Course project of DOE, 2010 spring By Group 11 : 沈坤,孙维,袁怡潇,于漠南,朱雯 1...
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Transcript of Course project of DOE, 2010 spring By Group 11 : 沈坤,孙维,袁怡潇,于漠南,朱雯 1...
1
Experiment on Farthest Throw of Catapult
Course project of DOE, 2010 spring
By Group 11:沈坤,孙维,袁怡潇,于漠南,朱雯
Photo art courtesy: smart_katalog_fortwo_2007.pdf, Daimler AG
Experiment on Farthest Throw of Catapult
2
•Introduction
•Factor Analysis
•Experiment and Analyzing
•Summary
Agenda
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Background• Catapult in history
– Application of the principal of leverage– A tool for attack
How to make it have a launch on the largest distance?
• Catapult in experiment– Composed of a band, a ball, some
bolts and the basic wooden structure
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Objectives
− A statistical model of significant factors in response to the cast distance of the catapult
− The optimal combination of the significant factors to maximize the cast distance
− An estimation of this “optimal distance”
Experiment on Farthest Throw of Catapult
5
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Related Chapters in Textbook
23 full factorial design
Response surface analysis --- The steepest ascent method
Fitting regression model
General linear model
Experiment on Farthest Throw of Catapult
6
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Related Papers
《利用响应曲面法确定竹叶中黄酮最佳提取条件》,冯涛、曹东旭、高辉、季光, 2003 年 6 月,《天津轻工业学院学报》。
《试验设计与优化》,李波、徐泽民、李方、张新申, 2003年 1 月,《中国皮革》。
《 Experiment of washing process 》,于航等。 (五字班 DOE 课程小组大作业报告)
《 An investigation on data entry effectiveness & efficiency 》,张重阳等。
(五字班 DOE 课程小组大作业报告)
Experiment on Farthest Throw of Catapult
7
•Introduction
•Factor Analysis
•Experiment and Analyzing
•Summary
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Response variable
Cast distance of the catapult− Range
0.5 through 3.5 meters Measurement
− band tape + number of floor tires
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Effect factorCatapult
The open angel of the cast armThe position of the apron
Tiredness
Concentration
Put the cast arm to the precise angel
Humidity
Air resistance
The right position of the ball
Temperature
Wind velocity
Put the cast arm to the precise angel
The height of the catapult
The radius of the ball
The precision of the band tape
The front fixture of the band
The back fixture of the band
OperatorMeasurement
CatapultEnvironment
Cast distance of the catapult
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Constant Variables & Noise Variables
Constant Variables
•Humidity•Air resistance•Temperature•Radius of the ball•Height of the catapult •Back fixture of the band
Noise Variables
•Elasticity of the band•Precise angel of arm•Launch orientation•Wind velocity•Vibration•Human factor•Concentration•Tiredness•Accuracy of reading
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Control the interference factor
The reading accuracy
• Two observers each read a value• Use the average to represent the result of that throw
The orientation and initial position of the throw
• Use hand to press the catapult on the ground to avoid vibration• Use the gap line of the tiles to align the catapult and the ruler
The precise angel of arm
• Pay a special attention on the scale mark• Release the arm decidedly and rapidly
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Control VariablesReal factor Range Category Influence Level
Front fixture of the band
1,2,3,4 Discrete Tension of the band 1,3 (a)
Position of the apron
1,2,3,4,5,6 Discrete Angel of the ball 4,6 (b)
Open angel of the cast arm
0~180 degree
Continuous
Cast speed of the ball
160 and180 degree (c)
(a)
(b)
(c)
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Real factor Variable name
Range Category Coded value
— +
Front fixture of the band
A 1,2,3,4 Discrete 1 3
Position of the apron
B 1,2,3,4,5,6 Discrete 4 6
Open angel of the cast arm
C 0~180 degree Continuous 160 180
The 23 factorial design
Replications: 5
Experiment on Farthest Throw of Catapult
14
•Introduction
•Factor Analysis
•Experiment and Analyzing
•Summary
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Factorial Design Qualitative Analysis
Quantitative Analysis
Estimating the Optimal Value
A Special Verification of
“factor B”
General Linear Model
Our experimenting and analyzing process
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
321
600
500
400
300
200
654
180170160A
Dis
tanc
e
B C
Di stance 与 A, B, C 的矩阵图
ABC
316464
180160180160180160180160
600
500
400
300
200
Distance
Di stance 的箱线图
31
500
450
400
350
300
64
180160
500
450
400
350
300
A
平均值
B
C
Di stance 主效应图数据平均值
64 180160
500
400
300
500
400
300
A
B
C
13
A
46
B
Di stance 交互作用图数据平均值
B*A
3. 02. 52. 01. 51. 0
6. 0
5. 5
5. 0
4. 5
4. 0
C*A
3. 02. 52. 01. 51. 0
180
175
170
165
160
C*B
6. 05. 55. 04. 54. 0
180
175
170
165
160
A 1
B 4C 160
保持值
> – –
– – – – < 250
250 300300 350350 400400 450
450 500500 550
550
Di stance
Di stance 的等值线图
B*A
3. 02. 52. 01. 51. 0
6. 0
5. 5
5. 0
4. 5
4. 0
C*A
3. 02. 52. 01. 51. 0
180
175
170
165
160
C*B
6. 05. 55. 04. 54. 0
180
175
170
165
160
A 3B 6C 180
保持值
> – – – – – – < 250
250 300300 350350 400400 450450 500500 550
550
Di stance
Di stance 的等值线图
The qualitative analysis of factors’ effects
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
The further analysis of response surface
We will show the process in Minitab.
Regression model:
When A=1, B=6, C=180 :
C)(B0.642500+ C)(A 1.59750
-C10.3300 +B106.450 -A214.550 +-1288.50=Distance
553.1=180)(60.642500+180)(1 1.59750
-18010.3300 +6106.450 -1214.550 +-1288.50=Distance
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
A GLM between distance and the significant factors and interactions− Resources: A, B, C, AC, BC
The function
The theoretical optimal solution:− Setting A at “1”, B at “6”, C at “180”
General Linear Model
18
Experiment on Farthest Throw of Catapult
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Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Special verification of “B”
Whether or not factor B is significant to Distance− Full factorial design: B is proved to have no significant
effect− General linear model: B’s effect seems to be significant
Advanced analysis: − Based on more data− 10 replications A1 B5
C180
A1 B6 C180
A1 B4 C180
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Data in detail:
Conclusion− B has a slight positive effect to the response variable
Distance Optimal style: A=1, B=6, C=180
Box-plot:
Special verification of “B”, cont
Experiment on Farthest Throw of Catapult
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Under A=1, B=6, C=180 20 replications 95% confidence interval
Our estimation of the “Largest distance”: (544.98, 551.02)
Estimating the Optimal Value
565560555550545540535530
99
95
90
80
70
605040
30
20
10
5
1
Di stance
百分比
均值 548标准差 6. 448N 20AD 0. 315P 值 0. 517
Di stance 的概率图正态
Experiment on Farthest Throw of Catapult
22
•Introduction
•Factor Analysis
•Experiment and Analyzing
•Summary
Experiment on Farthest Throw of Catapult
23
Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Our methodology
1 •Design, and Experiment
2 •Analysis of significant factors•Model (Regression, GML)
3 •Verification of insignificant factor (B)
4 •Estimation of response variable
Experiment on Farthest Throw of Catapult
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Experimenting and AnalyzingFactor AnalysisIntroduction Summary
Our final result
Optimal style: A=1, B=6, C=180
Optimal value: (544.98, 551.02)
Experiment on Farthest Throw of Catapult
25
The End !Thank you!Q & A
Photo art courtesy: smart_katalog_fortwo_2007.pdf, Daimler AG