Application of EntropyBased Measurement in Underground Engineering Risk Assessment

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Application of Entropy-Based Measurement in
Underground Engineering Risk Assessment
The 2nd China-Japan Seminar for Graduate Students
in Civil Engineering

• LI Junwei HUANG Hongwei
• Department of Geotechnical Engineering
• Tongji University, Shanghai, China, 200092
• lijunwei76_at_163.com
• huanghw _at_ mail.tongji.edu.cn

Aug.27-28 Nagasaki, Japan
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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.

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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.

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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

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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.

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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

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(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

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(m, n) Assessment Problem

• As to (m, n) assessment problem, the entropy
  weight of the i th assessment index is expressed
  as

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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.

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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

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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.

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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
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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.

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Table1 Hierarchy analysis on environmental effect
risk
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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
• Uu1, u2, u3, u4, u5
• Vinsignificant, considerable, serious,
  disastrous.

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Table2. Relationship between risk value,
probability, and consequence in sub-level
factors
Note Iinsignificant, IIconsiderable,
IIIserious, and IV disastrous. Risk
value 15 is risk qualitative index.
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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

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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(i1, 5)
• Hi0.928,0.976,0.946,0.873,0.678
• 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(i1, 5)are
• ? ?i 0.120,0.040,0.090,0.212,0.538

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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.

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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.

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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.

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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.

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Thank You !