AWNG-BP prediction technique study based on nonlinear combination – A case study of prediction of food supply chain in rural areas of Hubei Province,China

Abstract

The demands to food in China rural areas are strong while construction of food supply chain lags. Lack of statistical data presents difficulties in construction of food supply chain in China rural areas. This paper designed the prediction technique based on nonlinear combined AWNG-BP. Firstly, this prediction technique used BP neural network to nonlinearly combine conventional regression prediction, three exponential smoothing prediction and grey sequence prediction, in order to reduce negative effects on prediction results caused by data missing and abnormal data. Secondly, modified the inherent defect and especially solve structure optimization problems of general BP neural network, by modifying error function and introducing dynamic self-adapting and genetic algorithm of ecological niche. Thirdly, made sensitivity analysis to three input variables of the prediction technique based on nonlinear combined AWNG-BP, then turned the sensitivity analysis data into a sensitivity curve and synthesized the three sensitivity curves into an image. The image prediction results indicate: first, each single prediction technique has imbalanced effects on prediction results of food supply chain scale in rural areas of Hubei Province of China and the multiple regression and three exponential smoothing prediction affect system evidently; second, total consumption of cold chain food in Hubei Province has been in saturation and will decline slightly in future.

Keywords

Food supply chain prediction nonlinear combination genetic algorithm of ecological niche the sensitivity analysis based on image

1 Introduction

The rural economy in China has been developed rapidly and the living standard of rural residents is improved obviously, but the development of rural food supply chain lags so much that it cannot meet rural residents’ active demands to food. This deficit between supply and demand has caused huge social contradictions, therefore governments and related functional departments urgently need to know tendency and scale of future development of food supply chain in rural areas well to achieve reasonable planning and guidance to it. However, during the prediction of development scale of food supply chain in rural areas, several difficulties had been countered: first, food in rural areas of China is self-sufficient all the time and the food supply chain – this modern management mode – is introduced lately, so theoretical circle has not mastered law of development and approach of food supply chain in rural areas. Second, rural areas in China is vast and population flow is huge, the statistical work related to food is difficult to conduct, thus the statistical caliber in various area is different and the statistical data lacks greatly. Third, food supply chain is a complex nonlinear system, so the prediction accuracy of existing prediction technique is not ideal.

The combination prediction technique means appropriate methods are applied to combine various single prediction techniques to highlight the advantages and avoid disadvantages of single prediction technique, aiming at obtain better prediction results than that of single prediction technique [1]. In 1969, J.N. Bates and G.w.J. Granger first proved that the output results from prediction technique combined with two unbiased single prediction techniques evidently preceded the prediction results from each single prediction technique. Thereafter, foreign and domestic research scholars all were devoted to study prediction accuracy, combining mode and theoretical support of combined prediction technique and obtained abundant achievements [2 –4]. Spyros and Robert [5] combined two different prediction techniques and found that the error rate of prediction results could be reduced by 7.2% during the extrapolation experiment of 111-time series data. When the single technique was added to five in the combined prediction model, the error rate of prediction results could be reduced by 16.3%. In the same sample data, if prediction model based on econometrics was applied to predict and calculate, the same conclusion could be drawn. Meantime, the research showed, the prediction accuracy combined prediction models based on time series and based on regression statistics was 51% higher than the average accuracy predicted by any single model and 44% higher than the best accuracy of two single models.

Logistics scale in the area is important basis for formulating development policies and plans of logistics in the areas [6]. But there are many factors affecting logistics scale, so traditional single prediction technique cannot fully consider various factors affecting predicted objects and the prediction accuracy is low. Given this, we planned to apply the method of combination prediction, that is, nonlinearly combining the conventional regression prediction, three exponential smoothing prediction and grey sequence prediction using BP neural network, modify and optimize inherent defects of general BP neural network, propose a brand-new nonlinear combined AWNG-BP prediction technique and the sensitivity analysis method based on image, demonstrate with the example of food supply chain in rural areas of Hubei Province, China, testify adaptability, effectiveness and superiority of the new prediction technique and provide effective data support for the food logistics planning and construction by government and related functional department.

2 Data source and explanation

2.1 Determination of statistical index

Scale of Supply Chain is a comprehensive and obscure idea. For the reasons of economy, politics and policies in different countries and areas, there is certain deviation in understanding and implementation of the idea. But in different circumstances, three statistical indexes can be used to measure it: cost of supply chain, volume of freight and GDP ratio. The relevant statistic data of food supply chain in rural areas of China was badly missing, so we could not obtain specific values of the above three statistical indexes. And therefore, according to relevant literature, suggestions from experts and scholars and availability and authenticity of statistic data, and combining the real situation of food supply chain development in rural areas in Hubei, we assumed: the food supply chain development in rural areas in Hubei followed the general rules of supply chain system and total food consumption could show the food demand and scale of food supply chain system of this area in a certain period.

2.2 Data source and processing

We picked annual consumption of regular food (including meat, fish, egg products, vegetables, fresh and dried fruit, dairy product and pastry, etc.) in rural areas in statistical yearbook of Hubei Province from 2000 to 2009, formulated total food consumption in rural areas of Hubei Province from 2000 to 2009 by accumulating, and the statistical data was the scale of food supply chain in rural areas of Hubei Province. We took the circumstances of paroxysmal missing of data of some products in statistical yearbook as abnormal data in statistics, which would be obtained by interpolation method of statistics. See Table 1 for specific data.

Table 1
2000–2009 total food consumption of rural residents in Hubei Province (t*10,000)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Pork 5.91 5.77 6.02 6.73 4.31 6.69 6.69 6.64 5.48 5.60

Red meat 0.099 0.111 0.116 0.119 0.091 0.143 0.17 0.165 0.156 0.148

Other poultry 0.777 0.673 0.688 0.903 0.612 0.979 0.931 1.05 1.01 0.995

Egg and egg products 1.40 1.32 1.15 1.27 0.984 1.34 1.33 1.32 1.47 1.52

Fish 0.49 0.54 0.61 0.72 0.75 0.93 1.05 1.34 1.44 1.33

Fresh vegetables 54.7 50.8 46.4 49.8 34.6 47.7 44.2 44.6 40.7 41.6

Fruits 3.58 3.65 2.72 3.31 2.43 3.44 3.48 3.65 3.25 3.08

Dairy products 0.0142 0.07 0.0166 0.026 0.027 0.075 0.106 0.159 0.253 0.343

Total 66.97 62.93 57.72 62.87 43.80 61.29 57.95 58.92 53.75 54.62

	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009
Pork	5.91	5.77	6.02	6.73	4.31	6.69	6.69	6.64	5.48	5.60
Red meat	0.099	0.111	0.116	0.119	0.091	0.143	0.17	0.165	0.156	0.148
Other poultry	0.777	0.673	0.688	0.903	0.612	0.979	0.931	1.05	1.01	0.995
Egg and egg products	1.40	1.32	1.15	1.27	0.984	1.34	1.33	1.32	1.47	1.52
Fish	0.49	0.54	0.61	0.72	0.75	0.93	1.05	1.34	1.44	1.33
Fresh vegetables	54.7	50.8	46.4	49.8	34.6	47.7	44.2	44.6	40.7	41.6
Fruits	3.58	3.65	2.72	3.31	2.43	3.44	3.48	3.65	3.25	3.08
Dairy products	0.0142	0.07	0.0166	0.026	0.027	0.075	0.106	0.159	0.253	0.343
Total	66.97	62.93	57.72	62.87	43.80	61.29	57.95	58.92	53.75	54.62

3 Awng-bp prediction technique based on nonlinear combination

3.1 BP neural network and its optimization

BP neural network is a kind of feed forward artificial neural network, has typical features of artificial neural network and is a main application form of artificial neural network. But there are two inherent defects in BP artificial neural network, that is, algorithm and structure of artificial neural network. We proposed the following solutions for the two major problems existing in algorithm.

(1) Algorithm of BP neural network

The correcting algorithm of error of BP neural network was linear gradient descent. Connection weight and threshold value of this algorithm was adjusted based on constant study step and inertia factor. When self-correction could not be conducted based on the real error during training, once the optimal point was missed, convergence would slow down, even stop [7]. So, linear gradient descent algorithm had two evident disadvantages: ➀ being easily stuck in local optimum; ➁ convergence slowed down and even stopped.

For the two problems, we optimized algorithm of general BP neural network.

➀ Problem of being easily stuck in local optimum.

Error term (Formula 1) of general BP neural network was a kind of pattern of manifestation of squared error. The error formula dissatisfied positive definite condition in weight space, was not convex quadratic form and had many traps of local optimum, which was against process of optimizing. Therefore, we corrected error term as single-pole function (Formula 2) to basically solve the problem of being easily stuck in local optimum of general BP neural network. $E = \frac{1}{2} \sum_{K = 1}^{P} (O_{K} - D_{K})^{2}$ (1) $\begin{matrix} E & = & \frac{1}{2} \sum_{K = 1}^{P} [O_{K} (O_{K} - D_{K}) + \frac{1}{2} λ (D_{K}^{2} - O_{K}^{2}) \\ + \frac{1}{2} (1 - \frac{D_{K}}{O_{K}})^{2}] \end{matrix}$ (2)

Wherein, O_k = (o₁, o₂, …, o_p) was target vector;

D_k is output on output layer;

λ is adjustment coefficient.

➀ Problem of slow convergence.

We introduce the self-weight and adaptive threshold value to solve the two problems of the general BP neural network algorithm. The first is easily falling into partial optimum; the second is slow convergence, even without convergence. In the ordinary BP neural network algorithm, momentum factor α and study step length (study rate) η are two important parameters which determines the convergence speed of neural network and to some extent. Too large or too small of them will cause the problems in the convergence process [8]. Given this, we set the momentum factor α and study step length (study rate) η to the adaptive, real-time variable which can change with the error information. Namely in the relatively flat region of error function space, properly increasing the value of step length η and momentum factor α and speeding up the optimum-seeking speed of BP neural network; while in the relatively steep region of error function space, properly reduce the value of step length η and momentum factor α, and the optimum-seeking speed of BP neural network to avoid the aggravation of concussion. That method contributes to better seeking for the globally optimal solution and speeding up the convergence speed of BP neural network.

The calculation formula of self-adaption weight and threshold values: $v_{jk} (N + 1) = v_{jk} (N) + Δ v_{jk} (N + 1)$ (3) $\begin{matrix} Δ v_{jk} (N + 1) & = & η (N) \cdot Δ v_{jk} (N) \\ - α (N) (1 - η) \frac{\partial E (N)}{\partial v_{jk} (N)} \end{matrix}$ (4) $δ_{k} (N + 1) = δ_{k} (N) - α (N) \cdot \frac{\partial E}{\partial δ_{jk} (N)}$ (5) $w_{ij} (N + 1) = w_{ij} (N) + Δ w_{ij} (N + 1)$ (6) $\begin{matrix} Δ w_{ij} (N + 1) & = & η (N) \cdot Δ w_{ij} (N + 1) \\ - α (N) (1 - η) \frac{\partial E (N)}{\partial w_{jk} (N)} \end{matrix}$ (7) $θ_{j} (N + 1) = θ_{j} (N) - α (N) \cdot \frac{\partial E}{\partial θ_{ij} (N)}$ (8) $\begin{matrix} k = 1, 2, \dots, p; j = 1, 2, \dots, m; \\ j = 1, 2, \dots, m; i = 1, 2, \dots, n; \\ 0 < α < 1, 0 < η < 1 \end{matrix}$

Where, w_ij, v_ij are representatively the connection weights from input layer to middle layer and from middle layer to output layer;

θ_j, δ_k, are representatively the output threshold values of middle layer and output layer in each unit;

α is momentum factor and η is study step length (study rate).

The specific implementation pattern of momentum factor and study step length is:

Set 0 < α < 1; α₀ = 0.6, α_min = 0.1, α_max = 0.9 are set in the region. $if k = 0, 1 α (0) = α (1) = α_{o}$ (9) $\begin{matrix} if K \geq 2 \\ α (k) = (1 - \frac{E (k) - E (k - 1)}{E (k - 1)}) α (k - 1) \\ if α (k) > α_{max}, {α (k) = α_{max};} \\ if α (k) < α_{min}, {α (k) = α_{min};} \end{matrix}$ (10)

(2) Structure of BP neural network

Structure optimization of BP neural network could be regarded as the problem of optimal solution in structure space. The uncertain factor in structure space of BP neural network was the numbers of neurons in hidden layer. The numbers of neuron in hidden layer had great effects on convergence rate and prediction accuracy of BP neural network. If there were too much of it, there would appear too slow convergence rate and over fitting; on the contrary, web-based learning would not be enough and the requirement of training accuracy could not be met. With respect to algorithm optimization of BP neural network, the structure optimization of BP neural network was more difficult and there were no clear methods and rules to follow still. At present, common methods for structure optimization of BP neural network were empirical approach and trying method.

Niche genetic algorithm [9] was a kind of globally optimized heuristic algorithm [10] using living beings to find the positive features in reproduction of the same species and overcoming the disadvantages of general genetic algorithm through balancing chromosome’s structure. The core idea of this algorithm was: divide each generation of chromosome into several “cluster” and each cluster was a little environment; then, individual with larger fitness in each cluster could be selected to be excellent representatives to constitute a population; at last, a new generation of chromosome could be produced by selection, hybridization and variation. Introducing ecological niche technology in basic genetic algorithm could make all chromosomes breed and evolve in designated living environment, ➀ effectively control the procedure of selection, hybridization and variation and lower randomness [11]; ➁ control “inbreeding”, keep diversity of chromosomes at the utmost and avoid the algorithm being stuck in local optimization; ➂ at the same time, improve global searching ability and convergence speed of algorithm.

3.2 AWNG-BP prediction technique based on nonlinear combination

That nonlinear combined prediction model demanded little for data could reduce the effects of distorted or missing data on prediction results at the utmost and was especially fit for predict system short for statistical data, but it had difficulties in complex nonlinear approach function. Although BP neural network had very strong nonlinear mapping capabilities, it still had inherent disadvantages. Obviously, nonlinear combined prediction model and BP neural network could compensate mutually. Therefore, we proposed to adopt improved BP neural network to nonlinearly combine the three single prediction techniques (conventional regression prediction, three exponential smoothing prediction and grey sequence prediction) and formulate a kind of new prediction model of BP neural network based on nonlinear combination, adaption weight and niche genetic algorithm (hereafter referred as AWNG-BP prediction model based on nonlinear combination).

(1) AWNG-BP prediction model based on nonlinear combination

➀ Numbers of network layers: design a three-layer model structure including input layer, hidden layer and output layer.

➁ Numbers of neurons in layers and sample dimension: assume that there were three neurons in input layer of prediction model and the input data were fitted values (2002–2009) against scale of food supply chain in rural areas of Hubei Province predicted by multiple regression, three exponential smoothing prediction and grey sequence prediction; the numbers of neurons in hidden layer was decided by experiment via genetic algorithm of ecological niche; there was one neurons in output layer, outputting prediction results of scale of food supply chain in rural areas of Hubei Province. See Tables 2 and 3 for model structure and sample dimension.

Table 2
Model structure of AWNG-BP prediction model based on nonlinear combination

Training model

Input layer 3 neurons

(conventional regression prediction, three exponential smoothing prediction and grey sequence prediction)

Hiding layer determine the number of neurons according to the experimental results

Output layer 1 neuron

	Training model
Input layer	3 neurons
	(conventional regression prediction, three exponential smoothing prediction and grey sequence prediction)
Hiding layer	determine the number of neurons according to the experimental results
Output layer	1 neuron

Table 3

Sample dimension of AWNG-BP prediction model based on nonlinear combination

Sample	Input data						Output data
1	2000	2001	2002	2003	2004	2005	2006
2	2001	2002	2003	2004	2005	2006	2007
3	2002	2003	2004	2005	2006	2007	2008
4	2003	2004	2005	2006	2007	2008	2009

(2) Algorithm flow of AWNG-BP prediction model based on nonlinear combination

➀ Pre-processing of data

For sampling data had different dimension, in order to ensure authenticity and reliability of training results, input and output data should be processed with normalization. At the same time, to quicken the backward transmission of error and avoid slow change space of two tops of Sigmoid function, the data after normalization should be corrected. See Table 4 for preprocessed data.

Table 4

Data after preprocessing

Year	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009
Data after preprocessing	0.8500	0.7970	0.7002	0.7961	0.1500	0.7705	0.7053	0.7259	0.5964	0.6219

Data normalization processing: $x^{1} = \frac{x - x_{min}}{x_{max} - x_{min}}$ (11)

Data correction processing: $x^{2} = 1 - \frac{1}{e^{[0.1625 + \frac{(1.8971 - 0.1625) (x^{1} - x_{\min})}{x_{\max} - x_{\min}}]}}$ (12)

➁ Parameter determination: transmit function: Sigmoid function; weight value and threshold value: initial weight value and threshold value were produced by random function; expectant error: formula (2).

➂ Algorithm formulated two-layer circulation, internal and external, wherein, the internal circulation was to determine the numbers of neuron in hidden layer and external circulation was to obtain the final prediction results by gradual convergence of prediction error.

➃ External circulation adopted AWNG-BP algorithm, see Formula (3–10).

➄ Internal circulation adopted genetic algorithm of ecological niche:

Coding: the maximum empirical value of the numbers of neuron in hidden layer of prediction model was coding object, which was coded by binary system. If the gene bit in corresponding binary coding was 0, it indicated that this node was invalid or there were no network connections; if it was 1, there was corresponding node, and the weight value and threshold value were valid and needed to be assigned with starter and this node would join in the training of BP neural network. For example, if the maximum empirical value of the numbers of neuron in hidden layer was 15, chromosome would be initialized based on 15 bits. If one of chromosomes was coded as 110100110110111, it meant 1, 3, 4, 7, 8, 10, 11, 13, 14 and 15 gene bits were selected as neurons in hidden layer, that is, there were 10 neurons in hidden layer.

Population initialization: the number of population was assumed as m, m = 20. Chromosome was generated randomly according to the number of population.

Fitness function: reciprocal of error term.

Selection: strategies of championship + roulette. First, select two chromosomes with maximum values of fitness and enter into filial generation without cross and variation; then, select remaining chromosomes with roulette mechanism according to the value of fitness.

Cross and variation: single point crossed randomly with probability of 0.95; single point with random variation with probability of 0.05.

Obsolescence in ecological niche: in each generation of group, first, compare hamming distance - code distance - between any two individuals. The formula of hamming distance is:

$d (x_{i}, x_{j}) = ∥ x_{i} - x_{j} ∥ = \sum_{k = 1}^{l} | x_{ik} - x_{jk} |$ (13)

Wherein, k is gene bit of chromosome, l is length of gene string. For example, two chromosomes 10101 and 00110 were different from the first bit, fourth and fifth bits, and then the hamming distance was 3. When the distance was in the preassigned distance L, that is, x_i - x_j ≤ L, the individual with lower fitness was implied with a stronger penalty function to change its fitness value into a smaller value, that is: $F (min (x_{i}, x_{j})) = penalty$ (14)

In two chromosomes with distance in L, the inferior one’s fitness would be worse after processing in ecological niche and the probability obsoleted would be bigger in latter evolutionary process. In this way, there would be one excellent chromosome in distance L, which kept diversity of the group and certain distance among each chromosome to disperse in whole constrained space. If two chromosomes were same totally, either of two was selected to punish to reduce rate of coincident code of chromosomes. Assume: L = 2, penalty = 0.7.

➅ Data post-processing, i.e. inverse unification processing:

$\bar{y} = \frac{({\bar{y}}_{\max} - {\bar{y}}_{\min})}{1.8971 - 0.1625} [\ln (\frac{1}{1 - y^{'}})] - 0.1625 + {\bar{y}}_{\min}$ (15)

4 Analysis of examples of awng-bp prediction technique based on nonlinear combination

4.1 Training procedure

Assign initial value: η = 0.3, α = 0.6, wherein η and α are dynamic self-adaptive adjustment. Assume the internal circulation of prediction model is 100 times and 200 times respectively; and the external circulation is 100 times, 200 times and 300 times respectively. Combine the number of times in internal and external circulation to form six groups of training for prediction model and finally determine the number of neuron in hidden based on the results of training. The convergence results of corresponding training were showed as Figs. 1–6.

Fig.1

Convergence situation of 100 times of internal circulation and 100 times of external circulation.

Fig.2

Convergence situation of 100 times of internal circulation and 200 times of external circulation.

Fig.3

Convergence situation of 100 times of internal circulation and 300 times of external circulation.

Fig.4

Convergence situation of 200 times of internal circulation and 100 times of external circulation.

Fig.5

Convergence situation of 200 times of internal circulation and 200 times of external circulation.

Fig.6

Convergence situation of 200 times of internal circulation and 300 times of external circulation.

From the training results, no matter what values were assigned in internal circulation and external circulation, the training results of prediction model could be in stable convergence. From the average value of error and convergence rate, when internal circulation was 200 and external circulation was 300, the training error was minimum and the convergence rate was quickest. Therefore, the number of neuron in corresponding hidden layer of this training model was assigned 15, which was the number of neuron in hidden layer in final prediction model.

4.2 Prediction results

The well-trained prediction model was used to predict the scale of food supply chain in rural areas of Hubei Province, and the fitting and error results in prediction results were showed in Fig. 7 and prediction data is showed in Table 5.

Fig.7

Fitness Figure and Error Figure of Prediction Results of AWNG-BP Prediction Model Based on Nonlinear Combination.

Table 5

Prediction data of AWNG-BP prediction model based on nonlinear combination

Year	2010	2011	2012	2013	2014
Prediction data	0.6199	0.6318	0.6096	0.5915	0.5738
The value of anti-normalization	54.5521	54.9765	54.1942	53.5876	53.0221

4.3 Sensitivity analysis

There were 3 input values in AWNG-BP prediction model based on nonlinear combination, and we used the same sensitivity analysis method to analyze 3 values’ sensitivity: average divided the variable range of each input value into 8 phases and assign x_i to be the values of the 8 phases respectively, that is, the values of x_i equalled to (0.1500, 0.2500, 0.3500, 0.4500, 0.5500, 0.6500, 0.7500 and 0.8500). In the change of x_i, other two variables remained unchanged, that is, are (0.1500, 0.1500, 0.1500, 0.1500, 0.1500, 0.1500, 0.1500 and 0.1500) all the time. These were input values and were successively input in the trained prediction model, the value of y could be gotten in output layer, whose range should be in [0–l]. In order to compare and analyze sensitivity of three input values directly, we superimposed the corresponding y values of three input variables in one figure. See Table 6 and Fig. 8 for detailed information.

Table 6
Sensitivity analysis data of AWNG-BP prediction model based on nonlinear combination

Stage 1 2 3 4 5 6 7 8

x ₁ 0.1500 0.2500 0.3500 0.4500 0.5500 0.6500 0.7500 0.8500

y ₁ 0.2205 0.2486 0.2822 0.3219 0.3677 0.4192 0.4752 0.5338

x ₂ 0.1500 0.2500 0.3500 0.4500 0.5500 0.6500 0.7500 0.8500

y ₂ 0.2205 0.2435 0.2702 0.3011 0.3362 0.3756 0.4188 0.4652

x ₃ 0.1500 0.2500 0.3500 0.4500 0.5500 0.6500 0.7500 0.8500

y ₃ 0.2205 0.2142 0.2082 0.2026 0.1973 0.1923 0.1875 0.1830

Stage	1	2	3	4	5	6	7	8
x ₁	0.1500	0.2500	0.3500	0.4500	0.5500	0.6500	0.7500	0.8500
y ₁	0.2205	0.2486	0.2822	0.3219	0.3677	0.4192	0.4752	0.5338
x ₂	0.1500	0.2500	0.3500	0.4500	0.5500	0.6500	0.7500	0.8500
y ₂	0.2205	0.2435	0.2702	0.3011	0.3362	0.3756	0.4188	0.4652
x ₃	0.1500	0.2500	0.3500	0.4500	0.5500	0.6500	0.7500	0.8500
y ₃	0.2205	0.2142	0.2082	0.2026	0.1973	0.1923	0.1875	0.1830

Fig.8

Sensitivity curve of AWNG-BP prediction model based on nonlinear combination. Note: In Fig. 8, on the edge of horn mouth in the figure showed the values of y from top to bottom respectively, showed as note.

5 Discussions

Simulation experiment was used to conduct checking computations of various performance of each single and AWBG-BP prediction model based on nonlinear combination, see Table 7 for detailed results. Obviously, all the prediction models were feasible and efficient and could complete the prediction. Although performance of each single prediction model had own advantages in different statistical indexes, in general, the prediction accuracy was not high, indicating that the results using just single prediction model to predict scale of food supply chain in Hubei Province were not ideal. In comparison, various statistical indexes of performance in AWBG-BP prediction model based on nonlinear combination had improvement of 2–3 orders of magnitude and the prediction accuracy was evidently improved.

Sensitivity experiment was conducted against each single prediction technique of AWBG-BP prediction model based on nonlinear combination. The experiment results showed that during the prediction procedure of food supply chain in rural areas of Hubei Province, the order of effect degree of three single prediction techniques was multiple regression, three exponential smoothing prediction and grey sequence prediction, in which the maximum effect degree was 0.53 and the minimum was 0.18. Therefore, the effect of each single prediction technique on scale of food supply chain in rural areas of Hubei Province was unbalanced: effects of multiple regression and three exponential smoothing prediction on the system were far more significant than that of grey sequence prediction. This may be caused by that fluctuation of total food consumption in rural areas was wide, and grey generation in grey sequence prediction fuzzily processed this fluctuation. Although this procedure of grey turning white reduced effect of distorted data on prediction procedure, at same time it reduced change information contained in data. So in techniques combination, the significance of grey sequence prediction was less.

Table 7
Performance comparison of various prediction model

MSE CD MD MAPE

Conventional regression prediction model 3.8008 0.9994 –2.57e-13 0.02988

Three exponential smoothing prediction model 27.7331 0.9938 3.4196 0.09190

Grey sequence prediction model 28.6606 0.9962 –0.0011 0.06397

AWBG-BP prediction model based on nonlinear combination 0.0109 0.9991 0.0151 0.026134

	MSE	CD	MD	MAPE
Conventional regression prediction model	3.8008	0.9994	–2.57e-13	0.02988
Three exponential smoothing prediction model	27.7331	0.9938	3.4196	0.09190
Grey sequence prediction model	28.6606	0.9962	–0.0011	0.06397
AWBG-BP prediction model based on nonlinear combination	0.0109	0.9991	0.0151	0.026134

6 Conclusions

This paper took three important optimization measures to general BP neural network: first, optimize error function against the problem of BP neural network easily sticking in local optimum; second, optimize search algorithm of BP neural network with method of dynamic self-adaption against the problem of fluctuation and slow convergence rate in the late iteration of BP neural network; and third, optimize network structure of BP neural network with genetic algorithm of ecological niche against the problem of difficulty in determining network structure of BP neural network. The experiment data showed theses optimization measures could evidently improve the accuracy of prediction models and was suitable for predicting the complex nonlinear system with in missing history statistical data.

Food supply chain was a typical complex nonlinear system. In regard to various reasons, the history statistical data for food supply chain in rural areas in China was missing and inaccurate. The prediction result adopted single prediction technique was very unsatisfactory. Combining multiple regression, three exponential smoothing prediction and grey sequence prediction with improved BP neural network, building up AWBG-BP prediction model based on nonlinear combination and making full use of nonlinear combination of each single prediction technique could weaken effect of distortion and lake of data on output results and nonlinear capability of BP neural network, which obtained tremendous prediction effects and adaptability and was deserved to be promoted.

The sensitivity analysis method based on image can be more intuitive to discover the impact of the three individual prediction methods on nonlinear combination forecasting methods and easier to adjust the weight of nonlinear combination forecasting method. In this way, the unbiasedness of the nonlinear combination forecasting method will be smaller, and the accuracy will be higher.

From food supply chain market in rural areas of Hubei Province, because of effect of average per capita income and living and consumption habits, the scale of food supply chain in rural areas had been stable for late ten years, with smaller fluctuation (except for 2004 and 2005). From prediction data, it was obvious that the scale of food supply chain in rural areas would continuously increase and trend to descend slightly.

Footnotes

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 70160376), the Natural Science Foundation of Hubei Province (No. 2016CFB490), the China Postdoctoral Science Foundation (No. 2015M580648), the China Postdoctoral Special Science Foundation (No. 2017T100560) and Hubei Logistic Development Research Center Sponsored Project.

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