mws_che_reg_txt_nonlinearmodel_examples

mws_che_reg_txt_nonlinearmodel_examples - Chapter 06.04...

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06.04.1 Chapter 06.04 Nonlinear Models for Regression-More Examples Chemical Engineering Example 1 Below is given the FT-IR (Fourier Transform Infra Red) data of a 1:1 (by weight) mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC). Absorbance P is given as a function of wavenumber, m . Table 1 Absorbance as a function of wavenumber. Wavenumber, m ( 1 cm ) Absorbance, P (arbitrary unit) 804.184 0.1591 827.326 0.0439 846.611 0.0050 869.753 0.0073 889.038 0.0448 892.895 0.0649 900.609 0.1204 Regress the above data to a second order polynomial 2 2 1 0 m a m a a P Find the absorbance at 1 cm 1000 m Solution Table 2 shows the summations needed for the calculations of the constants of the regression model.
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06.04.2 Chapter 06.04 Table 2 Summations for calculating constants of model. i Wavenumber, m ( 1 cm ) Absorbance, P (arbitrary unit) 2 m 3 m 4 m P m P m 2 1 804.18 0.1591 6.4671 5 10 5.2008 8 10 4.1824 11 10 127.95 1.0289 5 10 2 827.33 0.0439 6.8447 5 10 5.6628 8 10 4.6849 11 10 36.319 3.0048 4 10 3 846.61 0.0050 7.1675 5 10 6.0681 8 10 5.1373 11 10 4.233 3.583 3 10 4 869.75 0.0073 7.5647 5 10 6.5794 8 10 5.7225 11 10 6.349 5.522 3 10 5 889.04 0.0448 7.9039 5 10 7.0269 8 10 6.2471 11 10 39.828 3.5409 4 10 6 892.90 0.0649 7.9726 5 10 7.1187 8 10 6.3563 11 10 57.948 5.1742 4 10 7 900.61 0.1204 8.1110 5 10 7.3048 8 10 6.5787 11 10 108.43 9.7655 4 10 7 1 i 6030.4 0.4454 5.2031 6 10 4.4961 9 3.8909 12 10 381.06 3.2685 5 10 2 2 1 0 m a m a a P is the quadratic relationship between the absorbance and the wavenumber where the coefficients 0 a , 1 a , 2 a are found as follows n i i i n i i i n i i n i i n i i n i i n i i n i i n i i n i i n i i P m P m P a a a m m m m m m m m n 1 2 1 1 2 1 0 1 4 1 3 1 2 1 3 1 2 1 1 2 1 7 n 3 7 1 10 0304 . 6 i i m 6 7 1 2 10 2031 5
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_che_reg_txt_nonlinearmodel_examples - Chapter 06.04...

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