Identification of Chinese Medicinal Materials in Question E of the 2021 Higher Education Society Cup National Undergraduate Mathematical Contest in Modeling

The spectral characteristics of different Chinese medicinal materials are quite different. Even the same medicinal material from different origins will show different spectral characteristics under the irradiation of near-infrared and mid-infrared spectra due to the differences in the chemical composition of inorganic elements and organic matter. Spectral characteristics, so these characteristics can be used to identify the type and origin of Chinese herbal medicines.
It is relatively easy to identify the types of Chinese herbal medicines, and the differences in the spectra of different types of Chinese herbal medicines are obvious. Figure 1 is a graph of the near-infrared spectral data of two different medicinal materials, and it is easy to see that the difference between the two is relatively large.
The authenticity of Chinese medicinal materials is mainly based on the place of origin, and the identification of the place of origin is particularly important for the quality identification of medicinal materials. However, the spectra of the same medicinal material from different origins in the same band are relatively close, which leads to large errors in spectral identification. In addition, the near-infrared difference of some Chinese medicinal materials is more obvious, while the difference of some medicinal materials is more obvious in the mid-infrared (see Figure 2 and Figure 3 for the near-infrared and mid-infrared spectral data curves from 5 different origins of a certain medicinal material) . When the sample size is not sufficient, we can comprehensively identify the origin of Chinese medicinal materials through mutual verification of near-infrared and mid-infrared spectral data.
Attachments 1 to 4 are the near-infrared or mid-infrared spectral data of some Chinese medicinal materials, where the No column is the serial number of the medicinal material, the Class column indicates the category of the Chinese medicinal material, the OP column indicates the origin of the medicinal material, and the first row of the remaining columns The data is the wave number of the spectrum ( unit cm -1 ) , and the data after the second row indicates the absorbance of the medicinal material with the number in this row under the irradiation of the corresponding band spectrum (Note: the absorbance is the corrected value of the instrument, and there may be negative values). Try to build a mathematical model to study and solve the following problems.
Question 1. Based on the mid-infrared spectral data of several medicinal materials in Annex 1 , study the characteristics and differences of different types of medicinal materials, and identify the types of medicinal materials.
Question 2. According to the mid-infrared spectral data of a certain medicinal material in Annex 2, analyze the characteristics and differences of medicinal materials from different origins, try to identify the origin of medicinal materials, and fill in the identification results of the origins of medicinal materials with numbers given in the table below in the form.
Question 3. According to the near-infrared and mid-infrared data of a certain medicinal material in Appendix 3, try to identify the origin of the medicinal material, and fill in the identification results of the origin of the medicinal material numbered in the table below .

 

Question 4. Attachment 4 gives the near-infrared spectral data of several medicinal materials. Try to identify the category and origin of the medicinal materials, and fill in the identification results of the categories and origins of the medicinal materials given in the table below.

 

 

 

 

Note 1. For information on authentic herbs, please refer to Baidu Encyclopedia ( https://baike.baidu.com/item/Authentic herbs/1950482?fr=aladdin) .
Note 2. For information on infrared spectroscopy, please refer to Baidu Encyclopedia ( https://baike.baidu.com/item/infrared spectroscopy).

 

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