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

Introduction Experiment and Analysis CONTENTS Mechanism Modeling Key Parameters Identification

Dimension 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. 1. Introduction 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. π theorem

where we use to represent dimensional products. 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: 1. Introduction

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

The fan rotates to push against air with the effect of input voltage and air flow directionally through the pipe. 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. The airball height is converted into output voltage using ultrasonic sensor. Airball Demo A B C D 1.Hardware Analysis 2. Mechanism Modeling

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

Table 1 Nominal data of fan A 614JH-EBM-Papst model fan is applied by Airball Demo. Based on the Theory of Electric Machine, we can get. 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. 2. Mechanism Modeling Figure 3 Characteristic ： Pressure over air flow

The first step to study this problem would be to decide on the factors that will have effects on Airball 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, 2. Mechanism Modeling

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

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

A Baumer UNAM /S14 model ultrasonic sensor is applied by Airball Demo. It is almost linear on [100mm, 1000mm] interval. Table 2 Ultrasonic sensor experiment data  Airball height measurement 2. Mechanism Modeling Height （ mm ） Sample resultSlopeAverage slope

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

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

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

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

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

4. Experiment and Analysis  Set GA parameters ： fitness: k1: k2: k3: Figure 6 Fitness curve  Run the GA program, then we can get the fitness curve and k1, k2, k3.

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

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