AIR POLLUTION – MONITORING MODELLING AND HEALTH

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272 Air Pollution <strong>–</strong> Monitoring, Modelling and Health Fig. 3. Sub-domains representation, in a two-dimensional projection (x,y), with different emission rates, and black points () represent the sensor position at 10 m height. In order to try some improvement for the inverse solution, the minimum value for the functional (22) is computed using the PSO scheme. This method is a stochastic technique and it deals with a population (candidate inverse solutions). Therefore, the numerical results represent the average from 25 seeds used by the PSO algorithm, working with 12 particles, with the following parameters: w = 0.2, c 1 = 0.1, and c 2 = 0.2. The total error obtained with the PSO was less than inverse solution computed from the quasi-Newton method. It is also important to point out that for the PSO approach no regularization operator was used ( = 0 in Eq. (22)). The inverse problem was also addressed by neural network. The MLP-NN was designed and trained to find the gas flux between the soil and the atmosphere. However, there are two previous steps before the application of MLP-NN. Firstly, it is necessary to determine the appropriated activation function, number of hidden layers for the NN, and the number of neurons for each layer. Secondly, the values of the connection weights (learning process) must be identified. The hyperbolic tangent was used as activation function. Different topologies for MLP-NN were tested with 6 inputs (measured points for 6 different sensors) and 12 outputs (emission for each subdomain). Good results were achieved for two neural networks with 2 hidden layers: NN-1 with 6 and 12 (6:6:12:12), and NN-2 with 15 and 30 (6:15:30:12) neurons for the hidden layers, respectively.
Strategies for Estimation of Gas Mass Flux Rate Between Surface and the Atmosphere 273 Table 3 shows the numerical values computed for the emission rate for each marked cell. Good results were obtained for all methodologies. The cells 12 and 14 had a worst estimation using optimization solution. Inversions with MLP-NN were better, in particular for the emission of the cells 12 and 14. Figures 4 and 5 show the emission estimation for the experiment-1 (5% of noise level) and experiment-2 (10% of noise level), only results obtained with NN-2 (6:15:30:12) are shown (the best results with MLP-NN). Sub-domain Exact Q-N PSO MLP-NN-1 MLP-NN-2 A 2 10 8.97 9.83 10.33 10.11 A 3 10 9.97 10.40 10.11 10.11 A 4 10 12.53 10.79 10.12 10.20 A 7 10 7.99 10.50 10.27 10.20 A 8 10 10.15 12.06 10.24 10.06 A 9 10 11.56 11.28 10.21 10.17 A 12 20 13.85 14.56 21.28 20.97 A 13 20 22.65 22.67 21.32 21.00 A 14 20 14.14 15.85 21.47 20.95 A 17 20 19.99 21.56 21.47 20.99 A 18 20 21.17 20.05 21.38 20.99 A 19 20 24.90 21.74 20.96 20.96 Table 3. Estimation of gas flux emission by the methodologies: quasi-Newton (Q-N), PSO, MLP-NN-1 (6:6:12:12) MLP-NN-2 (6:15:30:12). (a)
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AIR POLLUTION - MONITORING, MODELLI
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Contents Preface IX Chapter 1 Urban
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Preface This book provides a compre
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AIR POLLUTION – MONITORING MODELLING AND HEALTH

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