9. 科学的方法
F. James Rutherford and Andrew Ahlgren, Science for All Americans , 1989
1. 物事を調査し、結果を整理し、新
たな知見を導き出し、知見の正し
さを立証するまでの手続きであっ
て、(仮説検証)
2. その手続きがある一定の基準を満
たしているもののことである。
(査読)
研究の世界入門B
21. RSM : Response Surface Methodology
• A response surface approximates a response y which
is estimated using n design variables(x1,x2,…,xn) as
– y=f(x1,x2,…,xn) + ε
• There is no restriction on the function form, and
quadratic polynomial functions are often employed
• RSM is applied to an optimization of a product
development process or an decrease in dispersion
研究の世界入門B
22. Construction of a response surface
using a least square method
• A response surface approximates a response y
which is estimated using two design
variables(x1,x2) as
– y=β0+ β1x1 + β2x2 + β3x12 + β4x22 + β5x1x2
• A substitution is made as
– x12 =x3 x22 =x4 x1x2 =x5
– y=β0+ β1x1 + β2x2 + β3x3 + β4x4 + β5x5
Coefficients(β0 β1β2 β3β4β5) are estimated from more
than six design points (y, x1 x2 x3 x4 x5)
研究の世界入門B
24. Estimation of a coefficient vector β
• The coefficient vector which minimizes the squared error
summation is estimated as
L ( y X )T ( y X )
T
( yT T X T )( y X ) yT y T X T y yT X T X T X
y y 2 X y X X
T T T T T
L
2 X T y 2 X T X b 0
b
yT y 2 T X T y ( X )T X
b = (XTX)-1XTy
研究の世界入門B
25. A model construction process using RSM
Set a parameter range
応答値
Select design points x2 x1
0
Calculate responses
Estimate a surface Min
x2 x1
Calculate a minimum 0
研究の世界入門B
27. Exercise using a climate dataset
• Obtain a dataset on average temperature from a climate data server in Japan
Meteorological temperature Agency
(http://www.data.jma.go.jp/obd/stats/etrn/index.phpe )
• Construct a response surface of the which is estimated using two design
variables(Longitude, Latitude)
• Estimate a Longitude and a Latitude which minimize the temperature
• Specify a location using the estimated Longitude and Latitude in Google map
• Obtain an average temperature at the specified location to confirm the accuracy
Average temperature at Dec. 1, 2000 緯度 経度
盛岡 -0.3 39.69833 141.165
仙台 3.6 38.26167 140.8967
青森 0.5 40.82167 140.7683
山形 3.2 38.255 140.345
秋田 2.7 39.71667 140.0983
福島 4.5 37.75833 140.47
角館 0.9 39.60333 140.5567
八戸
研究の世界入門B -0.1 40.52667 141.5217