1. Prediction of Natural Gas Consumption with Feed-forward and Fuzzy Neural Networks N.H. Viet Institute of Fundamental Tech. Research Polish Academy of Sciences – Poland, J. Mańdziuk Faculty of Mathematics and Information Science Warsaw University of Technology – Poland.

2. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Presentation’s schedule Introduction Feed-forward neural networks Fuzzy neural networks Experimental results and conclusions

3. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Introduction Prediction of gas consumption is an important element in business planning. The challenges: the volatility of consumer profile, the strong dependency on weather conditions, the lack of historical data. The purpose of this work: an application to gas load prediction using various neural network models.

4. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Introduction Three types of prediction: One day (short-term) prediction, One week (mid-term) prediction, Four week (long-term) prediction.

5. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Introduction The data contains the daily gas loads and the average daily temperatures. Seasonality Strong dependency on temperature. An overview of the data:

6. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Introduction The inputs: Historical daily gas loads, Average daily temperatures Time factor (the season inputs) For the n-day period: [t + 1, t + n], two values were used: Where: One additional bit indicating the work day/weekend day in the case of daily prediction.

7. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Feed-forward model General network architecture: Previous daily loads Previous daily temperatures Time encoding

8. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Feed-forward model Chosen configurations: One day prediction: 9(3+3+3)-8(3+3+2)-3-1 One week prediction: 12(5+5+2)-10(4+4+2)-4-1 Four week prediction: 16(7+7+2)-10(4+4+2)-4-1

9. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Fuzzy neural model Why to use the fuzzy neural model?: Impreciseness of data (only average daily temperature is available), Fuzzy neural networks generally have a better performance,

10. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Fuzzy neural model Fuzzy neural network architecture: Membership layerDefuzzification layer

11. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Fuzzy neural model Fuzzy neural network dynamics: Gaussian membership function: Output:

12. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Fuzzy neural model FNN can be trained using the gradient-based technique. An equivalent rule sets:

13. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Experimental results and conclusions Training data: from Jan. 01, 2000 to Dec. 31, 2001. Testing data: from Jan. 01 2002 to Jul. 31, 2002. The moving window technique was used to generate the training and the testing samples. The following experiments were performed: Single feed-forward network (SingleN) Single fuzzy network (FuzzyN) 3 feed-forward networks (3AvgN) 3 temperature context networks (3TempN)

14. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Experimental results and conclusions Temperature context networks: Divide the training set into 3 overlapping subsets (denoted by Low, Medium and High ) using the average temperature, Train 3 types of networks with these sets independently, Combine 3 networks into one module while testing. Remark: training the networks within a particular context should be easier than in the entire input space.

15. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Experimental results and conclusions

16. N.H. Viet, J. Mańdziuk: Prediction of Natural Gas Consumption with Neural Networks Experimental results and conclusions An example of one week and four week prediction:

17. Thank you for your attention