Developing a cloud model based risk assessment methodology for tunnel-induced damage to existing pipelines

Abstract

This paper presents a cloud model (CM) based approach with step-by-step procedures for risk assessment of existing pipelines in tunneling environments (RAEPTE), where CM provides a basis for uncertainty transforming between qualitative concepts and their quantitative expressions. An evaluation index system of multiple layers and attributes is established for RAEPTE based upon the tunnel-induced pipeline failure mechanism analysis. The evaluation result is assessed by the correlation with CMs of each risk level. A confidence indicator is proposed to illustrate the reliability of evaluating results. Risk analysis for ten underground buried pipelines adjacent to the construction of Wuhan Metro Line Two in China is shown in a case study. Comparisons between different evaluation methods are further discussed according to results. The proposed approach is verified to be a more competitive solution, where the uncertainties of fuzziness and randomness are incorporated in the risk assessment system. This approach can serve as a decision tool for the safety risk assessment in other similar projects, and to increase the likelihood of a successful project in an uncertain environment.

Appendices

Appendix 1: Analytic hierarchy process

AHP, developed by Saaty (1988), structures the decision problem in levels which correspond to one understands of the situation: goals, criteria, sub-criteria and alternatives. The main idea is to break down the evaluation system into a hierarchy structure and compare each element according to a principle, and then acquire the compare matrix elements by pair-wise comparison method. In pair comparison of criterion, if the priority of an element i compared to element j is equal to c _ij, then the priority of the element j compared to element i is equal to 1/c _ij. The priority of element compared to it is equal to one. Table 6 shows the scale used to make the paired comparisons with the AHP. Assuming M factors (c _i, i = 1,2,…,m) involves in the evaluation index system, the matrix C _m×m of the paired comparisons is shown in Eq. (16)

$$ C = (c_{ij} )_{m \times m} = \left[ {\begin{array}{cccc} 1 & {c_{12} } & \ldots & {c_{1m} } \\ {1/c_{12} } & 1 & \ldots & {c_{2m} } \\ \ldots & \ldots & \ldots & \ldots \\ {1/c_{1m} } & {1/c_{2m} } & \ldots & 1 \\ \end{array} } \right] $$

(16)

Table 6 AHP scale of nine points used in the paired comparatives

In this research, AHP is used to determine subjective weights for the safety risk factors in RAEPTE. At first, m criteria are set up in the rows and columns of m × m matrix. Then, pair-wise comparisons of all the criteria are performed using the fundamental scale (see Table 6). When more than one decision-maker is involved in the evaluation process, it is necessary to add up and average the judgments of the various decision-makers. Mikhailov (2004) and Escobar et al. (2004) suggested using the geometric median as an average, when the personal assessments of the decision-makers are added up in a matrix of final decision, as shown in Eq. (17). Finally, the average over normalized columns is used to estimate the Eigen values of the matrix, and the weight of all the factors, represented by η [see Eq. (18)] can be obtained according to the eigenvector of the matrix C _m×m

$$ \overline{{c_{ij} }} = \left( {c_{ij1} \times c_{ij2} \times \cdots \times c_{ijp} } \right)^{1/p} $$

(17)

$$ \eta = \left[ {\eta_{1} ,\eta_{2} , \ldots ,\eta_{m} } \right] $$

(18)

One of the advantages of the AHP is that it allows identifying and taking into account the inconsistencies of the decision-makers, since they are rarely consistent in their judgments. Therefore, a Consistency Index (CI) and a Consistency Relationship (CR) are incorporated into the analysis. The CI, which is used to measure the quality of the judgments made by a decision-maker, is estimated by Eq. (18). Herein, λ_MAX stands for the largest eigenvalue of the matrix C _m×m. A CI lower than 0.10 is considered acceptable; if it is higher, it will be necessary to ask the decision-maker to make the assessments or judgments once again. The CR, which is used to represent a measure of the error made by the decision-maker, is estimated by Eq. (19). A CR depends on the value of CI and Random Index (RI). The value of CR should be lower than 10 % of the RI. The value of RI for 3–12 attributes is presented in Table 7.

$$ CI = \frac{{\lambda_{MAX} - m}}{m - 1} $$

(19)

$$ CR = \frac{CI}{RI} $$

(20)

Table 7 Consistency random index (RI)

Appendix 2: Entropy weighting

Entropy concept, proposed by Shannon (1963), is a measure of uncertainty in information formulated in terms of probability theory. Since the entropy concept is well suited for measuring the relative contrast intensities of criteria to represent the average intrinsic information transmitted to the decision maker (Zeleny and Cochrane 1982), the entropy weighting is used to decide the objective weights of attributes. Given a decision matrix with column vector x _i = (x _i1, x _i2,…,x _in) that shows the contrast of all alternatives with respect to ith attribute, an attribute has little importance when all alternatives have similar outcomes for that attribute. Moreover, if all alternatives are the same in relation to a specific attribute then that attribute should be eliminated because it transmits no information about decision-makers preferences. In contrast, the attribute that transmits the most information should have the greatest importance weighting. Mathematically this means that the projected outcomes of attribute i, denoted by P _ij, are defined by Eq. (21). The entropy E _i of the set of projected outcomes of attribute i is defined by Eq. (22)

$$ P_{ij} = \frac{{x_{ij} }}{{\sum\nolimits_{j = 1}^{n} {x_{ij} } }} $$

(21)

$$ E_{i} = - \left( {\frac{1}{{In\,{\kern 1pt} n}}} \right)\sum\limits_{j = 1}^{n} {P_{ij} In{\kern 1pt} {\kern 1pt} P_{ij} } $$

(22)

where n is the number of alternatives, E _i lies between zero and one. The degree of diversification d _i of the information provided by outcomes of attribute i can be defined by Eq. (23). Hence, the entropy weighting of an attribute, denoted by δ, is calculated by Eqs. (24) and (25)

$$ d_{i} = 1 - E_{i} $$

(23)

$$ \delta_{i} = \frac{{d_{i} }}{{\sum\nolimits_{i = 1}^{m} {d_{i} } }} $$

(24)

$$ \delta = \left[ {\delta_{1} ,\delta_{2} , \ldots ,\delta_{m} } \right] $$

(25)