Using Neural Networks to Predict Dye Concentrations in Multiple-Dye Mixtures

Abstract

A neural network is used to predict the concentrations of three dyes from their spectrophotometric absorbances. With this technique, the network achieves a peak of 5% and an average of 2.6% error over a range of dye concentrations of 0 to 0.15 g/l.The neural network is evaluated against two other models based on Beer's law, and performs significantly better over the entire range of concentrations measured. ' Assistant Professor, College of Textiles. 2 Graduate Student, IMSEI. 3 Graduate Student, College of Textiles.The Dye Applications Research Group ( DARG ) at North Carolina State University is currently investigating approaches to an optimized control system for dyeing fabrics. In order to achieve this goal, the system ( dyebath ) must be closely and accurately monitored to feed information in real-time to the controller [ 1 ] . This paper discusses the use of a neural network to predict concentrations in a multiple dye mixture from spectrophotometric absorbance measurements. ' Discussion of Beer's Law A plot of absorbance versus concentration, often called a &dquo;Beer's law plot,&dquo; is given as where A is the absorbance at a specified wavelength (normally ~m~ ) , a is the specific absorbance or extinction coefficient, I is the path length, and c is the concentration of the dye. This linear behavior is shown graphically in Figure 1 for the three dyes used in the experiment. It is important to remember that the absorbance value A assigned to each dye from this plot is given at one wavelength for each dye-425 nm for yellow, 520 nm for red, and 595 nm for blue dye-the Àmax values for these three dyes. DEVIATIONS FROM BEER'S LAW As the mean particle size of a single absorbing species increases ( usually as the result of increasing the dye or inorganic salt concentration), the solution absorbs less light, and the absorptivity usually decreases at the . wavelength of maximum absorbance [6]. However, fIGURE 1. Boer's law analysis of individual dyes. changes in the dye solubility state due to aggregation and other dye-dye interactions are not as easily characterized [ 5 ] . Therefore, it is insufficient to state that for some wavelengths, the effects of increasing dye or salt concentration will decrease the absorptivity of the dye in solution; changes in absorptivity may be negative or positive depending on which wavelength is being observed. The temperature of the dye solution can also affect the absorptivity of any given dye [ 6 ] .Previous studies have not accounted for heterogeneous dye interactions or changes due to different dye particle sizes increasing at different rates with respect to dye concentration or salt concentration. Classical at Kungl Tekniska Hogskolan / Royal Institute of Technology on August 21, 2015 trj.sagepub.com Downloaded from 546 analytical models predict that the spectrum for a mixture of absorbing species in a solution is equal to the sum of the individual spectra [ 2 ] . ' For mixtures of dyes, however, this assumption cannot be made; the spectra of mixtures of dyes in solutio...

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