Diagnosis of Critical Risk Sources in the Operation Safety of the Central Route Project of South-to-North Water Diversion Based on the Improved FMEA Method

School of Water Resources, North China University of Water Resources and Electric Power, Zhengzhou 450046, China Henan Collaborative Innovation Center for Water Efficient Utilization and Guarantee Engineering, Zhengzhou 450046, China Henan Province Key Laboratory of Water Environment Simulation and Treatment, Zhengzhou 450046, China School of Management and Economics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China Bureau of South-to-North Water Transfer of Planning, Designing and Management, Ministry of Water Resources, Beijing 100080, China


Introduction
The Central Route Project of South-to-North Water Diversion is large in scale, has long-distance water diversion, and faces a complex geological environment. The Central Route Project is a typical series system in which there are a large number of cross buildings and control buildings such as water diversion gates and control gates. These buildings are vital to the safe operation of the whole water conveyance channel. Any accidents in a single building or canal section in the system will cause serious consequences to the safety of the project. Furthermore, superimposed risks of every single project will increase the difficulty of the operation safety management of the Central Route Project of South-to-North Water Diversion. A safety accident in the operation of the Central Route Project will not only seriously affect people's lives but also cause huge economic losses and serious social problems. Therefore, it is necessary to comprehensively assess the risks that may happen in the operation of the Central Route Project to diagnose the key risk sources. Based on the assessment result, managers are able to take more targeted measures to guard the safety of the Central Route Project operation. FMEA is one of the important tools of quality management [1]. As a qualitative analysis methodology, FMEA quantifies the risk level through the analysis of potential or existing failure modes to determine the consequences that may happen or have happened [2]. According to the different failure modes that cause risks, managers can take targeted preventive and improvement measures to enhance product quality and ensure system reliability [3]. To identify the risk of each failure mode, the traditional FMEA method uses RPN to quantify the risk level [4]. The RPN is the product of the probability occurrence rate (O), severity (S), and the probability of not detecting the failure (D) mode [5]. In the application of the conventional FMEA method, managers may find it hard to evaluate the accurate value when assessing the grade number of each evaluation factor of failure modes [6]. When analyzing, an RPN value may correspond to different combinations that cannot be effectively distinguished. The RPN value of the risk is not a continuous sequence number. Besides, the calculation method of the RPN value does not have a sufficient scientific theory basis. The change in the grade value of a single evaluation factor may stimulate a sudden mutation of the RPN value and other defects [7]. Given the facts, scholars have proposed improved methods. Kumru and Kumru [8] used the fuzzy set theory to handle the information ambiguity and uncertainty in the FMEA evaluation process and solved the defect of the traditional FMEA model's incapability to describe the fault level accurately. Wang et al. [9] sorted the risk of failure modes with an improved FMEA method based on intuitive multiplicative preference relations and an improved TOPSIS method based on bidirectional projection distance, thus improving the accuracy of the risk ranking of failure modes. You et al. [10] leveraged the interval binary mixed weighted distance measure to improve the traditional FMEA model, which in turn solves the absence of the relative weight between the evaluation elements in the traditional FMEA model and the problem of different evaluation combinations producing the same RPN value. Chang and Sun [11] used data envelopment analysis to enhance the FMEA evaluation capability using a value of 1 to 10 instead of fuzzy sets for parameters. Barends et al. [12] proposed a modified probabilistic FMEA that replaces the estimated proportional frequency to determine the rate of occurrence "O" and detection coefficient "D," instead of the definite amounts used when calculating RPN. Dong [13] presented a costeffective FMEA tool based on the fuzzy utility theory that used the utility theory and fuzzy membership functions for the assessment of severity, occurrence, and detection. Can [14] considered the intuitionistic fuzzy scale to be more practical and logical than the traditional FMEA evaluation scale and proposed the use of the intuition evaluation scale to determine the evaluation value of the factor. Based on the above research, we hereby propose an improved FMEA method based on the fuzzy evidence reasoning theory to diagnose the key risk sources of the operation safety of the Central Route Project of South-to-North Water Diversion.     [15][16][17][18]. The fuzzy membership function of the linguistic variables of risk factors is shown in Figure 1. Each fuzzy language variable evaluates the evaluation elements O (frequency of occurrence), S (severity), and D (difficulty to detect). The evaluation criteria for the three elements of FMEA for the Central Route Project are shown in Table 1.

Fuzzy Evidence
Suppose that the FMEA evaluation team has k evaluators (EX 1 , EX 2 , ⋯, EX k ), and the weight of each evaluator EX k is λ k (λ k > 0), ∑ K k=1 λ k = 1. Each evaluator evaluates the three evaluation elements of N risk factors (F 1 , F 2 , ⋯, F n , ⋯, F N ), using fðH ij , α k ij ðF n , E FL ÞÞg to represent the confidence evaluation of the kth expert on the pth evaluation factor of the nth risk, whose grade is H ij . Such representation of the result is called a fuzzy confidence structure in evidence reasoning, α k ij ðF n , E FL Þ is the corresponding confidence, H ij indicates that the fuzzy grade of the evaluation set is between i and j, i and j indicate the fuzzy grade of the evaluation set, where i ≤ j; i = 1, 2, 3, 4, 5; j = 1, 2, 3, 4, 5; k = 1, 2, ⋯, K; n = 1, 2, ⋯, N; and L = 1, 2, 3 [19][20][21]. Usex n = fðH ij , α ij ðF n , E FL ÞÞg to represent the result of the FMEA evaluation team's comprehensive evaluation on the risk factor F n about the evaluation element E FL .x n is called the comprehensive confidence structure, and the confidence is 2.2. Explicit Confidence Matrix. The comprehensive confidence structurex n defuzzification formula is [20] Among them, h ij is the unambiguous value of H ij defuzzification, c = 0, and d = 10. When the membership function value of the language rating is 0, a 0 and b 0 are the critical values. When the membership function value of the language rating is1, the critical value is a 1 and b 1 [22,23]. The clear value of the evaluation level is shown in Table 2.
The risk factor F n is obtained after the weighted average of the clear value of the evaluation factor E FL : x n ðLÞ constitutes a clear confidence matrix: Use the vector normalization method to normalize the explicit confidence matrix: where

AHP Method to Determine the Subjective Weight of Risk Factors.
Steps of using the analytic hierarchy process to determine the subjective weight of risk factors are as follows: (1) establish the hierarchical structure model; (2) construct the judgment matrix A; (3) calculate the maximum eigenvalue λ max of matrix A and the eigenvector ω A corresponding to the eigenvalue; and (4) use ðλ max ðAÞ − nÞthat measures the degree of inconsistency of matrix A; CI = ð λ max − nÞ/ðn − 1Þ is the consistency index, and RI = ðCI 1 + CI 2 +⋯+CI n Þ/n is the random consistency index of judgment matrix A. The standard value of random consistency index RI is shown in Table 3. Usually, when the value of CR is less than 0.1, the judgment matrix A is considered passing the consistency test, otherwise restructuring the judgment matrix A until it passes the consistency test.

Gray
Relational Analysis Method to Determine the Objective Weight of Risk Factors. By standardizing the original evaluation matrix X ij , we get x ij = ðX ij − X j Þ/S j , the sample mean is X j = ð1/nÞ∑ n i=1 X ij , and the sample mean square . Then, we take the maximum set x 0 of each risk factor as the reference sequence, wherefx 0 g = fx 0 ðiÞg (i = 1, 2, ⋯, n), and the comparison sequence is x i (i = 1, ⋯, n), so the correlation coefficient calculation formula is Among them, m = min min jx 0 ðkÞ − x i ðkÞj is the minimum difference between the comparison sequence and the reference sequence element, M = max max jx 0 ðkÞ − x i ðkÞj is the maximum difference between the comparison sequence and the reference sequence element, Δ ij ðkÞ = jx 0 ðkÞ − x i ðkÞj represents the absolute value of the difference between the The correlation degree Y ij between the evaluation sequence of risk factor i and the reference sequence is The weight assigned according to the degree of correlation of the risk factor i is ω y ð ω 1 , ω 2 ,⋯,ω m Þ is the objective weight of the risk factor determined by the gray correlation degree.

The Principle of Minimum Discriminative Information
Determines the Weight of Risk Factor Combinations. The subjective weight ω A ðω 1 , ω 2 ,⋯,ω m Þ determined by the analytic hierarchy process and the objective weight ω y ðω 1 , ω 2 , ⋯,ω m Þ determined by the gray relational analysis method are used to determine the comprehensive weight ω z ðω 1 , ω 2 , ⋯,ω m Þ which has the highest similarity to the subjective and objective weights by the smallest discriminating information. When the sum of the two discriminating information reaches the smallest level, the comprehensive weight is similar to the subjective and objective weights, and establish the objective function: Among them, the comprehensive weight is ω z , which satisfiesω 1 + ω 2 +⋯+ω m = 1, and ω 1 , ω 2 , ⋯, ω m > 0.
Use the Lagrange function to get the value of minimum discriminative information: When there is an extreme value, the solution is

Key Risk Source Diagnosis Based on the TOPSIS Analysis Method
Based on determining the normalized matrix, the TOPSIS method is used to calculate the distance between the risk factor and its ideal solution to judge the priority of the risk factor.
(1) Determine the positive ideal solution S + and the negative ideal solution S − Among them, r + L = max fr nL g and r − L = min fr nL g represent the maximum and minimum values of elements in the explicit confidence matrix R, respectively.
(2) Use the Euclidean distance formula to calculate the distance between the risk factor and the positive ideal solution or the negative ideal solution (3) Calculate the relative closeness C n of each risk factor and the improvement risk sequence number. The calculation formula for the relative closeness is The greater the relative closeness, the longer the distance between the risk factor and the negative ideal solution, but the shorter the distance to the positive ideal solution, the larger the impact on the system. Meanwhile, the combination of the relative closeness and the comprehensive weights of risk factors generates the value of the importance risk priority number (IRPN). The larger the IRPN value, the higher the priority of the representative risk factor, and the more significant the risk factor, thus translating into the basis for the diagnosis of key risk sources [24,25]. The IRPN value calculation formula is    man-made sabotage F16, fire F17, sudden water pollution F18, traffic accident F19, and social dispute F20. The fuzzy confidence structure is used to express 20 risk factors evaluated by the five experts from the three evaluation factors. Taking Table 2 into consideration together with formulas (1) and (3), a clear confidence matrix is obtained after defuzzification. After performing vector normalization to formula (5), we get

Case Analysis
We collected the scattered information based on formula (8) to find the correlation degree of each risk factor. Formula (9) generates the objective weight ω y of the risk factor.

Calculation of Comprehensive Weights of Risk Factors
Based on the Principle of Minimum Discriminative Information. Integrate the subjective weight ω A of the risk factor with the objective weight ω y , and obtain the comprehensive weight ω Z through formulas (10)- (12). When the objective function takes the smallest value, the comprehensive weight isω Z , and the authentication information value is the smallest subject to the constraints of the subjective weight ω A and the objective weight ω y . The comprehensive weight ω Z is similar to the subjective and objective weights ω A and ω y . The subjective weight, objective weight, and comprehensive weight of risk factors are shown in columns 5-7 in Table 4.

Ranking of TOPSIS Risk Factors.
Identify the positive ideal solution S + and the negative ideal solution S − , and combined with the clear confidence matrix R, according to formulas (13) and (14), we get S + = ð0:0409 0:0393 0:0233Þ and S − = 0:0088 0:0091 0:0050 ð Þ . Based on formulas (15) and (16), the distance between each risk factor and the positive ideal solution S + is d + i and the distance between each risk factor and the negative ideal solution S − is d − i . Then, we obtain the relative closeness C i of each risk factor based on the two distances, thus gaining the comprehensive weight of the risk factor ω Z . We then use formula (18) to obtain the improvement risk sequence number. The arrangement of d + i , d − i , C i , weight, and the final IRPN value of each risk factor is shown in Table 4.
According to the IRPN ranking, the key risk factors of this section of the South-to-North Water Diversion Project include storm floods, geological conditions, geological disasters, and safety factors in designing. From the field investigation, there are areas with poor geological conditions such as expansive soil and coal mine goaf in this section of the project. Due to the terrain conditions, there are also a large number of high-filled and deep excavation projects. In addition, some problems in the engineering design stage were not considered enough. Therefore, geological disasters such as landslides are extremely prone to occur in this engineering section during continuous heavy rainstorms during the flood season. Once the disaster occurs, not only will it cause a lot of economic losses, but also the safety of life and property of the people along the route will be greatly threatened. The risk events occurred mainly in the flood season from late July to early August every year. Storm floods, geological conditions, geological disasters, and design safety factors are indeed the risk factors with a high-risk level in this section. In addition, as the only section of the middle line that passes through the main urban area, this section is greatly influenced by daily human activities and has many emergencies. Compared with other sections, the risk level of risk factors such as human activity impact and illegal operation within the protection scope is also higher. For key risk factors, this paper proposes specific countermeasures:

Summary
This essay improves the FMEA according to the fuzzy confidence theory and further overcomes the shortcomings of the traditional FMEA model that fails to depict the fault accurately. The TOPSIS method is used to diagnose key risk sources, which improves the accuracy of risk ranking. In the example selected from one of the project sections of the Central Route Project of South-to-North Water Diversion, the paper calculated the weights of risk factors and the number of risk sequences. The importance of the risk is determined according to the risk sequence number, which includes storm floods, geological conditions, geological disasters, design safety factors, building reliability, engineering construction quality, sudden water pollution, human activity impact, personnel management quality, extreme weather, protection scope of illegal activities, project maintenance management level, fire, equipment reliability, social disputes, traffic accidents, manmade sabotage, management system perfection, operation and maintenance construction management level, and illegal operation. The key risks are storm floods, geological conditions, geological disasters, and design safety factors. The diagnosis results are consistent with the actual situation in the field, indicating that the improved method is reasonable and effective. Finally, specific countermeasures are put forward for key risks, which provides help for improving the risk management level of project operation management units. However, the improved FMEA method is still insufficient in the selection of elements and only takes the frequency of occurrence, severity, and difficulty of inspection as the three evaluation elements. In a large-scale project such as the South-to-North Water Diversion Project, there are still some limitations in using only these three evaluation elements as the evaluation basis.
For example, in the process of engineering operation, maintenance cost and the difference of the impact on the project after risk correction and improvement and before risk occurrence are important evaluation factors of risk factors. It should also be taken into account in the application of the method, and the diagnostic results of key risk sources obtained by measuring the importance of risk factors with multiple evaluation factors are more accurate and scientific. This will be the direction of further research.

Data Availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest
It is declared by the authors that this article is free of conflict of interest.