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Abstract The principal component method is to recombine multiple correlated indexes into a group of noncorrelated comprehensive indexes to replace the original indexes for evaluation. The paper took the test data of growth and development of Euproctis pseudoconspersa Strand as a basis and used the principal component analysis method to analyze and investigate the test data. The research results indicate that the principal component analysis method is a model with actual operation value and evaluation reliability. When the electromagnetic radiation is higher than 100 K， the growth and development indexes of E. pseudoconspersa Strand are correlated to electromagnetic radiation frequency to some extent.
Key words Electromagnetic radiation; Euproctis pseudoconspersa Strand; Growth and development
Euproctis pseudoconspersa Strand is one of the important leafeating pests in Chinaюs tea region. It may bring a tea loss of 10%-30%， and even up to 60% sometimes， which is a great economic loss to tea garden. The control of E. pseudoconspersa Strand includes artificial trap method， medical control， pesticide and other biological control methods[1-3]. However， in numerous control technologies， there is no one using electrostatic interaction and electromagnetic radiation to control[4-5]. This paper aimed to use electromagnetic radiation technology and principal component analysis method[6-10]to analyze and study the test data of the growth and development of E. pseudoconspersa Strand. The principal component method is a simulation method to reintegrate multiple correlated indexes into a group of uncorrelated comprehensive indexes to replace the original indexes for evaluation. It has been widely applied in various evaluation system， such as the economic benefit of industrial enterprises[11-13]， comprehensive evaluation of road system and water resource carrying capacity.
Data Source and Research Method
All data used in this paper originate from the exploring experiments to investigate the effect of electromagnetic radiation on the growth and development of E. pseudoconspersa Strand. The basic condition and specific operations of this experiment were as below：
（1） The object of electromagnetic radiation was the overwintering egg mass of E. pseudoconspersa Strand. Four groups of electromagnetic wave with different frequencies were used to irradiate the overwintering egg mass of E. pseudoconspersa Strand for the same time， and a control group was set. （2） Culture conditions： Temperature at 30， with amplitude of variation of ÷2; relative humidity of 76%-82%; photoperiod of L≥D=12≥12.
（3） Test observation： After radiation process， the culture dishes with egg mass were placed in insect raising cage for culture and observation. The observation indexes included the egg incubation process， incubation rate， growth rate， pupation progress， eclosion progress and pupaюs biological characteristics of E. pseudoconspersa Strand at each instar， which are summarized in Fig. 1-Fig. 4 as below.
Due to large experimental observation data size， the data in Table 1 were average values obtained through statistics and processing. On basis of these data， the principal component analysis method was used to analyze the main observation indexes of the effect of electromagnetic radiation on the growth and development of E. pseudoconspersa Strand.
Processing Steps of Principal Component Analysis Method
The principal component analysis method was taken by this paper as the main method in data research， and its specific processing steps are as below：
Step 1： Standardize the statistic data.
The characteristic values with a cumulative contribution rate greater than 0.98 and their relative principal components were selected， and the number of principal components to be retained was determined， that is， the main impact index of electromagnetic radiation on the growth and development of tea caterpillar.
Step 5： Solve the loads of each principal component.
The calculation formula is：
Principal Component Analysis
It was known from the original statistic data in Table 1 that， there were 10 indexes for evaluating the effect of electromagnetic wave radiation of different frequencies on the growth and development of E. pseudoconspersa Strand： X1Daily growth rate of larva， X2Daily growth rate of pupa， X3Daily growth rate of adult， X4Hatching rate （H%， X5Average body length of female pupa， X6Average body length of male pupa， X7Pupation rate of female pupa（P%）， X8Pupation rate of male pupa（P%）， X9Eclosion rate of female pupa（E%）， and X10Eclosion rate of male pupa（E%）. These 10 indexes indicated the different evaluation of the growth and development stages of E. pseudoconspersa Strand under electromagnetic radiation.
The original data in Table 1 were standardized by programming through Matlab software[14-17]， and then the correlated coefficient matrix R among various indexes were worked out， as shown in Table 1. The eigenvalue and accumulative contribution rate of correlated coefficient matrix among various indexes were worked out， as shown in Table 2.
Here， in order to show the comprehensive degree of principal components， the paper selected the components when the accumulative contribution rate of variance is larger than 98% as the principal components， i.e.， two principal components were reserved， denoted as Y1 and Y2. Then， the corresponding eigenvectors of previous two characteristic roots could be figured out， as shown in Table 3.
Thatюs to say， the corresponding eigenvectors of characteristic roots Y1 and Y2 of two principal components were： e1=（-0.317， -0.321， -0.319， 0.314， 0.314， 0.293， 0.321， 0.317， 0.314， 0.319）， e2=（0.252， 0.069， 0.265， 0.240， 0.314， -0.742， 0.061， 0.191， 0.205， 0.270）.
Thereby， the linear relationships between the two principal components and various indexes were acquired as below：
Y1=-0.317X1-0.321X2-0.319X3+0.314X4+0.314X5+0.293X6+0.321X7+0.317X8+0.314X9+0.319X10 （1）
Y2=0.252X1+0.069X2+0.265X3+0.240X4+0.314X5-0.742X6+0.061X7+0.191X8+0.205X9+0.270X10 （2）
The factor load matrix of two principal components was calculated， as shown in Table 4.
It can be obtained from the eigenvalue and accumulative contribution rate of coefficient matrix R in Table 2 that， the principal indexes that can comprehensively evaluate the effect of electromagnetic radiation on the growth and development of E. pseudoconspersa Strand[18-20]were the first two principal components， which had the accumulative contribution rate reaching 98.56%. The proportion of each principal componentsю contribution rate is shown in Fig. 5. At the same time， from the factor load matrix of these two principal components （as shown in Table 4）， the role and importance degree of each evaluation index in principal components can be inferred. The factor lad matrix of principal component was mainly the correlated coefficient between principal components and various variables， which can reflect the weight proportion of each variable in principal components to some extent.
It was obtained from Fig. 1 that the first principal component Y1 covered a contribution rate of 96%， so it was the key control factor of comprehensive evaluation indexes. By reference to some practices in other researches， in order to more intuitively reflect the correlation between each evaluation index and principal components， the paper transformed the negative value in factor load matrix of principal components into positive value for analysis. Integrating with Table 4， it was able to get that the coefficients of main factors （Y1） to constitute the first principal component were similar. Thatюs to say， the first principal component could reflect the information of all evaluation indexes， particularly the index X7Pupation rate of female pupa. However， the second principal component covered a contribution rate of 3%. From Table 4， the main factor to constitute the second principal component was X6Average body length of male pupa， which significantly decreased compared with the comprehensive degree of the first principal component. From Table 4， X1， X2 and X3 were negatively correlated with the first principal component. The larger the values of X1， X2 and X3 were， the higher the influence degree of electromagnetic radiation on the growth and development of E. pseudoconspersa Strand. Combined with original statistic data， the value of X3 rose with the increase of electromagnetic radiation frequency， and when the electromagnetic radiation frequency ascended from 100 K to 10 M， the values of X1 and X2 became bigger and bigger， which conformed to the analytic result. However， the values of X1 and X2 in the control group （without electromagnetic radiation） were larger than the data under electromagnetic radiation of 10 K， which did not conform to the analytic result. The reasons for this small error might be：
（1） the experimental conditions were not controlled strictly. The statistic data of X1Larval development rate and X2Pupal day development rate in the control group were interfered by surrounding dielectric electromagnetic wave.
（2） the data given in Table 1 were average values processed， which might have calculating error;
（3） the principal component method is a simulation method to integrate multiple indexes into less indexes， which might have error in accurate statistics.
Results and Discussion
The principal component analysis method has been widely applied in many fields. In the handing and evaluation analysis of some biological experimental data， the principal component analysis method is also a model of actual operating value and evaluation reliability. On one hand， the principal component analysis method can synthesize and simplify the 10 evaluation indexes of the growth and development of E. pseudoconspersa Strand into two indexes. On the other hand， through principal component analysis， it was able to obtain the factor load of each index and clearly know the relation between different electromagnetic radiation frequencies and indexes， and the analytic result was good for inferring and verifying the standard of test operation and data reliability.
References
[1]SONG T， HUO XL， WU SZ. Bio electromagnetic properties and Applications[M]. Beijing： Beijing University of Technology press， 2008.
[2]ANTONY， BINU1. Detection of nucleopolyhedroviruses in the eggs and caterpillars of tea looper caterpillar Hyposidra infixaria （Walk.） （Lepidoptera： Geometridae） as evidence of transovarial transmission[J]. Archives of Phytopathology and Plant Protecton， 2014， 47： 1426-1430. [3]WANG YG. Problems should be paid attention to in tea plant pest control[J]. Yunnan Agricultural Science and Technology， 2002 （S1）： 218-219.
[4]WU H， WANG DW， WANG SM， et al. Effects of electromagnetic radiation on rat Sertoli cells in vitro[J]. Acta Biophysica Sinica， 2011， 27（1）： 38-46.
[5]WANG BZ. Computational electromagnetics[M]. Beijing： Science Press， 2002.
[6]TANG P， ZHANG HD， YE TH， et al. A novel method for chemistry tabulation of strained premixed/stratified flames based on principal componentanalysis[J]. Applied Mathematics and Mechanics （English Edition）， 2018， 39（6）： 855-866.
[7]FANG KN， FAN XY， ZHANG QZ， et al. Integrative sparse principal component analysis[J]. Journal of Multivariate Analysis， 2018， 166： 1-16.
[8]YONATHAN AFLALO， Ron KIMMEL. Regularized principal component analysis[J]. Chinese Annals of Mathematics， Series B， 2017， 38（1）： 1-12.
[9]RAYKOV TENKO， MARCOULIDES GEORGE A， LI TENGLONG. On the fallibility of principal components in research[J]. Educational and Psychological Measurement， 2017， 7（1）： 165-178.
[10]ZHAO LL. Generalised principal component analysis[J]. International Statistical Review， 2016， 84（3）： 554.
[11]WANG L， CHEN L， MA Q. Rabbit whole blood cell impedance frequency characteristic[J]. Journal of Zhejiang University （Medical Sciences）， 2009， 38（4）： 57-60
[12] ZHOU X， XIAO BG， ZHENG GC. Complete mitochondrial genome of the tea looper caterpillar， Ectropis obliqua （Lepidoptera： Geometridae） with a phylogenetic analysis of Geometridae[J]. Int J Biol Macromol， 2018.
[13]SHUAI CJ， JIA HE， XIE XC， et al. Effect of electromagnetic exposure at difference frequencies on Euproctis pseudoconspersaюs growth and development at different stages[J]. Journal of Chemical and Pharmaceutical Research， 2014， 6： 1072-1076.
[14]SHUAI CJ， NIE X， HE W. Influence of electromagnetic irradiation on grow and develop of tea caterpillars based on principal component analysis method[J]. Journal of Shaanxi University of Technology： Natural Science Edition， 2014， 30（3）.
[15]SOLOVюYOV IA， CHANDLER DE， SCHULTEN K. Magnetic field effects in Arabidopsis thaliana cryptochrome1[J]. Biophysical Journal， 2007， 92 （8）： 2711-2726.
[16]SONG SH， MARCO ANTONELLI， TONY WK， et al. Developing and assessing MATLAB exercises for active concept learning[J]. IEEE Transactions on Education， 2018： 1-9.
[17]LEE TSUNGLIN， LI TIENYIEN， ZENG ZG. RankRev： A Matlab package for computing the numerical rank and updating/downdating[J]. Numer. Algorithms， 2018， 77（2）： 559-576.
[18]ROSA DS， BLANCA M. Study of the interaction between biological cells of different shapes and sizes and electromagnetic fields produced by natural phenomena[J]. Natural Hazards， 2004， 31 （1）： 143-156.
[19]XI G， SONG Q， YANG CP. Research progress about effect of Ab nomal electromagnetic field on biological system[J]. Chinese Journal of Applied and Environmental Biology， 2003， 9（2）： 203-206.
[20]WU H， WANG DW， WANG SM， et al. Effects of electromagnetic radiation on rat Sertoli cells in vitro[J]. ActaBiophysica Sinica， 2011， 27（1）： 38-46.
Key words Electromagnetic radiation; Euproctis pseudoconspersa Strand; Growth and development
Euproctis pseudoconspersa Strand is one of the important leafeating pests in Chinaюs tea region. It may bring a tea loss of 10%-30%， and even up to 60% sometimes， which is a great economic loss to tea garden. The control of E. pseudoconspersa Strand includes artificial trap method， medical control， pesticide and other biological control methods[1-3]. However， in numerous control technologies， there is no one using electrostatic interaction and electromagnetic radiation to control[4-5]. This paper aimed to use electromagnetic radiation technology and principal component analysis method[6-10]to analyze and study the test data of the growth and development of E. pseudoconspersa Strand. The principal component method is a simulation method to reintegrate multiple correlated indexes into a group of uncorrelated comprehensive indexes to replace the original indexes for evaluation. It has been widely applied in various evaluation system， such as the economic benefit of industrial enterprises[11-13]， comprehensive evaluation of road system and water resource carrying capacity.
Data Source and Research Method
All data used in this paper originate from the exploring experiments to investigate the effect of electromagnetic radiation on the growth and development of E. pseudoconspersa Strand. The basic condition and specific operations of this experiment were as below：
（1） The object of electromagnetic radiation was the overwintering egg mass of E. pseudoconspersa Strand. Four groups of electromagnetic wave with different frequencies were used to irradiate the overwintering egg mass of E. pseudoconspersa Strand for the same time， and a control group was set. （2） Culture conditions： Temperature at 30， with amplitude of variation of ÷2; relative humidity of 76%-82%; photoperiod of L≥D=12≥12.
（3） Test observation： After radiation process， the culture dishes with egg mass were placed in insect raising cage for culture and observation. The observation indexes included the egg incubation process， incubation rate， growth rate， pupation progress， eclosion progress and pupaюs biological characteristics of E. pseudoconspersa Strand at each instar， which are summarized in Fig. 1-Fig. 4 as below.
Due to large experimental observation data size， the data in Table 1 were average values obtained through statistics and processing. On basis of these data， the principal component analysis method was used to analyze the main observation indexes of the effect of electromagnetic radiation on the growth and development of E. pseudoconspersa Strand.
Processing Steps of Principal Component Analysis Method
The principal component analysis method was taken by this paper as the main method in data research， and its specific processing steps are as below：
Step 1： Standardize the statistic data.
The characteristic values with a cumulative contribution rate greater than 0.98 and their relative principal components were selected， and the number of principal components to be retained was determined， that is， the main impact index of electromagnetic radiation on the growth and development of tea caterpillar.
Step 5： Solve the loads of each principal component.
The calculation formula is：
Principal Component Analysis
It was known from the original statistic data in Table 1 that， there were 10 indexes for evaluating the effect of electromagnetic wave radiation of different frequencies on the growth and development of E. pseudoconspersa Strand： X1Daily growth rate of larva， X2Daily growth rate of pupa， X3Daily growth rate of adult， X4Hatching rate （H%， X5Average body length of female pupa， X6Average body length of male pupa， X7Pupation rate of female pupa（P%）， X8Pupation rate of male pupa（P%）， X9Eclosion rate of female pupa（E%）， and X10Eclosion rate of male pupa（E%）. These 10 indexes indicated the different evaluation of the growth and development stages of E. pseudoconspersa Strand under electromagnetic radiation.
The original data in Table 1 were standardized by programming through Matlab software[14-17]， and then the correlated coefficient matrix R among various indexes were worked out， as shown in Table 1. The eigenvalue and accumulative contribution rate of correlated coefficient matrix among various indexes were worked out， as shown in Table 2.
Here， in order to show the comprehensive degree of principal components， the paper selected the components when the accumulative contribution rate of variance is larger than 98% as the principal components， i.e.， two principal components were reserved， denoted as Y1 and Y2. Then， the corresponding eigenvectors of previous two characteristic roots could be figured out， as shown in Table 3.
Thatюs to say， the corresponding eigenvectors of characteristic roots Y1 and Y2 of two principal components were： e1=（-0.317， -0.321， -0.319， 0.314， 0.314， 0.293， 0.321， 0.317， 0.314， 0.319）， e2=（0.252， 0.069， 0.265， 0.240， 0.314， -0.742， 0.061， 0.191， 0.205， 0.270）.
Thereby， the linear relationships between the two principal components and various indexes were acquired as below：
Y1=-0.317X1-0.321X2-0.319X3+0.314X4+0.314X5+0.293X6+0.321X7+0.317X8+0.314X9+0.319X10 （1）
Y2=0.252X1+0.069X2+0.265X3+0.240X4+0.314X5-0.742X6+0.061X7+0.191X8+0.205X9+0.270X10 （2）
The factor load matrix of two principal components was calculated， as shown in Table 4.
It can be obtained from the eigenvalue and accumulative contribution rate of coefficient matrix R in Table 2 that， the principal indexes that can comprehensively evaluate the effect of electromagnetic radiation on the growth and development of E. pseudoconspersa Strand[18-20]were the first two principal components， which had the accumulative contribution rate reaching 98.56%. The proportion of each principal componentsю contribution rate is shown in Fig. 5. At the same time， from the factor load matrix of these two principal components （as shown in Table 4）， the role and importance degree of each evaluation index in principal components can be inferred. The factor lad matrix of principal component was mainly the correlated coefficient between principal components and various variables， which can reflect the weight proportion of each variable in principal components to some extent.
It was obtained from Fig. 1 that the first principal component Y1 covered a contribution rate of 96%， so it was the key control factor of comprehensive evaluation indexes. By reference to some practices in other researches， in order to more intuitively reflect the correlation between each evaluation index and principal components， the paper transformed the negative value in factor load matrix of principal components into positive value for analysis. Integrating with Table 4， it was able to get that the coefficients of main factors （Y1） to constitute the first principal component were similar. Thatюs to say， the first principal component could reflect the information of all evaluation indexes， particularly the index X7Pupation rate of female pupa. However， the second principal component covered a contribution rate of 3%. From Table 4， the main factor to constitute the second principal component was X6Average body length of male pupa， which significantly decreased compared with the comprehensive degree of the first principal component. From Table 4， X1， X2 and X3 were negatively correlated with the first principal component. The larger the values of X1， X2 and X3 were， the higher the influence degree of electromagnetic radiation on the growth and development of E. pseudoconspersa Strand. Combined with original statistic data， the value of X3 rose with the increase of electromagnetic radiation frequency， and when the electromagnetic radiation frequency ascended from 100 K to 10 M， the values of X1 and X2 became bigger and bigger， which conformed to the analytic result. However， the values of X1 and X2 in the control group （without electromagnetic radiation） were larger than the data under electromagnetic radiation of 10 K， which did not conform to the analytic result. The reasons for this small error might be：
（1） the experimental conditions were not controlled strictly. The statistic data of X1Larval development rate and X2Pupal day development rate in the control group were interfered by surrounding dielectric electromagnetic wave.
（2） the data given in Table 1 were average values processed， which might have calculating error;
（3） the principal component method is a simulation method to integrate multiple indexes into less indexes， which might have error in accurate statistics.
Results and Discussion
The principal component analysis method has been widely applied in many fields. In the handing and evaluation analysis of some biological experimental data， the principal component analysis method is also a model of actual operating value and evaluation reliability. On one hand， the principal component analysis method can synthesize and simplify the 10 evaluation indexes of the growth and development of E. pseudoconspersa Strand into two indexes. On the other hand， through principal component analysis， it was able to obtain the factor load of each index and clearly know the relation between different electromagnetic radiation frequencies and indexes， and the analytic result was good for inferring and verifying the standard of test operation and data reliability.
References
[1]SONG T， HUO XL， WU SZ. Bio electromagnetic properties and Applications[M]. Beijing： Beijing University of Technology press， 2008.
[2]ANTONY， BINU1. Detection of nucleopolyhedroviruses in the eggs and caterpillars of tea looper caterpillar Hyposidra infixaria （Walk.） （Lepidoptera： Geometridae） as evidence of transovarial transmission[J]. Archives of Phytopathology and Plant Protecton， 2014， 47： 1426-1430. [3]WANG YG. Problems should be paid attention to in tea plant pest control[J]. Yunnan Agricultural Science and Technology， 2002 （S1）： 218-219.
[4]WU H， WANG DW， WANG SM， et al. Effects of electromagnetic radiation on rat Sertoli cells in vitro[J]. Acta Biophysica Sinica， 2011， 27（1）： 38-46.
[5]WANG BZ. Computational electromagnetics[M]. Beijing： Science Press， 2002.
[6]TANG P， ZHANG HD， YE TH， et al. A novel method for chemistry tabulation of strained premixed/stratified flames based on principal componentanalysis[J]. Applied Mathematics and Mechanics （English Edition）， 2018， 39（6）： 855-866.
[7]FANG KN， FAN XY， ZHANG QZ， et al. Integrative sparse principal component analysis[J]. Journal of Multivariate Analysis， 2018， 166： 1-16.
[8]YONATHAN AFLALO， Ron KIMMEL. Regularized principal component analysis[J]. Chinese Annals of Mathematics， Series B， 2017， 38（1）： 1-12.
[9]RAYKOV TENKO， MARCOULIDES GEORGE A， LI TENGLONG. On the fallibility of principal components in research[J]. Educational and Psychological Measurement， 2017， 7（1）： 165-178.
[10]ZHAO LL. Generalised principal component analysis[J]. International Statistical Review， 2016， 84（3）： 554.
[11]WANG L， CHEN L， MA Q. Rabbit whole blood cell impedance frequency characteristic[J]. Journal of Zhejiang University （Medical Sciences）， 2009， 38（4）： 57-60
[12] ZHOU X， XIAO BG， ZHENG GC. Complete mitochondrial genome of the tea looper caterpillar， Ectropis obliqua （Lepidoptera： Geometridae） with a phylogenetic analysis of Geometridae[J]. Int J Biol Macromol， 2018.
[13]SHUAI CJ， JIA HE， XIE XC， et al. Effect of electromagnetic exposure at difference frequencies on Euproctis pseudoconspersaюs growth and development at different stages[J]. Journal of Chemical and Pharmaceutical Research， 2014， 6： 1072-1076.
[14]SHUAI CJ， NIE X， HE W. Influence of electromagnetic irradiation on grow and develop of tea caterpillars based on principal component analysis method[J]. Journal of Shaanxi University of Technology： Natural Science Edition， 2014， 30（3）.
[15]SOLOVюYOV IA， CHANDLER DE， SCHULTEN K. Magnetic field effects in Arabidopsis thaliana cryptochrome1[J]. Biophysical Journal， 2007， 92 （8）： 2711-2726.
[16]SONG SH， MARCO ANTONELLI， TONY WK， et al. Developing and assessing MATLAB exercises for active concept learning[J]. IEEE Transactions on Education， 2018： 1-9.
[17]LEE TSUNGLIN， LI TIENYIEN， ZENG ZG. RankRev： A Matlab package for computing the numerical rank and updating/downdating[J]. Numer. Algorithms， 2018， 77（2）： 559-576.
[18]ROSA DS， BLANCA M. Study of the interaction between biological cells of different shapes and sizes and electromagnetic fields produced by natural phenomena[J]. Natural Hazards， 2004， 31 （1）： 143-156.
[19]XI G， SONG Q， YANG CP. Research progress about effect of Ab nomal electromagnetic field on biological system[J]. Chinese Journal of Applied and Environmental Biology， 2003， 9（2）： 203-206.
[20]WU H， WANG DW， WANG SM， et al. Effects of electromagnetic radiation on rat Sertoli cells in vitro[J]. ActaBiophysica Sinica， 2011， 27（1）： 38-46.