The Evaluation of the Integrated Risk for the South-to-North Water Transfer Project Using the Bayesian Network Theory

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1 Sept., 2010 Journal of Resources and Ecology Vol.1, No.3 J. Resour. Ecol (3) DOI: /j.issn x Water topic The Evaluation of the Integrated Risk for the South-to-North Water Transfer Project Using the Bayesian Network Theory SHE Dunxian 1,2,3*, YANG Xiaohua 1 and XIA Jun 2 1 School of Environment, Beijing Normal University, Beijing , China; 2 Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing , China; 3 Graduate University of Chinese Academy of Sciences, Beijing , China Abstract: The South-to-North Water Transfer (SNWT) Project is one of the four largest trans-boundary projects in China. With the construction and operation of the project, increased attention has been paid to the risk factors which are induced by the uncertainties. The analysis and management of integrated risk are also put before the project managers. It is extremely important to reduce and control the integrated risks involved in the operation of the project. In this study, Baoying Station on the eastern route of the SNWT Project was chosen as the study area, and Bayesian Network (BN) theory is used to evaluate the probability of the integrated risks. Based on the reasoning of BN, the final integrated risk probability of Baoying Station is estimated to be 0.025% and the risk level is lower level. Analysis of the scenario shows that the probability of integrated risk is most severe when management and maintenance conditions of the pump in use deteriorates. More attention should be paid to this important risk factor during the operation of the project. Key words: the South-to-North Water Transfer Project; integrated risk; Bayesian Network Theory; scenario analysis 1 Introduction The South-to-North Water Transfer (SNWT) Project is one of the four largest trans-boundary projects in China, the aim of which is to transfer water from southern China to northern China to meet the increasing demand for water in northern China (Feng et al. 2007; Zhang et al. 2009). This is the biggest worldwide water transfer project ever, not only in spatial span and length, but also in water transfer capacity. This project is a strategic act to ease water shortage in the Northern China Plain (Wang et al. 1999), to optimize allocation of water resources between river basins and to improve the ecological environment in the water-receiving districts (Huang et al. 2009). It also has great strategic significance for the protection and promotion of regional economic development, environmental improvement and social stability. The construction and execution of large water projects have always been emotional and controversial issues (Yevjevich 2001; Yang et al. 2005). With the construction and operation of the SNWT Project, more and more attention has been paid to the problem of risk induced by uncertainty factors during the operation of the project. The analysis and management of integrated risk is incumbent on the project managers, and identifying, evaluating, eliminating and controlling integrated risks is an extremely important issue during the management of the SNWT Project (Liu et al. 2007). Many risk evaluation methods (such as the analytic hierarchy process method, etc.) have been proposed during the past decades and have extensive application in many fields. However, because all of the foregoing methods utilize certainty knowledge to investigate uncertain problems, they have difficulty in reflecting the uncertainties involved in the risk problems and fail to identify the sources and processes that lead to the uncertainty. However, Bayesian Network (BN) theory, which was first proposed by Pearl in 1986, is an efficient tool for dealing with uncertainty problems. By a reasoning function, the BN can not only estimate the probability of Received: Accepted: Foundation: this study was supported by the National Basic Research Program of China(2010CB428406), National Key Technology R&D Program of China (Grant No. 2006BAB04A09) and the National Science Foundation of P.R.China (Grant No and ). * Corresponding author: SHE Dunxian. shedunxian@sina.com.

2 260 risk, but can also analyze the change in risk along with the change in risk factors. As a very effective risk evaluation tool, BN has been used broadly in the risk evaluation field (Varis et al. 2002; Borsuk et al. 2002; Little et al. 2004; Henriksen et al. 2007; Ticehurst et al. 2007). Farmani et al. (2009) proposed an integrated method based on BN and evolutionary multi-objective optimization. The new method was used to help water managers evaluate the costs and benefits of alternative actions, and to suggest optimal decision pathways under uncertainty. Ticehurst et al. (2007) developed an integrated model framework based on BN and used the constructed BN to evaluate the sustainability of eight coastal lake-catchment systems in Australia. Pollino et al. (2007) parameterized BN using both data and elicited information, and developed a methodology using a risk assessment case study, with the focus on native fish communities in Goulburn Catchment (Victoria, Australia). Sun et al. (2009) developed a new model to quantify river-water quality risk under the collective influence of multiple pollution sources by combining pollution sources model, water-quality model and BN. Accidental pollution of river-water quality in the SNWT Project has been evaluated by the new model. Zhou et al. (2010) proposed a new way to evaluate the dam risk by explaining the application of BN to dam-risk analysis. Two study areas have been selected to test the efficiency of the new method. However, to the best knowledge of the authors, there is no precedent in BN use that can be followed for the integrated risk analysis of the SNWT Project. On the other hand, taking into consideration the complexity of the enormous SNWT Project and BN s efficiency in risk analysis, BN has been used as a new method to evaluate the integrated risk of the SNWT Project in this study. In this study, a brief introduction of BN theory is presented in Section 2. Section 3 takes the Baoying Station on the eastern route of the SNWT Project as a study area to evaluate the probability of integrated risk. The scenario Journal of Resources and Ecology Vol.1 No.3, 2010 analysis is also used, in this section, to analyze the changes in integrated risk along with the changes in the risk factors. Finally, some conclusions are presented in Section 4. 2 BN theory 2.1 Brief introduction to BN BN, also known as probabilistic networks, belief network, causal maps, is a combination product of probability analysis and graph theory (Pearl 1986, 1988; Cowell et al. 1999;Jensen 2002). It is a tool which uses probability and the directed acyclic graph (DAG) to describe the relationship between variables, and it can be used in the representation and reasoning of uncertain knowledge. In short, BN is an assigned causal relationship network diagram. A BN can be described as follows: (1) Network nodes. The network nodes consist of a variable set which can be discrete or consecutive. These nodes can describe the research problem. (2) A set of directed links or arrow. The links connect the network nodes. If there is a directed link from node X to node Y, X is called a parent node of Y and Y is the child node of X. (3) Each of the network node has a conditional probability distribution (CPD) P(X i Parents (X i)) where Parents (X i) is the set of parent nodes of X i. CPD is used to quantify the influence of Parents (X i) to X i. In many cases, CPD can be denoted as conditional probability tables (CPT) (CPT is also called the probability parameters of network nodes). (4) A BN is a DAG, i.e. there is no directed loop structure in a BN. From the above analysis, it can be seen that a BN consists of two parts: network topology (the set of network nodes and directed links) and CPT of network nodes. A simple example of BN can be given bellow (Bromely 2005)(Fig. 1) In Fig. 1, we assume that the annual river flow (noted as Z3 in Fig. 1) is determined by two related factors, i.e. forest cover (noted as Z1) and annual rainfall (noted as Fig. 1 A simple example of BN.

3 SHE Dunxian, et al.: The Evaluation of the Integrated Risk for the South-to-North Water Transfer Project Using the Bayesian Network Theory 261 Z2). Under this assumption, when both forest cover and annual rainfall or only one of the two antecedent factors change, annual river flow may also change correspondingly. The value of annual river flow conditionally depends on forest cover and annual rainfall. Similarly, when the value of annual river flow changes, it can be induced only by changes of forest cover and annual rainfall or both of them. From the above analysis, a simple BN to describe the relationship between annual river flow, forest cover and annual rainfall can be established by connecting nodes Z1, Z2 and Z3 with directed links. The result is shown in Fig. 1. The left table in Fig. 1 represents the prior probability of nodes Z1 and Z2, and the right table represents the CPT of Z Construction of BN The construction process of a BN is a very complicated and difficult task. By negotiations between researchers, domain experts, and stakeholders, a proper final BN, which consist of network topology and CPT, can be established to describe the research problem. The construction process can be divided into two parts, i.e. a qualitative process and a quantitative process. The qualitative process is to establish the topological structure of BN, and the main aim of quantitative process is to determine CPT of all network nodes. The methods of constructing a BN can be summarized in the following three ways: Manual Modeling, Learning Modeling and Two-stage Modeling. In this study, only the procedure of Manual Modeling is presented in detail, the processes involved in the other two methods will not be discussed here. The process of Manual Modeling can be described as follows: Step 1: A risk factor set related to the results should be extracted according to the research problem. Some of the factors in the determined set are chosen to define the proper nodes in BN. Step 2: By analyzing the relationship between the defined nodes in (1), a proper network topology can be obtained. The constructed network should satisfy the conditions introduced in Section 2.1. The final BN will be obtained by several rounds of discussions between the experts and all stakeholders. Step 3: The value of network nodes will be defined by considering the practical significance of each node. For an effective BN, the definition of each node should be explained clearly and the value of each node can be determined by the analysis of the historical data and the practical situation. Step 4: Determine the CPT. Each node should be connected by a conditional probability for each possible state and this is the foundation of the BN s inference. Following the above four steps, a complete BN can be constructed. By the input of some evidence and reason, we can obtain the evaluation results by using the BN s reasoning function. 2.3 Reasoning theory of BN The reasoning for BN is a probability calculation process based on the network structure. When the values of some network nodes are known before the inference (called as the evidence), the probability of the other nodes can be evaluated. Considered that there are no clear input and output nodes in BN, any node can be taken as both of the input nodes or output nodes. Under this condition, a practical BN has a bidirectional reason function: the probabilities of child nodes, which represent the conclusions, can be evaluated from parent nodes, which represent the causes, and vice versa. The most basic and important forms of the BN s inference algorithm are causal inference, diagnostic inference and support inference. (1) Causal inference (top-down inference). Use the causes to deduce the conclusions. The purpose of causal inference is to infer the reasons for the results. When some reasons are given before the inference, the probability of the results which are caused by the forgoing reasons can be evaluated through the inference of BN. (2) Diagnostic inference (bottom-up inference). Use the conclusions to deduce the reasons. The purpose of diagnostic inference is to discover the reasons which cause the results, when the results have already occurred. If some of the results have occurred, the probability of the reasons leading to the results can be evaluated through diagnostic inference. (3) Support inference. The objective of support inference is to analyze the interrelationship between the reasons. Support inference can be summarized as using the diagnostic inference in the process of causal inference, and can be seen as a combination of the foregoing two methods. According to the requirements of the inference accuracy, the existing BN s inference algorithm can be divided into two broad categories: exact inference (Dechter 1996; Jensen et al. 1994; Lauritzen et al. 1998) and approximate reasoning (Shater et al. 1990; Liu et al. 2001a, 2001b). An exact inference algorithm requires the computational accuracy of probability calculation and it is suitable for BN with a simple and small-scale structure. On the other hand, the approximate inference algorithm can simplify the computational complexity by reducing the

4 262 computational accuracy under conditions that do not alter the correctness of the calculations. Approximate inference algorithms are mainly used in BN with complex and large-scale structures. 3 Integrated risk assessment of the SNWT Project 3.1 The study area Considering that the SNWT Project is a huge and complicated system, only the Baoying Station located in Jiangsu Province of the eastern route of the SNWT Project was selected as the study area to evaluate the probability of integrated risks. By the inference function of BN, the probability of the integrated risk can be estimated. On the other hand, risk probability can not give a clear quantitative understanding of the relative risk level. On the basis of the achievements of other researcher (Zhou 2009) and considering the practical situation of the SNWT Project, we have established a corresponding relationship between the risk probability and the risk level (Table 1). In Table 1, the logarithmic risk probability can be calculated by the following formula: P=lgp+5 (1) where P is the logarithmic risk probability and p is the risk probability which can be estimated by the inference function of BN. Journal of Resources and Ecology Vol.1 No.3, Determine the BN s structure of Baoying Station Baoying Station is part of the water supply system of the SNWT Project, and will be affected by many risk factors during the operating period. Considering that the integrated risk of the water supply system is triggered by one or more of various combined risk factors, and in order to simplify analysis, the major consideration of the integrated risk for Baoying Pump Station is focused on the engineering risks during the running-period of the water supply system. So, we determine a subset called A1 which represents the risk factors of the integrated risk for Baoying Station, where A 1={Integrated risk of Baoying Station, Engineering risk}. Baoying Station is an important part of the eastern route of the SNWT Project, and the engineering risk mainly relates to the risk factors during the running-period of the pump station. In order to guarantee that the project runs smoothly, we need to consider all of the risk factors which can induce the engineering risk. All of the factors have been incorporated into three main aspects which are given below Equipment quality Equipment quality of the pump station is important for making sure that the water supply system runs smoothly and the pump operates according to its design. The reserve ratio of pump and the service time of the pump are considered to be major risk factors involving equipment quality. (1) Reserve ratio of pump The reserve ratio of pump mainly describes the reserve condition of the pump unit. For a pump system, when the reserve ratio of pump in case A is higher than that in case B, the possibility that the pump station can not meet the demand of the water flow in the transfer project of case A is lowered than that of case B. The reserve ratio of pump can be calculated by the formula N Reserve/N Total, where N Reserve=(Q Actual-Q Designed)/Q Single is the reserve number of the pump, N Total is the total number of the pump, Q Actual is the total installation flow of the pump, Q Designed is the total designed flow and Q Single is the flow of a single pump. (2) Service time of pump Service time of pump mainly refers to the aging of the equipment, and is used as an index to judge the possibility of a mechanical failure of the system. The project has already in use from So, in considering the indexes of service time of the pump, we can estimate the aging extent of the equipment by the time difference between the construction year and the first service time of the pump station. The detailed classification method for the service time of pump can be given as follows: Table 1 The corresponding relationship between risk probability and risk level. Risk Probability Logarithmic risk Probability Risk Level Risk acceptability 10 1 to to 4.0 High Unacceptable. Need to improve the conditions and reduce the risk level to below the Medium 10 2 to to 3.0 Higher Unsuitable for the acceptance. The conditions should be improved before a reasonable deadline and make the risk level reduced to below the Medium 10 3 to to 2.0 Medium Conditional acceptable 10 4 to to 1.0 Lower Acceptable < to 0.0 Low No effect

5 SHE Dunxian, et al.: The Evaluation of the Integrated Risk for the South-to-North Water Transfer Project Using the Bayesian Network Theory 263 where Level 1 to Level 5 is the classification of the service year, and y is the time difference defined. From the above analysis, we can determine a subset called A 2 which represents the factors of the integrated risk of Baoying Station, where A 2={Equipment quality, Ratio of reserve pump, Service time of pump} Technical conditions The level of the technical conditions directly affects the efficiency and safety of the water supply system. Management and maintenance conditions of the pump station are considered to be the major risk factors involved. So, a subset A 3, which represents the factors of the integrated risk of Baoying Station, can be determined. Here, A 3= {Technical conditions, Management and maintenance conditions} Security of pump station system The security of the pump station system is another risk factor that will directly affect the safe operation of the water supply system. Two major factors that reflect the security of the pump station system are the pump station foundation conditions and the pump station flood conditions, (2) and these are considered in this study. From the above analysis, we can determine a subset called A 4, which represents the factors relating to the integrated risks of the Baoying Station, where A 4={Security of the pump station system, the pump station foundation conditions, and the pump station flood conditions}. In conclusion, three risk subsets A 2, A 3 and A 4, which represent the risk factors of equipment quality, technical conditions, and security of the pump station system respectively, are determined. Combined with the risk subset A1, the integrated risk set A=A 1 A 2 A 3 A 4 can be obtained for the Baoying Pump Station. By the construction process introduced in Section 2.2, we obtain the final structure of BN as shown in Fig Defining the valueof the network nodes According to practical conditions and the results of the discussions among domain experts, the value of the network nodes given in Fig. 2 is shown in Tables 2 and Determine conditional probability tables (CPT) A BN contains network topology and CPT. After determining the network structure in Section 3.2 and the value of variables in Section 3.3, one needs to determine the CPT of each node. The relationship between the nodes and the evaluation result of BN are directly impacted by the rationality of the value of CPT. According to the analysis in Section 3.2, the prior prob- Fig.2 The BN structure of Baoying Pump Station.

6 264 Journal of Resources and Ecology Vol.1 No.3, 2010 Table 2 The states of root nodes for the BN of Baoying Station. Nodes Level 1 Level 2 Level 3 Level 4 Level 5 Ratio of reserve (0, 5%] (5%, 10%] (10%, 15%] (15%, 50%] >50% pump (X6) Service year of 20 years [15, 20) [10, 15) [1, 10) [0, 1) pump (X7) Management and No management and Initial management and Good management and Perfect management Perfect management condition of maintenance system maintenance system maintenance system and maintenance and maintenance pump (X8) system system and established emergency response plans Pump station Inadequate bearing Inadequate bearing Poor slope stability, Better slope stability, Good slope stability foundation capacity of capacity of the the capacity of higher impact of by using the natural conditions (X9) the foundation,poor foundation, the foundations meets the confined water foundation slope stability, there poor slope stability, the basic is liquefaction there is liquefaction requirements potential in the design potential in the design intensity of foundation, intensity of local no engineering foundation treatment measures Pump station No precise hydrologic Hydrologic design Hydrologic design Hydrologic design Hydrologic design flood conditions design criteria criteria: 20 year flood criteria: 50 year flood criteria: 100 year criteria: 200 year (X10) flood flood ability of the root nodes X6, X7, X8, X9 and X10 can be determined as P(X6={15% to 50% }) =1, P(X7={1 to 10})=1, P(X8={4})=1, P(X9={5})=1 and P(X10={4})=1 for the Baoying Pump Station. The CPTs of the non-root nodes are obtained on the basis of discussions between domain experts. In detail, the method is mainly in the form of negotiations and meetings by inviting some of the domain experts to measure and analyze the importance of each risk factor (the network nodes) and the relationship or causal relationships between the nodes according to the actual situation and the risks that may occur when the project is up and running. A primary CPT will be obtained first after several rounds of meetings when the CPT will be analyzed and modified, and then when a more definitive CPT is finalized the correct situation will be determined. Fig. 3 The inference result of the BN for the Baoying Station.

7 SHE Dunxian, et al.: The Evaluation of the Integrated Risk for the South-to-North Water Transfer Project Using the Bayesian Network Theory Inference function of BN After determining the network topology and the CPT of each node, we can use the reasoning function of the BN to evaluate the probability of the integrated risks relating to Baoying Station. The inference result is shown in Fig. 3. From Figure 3, it can be seen that the probability of the integrated risk of Baoying Station is 0.025%. The logarithm probability can be calculated using Eq. (1), i.e. P= 1.4. According to the corresponding relationship between the risk probability and the risk level given in Table 1, the risk level of the Baoying Station is lower level when the project is running. Under the assumption in Section 3.2, that the integrated risk is wholly induced by the engineering risks, the probability of nodes X2 and X1 are the same in Fig Scenario analysis With the operation of the eastern route of the SNWT Project and the increase of the service time of the considered pump station, the risk factors (here, the root nodes are mainly considered, i.e. nodes X6, X7, X8, X9 and X10) that induce the integrated risk of Baoying Station will also change correspondingly. In order to investigate the changes in integrated risk along with increased service time, and to evaluate the importance of a single risk factor for the integrated risk, scenario analysis is used. By setting a series of various scenarios, the probability of the integrated risk will be evaluated and the law of changes will be analyzed. The results of the various scenarios are shown in Table 4. In Table 4, six cases are defined and the probability of the integrated risk (node X1) for each case is given in the last column of the table. By comparing Case 1 and Case 2, it can be seen that the probability of the integrated risk has increased from 0.025% to 0.031% in pace with the Table 3 The states of non-root nodes for the BN of Baoying Station. Nodes State Description Integrated risk of Yes Integrated risk occurs Baoying Station (X1) No Integrated risk does not occur Engineering risk Yes Engineering risk occurs (X2) No Engineering risk does not occur Equipment quality Good Good equipment quality (X3) Bad Bad equipment quality Technical conditions High High technical conditions (X4) Low Lowtechnical conditions Security of pump Safe Pump station is safe station system (X5) Unsafe Pump station is unsafe change of reserve ratio of pump (node X6) from 15% 50% to 10% 15%. This means that the decrease of reserve ratio of pump will cause an increase in the probability of integrated risk, and the rate of the increase is 0.006%. In the same way, the other scenarios can also be analyzed. By comparing Case 2 and Case 3, when the service time of the Baoying Station (node X7) increases from 1 10 to 10 15, the probability of the integrated risk increases from 0.031% to 0.038% and the rate of the increase is 0.007%. By comparing Case 3 and Case 4, when the management and maintenance conditions of the pump (node X8) deteriorates from Level 4 to Level 3, the probability of the integrated risk increases from 0.038% to 0.19% and the rate of the increase is 0.152%. By comparing Case 4 and Case 5, when the pump station foundation conditions (node X9) deteriorates from Level 5 to Level 2, the probability of the integrated risk increases from 0.19% to 0.20% and the rate of the increase is 0.01%. By comparing Case 5 and Case 6, when the pump station flood conditions (node X10) deteriorates from Level 4 to Level 1, the probability of the integrated risk increases from 0.20% to 0.21% and the rate of the increase is 0.01%. From the above analysis, it can be seen that the probability of the integrated risk changes most severely when management and maintenance conditions for the pump deteriorate and the rate of the increase of the risk probability is 0.152%. So, during the operation of the Baoying Station, much more attention should be paid to the management and maintenance condition of the pump in order to decrease the probability of the occurrence of integrated risk. 4 Conclusions The SNWT Project is one of the biggest water transfer projects in the world and with the operation of the project, various risk factors have attracted more and more attention from managers and experts. How to identify the probable risk factors and evaluate the extent of the risk has become a huge problem for managers of the project. A good and efficient risk evaluation and risk control scheme will largely decrease the probability of integrated risk, economic loss, and even the loss of human lives. In order to investigate the integrated risk of the SNWT Project, Baoying Station on the eastern route was taken as a study area and BN is used to evaluate the probability of the integrated risk. In the regard to the specific conditions of the study area, a BN has been constructed as a result of negotiations between experts, managers and stakeholders. Based on the reasoning of BN, the probability of integrat-

8 266 Journal of Resources and Ecology Vol.1 No.3, 2010 Table 4 Scenario analysis of the integrated risks for Baoying Station. Nodes Value Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 X6 0 to 5% % to 10% % to 15% % to 50% >50% X7 >= to to to to X8 Level Level Level Level Level X9 Level Level Level Level Level X10 Level Level Level Level Level X1(%) Yes ed risk has been evaluated. The scenario analysis is also taken to analyze the change in the integrated risk when one single risk factor changes from one situation to another. The major conclusions to be drawn are: (1) The probability of the integrated risk of Baoying Station when the project is running is 0.025%. The logarithmic probability is 1.4 and the risk level for the study area is lower level. (2) By scenario analysis, when the management and maintenance condition of the pump (node X8) deteriorates from Level 4 to Level 3, the probability of the integrated risk increases from 0.038% t0 0.19% and the rate of the increase is 0.152%. Compared to the changes in other risk factors, it can be found that more attention should be paid to the management and maintenance conditions of the pump during the running period of the project. In this study, the BN is firstly used for integrated risk analysis of a large water transfer project. Some good results and conclusions have been obtained by the reference function of the BN and the scenario analysis. However, there are still improvements to be made, especially in the construction of the BN. The BN s topological structure and CPT for all of the non-root nodes are obtained by negotiations between experts, managers and the stakeholders, and this can make the evaluation results somewhat imprecise. With the increase in the service time of the project, more data will be added to the operation data set, and by the learning process of the BN, a more precise BN topological structure and CPT will be determined, and thus more precise scientific evaluation results can be obtained. Acknowledgements This work is granted by the National Key Technology R&D Program of China (Grant No. 2006BAB04A09) and the National Science Foundation of P. R. China (Grant No and ). Cordial gratitude should be extended to all of the experts of the foregoing program for their professional suggestions and comments in the construction process of the Bayesian Network. References Borsuk M, P Reichert, P Burkhardt-Holm A Bayesian belief network for modelling brown trout (Salmo trutta) populations in Switzerland. In: Rizzoli. Integrated assessment and decision support, proceedings of first biennial meeting of IEMSS, June 24 27, Lugano, CH. Bromley J Guidelines for the use of Bayesian networks as a participatory tool for water resource management. Centre for Ecology and Hydrology, 117. Cowell R G, A P Dawid, S L Lauritzen, D J Spiegelhalter Probabilistic networks and expert systems. Statistics for Engineering and Information Science, New York: Springer-Verlag.

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