Wavelet Neural Network (WNN) is a new neural network model based on wavelet transform and forward multilayer (BP) neural network construction. Theoretical studies have proved that wavelet neural network has stronger information extraction and approximation and fault tolerance than classical multilayer neural network. Discrete wavelet neural network is constructed on the basis of continuous wavelet neural network, and the expansion factor and displacement factor are binary discretized. Its network structure is shown in Figure 1-1. Network training uses error back propagation algorithm, as follows:
Figure 1-1 The structure of discrete wavelet neural network
After the wavelet neural network model is established and trained, the optimal separation conditions can be found, that is, the pH value, CSDS and Curea corresponding to the maximum response function r. Using real number coding, the response value r of the trained WNN model is solved by genetic algorithm. The initial population number generated is 40, and a random number between 0 and 1, the crossover probability (Pc) is 0.5, and the mutation probability (Pm) is 0.01.
The genetic algorithm calculates that the searched rmax after 150 iterations will no longer change to 0.372. The buffer solution conditions corresponding to the optimized point obtained by the search are: SDS 26.4mmol/L, urea 3.75mol/L, and pH value of 10.0. The genetic algorithm repeats the calculation 10 times and all get the same result. From the three-dimensional graph of the variation of r with CSDS and Curea (fixed pH at 10.0, see Figure 2-1), it can also be seen that r is the global maximum here.
Figure 2-1 Response surface graph of r value with the change of urea and SDS concentration
The buffer solution was prepared according to the optimized conditions, and the MEKC separation diagram of 9 amino acids was obtained (see Figure 2-2). At this time, the r value is 0.351, and the relative error from the calculated value is 6.0%, which is the best in the orthogonal design table. Compared with 0.3116 under the conditions, an increase of 12.5%. Under this condition, the 9 amino acids were separated by baseline, and the CE peak distribution was more uniform.
Figure 2-2 MEKC spectra of 9 CEOC derivatized amino acids under optimal conditions
Buffer solution conditions: 25.0 mmol/L borate, 26.4 mmol/L SDS, 3.75 mol/L urea (pH=10.0); separation voltage: 18kV, capillary temperature: 25℃; peak: 1. Serine; 2. Threonine; 3. Alanine; 4. Glycine; 5. Valine; 6. Aspartic acid; 7. Glutamic acid; 8. Methionine; 9. Leucine.
According to the existing reports of CE chiral separation of adrenaline, Tris concentration (x1), buffer solution pH (x2), chiral reagent DM-β-CD concentration (x3) and separation voltage (x4) are selected as experimental optimization Parameters. It is necessary to select an appropriate experimental design method to arrange separation optimization experiments. Here we choose the uniform design method to arrange the experiment. x1 ranges from 10.0 to 50.0 mmol/L, x2 ranges from 2.5 to 4.5, x3 ranges from 5.0 to 45.0 mmol/L, and x4 ranges from 12.0 to 24.0 kV. Each experimental parameter takes 6 levels of change, and the U12 (1210) table is used to arrange the experiment (see Table 3-1). The number of experiments is twice the number of levels of each parameter. The number of experiments for each factor is expanded to 2 times, so that a total of Need 12 experiments.
For response indicators that need to minimize migration time, reverse unilateral conversion is performed. For the detection and analysis of optical isomer impurities of chiral drugs, if 0.1% impurities are to be detected, the resolution must be above 2.5, and the expected target value of resolution is 3.0. In this way, the response indicators R, t2, and h2 are converted into corresponding partial power functions d1 , d2, and d3, respectively . Once the local power function of each response index is obtained, the total power function D can be calculated : D=(d1 ´ d2 ´ d3)1/3.
According to the above process, the optimization model between D and each experimental parameter is established, and the multi-index optimization problem is transformed into the maximum value of D and the corresponding experimental conditions. The D value and the corresponding calculated value are obtained from the uniform design experiment. Except for experimental points 2 and 5, the relative errors of the other experimental points are all within 10%.
The parameters of the genetic algorithm are optimized. The initial population is selected as 80, and a random number between 0 and 1 is assigned. The crossover probability is 0.5 and the mutation probability is 0.8. The genetic algorithm is used to optimize the iterative process. When the iterative calculation reaches 200 times, Dmax has tended to converge and no longer changes. The genetic algorithm is a random search algorithm. The Dmax obtained each time is different, but both are between 0.9370 and 0.9382. The maximum relative difference is only 0.13%, which is much lower than the error of the established model. It can be considered as the multi-index hand of adrenaline. There are many optimal experimental conditions in the separation of sexual CE. The three optimal separation conditions calculated by GA are: (1) Tris concentration is 48.7 mmol/L , pH=3.91, DM-β-CD concentration is 15.1 mmol/L, D is 0.9382 ; (2) Tris concentration Is 42.7 mmol/L , pH=3.23, DM-β-CD concentration is 12.3 mmol/L, D is 0.9375 ; (3) Tris concentration is 42.2 mmol/L , pH=2.5, DM-β-CD concentration is 5.0 mmol /L, D is 0.9370 . The three separation voltages are all 24 kV, which is the maximum value allowed in the experimental design.
Take the obtained optimal separation condition 1 as an example, the fixed separation voltage is 24 kV, the Tris concentration is 48.7 mmol/L, and the contour map of the fitted total power function against pH and DM-β-CD concentration is made (Figure 3 -2) It can be seen from the figure that the value of D obtained under this condition is the global maximum.
Figure 3-3 Capillary electrophoresis separation spectrum of adrenaline enantiomers
(a): 15.1 mmol/L DM-β-CD in Tris-H3PO4 buffer pH 3.91, applied voltage 24.0 kV;
(b): 13 mmol/L DM-β-CD in 34 mM Tris-H3PO4 buffer pH 2.9, applied voltage 16.8 kV.