2. Application of Data Mining for creation of combustion models Teacher: Victor S. Abrukov Students: Pavel Ivanov, Dmitry Makarov, Alexey Sergeev Chuvash State University, Russia Department of Thermo Physics

3. Chuvash State University, Russia

4. Outline 1. Abstract 2. Introduction 1 3. Data Mining Approach of Data Analysis 4. Artificial Neural Networks Approach of Data Analysis 5. Introduction 2 6. Combustion Data 7. Goal of the work 8. Examples of ANN calculation combustion models 8.1. The model “Temperature Profile vs Burning Rate” 8.2. The model “Burning Rate vs Environment and Mixture” 8.3. The model “Mixture vs Environment and Burning Rate” 8.3. The model “Mixture vs Environment and Burning Rate” 9. Conclusions and Sources

5. Abstract Presented in this work are the results of ANN usage for the creation of new kinds of calculation models of propellant combustion that can solve hard experimental tasks of combustion research, as well as a discussion of perspectives of ANN usage from this point of view.

6. IntroductionIntroduction - 1 WORKING WITH A PROBLEM, IT IS USEFUL ALWAYS TO KNOW AN ANSWER

7. Data Mining Approach of Data Analysis The Data Mining is a complex of contemporary tools for data collection, its preprocessing, processing, analyzing, and presentation. The Data Mining involves such kinds of tools as Data Warehouse, data preprocessing tools, correlation analysis, decision trees, artificial neural networks (ANN), self-organization maps, etc. ANN have a head role from the point of view of creation of a calculation models. Other tools of Data Mining have the auxiliary role for data preprocessing, processing and data choosing for creation of ANN calculation models.

8. Artificial Neural Networks Approach of Data Analysis Artificial neural networks (ANN) is an universal tool for multidimensional approximation of experimental results. The Kolmogorov-Arnold theorems dealing with the capability of representation of multidimensional functions by means of superposition of functions of one variable is the basis of ANN application.

9. Artificial Neural Networks Approach of Data Analysis The real computer emulators of ANN are like the usual computer programs. The difference is that their creation is based on the use of a training procedure which executes by means of a set of examples (a data base of examples). The real computer emulators of ANN are like the usual computer programs. The difference is that their creation is based on the use of a training procedure which executes by means of a set of examples (a data base of examples). ANN use principles of human brain working. They are like children and need in training

10. A part of human neural networks

11. Scheme of human neuron

12. Scheme of artificial neuron Artificial neuron consist of inputs, synapses, summator and non-linear converter. It executes the following operations: W i is the weight of a synapse (i = 1..., n); S is the result of summation; Xi is the component of input vector (input signals) (i = 1..., n); Y is the output signal of a neuron; n is the number of inputs of a neuron; and f is the non-linear transforming (function of activation or transfer function)

13. Kinds of Artificial Neural Networks ANN represent some quantity of artificial “neurons” and can be presented often as “neurons” formed in layers (б).

14. Example of Artificial Neural Networks A scheme of ANN which consists of one input layer, one “hidden” layer, and one output layer

15. Example of Artificial Neural Networks The input signals (five arrows on the left of Fig. are the input layer of neurons) go through synapses into the “hidden” layer of neurons (five black circles), then into the output layer of neurons (three black circles). Before and after passing the “hidden” layer, the input signals vary in accordance with the synaptic weight of each synapse of “neurons” of the “hidden” layer and their transfer function, as well as in accordance with the synaptic weight of each synapse of “neurons” of the output layer and their transfer function. The synaptic weight is a number which reflects a comparative contribution of each “neuron's” calculation into a final result (the output signals – three arrows on the right of Fig.)

16. Training of Artificial Neural Networks The task of ANN training consists of finding such synaptic weights by means of which input information (five input signals) will be correctly transformed into output information (three output signals). During ANN training, a training tool compares the output signals to known target values, calculates the error, modifies the weights of synapses that give the largest contribution to error by means of one of the famous algorithms,1 and repeats the training cycle many times until an acceptable output signal is achieved. A usual number of training cycles is more than 10,000. The concrete weights values obtained during training have no physical sense individually. However, the totality of them have a sense as a “black box” which allows for the transfer of any input signals belonging to the input signals used during training to a new output signal

17. Training of Artificial Neural Networks A database for ANN training can be formed by means of various techniques. An art of creation of a database is the first art of ANN technologies

18. IntroductionIntroduction – 2 No Science without Data Base No Data Base without Data Analysis Tools

19. Combustion Data There are a great deal of experimental data about flame structure for various gaseous and condensed systems. The question is how we can generalize them? It is obvious that a flame structure is bound up with a composition of combustible mixtures and kinds of mixture components; pressure and initial temperature; heat of burning and burning rate. The question is how we can create generalization models for these dependences?

20. Goal of the work The goal is presentation of ANN calculation models of propellants burning A goal of the ANN models is to solve hard tasks involved with the experimental investigation of propellants burning in particularly to predict regularities of burning without additional experiments We would like to solve these tasks easy and fast

21. Examples of ANN usage At present time we have obtained three ANN calculation models.

22. 1. The model “Temperature Profile vs Burning Rate”. The model allows determining of a temperature profile of propellant burning wave by means of the data about a pressure, corresponding value of a burning rate, and heat of propellant burning (or adiabatic temperature).

23. 1. The model “Temperature Profile vs Burning Rate”. The scheme of construction of an ANN model was as follows. We have taken experimental data of the pressure during burning, p, burning rate, U, a portion of the heat released near the burning surface of the propellant, Q, and temperature profiles (values of temperature, T and coordinates, x) measured by means of thermocouples for some propellants which consisted of ammonium perchlorate (AP) and various binders with a constant mass proportion between AP and binder.

24. 1. The model “Temperature Profile vs Burning Rate”. In total, we had 60 rows which involved experimental data about burning. A part of the data which was used

25. 1. The model “Temperature Profile vs Burning Rate”. Then, the different sets of values of pressure, burning rate, heat of combustion and coordinates were stored on the input layer of ANN. The corresponding values of temperature were stored on the output layer of ANN By means of a training tool named the method of “back propagation of errors,” we have created the ANN calculation model. This model is a “black box” type with latent connections between variables.

26. 1. The model “Temperature Profile vs Burning Rate”. For checking the ANN model we used the experimental data that had not been used for training. The results we have obtained are presented below.

27. 1. The model “Temperature Profile vs Burning Rate” AP based propellant (p=40 atm, Q=150 cal/g, U=0.4 cm/s). T is a real value of temperature measured by means of thermocouples, T’ is a value of temperature which was calculated by the “black box” model. AP based propellant (p=40 atm, Q=150 cal/g, U=0.4 cm/s). T is a real value of temperature measured by means of thermocouples, T’ is a value of temperature which was calculated by the “black box” model.

28. 1. The model “Temperature Profile vs Burning Rate”. We have received also another example. Here we used the experimental data about nitrocellulose burning. The experimental data used for training of ANN (creation of the “black box” model) are presented below. Tad is adiabatic temperature in flame. We have received also another example. Here we used the experimental data about nitrocellulose burning. The experimental data used for training of ANN (creation of the “black box” model) are presented below. Tad is adiabatic temperature in flame.

29. 1. The model “Temperature Profile vs Burning Rate”. Experimental Data: Nitrocellulose burning

30. 1. The model “Temperature Profile vs Burning Rate”. Results of checking. Nitrocellulose (p=28 atm, U=20 mm/s, Tad =1400 C0). T is a value of temperature measured by means of thermocouples, T’ is a value of temperature which was calculated by the “black box” model. Results of checking. Nitrocellulose (p=28 atm, U=20 mm/s, Tad =1400 C0). T is a value of temperature measured by means of thermocouples, T’ is a value of temperature which was calculated by the “black box” model.

31. 1. The model “Temperature Profile vs Burning Rate”. An analysis of results obtained depicts that the “black box” model: “Burning Rate vs Temperature Profile” enough correctly “determines” the temperature profile for various propellants by means of data about burning rate, pressure, and heat of burning (or adiabatic temperature of flame). An analysis of results obtained depicts that the “black box” model: “Burning Rate vs Temperature Profile” enough correctly “determines” the temperature profile for various propellants by means of data about burning rate, pressure, and heat of burning (or adiabatic temperature of flame). In our opinion, this way of obtaining the temperature profiles can be promising in cases when we have blanks in experimental results for concrete propellants and would like to fill them. In our opinion, this way of obtaining the temperature profiles can be promising in cases when we have blanks in experimental results for concrete propellants and would like to fill them.

32. 1. The model “Temperature Profile vs Burning Rate”. We hope that this way of determining temperature profiles could be considered as a prospective tool for cases when we have no experimental results for concrete propellants and would like to have them. We hope that this way of determining temperature profiles could be considered as a prospective tool for cases when we have no experimental results for concrete propellants and would like to have them. In order to make it, all we need to do is to collect a lot of experimental data published in scientific and technical literature concerning temperature profiles for various propellants under various conditions. Then, we could create the common “black box” model: Burning Rate vs. Temperature Profile. In order to make it, all we need to do is to collect a lot of experimental data published in scientific and technical literature concerning temperature profiles for various propellants under various conditions. Then, we could create the common “black box” model: Burning Rate vs. Temperature Profile.

33. 2. The Model “Burning Rate vs Environment and Mixture”. The propellant we have used was a mixture of ammonium nitrate (AN) and ammonium perchlorate (AP) in a various ratio as oxidizer (80%) and hydroxyl-terminated polybutadien (HTPB) (20%) as fuel. The propellant we have used was a mixture of ammonium nitrate (AN) and ammonium perchlorate (AP) in a various ratio as oxidizer (80%) and hydroxyl-terminated polybutadien (HTPB) (20%) as fuel. The schemes of construction of the Model 1 was as follows. First, we have taken the data about the burning rates. The schemes of construction of the Model 1 was as follows. First, we have taken the data about the burning rates.

34. 2. The Model “Burning Rate vs Environment and Mixture”. Here, PD is AP particle diameter (from 3 to 180 microns), P is a pressure (from 0,5 to 7 atm), U is a burning rate. Here, PD is AP particle diameter (from 3 to 180 microns), P is a pressure (from 0,5 to 7 atm), U is a burning rate.

35. 2. The Model “Burning Rate vs Environment and Mixture”. Thus we have created the data base of five variables of the experiment. Then the different sets of values of quantity of AN and AP, values of AP particle diameters, and values of pressure are installed on the input layer of ANN. The corresponding values of burning rates are installed on the exit of ANN. Thus we have created the data base of five variables of the experiment. Then the different sets of values of quantity of AN and AP, values of AP particle diameters, and values of pressure are installed on the input layer of ANN. The corresponding values of burning rates are installed on the exit of ANN.

36. 2. The Model “Burning Rate vs Environment and Mixture”. After training procedure we have obtained the “black box” model which can be used in experimental investigation for the prediction (with a good accuracy) a burning rate value in much more range of values of the pressure (about 15 MPa) and the AP particles diameters (more 180 microns and less 3 microns) than it were used in real experiments. After training procedure we have obtained the “black box” model which can be used in experimental investigation for the prediction (with a good accuracy) a burning rate value in much more range of values of the pressure (about 15 MPa) and the AP particles diameters (more 180 microns and less 3 microns) than it were used in real experiments.

37. 2. The Model “Burning Rate vs Environment and Mixture”. Of course the model can determine the values of burning rate for values of pressure and AP particle diameters that were undetermined because of various reasons (i.e. ANN model can fulfill blanks in experimental results). Of course the model can determine the values of burning rate for values of pressure and AP particle diameters that were undetermined because of various reasons (i.e. ANN model can fulfill blanks in experimental results).

38. 2. The Model “Burning Rate vs Environment and Mixture”. Some of the results obtained are depicted in Fig. 1-10. Some of the results obtained are depicted in Fig. 1-10.

39. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.1. Burning rate vs Pressure for propellants with AN/AP = 2/8 and PD=160 micron (in reality we have no data for this PD, however ANN was able to fulfill blanks Fig.1. Burning rate vs Pressure for propellants with AN/AP = 2/8 and PD=160 micron (in reality we have no data for this PD, however ANN was able to fulfill blanks

40. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.2. Burning rate vs Pressure for propellants with AN/AP = 2/8 and PD=400 micron (in reality we have data for max PD=180 micron, however ANN was able to predict this dependence). Fig.2. Burning rate vs Pressure for propellants with AN/AP = 2/8 and PD=400 micron (in reality we have data for max PD=180 micron, however ANN was able to predict this dependence).

41. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.3. Burning rate vs AP’s Particle Diameter for propellants with AN/AP = 2/8 and P=7 atm. Fig.3. Burning rate vs AP’s Particle Diameter for propellants with AN/AP = 2/8 and P=7 atm.

42. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.4. Burning rate vs AP’s Particle Diameter for propellants with AN/AP = 2/8 and P=15 atm (in reality we have data for max P=7 atm, however ANN was able to predict this dependence). Fig.4. Burning rate vs AP’s Particle Diameter for propellants with AN/AP = 2/8 and P=15 atm (in reality we have data for max P=7 atm, however ANN was able to predict this dependence).

43. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.6. The value U for P=0 and PD=1 micron (in reality we have no data for P=0 atm and PD=1 micron, however ANN was able to estimate this value of U). Fig.6. The value U for P=0 and PD=1 micron (in reality we have no data for P=0 atm and PD=1 micron, however ANN was able to estimate this value of U).

44. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.7. The value U for P=15 and PD=1 micron (in reality we have no data for P=15 atm and PD=1 micron, however ANN was able to estimate this value of U). Fig.7. The value U for P=15 and PD=1 micron (in reality we have no data for P=15 atm and PD=1 micron, however ANN was able to estimate this value of U).

45. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.8. The value U for P=15 and PD=400 micron (in reality we have neither data for P=15 atm or PD=400 micron, however ANN was able to estimate this value of U). Fig.8. The value U for P=15 and PD=400 micron (in reality we have neither data for P=15 atm or PD=400 micron, however ANN was able to estimate this value of U).

46. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.9. The value U for P=0 and PD=0,1 micron – 100nm (!) (in reality we have neither data for P=0 atm or PD=100 nm (nano AP!), however ANN was able to estimate this value of U). Fig.9. The value U for P=0 and PD=0,1 micron – 100nm (!) (in reality we have neither data for P=0 atm or PD=100 nm (nano AP!), however ANN was able to estimate this value of U).

47. 2. The Model “Burning Rate vs Environment and Mixture”. Fig.10. The value U for P=15 atm and PD=0,1 micron – 100nm (!) (in reality we have neither data for P=15 atm or PD=100 nm (nano AP!), however ANN was able to estimate this value of U). Fig.10. The value U for P=15 atm and PD=0,1 micron – 100nm (!) (in reality we have neither data for P=15 atm or PD=100 nm (nano AP!), however ANN was able to estimate this value of U).

48. 3. The Model “Mixture vs Environment and Burning Rate” We have used the same propellants and the same data as above mentioned. We have used the same propellants and the same data as above mentioned. However, during training of ANN, we have installed on the input layer of ANN the different sets of values of pressure, burning rate and a quantity of AN. The corresponding values of quantity of AP and values of AP particle diameter were installed on the output layer of ANN. However, during training of ANN, we have installed on the input layer of ANN the different sets of values of pressure, burning rate and a quantity of AN. The corresponding values of quantity of AP and values of AP particle diameter were installed on the output layer of ANN.

49. 3. The Model “Mixture vs Environment and Burning Rate” The Model obtained can help to choose the mixture of propellant that provides a necessary burning rate (for various pressures and other parameters). The Model obtained can help to choose the mixture of propellant that provides a necessary burning rate (for various pressures and other parameters). Some of the results are depicted in Fig. 11- 13. Some of the results are depicted in Fig. 11- 13.

50. 3. The Model “Mixture vs Environment and Burning Rate” Fig.11. Normalized quantity of AP (between 10 and 0) and AP’s Particle Diameter that provide the U=0,63 (for various values of AN and P=1 atm). Fig.11. Normalized quantity of AP (between 10 and 0) and AP’s Particle Diameter that provide the U=0,63 (for various values of AN and P=1 atm).

51. 3. The Model “Mixture vs Environment and Burning Rate” Fig.12. Normalized quantity of AP (between 10 and 0) and AP’s Particle Diameter that provide the U=4 (for various values of P and AN=4). Fig.12. Normalized quantity of AP (between 10 and 0) and AP’s Particle Diameter that provide the U=4 (for various values of P and AN=4).

52. 3. The Model “Mixture vs Environment and Burning Rate” Fig.13. Normalized quantity of AP (between 10 and 0) and AP’s Particle Diameter that correspond to various values of U (for P=15 atm, which we have no in our data base and AN=4). Fig.13. Normalized quantity of AP (between 10 and 0) and AP’s Particle Diameter that correspond to various values of U (for P=15 atm, which we have no in our data base and AN=4).

53. CONCLUSION 1 Results of ANN usage for the creation of new kinds of calculation models of propellants burning that can help to solve hard experimental tasks of the combustion research fast and easily are prsented. Results of ANN usage for the creation of new kinds of calculation models of propellants burning that can help to solve hard experimental tasks of the combustion research fast and easily are prsented. ANN allows essentially expanding the area meaning of former experimental results and receiving of new “experimental” results for revealing of new unknown dependencies as well as for receiving of new unknown data. ANN allows essentially expanding the area meaning of former experimental results and receiving of new “experimental” results for revealing of new unknown dependencies as well as for receiving of new unknown data. The main advantages of ANN application are: ANN does not require additional real experiments in order to solve the various hard problems. ANN does not require additional real experiments in order to solve the various hard problems. ANN can be used everywhere where we have enough large quantity of experimental data but need essential additional information. ANN can be used everywhere where we have enough large quantity of experimental data but need essential additional information. ANN can be applied not only to investigate the propellants burning, but also to to investigate other objects of combustion. All you need to do is to create a congruent data base for ANN training. ANN can be applied not only to investigate the propellants burning, but also to to investigate other objects of combustion. All you need to do is to create a congruent data base for ANN training. We believe that ANN technologies can be considered in the future as a powerful tool, which supports high contact of experiment, computer simulation and calculation.

54. Sources Anatoly A. Zenin. Temperature Profile Measurement for AP- Based Propellant. Anatoly A. Zenin. Temperature Profile Measurement for AP- Based Propellant. Lewis, B., Pees, R. N., Taylor, H. S. Temperature Profile Measurement for Nitrocellulose. Lewis, B., Pees, R. N., Taylor, H. S. Temperature Profile Measurement for Nitrocellulose. Makota Kohga, et al. Influence of AP Particle Size on Burning Characteristics of AN/AP – Based Composite Propellants. Makota Kohga, et al. Influence of AP Particle Size on Burning Characteristics of AN/AP – Based Composite Propellants. Neural Networks for Instrumentation, Measurement and Related Industrial Applications (2003). Proceedings of the NATO Advanced Study Institute on Neural Networks for Instrumentation, Measurement, and Related Industrial Applications (9-20 October 2001, Crema, Italy)/ ed. by Sergey Ablameyko, Liviu Goras, Marco Gori and Vincenzo Piuri, IOS Press, Series 3: Computer and Systems Sciences – Vol. 185, Amsterdam. Neural Networks for Instrumentation, Measurement and Related Industrial Applications (2003). Proceedings of the NATO Advanced Study Institute on Neural Networks for Instrumentation, Measurement, and Related Industrial Applications (9-20 October 2001, Crema, Italy)/ ed. by Sergey Ablameyko, Liviu Goras, Marco Gori and Vincenzo Piuri, IOS Press, Series 3: Computer and Systems Sciences – Vol. 185, Amsterdam.

55. Conclusion 2 All you need in your life is love All you need in your scientific life is neural networks It can be artificial neural networks