt back propagation algorithm (trainlm) if enough memory is available or else scaled conjugate gradient back propagation (trainscg) will be used Selection of data The input and targeted output defining the problem are selected here to feed in to the program. The input and targeted output M-files are selected from workspace and loaded onto the program by clicking at the input and target boxes Validation and test data The allocation of some of the samples for training, validation and testing is carried out now in percentage. In this work 90 % is assigned for training, 5% is assigned for validation and 5 % is assigned for testing. Training will be adjusted within the percentage assigned for training. Validation is used to measure network generalization and training will be halted if generalization stops improving. Testing provides an independent measure of network performance during and after training.

10 Network size The network size is fixed here by selecting number of neurons for the hidden layer of the network. In this work 60 numbers of hidden neurons are selected and the value is entered in the box provided. If the network does not perform well, the training has to be repeated from this step by changing the number of neurons. This is to be repeated until required performance is achieved. In this work 12 number of inputs in each sample, 60 numbers of hidden layers, 1 number of output layers and 1 number of output data are assigned to define the network size Train network Training of network to fit the input and targets is carried out. Training has been done in trainlm back propagation. Training automatically stops when generalization stops improving. This is indicated by increase in mean squared error (MSE). MSE is the average squared difference between input and targets. Lower values of MSE are better. Zero means no error. R values measure the correlation between output and targets. R value of 1 means, there is closer relationship between NFT output and targeted output. The training has been done with 90% of the samples. MSE value is 3.38e-24 and R value is 9.999e-1. This shows training has given the best performance by providing a very low MSE and R value equal to 1. The training has been carried out with many trails by altering the number of neurons. The best result was found in the last trial. The training was generalized with 15 epochs.from this, the number of iteration, time taken for the convergence, performance status, validation checks, gradients etc., are found out. The iteration has started attaining very low MSE at epoch 7 and it has attained a lowest MSE value at epoch 15. The performance plot is presented in Figure 8.4.

11 257 Figure 8.4 Perfomance plot of the training network Figure 8.5 Training status of the network

12 258 The regression value R gives measure or relationship between training output and targeted output. The R value is 0.74 in early iterations then it reached 0.86 and At the end of 15 epochs, the R value has maximum of 1. This shows the presence of high correlation between output and targeted output. The various R values at various iterations are shown in Figure 8.6. Figure 8.6 Regression plot of the training network The results of the training of neural network are satisfactory and the results are saved. In order to apply the trained network to meet its purpose, simulink diagrams are formed to give different input and to get respective output. The display option is preferred to display the TDS value as output. Simulink library browser option of the network is chosen to formulate required simulink diagram. The simulink is saved as mdl file of MATLAB. The various inputs are given in constant value box of the source block parameter window. The input values are saved and the program is run. The output value is shown in the display box of the simulink window.

13 VALIDATION OF ANN MODELS The validity of the model is checked with the groundwater quality test results of TWAD Board, Chennai for Namakkal district. A bore holes whose groundwater quality is tested by TWAD board has been selected. The latitude and longitude of this bore holes is noticed. The surface and subsurface data of this borehole required for ANN model are arrived using interpolation option of the software ArcView. The inputs are fed in ANN model. TDS content of this borehole is determined from ANN model. The TDS content of this borehole from TWAD board result is compared with the output from the ANN model. The percentage of variance is noted. This procedure is repeated for some other boreholes also. The validity of the model is judged with water quality results of TWAD Board and ANN output. In order to study the practical feasibility in the application of the model, the water samples from 5 locations have been collected and they are tested for water quality parameters. The details of the sample locations are summarized in Table 8.2. The TDS content at these locations are found out from ANN model and the TDS contents at these locations are found out from water quality tests. The results are compared to find out the practical feasibility in the application of the model developed. Table 8.2 Details of samples collected for validation S.No Date Name of the sample locations Longitude Lattitude Well type 1 15/01/2011 Rasipuram Bore well 2 15/01/2011 Thoppapatty Bore well 3 15/01/2011 Muthugapatty Bore well 4 15/01/2011 Erumaipatty Bore well 5 15/01/2011 Namakkal Anna Nagar Bore well

14 SUMMARY AND APPLICATIONS OF ANN The time and cost involved in exploring the groundwater quality of a new location is usually high. At the same time, formulating an expression to findout the value of TDS content before collecting the water sample before excavating the well is very difficult. It is very tough due to high non linearity nature of the governing parameters.hence a method with an artificial intelligence to find out the value of TDS from these non linear and naturally drastic governing parameters is proposed in this work. For this, Artificial neural network is found apt based on its working principles. The method of using ANN program is as follows. A location is selected from the base map of the study area. The depth of each layer of substratum, the rainfall of the location, the water table at the locality are found out using surface contour options of ArcView 3.2a. The conductivity of the different layers and the land cover identities are fed into the program by the indices assigned. The type of soil and geomorphology of the selected location are found out from digitized soil and geomorphology maps. Thus arrived values of the input are fed to the ANN model developed. The value of TDS in mg/l is arrived as a single value out put. The validity of the model is checked with the groundwater quality test results of TWAD Board, Chennai for Namakkal district. 19 bore wells have been selected at random and the values of input are attributed for the bore well locations using ArcView. The validation with TWAD results is presented here for the ANN model developed for premonsoon season. And the TDS content at the bore well locations are found out using ANN model. The TDS content in the groundwater of selected bore wells from TWAD results are compared with ANN results. The validation results are summarized in Table 8.3. The practical feasibility of the application of ANN model is checked with the feasibility test results. Since the feasibility test samples are collected during postmonsoon season, the ANN model developed for postmonsoon season is used to validate the results. The validation results are summarized in Table 8.4.

15 Table 8.3 Validation of ANN results with TWAD results S.No TWAD Bore ID Date Longitude Lattitude Location of TWAD Bore Depth of top soil (m) Top soil type Geo-mor type * Depth of I layer (m) /7/ Singalandapuram HP1S16 9/7/ Aniapuram HP1S18 9/7/ Erumaipatti HP1S20 9/7/ Pattathayankuttai /7/ Thalambadi /7/ Ernapuram A 10/7/ Palapatty /7/ Velur HP1S15 10/7/ Nallipalayam HP2S12 10/7/ Ramadevam HP2S13 10/7/ Kilmugam /7/ Pudupatti /7/ Pallavanaickan pattimettur /7/ Pillanallur /7/ Ayeepalayam /7/ Sowdapuram /7/ Vennandur HP1S13 16/7/ Puduchatram HP1S14 16/7/ Elur *- Geomorphology type **- Hydraulic conductivity of I layer ***- Hydraulic conductivity of II layer ****- Hydraulic conductivity of III layer K1 ** Depth of II layer (m) K2 *** Depth of III layer (m) K3 **** Rainfall Land Cover Water Level (m) TDS from ANN Result TDS from TWAD Result % of Variations 261

16 Table 8.4 Validation of ANN model results with field test sample results S.No Date Longitude Lattitude Name of the bore location Depth of top soil (m) Top soil type Geo-mor type * Depth of I layer (m) K1 ** Depth of II layer (m) K2 *** Depth of III layer (m) K3 **** Rainfall Land Cover Water Level (m) TDS from ANN result TDS from test result % of Variations 1 15/01/ Rasipuram /01/ Thoppapatty /01/ Muthugapatty /01/ Erumaipatty /01/ Namakkal anna nagar *- Geomorphology type **- Hydraulic conductivity of I layer ***- Hydraulic conductivity of II layer ****- Hydraulic conductivity of III layer

17 263 The results of ANN model produce a maximum positive variation of 15.8% and a minimum variation of % from TWAD results. The positive and negative variations give rise to an average variation of -1.3 %. 13 results consist of negative variations and the remaining 6 results consist of positive variations. The results of ANN model produce a maximum positive variation of 1.5 % and a minimum variation of % with field test results. The positive and negative variations give rise to an average variation of 0.26 %. Hence, it can be said that the result from ANN model is fit for the determination TDS from hydrogeological data at any location during premonsoon and postmonsoon seasons.