Xianping WANG,Guishou CAO,Xiaohua YANG,Qianru ZHANG,Kai LI,Hongyan LI,Zemin DUAN

Pomology Institute,Shanxi Academy of Agricultural Sciences/Shanxi Provincial Key Laboratory of Fruit Germplasm Innovation and Utilization,Taiyuan 030031,China

Study on the Model of Excessive Staminate Catkin Thinning of Proterandrous Walnut Based on Quadratic Polynomial Regression Equation and BP Artificial Neural Network

Xianping WANG,Guishou CAO,Xiaohua YANG,Qianru ZHANG,Kai LI,Hongyan LI,Zemin DUAN*

Pomology Institute,Shanxi Academy of Agricultural Sciences/Shanxi Provincial Key Laboratory of Fruit Germplasm Innovation and Utilization,Taiyuan 030031,China

The excessive staminate catkin thinning(emasculation)of proterandrous walnut is an important management measure for improving yield.To improve the excessive staminate catkin thinning efficiency,the model of quadratic polynomial regression equation and BP artificial neural network was developed.The effects of ethephon,gibberellin and mepiquat on shedding rate of staminate catkin of proterandrous walnut were investigated by modeling field test.Based on the modeling test results,the excessive staminate catkin thinning model of quadratic polynomial regression equation and BP artificial neural network was established,and it was validated by field test next year.The test data were divided into training set,validation set and test set.The total 20 sets of data obtained from the modeling field test were randomly divided into training set(17)and validation set(3)by central composite design(quadric rotational regression test design),and the data obtained from the next-year field test were divided into the test set.The topological structure of BP artificial neural network was 3-5-1.The results showed that the prediction errors of BP neural network for samples from the validation set were 1.355 0%, 0.429 1%and 0.353 8%,respectively;the difference between the predicted value by the BP neural network and validated value by field test was 2.04%,and the difference between the predicted value by the regression equation and validated value by field test was 3.12%;the prediction accuracy of BP neural network was over 1.0%higher than that of regression equation.The effective combination of quadratic polynomial stepwise regression and BP artificial neural network will not only help to determine the effect of independent parameter but also improve the prediction accuracy.

Walnut;Staminate catkin of walnut(SCW);Thinning;BP artificial neural network;Regression;Prediction

W alnut(Juglans regia)originated in China.Scientific investigation and geological excavations have proven that more than 2 500 years ago or in earlier period,there had been six walnut species. China is one the world’s three major centers of origin of walnut.In the 1st-2ndcentury,the economic cultivation of walnut appeared.A total of 380 walnut germplasms have been identified[1], and they are widely distributed in the northwestern,northern and eastern provinces.The acreage and yield of walnut in China all rank first in the world.In 2010,the harvested acreage of walnut was about 300 000 hm2,and the yield was about 3 541.2 kg/hm2. Compared with the general yield(6-7 t/hm2)of walnut in America,the gap is very obvious[2].

Walnut is a monoecious and cross-pollinated plant,including proterandrous and protogynous types.

Materials and Methods

Field test

The test was carried out in the Pomology Institute of Shanxi Academy of Agricultural Sciences in 2004.The tested walnut species was 28-year-old Liaohe No.1.According to the design requirements by BP neural network, the field tests were divided into BP modeling test and BP model validating test.Based on the competition of BP modeling test,the validating test was carried out next year.The substances used for emasculation included 95% ethephon(Eth),99%gibberellin(GA) and 95%mepiquat(Pix).

Design and conducting of mathematical modeling testThe test adopted the quadratic general rotary utilized design of central composite design(CCD).A total of 3 factors,5 levels and 20 test combinations were designed.Based on X1(Eth),X2(GA), X3(Pix)and effective concentration ranges of ethephon,gibberellin and mepiquat,the encoding was performed using linear transformation according to following equations(Table 1):

Wherein,Z2j,Z1jand Z0jrepresent the upper,lower and zero levels of each factor;△j and R represent the variation interval and asterisk arm value of each tested factor.

The test was carried out in Jinzhong at the expanding-elongation phase of staminate catkin of walnut. The walnut branches with uniform growth were selected.The test adopted the randomized block design. There were 3 replicates for each test combination,and there were 80-120 male flowers in each replicate.After a 24-h treatment,the shedding rate of staminate catkin in each test combination was investigated day by day in the first 5-7 d.The effect of each test treatment was expressed as the average shedding rate of staminate catkin.

Design and conducting of mathematical model validation test

Based on the modeling test,the model validating test was carried out next year.The tested material,test location and investigation method were all as described above.According to the need to retain an appropriate proportion of staminate catkin and the results of modeling test,the shedding rate of staminate catkin of walnut was controlled in the range of 85%to 95%.The water treatment was treated as CK. The encoded values of X1,X2,X3were 0.087 9,-0.504 5 and 0.025 6,respectively.

Design of BP artificial neural network

Constitution of training set,validation set and test set of BP neural networkAccording to the requirements by BP neural network design, all the test data obtained from the 2-year field tests were divided into training set,validation set and test set. The 20 set of data obtained by BP modeling test were divided into training set and validation set.The training set was composed of 17 sets of data,and the validation set was composed of 3 sets of data.All the 3 sets of data obtained by BP model validating test in the next year were divided into the test set.

Topological constitution of BP neural networkThe BP neural network was composed of input layer,output layer and hidden layer.The number of nodes in the input layer was the number of tested factors(n=3);and the number of nodes in the output layer was the number of response index (m=1);the number of nodes in the hidden layer was determined by comparing the effects of different network parameters on fitting residual.

Analysis and calculation of test results

The quadratic polynomial regression analysis of test results,the analysis of test results by BP neural network model and the generation of figures and tables were all performed using the DPS 14 software.The prediction error of different model was calculated according to the following formula:

Results and Analysis

Test results

The effects of various tested factors(X1,X2,X3)and treatment combinations on shedding rate of staminate catkin of walnut(Y,%)were shown in Table 2.For the central composite design,the change range of average staminate catkin shedding rate of walnut reached 24.29%.So it was indicated that the results of field test were affected by a variety of factors.

Regression analysis of test results

In accordance with Table 1,the tested factors of X1,X2,X3were treated as independent variables,and the average staminate catkin shedding rate of walnut was treated as dependent variable.Then the quadratic polynomial stepwise regression analysis was performed. The obtained mathematical regression formula of the objective function was as follows:

The values of multiple correlation coefficient(R),determination coefficient(R2),residual standard deviation (SSE),adjusted correlation coefficient(Ra)and adjusted determination coefficient(Ra2)were 0.909 869, 0.827 862,11.826 6,0.865 109 and 0.748 414,respectively.

As shown in the mathematical regression model of the objection function,after the stepwise regression analysis and calculation,the X2was deleted in the linear term and quadratic term,indicating that the X2only played a meaningful role in the interaction.

In the mathematical regression model,the action coefficients of various tested factors were analyzed.The results showed that the regression coefficient b1of linear term X1was＞0; the regression coefficient b3 of linear term X3was＜0;the regression coefficient of quadratic term X32was＜0; among the interaction terms,the b13＞b12＞b23.It suggested that among the linear terms and interaction terms,the X1and X3play major roles.Their main effects and interaction effect were shown in Fig.1 and Fig.2.

In a given range(R),the step size of X1,X2and X3was all assigned as 1, and the objective function(y)was assigned between 85%and 95%.According to the mathematical model,a total of 125 combination programs were obtained.Among them,a total of 23 combinations were in line with the given intervals of the objective function.The statistics results of frequency analysis can provide a reference for production practice.

Analysis of test results using BP artificial neural network model

Determination of parameters of BP artificial neural network model

The BP neural network was composed of three layers,including input layer, output layer and hidden layer.After comparing the effects of different network structures and parameters on the fitting residuals of training samples,the topological structure of 3-5-1 was selected for the BP neural network.The raw data was normalized and then iteratively trained 1 000 times,and the fitting residual was 0.002 205 450 385 154 9.The fitting results by the BP neural network were analyzed(Table 3),and the results showed that the fitting residual of the BP neural network met the requirements by this test.

Comparison of application effect between quadratic regression model and BP neural network modelThe investigation results of staminate catkin shedding rate of walnut in validating field test(Table 4)showed that large amounts of male flowers fell off on the 4thd after the test treatment. The average shedding rate reached 84.08%,which was increased by over 70%compared with that of the CK, meeting the requirements by control target(85%-95%).

The predicted values by the regression equation and BP neural network and the results of validating field test were compared(Table 5).It showed that the difference between the predicted value by BP neural network and the actual value in field testwas 2.04%,and the difference between the predicted value by regression equation and the actual value in field test was 3.12%.The prediction accuracy of BP neural network was over 1.0%higher than that of regression equation.

Table 1Types,concentrations and encoding schemes of substances used for emasculation of walnut mg/kg

Table 2Test programs and test results

Table 3Simulation validation of BP neural network structure%

Table 4Shedding rates of staminate catkin of walnut in validating field test%

Table 5Comparison of shedding rate of staminate catkin among regression prediction,BP prediction and validating field test

Discussion

During the rapid growth and numerous blooming of staminate catkin of proterandrous walnut,the female flower development is at a critical stage.The consumption of large quantities of nutrients and moisture by staminate catkin affects the development and fruit setting of female flowers.Moreover,walnut has large amounts of male flowers with large amounts of pollens,and the male flowers are all long-distance transmitted wind-pollinated flowers.However, 90%of the male flowers of walnut are invalid.Zhao et al.[21]found that removing 90%of the male flower buds at the germination phase or removing 60%and 90%of the male flower buds at the elongation period,along with fertilization at the flowering stage, could significantly improve the fruit setting rate,thereby improving yield. Zhang et al.[22]conducted a test in Yangbi County,Yunnan Province.The results showed that after the excessive staminate catkin in walnut was thinned,the female flowers obtained more nutrients,so their development and fruit setting were improved.Compared with that of the control,the fruit setting rate of the treatment group was increased by 12%-17%.But so far, manual operation is still the main method of walnut emasculation.According to the survey,the 18-year-old walnut tree has around 2 000 male flowers,and the 70-80-year-old walnut tree has about 3 150 male flowers, sometime even up to 12 741.Even worse,the duration suitable for walnut emasculation usually lasts for only 7-10 d in spring.Therefore,in the production and management of walnut, there are rare orchards which carry out excessive staminate catkin thinning.In 1996,some domestic scholars used alcohol for excessive staminate catkin thinning in walnut,and up to 51.1%of the male flowers had been thinned. Wang et al.[3]applied the ethephon in the walnut emasculation,and they carried out validating field test the following year and validated the feasibility of the technique.They pointed out that under the premise of saving the cost of production,in accordance with the appropriate mathematical model, the balanced combination of the 2 kinds of chemicals with growth-inhibiting effect and shedding effect is entirely feasible for walnut emasculation.

The classical mathematical theory points out that when the regression equation is significant,the difference between the predicted value and actual value is not only related to the adopted statistical significance level and adopted sample size for statistical analysis but also related to the value of observation point.In general,only when the value of observation point is near the average value of observation points,the prediction makes sense. Moreover,the value of observation point must be in the sampling range for fitting regression equation,and cannot be extrapolated.The studies and practices have all shown that the prediction,application and analysis of mathematical model widely used by regression analysis can not go beyond the restriction of original data and the background conditions generated by original data,such as varieties,culti-vation and management technical measures and ecological environment. On one hand,the statistical model is established based on a large amount of data or test model.In the case of that the test data is less than that required by modeling,the modeling cannot be completed or the established model is out of work.Even under the condition of same basic data,the regression analysis results are usually different,or even differ significantly due to different mathematical models adopted for regression analysis.On the other hand,some undesirable accidents often occur in actual agricultural production,and traditional mathematical methods are difficult to describe the complex system of agricultural production.Therefore,only the appropriate selection and utilization of mathematical method can relatively accurately reflect the practical features of large agricultural production system.

After decades of research,BP neural network has around widespread attention due to it being able to solve complex nonlinear function approximation problem.It has been demonstrated that the three-layer forward network(including a hidden layer)can approximate any multivariate function.During the application, the network layers,each neuron number,fitting error,learning rate and sample data all should be determined according to the specific circumstances[11].Yi et al.[9]pointed out that although the overall prediction effect of regression analysis is relatively ideal, the prediction effect of BP neural network is very satisfactory.Yao et al.[23]fount that the BP neural network model had a strong learning ability.When the human activities or environment factors were greatly changed,it does not require special tests and identification parameters;the new information is only needed to be input and retrained,thus the changes in the system all can be tracked.However,BP neural network also has defects of slow convergence of learning process, poor global search ability,easy falling into local minimum,poor robustness and poor network performance[13]. Moreover,the personal experience and subjective judgements of data processor play an important role.This effect is produced not only on the design of network topology but also on the selection of network training sample data,selection of training parameters and comparison of error.In addition,the selection of samples for the training process of BP neural network has great effect on model determination and predictive application.So the intrinsic characteristics and laws of overall samples must be taken into account[24].The network training sample data includes the results obtained by complete design[17],orthogonal design[19],composite design[18]and surface design[16],as well as the accumulated observation(survey)data.Li et al.[25]pointed out that under the premise of large sample size,the accuracy of training results of BP neural network is higher than those of other mathematical models.The small sample size in researches and relatively insufficient training samples in the training all have certain effect on the prediction accuracy.In this study,the data was composed of training sample(17), model input(3)and model output(1), and the appropriate training parameters were selected.The overfitting and overtraining of the model were avoided,meeting the requirements by predictive application.

Conclusions

The quadratic polynomial stepwise regression analysis is adopted for the field test results.Thus the minor factors can be removed,but the important factors affecting the objective function can be retained.In addition, through analyzing the main effects, quadratic effects and interaction effects of important factors,the practical utilization value of the mathematical model is cleared.

In the premise of no requirements for establishing complex mathematical models and analyzing effects of various factors,the BP neural network model can get relatively accurate predictions by determining the reasonable network structure and training parameters.

The effective combination of quadratic polynomial stepwise regression analysis and BP artificial neural network not only can determine the effects of various factors but also can obtain relatively accurate predictions.

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Responsible editor:Tingting XU

Responsible proofreader:Xiaoyan WU

雄先型核桃雄花疏除的二次回歸與BP神經(jīng)網(wǎng)絡(luò)模型研究

王賢萍，曹貴壽，楊曉華，張倩茹，李凱，李鴻雁，段澤敏*
（山西省農(nóng)業(yè)科學院果樹研究所/果樹種質(zhì)創(chuàng)制與利用山西省重點實驗室，山西太原030031）

雄先型核桃雄花疏除（去雄）是提高產(chǎn)量的重要管理措施，為提高核桃去雄的效率，建立二次回歸與BP神經(jīng)網(wǎng)絡(luò)模型。分別以乙烯利、赤霉素和甲哌鎓為自變量和核桃雄花脫落率為響應指標，進行田間建模試驗，建立了二次多項式回歸方程和BP神經(jīng)網(wǎng)絡(luò)模型，并于翌年進行BP模型田間確認試驗。試驗數(shù)據(jù)分為訓練集、確認集和試驗集，中心組合（二次旋轉(zhuǎn)回歸試驗設(shè)計）田間建模試驗得到的20組數(shù)據(jù)隨機劃為訓練集（17）和確認集（3）數(shù)據(jù)，試驗集為翌年田間確認試驗得到的數(shù)據(jù)，BP神經(jīng)網(wǎng)絡(luò)的拓撲結(jié)構(gòu)為3-5-1。①BP神經(jīng)網(wǎng)絡(luò)對確認集樣本的預測值誤差分別為1.3550%、0.4291%、0.3538%；②BP神經(jīng)網(wǎng)絡(luò)的預測值與田間確認試驗結(jié)果相差為2.04%，回歸預測值與田間確認試驗結(jié)果相差為3.12%；③BP神經(jīng)網(wǎng)絡(luò)預測比回歸預測提高預測精度1.0%以上。將二次多項式逐步回歸分析和BP神經(jīng)網(wǎng)絡(luò)方法有效的結(jié)合使用，既可明確各因子的作用效應亦可得到相對準確的預測結(jié)果。

核桃；雄花序；疏除；BP神經(jīng)網(wǎng)絡(luò)；回歸；預測Most of the cultivated walnut species are proterandrous.The excessive staminate catkin thinning(emasculation)is a traditional technique to improve the fruit setting rate and yield.In general,at the germination period, 90%of staminate catkin is removed. Thus the fruit setting rate will be significantly improved,and the yield of walnut will be also increased by over 10%.However,the emasculation of walnut is currently carried out by hand.To improve the excessive staminate catkin thinning efficiency, alcohols were first adopted in 1996 by some Chinese scholars.Wang et al. ever applied the ethephon in the excessive staminate catkin thinning of walnut and established the corresponding mathematical model[3].In recent years,with the rapid development of artificial neural network theory,the BP(back propagation algorithem)neural network has been widely used in the prediction of crop pests and diseases[4-7],soil nutrients and moisture content[8-11]and grain yield[12-13]and optimization of extraction process of plant functional ingredients[14-20].However,the application of BP artificial neural network in the emasculation and standardized cultivation of walnut has not been reported.This study aimed to investigate the BP neural network model of excessive staminate catkin thinning of walnut based on the field test results of walnut emasculation so as to provide technical basis for improving the yield and efficiency of walnut.

山西省科技廳科技攻關(guān)項目“核桃化學去雄技術(shù)”（002023）。

王賢萍（1961-），女，山西祁縣人，研究員，從事農(nóng)產(chǎn)品安全與果品加工研究，E-mail：Wangxpzls@163.com。*通訊作者，研究員，從事果樹栽培生理與果品加工研究，E-mail：duanzmzls@163.com。

2015-02-10

修回日期 2015-05-25

Supported by Key Science and Technology Program of Shanxi Province,China (002023).

*Corresponding author.E-mail:duanzmzls@163.com

Received:February 10,2015 Accepted:May 25,2015