• Journal of the Korean Chemical Society
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• v.49 no.6
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• pp.531-536
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• 2005

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.395-403
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• 2002

In the third phase of the response surface methods, the first-order model is assumed and the curvature of the response surface is checked with a fractional factorial design augmented by centre runs. We further assume that a true model is a quadratic polynomial. To choose an optimal design, Box and Draper(1959) suggested the use of an average mean squared error (AMSE), an average of MSE of y(x) over the region of interest R. The AMSE can be partitioned into the average prediction variance (APV) and average squared bias (ASB). Since AMSE is a function of design moments, region moments and a standardized vector of parameters, it is not possible to select the design that minimizes AMSE. As a practical alternative, Box and Draper(1959) proposed minimum bias design which minimize ASB and showed that factorial design points are shrunk toward the origin for a minimum bias design. In this paper we propose a robust AMSE design which maximizes the minimum efficiency of the design with respect to a standardized vector of parameters.

• Korean Journal of Remote Sensing
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• v.33 no.5_1
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• pp.559-570
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• 2017

A partial least squares regression (PLSR) model was developed to map the internal soluble solids content (SSC) of apples using a ground-based hyperspectral scanner that could simultaneously acquire outdoor data and capture images of large quantities of apples. We evaluated the applicability of various preprocessing techniques to construct an optimal prediction model and calculated the optimal band through a variable importance in projection (VIP)score. From the 515 bands of hyperspectral images extracted at wavelengths of 360-1019 nm, 70 reflectance spectra of apples were extracted, and the SSC ($^{\circ}Brix$) was measured using a digital photometer. The optimal prediction model wasselected considering the root-mean-square error of cross-validation (RMSECV), root-mean-square error of prediction (RMSEP) and coefficient of determination of prediction $r_p^2$. As a result, multiplicative scatter correction (MSC)-based preprocessing methods were better than others. For example, when a combination of MSC and standard normal variate (SNV) was used, RMSECV and RMSEP were the lowest at 0.8551 and 0.8561 and $r_c^2$ and $r_p^2$ were the highest at 0.8533 and 0.6546; wavelength ranges of 360-380, 546-690, 760, 915, 931-939, 942, 953, 971, 978, 981, 988, and 992-1019 nm were most influential for SSC determination. The PLSR model with the spectral value of the corresponding region confirmed that the RMSEP decreased to 0.6841 and $r_p^2$ increased to 0.7795 as compared to the values of the entire wavelength band. In this study, we confirmed the feasibility of using a hyperspectral scanner image obtained from outdoors for the SSC measurement of apples. These results indicate that the application of field data and sensors could possibly expand in the future.