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Name ： Zhisheng Team Advisor ： Zhang Chenghui, Li Ke

Airball Demo Modeling —— Dimensional Analysis Method Based on Genetic Algorithm for Key Parameters Identification. Name ： Zhisheng Team Advisor ： Zhang Chenghui, Li Ke. Introduction. 1. 2. 3. 4. CONTENTS. Mechanism Modeling. Key Parameters Identification. Experiment and Analysis.

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Name ： Zhisheng Team Advisor ： Zhang Chenghui, Li Ke

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  1. Airball Demo Modeling ——Dimensional Analysis Method Based on Genetic Algorithm for Key Parameters Identification Name：Zhisheng Team Advisor： Zhang Chenghui, Li Ke

  2. Introduction 1 2 3 4 CONTENTS Mechanism Modeling Key Parameters Identification Experiment and Analysis

  3. 1. Introduction Dimensional Analysis and Modeling are widely used techniques in fluid mechanics. A qualitative description of physical quantities can be given in terms of basic dimensions such as mass , length and time . Dimension The basis for Dimensional Analysis’ application to a wide variety of problems is found in the Buckingham π theorem：if an equation involving n variables is dimensionally homogeneous, it can be reduced to a relationship among n-m independent dimensionless products，where m is the the minimum number of basic dimensions. πtheorem

  4. 1. Introduction Supposing an physical expression as , which involves n variables and m basic dimensions. It can be reduced to a relationship among n-m independent dimensionless products: where we use to represent dimensional products.

  5. 2. Mechanism Modeling 1.Hardware Analysis 2.Modeling Figure 1 Airball Demo

  6. 2. Mechanism Modeling The fan rotates to push against air with the effect of input voltage and air flow directionally through the pipe. • Hardware Analysis A B The flow of air in the pipe generates a driving force on airball. The airball move through the pipe and finally keep in a certain height. C The airball height is converted into output voltage using ultrasonic sensor. D Airball Demo

  7. F 2. Mechanism Modeling 2. Modeling Based on Newton motion law, force analysis of airball is illustrated in Figure 2. The equation of airball is established as follows， G=mg Figure 2 Force analysis of airball

  8. 2. Mechanism Modeling A 614JH-EBM-Papst model fan is applied by Airball Demo. Based on the Theory of Electric Machine, we can get . Table 1 Nominal data of fan

  9. 2. Mechanism Modeling Pressure over air flow is illustrated in Figure 3. If pressure is definite, the speed characteristics of electric machine is directly proportional to air flow and air flow varies directly as the speed of air in the pipe. Thus, we can get if pressure is zero, Concerning about the influence of Airball Demo on pressure，so the speed of air is modified to： where k1, k2 need to be identified. Figure 3 Characteristic：Pressure over air flow

  10. 2. Mechanism Modeling The first step to study this problem would be to decide on the factors that will have effects onAirball Demo. We expect the list to include the pipe diameter , the fluid density , the airball diameter and the velocity , at which the fluid is flowing through the pipe. Thus we can express this relationship as • Applying Dimensional Analysis and pi theorem,

  11. 2. Mechanism Modeling • Next we express all the variables in terms of basic dimensions. Using , , as basic dimensions it follows that where dim represents the dimension of certain physical quantity. • Choosing , , , thus we get dimensionless products as follows:

  12. 2. Mechanism Modeling • thus • So we can write • Finally, give the relationship among dimensionless products， that is，

  13. 2. Mechanism Modeling • Airball height measurement A Baumer UNAM 186903/S14 model ultrasonic sensor is applied by Airball Demo. It is almost linear on [100mm , 1000mm] interval. Table 2 Ultrasonic sensor experiment data

  14. 2. Mechanism Modeling • Conclusion Based on the work mentioned above, the model of Airball Demo is got, that is

  15. 3. Key Parameters Identification Introduction to model parameters identification using Genetic Algorithms(GA) The method of programming Data acquisition k1,k2,k3

  16. 3. Key Parameters Identification • Introduction Genetic Algorithms is used to identify model parameters：k1, k2 and k3. Objective functionis: Fitness function is: Figure 4 parameters identification schematic diagram

  17. 3. Key Parameters Identification • Data acquisition Step voltage input are imposed on Airball Demo. The height output is sampled in Automation Studio software based on the fixed interval time. Figure 5 Airball Demo step response curve

  18. Start Initializing the GA paprmeters Select,cross,mutation Initializing the population Calculating the fitness Calculating the fitness N Exit Y End 3. Key Parameters Identification • The method of programming

  19. 4. Experiment and Analysis • Set GA parameters： • Run the GA program, then we can get the fitness curve and k1, k2, k3. fitness: 0.2163 k1: 0.0547 k2: 0.2437 k3: 0.5872 Figure 6 Fitness curve

  20. 4. Experiment and Analysis The simulated curve in AS environment is shown in Figure 7. Figure 7 Simulated curve The Airball Demo curve is shown in Figure 8. Figure 8 Airball Demo curve

  21. Thank you

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