(338h) Extended Kalman Filter Based on Generalized Regression Neural Network Simultaneous Determination of 2-Chlorophenol and 4-Chlorophenol

1. Introduction Homologue organics have very similar chemical behavior, and they have been simultaneously determined mainly electrochemically and chromatographically. Among the most widely used analytical methods are those based on the UV-visible spectrophotometry techniques, due to both the simplicity and rapidness of the method 1-6. However, the simultaneous determination of these organics such as phenols and chlorophenols by the use of the traditional spectrophotometry techniques is difficult, since the absorption region and the superimposed curves are not suitable for quantitative evaluation7. In this work, a new correction absorbance relationship of quantitative analysis has been proposed, and nonlinear Kalman Filter based on generalized regression neural network has been applied to chemometrics firstly.

2. Theories and Methods

2.1 Nonlinear Absorbance Relationship: Absorbance had been expressed as A=¦ÅbC= aC in Beer's law, and for binary mixture, the absorbance can be showed as follow

Amix=A1+A2=a1C1+a2C2 (1)

The formula (1) is foundation of spectrophotometry analysis for mixture. the equation is strict true for infinite dilute solution or mixture composed of independent compositions that without any interaction. According to the Beer's law, the simultaneous determination of two or more compositions in the same sample without any previous chemical separations has been developed from several mathematical procedures, such as classical least square(CLS) 8, partial least square(PLS) 9, ratio-derivative spectrophotometry 2, double Fourier transform filtering 3 and linear Kalman filter method(LKF) 10-11, but only a few mixtures could be identified efficaciously. The reason of most of difficult to identify mixture system is ignore of the distortion from interaction, other than from test noise. So the interaction effects in real mixture have un-neglect contributed to total absorbance that should be compensated in the basic analysis equation. Here, for the binary mixture of 2-chlorophenol (2-CP) and 4-chlorophenol (4-CP), the correction formula of nonlinear absorbance can be expressed as

A=¦Á1 C2-CP+¦Á2 C4-CP+¦Á3tanh(C2-CP) +¦Á4tanh(C4-CP) +¦Á5tanh(C2-CP+ C2-CP) (2)

The formula (2) is composed of three parts. The first one is the contribution from two individual compositions. Secondly, described the one's changing by another's being. The last is factor of interactions.

2.2 Extended Kalman Filter (EKF)

R Kalman10 proposed a recursive solution to the discrete-data linear filtering for dealing with problems in satellite orbit determination in 1960, then the Kalman filter was applied to take multicomponent analysis computations by Poulisse H.11 in 1979, and more linear Kalman filter simultaneous determination mixture has been reported later 12. But all the application in chemometrics used the linear Kalman filter that prefer to linear dynamics system. In this work, extended Kalman filter has been applied to dispose of the simultaneous determination problem firstly. For a non-linear dynamics system 13

Xk=f[ Xk -1,k-1] +µ¤[Xk -1,k-1]Wk -1 (3)

Ak=h [ Xk -1,k-1] + Vk (4)

The random variables Wk and Vk represent the process and measurement noise. The nonlinear function h in the measurement equation (4) relates the state Xk to the measurement absorbance Ak EKF calibration coefficient matrix was obtained by generalized regression neural network method.

3. Experimental Reagents and Apparatus: All reagents were of analytical reagent grade. Pgeneral model TU 1901 UV-visible spectrophotometer and 1- cm quartz cells were used for all absorbance measurements. All spectra were recorded from 250nm to 290 nm with a 0.5 nm slit width. All of the experiments were carried out at 25 °æ. Distilled water was used throughout the work.

4. Results and Discussion

Calibration EKF Coefficient Matrix Set: The concentration ranges used to establish the calibration set were 1.00¨C14.00 mg L-1 for 2-CP or 4-CP. a complete set with 30 standard binary mixture samples and 61 wavelengths (260-290nm, split o.5nm) for each mixture sample were made. The objective of this design was to span the concentration of the chemicals in the samples of the calibration set in order to obtain a high level of variability. The generalized regression neural network method was used for the calibration set of extended Kalman filter coefficient matrix. The Jacobian calibration matrix H or µg can be obtained in different wavelength. All the partial relation coefficients are above 0.99, and all simulated confidence levels are above 0.99. The confidence levels are calculated from definition of F distribution, which can be calculated from in-completed Beta function. Nonlinear Kalman Filter Estimated: Figure2 showed fluctuation and convergence processes of EKF estimated calculation for the mixture of 4-CP and 2-CP.

Recovery Test: The EKF results of recovery test in range 260-290nm have been showed in table1. All the data from table.1 compared with results of recovery test from CLS, PLS and linear Kalman filter methods. The errors from ratio derivative methods are too large to complete the recovery test for this binary mixture. Assuredly, the extremely well done recovery test by EKF method is much better than other methods such as CLS, PLS and linear Kalman filter method. We also set the calibration EKF coefficient matrix between 260-285nm as well as 250-280 nm, and recounted the recovery test according to those matrixes respectively. The results are consistent with table 2 stably. That means the experiment has not any relation with the setting of EKF, it is important for an objective test.

Table 1 Recovery values for synthetic mixtures obtained by using EKF

5. Conclusion

(1). The nonlinear absorbance formula for mixture of 2-CP and 4-CP can be expressed as formual 2

(2). This is the first report about extended Kalman filter based on generalized regression neural network has been applied to simultaneous determination for binary mixture.

(3). Extended Kalman filter simultaneous determination of 4-CP and 2-CP is more accurate than CLS, PLS and linear Kalman filter, and its estimated results has no relation with setting of filter.

6. References

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Corresponding Author: Ph.D WANG Leo Qiang, Professor of Chemical Engineering, College of Material Science and Chemical Engineering, Tianjin University of Science and Technology, 13th Street, TEDA, Tianjin 300457, China Tel: 86-22-60601130; Fax: 86-22-88250237 Email: wang_q@tust.edu.cn