Zhenxiang Xing

Hao Guo

Shuhua Dong

Qiang Fu

Jing Li

RBF Neural Network Based on K-means Algorithm with Density Parameter and its Application to the Rainfall Forecasting

Keywords: Rainfall forecasting, Radial Basis Function Neural Network, Density parameter, K-means

The Radial Basis Function (RBF) neural network is a feed-forward artificial neural network with strong approximation capability. A K-means algorithm based on density parameter was introduced to determine clustering center aimed to improve the training rate of the RBF. It could reduce sensitivity of traditional K-means algorithm for initial clustering centers. A rainfall forecasting model of RBF based on K-means algorithm was built, which was applied to forecast monthly rainfall in Shuangyashan City during the flood season, aiming to test the effectiveness of this model. The case study showed that the mean relative error of rainfall forecasting in flood season (from June to September) of the year 2006, 2007 and 2008 was 10.81%, and the deterministic coefficient was 0.95. It demonstrated a higher forecasting accuracy comparing to a RBF model based on a standard K-means algorithm and BP (Back Propagation) model, and the rainfall forecasting results satisfied the requirements of hydrologic prediction.

Introduction

The rainfall is an important process with higher uncertainty in natural water cycle. A rainfall forecasting method with high-accuracy could predict the change amount of precipitation, which could provide important significance to decision-making of flood control and disaster reduction. There are a lot of methods for rainfall forecasting, such as the regression analysis [START_REF] Qing | A Precipitation Forecast Model Based on Regression Analysis and Time Series Analysis [J][END_REF], the grey prediction [START_REF] Caiyuan | Grey Prediction Model in the Application of the Upper Yangtze River Basin Surface Rainfall Forecast [J][END_REF], the fuzzy prediction [START_REF] Caizhi | Research on fuzzy Markov Chain Model with Weights and its Application in Predicting the Precipitation State[END_REF], and artificial neural network [4.5] and so on. The artificial neural network has many advantages of rainfall forecasting, which has strong ability to deal with nonlinear problem and high generalization ability. So the BP neural network and the RBF neural network is widely used network model. Compared with the BP network, the number of hidden layer of RBF network can be adaptive adjusted in training phase. In addition, input layer and hidden layer of RBF use linear connection instead of weights. It seems that the RBF has advantages compared with BP, which can greatly improve the convergence speed of network. RBF also has better approximation capability of nonlinear function. In this paper, a RBF model was trying to be used to forecast the precipitation in Naolihe catchment in Sanjiang plain.

Radial Basis Function Neural Network

The Radial Basis Function Neural Network (RBF) is a three-layer feed forward network with single hidden layer [START_REF] Yanping | Study on the Surrogate Model of Groundwater Numerical Simulation Model Based on Radial Basis Function Neural Network[END_REF], such as input layer, hidden layer, output layer. The network also can approximate any continuous function with arbitrary precision theoretically. In RBF network is, the hidden layer space is constructed by the RBF, so an input vector can be directly (do not need the weights) mapped into hidden space. The mapping relationships between hidden layers to output layers were described as a linear function and the outputs of network are linear weighted sum of hidden unit output [START_REF] Defeng | Neural Network Application Design of Matlab[END_REF]. Gaussian function is commonly used as the radial basis function in RBF network. The expression of activation function is:

          2 2 || || 2 1 exp ) ( i p i p c x c x   (1)
where φ is activation function;

|| || i p c x  is the European norm;   T p m p p p x x x x , , , 2 1
  is the p th input samples; p=1,2,…,P (P is the total number of samples); c i are a center of Gaussian function;  are a variance of Gaussian function.

The outputs of network are obtained through the RBF structure

           h i i p ij j c x w y 1 2 2 || || 2 1 exp  (2)
where w ij denote weights between the hidden layer to output layer; i=1,2,…,h (is number of nodes in a hidden layer); y j denote actual outputs from the j th of output corresponding with input sample; and other symbols have the same meaning as above.

K-means Algorithm Based on Density Parameter

In an RBF neural network, three parameters are needed to be solved, which are the centers of basis function in hidden layer, the variance and the weights of the hidden layer to output layer. The key to build a good network is to select an adaptive basis function center. There are many methods, such as the randomly selected algorithm, the self-organization selected algorithm, the clustering analysis algorithm and the orthogonal least squares algorithm to do this job. Among the methods above, the Kmeans clustering algorithm is one of the fairly effective learning algorithms. The K-means algorithm is a clustering algorithm based on distance, i.e., a distance is the assessment criteria of the comparability. The traditional K-means algorithm is easy to understand, which is easier for programming. However, it is obvious that Kmeans algorithm is sensitive to the initial clustering center and clustering results fluctuate when given different initial input. It will infect the final characteristics of sample groups. The K-means algorithm based on density parameters can reduce the influence caused by initial clustering centers to clustering results comparing to a traditional algorithm. Therefore, the K-means algorithm based on density parameter of RBF is applied to forecast the rainfall in this paper.

The Concept of Density Parameter

The aggregation of sample data: S= {x 1 , x 2 ,…, x n }, the initial clustering centers:

z 1 , z 2 ,…, z k . Define 1 an Euclidean distance between each two samples 2 / 1 2 2 2 2 2 1 1 ) | | ... | | | (| ) , ( jp ip j i j i j i x x x x x x x x d        (3)
where x i ={ x i1 ,x i2 ,…,x ip } and x j ={ x j1 ,x j2 ,…,x jp } are samples with p-dimension. Define 2 an average distance between samples

   ) , ( 1
2 j i n x x d C MeanDist (4)
where n is the total number of samples. Define 3 the density parameter [START_REF] Jianhui | Research and Application of K-means Clustering algorithm[END_REF] In the density space, neighborhood of any point is defined as the region which point p is the center and MeanDist is the radius. The number of points in region is known as the density parameter based on MeanDist, called density (p, MeanDist).

K-means Algorithm Based on Density Parameter

The Euclidean distance is used as similarity measure of the K-means algorithm. The mutual farthest k data objects are more representative than random k data. It is considered that noisy data are often mixed in practical data. In order to avoid selecting the noisy points, we can get k points in the high density area as the initial clustering center by following steps [START_REF] Jianhui | Research and Application of K-means Clustering algorithm[END_REF]:

(1) Calculate the distance between any two data according to formula (3), called as d (x i , x j );

(2) Calculate the average distance of total data according to formula (4), called as MeanDist;

(3) Calculate the density parameters of all data, named as density (p, MeanDist), and composing a data set named D. (4) Find the maximum value from D, z k =

density n i MeanDist p density i ) ..., 2 , 1 ( | ) , ( max{  } ) , ( D MeanDist p i  .If d (p i , z k ) < MeanDist, the density (p, MeanDist) is deleted from D; z k is the k th of cluster center.
(5) Repeat the step (3) and step (4) until finding cluster centers, and the number of cluster centers is k. Therefore, cluster centers can be obtained in accordance with the method, that is, the final center of the basis function of RBF network.

The Rainfall Forecasting Model Based on RBF

The Structure of RBF Network

The number of input layer neurons

It has much significance to choice the number of input neurons for RBF network. The unreasonable choice will affect training ability of the network, and even lead to model crash. Therefore, the node number of input neurons of RBF network is determined by autocorrelation analysis technology in this article.

The number of hidden layer neurons

The hidden layer neurons are used to store connection weights and thresholds between input layer and hidden layer. It is characterized in terms of reflecting inherent law between training sample and expected output. There are no accurate and scientific methods to determine the hidden layer neurons at present, and as well as more determined by empirical formula and numerical test. The traditional method is also used in this paper, and the empirical formulas are [START_REF] Zhu | Data Mining[END_REF]:

a m n n    1 2 (6) 1 2 log 2 n n  (7)
where n 2 is the number of hidden layer neurons, n 1 is the number of output layer neurons, m is the number of input layer neurons, a is a constant between [0, 1].

The Rainfall Forecasting Model

The network model is built by RBF tool box of MATLAB, the program language as follows:

net =newrb(p,t,goal,spread,mn,df) where p and t are the input vector and the output vector of sample respectively; goal is the mean square error for the purpose of preventing excessive fitting. In this paper, goal was set as 0.001; mn is the maximum number of neurons; df is the number of neurons to add between displays; spread is the width of the radial basis function, and in this paper it is determined by the distance between each center of hidden layer neurons, and the formula is

i d b pread   s (8)
where b is the overlap coefficient, and usually this value are set as an integer greater than 1 [START_REF] Meijuan | Research on Radial Basis Function Neural Network Learning Algorithms[END_REF]; d i is the minimum distance of basic function centers of the hidden layer, the basis function center is obtained by K-means algorithm based on density parameters.

The Experimental Data

The rainfall forecasting model of RBF based on K-means algorithm was built, which was taken precipitation in Shuangyashan City of Sanjiang plain in each flood season from 1955 to 2005 (June to September) as an example. The precipitation of the year from 1955 to 2003 was used for network training, and that from 2004 to 2005 was used for network testing, forecasting the rainfall of the year 2006, 2007 and 2008.

Data Preprocessing

Input and output data of RBF network should be within [0, 1], so the precipitation need to be normalized before training model according to following formula,

min max min x x x x y i i    (9)
where x i and y i is the rainfall before and after normalizing respectively; x min and x max are the minimum and maximum values of all rainfall. The processed data will be used as the samples of the RBF neural network model.

Identifying and Training RBF Network

The key point to build RBF neural network is to determine number of nodes in input layer and hidden layer, which is based on the characteristics of rainfall. The correlation analysis of rainfall series in flood season in Shuangyashan was built, and we can estimate that the rainfall series is suitable for the AR (p) model. The order of Markov process should be four by analyzing the AIC criterion. That is to say, the input layer neurons of RBF network are four. According to the empirical formulas and trial calculation, number of nodes in hidden layer is eight. Therefore, the structure of network in this paper is 4:8:1. To achieve converging, the rainfall of the year from 1955 to 2003 is trained 172 times by using neural network which has been constructed above, and the fitting error of network is 0.001. The rainfall of the year 2004 and 2005 is used to test and verify the generalization ability of the RBF network model. The mean prediction relative error is 10.9736% and the deterministic coefficient is 0.95. In conclusion, the constructed RBF network could be applied to forecast rainfall in Naolihe catchment.

Results and Analysis

The calculation in Table 1 show that the mean relative error of rainfall forecasting in 2006, 2007 and 2008 is 10.81% by using established RBF network model, the deterministic coefficient is 0.95; the relative error using K-means algorithm is 14.30%, and the deterministic coefficient is 0.86. The mean relative error of BP network model is 14.38%, the deterministic coefficient is 0.87.Meanwhile, fitting time and convergence times of the established RBF network model are reduced, which are 80s and 172 times respectively; and the standard K-means algorithm's fitting time and convergence times are 97s and 235 times, while the BP network model's are 125s and 302 times. Therefore, compared with RBF model of standard K-means and BP model, the computing speed of the RBF network that has been constructed in this paper are increased by 18% and 36% respectively, and the mean relative error are reduced by 24% and 25%.The fitting figure between observed rainfall and forecasted rainfall in training period, testing period and forecasting period was shown in Fig 1 . (The first 182 series is training period, series of183 th to 190 th is testing period, and other series is forecasting period).

Conclusions

The K-means algorithm is commonly used as learning algorithm in RBF neural network. The initial clustering centers are selected randomly based on the traditional K-means algorithm, which result in different convergence abilities. The method of density parameters was trying to be used to reduce the sensitivity of selecting randomly for clustering centers in this paper, and to calculate the width of basis function of the RBF network. And then a rainfall forecasting model of RBF based on K-means algorithm was built, which was applied to forecast monthly rainfall in Shuangyashan City in Heilongjiang Province. The case study results and conclusions were shown as follows: 1) Comparing with the traditional K-means algorithm, the RBF network model based on the density parameter had its advantages for determining the number of clustering results and the centers of basis function. And the model had higher convergence rate and forecast accuracy.

2) The accuracy of RBF network model on account of rainfall forecasting during flood season in Shuangyashan City had been improved greatly compared with BP network model. The mean relative error of monthly rainfall in 2006, 2007 and 2008 were reduced by 24% and the deterministic coefficient was increased by 10%. So the model built in this paper could be used as an effective method for rainfall forecasting or other time series forecasting with strong uncertainties. 3) In this paper, number of nodes in the network was determined by empirical formula and numerical test. In order to further increase the calculation precision of model forecasting, some intelligent optimization algorithms such as genetic algorithm could be adopted to optimize number of nodes in hidden layers in the future research.

Fig. 1 .

 1 Fig.1. The fitting figure between observed rainfall and forecasted rainfall

Table 1 .

 1 The results of rainfall forecasting compared impoved RBF network with standard K-means RBF network and BP network

			a		b		c
	Time	Observed rainfall /mm	Forecas -ted rainfall /mm	relative error /%	Forecas -ted rainfall /mm	relative error /%	Forecas -ted rainfall /mm	relative error /%
	0606	127.9	105.76	-17.31	106.68	-16.59	99.86	21.92
	0607	148.7	130.88	-11.98	125.03	-15.92	120.86	18.72
	0608	64.9	70.00	7.86	72.05	11.01	70.14	8.08
	0609	17.2	20.07	16.70	18.80	9.30	20.00	16.29
	0706	65.9	70.22	6.56	75.01	13.82	73.03	10.83
	0707	35.8	41.04	14.64	40.37	12.77	42.08	17.53
	0708	156.1	142.37	-8.79	132.50	-15.12	140.66	9.89
	0709	39.6	35.40	-10.60	45.09	13.87	43.53	9.92
	0806	109.9	100.56	-8.50	95.65	-12.97	104.40	5.00
	0807	48.4	52.37	8.21	42.38	-12.44	40.07	17.21
	0808	101.0	110.20	9.11	118.00	16.84	117.84	16.68
	0809	29.3	32.05	9.39	35.46	21.03	35.30	20.49
	MRE	-	-	10.81	-	14.30	-	14.38
	DC	-	0.95	-	0.86	-	0.87	-
				a. The improved RBF network that has been built in this paper;
				b.RBF network based on standard K-means; c. BP network;
			MRE is the mean relative error; DC is the deterministic coefficient

Acknowledgment

Funds for this research was provided by the national natural science foundation (51109036; 51179032), the specialized research fund for the doctoral program of higher university of the Ministry of Education (20112325120009) the special scientific research funds for Ministry of water resources public welfare industry (201301096), The leader talent echelon back-up headman funding projects of Heilongjiang province (500001), the studying funds of postdoctoral in Heilongjiang province (LBH-Q12147), the science and technology project of Heilongjiang Provincial Education Department(11541022).


Yanjun Zuo

Huixuan Zhu

Peng Cao

Design of Transplanting Mechanism with B-Spline Curve Gear for Rice Pot Seedling Based on UG

Keywords: Rice pot seedling transplanting, B-Spline, UG, Virtual design

In allusion to the existing rice pot seedling transplanter exists the defects of complex structure, high cost and low efficiency, the transplanting mechanism with b-spline curve gear for rice pot seedling was designed based on parametric modeling software UG NX 8.0. Firstly, the 3-D models of part were built, and then assembled. Secondly, the interference detection of assembly model was done. Finally, relevant 2-D engineering drawings were generated for manufacture. It is provides the reference for the design of rice pot seedling transplanter, and preparation for further simulation and analysis with softwares of Adams and Ansys.

Introduction

Rice is one of the main food crops. and perennial planting area is about 30 million hm2 in China. The area account for national grain and world's rice planting areas are about 30% and 20%, it only less than India and is the second largest in the world [START_REF]National Bureau of Statistics of the People's Republic of China[END_REF][START_REF] Longping | Research Development of Super Hybrid Rice Breeding[END_REF]. Therefore, our rice production has a pivotal position to food security not only for China but also for world. There are two modes of rice planting (direct seeding and transplanting) at present [START_REF] Yazhou | Introduction of Development for Rice Transplanting Machine in Our Country[END_REF], but the Asia is given priority to rice seedling transplanting, the mechanization levels of Japan and Korea are highest and more than 98% during Asia. The cultivation mode of rice transplanting is also divided seedling transplanting and pot seedling transplanting, comparing with seedling transplanting, the pot seedling transplanting has the advantages of seedling no hurting and no need recovering, production increasing and so on [START_REF] Lianxing | Effect of Mechanized Transplanting Methods on Rice Yield & Rice Population Growth Trends[END_REF]. Since Japan invents the first transplanter for rice pot seedling in 1975, each large agricultural machinery company has producted their own models in succession, such as Yanmar, Iseki and so on. The material structure and processing technology have improved through the forty years development, but the its basic structure and working principle are still the same [START_REF] Naokatsu | Seedling Transplanting Mechanism of Transplanting Machine[END_REF][START_REF] Lei | The Application and Development of Rice Pot Seedling Technology[J][END_REF][7][START_REF] Dachiya | New Technique of Rice Cultivation[J][END_REF][START_REF] Osamu | Agricultural Mechanization in 21st Century [J][END_REF][START_REF] Hu | The Research of Auto-transplanter's Picking Seedling Mechanism and Seeding Mechanism[END_REF]. The transplanting machines of rice pot seedling use 3 devices to achieve the 3 actions of taking, transportation and planting separately, which gives rise to complex structure, high cost and low efficiency, so the promotion area is limited [7,[START_REF] Yanzhong | Development and Application of Mechanization Technology for Rice Pot Seedling Transplanting[END_REF][START_REF] Yutian | Rice Practical Cultivation[END_REF]. The rice transplanter is main except rice pot seedling transplanting machine with double cranks, which is invented by Zhao Yun et al. The double cranks transplanting machine can use a mechanism to achieve 3 actions orderly for rice pot seedling, has relatively simple mechanism, but the disadvantages of large vibration and low efficiency are existent because of the characteristics of bar mechanism [START_REF] Zhao Yun | Transplanting Mechanism of Pot Seedling Transplanting Machine with Double Cranks[END_REF]. Therefore, the study on transplanting mechanism for rice pot seedling to efficient, light simplified and full-automatic, is very necessary.

In the study, UG NX 8.0 was applied for the design of transplanting mechanism with b-spline curve gear for rice pot seedling. The 3-D models of each part can be built and assembled easily, and interference detection of assembly models was done through the software. Therefore, virtual design can promoted standardization, normalization and serialization to physical prototype based on virtual manufacturing, assembly and test.

2

Characteristics of UG NX 8.0

Software of UG NX 8.0 is developed by SIEMENS, it is a flagship digital software for solution of NX. The software is comprehensive 3-D modeling software which gathers CAD, CAE and CAM, it sets up a new standard for machinery industry and is favoured by insider. In order to meet the requirements of users which can develop new product quickly, UG has more extensive product design module, such as modeling, simulation, assembly, bending and so on, and also has high performance of charting capability, so it is used widely in machinery, automobile and other manufacturing industries. In addition, UG can realize seamless joint with other virtual simulated softwares, such as Adams and View 2010, the model that is built in UG, can be operated directly after import [START_REF] Qiucheng | The Article of UG-CAE[END_REF].

Results and Discussion

Working Principle

The sketch of transplanting mechanism for rice pot seedlings is shown in figure 1

Part Design

The characteristics of criterion, voxel and basic shape design that were needed, could be built by 3-D capabilities in UG, such as base level, base coordinate, sphere, cylinder, square body, cone, stretching, rotating, draft, and slightly, convex platform, slotting and so on. Because the pitch curve of non-circular gear was irregular, the pitch curve was imported using interface of UG, and then stretched. The 3-D model of non-circular gear was obtained as shown in figure 2a, the other five more important or distinctive parts were all simple, the 3-D modeling process was not need to special instruct, the models were shown in figure 2.

Assembly Design

Based on section of 3.2, using the assembly module which is the built-in modules of UG, the assembly was done through adding the relevant constraints. There are tow types of assembly in the whole machine assembly, they are step by step assembly and whole assembly. The whole assembly can be used under the condition of less mechanism and simple, all the parts are imported into the assembly drawing and imposed constraints in turn. The characteristics of transplanting mechanism are that components and parts are more, the structure and positional relationship are all relatively complicated, so the type of step by step assembly would be used in this paper. The transmission component with non-circular gear and transplanting component were assembled into sub assembly by the top-down order, and shown in figure 3. The whole machine assembly of transplanting mechanism has been assembled by adding the relevant constraints continuely after the tow components completing, the 3-D virtual prototype model was shown in figure 4.

Interference Detection

Based on section of 3.3, each parts and components were related by adding the relevant constraints, but its relationship of mutual cooperation must be checked. In UG the specific methods of interference detection was that, Menu → Analysis → Examine geometry, check geometrical characteristics of each part in the pop-up menu, and then the system would analyze automatically for transplanting mechanism assembly, the interference detection results were obtained and shown in figure 5. It is know that the whole mechanism without interference from the figure 5.

Generation of 2-D Engineering Drawings

Based on above sections, 2-D engineering drawings were generated from corresponding parts and assemblies in the drawing module, and automatic dimensioning was done in each drawing. 3-D models and 2-D engineering drawings were related with each other, namely any modification of dimensions made in 3-D part and assembly module would be reflected in drawing module and vice versa, which improving the efficiency. The different angle of projection views, local amplification figure, sectional view and so on, would be produced according to needs in the process of generating 2-D engineering drawings. Some necessary annotations were inserted into drawings as these were required for manufacture, such as weld symbol, geometric tolerance, surface finish symbol, BOM (Bill of Material) and so on. The 2-D assembly drawing was obtained after further processing to the figure 4, and shown in figure 6, the 300mm is the rice row spacing. (1)In allusion to the existing rice pot seedling transplanter exists the defects of complex structure, high cost and low efficiency, the necessity of efficient, light simplified and full-automatic was put forward to study on transplanting mechanism for rice pot seedling.

(2)UG NX 8.0 was applied to accomplish parts design, assemblies design, interference detection and generation of 2-D engineering drawings. Results showed that the design was reasonable and feasible.

(3)The created parts and assemblies will be preparation for further simulation and analysis with softwares of Adams and Ansys, it is provides the reference for the design of rice pot seedling transplanter.

Fig. 1 .

 1 Fig. 1. The sketch of transplanting mechanism for rice pot seedlings 1. Sun gear 2. Middle gear 3. Planet gear 4. Cam 5. Seedling clip 6. Seedling-pushing rod 7. Spring place 8. Spring 9. Shifting fork 10. Sun shaft 11. Middle shaft 12. Planet shaft 13. Transplanting arm 14. Planet carrier

Fig. 2 . 3 .

 23 3-D models of transplanting parts a) Planet carrier b) Transplanting arm Fig. Sub assembly of transplanting mechanism

Fig. 4 .Fig. 5 .

 45 Fig. 4. 3-D virtual prototype model of transplanting mechanism

Fig. 6 .

 6 Fig. 6. 2-D assembly drawing of transplanting mechanism 1. Positioning board 2. Cam bushing 3. Cam 4. Transplanting arm 5. Screw 6. Spring washer 7. Packing paper of cam 8. Right shell of planet carrier 9. Circlip 10. Deep groove ball bearing 11. Left shell of planet carrier 12. Planet gear 13. Middle gear 14. Middle shaft 15. Sun gear 16. Skeleton seal ring 17. O seal ring 18. Planet shaft 19. Bolt 20. Elastic washer 21. Flat washer 22. Hex nut 23. Deep groove ball bearing 24. Flat washer 25. O-rubber seal ring 26. Flange 27. Locking pin

  , it is composed by transmission component with non-circular gear and transplanting component. The sun gear, middle gear and planet gear are non-circular gear. Planet carrier and sun shaft are solid joint, planet gear and transplanting arm(including cam, shifting fork, spring, spring place, seedling-pushing rod and seedling clip) are solid joint. Power income from sun shaft, planet carrier rotates uniformly, transplanting arm rotates reversely through middle gear, shifting fork is swaied by combined effect of cam and spring, the movement of seedling-pushing rod is formed by sway of shifting fork, the open and close of seedling clip are realized by movement of seedling-pushing rod. The whole transplanting process is achieved for rice pot seedling by the above actions.

* The paper is supported by the National Natural Science Fund Projects (Project number is 51175073), the Special Fund for Agro-scientific Research in the Public Interest (Project number is 201203059-01), the Northeast Agricultural University Doctor Startup Fund (Project number is 2012CRB56).

Acknowledgment

The paper is supported by the National Natural Science Fund Projects (Project number is 51175073), the Special Fund for Agro-scientific Research in the Public Interest (Project number is 201203059-01), the Northeast Agricultural University Doctor Startup Fund (Project number is 2012CRB56).


Zhenxiang Xing

Jing Li

Meixin Liu
email: cliumeixinneau@sina.com

Qiang Fu

Hao Guo

The Catchment water-based system Health evaluation based on the TOPSIS model

Keywords: Naolihe Basin, water-based system, health assessment, entropy weight method, TOPSIS

The health status of Naolihe Basin has already varied significantly affected by the climate change and human activity. Therefore, it is reasonably much important to analyze and evaluate the health status of river, which could provide basis for the comprehensive development and protection in the Naolihe Basin. So, this paper takes Baoqing country as the study region, uses the stable state, the harmonious degree and evolution rate to describe the health status, and establishes the health evaluation index system of water-based system in Baoqing country based on the concept of water-based system. The entropy method is used to the weight vector of steady state index and harmonious degree index, the TOPSIS was applied to analysis the health status of water-based system of Baoqing country during 2005 to 2009. The comprehensive evaluation result shows that the water-based system of Baoqing country is in the state of comparative healthy, the main reason is that water resources of the study area are relatively insufficient, and drinking water security and water consumption cannot obtain the complete guarantee, which leads to lower steady state.

Introduction

Water-based system refers to habitats carrying system that is made up of water and related wading medium and engineering in a certain hydrological scale and spatial dimensions. Space for different hydrological scale, water-based system has different characteristics. The system covers the water, air, soil, biological, social economy and many other aspects, which is a comprehensive on river health, the development and utilization of drainage basin water resources and regional water resources carrying capacity, etc. It is a huge system on real significance [START_REF] Ning | Study on the concept, connotation and evolvement of the base-system of water [J][END_REF][START_REF] Ning | Integrating the hydrological technology for analyzing the base-system of water [J][END_REF].

At present, the study of water-based system is still in its primary stage, with few related research and application. Zhou Huicheng etc. [START_REF] Huicheng | Multi-objective fuzzy assessment of health of Dalian water-based system[END_REF][START_REF] Huicheng | Evaluation of Dalian water-based system based on index weight reliability analysis[END_REF] put forward the concept of city water system, which established water system health index of Dalian city. Xiang Biwei etc. [START_REF] Biwei | Fuzzy Comprehensive Assessment of Water-based System Health for Dongjiang Basin Based on AHO Method[END_REF] established the water-based system of Dongjiang River Basin and constructed the index system of ecosystem health assessment of the Dongjiang River Basin Water System based on the water-based system. The rough set theory and set pair analysis were applied to the water-based system in Dongjiang River Health Assessment by Huang Guoru etc [START_REF] Guoru | Health state assessment of water-based system for Dongjiang basin based on rough set theory and set pair analysis[END_REF].

BaoQing is located in the northeast of Heilongjiang province, belongs to Shangyashan city. BaoQing's economy keeps developing fast and rich in resources [START_REF] Wenhui | Baoqing County of Sanjiang Plain Land Use Change TuPu Analysis[END_REF]. It is an important commodity grain base. However, economic development have done much harm to the resource environment and threatened the regional Health.

Regional Health Assessment Index Based on Water-Based Systems

To consider the influence of the consistency of the system variables, contradictory, and time variability on the system, we need to describe the characteristics of the system in water base system. When we evaluated the health status of water-based systems, we used the three characteristic properties of water-based systems to characterize the state of water-based systems, namely stability, harmony and evolutionary. Meanwhile we used the stable state, the harmonious degree and evolution rate to describe. Because the economy of studied areas was dominated by agriculture, we put forward table 1 and 2 through the study of theories related and the combination of natural and social characteristics of the study area. Table 1 represents the index and standard value of steady state and 2 represents the index and standard value of harmonious degree. The evolution rate represents the degree of change of water-based systems on the time scale to track and characterize the stability and harmony of water-based system. So evolution rate can be divided into steady state evolution rate and the harmonious degree evolution rate. By using the calendar feature values of steady-state and harmony to draw the break point diagrams of steady-state and harmony, we select the slope of the process line as a characteristic value of evolution rate. Index and standard value of evaluation rate are shown in table 3.

Ⅰ <40 <30 <5 >90 <100 <0.5 >20 Ⅱ 40~50 30~60 5~10 80~90 100~150 0.5~2 11~20 Ⅲ 50~60 60~70 10~15 70~80 150~225 2~3 6~11 Ⅳ >60 >70 >15 <70 >225 >3 <6
Note:a,Ⅰ ~ Ⅳ level respectively: very stable, stable, basically stable and unstable; Un: urbanization progress; Pd: population density (per˙ (km 2 ) -1 );

Pswla: proportion of soil and water loss area (%);

Pcse: proportion of controlling soil erosion (%);

Cf: consumption of fertilizer; Cp: consumption of pesticides; Ga: green area.

Table 2. Index and standard value of harmonious degree rank Lwcpc /L ˙(perḋ

) -1 Rufiw /% Iwd /% Hwccpp /% Pwa /% Prdws /% Pw /% Peia /% Ⅰ >300 >60 >90 <30 >10 >90 >50 >90 Ⅱ 200~300 50~60 80~90 30~40 5~10 80~90 50~30 80~90 Ⅲ 150~200 40~50 70~80 40~50 3~5 70~80 20~30 60~80 Ⅳ <150 <40 <70 >50 <3 <70 <20 <60
Note: Ⅰ ~ Ⅳ level respectively: very harmonious, harmonious, basic harmonious and disharmony;

Lwcpc: life water consumption per capita; Rufiw: repeating utilization factor of industrial water;

Hwccpp: high water consumption crop planting proportion; Iwd: industrial water disposal;

Pwa: proportion of water area; Prdws: proportion of rural drinking water standards;

Pw: proportion of woodland; Peia: proportion of effective irrigation area

    ' * * * 1 2 Z*= (max / ),(min / ) 1, 2,..., , ,..., ij ij n Z j J Z i J i n Z Z Z     (1)
    ' 1 2 Z = (max / ),(min / ) 1, 2,..., , ,..., ij ij n Z j J Z i J i n Z Z Z         (2)
where: Z ij is the element of the standardized weighted matrix, J、J' stand for index of the bigger the optimal type and index of the smaller the optimal type.

Calculate positive ideal reference solution S i + and negative ideal reference solution S i of each monitoring site by using the Euclidean distance coefficient.

*2 1 S ( ) ( 1, 2,..., ) n i ij j i Z Z i n       (3) 2 1 S ( ) ( 1, 2,..., ) n i ij j i Z Z i n        (4)
Once the distance from each monitoring site was determined, the relative closeness coefficient C i * of each monitoring site can be computed by equation ( 5)

* * * / ( ),0 1 ( 1, 2,..., ) i i i i i C S S S C i n        (5)
If an index value of the monitoring site is same with the positive ideal reference solution, then C i * =1; If an index value of the monitoring sites is same with the negative ideal reference solution, then C i * =0.

TOPSIS method was used for water-based system health evaluation. First of all, we confirm the characteristic values of stable state and the harmonious degree of water-based systems. Then we obtain the evolution rate by the characteristic values.

In the end, the stable state, the harmonious degree and evolution rate are assessed comprehensively.

Determine the Index Weight

There are currently a lot of methods to confirm index weight in the multi-index comprehensive evaluation, such as the Delphi method and Analytic Hierarchy Process (AHP), Mean square deviation method, Membership frequency method and Principal

Component Analysis (PCA) [START_REF] Yan | The fuzzy synthetic evaluation of water resource sustainable development and utilization in Xi'an city based on AHP[END_REF]. Entropy method can obtain the weight by mining data own information and eliminate the influence of subjective judgment of the index weight [START_REF] Md Masud Hasan | Entropy, consistency in rainfall distribution and potential water resource availability in Australia[END_REF][START_REF] Yanfang | Matter-element Model Based on Coefficients of Entropy for Comprehensive Evaluation of Irrigation Water Quality[J][END_REF], and make the index weight results more objective. The index of steady state and index of harmonious degree are calculated by the Entropy method.

 

Determine the characteristic value of steady state rank and harmony degree rank

We select the standard values to establish matrix in table 1 and 2. Though the normalized processing and weight vector, weighted normalized matrix is obtained.

Finally we calculated the Euclid approach degree of each level, namely, the standard value of steady state rank and harmony degree rank, shown in table 4.

Calculate the characteristic value of steady state and harmony degree

Characteristic matrix is composed of the index value and standard values of steady state and harmony degree of study area. By taking the characteristic matrix to the TOPSIS model, we calculate the approach degree to obtain the characteristic value of steady state and harmony degree in Baoqing during 2005-2009. Then by comparing the characteristic value of steady state rank and harmony degree rank, we obtain steady state rank and harmony degree rank, shown in table 5.

Assessment of Evolution Rate

According to the characteristic value of stable state and the harmony degree in table 5, we calculate the evolution rate of steady state and harmony degree. Combining the table 3, we obtain the evolution rate of water-based systems during 2006-2009, shown in table 6.

Comprehensive Assessment of the Health of Water-Based Systems

Based on the analyzing the stable state, the harmonious degree and evolution rate respectively, we can a comprehensive evaluation for the health of water-based systems. According to the actual situation of the study area, we assigned the weight of stable state, evolution rate of steady state, harmony degree and evolution rate of harmony degree. Finally, the weight was 0.4, 0.4, 0.1, 0.1. In addition, due to the smaller numerical of the evolution rate, we cannot directly combine the evolution rate with stable state and harmony degree. Therefore, we need to normalized calculation for evolution rate, and then make a comprehensive evaluation. If the value  0.62, system is in healthy state; If the value0.42~0.62, system is in healthier state. The evaluation results listed in table 7.

The Evaluation Results Analysis

We can see from

Conclusions

In this paper, a water-based system evaluation model is introduced to catchment health assessment, and the health evaluation index system of water-based system was established according to the actual situation of Baoqing country of Naoli river basin, and then the TOPSIS model was used to evaluate catchment health status. Through the study, several conclusions were drawn as follow:

(1)The health status of water-based system of Baoqing country was relatively lower, the main reason was that water resources of the study area are relatively insufficient, and drinking water security and water consumption cannot be guaranteed completely, which lead to the lower steady state.

(2)In order to improve the health status of water-based system of Baoqing country, relies on improving the rate of water resources should be improved, increasing the irrigation area should be developed, and the awareness of savings water should be raised, and so on.

(3)The evaluation index system for Baoqing was not mature completely due to the limitation of data and research methodology, and certain limit of determination of evaluation indexes cause agricultural characteristics of Baoqing. A further research should be considered with more data of industrial and environmental index.

Table 1 .

 1 Index and standard value of steady state

								Ga
	rank	Un	Pd/per( km 2 ) -1	Pswla/ (%)	Pcse/ (%)	Cf kg˙(km 2 ) -1	Cp /t( km 2 ) -1	/m 2 ˙ per -1

Table 3 .

 3 Index and standard value of evaluation rate

			harmonious degree
	rank	steady state evolution rate
			evolution rate
	Ⅰ	<-0.02	<-0.02
	Ⅱ	-0.02~0	-0.02~0
	Ⅲ	0~0.2	0~0.2
	Ⅳ	>0.2	>0.2
	3

Comprehensive Evaluation of the Health of Water-Based Systems

TOPSIS model is a method for multi-objective-decision-making, also known as approaching ideal solution [8~11]. According to nature of the index itself and index data, two contrast regimens are calculated, namely virtual positive ideal solution and virtual negative ideal solution. The formula as follows:

2 Steady State and Harmonious Degree Evaluation

	  稳	0.1266,0.1171,0.1059,0.1449,0.1076,0.1303,0.1300,0.1376
	 		 0.1218,0.1219,0.0916,0.1218,0.1225,0.1025,0.1025,0.0927,0.1226

和

3.

Table 4 .

 4 Grade standards of steady state and harmonious degree

	steady state rank	standard deviation	harmony degree rank	standard deviation
	Ⅰ	>0.66	Ⅰ	>0.63
	Ⅱ	0.48~0.66	Ⅱ	0.36~0.63
	Ⅲ	0.24~0.48	Ⅲ	0.18~0.36
	Ⅳ	<0.24	Ⅳ	<0.18

Table 5 .

 5 Grades of steady state and harmonious degree

	years	characteristic value	steady state rank	years	characteristic value	harmony degree rank
	2005	0.48	Ⅲ	2005	0.55	Ⅱ
	2006	0.45	Ⅲ	2006	0.50	Ⅱ
	2007	0.49	Ⅲ	2007	0.42	Ⅲ
	2008	0.49	Ⅲ	2008	0.48	Ⅲ
	2009	0.41	Ⅲ	2009	0.52	Ⅱ

Table 6 .

 6 Grades of evaluation rate

	years	2006	2007	2008	2009
	evolution rate of steady state	-0.01	0.03	-0.003	-0.08
	rank	Ⅳ	Ⅲ	Ⅳ	Ⅳ
	evolution rate of harmony degree	-0.05	0.08	0.05	0.04
	rank	Ⅳ	Ⅲ	Ⅲ	Ⅲ

Table 7 .

 7 Assessment result of Baoqing water-based system

	years	2005	2006	2007	2008	2009
	characteristic value	0.514	0.472	0.466	0.558	0.462
	rank	healthier	healthier	healthier	healthier	healthier

Table 5

 5

, the steady state of Baoqing was in grade Ⅲ. The main reason lies in the study area less water, leading to safe drinking water and water consumption cannot get effective guarantee. Therefore, when efforts to increase water resources development,it is easy to cause instability of water-based system. The level of harmony degree is superior to the steady state level, in the majority with Ⅱ level. This is mainly because the study area is mainly dominated by agriculture, while the study about renovation and destruction of water-based systems is relatively less.

Comprehensive health state of water-based systems was in a relatively healthy state and has also been picking up in 2007.

Acknowledgment

Funds for this research was provided by the national natural science foundation (51109036; 51179032), the specialized research fund for the doctoral program of higher university of the Ministry of Education (20112325120009) the special scientific research funds for Ministry of water resources public welfare industry (201301096), The leader talent echelon back-up headman funding projects of Heilongjiang province (500001), the studying funds of postdoctoral in Heilongjiang province (LBH-Q12147), the science and technology project of Heilongjiang Provincial Education Department(11541022).


Jihong Yang

Haiwei Li

Yin Zhan&liangshu Shi

Jinqiang Wang

Zhengchao C Chen
email: zcchen@ceode.ac.cn

A Method to Determine the Maximum Side Perspective of Satellite with the Constraints of Mapping accuracy

Keywords: DEM accuracy, satellite side perspective, ortho-rectification, geolocation accuracy

In order to shorten the revisit period, and improve the efficiency of imaging, currently, all the in orbit high resolution remote sensing satellites adopt side-view imaging technology. When satellites imaging with a side perspective, it would inevitably cause the degradation of image quality, like spatial resolution reduction, image deformation incensement, and the reduction of positioning accuracy. In addition, with the increase of the side perspective, the error of DEM data will be amplified in the process of ortho-rectification, which, thus, will bring bigger error for image mapping accuracy. To address this problem, embarked from the impact of side view and DEM precision on image point error, this paper used Quick bird image data of the same area but different side perspectives, and simulate the impacts of different DEM elevation error on different side view image. At last we put forward a method to determine the maximum side perspective with map precision constraints, and set up a conversion relationship among satellite side view, DEM error and image point error. Finally, the paper combines the errors of 1:50000 DEM, ASTERGDEM and the requirement of ortho-image drawing, discusses and gives the values of maximum side perspective in the mountains and plains.

Introduction

Along with the continuous improvement of remote sensing satellites' spatial resolution, it also brought adverse effects of the image width and image acquisition efficiency reduction. In order to shorten the return cycle and to improve the efficiency of imaging, currently, on-orbit high resolution remote sensing satellites use the sideview imaging technology to improve the flexibility towards observation objects and image acquisition efficiency. As is well-known, when the satellites side-view imaging, the observation path is increased, the relative geometric relationship between satellite and ground objects is changed, which caused the degeneration of image quality [1] (such as the spatial resolution reduced, image deformation increase, etc.) According to the principle of projection, from a point in space (viewpoint) observing the surface, each point on the surface along with topographic relief will generate geometric distortion on the image. The specific performance on the optical remote sensing imageries is as follows: the ground point, which is away from the viewpoint and with higher elevation, will fall to the opposite side of the viewpoint [START_REF] Yong | Remote Sensing Refined Explanation[END_REF] . Ortho-rectification is to make use of terrain elevation model (DEM) to perform terrain distortion correction for each pixel in image, and make the image meet the orthographic projection, thus eliminating this distortion.

According to the error analysis of satellite imagery ortho-rectification model, the main factors affect the accuracy of ortho-rectification are as follows: orthorectification model error, satellite orbital attitude error, control point accuracy, DEM error, etc [START_REF] Han | Research on the Influence of Correcting Precision Caused by Satellite Incidence Angle[END_REF] . In which the ortho-rectification model commonly used strict physical model and rational polynomial model (RPC). Strict physical model are considered to be theoretically rigorous, thus, It can be considered without error;The RPC model is a simulation of strict physical model, the model conversion error is generally less than 1m (Liu Shijie, 2008); The error of satellite orbit and attitude is decided by the control accuracy of the satellite itself and the in-orbit state, which cannot be changed by the average user. The precision of control points can be controlled through field measurement, currently using GPS can get higher precision. DEM data are input parameters of ortho-rectification, which generally directly adopt national fundamental geographic information data, the precision of is slightly different in the mountains and plains. In addition, when the satellites side-view imaging, their orbit and attitude control precision and measurement accuracy will decrease because of satellites or remote sensors' side swing [START_REF] He | Study of Influence of Swinging on the Systemic Parameters of the Satellite and CCD Camera[END_REF] ; Furthermore, according to the theory of projection, the increase of side perspective will definitely magnify the effects caused by DEM error. Therefore, the satellite side perspective is also one of the main error sources of satellite images ortho-rectification.

It can be seen from the above error analysis of ortho-rectification, in general case, the factors to be considered most by users are side perspective and DEM errors. Many scholars have carried out some research work about the effects on image quality degradation and ortho-rectification precision caused by side perspective, and the effects on ortho-rectification precision caused by DEM errors. Such as Han Wenli, Yuan Xiuxiao, and Wang Xuejun, etc. Han Wenli(2010) quantitatively analyzed the impact on ortho-rectification precision caused by side perspective in theory, and proved the validity of its conclusions through experiments. The conclusions indicate that with increment of the side perspective, the image ortho-rectification accuracy will gradually decline, and the decrease amplitude is quite obvious [START_REF] Han | Research on the Influence of Correcting Precision Caused by Satellite Incidence Angle[END_REF] . Taking into account changes of the side perspective, Yuan Xiuxiao et al., 2009, established the geometry model of high-resolution satellite remote sensing image processing, which improved the image positioning accuracy on the ground targets. It concluded that the change of the side perspective is a factor that cannot be neglected in the high-resolution satellite remote sensing image geometry processing model [START_REF] Yuan | A Rigorous Geometric Model Considering the Variety of Side Watch Angle for High-resolution Satellite Imagery[END_REF] . Wang Xuejun et al., 2008, selecting different DEM scales, conducted ortho-rectification to the data with different side perspectives acquired by SPOT5. It certified that when SPOT5 imaging, the side perspective is the key factor leading layer-over phenomenon of SPOT5 orthophoto products, with the premise of ensuring the accuracy of ground control points. It also certified that in the calibration process the improvement of DEM accuracy cannot effectively eliminate layer-over phenomenon of the mountains with complex terrain and large elevation drop. About the impact on image correcting accuracy caused by DEM data, Shi Yuhua (2007) , using two different DEM data, calibrated the same scene image. The results show that the ortho-rectification accuracy is higher with small basic grid and high-precision DEM data [START_REF] Shi | Research of Quickbird Image on Orthocorrection and Updating of Relief Map[END_REF] .

However, these studies only consider the impact of unilateral side perspective or DEM error on ortho-rectification precision, and failed to combine both. Actually it is a coupling effect between side perspective and DEM error: DEM error will be amplified with the increase of side perspective; Errors caused by side perspective will change along with the change DEM data.

As the input conditions of orthorectification the accuracy of DEM data are often unable to change. Therefore, in practice, it is more significant to study how to determine the maximum satellite observation side perspective in the premise that there is some error in DEM data, as well as guarantee certain accuracy of ortho-rectification and mapping. Aiming at this problem, this paper adopted Quickbird image data with different side perspectives in Beijing, proposed a method to determine the maximum satellite imaging side perspective with certain constraints of mapping accuracy by simulating different influence law on the accuracy of image ortho-rectification caused by DEM elevation error, and established a quantitative conversion relationship among satellite side perspective, DEM error, and the error of ortho-rectification image points.

2

Experiments and Methods

Experimental DATA

The experimental area is the northern part of Beijing, including plain and mountain. Experimental data are multispectral image collected by using high-resolution Quickbird satellite in 2002 to 2012. With 2.44 m resolution, side perspective spanning from 5.6°to 43.7°ten different angles in total. Image side perspective spanned broadly, evenly distributed, specifically details can be seen in the table below.

Experimental Methods

According to the principle of photogrammetry, the comparation between image point error caused by the side perspective and imaginary horizontal photograph as Figure 1(a) shows. P is the tilted photograph and P0 is the imaginary horizontal photograph with the same observation conditions. They intersect at isocon line hc. Imagine that ground point M is(m)on tilted photograph P and(m 0 )on horizontal photograph P 0 , respectively. After two photograph overlapping along isocon line,the position of (m) in the horizontal photograph is m, obviously mm 0 is the tilt error. With the increase of side perspective, the tilt error will become bigger. Image point error caused by the relief is shown as follows(right). To facilitate discussion, assume that photograph is horizontal, and the height difference between ground point A and the datum is h. The image point of ground piont A is point a on the photograph; the projection of A on the datum is A 0 , whose image point is a 0 . aa 0 is the displacement of image points caused by the relief. As can be seen, the displacement of image points will increase with the increasement of height difference h [7][START_REF] Okamoto | Orientation Theory for Satellite CCD Line-Scanner Imageries of Mountainous Terrains[END_REF][START_REF] Okamoto | Orientation theory of CCD line-scanner images[END_REF] . During the process of ortho-rectification, image points error will be affected by side perspective and relief at the same time. In the existing research results, different influence factors are often analyzed independently, which ignores the mutual influence and internal relations of different factors and is not real and comprehensive enough to reflect the objective situation of data. Because the strict physical model to calibrate the satellite image contains quantities of trigonometric functions and complex variables. If directly use strict physical model to deduce the error model of ortho-rectification, it will be very complicated. It is also why many scholars assume that the variables are independent in the derivation of the law of ortho-rectification error [10][11] . In addition, RPC model is an approximate mathematical simulation of the physical model. RPC model without satellite orbit and attitude parameters, there is no way to establish the error model of ortho-rectification, DEM and orbit attitude parameters. Based on these considerations, this paper used the real images with different side perspectives and corresponding parameters,analyzed the relationship among side perspective,DEM accuracy,and ortho-rectification precision, when inputting different DEM elevation data, and derived the function among variables based on experimental data statistics. The specific process is shown in figure 2.

Image

Figure 2 the analysis process of the effects on ortho-rectification precision caused by side perspective and DEM error

According to the figure 2, the concrete steps and methods are as follows: Input the satellite images and their corresponding parameters, original DEM data into RPC model, when the side perspective is given. Using RPC model, conduct ortho-rectification against specified pixel. Record the calibrated coordinates as the initial value of the corrected geographical coordinates.

Change the DEM elevation value without other parameters changed. Conduct ortho-rectification against specified pixel by using RPC ortho-rectification model, then Obtain the corrected value of geographical coordinates which is derived from formula (1). The displacement of the coordinates in step ① is also calculated by formula (1). Given the different DEM elevation values, obtain the ortho-rectification error( one column in Table 2)with the same side perspective and different DEM elevation error. Figure 3 shows that using experimental data with different side perspectives, the paper calculated the influence law distribution on ortho-rectification accuracy caused by DEM error. From the numerical distribution and the fitting results in figure 3, it can be seen that under the same side perspective, pixel positioning errors increase with the increasement of DEM elevation values;the larger the side perspective is, the greater the pixel positioning is. And the pixel positioning is more obviously affected by DEM values. The change is completely linear relationship, and fitting precision R 2 is 1. For instance, with the side perspective 5.6°, the positioning error is 2.08m, when DEM error is 20m. While it increases to 20.8m, when DEM is 200m, which increased 10 times. Figure 4 shows the impact on ortho-rectification accuracy caused by side perspectives with certain elevation error. It can be seen that under certain DEM elevation error, the image positioning error will be bigger with larger side perspectives. After fitting, the variation can be expressed by a quadratic polynomial. Fitting accuracy R 2 is almost equal to 1, like, when the elevation error is 20m, R 2 = 0.9996. 2 and Figure 3, Figure 4, various variations combine the impact on image points displacement caused by DEM elevation values and side perspective. They reflect the variations and quantitative relationship of the three variables.

2 ) ( ) ( y x S      (1)
According to figure 3, it can be seen that with certain side perspective, the impact relationship on ortho-rectification accuracy caused by DEM error is completely linear, and the slope of the fitting line increases with the increasement of side perspectives.

In order to investigate the relationship between the fitting line slope and side perspective, the slope and intercept of all the test data are presented in table 3. As can be seen from the table, the slope of the fitted line increases with the increasement of side perspectives, but the intercepts are relatively small. The Maximum of intercept is no more than 0.0024 cm, which can be ignored as infinitesimal in practical applications. In order to further give the quantitative relationship of fitting line slope and side perspective, Figure 5 shows the slope distribution curve of the fitting line along with the change of side perspective and fitting results of experimental data in this paper. From numerical distribution and fitting results in the figure 5, it can be seen that it is also a linear relationship between the side perspective and fitting line slope. Fitting accuracy R2 reached 0.9769. Therefore, the relationship between fitting line slope of DEM error and ortho-rectification and satellite side perspective can be considered linear. (Eq. 2):

b angle a slope    (2)
In which slope is the slope of the fitting line; angle is the side perspective; a, b is coefficient of line fitting. According to the physical meaning, combining Figure 3 and Equation 2, slope y is the ratio of correcting error and elevation error. Namely:

H S slope   /  (3)
Where S  is correcting error; H  is DEM error.

APPLICATION

This paper, by using QuickBird satellite images in Beijing,deduced the effects on the precision of image ortho-rectification caused by side perspective and DEM error, and provided the quantitative functional relationship among the three. With this function, if given the actuary request of image ortho-rectification and DEM accuracy, it is possible to determine the largest satellite imaging side perspective. Thus, before collecting data, it can help avoid the potential trouble of ortho-rectification accuracy overrunning in later phase.

Based on the Quickbird test data statistics model, this paper, using the 1:50 000 DEM of China and the American ASTER GDEM to perform ortho-rectification, respectively calculated the maximum allowable side perspective on the mountains and plains.

According to the requirements of GBT 13977-1992 "1:5000,1:10000 topographic maps and aerial photogrammetry field work norm", plane position mean error of feature points on the map is less than 0.5mm on plains and hilly lands, 0.75mm on mountainous and alpine areas.

Corresponding 1:10000 topographic mapping requirements, the error of image calibration is no more than 5m on plains and hilly lands,7.5m on mountainous and alpine areas.

In addition, the grid size of our nationwide 1:50000DEM 25×25 m is known. The elevation mean error of grid points comparing to the near field elevation control point is not more than 4m on plains, not more than 11m on mountains[1]. The elevation accuracy of American ASTER GDEM is 20m(ASTER Global DEM Validation Summary Report. 2009).

1) According to formula (5), When the national 1:50000 DEM is used of H  plains is 4m, and S  is 5m. Then in order to meet the mapping requirements of 1:10000, the side perspective on the plain areas of Quickbird image must be less than or equal to 50 °. H  of mountains is 11m, and S  is 7.5m, the corresponding side perspective must be less than or equal to 27.3°.

2)when American ASTER GDEM is used, H  of plains and mountains is 20m, in order to meet the mapping requirements of 1:10000, the error of image calibration is no more than 5m on plains and hilly lands and 7.5m on mountainous and alpine areas.

Taking elevation value 5m into computation, the imaging side perspective of Quickbird should be less than or equal to 10 °。 Note that the formula ( 6)is deduced based on the results of data regression statistics in Beijing experimental zone. Due to the limitations of statistical samples and terrain differences, these results are only for reference.

In addition, given the current main on-orbit high-resolution commercial satellites, including QuickBird, WordView, IKONOS, etc. Due to the similarity of Orthorectification error and solutions, the method should also be applicable to other similar type of satellite platforms.

Conclusions

This paper established the quantitative conversion relationship among satellite side perspective, DEM error,ortho-rectification,and image rectification, proposed a method to determine the maximum imaging side perspective with map precision constraints, and provided guidance on data selection and processing. When known DEM data accuracy and the accuracy that ortho-rectification expected to achieve, the maximum side perspective of the satellite can be calculated to meet those conditions. On the other hand, when the existing satellite data side perspective is known, the minimum accuracy of DEM data can be calculated to achieve the expected orthorectification precision. Because the model in this article is obtained by the analysis of real data, thus, the authenticity of the results is guaranteed, and the conclusion is also in line with the actual situation. In addition, the ideas and methods adopted by this paper are also applicable to the analysis and study of other sensors with the same kind.

  Figure 1 the error of displacement of image points caused by side perspective and relief((a): side perspective; (b): relief)

2

 2

Figure 3 Figure 4

 34 Figure 3 the effect of elevation error to the position error at different side perspective

Figure 5

 5 Figure 5 the relationship of side perspective and line slope

Equation 4 can be derived from combining Equations 2

 2 the approximate relationship among side perspective, DEM error and error of pixel correcting.Using the experimental data in this paper, it can derive that a equals to 0.025, and b equals to -0.0867. Because b is less than 9cm, which can be regarded as infinitesimal and ignored. The simplified function among side perspective, DEM error and pixel correcting accuracy can be derived from inputting the formula 4 with a = 0.025 and discarding b.

  a special case of 4. When the precision requirements of positioning error, DEM data accuracy are known, the maximum side perspective of QuickBird satellite can be caculated, which meet the accuracy requirements.

Table 1

 1 Test data tables side perspective Statistics

	Satellite Name	Side perspective( °)

Table 2 the correcting error(m) at different side perspective and DEM error of QuickBird image

 2

		5.6°	10.4 °	14.4 °	16.3 °	22.1 °	28.2 °	31.4 °	34.3 °	38.9 °	43.7 °
	20m	2.080815	4.101156	5.566553	6.112367	9.033995	11.74509	13.44905	14.92516	17.84973	22.63661
	40m	4.162622	8.202106	11.13377	12.22391	18.0683	23.49034	26.89715	29.84912	35.70007	45.27226
	60m	6.24443	12.30424	16.70032	18.33628	27.10355	35.23445	40.3462	44.77428	53.54963	67.9079
	80m	8.325118	16.4054	22.26658	24.44782	36.13786	46.97954	53.79524	59.69846	71.39936	90.54354
	100	10.40693	20.50635	27.83285	30.55962	45.17216	58.72381	67.24335	74.62242	89.24892	113.1792
	m
	120	12.48873	24.6075	33.3994	36.67116	54.20646	70.4689	80.69239	89.5466	107.0979	135.8148
	m
	140	14.56955	28.70964	38.96566	42.78353	63.24076	82.21301	94.1405	104.4708	124.9468	158.4495
	m
	160	16.65135	32.81059	44.53192	48.89507	72.27507	93.95727	107.5895	119.3947	142.7957	181.0839
	m
	180	18.73204	36.91174	50.09847	55.00687	81.30906	105.7014	121.0376	134.3189	160.6447	203.7186
	m
	200	20.81385	41.01269	55.66474	61.11842	90.34337	117.4465	134.4854	149.2429	178.4936	226.3533
	m

Table 3 the slope and intercept of fitting straight line between DEM error and correcting precision with different side perspectives

 3

	Side
	perspective	5.6	10.4	14.4	16.3	22.1	28.2	31.4	34.3	38.9	43.7
	(°)
	Slope	0.1041	0.2051	0.2783	0.3056	0.4517	0.5872	0.6724	0.7462	0.8925	1.1318
	Intercept (m)	-0.0002	-0.00009	0.0007	0.0006	0.00005	0.0011	0.0006	0.0013	0.0017	0.0024

Acknowledgment

In this paper, the test data are provided by Beijing Aerospace Shi Jing Information Technology Co, Ltd.


Xu Han
email: hanxu@muc.edu.cn

Li Wang

Hui Wang

Shuqin Wang

Efficiency Evaluation of Agricultural Informatization Based on CCR and Super-efficiency DEA Model

Keywords: DEA, CCR, efficiency evaluation, informatization

In this research, we want to evaluate the efficiency of input / output in agricultural informatization (AI) and the redundancy of AI by using DEA method. An index system evaluating the input and output in agricultural informatization was built with the support of CCR Model and Super-efficiency DEA Model, which contains 9 indices. We processed the data of agricultural informatization in Huaihua and Xiangxi, two areas in Hunan province, with DEMP and EMS software and analyzed the efficiency of agricultural informatization in different 5 years and figure out the tendency of developing status in AI from 2009 to 2013. The results show that the CRSTE, VRSTE, SCALE efficiency of AI in two areas is efficient and the inputs and outputs about AI in 2009 and 2011 have spaces of improving. In general, the developing tendency of AI efficiency in two areas is stable in these years even though they are not developed areas in agricultural informatization. The index system of AI evaluation in this research could be better and reliable in future if we get more data and add more indices in it, but it is hard for us now to get more data because of the limitation of incomplete statistical data released by local governments.

Introduction

With the development of information communication technologies (ICTs), the trend of informatization is spreading fast on the world. Agricultural informatization is an important component in our information society, and it is the inevitable outcome that modern information technology combines with agricultural interior demand.

Everett [START_REF] Rogers | Informatization, globalization, and privatization in the new millennium[END_REF] defines informatization as the process through which new communication technologies are used as means for furthering development as a nation becomes more and more an information society [START_REF] Rogers | Informatization, globalization, and privatization in the new millennium[END_REF]. As a description of the development, informatization refers to the extent of a geographical area, economy or society continues to develop based information and information communication technologies, in other words, it refers to the degree of workforce size enhanced based on the information and information communication technologies [2]. Agricultural Informtization refers to the information communication technologies (ICTs) are comprehensively applied in the fields of agriculture, and penetrating into agricultural production, marketing, consumption, and rural social, economic, technological, and other specific aspects of the whole process [START_REF] Zhang Lingxian | Evaluation of the rural informatization level in four Chinese regions-A methodology based on catastrophe theory[END_REF].

The efficiency evaluation of AI in this research refers to the production inputs benefit which is achieved by calculating indices about the ICTs supporting agriculture and the output in agriculture. The indices needed in evaluation are different from other researches because of the different research aims.

Methods in informatizaiton measurement and evaluation abroad [START_REF] Liu Yunwen | Informatization Measurement Theories Comparative Study in Domestic and Foreign[END_REF] usually are Machlup method, Porat method, Informatization Index method. The methods above aims to mainly figure out the informatization level of certain society or economy unit, however they do not focus on the efficiency and can't tell whether it is reasonable in input of the indices related with the AI. Methods in informatizaiton measurement and evaluation in China are Delphi method, Analytic Hierarchy Process (AHP) method, The method for the measurement of informatization level used in China, raised by National Information Center, combines Machlup method and Porat method, and includes 6 factors and 21 indices. [START_REF] Zhiyu | Study on Rural Information Undertaking Public Satisfaction Index Model[END_REF] These methods above applied in domestic rural or agricultural informatization research mostly play extra effort on measurement of AI and service ability.

Comparing the researches on evaluating the level of AI, development status of AI and service ability of AI, the research on the efficiency of AI is rare.

Data Envelopment Analysis (DEA) method is seldom used in researches on evaluation of AI, but Machlup Method, Porat Method, AHP method, and Factor Analysis method are common methods in such researches. DEA method needs lesser indices than other methods discussed above to evaluate the efficiency of AI and overcome the shortage of data collecting difficulty.

Methodology

CCR Model

Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers [START_REF] Charnes | Measuring the Efficiency of Decision-making Units[END_REF]. It is used to empirically measure productive efficiency of decision making units (or DMUs). Non-parametric approaches have the benefit of not assuming a particular functional form/shape for the frontier, however they do not provide a general relationship (equation) relating output and input [START_REF] Aristovnik | Relative efficiency of police directorates in Slovenia: A non-parametric analysis[END_REF]. ( )

CCR

{ ∑ ∑ ∑ In D1, set ( ) ( ).
Description of CCR Efficiency Model:

1) Suppose there are n DMUs: DMU 1 , DMU 2 ,..., and DMU n .

2) Suppose m input items and s output items are selected with the properties.

3) Let the input and output data for DMU j be {x 1j , x 2j , •••, x mj )and (y 1j , y 2j ,---, y sj )

4) The calculation of total efficiency of DMU l can be changed to linear programming problem in next slide.

5) Let Xl=(x 1l , x 2l , •••, x ml ), Yl= (y 1l , y 2l ,---, y sl ) 6) We assume the return scale in CCR Model is not changed.

7) θ is the efficiency rate ,θ is at most 1(0≤θ≤1)

Economy Meaning of θ: when the output Y is alternative by k DMUs output with a linear combinations, θ is the compressibility of its input X, θ is also known as the efficiency rate value.

1) If θ=1, the DMU being examined is the point of being efficient frontier surface, and it is efficient status.

2) If θ<1, the DMU being examined is invalid status, 1-θ is the more input of the DMU being examined than efficient status.

DEA efficient economic meaning: output can't be any increased unless one or more inputs to increase or reduce other types of output. Under the same condition, input can't be any decreased.

Super-efficiency DEA Model

When there are many DMUs which are efficient and their efficiency of evaluation is 1(θ=1), CCR CCR model: in the process of evaluating DMU l efficiency, all inputs and outputs, including the inputs and outputs of themselves as part of the calculation.

An efficient decision-making unit can make it into a pro-rata increase, while the efficiency of the value does not change, the proportion of its investment increased is the super-efficiency evaluation value.

Data

Using the DEA and Super-efficient DEA model to evaluate the inputs and outputs of agricultural informatization (AI) in Huaihua and Xiangxi based on the data from 2009 to 2013 collected from statistical bulletin of national economic and social development in Hunan Province, We can analysis the data of inputs and outputs of agricultural informatization in two areas, and find out the aspects which can be improved in AI investment, also we can figure out the tendency of AI in two areas.

We built an index system containing 9 indices in concern of the feasibility and accuracy, and the data is collected from statistical bulletin of national economic and social development published by Statistical Bureau of Hunan Province.

In

Empirical Results and Discussion

The data was processed by DEAP (Data Envelopment Analysis Program, Version 2.1) using CCR model, the results are listed in table2. And we also used EMS software (Efficiency Measurement System, Version 1.3) using to process the data with Super-efficiency CCR model, the results are listed in table3. 2) The CRTES values of Huaihua in 2009 and 2011 are below 1, but greater than 0.9, which means the inputs and outputs about AI in these years have spaces of improving.

3) The scale merit of Huaihua increased in 2009 and 2011, which means the technical efficiency from CRS DEA is increased by expand the scale of AI investment.

Results

Analysis in table 3 and figure 1 1) In 2011, it is inefficient considering the inputs and outputs in AI in Huaihua.

2) From 2010 to 2013, the efficiency of AI in Huaihua is gradually increased, but the efficiency in Xiangxi is relatively gentle and does not changed so much.

3) The efficiency from 2009 to 2010 in both areas is decreased, but the reasons are different. The increase of electricity for rural use leads to the decrease of efficiency in Huaihua, however, the decrease of rural radio coverage leads to the decrease of efficiency in Xiangxi.

Discussion

The efficient status (θ=1) does not means developed status or developing rapidly of AI, but only tell us that considering the output in those years, the inputs is not redundant.

Even the efficiency status of AI in Xiangxi is efficient, the developed degree in this area is lower than Huaihua, which can be seen from the data in table 1.

If we want to describe the development status of AI in undeveloped areas, more indices should been take into account in statistical bulletin.

Conclusions

The CCR model and Super-efficiency CCR Model are suitable to describe whether there any redundancy comparing inputs with outputs in AI, but can't figure out the development level of AI.

The index system can be modified better if more indices data is collected, and describe the efficiency of inputs and outputs comprehensively.

Even the efficiency status of AI in the two areas is efficient, the developing level of AI is still low, especially in the popularity rate of Internet.

  Model is one basic DEA model. CCR Model is proposed by Charnes, Cooper and Rhodes in 1978.

  model can't tell which is better among these DMUs. Anersen (1993) proposed the super-efficiency DEA model to sort efficient DMUs and give them ranking. -efficiency DEA Model Compare with CCR Model Super-efficiency DEA Model: in the process of evaluating DMU l efficiency, the inputs and outputs of DMU l are alternated by the linear combination of inputs and outputs of the other DMUs excluding themselves.

Fig. 1 . 1 Results Analysis in table 2 1 )

 111 Fig. 1. Tendency of AI in Huaihua and Xiangxi

Table 1 .

 1 Data about invest and output of AI in Huaihua and Xiangxi is listed in table 1: Data about invest and output of Agricultural Informatization in Huaihua and Xiangxi

	the index system, Y1 means "Added Value of Agriculture(Billion Yuan)", Y2 means "Farmers'
	Per Capita Income(Yuan)", X1 means "Main Business Volume of Post(Billion Yuan)", X2 means
	"Electricity for Rural Use(Million kWh)", X3 means "Rural Telephone Subscribers(Million)", X4
	means "Cell phone Subscribers(Million)", X5 means "Rural TV Coverage(%)", X6 means "Rural
	Radio Coverage (%)", X7 means "Internet Accounts(Million)".
	City	Year	Y1	Y2	X1	X2	X3	X4	X5	X6	X7
	Huaihua	2009	4.602	2905	4.246	0.184	0.808	1.6246	97.1%	91.5%	0.145
		2010	5.291	3520	5.833	0.211	0.7217	2.048	97.5%	91.5%	0.2144
		2011	5.52	3573	2.511	0.228	0.602	2.335	98.0%	92.8%	0.242
		2012	8.16	4701	2.743	0.3127	0.575	2.6395	98.5%	93.1%	0.3215
		2013	8.3	5849	3.001	0.3441	0.4834	3.0664	98.5%	93.3%	0.3604
	Xiangxi	2009	6.23	2858	2.797	0.2492	0.3178	0.9856	92.0%	89.0%	0.0993
		2010	6.51	3173	3.421	0.2604	0.2882	1.1153	93.8%	72.9%	0.138
		2011	6.934	3674	1.382	0.27736	0.272	1.0114	94.5%	73.5%	0.1702
		2012	7.22	4229	1.526	0.2888	0.2537	1.229	95.5%	87.0%	0.1996
		2013	7.45	5260	1.64	0.298	0.24	1.293	95.7%	97.0%	0.231

Table 2 .

 2 DEA value of AI in Huaihua and Xiangxi(2009)(2010)(2011)(2012)(2013)

		CRSTE	VRSTE	SCALE	SCALE MERIT
	Year
		Huaihua	Xiangxi	Huaihua	Xiangxi	Huaihua	Xiangxi	Huaihua	Xiangxi
	2009	0.999	1.000	1.000	1.000	0.999	1.000 increase	-
	2010	1.000	1.000	1.000	1.000	1.000	1.000	-	-
	2011	0.968	1.000	1.000	1.000	0.968	1.000 increase	-
	2012	1.000	1.000	1.000	1.000	1.000	1.000	-	-
	2013	1.000	1.000	1.000	1.000	1.000	1.000	-	-
	Average	0.993	1.000	1.000	1.000	0.993	1.000
	In table 2, CRSTE means "technical efficiency from CRS DEA", VRSTE means "technical
	efficiency from VRS DEA", SCALE means "scale efficiency = CRSTE / VRSTE".

Table 3 .

 3 Super-efficiency DEA value of AI in Huaihua and Xiangxi (2009-2013) Based on the data in table 3, we can figure out the tendency of agricultural informatization in Huaihua and Xiangxi areas.

	Year	Huaihua	Rank	Xiangxi	Rank
	2009	128.58%	2	133.00%	1
	2010	101.97%	4	104.12%	5
	2011	99.76%	5	116.01%	3
	2012	114.02%	3	107.65%	4
	2013	203.68%	1	131.48%	2

Acknowledgment

Fund for this paper was provided by MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Project No. 12YJA630123). Research in this paper is also supported by School of Information Engineering, Minzu University of China, Beijing.