Application of Entropy-Based Measurement in Underground Engineering Risk Assessment

1. The 2ndChina-Japan Seminar for Graduate Students in Civil Engineering Application of Entropy-Based Measurement in Underground Engineering Risk Assessment LI Junwei HUANG Hongwei Department of Geotechnical Engineering Tongji University, Shanghai, China, 200092 lijunwei76@163.com huanghw @ mail.tongji.edu.cn Aug.27-28 Nagasaki, Japan

2. Outline 1. Introduction 2. Ideas of Information Entropy & Entropy Weight; 3. Establish Risk Assessment Model in Underground Engineering; 4. Entropy-based Risk Measurement Method in Underground Engineering; 5. Conclusion. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

3. 1. Introduction • Commonly and conventionally risk measurement method: probability distribution statistic values of the objective function. • Various Risk Understandings  Various Risk Definition (No Authoritative definition) •  Various risk measurement methods: • Analytic Hierarchy Process (AHP), • Bayesian Analysis Method, • Brainstorming Method, • Delphi Method, • Fault Tree Method and • Event Tree etc. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

4. 1.Introduction • Shanon presented the idea of entropy in 1948. The definition of "Entropy" presents a quantitative measure of uncertainty associated with a probability distribution or the information content of the distribution . • So the uncertainty can be quantified with entropy taking into account all different kinds of available information. Thus, entropy is a measure of the mount of uncertainty and is a measure of the lack of information about a system. • Entropy in[0, 1] Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

5. 1.Introduction • Using entropy firstly, the present paper introduces the risk measure method, and based on the entropy theory, the entropy-based risk assessment method is introduced into underground engineering risk assessment. • And take the risk analysis and assessment on the effect of construction phase of soft soil shield tunnelling on the environment in urban area for example, the entropy measuring risk method is introduced and the solution process is given in details. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

6. 2. Idea of Information Entropy & Entropy Weight 2.1 Information Entropy, the Entropy of Assessment Index and Entropy Weight As for the continuous random variable, the definition of entropy is expressed as: And as for discrete random variable, the definition of entropy is expressed as: Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

7. (m, n) Assessment Problem In terms of a assessment problem with m assessment indexes and n assessment objects, it could be abbreviated as (m, n) assessment problem, then, the entropy of the i th assessment index is defined as: where: Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

8. (m, n) Assessment Problem • As to (m, n) assessment problem, the entropy weight of the i th assessment index is expressed as: Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

9. 2.2 Entropy-based risk measurement method in risk analysis • In engineering practices, many risk assessment and decision-making problems are carried on with much uncertainty. the aim of the risk analysis is to describe or evaluate some kinds of condition of the system so as to do risk management further and lower the risk or control the risk of system in related condition. This is attributed to that available information is always incomplete. The aim of the risk measurement is to determine and quantify the dangerousness of a certain assessment object or regulation plan may cause or risk of realizing the objective at the known environmental condition. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

10. 2.2 Entropy-based risk measurement method in risk analysis The analysis procedure of proposed entropy-based risk assessment method is that: (1) determining the probable risk value of every index by means of expert investigation method, and obtaining the risk assessment matrix; (2) obtaining the entropy and entropy weight of every index. Based on this idea, the following entropy-based measurement model in risk analysis is established. In (m, n) assessment problem, the risk value of the assessment problem is determined: Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

11. 2.2 Entropy-based risk measurement method in risk analysis • As for the present research work, the definition of risk is expressed as uncertainty of the assessment index or research object and thereafter the idea of entropy weight is proposed, which is defined by means of the weighting value of available information to measure risk in assessment of risk events in different level. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

12. Technical risk Environmental effect risk Capital risk Policy & law risk General Risk Natural risk Contract risk Construction risk Soil property risk Social risk 3. Establish Risk Assessment Model in Underground Engineering The general risk (sometimes called top-level risk) in underground engineering exploitation at pre-feasibility study period to be taken into consideration is shown in Fig.1. Fig.1 General risk classification in Underground Engineering Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

13. 3. Establish Risk Assessment Model in Underground Engineering The present paper takes the risk analysis and assessment on effect of construction phase of shield tunnelling on environment in soft soil urban area for example; risk analysis process is introduced in details by means of entropy-based risk measurement method. The second and third level risks events or assessment indexes of environment effect risk assessment problem in this paper are given in Table1. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

14. Table1Hierarchy analysis on environmental effect risk Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

15. 4. Entropy-based Risk Measurement Method in Underground Engineering 4.1 Establish bottom hierarchy risk fuzzy subset Firstly, according to hierarchy relationship of risk factors of risk assessment model established in this paper, the fuzzy field of every risk factor in different risk level should be determined. Take the cultural environment effect for example: U={u1, u2, u3, u4, u5 }; V={insignificant, considerable, serious, disastrous}. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

16. Table2. Relationship between risk value, probability, and consequence in sub-level factors Note:I=insignificant, II=considerable, III=serious, and IV= disastrous. Risk value 1~5 is risk qualitative index. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

17. 4.2 Entropy-based risk assessment method • According to the introduction in this paper, the assessment belongs to (5, 10) assessment problem. The obtained assessment matrix is: • Normalize the assessment matrix,we can obtain Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

18. 4.2 Entropy-based risk assessment method • Based on the matrix R1, compute the information quantity of 10 experts providing for the assessment. The result could be expressed as the information entropy. The information entropy of every assessment object is Hi（i=1, 5）: • Hi={0.928，0.976，0.946，0.873，0.678} • Then the relative weight of information quantity provided by 10 experts for 5 assessment indexes (or risk factors), that is the value of entropy weight i（i=1, 5）are: •  i = {0.120，0.040，0.090，0.212，0.538} Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

19. 4.3 Entropy-based risk measurement results discussion • (1). The larger entropy of a assessment index is, the less entropy weight is, which means this index is more unimportant. • (2).As for the entropy weight, it has a special meaning. It is not the actual importance coefficient of the assessment object in decision-making or assessment problem. Instead, it means relative degree of competition for how much they provide the information quantity when the set of the assessment objects are determined and given. • (3). Form the viewpoint of information, the value of entropy weight presents how much useful information that has been provided for the analysis. • (4).The value of entropy weight is significantly related to how much experts has grasped the assessment index. The entropy weight of index u2 is least, which means that experts have least knowledge of it. This assessment result reflects the fact of difficulty in shield tunneling construction crossing the running metro underground railway in urban soft soil. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

20. 4.4 Cultural environment effect risk analysis on shield tunnel construction period in soft soil • According to the model proposed in present paper, the total risk of cultural environment effect could be determined: • Obviously, the risk of cultural environment effect in shied tunneling construction period in urban soft soil area is large relatively. The result also shows that the quantity of information provided by the experts by means of experts investigation is less. So decision making will take much risk relatively. And therefore, the reliability will be small. But, if one believes that the information is relatively less, decision maker could ask for increasing the assessment index to acquire much more information and make decision again. By this way, the decision will be more accurate and reliable. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

21. 5. Conclusion • In underground engineering exploitation, at a certain known environment state, all kind of risk events has its own uncertainty. The entropy-based risk measurement method model is proposed in the paper. The model could be used to evaluate the quantity of information obtained form experts' investigation and the value of risk. The quantity of information could be expressed as the entropy. And the relative degree of importance of the index information is expressed as entropy weight. The relationship between them is that: the more the entropy is, the less the entropy weight is and the provided quantity of information is less, and vice versa. This assessment method could provide a ideal rule to measure the risk with a well precision. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

22. 5.Conclusion • Additionally, If one wants to improve the evaluation precision, he could increase quantity of information of a certain assessment index. Then with much more information, a much more precise and reliable decision could be made again and with less risk. Therefore, the model has much more practical meanings. Department of Geotechnical Engineering, Tongji University, Shanghai, China,200092

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