1. 燕山大学电气工程学院，河北 秦皇岛 066004
2. Department of Electrical and Computer Engineering, McGill University, QC H3A 2A7, Canada
A Piecewise Mathematical Model for COD Measurement of Water by UV Spectrometry
TIAN Guang-jun1, XU Guang-yao1, TIAN Qing2
1. School of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China
2. Department of Electrical and Computer Engineering, McGill University, QC H3A 2A7, Canada
Abstract：The relationship between the UV absorbance and the COD significantly deviate from the linear relationship when the samples reach a certain concentration(still within the concentration range where Lambert-Beer’s law is often applied)when using UV spectroscopy to analyze COD in water, this phenomenon has been mentioned in many scholars’ literature on UV spectroscopy. In thisregard, the S2000 micro-fiber spectrometer and the PX-2 pulsed xenon lamp of Ocean Optics were selected for experiments in a dark room with a temperature of 20 ℃(±0.5 ℃) and humidity of 35%(±5%),andUV absorption spectra of 34 groups of potassium hydrogen phthalate solutions with COD values of 40～680 mg·L-1 were measured for analytical modeling. The dominant wavelength band was selected by correlation coefficient method combine withthe UV absorption characteristics of the sample, and the dominant wavelength was determined to be 275 nm after compared the dynamic characteristics of the COD-absorbance curves at the second characteristic peak of the ultraviolet absorption spectrum of the sample with the wavelength commonly used in water quality COD analysis. A point-by-point extension method is used, which select robust linear regression and the unary nonlinear least squares regression in low concentration segment and higher concentration segment, respectively, repeated fitting of linear or exponential equations and sliding prediction of the next data point,and the segmentation points of the COD-absorbance relationship model of the low concentration segment and the higher concentration segment are determined to be 300 and 560 mg·L-1, respectively, according to the root mean square error and the relative error,and a low concentration segment model and a higher concentration segment model were obtained. The comparison of the fitting accuracy of the linear or nonlinear model in a low concentration range, higher concentration range and the full concentration range at the dominant wavelength indicates that the linear-exponential segmentation model for the relationship between absorbance and COD of water quality in the range of 40 to 300 mg·L-1 and 300 to 560 mg·L-1 has the highest precision, and the prediction effect on the prediction set samples is better: the prediction root mean square error of the model at low concentration is 4.944 9, 6.768 9 at higher concentration and 5.664 7 overall, the prediction effect is ideal for the prediction set. The research result provides a reference value for the measurement and analysis of water with higher COD by UV spectroscopy.
Key words：Ultraviolet absorption spectrum; COD measurement; Model critical point; Linear-exponential piecewise model
田广军，徐光耀，田 青. 紫外光谱法水体COD测量的线性-指数分段数学模型[J]. 光谱学与光谱分析, 2020, 40(06): 1741-1746.
TIAN Guang-jun, XU Guang-yao, TIAN Qing. A Piecewise Mathematical Model for COD Measurement of Water by UV Spectrometry. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2020, 40(06): 1741-1746.
[1] Storey M V, Van d G B, Burns B P. Water Research, 2011, 45(2): 741.
[2] Kokkali V, Delft W V. TrAC Trends in Analytical Chemistry, 2014, 61: 133.
[3] Guan L, Tong Y, Li J, et al. Optik, 2018, 164: 277.
[4] Figueiró C S M, Bastos de Oliveira D, Russo M R, et al. Aquaculture, 2018, 490: 91.
[5] Carré E, Pérot J, Jauzein V, et al. Water Science & Technology A Journal of the International Association on Water Pollution Research, 2017, 76(3): 633.
[6] Li J C, Huang P J, Hou D B, et al. Applied Mechanics & Materials, 2013, 316-317(1): 606.
[7] Guo X J, Xi B D, Yu H B, et al. Water Science and Technology, 2011, 63(5): 1010.
[8] Chen H, Zheng B. Water Science and Technology, 2012, 65(5): 962.
