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Wind Speed Data Analysis for Various Seasons during a Decade by Wavelet and S transform

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The prediction of Weather forecasting can be done with the Wind Speed data. In this current paper the concept of using Wavelet and S-transform together for the analysis purpose of Wind data is introduced first time ever. In winter due to low convection process the agitation between wind particles is less. So, the Haar Wavelet is used to detect the discontinuity in the less agitated wind data samples of Winter. But due to abrupt changes in wind data in summer, it is difficult to track the data. So, in that case the concept of the Stransform is introduced.

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International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 DOI:10.5121/ijfcst.2013.3404 31 Wind Speed Data Analysis for Various Seasons during a Decade by Wavelet and S transform Sabyasachi Mukhopadhyay1 , Prasanta K Panigrahi1 1 Department of Physical Sciences, IISER, Kolkata ABSTRACT The prediction of Weather forecasting can be done with the Wind Speed data. In this current paper the concept of using Wavelet and S-transform together for the analysis purpose of Wind data is introduced first time ever. In winter due to low convection process the agitation between wind particles is less. So, the Haar Wavelet is used to detect the discontinuity in the less agitated wind data samples of Winter. But due to abrupt changes in wind data in summer, it is difficult to track the data. So, in that case the concept of the S- transform is introduced. KEYWORDS Continuous Wavelet Transform, S-transform, Wind Speed. 1. Introduction The present paper is focused on time-frequency analysis of wind speed data. Currently wind energy is a hot topic as it is one of the important non-conventional energies. We know that Weibull distribution is a very popular tool for wind energy purpose [2, 5]. The usefulness of signal processing tools are increasing in case of wind engineering purpose. For low wind speed analysis purpose use of discrete Hilbert transform (DHT) along with weibull distribution is shown in ref [2]. The discrete Hilbert Transform (DHT) can be used as minimum phase type filter for characterizing and forecasting purpose of Wind speed data is showed by Mukhopadhyay et al., [4]. Mukhopadhyay et al., also showed the optimized DHT and RBF neural network basis analysis for Wind power forecasting purpose [3]. The utility of Wavelet in weather related application was already shown by Panigrahi et al., [1]. The application of wavelet transform in the field of Ocean technology was shown by Liu et al., [8]. In 2005, the wavelet transform was used for wind data simulation of Saudi Arabia region by Siddiqi et al., [10]. Thereafter in 2010, the wavelet transform was used to analyze the wind data in Dongting lake cable stayed bridge region by He et al., [9]. Wind speed data of summer of Eastern region of India was analysed by the continuous wavelet transform and multifractality by Mukhopadhyay et al., [7]. Mukhopadhyay et al., previously applied s transform along with wavelet transform for wind speed data analysis over a year [12]. In this current work, authors are basically interested on the analysis of average wind speed data over a decade on the basis of Wavelet and S-transform.
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 32 2. Methodology In winter (December-January) due to less agitation between wind particles, these wind data are easily analysed with the Continuous Wavelet Transform. Here we used the Daubechies-4 wavelet to detect the continuity between the data of winter. But in summer (April-June) due to high agitation between wind particles, these wind data are first fed into Median Filter to remove the fluctuations. Thereafter these data are fed into S-transformer to get the desired result. In the current work, the below flow chart is followed: Wind data Median Filtering S-Transform The desired output Figure-1 Flow chart of steps for s-transform analysis of Wind data of summer 3. Results and Discussions In below for experiment purpose we took avaerage wind speed data during a decade consists of 3months, such as- December, January and February. In each case of data, we applied Daubechies- 4 Continuous Wavelet transform and tried to follow the continuity of the data plot shown in Figure-2a-2c. Sample Sequence Scale Absolute Values of Wavelet Coefficients for different scale 5 10 15 20 25 30 20 40 60 80 100 120 Fig-2a Daubechies-4 Continuous Wavelet Transform for average wind speed data (during a decade) plot in case of December
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 33 Sample Sequence Scale Absolute values of wavelet coefficients for different scales 5 10 15 20 25 30 20 40 60 80 100 120 Figure-2b Daubechies-4 Continuous Wavelet Transform for average wind speed data (during a decade) plot in case of January Sample Sequences Scales Absolute values of Wavelet Coefficients for different scales 5 10 15 20 25 30 20 40 60 80 100 120 Figure-2c Daubechies-4 Continuous Wavelet Transform for average wind speed data (during a decade ) plot in case of February
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 34 Here, we noticed that in case of Figure-2c we couldn’t track the continuity of the average wind data in February month. Because from February due to rise in convection process, the agitation also exceeds. So, due to the agitations in wind speed data in we couldn’t track it by Daubechies-4 Continuous Wavelet Transform. We also tried with other wavelets such as Symlets, Coiflets, Morlets etc on highly agitated wind speed data but were unable to get the desired results. So, for resolving this kind of problem, we employed s-transform for tracking the high fluctuations average wind speed data during a decade of summer. These fluctuated data are first fed into median filter. The plots are shown in the below Figure-3a to 3c. 0 5 10 15 20 25 30 35 15 20 25 30 35 40 45 Sample Sequence Amplitude Wind data after median filtering Figure-3a Average wind speed data (during a decade) plot of April after Median Filtering
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 35 0 5 10 15 20 25 30 35 5 10 15 20 25 30 35 40 45 Sample Sequence Amplitude Wind data Median Filtering Figure-3b Average wind speed data (during a decade) plot of May after Median Filtering 0 5 10 15 20 25 30 35 5 10 15 20 25 30 35 40 45 Sample Sequence Amplitude Wind data after filtering Figure-3c Average wind speed data (during a decade) plot of June after Median Filtering After median filtering these average wind speed data of decade are fed into s-transform analysis purpose to get the desired result. The plots are shown in below Figure-4a to 4c.
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 36 time frequency ST of Wind data 5 10 15 20 25 30 20 40 60 80 100 120 Figure-4a S-transform of average wind speed data (during a decade) in April time frequency ST of Wind data 5 10 15 20 25 30 20 40 60 80 100 120 Figure-4b S-transform of average wind speed data (during a decade) in May
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 37 time frequency ST of Wind data 5 10 15 20 25 30 20 40 60 80 100 120 Figure-4c S-transform of average wind speed data (during a decade) in June 4. CONCLUSIONS From the above results and discussions, it is clear that Daubechies-4 Continuous Wavelet Transform is useful only for stratified average wind speed data analysis of winter for a decade. But in summer of decade S-transform on median filtered average wind speed data is very useful for the stratified Wind speed data analysis purpose. The authors hope that the current work will certainly establish a new era for the application of wavelet and s-transform in case of Wind Engineering purpose. REFERENCES 1. Panigrahi, P.K., Maniraman, P., Lakshmi, P.A., Yadav, R.R.: Correlations and periodicities in Himalayan tree ring widths and temperature anomalies through wavelets, http://arxiv.org/abs/nlin/0604002v1 (2006) 2. Bhattacharya, P., Mukhopadhyay, S.: Weibull Distribution for Estimating the Parameters and Application of Hilbert Transform in case of a Low Wind Speed at Kolaghat, The International Journal of Multiphysics, Volume-5, No-3 (2011) 3 .Mukhopadhyay.S, et al.: Optimized DHT-Neural Model as a replacement of ARMA-Neural Model for the Wind Power Forecasting purpose, IEEE International Conference Proceeding, India (2013) (Accepted) 4. Mukhopadhyay, S., Bhattacharya, P., Bhattacharjee, R., Bose, P.K.: Discrete Hilbert Transform as Minimum Phase Type Filter for the Forecasting and the characterization of Wind Speed, CODIS International IEEE Conference Proceeding, Kolkata, India (2012) 5. Bhattacharya, P., Mukhopadhyay, S., Ghosh, B.B., Bose, P.K.: Optimized Use of Solar Tracking System and Wind Energy, Elsevier Procedia technology, Volume-4, Page no- 834-839 (2012) 6. Stockwell, R.G., Manisha, L and Lowe, R.P.: Localization of the complex spectrum: the S transform, IEEE Trans. Signal Processing, 44, pp:998-1001 (1996)
International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 38 7. Mukhopadhyay, S., Mandal, S., Panigrahi, P.K., Mitra, A.: Heated wind particle’s behavioral study by the continuous wavelet transform as well as the fractal analysis, Computer Science & Information Technology, pp:169-174 (2013) 8. Liu, C.P., Miller, G.S.: Wavelet Transform and Ocean current data analysis, Journal Of Atmospheric & Ocean Technology, Volume-3, pp:1090-1099 (1996) 9. X. H. He et al.: Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge, http://www.scirp.org/journal/eng (2010) 10. Siddiqi, A.H., Khan, S., Rehman, S.: Wind Speed simulation using Wavelets, American Journal Of Applied Sciences 2 (2), pp: 557-564 (2005) 11. Mallat, S.G.: A Wavelet Tour of Signal Processing, 2nd ed.; Academic Press: Orlando, FL, USA, (1998) 12. Mukhopadhyay, S., Barmase, S., Panigrahi, P.K., Mitra, A., “Detecting monthly stratigraphic discontinuities using wavelet and s-transform analysis of wind speed data”, Springer Digital Library, 2013 (Accepted). Authors Sabyasachi Mukhopadhyay: Mr. Sabyasachi Mukhopadhyay completed B.Tech in Electronics & Communication Engg. from College of Engineering & Management, Kolaghat in July,2012. Currently he is pursuing his research work as Project Assistant in Physical Sciences department of IISER, Kolkata. Till now he has 19 numbers of International Journals, International/ National Conference Proceedings with winning the best research paper award once. His areas of research interests are Digital Signal & Image Processing, Renewable Energy and Graph Theory. Prasanta K. Panigrahi: Currently Prof.(Dr.)Panigrahi is the Chairman of the Physical Sciences Department and the Dean of faculties of IISER, Kolkata. He completed his PhD from University of Rochester, New York, USA. He also had Post Doctorial research work from University of Illinois at Chicago, USA. He delivered invited talks in eminent universities of India and Overseas. He is the elected Fellow of the Gujarat Academy of Science, India. Recently he has become a fellow of NASI, Allahabad. He is Referee of Physical Review Letters, Physical Review B, Journal of Physics, Pattern Recognition Letters, Physics Letter A, Pramana, European Physics Letters. Till now he has more than 800 publications in reputed Journals and Conference Proceedings. His areas of research interest are BoseEinstein Condensates, Cold fermions, Nonlinear Dynamics, Quantum Computation and Quantum Information, Non- Commutative Field Theory and Many body physics, Wavelet Transform.

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Wind Speed Data Analysis for Various Seasons during a Decade by Wavelet and S transform

  • 1. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 DOI:10.5121/ijfcst.2013.3404 31 Wind Speed Data Analysis for Various Seasons during a Decade by Wavelet and S transform Sabyasachi Mukhopadhyay1 , Prasanta K Panigrahi1 1 Department of Physical Sciences, IISER, Kolkata ABSTRACT The prediction of Weather forecasting can be done with the Wind Speed data. In this current paper the concept of using Wavelet and S-transform together for the analysis purpose of Wind data is introduced first time ever. In winter due to low convection process the agitation between wind particles is less. So, the Haar Wavelet is used to detect the discontinuity in the less agitated wind data samples of Winter. But due to abrupt changes in wind data in summer, it is difficult to track the data. So, in that case the concept of the S- transform is introduced. KEYWORDS Continuous Wavelet Transform, S-transform, Wind Speed. 1. Introduction The present paper is focused on time-frequency analysis of wind speed data. Currently wind energy is a hot topic as it is one of the important non-conventional energies. We know that Weibull distribution is a very popular tool for wind energy purpose [2, 5]. The usefulness of signal processing tools are increasing in case of wind engineering purpose. For low wind speed analysis purpose use of discrete Hilbert transform (DHT) along with weibull distribution is shown in ref [2]. The discrete Hilbert Transform (DHT) can be used as minimum phase type filter for characterizing and forecasting purpose of Wind speed data is showed by Mukhopadhyay et al., [4]. Mukhopadhyay et al., also showed the optimized DHT and RBF neural network basis analysis for Wind power forecasting purpose [3]. The utility of Wavelet in weather related application was already shown by Panigrahi et al., [1]. The application of wavelet transform in the field of Ocean technology was shown by Liu et al., [8]. In 2005, the wavelet transform was used for wind data simulation of Saudi Arabia region by Siddiqi et al., [10]. Thereafter in 2010, the wavelet transform was used to analyze the wind data in Dongting lake cable stayed bridge region by He et al., [9]. Wind speed data of summer of Eastern region of India was analysed by the continuous wavelet transform and multifractality by Mukhopadhyay et al., [7]. Mukhopadhyay et al., previously applied s transform along with wavelet transform for wind speed data analysis over a year [12]. In this current work, authors are basically interested on the analysis of average wind speed data over a decade on the basis of Wavelet and S-transform.
  • 2. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 32 2. Methodology In winter (December-January) due to less agitation between wind particles, these wind data are easily analysed with the Continuous Wavelet Transform. Here we used the Daubechies-4 wavelet to detect the continuity between the data of winter. But in summer (April-June) due to high agitation between wind particles, these wind data are first fed into Median Filter to remove the fluctuations. Thereafter these data are fed into S-transformer to get the desired result. In the current work, the below flow chart is followed: Wind data Median Filtering S-Transform The desired output Figure-1 Flow chart of steps for s-transform analysis of Wind data of summer 3. Results and Discussions In below for experiment purpose we took avaerage wind speed data during a decade consists of 3months, such as- December, January and February. In each case of data, we applied Daubechies- 4 Continuous Wavelet transform and tried to follow the continuity of the data plot shown in Figure-2a-2c. Sample Sequence Scale Absolute Values of Wavelet Coefficients for different scale 5 10 15 20 25 30 20 40 60 80 100 120 Fig-2a Daubechies-4 Continuous Wavelet Transform for average wind speed data (during a decade) plot in case of December
  • 3. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 33 Sample Sequence Scale Absolute values of wavelet coefficients for different scales 5 10 15 20 25 30 20 40 60 80 100 120 Figure-2b Daubechies-4 Continuous Wavelet Transform for average wind speed data (during a decade) plot in case of January Sample Sequences Scales Absolute values of Wavelet Coefficients for different scales 5 10 15 20 25 30 20 40 60 80 100 120 Figure-2c Daubechies-4 Continuous Wavelet Transform for average wind speed data (during a decade ) plot in case of February
  • 4. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 34 Here, we noticed that in case of Figure-2c we couldn’t track the continuity of the average wind data in February month. Because from February due to rise in convection process, the agitation also exceeds. So, due to the agitations in wind speed data in we couldn’t track it by Daubechies-4 Continuous Wavelet Transform. We also tried with other wavelets such as Symlets, Coiflets, Morlets etc on highly agitated wind speed data but were unable to get the desired results. So, for resolving this kind of problem, we employed s-transform for tracking the high fluctuations average wind speed data during a decade of summer. These fluctuated data are first fed into median filter. The plots are shown in the below Figure-3a to 3c. 0 5 10 15 20 25 30 35 15 20 25 30 35 40 45 Sample Sequence Amplitude Wind data after median filtering Figure-3a Average wind speed data (during a decade) plot of April after Median Filtering
  • 5. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 35 0 5 10 15 20 25 30 35 5 10 15 20 25 30 35 40 45 Sample Sequence Amplitude Wind data Median Filtering Figure-3b Average wind speed data (during a decade) plot of May after Median Filtering 0 5 10 15 20 25 30 35 5 10 15 20 25 30 35 40 45 Sample Sequence Amplitude Wind data after filtering Figure-3c Average wind speed data (during a decade) plot of June after Median Filtering After median filtering these average wind speed data of decade are fed into s-transform analysis purpose to get the desired result. The plots are shown in below Figure-4a to 4c.
  • 6. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 36 time frequency ST of Wind data 5 10 15 20 25 30 20 40 60 80 100 120 Figure-4a S-transform of average wind speed data (during a decade) in April time frequency ST of Wind data 5 10 15 20 25 30 20 40 60 80 100 120 Figure-4b S-transform of average wind speed data (during a decade) in May
  • 7. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 37 time frequency ST of Wind data 5 10 15 20 25 30 20 40 60 80 100 120 Figure-4c S-transform of average wind speed data (during a decade) in June 4. CONCLUSIONS From the above results and discussions, it is clear that Daubechies-4 Continuous Wavelet Transform is useful only for stratified average wind speed data analysis of winter for a decade. But in summer of decade S-transform on median filtered average wind speed data is very useful for the stratified Wind speed data analysis purpose. The authors hope that the current work will certainly establish a new era for the application of wavelet and s-transform in case of Wind Engineering purpose. REFERENCES 1. Panigrahi, P.K., Maniraman, P., Lakshmi, P.A., Yadav, R.R.: Correlations and periodicities in Himalayan tree ring widths and temperature anomalies through wavelets, http://arxiv.org/abs/nlin/0604002v1 (2006) 2. Bhattacharya, P., Mukhopadhyay, S.: Weibull Distribution for Estimating the Parameters and Application of Hilbert Transform in case of a Low Wind Speed at Kolaghat, The International Journal of Multiphysics, Volume-5, No-3 (2011) 3 .Mukhopadhyay.S, et al.: Optimized DHT-Neural Model as a replacement of ARMA-Neural Model for the Wind Power Forecasting purpose, IEEE International Conference Proceeding, India (2013) (Accepted) 4. Mukhopadhyay, S., Bhattacharya, P., Bhattacharjee, R., Bose, P.K.: Discrete Hilbert Transform as Minimum Phase Type Filter for the Forecasting and the characterization of Wind Speed, CODIS International IEEE Conference Proceeding, Kolkata, India (2012) 5. Bhattacharya, P., Mukhopadhyay, S., Ghosh, B.B., Bose, P.K.: Optimized Use of Solar Tracking System and Wind Energy, Elsevier Procedia technology, Volume-4, Page no- 834-839 (2012) 6. Stockwell, R.G., Manisha, L and Lowe, R.P.: Localization of the complex spectrum: the S transform, IEEE Trans. Signal Processing, 44, pp:998-1001 (1996)
  • 8. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.4, July 2013 38 7. Mukhopadhyay, S., Mandal, S., Panigrahi, P.K., Mitra, A.: Heated wind particle’s behavioral study by the continuous wavelet transform as well as the fractal analysis, Computer Science & Information Technology, pp:169-174 (2013) 8. Liu, C.P., Miller, G.S.: Wavelet Transform and Ocean current data analysis, Journal Of Atmospheric & Ocean Technology, Volume-3, pp:1090-1099 (1996) 9. X. H. He et al.: Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge, http://www.scirp.org/journal/eng (2010) 10. Siddiqi, A.H., Khan, S., Rehman, S.: Wind Speed simulation using Wavelets, American Journal Of Applied Sciences 2 (2), pp: 557-564 (2005) 11. Mallat, S.G.: A Wavelet Tour of Signal Processing, 2nd ed.; Academic Press: Orlando, FL, USA, (1998) 12. Mukhopadhyay, S., Barmase, S., Panigrahi, P.K., Mitra, A., “Detecting monthly stratigraphic discontinuities using wavelet and s-transform analysis of wind speed data”, Springer Digital Library, 2013 (Accepted). Authors Sabyasachi Mukhopadhyay: Mr. Sabyasachi Mukhopadhyay completed B.Tech in Electronics & Communication Engg. from College of Engineering & Management, Kolaghat in July,2012. Currently he is pursuing his research work as Project Assistant in Physical Sciences department of IISER, Kolkata. Till now he has 19 numbers of International Journals, International/ National Conference Proceedings with winning the best research paper award once. His areas of research interests are Digital Signal & Image Processing, Renewable Energy and Graph Theory. Prasanta K. Panigrahi: Currently Prof.(Dr.)Panigrahi is the Chairman of the Physical Sciences Department and the Dean of faculties of IISER, Kolkata. He completed his PhD from University of Rochester, New York, USA. He also had Post Doctorial research work from University of Illinois at Chicago, USA. He delivered invited talks in eminent universities of India and Overseas. He is the elected Fellow of the Gujarat Academy of Science, India. Recently he has become a fellow of NASI, Allahabad. He is Referee of Physical Review Letters, Physical Review B, Journal of Physics, Pattern Recognition Letters, Physics Letter A, Pramana, European Physics Letters. Till now he has more than 800 publications in reputed Journals and Conference Proceedings. His areas of research interest are BoseEinstein Condensates, Cold fermions, Nonlinear Dynamics, Quantum Computation and Quantum Information, Non- Commutative Field Theory and Many body physics, Wavelet Transform.