Academia Journal of Scientific Research 3(12): 184-191, December 2015 DOI: 10.15413/ajsr.2015.0148 ISSN 2315-7712 ©2015 Academia Publishing

Research Paper

Prediction of ventilation coefficient, using a conjunction model of wavelet-Neuro-fuzzy Model: A Case Study Delhi, India

Accepted 9th November, 2015 ABSTRACT Air pollution in big cities has been a severe environmental problem all over the world. Major countries started air quality management systems to monitor and control pollution rates in their cities. It was observed that hazardous emission into the air is a sign of environmental force that affects directly health of the nation, agriculture andclimate change; consequently leading to major loss on the nation’s economy. The main aim of this work is to introduce and develop a conjunction model of Wavelet-Neuro-fuzzy model foraccurate prediction of the ventilation coefficient over the capital region of Delhi. A data set collected over six-year period (2008-2013) by SODAR (Sound Detection And Ranging) were used as input to the model. A low level of error prediction confirmed the fact that the developed models are an effective instrument of the air quality management in big cities. Experimental results show that a conjunction model of Wavelet-Neuro-fuzzy model provides good modeling results. Key words: Artificial Neural Network (ANN) Air pollution, Economic Development

INTRODUCTION Emerging and the established countries allover the world are characterized by their economic development and vastpopulation, resulting in increased human activity that, in turn, can lead to high pollution levels. Subsequently, the air quality in these cities is rigorously affected. The product of mixing depth and the average wind speed is called ventilation coefficient, it is an atmospheric condition which gives an indication of the air quality and pollution potential, i.e., the capability of the atmosphere to dilute and disperse the pollutants over aarea. The higher value of the ventilation coefficient, the more efficiently the atmosphere is able to dispose the pollutants and thus the air is better quality. In contrast, lower value of ventilation coefficients lead to poor dispersal of pollutants causing stagnation and poor air quality leading to possible pollution related hazards. The ventilation coefficient is directly related to the mixing depth and the average wind speed through the mixing layer (Iyer et al., 2013). A variation in the values of the mixing depth and the average wind speed causes a

change in the ventilation coefficient. These processes need to be modelled by making use of events that happened in the past to predict.

There are many different methods of mathematical modelling, which have been developed to forecast long-term precipitation. In these methods, a statistical approach, such as time series modelling, is a conventional method that has been widely used. Statistical modelling has many advantages over mathematical models. But the shortcomings of the statistical approach include handling nonlinear characteristics of data because the statistical models are usually based on the linear correlations of the data can be expressed with a correlation coefficient. To overcome the shortcomings of the statistical methods, other models that address the nonlinearity includes artificial neural network (ANN), fuzzy inference system (FIS), wavelets etc. ANN is a pattern matching technique that uses a pair of input and output sets. ANN has been generally applied to forecast stream flow, precipitation, and drought.

Nishant Kumar1, Kulwinder Singh Parmar2, Kirti Soni3*, Naveen Garg3 and Ravinder Agarwal1 1Thapar University, Patiala (Punjab) 2Dr. B. R. Ambedkar, National Institute of Technology, Jalandhar, Punjab 3CSIR-National Physical Laboratory, Delhi, India. *Correspondence author. E-mail: 2006.kirti@gmail.com.

Academia Journal of Scientific Research; Kumar et al. 185 FIS is data-driven model similar to ANN for representing linguistic fuzzy if-then rules that are difficult to formulate through a model with crisp parameters. In Fuzzy logic data was divided into training and testing phases. The model results were compared with measured data. The comparison depends on statistical characteristics, different error modes and contour map method. Hence the fuzzy model provides more accurate and reliable results. Wavelet analysis is used for good times and frequency multi resolution and it can diagnose signal main frequency component, with local information of the time series. Wavelet transforms provide useful decompositions of the original time series, wavelet-transformed data improve the ability of forecasting model by capturing useful information on various resolution levels (Naurani et al. 2011). Wavelet analysis is an effective tool than the Fourier transform in analyzing non-stationary time series. Several studies have been performed using wavelet transform to analyze time series.

Artificial neural networks have become anextensively used tool in numerous air pollution and meteorological applications. Yi and Prybutok (1996) reported MPNN for surface ozone predictions, along with Comrie (1997). A number ofpredictive models were also prepared for other pollutants such as for Carbon Mono –oxide (CO) (Moseholm et al., 1996) and for Sulfurdioxide (SO2) (Božnar et al. 1993). Marzban and Stumpf (1996) applied MPNN for predicting the existence of tornadoes.

The present study aims to introduce and develop a reliable model for predication the ventilation coefficient, which is the product of mixing depth and the average wind speed, over Delhi for the period(2008 to 2013) period. In this present study, a conjunction model of Wavelet-Neuro-Fuzzy is introduced for predication the ventilation coefficient of Delhi.

Data and observation site

Daily average SODAR (Sonic Detection And Ranging) data for about 6 years (2008-2013) for the Capital of India, Delhi (28.38°N, 77.12°E) are analyzed to derive the mixing layer height (MLH) and then compute ventilation coefficients. Mixing layer height (MLH) has been measured using CSIR-National Physical Laboratory (NPL) designed, developed and fabricated monostatic SODAR system. The SODAR was operated at a frequency of 2.25 kHz with 50-350 ms (selectable) pulse duration, a cycle time of (2-20) s (selectable) and electrical transmitting power of 50 W, acoustic power 10 W. The antenna was a parabolic dish 1.22 m in diameter and the beam width was 15◦. Highly directional short bursts of sound energy are radiated into the atmosphere, which, after scattering from atmospheric fluctuations of eddy sizes within the inertial sub range (0.1–10 m), are received back by the receiving antenna. The signals are processed to produce an online facsimile

display of the dynamics of MLH thermal structures.

On the basis of a Holzworth model using radiosonde data for Delhi (Singal et al., 1984, 1994, 1997, Operation manual 2008) the mixing height was obtained by using the following empirical relation.

y= 4.24*x+95 (1)

where, y is the mixing height (m) for unstable atmospheric boundary layer, x is the depth of the SODAR measured thermal plumes (m).

Other details of the technique and instrument are defined elsewhere (Singal et al. 1985, 1994, Asimakopoulos et al. 1992 Roy et al., 2011, Gera et al., 2013a, 2013b).The data on wind speed (WS) were downloaded from the website of weather underground (http://www.wunderground.com/).

The VC is obtained as the product of the average WS and the MLH. The ventilation coefficient (VC) is then computed as:

VC = [mixing height(m) × mean wind speed(m/s)] (2)

The daily mean value of ventilation coefficient calculated at New Delhi for the last six years from 2008 to 2013have been considered in the present study. Out of 650 data sets from 2008 to 2013, 497 have been used to train the model for ventilation coefficient and 150 data sets have been used for the test model. First three data points are used as the input values. METHODOLOGY

Artificial Neural Network (ANN)

Artificial Neural Network (ANN) is commanding non-linear modelling approach. Which is based upon human brain functioning. It identifies and learns the correlated patterns between inputs values and objective values. It networks with nodes or neurons, which are interconnected to each other. A general three-layered neural network, consists of several elements nodes. These systems hold an input layer comprising of hubs speaking to diverse input variables, the hidden layer comprising of numerous concealed hubs and an output layer comprising of output variables.

A three layered FFNN (feed forward neural network) based on backpropagation has been selected. There are three input nodes, three hidden nodes with tan sigmoid transfer function and one output node with the linear transfer function. So for predicting the output, past three inputs have to be estimated. The momentum and learning rate has kept to 0.9 and 0.1 and it trained for 1000 epochs.

Wavelet transform

Wavelet could be described as a pulse of short time with

Academia Journal of Scientific Research; Kumar et al. 186 finite energy that integrates to zero. Wavelets are situated both in time and space. The first step of wavelet transforms corresponds to mapping signal f to its wavelet coefficients. By means of this procedure two components are received, i.e.a smooth version named approximation and other component that corresponds to the deviations or the information of the signal (Parmar et al., 2013). A decomposition of the signal f into a low frequency part a1and a high frequency part d1at level 1 represented by

f=a1 + d1.

Similarity the same procedure is performed on a1 in order to obtain a decomposition in the finer scales:

a1 = a2 + d2.

Recursive decomposition for the low frequency components follows the directions. Adaptive network based fuzzy inference systems (ANFIS)

The adaptive Neuro-fuzzy interface system (ANFIS) procedure is used internationally, as an estimator (Figure 1). It is able to estimate real continuous function on a compact set to a degree of accuracy. (Jin et al., 2013). Rules. The if-then rules have to be determined somehow. This is generallycompleted by ‘knowledge acquisition’ from an expert. This is a time consuming procedure that is fraught with problems. Membership functions. A fuzzy set is completely determined by its membership function. This has to be estimated. If it’s Gaussian, then what are the parameters? The ANFIS methodology learns the rules and membership functions from the dataset.ANFIS is an adaptive network. An adaptive network is a network of nodes and directional links. Associated with the network is a learning rule –e.g. back propagation. It’s titled adaptive as some, or all, of the nodes have factors which disturb the output of the node. These networks are learning aassociationamong inputs and outputs.

Adaptive networks cover a number of different approaches, though, for our purposes, we will observe in some detail the techniquesuggested by Jang documented as ANFIS. The ANFIS architecture is given below. The circular nodes represent nodes that are fixed, but the square nodes are nodes that have factors to be learnt.

A Two Rule Sugeno ANFIS has rules of the form:

111111ryqxpfTHENBisyandAisxIf

222222ryqxpfTHENBisyandAisxIf

For the training of the network, there is a forward pass and a backward pass. We now look at anisolated layer in turn for the forward pass. The forward pass propagates the input vector through the network, layer by layer. In the backward pass, the error is sent back through the network in aanalogousway to backpropagation. Layer 1

The output of each node is:

2,1)(,1

iforxOi

Ai

4,3)(2

,1

iforyOi

Bi

Thus, the )(,1

xOi

is basically the membership grade for

x and y .

The membership functions could be anything however, for illustration purposes, we will use the bell shaped function represented by:

i

b

i

i

A

a

cx

x2

1

1)(

whereiii

cba ,, are parameters to be learnt. These are the

principle parameters.

Layer 2

Each node in this layer is fixed. This is where the t-norm is used to ‘AND’ the membership grades –e.g., the product:

2,1),()(,2

iyxwOii

BAii

Layer 3

Layer 3 comprisesfixesnodes, whichcomputes the ratio of the firing strengths of the rules:

21

,3

ww

wwO

iii

Layer 4 The nodes in this layer are adaptive and complete the subsequent of the rules:

)(,4 iiiiiii

ryqxpwfwO

The factors in this layer (iii

rqp ,, ) are to be determined

and are stated to as the consequent parameters

Academia Journal of Scientific Research; Kumar et al. 187

Table 1.Statistical information of ventilation coefficient of New Delhi.

Data No. of Sample Mean Standard Deviation Variance Maximum Minimum Median Skewness Kurtosis Whole 650 1120 745 556645 5455 115 940 1.48 3.21 Training 500 1010 640 409425 3660 115 860 1.13 1.31 Testing 150 1480 935 875365 5455 160 1265 1.38 2.20

Layer 5 There is a single node at this time that calculates the overall output:

i i

i ii

i

i

ii

w

fwfwO

,5

This then is how, typically, the input vector is fed through the network layer by layer. Now we study how the ANFIS learns the premise and consequent factors for the membership functions and the rules.

There are a number of possible methods, but we will discuss the hybrid learning algorithm reported by Jang, Sun and Mizutani (Neuro-Fuzzy and Soft Computing, Prentice Hall, 1997) which uses a mixture of Least Squares Estimation (LSE) and Steepest Descent. This can get very complicated (!) so here I will provide a very high level description of how the algorithm operates.

It can be shown that for the network defined if the premise components are fixed the output is linear in the consequent parameters.

We divide the total parameter set into three:

S = set of total parameters

1S = set of premise (nonlinear) parameters

2S = set of consequent (linear) parameters

Therefore, ANFIS uses a two pass learning algorithm:

Forward Pass. Here 1

S is unmodified and 2

S is

computed using a LSE algorithm.

Backward Pass. Here 2

S is unmodified and 1

S is

computed using a gradient descent algorithm such as back propagation. Thus, the hybrid learning algorithm uses a combination of steepest descent and least squares to adapt the parameters in the adaptive network. RESULTS AND DISCUSSION

Statistical overview Statistical properties are presented in Table 1. The

minimum value (115) and maximum value (5455) shows that the ventilation coefficient variation has a long range. It can be seen that the time series show high randomness and scattered distribution about the mean as the standard deviation (745) and variance are high. The training data considers the minimum and maximum inputs of data. This implies the trained neural network is not facing any difficulties in extrapolation. Neuro-fuzzy-wavelet coupled model Using MATLAB, 2009 software, programs are developed for wavelet-Neuro-fuzzy, Neuro-fuzzy, artificial neural network modeling. Before performing wavelet decomposition, three issues need to be resolved that are selection of mother wavelet, order of mother wavelet and the number of level decomposition. Attributes of the mother wavelet and the characteristics of the signal should be considered carefully, while choosing the appropriate wavelet. Daubechies are the most appropriate for treating random and spikes series. For these families of wavelet, the smoothness increases as the order of function increases and suitable wavelet and hence suitable higher order wavelet must be taken into account. In this work, wavelet of order 2 to 8 has been considered and it was observed that the decomposed series by wavelet of order 8 are giving the best results (Figure 2 and 3).

Figure 4, 5 and 6 shows the signal approximation, A3 and detailed parts D1 to D3. Approximation curves correspond to low frequency bands and represent the trends of the ventilation coefficient. Skewness is a measure of the symmetry of the data around the data mean and is zero for an ideal normal curve. Kurtosis refers to the degree of flatness.

Experimental results

The numerical experiments of predicting the future level of ventilation coefficient have been performed. The instrumental record data for training and testing have been collected from 2008 to 2013. 500 data points have been used for learning and the other part of 150 data points for testing only. The results of learning and testing have been assessed on the basis of mean absolute error (MAE) and the predicted value. The observed and predicted TSP values in both training and testing cases is shown in Figures 7 and 8. In Table 1, we show the performance results obtained based the Neuro-Fuzzy-Wavelet model.

The mean absolute value is

Academia Journal of Scientific Research; Kumar et al. 188

L a y e r 1 L a y e r 2 L a y e r 3 L a y e r 4 L a y e r 5

1w 1

w 11fw

X

F

Y 2w 2

w 22fw

A 1

A 2

B 1

B 2

Figure 1. An ANFIS architecture for a two rule Sugeno system.

Figure 2. Detailed and approximation coefficient using Daubechics (Db8) wavelet.

Figure 3. A3aactual and trained results and model output with surface view.

Academia Journal of Scientific Research; Kumar et al. 189

Figure 4. D1 actual and trained results and model output with surface view

Figure 5. D2 actual and trained results and model output with surface view.

Figure 6. D3 actual and trained results and model output with surface view.

Academia Journal of Scientific Research; Kumar et al. 190

Figure 7. Actual output and predicated time series of average ventilation coefficient of training data using Neuro-Fuzzy-Wavelet.

Figure 8. Actual output and predicated time series of average ventilation coefficient of testing data using Neuro-Fuzzy-Wavelet

Academia Journal of Scientific Research; Kumar et al. 191

𝑀𝐴𝐸 =1

𝑁 𝑑𝑖 − 𝑦𝑖

𝑁

𝑖=1

Where d denote the actual measurement, y is the predicted value and N is the number of days under predicted.

The relative error

∈= 𝑑 − 𝑦

𝑑

The Neuro- fuzzy- wavelet predictive model has been developed and tested. The trained predicted output is obtained from the decomposed wavelet coefficients by simple summation represented by S(n)= D1+D2+D3+A3

Training and tested results by Neuro-fuzzy-wavelet to predict 150 days ahead ventilation coefficient of New Delhi using Db8 wavelet as follows: Training data: Mean Absolute Error MAE1= 0.0058 Relative error ∈1 = 5.8792 Testing data: Mean Absolute Error MAE2= 0.0312 Relative error ∈2 =7.1881 Conclusion In this paper, a conjunction model of Wavelet-Neuro-fuzzymodelshave been introduced and developed for prediction of the ventilation coefficient over the capital region Delhi. The results of the prediction modelling were very satisfactory as Wavelet-Neuro-fuzzy model has mean absolute error only 0.0058 in testing series and 0.0312 in training series. A low level of error prediction confirmed the fact that the developed modelis an effective tool of the air quality management in metro cities. This new Wavelet- Neuro-Fuzzy model can help the nations in the atmospheric management. REFERENCE Asimakopoulos D, Deligiorgi D, Drakopoulos C, Helmis C, Kokkori K, Lalas

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Cite this article as: Kumar N, Parmar KS, Soni K, Garg N, Agarwal R (2015). Prediction of ventilation coefficient, using a conjunction model of wavelet-Neuro-fuzzy Model: A Case Study Delhi, India. Acad. J. Sci. Res. 3(12): 184-191. Submit your manuscript at http://www.academiapublishing.org/ajsr